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NASA
Reference
Publication
1311
June 1996

Computer Program for Calculation of
Complex Chemical Equilibrium
Compositions and Applications
II. Users Manual and Program Description

Bonnie J. McBride and Sanford Gordon

•

.

,

National Aeronautics and
Space Administration

lewis Research Center
Cleveland, Ohio 44135

NASA
Reference
Publication
1311

1996

Computer Program for Calculation of
Complex Chemical Equilibrium
Compositions and Applications
II. Users Manual and Program Description

Bonnie J. McBride
Lewis Research Center
Cleveland, Ohio
Sanford Gordon
Sanford Gordon and Associates
Cleveland, Ohio

..

"1tl

National Aeronautics and
Space Administration
Office of Management

Scientific and Technical
Information Program

Contents
Chapter
1. Introduction ..................................................................................................................... . 1
2. Description of Program Input. ......................................................................................... .3
2. 1 General Rules ......................................................................................................3
2.1.1 File Names ............................................................................................ 3
2.1.2 Datasets ................................................................................................4
2.1.3 Keywords .............................................................................................4
2. l .4 Mandatory Keywords ...........................................................................4
2.1.5 Optional Keywords ...............................................................................4
2.1.6 Types of Variables ................................................................................5
2.1.7 Delimiters ............................................................................................. 6
2.2 Specific Free-form Variables for CEA Datasets .................................................... 6
2.3 Dataset reac ...................................................................................................... 6
2.3.1 Identification and Order .......................................................................7
2.3.2 Names of Reactants ...............................................................................7
2.3.3 Relative Amount of Reactant.. ............................................................... 8
2.3.4 Reactant Temperature ........................................................................... 8
2.3.5 Assigned Enthalpy or Internal Energy .................................................. 9
2.3.6 Exploded Chemical Formula ................................................................ 9
2.3.7 Density of Reactant.. ........................................................................... ] 0
2.3.8 Option To Use thermo.lib ................................................................... 10
2.4 Dataset prob .................................................................................................... 12
2.4.1 Case Identification ............................................................................ 12
2.4.2 Problem Type ................................................................................... 12
2.4.3 Fuel-Oxidant Mixture Values ............................................................ 13
2.4.4 Option To Include Ionized Species ................................................... 13
2.4.5 Options for Rocket Problems ............................................................ 14
2.4.6 Options for Shock Problems ............................................................. 14
2.4.7 Temperature Schedule ...................................................................... 15
2.4.8 Pressure Schedule ............................................................................. I 5
2.4.9 Specific Volume Schedule ................................................................ 16
2.4.10 Density Schedule .............................................................................. 16
2.4.11 Assigned Enthalpy ............................................................................ 16
2.4.12 Assigned Internal Energy ................................................................. 17
2.4.13 Assigned Entropy ............................................................................. 17
2.4.14 Assigned Values for Shock Problems ................................................ 17
2.4.15 Assigned Values for Rocket Problems ............................................... 18
2.5 Dataset outp .................................................................................................... 20
2.5.1 cal .................................................................................................... 20
2.5.2 deb (or dbg) .....................................................................................20
2.5.3 mass f ...............................................................................................20
2.5.4 plot ................................................................................................. 20
2.5.5 short ............................................................................................... 23
2.5.6 tr ac ................................................................................................. 23
2.5.7 tr an ................................................................................................. 23
2.5.8 Examples of outp Datasets .................................................................. 23

iii

2.6 Options Involving Species To Be Considered ..................................................... 23
2.6.1 Dataset only ..................................................................................... 24
2.6.2 Dataset omit ..................................................................................... 24
2.6.3 Dataset inse ..................................................................................... 24
2.7 Dataset end ....................................................................................................... 24
2.8 Thermodynamic and Thermal Transport Property Data Bases ............................ 25
3. Description of Program Output ...................................................................................... 27
3.1 Input Data ......................................................................................................... 27
3.2 Intermediate Input Data ..................................................................................... 27
3 .2.1 True/False Options .............................................................................. 28
3.2.2 Schedules of Assigned Values ............................................................. 28
3 .2.3 Reactant Information .......................................................................... 28
3.2.4 Species Being Considered ................................................................... 29
3.2.5 Species With Thermal Transport Properties ......................................... 29
3.2.6 Enthalpies and Relative Atoms Per Kilogram ...................................... 29
3.3 Tables of Results ................................................................................................ 29
3 .3 .1 Thermodynamic Mixture Properties ...................................................3 0
3 .3 .2 Thermal Transport Mixture Properties ................................................ 3 0
3.3.3 Rocket Performance Parameters ..........................................................30
3.3.4 Shock Parameters ............................................................................... 30
3.3.5 Chapman-Jouguet Detonation Parameters ........................................... 30
3.4 Intermediate Output Data ................................................................................... 30
3.4.1 Number of Iterations .......................................................................... 31
3.4.2 Iteration Matrices and Compositions ................................................... 31
3.4.3 Condensed-Phases Test ......................................................................32
3.4.4 Derivative Matrices ............................................................................ 32
4. Modular Form and Modification of Program ................................................................ 3 3
4.1 Main Program and BLOCKDATA Module ........................................................ 33
4.2 General Input Module ...................................................................................... .36
4.3 Data-Preprocessing Module ............................................................................... 36
4.4 Applications Module ........................................................................................ .36
4.5 Additional Input-Processing Module ................................................................. 3 7
4.6 Equilibrium Module ..........................................................................................37
4.7 Transport Properties Module ............................................................................. 37
4.8 Output Module ..................................................................................................38
4.9 Modifications .................................................................................................... 38
4.9.1 PARAMETER Statements ............................................... ;................... 39
4.9.2 Changing Number of Possible Reaction Products ................................ 40
4.9.3 Eliminating an Application ................................................................ .40
4.9.4 Adding an Application ...................................................................... .40
5. Routines .......................................................................................................................... 41
5.1 Main Program ................................................................................................. 41
5.2 BLOCKDATA ................................................................................................. 42
5.3 Subroutine CPHS .............................................................................................42
5.3.1 General. .............................................................................................. 42
5.3.2 Entry ALLCON ..................................................................................42
5.4 Subroutine DETON .........................................................................................43
5.5 Subroutine EFMT ............................................................................................ 43
5.6 Subroutine EQLBRM ...................................................................................... 43
5.7 Subroutine FROZEN ....................................................................................... 43
5.8 Subroutine GAUSS .......................................................................................... 44
5.9 Subroutine HCALC ......................................................................................... 44
5.lO Subroutine INFREE .........................................................................................45
5.11 Subroutine INPUT ........................................................................................... 45
5.12 Subroutine MATRIX .......................................................................................46

iv

5.13 Subroutine NEWOF .........................................................................................47
5.14 Subroutine OUTl ............................................................................................ 47
5.14.1 Entry OUT2 .....................................................................................47
5.14.2 Entry OUT3 .....................................................................................48
5.14.3 Entry OUT4 .....................................................................................48
5.15 Subroutine REACT ..........................................................................................48
5.16 Subroutine RKTOUT ....................................................................................... 49
5.17 Subroutine ROCKET ....................................................................................... 49
5.18 Subroutine SEARCH and Entry READTR ....................................................... 50
5.19 Subroutine SETEN .......................................................................................... 50
5.20 Subroutine SHCK ............................................................................................ 51
5.21 Subroutine THERMP ....................................................................................... 51
5.22 Subroutine TRANIN ........................................................................................51
5.23 Subroutine TRANP ..........................................................................................52
5.24 Subroutine UTHERM ...................................................................................... 53
5.25 Subroutine UTRAN .........................................................................................54
5.26 Subroutine VARFMT ...................................................................................... 54
6. Error Messages ............................................................................................................... 55
6.1 DETON Message ............................................................................................. 55
6.2 EQLBRM Messages ......................................................................................... 55
6.3 FROZEN Message ........................................................................................... 57
6.4 HCALC Messages ............................................................................................ 58
6.5 INFREE Messages ...........................................................................................58
6.6 INPUT Messages ............................................................................................. 58
6.7 REACT Messages ............................................................................................ 60
6.8 ROCKET Messages .......................................................................................... 61
6.9 SEARCH Messages ..........................................................................................63
6.10 SHCK Messages ............................................................................................... 63
6.11 TRANIN Message ............................................................................................ 64
6.12 UTHERM Message .......................................................................................... 64
6.13 UTRAN Message ............................................................................................. 64
7. Example Problems ..................................................................................................... ..... 65
7.1 Examples l and 2 ............................................................................................ 67
7.1.1 Example 1 .......................................................................................... 67
7.1.2 Example 2 ..........................................................................................67
7.2 Examples 3 and 4 ............................................................................................68
7.2.1 Example 3 ..........................................................................................68
7.2.2 Example 4 ..........................................................................................68
7.3 Example 5 ....................................................................................................... 68
7.4 Example 6 .......................................................................................................69
7.5 Example 7 .......................................................................................................69
7.6 Examples 8, 9, and 10 ...................................................................................... 69
7.6. l Example 8 .......................................................................................... 70
7.6.2 Example 9 .......................................................................................... 70
7.6.3 Example 10 ........................................................................................ 70
7.7 Example 11 ..................................................................................................... 70
7.8 Example 12 ..................................................................................................... 71
7.9 Example 13 ..................................................................................................... 71
7.10 Example 14 .....................................................................................................71
Appendixes
A. Format for Thermodynamic Data ........................................................................ 73
Table A.1.-General Format for Nine-Constant Functional Form ................ 73
B. Names of Species in Thermodynamic Data File (thermo.inp) ...............................75
Table B.1.-Names of Gas-Phase Products in thermo.inp .............................76
Table B.2.-Names of Condensed-Phase Products in thermo.inp .................80

v

Table B.3.-Names of Reactants in thermo.inp ............................................82
C. Thermodynamic and Density Data for Reactants ................................................. 83
Table C.1.-Thermodynamic and Density Data for Reactants ......................84
Table C.2.-Reactant Thermodynamic Data in thermo.inp Format... ............86
D. References for Reactant Data in Table C. l.. .........................................................91
Table D.1.-References for Reactant Data in Table C.1 ............................... 92
E. Format and List of Species with Thermal Transport Property Data ....................... 95
Table E.1.-Format for Thermal Transport Property Data ........................... 96
Table E.2.-Viscosity and Thermal Conductivity Coefficients
in thermo.inp .............................................................................................. 97
F. COMMON Variables Used in Equilibrium Module ............................................ 107
Table F.1.-COMMON Variables That Must Be Initialized Before
Entering Equilibrium Module .................................................................... l 08
Table F.2.-COMMON Variables Calculated by Equilibrium Module ....... 110
G. Example Problems ............................................................................................ 111
References ........................................................................................................................ . 177

vi

Chapter 1

Introduction
This is the second part of a two-part report describing the NASA Lewis Research
Center's computer program CEA (Chemical Equilibrium with Applications). The program is
used to obtain chemical equilibrium compositions of complex mixtures with applications to
several types of problems. Part I (Gordon and McBride, 1994) states the various assumptions
on which the calculations are based and analyzes the appropriate equations and mathematical
methods for their solution. The equations describe the conditions for chemical equilibrium
and for applications such as rocket performance, shocks, and detonations. The
thermodynamic and thermal transport property data bases are also briefly described.
This second part is a users manual. Chapter 2 presents details for preparing input
files. The format for input differs considerably from that used in earlier versions of the CEA
program (Gordon and McBride, 1976; McBride et al., 1994). The output tables for various
types of problems and options are described in chapter 3. Chapter 4 presents the overall
modular organization of the program with information on how to make modifications.
Chapter 5 presents information on the function of each subroutine. Error messages and their
significance are discussed in chapter 6. Chapter 7 gives a number of examples that illustrate
various types of problems handled by CEA and cover many of the options available in both
input and output.
Seven appendixes are also included. Appendixes A to D give information on the
thermodynamic data used in CEA. Appendix A gives the format for the thermodynamic data
file thermo.inp, and appendix B lists species names contained therein. This file contains data
in the form of least-squares coefficients for reactants as well as for products. Some of the
reactant data are itemized in appendix C; references for these data appear in appendix D.
Appendix E presents the format for thermal transport property data. Appendix F contains
some information on common variables used in or generated by the equilibrium module
discussed in section 4.6. Finally, appendix G lists the tabular output for the example problems
discussed in chapter 7. The mathematical symbols used in this report are defined in Gordon
and McBride (1994).
The CEA program consists of the following five files: the source program (ceajor),
thermodynamic data (thermo.inp), thermal transport properties (trans.inp), sample problems
(cea.inp), and readme.txt. After the ceajor file has been compiled, the unprocessed
thermodynamic and transport property data should be processed once (see section 2.8).
These processed data (in binary form) are stored in thermo.lib and trans.lib, where they
remain available for future use in running problems. Additional information on the
thermo.inp and trans.inp files is given in section 2.8 and appendixes A to E.
The CEA program was written in ANSI standard FORTRAN 77. CEA should work on
any system with sufficient storage. There are approximately 6300 lines in the source code,
which uses 225 kilobytes of memory. The compiled program takes 975 kilobytes. Input data
bases thermo.inp and trans.inp use approximately 850 and 32 kilobytes, respectively; the
binary forms thermo.lib and trans.lib take approximately 425 and 20 kilobytes, respectively.
These storage requirements for the program and the data files may be easily adjusted as
discussed in the following chapters.

Chapter 2

Description of Program Input
The CEA program requires two types of input. One type consists of files of
thermodynamic data (thermo.inp) and thermal transport property data (trans.inp), which are
common to all problems. These two files accompany the CEA program. The second type is
input for the specific problem to be solved and is prepared by the user. The problem input
consists of seven categories of input datasets. These seven datasets are in a general free-form
format that was not used in previous versions of the CEA program (e.g., Gordon and
McBride, 1976, or McBride et al., 1994). Most of the material in this chapter describes the
general rules (see section 2.1) as well as details for preparing input datasets (see sections 2.2
to 2.7).
Thermo.inp and trans.inp are not in the free-form format because the data were
generated by other programs (e.g., McBride and Gordon, 1992). Section 2.8 gives some
information on processing these files before running specific problems. Because these files
contain unprocessed thermodynamic and thermal transport data, we recommend that you first
preprocess these files with the CEA program, which will store the data in binary form in two
libraries called thermo.lib and trans.lib (see section 2.8). The CEA program will then use
these processed libraries for all future runs. The prefixes thermo and trans in the input data
files could have been any other names; they were selected to be consistent with the prefixes
automatically assigned by CEA to the library files.

2.1

General Rules

The general rules for preparing input pertain to file names, keywords, types of
variables, and delimiters.
2.1.1 File Names
All input files must be named with an arbitrary prefix and the suffix .inp (i.e., (input
prefix).inp). Output files for listing are automatically given the same prefix as the input file
and the suffix .out. As an option, additional output files of columns of numbers can be
obtained for plotting purposes. These files will also be given the same prefix and the suffix
.pit.

3

2.1.2 Datasets
All useful program input is divided into sets of records called datasets. The first
record of each dataset starts with a keyword. Records that start with the symbols "#" and "!"
or totally blank records will be considered comments (i.e., they will be printed but not used).

2.1.3 Keywords
The keywords must be
1. The first nonblank characters in a record

2. All lower-case letters
3. A word that starts with one of the following sets of three or four letters: prob, reac,
only, omit, inse, outp, end, ther, and tran. Additional characters may be
used in the keywords but will be ignored by the program (e.g., problem is equivalent to
prob). The last two keywords must begin records that precede formatted data bases. The
first seven keywords precede data in CEA's free form.

2.1.4 Mandatory Keywords
There are three mandatory keywords for every problem. These words, with a brief
description of any associated data, are as follows:
Keyword
prob

Data
Problem type and associated
input (see section 2.4)

reac

Reactant names and associated
input (see section 2.3)

end

No data. Keyword signals the
end of the problem.

2.1.5 Optional Keywords
There are four optional keywords for every problem. Three are always followed by
product species names typed exactly as used in the coefficients data base (see appendix B).
The keywords are as follows:

4

Keyword
only

Data
et of names o species t at are the only
ones to be considered in the problem

omit

Set of names of species that are to be
omitted as possible products

inse

Set of names of condensed species to be
tried (inserted) with gaseous species for
initial equilibrium iterations

outp

Nonstandard options for output

2.1.6 Types of Variables
There are three types of variables, each limited to 15 characters. Additional characters
will be ignored. The variables are as follows:
ype
iteral

Characteri sties
First character is alpha etic.
All initial characters are lower case, with three
exceptions which follow:
Chemical element symbols start with upper-case
letters; the second letter may be either upper or
lower case.
Reactant names may start with either upper- or
lower-case letters.
Case (problem) identification may be either
upper- or lower-case letters or numbers (see
section 2.4.1).
Sometimes the program checks for embedded
lower-case character strings as well as initial
character strings. For example, the symbol for
pressure is p and the embedded string indicates the
units.
Examples:

p,bars
p(bars)
pressure:bars
Numeric

Any legimate integer, decimal, or floating-point
number

Species names

The set of characters used with the coefficient data
bases to identify the species. These names never
have embedded blanks, tabs, or equal signs
because these characters are delimiters.

5

2.1. 7 Delimiters
There are several delimiters for separating variables. These delimiters, which follow
the variable, are as follows:
Delimiter
One or more
blanks or tabs

Variables separated
Any vana es (literals, numerics, or
species names).

Equal sign

Literals (may be used in
combination with blanks and tabs)

Comma

Numerics (may be used in
combination with blanks and tabs)

Example:

problem

tp

p,atm=l, 2,3,

t= 3000 2000 1000,500

(Note that p, atm is one literal variable; commas separate only numeric variables.)

2.2 Specific Free-Form Variables for CEA Datasets
As discussed in the general rules, CEA input consists of datasets and comments.
Comments start with either "#" or "! ". Datasets start with keywords. Datasets in the freeform format that are headed by the keywords reac, prob, end, only, omit, inse, and
outp are discusse.d here. (Note that when defining keywords and literals in the following
sections, only the abbreviated character strings checked by the program are listed.)
Free-form datasets have the following order:
1. If the thermodynamic and transport data bases have not been processed, any free-form
input must follow these data.
2. Datasets may be in any order, except for the end dataset, which must be the last record
for any problem.
3. Variables or species names within a dataset may be in any order, with one exception in the
reac dataset (see section 2.3.1). Also, any numerics associated with a literal variable
must follow the literal.

2.3 Dataset reac
The reac dataset includes names and parameters for the reactants. It replaces the
fixed-format REACTANT records of previous versions of the CEA program (e.g., Gordon
and McBride, 1976, or McBride et al., 1994). The details for preparing a reac dataset are
given in the following subsections.
Chemical species (products as well as reactants) are identified in two forms in the CEA
program. One form may be a name or a conventional formula of the species (without

6

subscripts), such as H2 O for water, CH4 for methane, or Air for air. This form is discussed in
section 2.3.2. The other form for identifying a species is referred to as the "exploded" form
or formula and is discussed in section 2.3.6. Both forms are required in the CEA program
and both forms are given in the thermodynamic data file, thermo.lib. ·"fhe exploded formula
may be specified directly in the reac dataset or obtained from thermo.lib if it contains the
species. Some comparisons of these two ways are given in section 2.3.8.
Most types of problems require a value for the enthalpy (or internal energy) of the reactant
mixture at some specified temperature. Energies are discussed in section 2.3.5; and
temperatures, in section 2.3.4. As in the case for exploded formulas, enthalpies (or internal
energies) may be specified in the reac dataset or optionally obtained from thermo.lib. Some
comparisons of these two options for specifying energy are given in section 2.3.8.
2.3.1 Identification and Order
Each reactant and its parameters are identified by one of three sets of initial
characters: fu, ox, and na. Each of these literal variables must precede the reactant name. All
associated parameters follow the reactant name in any order. This information will be printed
in the final tables. Summarizing, the reactant identifiers are
Initial
characters

Data

fu

Fuel name o lowed by associated data

ox

Oxidant name followed by associated data

na

Name and data of reactant not identified as a
fuel or oxidant. When name is used in any
particular dataset, all reactants must use the
name label.

Examples:
reac fuel Jet-A(L)
oxid Air ...
reac name H2 ...

name 02 ...

name Ar ...

(Note that the ellipses represent additional input not shown here.)
2.3.2 Names of Reactants
Restrictions on names of reactants are as follows:
1. As many as 15 characters will be stored. The names must not contain any embedded
blanks, tabs, or equal signs, since they are delimiters (see section 2.1.7). Upper-case letters
are acceptable. The first character must not be a "+", "-", ".", or number.
2. Section 2.3.8 presents some examples using the option for obtaining the exploded
chemical formula and the enthalpy (or internal energy) from thermo.lib. When this
option is used, the input name must match exactly the name used in thermo.inp. These
names are given in appendix B. (Note that the list in appendix B is current as of the date
of publication of this report but is often added to.) For example, Jet-A ( L) and Air

7

L

used in an example in section 2.3.1 are exactly the names required to identify these
species (including upper- and lower-case letters). By contrast, names such as jet-A( 1)
and air are incorrect.

2.3.3 Relative Amount of Reactant
Amounts of oxidants are given relative to total oxidant, and amounts of fuels are
given relative to total fuel. If reactants are not specified as fuels or oxidants, the amounts of
reactants are relative to total reactant. All values must follow a literal with one of the initial
characters m or w defined here:
Initial
character

Data

m

Amount given in moles. n a particular dataset, if
any reactant amount is given in moles, the other
reactants must be given in moles as well.

w

Amount given in weight fraction or weight
percent. Values for fuels are relative to total fuel.
Similarly, values for oxidants are relative to total
oxidant. If these values are not normalized, they
will be normalized by the rogram.

Examples:

reac name 02 mole3=.5, _

name H2 moles=l, _

reactant fuel CH4 wt%=30
fuel C6H6 wt%=70
oxid Air wt%=100 _
2.3.4 Reactant Temperature
For combustion problems (hp, uv, or rocket (ro or rkt)) a temperature must be
specified for each reactant whose enthalpy or internal energy value is taken from the product
or reactant thermodynamic data files. The temperature value follows a literal that starts with t.
Units are indicated by one of the following embedded characters:

8

Em e ded
character

Temperature unit

k

Kelvin (default unit if
not specified)

r

Rankine

c

Celsius

f

Fahrenheit

Example:
reac fuel ...
oxidant
fuel= ...

t,f=212 ...
t,r=672
t,k=373,

2.3.5 Assigned Enthalpy or Internal Energy
For a number of problems (hp, uv, or rocket (ro or rkt), detonation (det), or
shock (sh)), a value of enthalpy or internal energy must be assigned for each reactant whose
value is not taken from thermo.lib. The symbols used to specify enthalpy or internal energy
and the unit of energy are as follows:
Im ti a
character
h
u

Embedded
characters
c
kc
j

kj

a ue
enthalpy
Assigned internal energy

Ent alpy or
internal energy unit
Calones per mole
Kilocalories per mole
Joules per mole (default unit
if not otherwise specified)
Kilojoules per mole

Examples:

reac fuel AA
fuel BB

oxid XX

h,cal/mol=123.
t,k=445 ...
h,j/mol=-9996.3
t,r=lOO
h, kj/mol=556
t, r=lOOO ...

Some additional examples are given in section 2.3.8.
2.3.6 Exploded Chemical Formula
For each reactant the CEA program requires the atomic symbols and their
corresponding relative numbers (stoichiometric coefficients). This information must be part
of the user's input when the thermodynamic data are not obtained from thermo.lib. The
requirements for the exploded formula are as follows:
1. Atomic symbols must start with an upper-case letter. A second letter may be either upper
or lower case.
2. Relative numbers may be either integers or fractions.

9

3.

The exploded formula is required to be in the reac dataset for two situations:
a. When the reactant name is not in thermo.lib
b.

When an enthalpy or an internal energy is given with the reactant input (see
section 2.3.8)

Examples (note that spaces are used to separate atomic symbols and numbers):

reac name Water-vapor H 2 o 1 _
name Species-X Al 6 Si 4 O 9 _
name Species-Y C 1 H 1.0769 reac oxid Air N 1.56168 o .419590 Ar .009365 C
.000319 ...
Some additional examples given in section 2.3.8 compare the options of specifying the
exploded formula in the reac dataset or obtaining it from thermo.lib.
2.3. 7 Density of Reactant
Calculating the density of the total reactant is an option. It will be calculated
according to equations (9.12) and (9.13) in Gordon and McBride (1994) only if a density is
given for each reactant in the current prob dataset. (Note that this information is not stored
in the thermodynamic data library.) Each value follows a varfa ble starting with the letters
rho, with possible embedded characters to indicate units as follows:
Em edded
characters
kg
g

Density units
ilograms per cubic meter
Grams per cubic centimeter
(default unit if kg is not
specified)

Example:

reac fuel=B2H6(L)

rho,g/cc= .4371 _

2.3.8 Option To Use thermo.lib
The exploded chemical formula and either the enthalpy or internal energy for each
reactant may be specified in the reac dataset or may be taken from thermo.lib. If either the
exploded chemical formula or a required enthalpy (or internal energy) or both are missing
for a reactant in reac, CEA will try to find the information in the library by using the
reactant name. If a search for a species in thermo.lib is successful, the exploded formula and
energy data for that species from the library will override any data that might be in the reac
dataset.
Example (tp problem that does not require an enthalpy):

reac ox=02 wt%=30
Since 02 is in thermo.lib, the exploded formula will be taken from there.

10

Examples (all for an hp problem that requires an enthalpy for each reactant):

reac

ox 02

wt%=30

gives error message; a temperature must be specified.

reac

ox 02

wt%=30

t,k=300

obtains exploded formula and enthalpy (ENERGY /R=6. 5 3 7 7 7 K) from thermo.lib.

reac

ox=02

wt%=30

t,k=300

h,j/mol=SS

obtains exploded formula and enthalpy (ENERGY /R=6. 5 3 7 7 7 K) from thermo.lib. This is
equivalent to 54.3584 J/mol. The value of h, j /mol = 55 in the reac dataset is overridden
because the exploded formula for 0 2 was not given.

reac

oxid 02

wt%=30

O 2

t,k=300

h,j/mol=SS

uses data exactly as specified in the above reac dataset and does not take any information
for this reactant from thermo.lib. Specifying a temperature is optional in this example.

reac

ox 02

wt%=30

o 3

t,k=300

overrides the exploded formula (given intentionally incorrect as O 3 in the above reac
dataset) and obtains the correct exploded formula 0 2 and ENERGY /R=6. 5 3 7 7 7 K from
thermo.lib.

reac

ox 02(L)

wt%=30

t,k=88

selects the one enthalpy value in thermo.lib for 02 ( L) that corresponds to a temperature of
90.17 K, inasmuch as 88 K is within I 0 K of the one thermo.lib temperature value of 90.17 K
(see section 5.24).

reac

ox=02(L)

wt%=30

t,k=78

gives a fatal error message, inasmuch as 78 K is more than 10 K from the thermo.lib value of
90.17 K (see section 5.24).
Giving the exploded formula and enthalpy, as illustrated in the fourth example above, is
required when the reactant is not contained in thermo.lib. Otherwise, unless there is some
special reason not to do so, we prefer to use the simple method of obtaining the reactant
information from thermo.lib, as illustrated in the second example above. In chapter 7, which
gives examples of a number of problems, most of the examples use this simple method.

11

2.4 Dataset prob
The dataset prob includes all the input parameters associated with any problem with
the exception of reactant information discussed previously. Some of these parameters are
required and some are optional.

2.4.1 Case Identification
Case identification is an optional literal or numeric variable that follows the word

case. The case identification will be printed on the final tables. As mentioned in section
2.1.6 the case identification may start with a number or either an upper- or lower-case letter.
Examples:

case=150
case=example2
case

Example 2

(The last example is unacceptable because blanks are not allowed in literal variables.)

2.4.2 Problem Type
For every problem one and only one problem type must be specified. The initial
characters for various types of problems are as follows:
Imtrn
characters
tp or pt

Assigned-temperature and -pressure
problem

hp or ph

Assigned-enthalpy and -pressure problem

sp or ps

Assigned-entropy and -pressure problem

tv or vt

Assigned-temperature and -volume (or
density) problem

uv or vu

Assigned-internal-energy and -volume (or
density) problem

sv or vs

Assigned-entropy and -volume (or density)
problem

ro or rkt

Rocket problem

sh

Shock problem

det

12

ype of prob em

Chapman-Jouguet detonation problem

2.4.3 Fuel-Oxidant Mixture Values
If the reactant amounts are not completely specified in the reac dataset, 1 to 26
numerical values may follow the following initial characters:
Imt1al
characters

Percent ue by we1g t

%f
f

Va ues

Io or
f/a

Fuel-to-oxidant weight ratios

o If

Oxidant-to-fuel weight ratios

phi

Equivalence ratios in terms
of fuel-to-oxidant weight
ratios (eq. (9.19) in Gordon
and McBride, 1994)

r

Chemical equivalence ratios
in terms of valences (eq.
(9.18) in Gordon and
McBride, 1994)

Examples:

r,eq.ratio= .9, 1, 1.1, 1.5, ...
%fuel 40 50 60 _
2.4.4 Option To Include Ionized Species
The parameter ions instructs the CEA program to consider ionized species as
possible products.
Example:

problem hp

ions

case=20 _

13

2.4.S Options for Rocket Problems
The following options are available for rocket performance problems:
Im tla c aracters

fac

eq

ption
Assumes a inite-area combustion
chamber, f ac. If the area is not
given, the CEA program will default
to the infinite-area combustor
assumption, iac.
Assumes equilibrium composition
during expansion.

fr or fz

Assumes frozen composition during
expansion (not available with fac
option).

nfr or nfz

Is followed by integer which is the
column number for freezing
composition. Default is l (the
combustion point).

dbg or deb

Prints intermediate output for the fac
chamber and throat iterati0'1
procedure.

Examples:

Calculate rocket performance parameters assuming
both equilibrium compositions during
expansion and compositions frozen at the chamber
composition.
problem

rocket equilibrium frozen _

prob rkt fac dbg
2.4.6 Options for Shock Problems
The following options are available for shock problems:
Initials
characters

Option

inc

Calcu ate incident shoe parameters.

ref

Calculate reflected shock parameters.

eq

Assume equilibrium compositions.

fr or fz

Assume frozen compositions.

dbg or deb Print intermediate output for shock
iteration procedure.

14

Examples:

# Calculate incident shock parameters assuming
# frozen compositions.
#
prob shock inc frz

problem shock

incident

frozen

equil reflected -

2.4.7 Temperature Schedule
Assigned values of temperature are required for tp or tv problems and for initial
values for the det problem. An assigned combustion temperature is optional for an iac
rocket problem. From 1 to 26 numerical values may be assigned after the variable starting
with t, with one of the following embedded characters to indicate units:
Embe de
character
k

Temperature umt
Kelvin (t e de ault umt if
units are not specified)

r

Rankine

c

Celsius

f

Fahrenheit

Examples:

t,k= 3000,2000,1000
t(r) = 2500 2000 _
prob

tp

problem

t(r)=2500,2000 500 detonation

t =298.15 500, -

2.4.8 Pressure Schedule
A schedule of 1 to 26 numerical values for pressure is required for the following
types of problems: tp, hp, sp, ro or rkt, sh, and det. These values of pressure follow
the variable starting with p, with one of the following embedded character strings for units:
Embe e
characters

essure umts

bar

Bars (de ault umt)

a tm

Atmospheres

psi

Pounds per square inch absolute

mmh

Millimeters of mercury

15

Examples:

prob

tp p,bar=l,10,50 _

problem

rocket p(psia) 1000 500 -

2.4.9 Specific Volume Schedule
A schedule of 1 to 26 numerical values of volume is required for the following types
of problems: t v, u v, or s v. This schedule follows the variable starting with v, with one of the
following embedded character strings for units:
Embed ed
characters

Volume umts

kg

ubic meters per kilogram

g

Cubic centimeters per gram
(default unit if kg is not
specified)

Examples:

problem

tv

v,cc/g= 9.e+05 8.e+05, 7.e+07,

problem

tv

v,m**3/kg=900,8.e+03, 7.e+04 _

2.4.10 Density Schedule
A schedule of densities may be specified instead of specific volume for t v, u v, or s v
problems (see section 2.4.9). This schedule consists of 1 to 26 numerical values that follow
the variable starting with rho, with one of the following embedded character strings for units:
Embed ed
characters

Density units

kg

Kilograms per cubic meter

g

Grams per cubic centimeter
(default unit if kg is not
specified)

Examples:

problem tv rho,g/cc=9.e-05, 8.e-06, 7.e-07 _
problem

tv

rho-kg/m**3= .09,8.e-03,7.e-04 _

2.4.11 Assigned Enthalpy
Rocket or hp problems require enthalpies to be assigned. Enthalpies of individual
reactants may be assigned in the reac dataset (see section 2.3.5), or enthalpies for the entire
reactant mixture may be assigned in the prob dataset. In the latter case, enthalpies must be in

16

units of h!R [(g-mole)(K)/(g of mixture)]. This value will.override any enthalpies that may be
given in the reac dataset.
Example:

prob hp h/r=2345
2.4.12 Assigned Internal Energy
The uv type of problem requires internal energies to be assigned for the mixture.
These energies may be assigned in the reac dataset (see section 2.3.5), or internal energies
for the entire reactant mixture may be assigned in the prob dataset. In the latter case, internal
energies must be in units of u!R [(g-mole)(K)/(g of mixture)]. This value will override any
internal energies that may be given in the reac dataset.
Example:

prob uv

u/r=l935 _

2.4.13 Assigned Entropy
The s v and s p types of problems require an entropy of the reactant mixture to be
assigned. These entropies must be in units of s!R [g-mole/(g of mixture)].
Example:

prob sp-

s/r=l.363 _

2.4.14 Assigned Values for Shock Problems
Initial Mach numbers (mach) or incident shock velocities (ul) may be assigned for
shock problems. Velocities are in units of meters per second. The number of assigned values
for either Mach number or velocity is limited to the number of columns in the output
(generally, 13 or 7). In any one particular problem, either parameter may be assigned but not
both.
For each of these velocities, there is a corresponding pair of assigned initial
temperatures and pressures. If the schedules of temperatures and pressures are not the same
length as the u 1 (or machl) schedule, the last value of the tor p schedule will be used to fill
in the missing values. Refer to example 7 in appendix G (or the first example below). For this
case, seven u 1 values, no t schedule, and two pressures are given in the prob dataset. With
no t schedule, the temperature given with the reactants is used throughout. The first pressure
is used for the first u 1 value, and the second pressure is used for the remaining values. If
there had been a t schedule, these values would be paired one to one with the initial pressure
and velocity schedules. Again, if the t schedule is too short, the last t value will be used to fill
in any missing values.
Examples:
EXAMPLE 7: ...

problem case=7 p,mmhg=l0,20,
shock ul=l000,1100,
1200,1250,1300,1350,1400,
incd froz eql _

17

prob case 21 shock incd eql machl = 3, 4, 5,
tlk=298,320,340, plbar= .01,.02,.03
2.4.15 Assigned Values for )locket Problems
A number of variables are involved in rocket (ro or rkt) problems. Some are
required for all such problems; others are optional. Some comments on the requirements
follow:
1. One or more chamber pressures must be assigned. The assignments for chamber pressure
follow the rules for pressure discussed in section 2.4.8.
2. Assigning chamber temperature is an option, and the rules for its assignment follow those
for temperature discussed in section 2.4.7. (Note that, generally, temperature is not
assigned for rocket problems but is determined from the enthalpies of the reactants.)
3. Exit conditions may be assigned either in terms of ratios of chamber pressure to exit
pressure or exit area to throat area (see pi... p, sub, and sup in the table below).
4. For the f ac option, an assignment must be made for either the contraction ratio (see ac
below) or the ratio of the mass flow rate to the chamber area (see mdot below).

18

The initial characters and a brief description of the rocket variables follow:
lnit1a
characters
p
pi... p

Associate numenca values
hamber pressure (see section .4. )
Ratio of chamber pressure to exit pressure (PinlPe or PiJfe),
not assignable for chamber and throat (1 to 22 values). (Note
that the second pin pi...p is embedded. For example, pip,
pi/p, pinj /pe, etc.)

sub

Subsonic area ratios (1 to 13 values)

sup

Supersonic area ratios (1 to 13 values)

mdot or
ma

For f ac option, ratio of mass flow rate to chamber area,
2
(kg/s)/m

ac

For f ac option, contraction ratio (ratio of finite chamber area
to throat area (A/A 1))

nfz or
nf r

Option for freezing composition at the throat (nfz=2) or at a
supersonic exit condition (nfz>2). The output table has
equilibrium properties through point nf z and frozen
thereafter. If nfz>2, only NCOL - nfz additional exit
points are allowed (where NCOL is the number of columns in
the output set in the FORTRAN PARAMETER statement,
usually 7 or 13).

tcest

Initial chamber temperature estimate in units of kelvin. The
default value is 3800 K. (Setting this variable may be
necessary only when a condensed species has been inserted in
an inse dataset and 3800 K is outside its temperature range.)
Assigned chamber temperature, an option (see section 2.4.7)

t

Examples:
prob

rocket pi/pe=3,10,30,300, p,psia=3000, froz
tcest=l 10 0 ...

prob

rocket p,bar=50, subsonic,ae/at=5,
supersonic,ae/at=l0,20,100, nfz=2
equilibrium frozen

problem

rocket fac p,atm=50, ac/at=l.58,
supar=25,50,75, pi/pe=l0,100, -

19

2.5 Dataset outp
Tables of calculated results are discussed in chapter 3. The outp dataset contains
several variables that permit some options in these tables. The variables cal, short, deb (or
dbg), mas sf, and plot involve only the output. However, the variables trac and tran
(or trn) involve some aspects of the calculation procedure as well. Examples are given in
sections 2.5.2 and 2.5.8.

2.5.1

cal

The default unit for energy in the table output is joules. The variable cal calls for
the output energy unit to be calories.

2.5.2 deb (or dbg)
The variable deb permits the printing of intermediate output, which is useful in
debugging the iteration process for obtaining the equilibrium composition. The points for
which this information is desired can be specified by listing the column numbers.
Examples:
outp

cal deb=S

output deb=l,4,6
For each iteration the data printed include matrix arrays for obtaining corrections to species
compositions, current compositions, and corrections to current compositions. This
information is printed for each iteration until either equilibrium or the maximum number of
iterations permitted by the program is reached.

2.5.3 mass£
Until recently, the CEA program permitted equilibrium product compositions in final
output tables to be expressed only in terms of mole fractions. The massf option in the
outp dataset now specifies that compositions in the final tables are to be given in mass
fractions.

2.5.4 plot
The variable plot is to be followed by a list of properties and/or species names
whose values are to be stored in the (input prefix).plt file in columnar rather than horizontal
form. The columns of numerical data in E-format are stored in the order requested. No
alphabetic information is stored in this file. The numerical values are in the same units as in
the file (input prefix).out. Allowance is made for eight columns of mixture properties,
including mole or mass fractions, with a maximum of 100 values in each column. If more
data are required, more runs can be made. For properties, the initial letters and possible
embedded characters are listed following plot. For mole or mass fractions (equilibrium
only), the full name of each species must be used. (See appendix B for exact names to be
used.) Note that the plot dump is not currently set up for shock problems. The following
variables may be listed:

20

1. Thermodynamic properties-all problems except shock problems
Initial
characters

operty

p

Pressure

t

Temperature

rho

Density

h

Enthalpy

u

Internal energy

g

Gibbs energy

s

Entropy

m

Molecular weight (1/n)
(eq. (2.3a) in Gordon
and McBride, 1994)

mw

Molecular weight (eq.
(2.4a) in Gordon and
McBride, 1994)

cp

Specific heat

gam

Gamma(s)

son

Sonic velocity

2. Thermal transport properties
Initial
characters
vis
cond
cond ... fz

pran
pran ... fz

Property
Viscosity
Equilibrium thermal conductivity from
table of equilibrium properties
Thermal conductivity from rocket
output tables assuming frozen
composition during expansion. (Note
that f z may be embedded anywhere
after initial cond.)
Equilibrium Prandtl number from table
of equilibrium properties
Frozen Prandtl number from rocket
output tables assuming frozen
composition during expansion. (Note
that f z may be embedded anywhere
after initial pran.)

21

3.

Rocket performance parameters-rocket problems only. The following codes are for data
from the equilibrium tables. In order to get data from the frozen tables, an f z must be
embedded in the word after the letters listed. Frozen compositions are the same as the
compositions at the equilibrium freezing point and are therefore not dumped. When
rocket output tables are more than one page long, the combustion and throat values are
repeated for convenience on pages past the first. However, these repeated values are
omitted in the (input prefix).plt file.
Imtrn
characters

Property

pip

Pressure ratio, Pin/Pe for f ac
problems and PinrfPe for i ac
problems

pi/p

Same as pip

mach

Mach number

ae

Area ratio, A/A 1

cf

Coefficient of thrust, CF

ivac

isp

4.

Vacuum specific impulse, I, ac
Specific impulse,

/sp

Chapman-Jouguet detonation parameters-detonation problems only. The following
properties are for unburned gas and all require an embedded 1 after the initial letters:
Initia
characters
son ... 1
gam... 1

Property
Sonic ve ocity
Gamma

h ... 1

Enthalpy

t ... 1

Temperature

p ... 1

Pressure

The following strings may be embedded
Embe ed
characters
vel
mach

22

Property
etonat1on velocity
(e.g., detvel)
Mach number

2.5.5 short
The variable short permits printing only the input file, error messages, and final
tables. Other information, such as atom ratios and a list of species being considered during
the calculations, is suppressed.

2.5.6

trac

The option trac instructs the CEA program to print compos1hons of species with
mole or mass fractions greater than or equal to the assigned trace value. When this option is
used, the criteria for equilibrium composition convergence are tighter to ensure accuracy of
the trace species. With this option, mole or mass fractions are printed in E -format.

2.5.7

tran

The option tran (or trn) instructs the CEA program to calculate thermal transport
properties and add them to the output tables.

2.5.8 Examples of outp Datasets
Some examples of outp datasets that use the information discussed in the previous
sections are as follows:

output

trace=l.e-10, calories transport short

outp debugcols=l,3
output

transport

plot=p t C02 vis cond condf z

output trace=l.e-15
gamfz
outp plot=tl hl
sonicvel

plot pi/p

sonic! t h

h ivac N2

Ar cpf z

detvel roach.number

2.6 Options Involving Species To Be Considered
The only, omit, and inse datasets control which species are to be considered by
the CEA program either in the current problem or in the current equilibrium composition
iteration. If no only or omit datasets are included in the input for the current problem, all
gaseous species in the product thermodynamic data file for the current chemical system will
be considered as possible products. (See section 2.6.3 for information on consideration of
condensed species.) All three datasets must contain species names exactly as given in the
thermodynamic data file with no embedded blanks, tabs, or equal signs. A current list of these
species names, which were extracted from thermo.inp, is given in appendix B. This list is
continually updated.

23

2.6.1 Dataset only

The dataset only permits the user to list only those species names from the product
thermodynamic data file, thermo.lib, that are to be considered in the current problem. Names
must be exactly as given in the data file (appendix B) with no embedded blanks, tabs, or equal
signs.
Example:

only Ar

co

C02 H2 H20 HNO H02 NH NO

N2

02

OH

2.6.2 Dataset omit

The dataset omit specifies which product species are to be omitted from
consideration for the current problem. Species names must be exactly as given in the product
thermodynamic data file, thermo.lib (appendix B), with no embedded blanks, tabs, or equal
signs.
Example:

omit

C8Hl7,n-octyl C8H18,isooctane C8H18,n-octane
C9H19,n-nonyl

2.6.3 Dataset inse

The dataset inse specifies which condensed species are to be included as possible
products for the first point in the schedule of points for the current problem. Species names
must be exactly as given in the product thermodynamic data file, thermo.lib (appendix B).
This dataset is usually optional but occasionally may be required to obtain convergence.
Example:

insert

BeO(L)

2.7 Dataset end
There are no variables in dataset end. The keyword signals the end of input for a
particular problem.

24

2.8 Thermodynamic and Thermal Transport
Property Data Bases
Inputs for thermodynamic and thermal transport properties are exceptions to the free
form. Generally, they are processed once before running particular problems, and the
processed data are automatically saved for further use. The format for representing the
thermodynamic data is given in appendix A, and the names of species in the thermo.inp file
(see below) are given in appendix B. The format for thermal transport property data is given
in appendix E. The following keywords start the text on the single records that precede these
data bases:
Keyword
ther

Data m succeedmg records
Unprocesse ( ormatted) t ermodynamic data.
is input de is ca led
thermo.inp. CEA processes the data·from thermo.inp and then automatically
stores the processed (unformatted) data in a file named thermo.lib (see sections
4.3 and 5.24). After thermo.inp has been processed, it need not be processed
again. However, if the user desires to make changes to the thermo.inp file, the
new file must be processed. These changes might include adding, deleting, or
updating species data or creating special sets of thermodynamic data for
special purposes.

tr an

Unprocessed (formatted) thermal transport property data. This input file is
called trans.inp. CEA processes the data from this file and then automatically
stores the processed (unformatted) data in a file named trans.lib (see sections
4.3 and 5.25). The file trans.lib is optional and is required only if thermal
transport properties of the reaction mixture are desired. After tran has been
called once, it need not be called again.

25

Chapter3

Description of Program Output
The program prints five kinds of output: input data used to specify the problem,
tables of results, output files for plotting purposes, information concerning iteration
procedures, and other intermediate output. The latter three types of output are optional.
Examples of problems that generate various types of data are given in chapter 7. The actual
tabular outputs for these problems are given in appendix G.

3.1 Input Data
Input data are described in chapter 2. The general procedure used in the CEA
program is to list the free-form input data as they are read in and before they are processed
by the program. The purpose is to show, as clearly as possible, what is actually on the input
records. All problems list the following input data:
1. Comments
2. The prob dataset
3. The reac dataset
4. The outp dataset (if present)
5. The only or omit dataset (if present)
6. The inse dataset (if present)
7. The end dataset

3.2 Intermediate Input Data
A number of items of intermediate input information are printed after the input
datasets. This intermediate information is often useful for debugging, such as verifying that
input data have been correctly interpreted by the CEA program. Printing this intermediate
information is optional, however, and may be suppressed by using the option short in the
outp dataset. Intermediate data that are related to input are discussed in the following
subsections.

27

3.2.1 True/False Options
The listing of true/false options contains three lines of information regarding a
number of program parameters that have been set "true" or "false" depending on the input
data. The first line starts with the word OPTIONS:. The default value of all parameters is
"false" with the exception of SIUNIT=T and TRACE=0.00000. The parameters include
1. Specifying the type of problem (TP, HP, SP, TV, UV, SV, DETN, SHOCK, or RKT), one
of which has been set to " t r u e "
2. In shock problems, specifying whether incident shocks (INCD=T) and/or reflected shocks
are to be considered (REFL=T)
3. In rocket problems, specifying whether performance is to be calculated based on
equilibrium composition during expansion (EQL=T) and/or frozen composition during
expansion (FROZ=T)
4. Specifying whether ionized species are to be considered (IONS=T)
5. Specifying that energy unit is to be in calories in final tables (SIUNIT=F)
6. Specifying that intermediate information is to be printed during the iteration procedure
for fac rocket problems (DEBUGF=T)
7. Specifying that intermediate information on shock iteration procedures is to be printed
(SHKDBG=T)
8. Specifying that intermediate information on detonation iteration procedures is to be
printed (DETDBG=T)
9. Specifying that thermal transport properties are to be calculated and printed in final tables
(TRNSPf=T)
10. Specifying the value for the trace parameter for consideration of minor species. (The
default value, TRACE=0.00000, instructs the program to print compositions in fixed
format only for those species with mole fractions greater than 0.000005.)

3.2.2 Schedules of Assigned Values
These lines list the schedules of parameter values that were read in with the input, such
as schedules of temperatures and pressures. For rocket problems, a list of assigned values of
area ratios and/or pressure ratios is printed. For shock problems, a list of assigned Mach
numbers or incident velocities is printed. For detonation problems, a list of initial
temperatures and pressures is printed.

3.2.3 Reactant Information
The reactant information contained in the reac dataset is listed in columns to
simplify checking the data, if necessary. Some of this information is repeated in the final
output tables.

28

3.2.4 Species Being Considered
This set of species is preceded by the heading SPECIES BEING CONSIDERED IN
THIS SYSTEM (CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES).
The species listed are all those in thermo.lib that subroutine SEARCH has found to be
contained in the current problem's chemical system. Each species in the list is preceded by
some identification, such as J12/65. The J (or j) refers to JANAF data (Chase, 1985). The
number refers to the month and the year in which the data were published or calculated
(12/65 is December 1965). Other identification codes are discussed in McBride et al. ( 1993).
Lower case codes indicate that data have been revised since McBride et al. (1993). These data
were fitted with seven coefficients for
rather than five. If the original data are different, the
identification code will be different.

c;

3.2.5 Species With Thermal Transport Properties
If the option tran is included in the outp dataset, a list of species is printed for
which thermal transport property data are contained in the trans.lib file. Also printed are
those pairs of species for which binary interaction data are contained in the trans.lib file.

3.2.6 Enthalpies and Relative Atoms per Kilogram
After the list of chemical species is a listing of the enthalpies or internal energies of
the total fuel and oxidant and the total reactant. These values are obtained, respectively, from
the following equations in Gordon and McBride (1994): equation (9.6) or (9.8) multiplied
by T and equation (9.7) or (9.9) multiplied by T. After this is a list of the kilogram-atom per
kilogram of each element in the total fuel and oxidant (eq. (9.1)) and in the total reactant
(eq. (9.5)).

3.3 Tables of Results
The final output of the program is in the form of tables that are designed to be selfexplanatory. Although each problem has its own kind of table, all the tables have many
features in common. These features are
l. Heading
2. Case identification
3. Reactant data
4. Proportion of oxidant to fuel
5. Density of reactant mixture if available
6. Thermodynamic mixture properties and derivatives
7. Thermal transport mixture properties (if tr an is specified in the outp dataset)
8. Equilibrium composition (mole fractions or mass fractions)

29

3.3.1 Thermodynamic Mixture Properties
The following thermodynamic mixture properties and derivatives are printed for all
problems: P, T, p, h, s, M (l/n), (aln V/aln T)p, (aln V/aln P)T' Cp, Ys, and a. The molecular
weight MW is also printed when condensed products are present. Two sets of units are
currently available for these properties. The default set is the SI set of units. This set is also
obtained when s i unit is specified in the out p dataset. The second set is a mixed set of
units with energy in calories, temperature in kelvin, pressure in atmospheres, and velocity in
meters per second. This set is obtained when cal is specified in the outp dataset.

3.3.2 Thermal Transport Mixture Properties
Thermal transport properties of the equilibrium mixture are optionally calculated and
printed if the outp dataset contains the word tr an. These properties are viscosity and two
sets of values for specific heat, thermal conductivity, and Prandtl number. The two sets are
based on the assumption of an equilibrium reaction contribution or no reaction contribution
(frozen composition). As pointed out in section 5.2.3 of Gordon and McBride (1994), the
equilibrium contribution to specific heat is obtained by different methods for the value given
in section 3.3.1 and here. For mixtures consisting of gaseous products only, the two values
will agree in most cases to all figures given.

3.3.3 Rocket Performance Parameters
In addition to the propertie& discussed in sections 3.3.1 ar d 3.3.2, the rocket problem
(rkt or ro) lists the following rocket performance data: Pinr/Pe (for the iac model) or
Pin/Pe(for the fac model), Mach number, A/arc*, CF,/vac•and l 8P. For the fac model, the
parameters Pin/Pinr and either m/Ac or Ac/A 1are also listed. These parameters are discussed in
chapter 6 in Gordon and McBride (1994).

3.3.4 Shock Parameters
In addition to the properties discussed in sections 3.3. l and 3.3.2, the shock problem
lists data discussed in chapter 7 of Gordon and McBride (1994). For incident shock waves,
the parameters listed are Af, u 1, u2 , P21P 1, T2/T1, M 21M1, p 2/p 1, and v2 • For reflected shock waves,
the parameters are u 5, P 5/P 2, T51T2 , M 51M2 , p5/p 2, and u 5+v 2 .

3.3.5 Chapman-Jouguet Detonation Parameters
In addition to the properties discussed in sections 3.3. l and 3.3.2, this problem lists
the following properties: PIP 1, TIT1, MIM1, p/p 1, Mach number, and detonation velocity. These
parameters are discussed in chapter 8 of Gordon and McBride (1994).

3.4 Intermediate Output Data
The option of printing intermediate output (deb or dbg in the outp dataset) is
provided primarily as a means of obtaining additional information for debugging. There is
usually no point in using this option when the program is working well. We have used this
option in the past for the following reasons:

30

1. To find programming errors
2. To study the iteration process and rate of convergence
3. To verify that thermodynamic data have been properly prepared
4. To study the test for inclusion of condensed species

3.4.1 Number oflterations
The output discussed in this section is automatically printed for all problems (except
shock problems) unless short is included in the outp dataset (see section 2.5.5). Following
the data discussed in section 3.2.6 is a line containing the terms POINT, ITN, and T and the
chemical symbols of the elements for the problem (for example 3 the elements are N, 0, Ar,
C, and H). The numbers under this heading are printed out after any current estimate
converges during the course of the iteration process. The numbers under POINT refer to the
columns of data in the final tables. (One exception to this, for the fac rocket problem, is
discussed at the end of this section.) ITN gives the number of iterations required to converge
to equilibrium composition for the current estimate; T is the final temperature for the current
estimate. The numbers under the chemical symbols are values of rti (see section 2.3.1 of
Gordon and McBride, 1994). In general there is only one line for each point unless there has
been an addition, deletion, or switching of phases of a condensed species (see discussion of
example 5, section 7.3).
For rocket and detonation problems, more than one line may be printed for
conditions other than a change in condensed species. For a rocket problem, these conditions
are for the throat and for an assigned area ratio, where a line is printed out for each estimate
of pressure ratio during the iteration process. For example, the four lines for point 6 of
example 8, appendix G, which is for an assigned area ratio, show that four separate
convergences were required to find the correct pressure ratio for the assigned area ratio. For
each of points 7 to 9 two convergences were required. For the throat, additional information
is given for pressure ratio and temperature estimates. For a detonation problem, a line is
printed for each set of temperature and pressure estimates.
As mentioned earlier in this section, the f ac rocket problem is an exception to the
statement that numbers under the word POINT refer to the columns of data in the final output
tables. Solving for the end of combustion chamber and throat conditions in the f ac problem
involves an iteration loop that temporarily includes a point labeled 2 and corresponds to an
infinite-area combustor (see section 6.4 of Gordon and McBride, 1994). When this iteration
loop is completed, the message END OF COMBUSTOR ITERATION is printed. The data
with index 4 (end of combustion chamber) are transferred to index 2 and appear in column 2
in the output tables. Index 3 refers to throat conditions, as usual for the f ac problem. The
next point in the schedule of exit points is assigned as point 4 and corresponds to column 4
in the output tables as usual (see example 9, section 7.6.2).

3.4.2 Iteration Matrices and Compositions
An option is provided to list intermediate output concerning the iteration process for
obtaining equilibrium compositions and temperatures. The intermediate data will be listed for
all points specified by the parameter debug in the outp dataset as illustrated in example 14,
section 7.10 and appendix G. The option debug=S given in the outp dataset instructs the
program to list intermediate output for point 5.
After the first line, which gives the iteration number, is the iteration matrix
corresponding to table 2.1 or 2.2 in Gordon and McBride (1994). The next line contains the
words SOLUTION VECTOR and is followed by a line containing the chemical names of the
current components. This line is followed by a line containing the solution vector to the
matrix. The next line gives the current values of some parameters, that is, T, n (ENN), In n
(ENNL), P (PP), ln(P/n) (LN PIN), and the control factor f.... (AMBDA). The next group of

31

lines contains information on the individual species used in setting up the preceding matrix
and the values of corrections to compositions. Even though listed under the heading DEL LN
NJ, these corrections are L\ln n1 only for gases but are iln1 for condensed species. The
corrections for gases are obtained from the matrix solution and equation (2.18) (for
assigned-pressure problems) or equation (2.40) (for assigned-volume or -density problems)
from Gordon and McBride (1994). In addition to these corrections the information on the
individual species includes the chemical name or formula, n1, ln n1, dimensionless enthalpy
(HOj/RT:= lfj /RT), dimensionless entropy (SOj/R=S; /R), dimensionless standard-state Gibbs
energy (GOj/RT= µ~/RT), and dimensionless Gibbs energy (Gj/RT=µ/RT). Following this is
additional information pertaining to testing for condensed species, which is discussed in the
next section.
3.4.3 Condensed-Phases Test
The test for condensed phases is made after every convergence for equilibrium
compositions. Details of this convergence test are listed with other intermediate output as part
of the debug option discussed in the previous section. After the data for the last iteration,
information concerning each condensed species is given. This information consists of the
name, the temperature interval for which thermodynamic data exist, and the current number
of moles of the condensed species. For those species whose temperature interval bands the
current value of temperature, the quantity given by equation (3.7) in Gordon and McBride
(1994) (divided by the molecular weight of the species) is calculated and listed with the
notation [(GOj - SUM(Aij*Pli)]/M. After all condensed species have been tested, only that
species with the largest negative value as shown by MAX NEG I1ELTA G is included as a
possible reaction species, and the iteration procedure is restarted. Dividing the quantity GOj SUM(Aij*Pii) by molecular weight usually improves the chances of selecting an appropriate
condensed species. The condensed-phases test is illustrated in example 14, section 7.10.
3.4.4 Derivative Matrices
The two derivative matrices (tables 2.3 and 2.4 in Gordon and McBride, 1994) and
their solutions are also given for the fifth point of example 14, section 7.10. These derivative
matrices are set up after the composition converges. The derivative matrix for derivatives with
respect to temperature follows the notation T DERIV MATRIX and is followed by the
notation SOLUTION VECTOR and a line containing the solution to the previous set of
equations. The derivative matrix for derivatives with respect to pressure follows the notation
P DERIV MATRIX and again is followed by the notation SOLUTION VECTOR and a line
containing the solution to this matrix. Then several lines of output summarize the results for
the point. The printed variables are labeled POINT, P, T, H/R, SIR, M, CP/R, DLVPT, DLVTP,
GAMMA(S), and V. The corresponding FORTRAN symbols, defined in appendix F, are Npt,
Ppp, Ttt, Hsum, Ssum, Wm,Cpr, Dlvpt, Dlvtp, Gammas, and Vlm, respectively.)

32

Chapter 4

Modular Form and Modification
of Program
To facilitate adding or deleting applications of the program, CEA was organized into
eight modules. These modules are concerned with general input, preprocessing of
thermodynamic and thermal transport property data, additional input processing, four
applications, equilibrium calculations, thermal transport property calculations, and output.
The general flow of these modules and associated routines is given in figure 4.1.
A subroutine tree diagram is given in figure 4.2. From this diagram, as well as from
figure 4.1, it is clear that, for example, the rocket application could be eliminated by omitting
subroutines ROCKEf, RKTOUT, and FROZEN and by omitting the statement that calls
ROCKET in the main program.
This chapter gives the general purpose of each module. Some details of the individual
routines are given in chapter 5.

4.1 Main Program and BLOCKDATA Module
Some details of the main program are described in section 5.1. Among other things,
the main program contains all the OPEN and CLOSE statements and interactively calls for the
standard input file. It also calls for the routines in two modules:
1. The general input module for processing input (see section 4.2)
2. The applications module for solving various types of problems (see section 4.4)
Flow returns to the main program after the completion of a problem or when a fatal error has
occurred.
BLOCKDATA (see section 5.2) is loaded with the program and contains data, such as
atomic weights, that remain constant for all problems.

33

General input

I

Main program
BLOCK DATA

I-

INPUT
INFREE
REACT
SEARCH
READ TR

-

I

'

Preprocess data

-

UTHERM
UTRAN

I

Additional input
processing

Applications
(1) tp, hp, sp, tv, UV, SV
problems -THERMP
(2) Rocket problems -ROCKET
FROZEN
RKTOUT
(3) Shock problems -SHCK
(4) Detonation problems -DETON

NEWOF
SETEN
HCALC

Equilibrum
'

'

Output
OUT1
OUT2
OUT3
OUT4
EFMT
VARFMT

,,
Transport
properties
TRAN IN
TRANP

Figure 4.1.-Program modules.

34

EQLBRM
CPHS
ALLCON
MATRIX
GAUSS

SEARCH (READTR)

INPUT

-E

UTHERM
UTRAN
IN FREE
REACT
NEWOF
EQLBRM

E

CPHS (ALLCON)

-----------1-fo--- MATRIX

THERMP
OUT1 (OUT2, OUT3, OUT4)

GAUSS
VARFMT
L - - EFMT

-----~....--

SETEN
TRANP -----------T'"~- TRANIN
L - - GAUSS
NEWOF
CPHS
EQLBRM

main

E

CPHS (ALLCON)

-----------1--- MATRIX

SHCK - - - - HCALC
OUT1 (OUT2, OUT3, OUT4)

------.~--

GAUSS
VARFMT

L - - EFMT

SETEN
TRANP -----------T'"~- TRANIN
L - - GAUSS
NEWOF
EQLBRM

E

CPHS (ALLCON)

-----------1-fo--- MATRIX
GAUSS

DETON ---HCALC
OUT1 (OUT2, OUT3, OUT4)

-----c-

VARFMT
EFMT

SETEN
TRANP -----------.-~- TRANIN
L - - GAUSS
NEWOF

CPHS (ALLCON)
EQLBRM ----+---MATRIX
GAUSS
FROZEN - - - - - C P H S
ROCKET--+-- RKTOUT
OUT1 (OUT2, OUT3, OUT4)
1
L - - VARFMT
SETEN
TRANP

E

VARFMT
1
L - - EFMT

LTRANIN
GAUSS

Figure 4.2.-Subroutine tree diagram.

35

4.2 General Input Module
The general input module contains four subroutines and an entry. The four
subroutines and entry are INPUT, SEARCH, entry READTR, INFREE, and REACT. The first
three are called from the main program to accomplish the following:
1. INPUT - to read and process input
2. SEARCH-to select the appropriate thermodynamic data for the current problem
3. READTR- to select the appropriate thermal transport property data for the current
problem (if transport property calculations have been requested)
Subroutine INFREE is called by INPUT to convert the free-form input data to
character and numerical variables. Subroutine REACT is called to process the reactants data.
INPUT also calls UTHERM and UTRAN (described in the next section).

4.3 Data-Preprocessing Module
The data-preprocessing module consists of subroutine UTHERM to preprocess
thermodynamic data and subroutine UTRAN to preprocess thermal transport property data.
Subroutine INPUT calls these routines when it encounters the keywords ther and tran,
respectively. UTHERM reads the formatted data from the thermo.inp file, processes the data,
and stores the results in unformatted form in the thermo.lib file. Similarly, UTRAN reads the
trans.inp file and stores the processed unformatted data in trans.lib. For any particular
problem these libraries are searched for the appropriate data for the chemical system of the
problem.
These routines have no other connection to the rest of the CEA program. They could
be removed and run as separate programs simply for the purpose of preprocessing the
thermodynamic and thermal transport property libraries.

4.4 Applications Module
The applications module contains the six subroutines THERMP, ROCKET, SHCK,
DETON, FROZEN, and RKTOUT. The first four subroutines are called from the main
program according to the type of problem specified in the prob dataset. The appropriate
subroutine controls the flow of the program until the problem is completed, after which
control is returned to the main program. These subroutines do the calculations unique to the
problem type. They all call other subroutines in the four modules discussed in sections 4.5 to
4.8 and shown in figure 4.1. For rocket problems only, the other two routines are called from
ROCKET (FROZEN for calculating rocket properties based on frozen composition and
RKTOUT for printing output unique to rocket problems).

36

4.5 Additional Input-Processing Module
The application subroutines discussed in the previous section call the three subroutines in this input-processing module to accomplish the following purposes:
I. NEWOF-to adjust the initial variables that vary with assigned fuel-oxidant ratios. These
0

variables include values of h; , p0 , r, and either u0 ' !R or h 0 /R for each oxidant-to-fuel
ratio. (The variables are defined in Gordon and McBride, 1994.)
2. SETEN-to obtain initial estimates for composition and temperature for a current point
from a previously calculated point
3. HCALC-to calculate thermodynamic properties of the reactant mixture for shock and
detonation problems only. Enthalpy is always calculated, but specific heat and entropy
are calculated only if thermodynamic coefficients are available for the reactants.

4.6 Equilibrium Module
The equilibrium module calculates compositions and thermodynamic properties for a
particular point Npt. The module is controlled by subroutine EQLBRM, which calls three
subroutines and one entry:
l. CPHS-to calculate thermodynamic functions of the individual gaseous species with entry

ALLCON for calculating thermodynamic functions of the individual condensed species
2. MATRIX- to set up the matrices as shown in tables 2.1 to 2.4 of Gordon and McBride
(1994)
3. GAUSS-to solve the sets of equations represented by the matrices
Appendix F gives two tables of program variable definitions:
I. Table FL-COMMON variables that must be initialized prior to entering the equilibrium
module
2. Table F2.-COMMON variables that are calculated by the equilibrium module

4. 7 Transport Properties Module
The transport properties module consists of two subroutines, TRANIN and TRANP,
which are used only if the thermal transport option tran appears in the ou'tp dataset.
TRANIN is called from one of the applications routines for each point Npt after either the
equilibrium or frozen thermodynamic properties of the mixture have been calculated. It
selects the most abundant gases, reads in any data for these species from input/output unit

37

IOSCH, and estimates any missing data. It then calls TRANP to calculate the thermal transport
properties of the mixture.

4.8 Output Module
The output module consists of the three subroutines, VARFMT, EFMT, and OUTl,
with three entries, OUT2, OUT3, and OUT4. OUTl lists data given in the reac dataset as well
as olf, %F, r, and p0 • OUT2 lists the properties P, T, p, h, s, (a ln Via ln P)y; (a ln Via In T)P, cP,
Ys' and a. (The variables are defined in Gordon and McBride, 1994.) OUT3 lists equilibrium
mole or mass fractions of the reaction species. OUT4 lists the transport mixture properties 'fl,
A, cP' and Prandtl number.
Subroutine VARFMT is called from OUT 1, OUT2, and OUT3, and subroutine EFMT
is called from OUT2 and OUT3. VARFMT adjusts the number of decimal places in a variable
format according to the size of the numbers. EFMT sets up a special E-format for printing
density p and mole or mass fractions.

4.9 Modifications
Many users have modified various versions of the CIA program to meet their
particular needs. These changes might include modifying one or more individual
subroutines; adding or deleting an entire application; changing dimensions, such as for the
number of species or the number of points permitted in a problem; and adding or deleting
species to the thermodynamic data file, thermo.inp, or the thermal transport property data file,
trans.inp.

38

4.9.1 PARAMETER Statements
Some changes concerning dimensions or assignment of input/output units are
facilitated by the use of PARAMETER statements. The variables in these statements are
defined as follows:
Parameter
MAXNGC

pecies t at can be considered m any pro em.
For condensed species, each temperature interval
of a species counts as a separate species.

MAX NG

Gaseous products that can be considered in any
problem

MAX NC

Condensed-species temperature intervals that can
be considered in any problem. The number of
intervals may be considerably greater than the
number of condensed species.

MAX TR

Gaseous products that can be considered in any
problem in thermal transport property calculations

MAX EL

Elements that can be considered in any problem

MAXMAT

Rows permitted in the composition iteration matrix

MAXR

Reactants permitted in a reac dataset

NCOL

Columns of data that can be rioted on a page

The numbers to which these parameters are set depends to a large extent on the nature
of the problems to which the CEA program is applied. Currently, for the large-scale computer
version of CEA, we are using slightly larger numbers than the largest number required in any
of many problems that we have run with the program. These numbers for most present-day
computers and for smaller capacity computers are as follows:
Parameter
MAXNGC

600

300

MAXNG

400

200

MAX NC

300

200

MAX TR

50

40

MAX EL

20

15

MAXMAT

50

40

MAXR

24

24

NCOL

13

7 or 8

39

The names and current assigned values of input/output units m the parameter
statements are as follows:
on tents

Input output
unit
IOSC

urrent
value

File type

13

Unformatted

Scratch file for processing thermodynamic
and thermal transport property data

IOTHM

14

Unformatted

thermo.lib (thermodynamic property data)

IOPLT

15

Formatted

(input prefix).plt file of numerical
parameters dumped for plotting purposes

IOT RN

18

Unformatted

trans.lib (thermal transport property data)

4.9.2 Changing Number of Possible Reaction Products
The parameters involved with increasing or decreasing the number of possible
products are MAXNGC, MAXNC, and MAXNG. We have found that the numbers set for
these parameters for the small-scale version (see previous section) accommodate most
problems. However, depending on the user's requirements, these numbers may be reduced
considerably more, if so desired. Inasmuch as a single gaseous species requires more than
I 00 storages, reducing MAXNG by 300 saves more than 30 000 storages.

4.9.3 Eliminating an Application
Any application module may be removed simply by removing the statement calling
the controlling subroutine (THERMP, ROCKET, SHCK, or DETON) and then removing the
subroutine (or subroutines) in the application module. The calling statements are near the end
of the main program.

4.9.4 Adding an Application
An application may be added by means of the following steps:
1. Giving the new type of problem a logical name
2. Revising subroutine INPUT to include all new input variables
3. Programming an applications module (see section 4.4)
4. Calling the module in the main program when the problem name variable is "true" after
the input data have been processed in INPUT

40

Chapter 5

Routines
The CEA program consists of a main program, BLOCKDATA, 24 subroutines, and 5
entries. The function of each of these is described in this chapter. Most of the program
variables mentioned in these sections are in labeled COMMON.

5.1 Main Program
Generally, the main program performs the following functions:
1. It uses the OPEN and CLOSE statements to define all input/output (1/0) unit numbers and
corresponding files for the entire program. The standard input file uses 1/0 unit 5. All
input data files are required to have the suffix .inp. The standard output file uses 110
unit 6 and has the suffix .out added to the input file prefix. Four other input/output units
are used with numbers defined in PARAMETER statements. See section 4.9.1 for a
description of these files.
2. It uses some interactive statements to read input files and to define output files.
3. It calls subroutine INPUT to read and process data from the input file through an end
dataset or the end-of-file.
4. It calls subroutine SEARCH to read and store thermodynamic data from thermo.lib
appropriate to the current chemical system processed in the input.
5. It calls entry READTR in subroutine SEARCH if the option t r an is included in the
outp dataset. Thermal transport data are read in READTR from input/output unit
IOTRN, and data selected for the current chemical system are stored on input/output unit
IOSCH.
6. It sets the initial composition estimates as follows:
a. Enn-total number of moles per gram of mixture=O.l
b. EnU, I)- number of moles of species j per gram of mixture
=0.1 /Ng for gases (where Ng is the number of gases)
=0 for condensed species

41

7.

It inserts any condensed species for consideration that appears in an inse dataset.

8. It calls either THERMP, ROCKET, SHCK, or DETON according to the problem type
found in the prob dataset.

5.2 BLOCKDATA
BLOCKDATA contains the following types of data:
1. Fundamental constants (Cohen, 1987)
2. Data for the chemical elements
3. Initial setup for the variable format array Fmt
The chemical symbols for the elements are stored in the Symbol array; the atomic weights
(Anon., 1995), in the Atmwt array; and the valences, in the Valnce array.
The variable format Fmt is used to adjust the number of decimal places in the output
variables according to the sizes of the numbers. The format is also used to print a label and
from 1 to NCOL associated numbers. NCOL is set by a PARAMETER statement to be the
number of columns of output (generally, 7 or 13 depending on t 1e paper width). The labels
contain 15 characters.

5.3 Subroutine CPHS
5.3.1 General
Subroutine CPHS is called from subroutines SHCK and EQLBRM. For an assigned
temperature Tt, it calculates thermodynamic properties of individual species by using
equations (4. 9) to (4.11) from Gordon and McBride ( 1994). These dimensionless properties
are for heat capacity, enthalpy, and entropy, respectively. For gaseous species, subroutine
CPHS uses one of three sets of coefficients: CoefG ,i, 1) for the temperature interval T g( 1) to
Tg(2); CoefG,i,2) for the interval Tg(2) to Tg(3); and CoefG,i,3) for the interval Tg(3) to
Tg(4). The index j G=l,Ng) refers to the jth gaseous species among the Ng gaseous species
being considered in the current chemical system, and the index i (i= 1,9) refers to the ith
coefficient. At present the four Tg temperatures in the CEA program are 200, 1000, 6000,
and 20 000 K. The calculated properties are stored in the COMMON arrays Cp, HO, and S,
respectively.
5.3.2 Entry ALLCON
Subroutine CPHS has an entry ALLCON that calculates the properties of condensedphase species. ALLCON is called from subroutine EQLBRM. ALLCON calculates
thermodynamic properties of all condensed-phase species by using equations (4. 9) to (4.11)
from Gordon and McBride ( 1994). Properties are calculated for the current temperature Tt
by using the coefficients stored in the Cft(jj,i) array (see section 5.18). The index i is for the
ith coefficient, and ii is for the temperature interval Gj=l,MAXNC). The temperature intervals
are stored in the Temp(2,jj) array. The calculated properties for molar heat capacity,

42

enthalpy, and entropy are dimensionless and stored m COMMON arrays Cp, HO, and S,
respectively.

5.4 Subroutine DETON
Subroutine DETON does the calculations required to obtain Chapman-Jouguet
detonation properties as described in chapter 8 of Gordon and McBride ( 1994). Detonation
calculations are limited to gaseous reactants. When initial temperatures are given in the prob
dataset, subroutine HCALC is called to get the thermodynamic properties of the initial
mixture. If the reactant is not found in thermo.lib, an error message will be printed. When
there is only one initial temperature, it may be specified in either the prob or reac dataset.
In the latter case, if the enthalpy corresponding to the initial temperature is known, it may be
included in the reac dataset. We usually prefer to specify the initial temperature or
temperatures in the prob dataset unless the reactant species is not included in thermo.lib.

5.5 Subroutine EFMT
Subroutine EFMT (E-format) is called from entries OUT2 and OUT3. It writes
statements in a special exponent form. This form is similar to the standard FORTRAN Eformat, but the letter E and some of the spaces have been removed for compactness. It is used
to write density and mole or mass fractions with the trace option.

5.6 Subroutine EQLBRM
Subroutine EQLBRM is the executive routine for calculating equilibrium
compositions and mixture properties for point (output column) Npt. It is called from one of
the application routines THERMP, SHCK, DETON, or ROCKET. Subroutine EQLBRM, in
turn, calls subroutines CPHS, MATRIX, and GAUSS. Before calling EQLBRM, several
variables will have already been set, such as the type of problem, the assigned or initial
estimated values of the thermodynamic states for the problem, and initial estimates of
composition. The COMMON variables that need to be set before entering EQLBRM are
tabulated in appendix F (table F.1).
The iteration procedures used in subroutine EQLBRM are described in chapters 2 and
3 of Gordon and McBride ( 1994). The COMMON variables that are set in EQLBRM for
output purposes are given in appendix F (table F.2).

5.7 Subroutine FROZEN
Subroutine FROZEN is called from ROCKET to calculate the temperature and
thermodynamic properties for the following assigned theoretical rocket performance
conditions:

43

1. Composition frozen at either combustion (Nfz=l), throat (Nfz=2), or any downstream
point (Nfz>2)
2. An assigned exit pressure (Pp)
3. An assigned entropy equal to the entropy at combustion conditions (Ssum(l))
The iteration procedure used for obtaining the exit temperature is discussed in section 6.5 of
Gordon and McBride ( 1994).
If a temperature is reached that is 50 K below the range of a condensed combustion
species (Temp(l,j) to Temp(2,j)), calculations are stopped. Then, Tt is set to zero and control
is returned to ROCKET where a message is printed and data for all preceding points are
listed.

5.8 Subroutine GAUSS
Subroutine GAUSS is called from subroutine EQLBRM to solve the set of
simultaneous linear iteration equations constructed by subroutine MATRIX. It is also called
from subroutine TRANP to solve the simultaneous linear equations needed to obtain the
mixture thermal transport properties. The simultaneous equations are solved by using a
modified pivot technique to perform a Gauss reduction. In this modified pivot technique,
ortly rows are interchanged. The row to be used for eliminating ;1 variable is selected on the
basis that the largest of its elements, after division by the leading element, must be smaller
than the largest elements of the other rows after division by their leading elements.
The solution vector is stored in X(k). In the event of a singularity, Msing is set equal
to the number of the first singular row. Msing is tested later in subroutine EQLBRM. In
addition, Imat (which is equal to the number of row.s) is set equal to Imat - 1.

5.9 Subroutine HCALC
Subroutine HCALC calculates thermodynamic properties for gaseous reactants in
shock and detonation problems. It is called from subroutines SHCK and DETON only when
there is at schedule in the prob dataset. If the reactants are species that are included in the
first part of thermo.lib (containing data for products), the thermodynamic coefficients will
have already been stored in the common variable Coef(j,i,k), and these coefficients will be
used to obtain the required thermodynamic properties. If the coefficients are in the last part
of thermo.lib (reserved for reactants only), thermo.lib will be searched for the appropriate
coefficients. If found, they will be stored at the end of the data already stored in the Coef
array. The first index in this array indicates the species number. For the reactants these
numbers are stored in the Jray array for future use. Subroutine HCALC also calculates the
properties of the reactant mixture. The mixture properties h 0/R, c 0/R, and s0/R (eqs. (9.7),
(9.21), and (9.22), respectively, in Gordon and McBride, 1994) are stored in HsubO, Cpmix,
and Ssum(Npt), respectively, for the current temperature Tt.

44

5.10 Subroutine INFREE
Subroutine INFREE is called from subroutine INPUT. It reads, writes, and analyzes
input for a complete dataset. As many as 132 characters are read and sorted for each record.
The record is just printed without further analysis if the characters are all blanks and tabs or if
the first nonblank or nontab character is a"#" or an "!". Character strings are formed by
concatenating the characters between one or more special characters defined to be delimiters
(see section 2.1.7). These strings are stored in the call-vector character array Cin. Variables
starting with a"+", a"-", or an integer are assumed to be numeric. Other Cin variables are
assumed to be literal.
Delimiters can be any consecutive combination of blanks and tabs. Other delimiters
are an equal sign following a literal variable and a comma following a numerical variable.
Numerical variables are converted to double-precision variables and stored in the Dpin array.
The variables in the call vector are defined as follows:
Variable
Code

Description
Cin(l) assumed to be the keyword

Readok

Logical variable that is set to "false" when either there is an error in reading
a record or a keyword is not found

Cin

Character strings between delimiters. As many as 15 characters are stored.
Additional characters are ignored.

Nein

Number of variables stored in Cin

Lein

Integer array giving information about corresponding variable in Cin as
follows:
1. If Cin(i) is literal, Lcin(i) gives the number of characters with a
negative sign.
2. If Cin(i) is numeric, Lcin(i) gives the index of the previous literal.

Dpin

Array with numerics in Cin converted to double precision

Ndp

Integer giving the number of double-precision numbers in Dpin

5.11 Subroutine INPUT
Subroutine INPUT calls subroutine INFREE, which deciphers the characters in the
free-form input. (See subroutine INFREE, section 5.10, for definitions of the call-vector
variables.) It then checks for keywords. The data corresponding to the keywords are
processed and stored as follows:
1. For the keywords only, inse, and omit, species names are stored in the COMMON
variables Prod, Ensert, and Omit, respectively.
2. For the keywords outp, reac, and prob, the dataset information stored by subroutine
INFREE in the Cin, Lein, and Dpin arrays is examined, and the required COMMON data
are stored.

45

3. For the keyword reac, subroutine REACT is called for further processing the reac
data.
4. For the keyword prob, the literals that do not have associated numerical data are sorted
and stored first. The numerical data are then analyzed and stored.
5. For the keywords thermo and tran, subroutines UTHERM and UTRAN are called,
respectively, to process and convert the thermodynamic and thermal transport data to
unformatted form.
6. For the keyword outp, if plotting parameters are listed, the input/output unit IOPLT is
opened, and numerical data corresponding to the parameters are dumped as a (formatted)
text file to input/output unit IOPLT. The file contains no alphanumeric information. Data
that are generally listed horizontally in the standard output are listed vertically in this file.
This file is named with the same prefix as the standard input but with the suffix .pit.
7. For the keyword end, after some additional processing, control is transferred to the main
program.

5.12 Subroutine MATRIX
Subroutine MATRIX is called from subroutine EQLBRM to set up an appropriate
matrix corresponding to one of tables 2.1 to 2.4 in Gordon aild McBride ( 1994). These
matrices are set up for the following purposes:
1.

The matrix in table 2.1 corresponds to the iteration equations for determining
equilibrium compositions for the following assigned-pressure problems:
a. tp (assigned temperature and pressure) (Tp=.TRUE., Vol=. FALSE.)
b. hp (assigned enthalpy and pressure) (Hp=.TRUE., Vol=.FALSE.)
c. sp (assigned entropy and pressure) (Sp=. TRUE., Vol=. FALSE.)
The logical variable Convg is "false" for these three problems.

2.

The matrix in table 2.2 corresponds to the iteration equations for determining
equilibrium compositions for the following assigned-volume (or -density) problems:
a. t v (assigned temperature and volume or density) (Tp=. TRUE • ,
Vol=. TRUE.)

b. u v (assigned internal energy and volume or density) (Hp=. TRUE. ,
Vol=. TRUE.)

c. sv (assigned entropy and volume or density) (Sp=.TRUE., Vol=.TRUE.).
These matrices are initially set up like those in table 2.1, and then, where necessary,
elements of the matrices are corrected to match table 2.2. The logical variable Convg is
false for these three problems.
3. The matrix in table 2.3 corresponds to the equations for calculating derivatives with
respect to the logarithm of temperature at constant pressure. The logical variables are set

46

the same as for the matrices of tables 2.1 and 2.2 except for setting Convg=.TRUE. and
Pderi v=.FALSE.
4.

Similarly, the matrix in table 2.4 corresponds to the equations for calculating derivatives
with respect to the logarithm of pressure at constant temperature. The logical variables are
set the same as for table 2.3 except for Pderiv=.TRUE.

The elements in the matrices (G(i,j)) are generally summations of properties of
product species. The matrix is cleared and then filled by two DO loops-one for gases
U=l,Ng) and one for condensed species (k=l,Npr). The appropriate contribution of each
species is summed into the matrix elements.

5.13 Subroutine NEWOF
Subroutine NEW OF combines the properties of total oxidant and total fuel (calculated
either in subroutine REACT or subroutine HCALC) for a particular oxidant-to-fuel ratio to
give properties for the total reactant. NEWOF is called from either THERMP, ROCKET,
SHCK, or DETON for each mixture ratio that was set in subroutine INPUT (Oxf array). The
total reactant properties are calculated by using equations (9.5) to (9.22) from Gordon and
2
McBride (1994). Values of b;< >, b;rmula of a reactant is not
included in the dataset or if a required enthalpy or internal energy value is missing, the
thermodynamic library thermo.lib will be searched for data for that reactant. The error
message is printed if the search is unsuccessful. Control is returned to the main program,
which continues with the next problem, if any.
(symbol of chemical element) NOT FOUND IN BLOCKDAT A (REACT)
Fatal error. The symbol for a chemical element in the exploded formula of a reactant
in the reac dataset was not found in BLOCKDATA. Control is returned to the main
program, which continues with the next problem, if any.
T= (value of temperature) K MORE THAN 10 K FROM (value of temperature) FOR
(name of species) (REACT)
Fatal error. For reactants in thermo.lib, where there is an assigned enthalpy and
corresponding temperature but no thermodynamic coefficients, the temperature given in the
reac dataset must be within 10 K of the temperature in thermo.lib. Control is returned to the
main program, which continues with the next problem, if any.
WARNING!! AMOUNT MISSING FOR REACTANT (reactant number). PROGRAM
SETS WEIGHT PERCENT= 100. (REACT)
If the problem contains only one fuel, or one oxidant, or one reactant in the reac
dataset and the amount was not given, the CEA program will automatically set the amount to
be 100% and continue.

60

6.8 ROCKET Messages
FATAL ERROR!! EITHER mdot/a or ac/at MISSING FOR THE fac PROBLEM
(ROCKET)
The f ac option for rocket performance calculations requires either the mass flow
rate per unit chamber area mIA or the contraction area ratio AJA, to be assigned in the prob
dataset. If neither one is assigned, this message is printed and the program goes on to the next
problem.

INPUT VALUE OF mdot I a =(value of mIA) IS TOO LARGE. GIVES
CONTRACTION RATIO ESTIMATE LESS THAN 1 (ROCKET)
Fatal error. In the rocket finite-area-combustor model f ac, an option is provided to
assign mIA. If this assigned value gives a contraction ratio less than I, the error message is
printed and control is returned to the main program, which continues with the next problem,
if any.

WARNING!! AREA RATIO CALCULATION CANNOT BE DONE BECAUSE
GAMMAs CALCULATION IMPOSSIBLE (ROCKET)
The iteration procedure for obtaining a pressure ratio corresponding to an assigned
area ratio requires a value of Ys as well as some other parameters (eq. (6.23) of Gordon and
McBride, 1994). If a value of Ys cannot be calculated for this point, the error message is
printed and the CEA program proceeds to the next point. The problem can be rerun using
estimated pressure ratios to obtain area ratios at or near the desired value.

WARNING!! ASSIGNED pi/pe =(value of assigned P/Pe) IS NOT PERMITTED TO
BE LESS THAN Pinj/Pc =(value of Pin/Pc). POINT OMITTED (ROCKET)
In a rocket finite-area-combustor model f ac it is not possible for an assigned input
value of pi I pc to be less than Pin/Pc (the ratio of. pressures at the beginning and end of the
combustion chamber). If such a value is assigned in the input, this error message is printed,
the point is omitted, and the program continues with the next assigned point.

WARNING!! ASSIGNED subae/at =(value of assigned A/A,) IS NOT PERMITTED
TO BE GREATER THAN ac/at =(value of A/A,). POINT OMITTED (ROCKET)
In a rocket finite-area-combustor model fac, it is physically impossible for a
subsonic area ratio to be greater than the contraction ratio. The CEA program omits this
incorrectly assigned area ratio and continues.

WARNING!! CALCULATIONS WERE STOPPED BECAUSE NEXT POINT IS MORE
THAN 50 K BELOW THE TEMPERATURE RANGE OF A CONDENSED SPECIES
(ROCKET)
For frozen composition, calculations a temperature was calculated to be more than
50 K below the temperature range of an included condensed species. Output tables are
printed for all previous points and the program continues.

61

WARNING!! DID NOT CONVERGE FOR AREA RATIO= (value of area ratio)
(ROCKET)
The CEA program permits a maximum of 10 iterations to converge to the pressure
ratio corresponding to the assigned area ratio. The usual number of iterations required is 1 to
5. The only time the number of iterations has exceeded 10, in our experience, has been for an
assigned area ratio very close to 1, such as 1.0 < Ae!A 1 < 1.0001. The reason is that the
converged throat conditions do not correspond exactly to an area ratio of 1 (see eq. (6.16) of
Gordon and McBride, 1994). If the number of iterations exceeds 10, the point is omitted and
the program continues with the next assigned point.

WARNING!! DIFFICULTY IN LOCATING THROAT (ROCKET)
The test for convergence for throat conditions is given in equation (6.16) of Gordon
and McBride ( 1994). If this test is not passed in 23 iterations, this warning message is printed
and the program continues with the next point.

WARNING!! DISCONTINUITY AT THE THROAT (ROCKET)
Under some unusual circumstances involving condensed species in the region of the
throat, a special technique is used to obtain throat conditions. This technique involves a
discontinuous velocity of sound at the throat. Details are given in Gordon ( 1970).

WARNING!! FOR FROZEN PERFORMANCE, POINTS WEHE OMITTED WHERE
THE ASSIGNED PRESSURE RATIOS WERE LESS THAN THE VALUE AT POINT
nfz =(value of nfz) (ROCKET)
Pressure ratios may be assigned only downstream of the pressure ratio where freezing
is assigned to occur. Pressure ratios not meeting this requirement are omitted, and the
calculations continue.

WARNING!! FOR FROZEN PERFORMANCE, POINTS WERE OMITTED WHERE
THE ASSIGNED SUPERSONIC AREA RATIOS WERE LESS THAN THE VALUE AT
POINT nfz =(value of nfz) (ROCKET)
Area ratios may be assigned only downstream of the area ratio where freezing occurs.
Area ratios not meeting this requirement are omitted, and the calculations continue.

WARNING!! FOR FROZEN PERFORMANCE, SUBSONIC AREA RATIOS WERE
OMITTEDSINCEnfz IS GREATER THAN 1 (ROCKET)
Area ratios may be assigned only downstream of the area ratio where freezing is
assigned to occur. Inasmuch as in this problem freezing is assigned to occur at n f z > l (the
throat or some supersonic point), all subsonic area ratios are omitted and the calculations
continue.

62

WARNING!! FREEZING IS NOT ALLOWED AT A SUBSONIC PRESSURE RATIO
FOR nfz GREATER THAN 1. FROZEN PERFORMANCE CALCULATIONS WERE
OMITTED (ROCKET)
For nfz > 1, throat conditions will be based on equilibrium compositions. For this
situation, it is therefore not permitted to assign freezing to occur at a subsonic pressure ratio.
Frozen performance is omitted and the program continues.

WARNING!! nfz NOT ALLOWED TO BE> 2 IF THE TOTAL NUMBER OF
POINTS IS> (number) (ROCKET)
The CEA program permits freezing at a point greater than 2 if there is only one page
of the equilibrium output ·table. The reason is that a second page wipes out the information
from the first page except for the combustion and throat columns. This message is printed
when the total number of assigned pressure ratios and area ratios (both subsonic and
supersonic) is greater than NCOL (the number of columns in the output listing) minus 2 (the
number of columns for combustion and throat). In this situation, frozen performance is
omitted and the program continues.

6.9 SEARCH Messages
INSUFFICIENT STORAGE FOR (number ot) SPECIES (SEARCH)
Fatal error. This statement shows that for the chemical system under consideration, the
program found more possible species in thermo.lib than can be accommodated by storages
reserved for the thermodynamic data in labeled COMMON /THERM/. This excess number of
species is given in this error message. When this situation occurs, the names of the possible
species are printed, and control is returned to the main program, which continues with the
next problem, if any.
This situation can be resolved in two ways. First, the program can be recompiled with
MAXNGC in the parameter statements increased to accommodate the excess species (see
section 4.9.1). Secondly, an omit dataset can be used to eliminate the required number of
excess species.

WARNING!! (name of species) MISSING IN thermo.lib FILE (SEARCH)
The species name was listed in the dataset only, but the species was not found in
thermo.lib. The species is ignored and the program continues.

6.10 SHCK Messages
WARNING!! ONLY (NCOL) u 1 OR mach 1 VALUES ALLOWED (SHCK)
The number of assigned values of u 1 or roach 1 in dataset prob exceeded the
maximum allowed. This maximum is NCOL (number of columns), which is set in a
PARAMETER statement. NCOL is usually 7 or 13 depending on the width of the paper used
for printing output. The excess points are ignored and the program continues.

63

WARNING!! NO CONVERGENCE FOR ul =(value of u 1). ANSWERS NOT
RELIABLE, SOLUTION MAY NOT EXIST (SHCK)
This message usually occurs when the assigned values of u 1, T1, and P 1 do not have a
solution. For example, for example 7 in section 7.5, no solution exists for values of shock u 1
less than approximately 1095 mis using the current set of thermodynamic data. The message
will therefore be printed for this problem for these low values, and the program continues.

WARNING!! TEMPERATURE= (value) IS OUT OF EXTENDED RANGE FOR POINT
(value) (SHCK)
Fatal error. This message is printed whenever a converged temperature for a shock
problem is higher than the highest Tin the temperature range times 1.25 or if the assigned
temperature t 1 is less than the lowest Tin the range divided by 1.5. The program prints all
the converged values up to this point and continues .with the next problem, if any.

6.11

TRANIN Message

WARNING!! MAXIMUM ALLOWED NO. OF SPECIES (number) WAS USED IN
TRANSPORT PROPERTY CALCULATIONS FOR POINT (number of point)
(TRANIN)
The number of gaseous species used in the thermal transport properties calculations
was cut off at the maximum number MAXTR set in a PARAMETER statement. The omitted
species are the ones with the smallest mole fractions.

6.12 UTHERM Message
ERROR IN PROCESSING thermo.inp AT OR NEAR (name of species) (UTHERM)
Fatal error. An error occurred in reading or processing the thermo.inp file. After the
message is printed, the program terminates.

6.13

UTRAN Message

ERROR IN PROCESSING trans.inp (UTRAN) (name of 1 or 2 species)
Fatal error. An error occurred in reading or processing the trans.inp file. After the
message is printed, the program terminates.

64

Chapter7

Example Problems
Fourteen example problems are given to illustrate some features of the program. The
output for these problems is given in appendix G. Inasmuch as the thermodynamic and
thermal transport data are updated periodically, the answers given for these examples may
change somewhat from time to time. In the prob datasets the case designations were chosen
to match the example numbers. Examples 1 and 14 are assigned-temperature and assignedpressure problems, t p; example 2 is an assigned-temperature and assigned-volume (or
assigned density) problem, tv; three are combustion problems (examples 3 and 5 are for
combustion at constant pressure, hp, and example 4 is for combustion at constant volume,
uv); example 6 is a detonation problem, det; example 7 is a shock problem, sh; and six
(examples 8 to 13) are rocket problems, ro or r:kt. These problems were run with NCOL set
to 8 (see section 4.9.1).
It would not be practical to illustrate every possible variation of options permitted by
the program. However, the example problems were selected to illustrate many of the possible
variations and in particular those variations that we feel might often be used. Included in the
features illustrated are the following:
1.

Specifying proportions of various reactants
a. Relative weights of reactants
i. Complete information in reac dataset: example 5
ii. Information in reac and prob datasets: examples 2 to 4, 6, 8 to 10, 12,
and 13
b. Relative moles of reactants
1.

Complete information in reac dataset: examples 7, 11, and 14

ii. Information in reac and prob datasets: example 1
c. Type of information provided in prob dataset (in addition to that given in reac
dataset):
1.
11.
111.

o/f: examples 3, 4, 8 to 10, and 12
Chemical equivalence ratio r: examples l and 6
Fuel-air equivalence ratio : example 2

iv. Percent fuel by weight, %fuel: example 13

65

2.

Exploded formula
a. Obtained directly from thermo.lib: l to 4, 5 (partly), and 6 to 13
b. Specified in reac dataset: 5 (partly) and 14

3.

Specifying enthalpies or internal energies
a. In reac dataset: example 5 (partly)
b. In prob dataset: example 4
c. Automatically calculated by program from data in thermo.lib: examples 3, 5
(partly), and 6 to 13
d. Not needed: examples 1, 2, and 14

4. Pressure units
a. atm: examples 1 and 14
b. psia: examples 5 and 11 to 13
c. mm Hg: example 7
d. bar: examples 3, 6, and 8 to 10
e. Not required: examples 2 and 4
5.

inse: example 13

6. omit: examples 3 to 5
7. only: examples l and 2
8. trace (composition in floating-point format): examples 3, 4, and 13
9.

Considering ions: example 11

10. Propellant density: example 12
11. Output units
a. In SI units: examples 3, 4, 7 to 12, and 14
b. Not in SI units: examples 1, 2, 5, 6, and 13
12. Output composition units
a. Mass fractions: example 12
b. Mole fractions: all examples except 12
13.

Transport properties included: examples 2, 6, and 11

14.

Dump for plotting: example 12

15.

Special thermodynamic derivatives: example 13

66

16.

Two definitions of molecular weight: examples 5, 13, and 14 (discussed in section 7.10)

17.

Internal thermodynamic consistency: examples 1 to 4

The following discussion of the 14 example cases includes the features outlined above
plus some additional features of the program.

7.1 Examples 1 and 2
Examples 1 and 2 are used, among other things, to demonstrate internal consistency
in the CEA program for assigned-temperature and assigned-pressure problems, tp; and
assigned-temperature and assigned-volume problems, t v. The same reactants are used in the
two examples, and part of the output from example I is used as input for example 2.

7 .1.1 Example 1
Example 1 is an example of a t p problem. Properties will be calculated for all
combinations of temperatures and pressures specified. In this example, two temperatures
(3000 and 2000 K) and three pressures (I, 0.1, and 0.0 I atm) are specified, for a total of six
combinations. Each of these six combinations will be run for two equivalence ratios (r=l and
1.5). The exploded formulas for the fuel (H2) and oxidant (Air) are obtained automatically
from thermo.lib (see section 2.3.8). Enthalpies of the reactants are not needed for a tp
problem.

7 .1.2 Example 2
Example 2 is an example of an assigned-temperature and assigned-volume (or
-density) problem, tv. As previously stated, examples 1 and 2 are used to demonstrate
internal consistency in the CEA program for t p and t v problems. The combustion mixture
densities taken from example I output for the equivalence ratio of I and for 3000 K were
used as part of the input for example 2. It may be seen in the output of example 2 that the
pressures of L 0.1, and 0.01 atm, used as input in example I, are reproduced exactly. The
equivalence ratio was specified here in terms of  rather than r as in example l. For
stoichiometric conditions, the two definitions give equal values (see discussion in chapter 9 of
Gordon and McBride, 1994).
Example 2 also includes thermal transport properties (tran in the outp dataset). As
discussed in section 5.2.3 of Gordon and McBride (1994), the specific heat for thermal
transport property calculations cp,equil is calculated by a different method from the more
general specific heat cP eq· When no condensed species are present, the two methods should
give the same numerical values of specific heat, except possibly for rounding errors. This
agreement, which occurs here as well as in examples 6 and 11, confirms the accuracy of the
calculations.

67

7 .2 Examples 3 and 4
Examples 3 and 4 illustrate, among other things, internal consistency in combustion
problems (example 3 for combustion at constant pressure, hp; and example 4 for combustion
at constant volume, uv). The same propellants are used in the two examples, and part of the
output of example 3 is used as input for example 4.

7 .2.1 Example 3
Example 3 is an example of a combustion problem at constant pressure, hp. Three
pressures were selected: 1, 10, and 100 bars. Reactant enthalpies and exploded formulas for
all reactants in this problem will be obtained automatically from thermo.lib. Note that the fuel
and oxidant do not have to be at the same initial temperature. In this problem, the air is
preheated to 700 K. The results of the enthalpy calculation for the oxidants may be seen in
reactants data in the output.
This example also illustrates the option of listing compositions whose amounts are
smaller than those listed in the fixed-point output (i.e., smaller than 0.000005). This is
accomplished by using the trace option in the outp dataset. In this example,
trace=l .E-15.
Some of the output of this case will be used as input for example 4.

7.2.2 Example 4
Example 4 illustrates combustion at constant volume (or density), uv. This type of
problem generally requires as input the internal energies of the reactants at some initial
temperature as well as the assigned volume (or density). In this case, we are using as input the
density and internal energy of the combustion mixture resulting from the first point of
example 3. The reason for this selection is to verify the internal consistency and accuracy of
the calculation procedures. Verification will be accomplished if the same combustion
temperature and pressure are obtained as in example 3. From example 3, the value for density
3
is 14.428 kg/m . The input for internal energy is required to be in the form of u/R, where u is
internal energy and R is the universal gas constant in consistent units. From example 3, output
u=-375.27 kJ/kg is obtained. This gives u/R=-375.27/8.31451=-45.1343 (kg-mol)(K)/kg.
As expected, the resulting combustion temperature of 2419.33 K and combustion pressure of
100 bars match those of example 3 exactly.

7 .3 Example 5
Example 5 is for a typical solid propellant. The relative amounts of reactants are
given in weight percents. Unless an inse dataset is present, the CEA program initially
considers only gaseous combustion products. An initial combustion temperature of
2223.217K was reached in 15 iterations. This information may be seen in the output under
the heading POINT ITN. The program then checks for the possibility that condensed species
should have been considered. In this example, it determined that the solid phase Al 20 3 (a)
should be added. (The solid phase exists below the melting point of 2327 K.) With Al 20 3 (a)
added, the temperature converged in seven iterations to 2800.188 K. The program now
checks for the appropriate phase and determines that the phase at this temperature is liquid
and makes the appropriate switch. This may be seen by the message PHASE CHANGE,
REPLACE AL203(a) WITH AL203(L). The next convergence took just two iterations and
gave a final combustion temperature of 2724.464 K.

68

Had the keyword inse followed by AL203(L) been used in the input, convergence
would have been reached in 15 iterations rather than 24 iterations needed with no inse
being used. However, the use of inse often implies some prior knowledge of which
condensed species or phases exist. If one is starting a new problem, it may be better to just let
the program figure this out rather than inserting a possibly incorrect condensed species that
the program must then remove. The inse option may be used only for the first point. After
the first point the insertions and removals of condensed phases are all handled automatically
by the program.
In some situations, however, the keyword inse is required, as in a combustion
problem when temperature is driven down too low without the appropriate condensed species
present. When this happens, an error message will be printed.

7 .4 Example 6
Example 6 is an example of a detonation problem, det. Calculations will be made
for all combinations of pressures and temperatures specified. In this example, two pressures
(l and 20 bars) and two temperatures (298.15 and 500 K) have been scheduled. When
temperatures are specified in the prob dataset, enthalpies for the det problem are calculated
automatically by the program for the assigned temperatures. For this situation, this implies
that only those gaseous species whose thermodynamic data are in the thermo.lib file (such as
H., and 0-i in this example) may be considered as possible reactants. This example also
includes thermal transport property calculations (see discussion in section 7.1.2).

7 .5 Example 7
Example 7 is an example of a shock problem, sh. The input permits a schedule of
either velocities ul or Mach numbers machl, but not both in the same input dataset. For this
example, a set of velocities was assigned. Only the incident shock conditions were calculated.
To obtain reflected shock conditions, the prob dataset would have required refleq for
reflected shocks based on equilibrium incident conditions and/or reflfr for reflected
shocks based on frozen incident conditions. The message that starts with WARNING!! NO
CONVERGENCE FOR u 1= 1000.0 usually indicates that no solution exists for the assigned
condition.

7.6 Examples 8, 9, and 10
Examples 8 to 10 illustrate some similarities and differences in rocket performance
calculations for the two models of an infinite-area combustor, iac, and a finite-area
comb us tor, f ac. All three examples are for the same propellant, chamber pressure, o/f ratio,
pressure ratios, and area ratios. Example 8 is for the iac assumption. Inasmuch as the default
is for the iac assumption, this information is not required in the prob dataset. Examples 9
and I 0, by contrast, are for the f ac assumption, and this needs to be specified in the prob
dataset. A subsonic area ratio of 1.58 (subar=l. 58) was assigned in order to compare the
results with those obtained when using the same assigned value of Ar/A 1 (the contraction ratio
assigned for examples 9 and IO). The outputs for examples 8 to IO will be compared in the
discussion of examples 9 and I 0.

69

7 .6.1 Example 8
Example 8 illustrates a typical rocket performance problem based on the model of an
infinite-area combustor, iac. Note that there are nine output points (columns): the chamber,
the throat, three pressure ratios, one subsonic area ratio, and three supersonic area ratios.
Since NCOL (number of columns or points) was set to 8 in the program, output for the last
supersonic area ratio was printed on the second page along with the chamber and throat,
which are repeated for convenience.

7.6.2 Example 9
Examples 9 and 10 are for the f ac model. Two options are permitted with this
model. The first option, assigning the contraction ratio AJA 1 (acat) is illustrated in
example 9. The second option, assigning the mass flow rate per unit area m/Ac (ma) is
illustrated in example 10. The results of example 9 for an assigned value of Ac!Ar=I.58 were
used to calculate a value of m/Ac=l333.9. This value was used as input in example 10 in
order to verify the consistency of the results.

7.6.3 Example 10
As mentioned in the previous section, example 10 is identical to example 9 except for
using a value of m/Ac instead of A/A1 as input. The input value of ma=l333.9 for
example 10 was calculated from the results of example 9. As expected, the value of
A/At=l.5800 calculated in example 10 matches the example 9 input value of 1.58. This
result confirms the accuracy and consistency of the calculations and iteration procedures.
As pointed out in Gordon ( 1988), the calculated values of specific impulse for the
f ac and i ac rocket models are extremely close for the same assigned area ratios. For
example, at an area ratio of 75, the iac rocket model in example 8 gives a specific impulse
of 4399.7 mis, which compares closely with 4399.0 m/s obtained for the fac model of
examples 9 and 10. The difference is only 0.02%.

7.7 Example 11
Example 1 l illustrates including ions as possible combustion species (the option
ions is part of the prob dataset). At the high combustion temperature of 5686 K, about
1.5% of the species are the result of ionization. This example also shows that it is possible to
assign a schedule of points for expansion in a rocket that includes a mixture of pressure
ratios, subsonic area ratios, and supersonic area ratios. Note in the output that two area ratios
are assigned the value of 10. Their corresponding Mach numbers indicate which is subsonic
and which is supersonic. Example 11 also includes thermal transport property calculations
(see discussion in section 7.1.2).

70

7 .8 Example 12
Example 12 is another example of rocket performance. Several options are illustrated
in this example: the nfz option for freezing composition, the calculation of reactant density,
the option of obtaining compositions as mass fractions rather than mole fractions, and the
plot option for obtaining an output dump for plotting purposes. By setting nfz=2, frozen
composition rocket performance calculations are based on compositions frozen at the second
point. By including densities of all individual reactants (rho in the reac dataset), the
program will calculate the reactant mixture density. By including massf in the outp
dataset, compositions are given as mass fractions. By including plot in the outp dataset, a
dump of values for the parameters following plot is generated in the file (input suffix).plt.
(see section 2.5.4).

7 .9 Example 13
Example 13 illustrates some unusual values of thermodynamic derivatives that occur
when two condensed phases are present simultaneously. The appropriate equation for Ysr,
which is needed to calculate velocity of sound under these conditions, is equation (3.9) 'in
Gordon and McBride (1994). As may be seen in the output of example 13 for the second
and third points, Ys.r equals 0.9979 and 0.9974, respectively. This topic is covered more
completely in Gordon ( 1970).

7.10 Example 14
Example 14 was chosen for three reasons. The first was to check out the size of the
error caused by assuming zero volume of condensed species in the equation of state (eq.
(2.1 a) in section 2.2 of Gordon and McBride, 1994 ). The second was to look at an example
of the two definitions of molecular weight given as equations (2.3b) and (2.4a) in Gordon
and McBride (1994). The third reason was to illustrate debug output (see section 3 .4 for
further discussion). The reactants are hydrogen and oxygen. This example is a t p problem
where the pressure (0.05 atm), the schedule of temperatures (1000, 500, 350, 305, 304.3,
304.2, 304, and 300 K), and the relative number of moles of hydrogen to oxygen were
chosen to produce a large calculated mole fraction of liquid water for some conditions.
For T=304 K the mole fraction of liquid water is 0.24681. Using the density
3
0.99539 g/cm at this temperature (Lide, 1992-1993), the volume of water in 1 mole of
3
mixture is calculated to be 4.5 cm , in contrast to 375 900 cm 3 for the gases. Therefore, even
though the mole fraction of the condensed species is about 25%, the relative volume of the
condensed phase is only 0.001 %. Thus, in this example, the assumption of negligible volume
for condensed species that is incorporated into the equation of state (eqs. (2.1 a) and (2.1 b) in
Gordon and McBride, 1994) is valid for most practical purposes. For other problems with
higher pressures than in this case, the relative volume of the condensed species will be
generally be greater than here but less than 0.1 %.

71

For those problems with combustion products containing condensed phases, two
values of molecular weight are given in the output (see final table in example 14,
appendix G). These values are based on definitions given in section 2.2 of Gordon and
McBride (1994). Note that in the present example the product compositions remain constant
if all phases of water are combined. It is therefore to be expected that the molecular weights
of the mixture would be the same for all points. This is indeed the case for the molecular
weight MW, where the value for all points is 19.287. However, the molecular weight M
increases for those points with increasing amounts of liquid water, consistent with the
assumptions incorporated in the equation of state (eq. (2.1) in Gordon and McBride, 1994).
The molecular weight Mis obtained by means of equations (2.3a) or (2.3b), MW is given by
equation (2.4a), and the relationship between M and MW is given by equation (2.4b) in
Gordon and McBride (1994). For the T=304 K point equation (2.4b) gives
MW=25.607x0.75319=19.287, which matches exactly the molecular weight of 19.287 given
in the table.
Lewis Research Center,
National Aeronautics and Space Administration,
Cleveland, Ohio, January 28, 1996.

72

Appendix A

Format for Thermodynamic Data
The library of thermodynamic data contains data for both reaction products and
reactants. All reaction products and some reactants are in the nine-constant functional form
discussed in section 4.2 of Gordon and McBride ( 1994). The format for these data is given
here. Thermodynamic data are provided with the program on a separate file, thermo.inp.
Sections 2.8 and 5.24 discuss the processing of the thermo.inp data and the storing of the
processed data in thermo.lib for subsequent use in the CEA program. Names of species
contained in thermo.inp are listed in appendix B.
The general format is given in table Al. This format is applicable for all gaseous
species and for those condensed species whose data extend over a temperature range. For
those condensed species with data given at only one temperature, the format is somewhat
different. On record 2, instead of the last number being a heat of formation, it is an assigned
enthalpy. (Note that if the temperature is 298.15 K, the heat of formation and the assigned
enthalpy are equivalent.) The first number in record 2 (number of temperature intervals) is
always zero. On record 3, only one number is given, the temperature of the assigned enthalpy
on record 2. Two examples are given. Example Al, for chlorine gas, illustrates the general
format. Example A2, for liquid acetylene, illustrates the format for a condensed species with
data given at only one temperature. The general equations for dimensionless heat capacity,
enthalpy, and entropy (eqs. (4.6) to (4.8) from Gordon and McBride, 1994) are repeated for
convenience.
TABLE A.1.-GENERAL FORMAT FOR NINE-CONSTANT FUNCTIONAL FORM
1:ormat
Record
Constants
Columns
Species name or formula
1-2-J.
A2-J.
Comments (data source)
A'i6
25-80

2

3

Number of T intervals
Optional identification code
Chemical formulas, symbols, and' numbers
Zero for gas and nonzero for condensed phases
Molecular weight
Heat of formation at 298. 15 K, .L mol
Temperature range
l\iumbcr of coefficients for

,\6

5(:\2,Hi.2)
II
Ft:U
1·13.5

2
-J.-9
11-50
52
53-65
66-80

21'10.3
II
81 . 5.1

2-21
23

Fl5.3

6(i-80

h rst five coefficients for C~, R

5Dl6.8

1-80

I ,ast three coefficients for C" 0 R
Integration constants h, and h,
Re Jcat 3, -J., and 5 for each interval

3Dl , eq. (9.1)
Bratio is discussed in sec. 3.2.
aij , eqs. (4.9) to (4.11) for
condensed species and each
temperature interval
aij, eqs. (4.9) to (4.11) for gases

NEWOF

SEARCH

Coef

MAXNG,9,3

R*8

THERM

SEARCH

No

Debug

NCOL

L*4

MISCL

INPUr

No

Elmt

MAXEL

En

MAXNGC,
NCOL

C*2
R*8

CDATA
COMP

Yes
Yes

Enln

MAXNGC

R*8

COMP

Yes

Inn,

Enn

-----------------

R*8

COMP

Yes

n, eq. (2. la)

Ennl

-----------------

R*8

COMP

Yes

In n

Gonly

----------------

L*4

MISCL

REACT
Main
SET EN
Main
SErEN
Main
SEfEN
Main
SEfEN
Main

and three temperature intervals
If true, print intermediate output
for output column number Npt.
Element chemical symbol
n,, eq. (2.2); second index is Npt

Yes

Hp

----------------

L*4

MISCL

No

HsubO

----------------

R*8

MISCR

If z

MAXNC

1*4

INDX

Main
DEJ'ON
INPUf
ROCKEf
SHCK
THERMP
DEfON
HCA!£
NEWOF
INPUT
SHCK
REACT
SEARCH

If true, all product species are
gaseous.
If true, either enthalpy and
pressure or internal energy and
volume (or density) have been
assigned.

Ions

----------------

L*4

MISCL

INPlTr

No

Jcm

MAXEL

1*4

TRNP

SEARCH

Yes

Jcond

45

1*4

INDX

Main
SET EN

Yes

108

No

h 0 iR, assigned specific enthalpy
of mixture divided by universal
gas constant, eq. (9.7)

No

Positive integer numbering
condensed phases of a species
starting with l and increasing
with temperature ranges
If true, ionic species are to be
considered.
Indices of species currently used
as components (usually
monatomic gases)
Indices of condensed species
currentl bein considered

Dimension

Type

TABLE F. l. -Continued.
Where set
Reset?
COMMON
label

Jliq

----------------

I*4

MI SCI

NEWOF
SEI'EN

Yes

Jsol

----------------

I*4

MI SCI

Yes

Jx
Ls ave

MAXEL
----------------

I*4
1*4

INDX
MI SCI

NEWOF
SEI'EN
SEARCH
INPUT
SEfEN

Mw

MAXNGC

R*8

THERM

No

Ne

----------------

1*4

INDX

HCALC
SEARCH
SEARCH

No

Ng

----------------

I*4

INDX

SEARCH

Yes

Ngc
Ngpl
Nlm

----------------

-------------------------------

I*4
I*4
1*4

INDX
INDX
INDX

No
No
Yes

Npr

------------- ---

1*4

INDX

Npt

----------------

1*4

INDX

Nspx

----------------

I*4

lNDX

SEARCH
SEARCH
Main
REACT
Main
SEARCH
DEfON
NEWOF
ROCKET
SHCK
THERMP
SEARCH

Pp

----------------

R*8

MISCR

Variable

Yes
Yes

Yes
No

Description (symbols and
equations from Gordon and
McBride, 1994)
Index of condensed species that
is included simultaneously
with another condensed phase
of same species. Jsol is for
the adjacent species; Jliq is
for the higher temperature
interval.
See Jliq.
Indices of monatomic gases
0 when processing input; Nlm+ 1
in EQLBRM after
convergence when ionic
species are included as
products, and Nlm when they
are not
Molecular weight of product
species
Number of temperature intervals
for all possible condensed
products for current problem
Number of possible gaseous
products for current problem

Ng+Nc
Ng+l
Number of elements in current
chemical system
Number of condensed species
currently being considered
Index of column for data saved
for output ( l:SNpt:SNCOL)

No

Ngc plus number of monatomic
gases without thermo data

DEI'ON
ROCKET
SHCK
THERMP
SEARCH
BLOCKDATA

Yes

Assigned pressure in bars for
current point

No
No

Species names
Universal gas constant,
8314.51 J/(kg-mol)K
s 0 / R, assigned specific entropy
of mixture divided by
universal gas constant
If true, shock problem.
If true, listed output is
abbreviated.
SIZE as discussed in sec. 3.2 of
Gordon and McBride (1994)
If true, entropy and pressure (or
volume) have been assigned.
Value of summation in eq. (2.2)

Prod

O:MAXNGC

Rr

----------------

C*l5
R*8

CDATA
MISCR

so

----------------

R*8

MISCR

INPlff
ROCKET

No

Shock
Short

----------------

----------------

L*4
L*4

MISCL
MISCL

INPUT
INPUT

No
No

Size

----------------

R*8

MISCR

Yes

Sp

----------------

L*4

MISCL

SUilU1

----------------

R*8

COMP

Temp

2,MAXNC

R*8

THERM

INPUT
NEWOF
INPlff
ROCKE!'
Main
SEI'EN
SEARCH

No
Yes
No

Temperature ranges for
thermodynamic properties of
all condensed roducts

109

Variable

Dimension

Type

TABLE F.l.-Concluded.
COMMON
Where set
Reset?
label

Tg

4

R*8

THERM

SEARCH

No

Tp

----------------

L*4

MISCL

No

Trace

----------------

R*8

MISCR

DEI'ON
INPUT
ROCKET
SHCK
INPUT
SHCK

Tt

----------------

R*8

MISCR

Yes

Vol

----------------

L*4

MISCL

DEfON
ROCKEf
SEfEN
SHCK
THF_RMP
INPUT

Vv

----------------

R*8

MISCR

THERMP

No

Variable
Cp
Cpr
Div pt
Dlvtp
Gammas
HO
Hsum
Mu
Ppp

s

Ssum
Totn
Ttt
Vim
Wm

110

No

No

Description (symbols and
equations from Gordon and
McBride, 1994)
Temperature ranges for
thermodynamic properties of
gases
If true, temperature and pressure
(or volume) have been
assigned.
IfTrace>O, print mole (or
mass) fractions::<: Trace in

special E-format
Current temperature in kelvin

If true, volume has been
assigned.
Assigned specific volume times
10-5 ' (m3 /k )I o-s' . (2. la)

TABLE F.2. -COMMON VARIABLES CALCULATED BY EQUILIBRIUM MODULE
Dimension Type
COMMON
Where set
Description (symbols and equations from
label
Gordon and McBride, 1994)
R*8
CPHS
Molar heat capacity for species divided by
MAXNGC
THERM
universal gas constant, eq. (4.9)
NCOL
R*8
PRTOUf
EQLBRM
Specific heat of mixture divided by universal gas
constant, eq. (2.59)
PRTOUT
EQLBRM
Derivative defined by eq. (2.51)
NCOL
R*8
NCOL
R*8
PRTOUT
r'.Ql13RM
Derivative defined by eq. (2.50)
NffiL
R*8
PRTOUf
EQLBRM
Isentropic exponent, eqs. (2.71)
CPHS
R*8
MAXNGC
THERM
Molar standard-state enthalpy of species divided
by universal gas constant, eq. (4.10)
R*8
PRTOUT
Specific enthalpy of mixture divided by
NCOL
MATRIX
universal gas constant, eq. (2.14)
R*8
MATRIX
Molar Gibbs energy for each species
MAXNGC
THERM
NCOL
R*8
PRTOUT
EQLBRM
Static pressure in bars stored for output
TIIERM
CPHS
Molar standard-state entropy of species divided
R*8
MAXNGC
by universal gas constant, eq. (4.11)
NCOL
R*8
PRTOlff
EQLBRM
Specific entropy of mixture divided by universal
gas constant, eq. (2.16)
R*8
PRTOUT
NCOL
DQLBRM
Totn(i)=sum of EnU,Npt) for all species,
denominator of eq. (2.4a)
R*8
PRTOlff
EQLBRM
Temperature in kelvin stored for output
NCOL
R*8
PRTOUT
EQLBRM
Specific volume times 10 5 , (m3 /kg)10 5 ,
NffiL
eq. (2. la)
PRTOlJf
E LBRM
Molecular wei ht of mixture, c . (2.3a)
NCOL
R*8

AppendixG

Example Problems
This appendix presents the output for the example problems discussed in chapter 7.

111

*******************************************************************************
NASA-LEWIS CHEMICAL EQUILIBRIUM PROGRAM CEA, MARCH 1996
BY BONNIE MCBRIDE AND SANFORD GORDON
REFS: NASA RP-1311, PART I, 1994 AND NASA RP-1311, PART II, 1996

*******************************************************************************

SAMPLE PROBLEMS

EXAMPLE l:
(a) Assigned-temperature-and-pressure problem (tp) .
(b) Reactants are H2 and Air. Since "exploded" formulas are not given,
these formulas will be taken from the thermodynamic data library,
thermo.lib.
(c)
Calculations are for two equivalence ratios (r,eq.ratio =l,1.5).
(d) Assigned pressures are l, 0.1, and 0.01 atm (p(atm)=l, .1, .01).
(e) Assigned temperatures are 3000 and 2000 K (t(k)=3000,2000).
(f)
'only' dataset is used to restrict possible products.
(g) Energy units in the final tables are in calories (calories) .
'problem' dataset:
problem case=Example-1 tp p(atm)=l,.l,.Ol,t(k)=3000,2000,
r,eq.ratio=l,1.5
'reactants' dataset:
reac
fuel= H2 moles
l.
oxid= Air moles
l.
'only' dataset:
only Ar
c CO C02 H H2 H20 HNO H02
HN02 HN03
NO
N2
N203 0 02 OH 03
'output' dataset:
output calories
'end' dataset
end
OPTIONS: TP=T
RKT=F FROZ=F
T,K =

P,BAR

HP=F SP=F TV=F UV=F SV=F DETN=F SHOCK=F REFL=F
EQL=F IONS=F SIUNIT=F DEBUGF=F SHKDBG=F DETDBG=F

3000.0000

TRACE= O.OOE+OO

=

NH

INCD=F
TRNSPT=F

2000.0000
S/R= O.OOOOOOE+OO

1.013250

0 .101325

H/R= O.OOOOOOE+OO

U/R= O.OOOOOOE+OO

0.010132

REACTANT
MOLES
(ENERGY/R) I K
EXPLODED FORMULA
F: H2
1.000000
O.OOOOOOE+OO
H 2.00000
0: Air
1.000000
O.OOOOOOE+OO
N l . 56170 0 0.41959 AR 0.00937

112

N

TEMP,K
0.00

c

DENSITY
0.0000

0.00 0.0000
0.00032

SPECIES BEING CONSIDERED IN THIS SYSTEM
(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES)
*Ar
*C02
HN02
*H2
*NH
N203
*02

1 6/88
1 7/88
tpis89
tpis78
111/89
1 4/90
tpis89

O/F

ll.1/88
1 6/94
1 4/90
1 8/89
tpis89
1 1/90
1 5/90

*C
*H
HN03
H20
*NO
*O
03

tpis79
112/89
1 5/89
1 6/88
tpis78
tpis78

*CO
HNO
H02
*N
*N2
*OH

34.297046

ENTHALPY
(KG-MOL) (K)/KG
KG-FORM.WT./KG
*H
*N
*O
*Ar

*C

POINT !TN

EFFECTIVE FUEL
h(2)/R
O.OOOOOOOOE+OO

EFFECTIVE OXIDANT
h(l)/R
O.OOOOOOOOE+OO

MIXTURE
hO/R
O.OOOOOOOOE+OO

bi(2)
0.99212255E+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO

bi(l)
O.OOOOOOOOE+OO
0.53915548E-01
0.14485769E-01
0.32348639E-03
0.11047560E-04

bOi
0.28107807E-01
0.52388068E-Ol
0.14075373E-Ol
0.31432170E-03
0.10734572E-04

T

H

N

0

AR

-11.767

-14.452

-17.112

-27.077

-12.631

-13.684

-17.810

-26.104

-12. 811

-15.668

-18.090

-29.507

-13. 414

-14.837

-18.560

-28.409

-14.310

-16.920

-19.495

-32.012

-14.202

-15.991

-19.318

-30. 716

c
1

13

2

6

3

5

4

7

5

6

6

8

3000.000
-25.140
2000.000
-28.010
3000.000
-26.387
2000.000
-28.858
3000.000
-27.378
2000.000
-29.736

113

THERMODYNAMIC EQUILIBRIUM PROPERTIES AT ASSIGNED
TEMPERATURE AND PRESSURE
CASE

Example-1
REACTANT

FUEL
OXIDANT
O/F=

MOLES

H2
Air
34.29705

ENERGY
CAL/MOL
0.000
0.000

1.0000000
1.0000000
%FUEL=

2.833098

R,EQ.RATIO= 1.000000

TEMP
K

0.000
0.000

PHI,EQ.RATIO= 1.000000

THERMODYNAMIC PROPERTIES
P, ATM
T, K
RHO, G/CC
H, CAL/G
U, CAL/G
G, CAL/G
S, CAL/ (G) (K)

1.0000
1.0000 0.10000 0.10000 0.01000 0.01000
3000.00 2000.00 3000.00 2000.00 3000.00 2000.00
9.1864-5 1.4990-4 8.0877-6 1.4957-5 6.6054-7 1.4878-6
658.91 -203.80 1367.61 -192.33 2655.92 -165.41
395.29 -365.35 1068.18 -354.25 2289.29 -328.19
-7973.51 -5290.34 -8615.20 -5662.69 -9379.92 -6036.36
2.5433
3.3276
2.7352
2. 8775
4. 0119
2.9355

M, (1/n)
(dLV/dLP)t
(dLV/dLT)p
Cp, CAL/ (G) (K)
GAMMAS
SON VEL,M/SEC

22.615
24.601
19. 910
24.547
16.261
24.417
-1.03437 -1. 00062 -1.07935 -1. 00143 -1.07486 -1. 00352
1.0200
2.5468
1.0452
2.4145
1.6948
1.1090
1. 6795
0.4539
0.5187
3.4666
3. 7240
0.6801
1.1311
1.2263
1. 2035
1.1318
1.1677
1.1203
1317.6
1117. 0
910.4
1184.7
902.9
891. 8

MOLE FRACTIONS
*Ar
*CO
*C02
*H
H02
*H2
H20
*N
*NO
*N2
*O
*OH
*02

0.00711
0.00017
0.00007
0.04069
0.00001
0.06708
0.20936
0.00001
0.01247
0.58613
0.01560
0.04205
0.01925

0.00773
0.00001
0.00025
0.00009
0.00000
0.00304
0.34216
0.00000
0.00049
0.64416
0.00002
0.00100
0.00104

0.00626
0.00018
0.00003
0.14315
0.00001
0.08301
0.09741
0.00003
0.01389
0.51456
0.05864
0.05562
0.02721

0.00772
0.00002
0.00024
0.00041
0.00000
0.00633
0.33736
0.00000
0.00073
0.64261
0.00010
0.00216
0.00232

0.00511
0.00017
0.00001
0.31984
0.00000
0.04144
0 .01193
0.00009
0.00974
0.42102
0.14381
0.03048
0.01637

0.00767
0.00004
0.00022
0.00185
0.00000
0.01309
0.32683
0.00000
0.00108
0.63903
0.00047
0.00460
0.00510

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONS
WERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONS
*C
N203

114

HNO
03

HN02

HN03

*NH

O/F

22.853060

ENTHALPY

(KG-MOL) (K) /KG
KG-FORM. WT. /KG

*H
*N
*O

*Ar
*C

POINT ITN

EFFECTIVE FUEL
h(2)/R
0.00000000E+OO

EFFECTIVE OXIDANT
h(l)/R
O.OOOOOOOOE+OO

MIXTURE
hO/R
O.OOOOOOOOE+OO

bi(2)
0.99212255E+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO

bi(l)
O.OOOOOOOOE+OO
0.53915548E-Ol
0.14485769E-Ol
0.32348639E-03
O.ll047560E-04

bOi
0.41593093E-Ol
0.51655228E-01
0.13878477E-Ol
0.30992476E-03
0.10584410E-04

T

H

N

0

-11.376

-14.517

-17.824

-27.214

-10.689

-13.763

-21.840

-26.262

-12.569

-15.737

-18.424

-29.649

-11.843

-14.915

-21.838

-28.566

-14.102

-17.003

-19.691

-32.180

-13.001

-16.068

-21.831

-30.871

AR

c
1

5

2

6

3

5

4

7

5

6

6

8

3000.000
-24.401
2000.000
-21. 257
3000.000
-26.155
2000.000
-23.564
3000.000
-27.343
2000.000
-25.879

115

THERMODYNAMIC EQUILIBRIUM PROPERTIES AT ASSIGNED
TEMPERATURE AND PRESSURE
CASE

Example-·l
REACTANT

FUEL

OXIDANT
O/F=

H2
Air
22.85306

ENERGY
CAL/MOL
0.000
0.000

MOLES
1.0000000
1.0000000

%FUEL=

4.192334

R,EQ.RATIO= 1.500000

TEMP
K

0.000
0.000

PHI,EQ.RATIO= 1.500764

THERMODYNAMIC PROPERTIES
P, ATM
T, K
RHO, G/CC
H, CAL/G
U, CAL/G
G, CAL/G
s, CAL/ (G) (K)

1.0000 0 .10000 0.10000 0.01000 0.01000
1.0000
3000.00 2000.00 3000.00 2000.00 3000.00 2000.00
8.1298-5 1.2975-4 7.1204-6 1.2964-5 5.6650-7 l . 2930-6
712.66 -120.74 1545.93 -116 .35 3217.90 -102.27
414.78 -307.39 1205.82 -303.16 2790.41 -289.56
-8817.98 -5830.59 -9543.81 -6260.51 -10423.3 -6691. 09
3.1769
2.8549
3.6966
3.0721
4. 5471
3.2944

M, (1/n)
(dLV/dLP)t
(dLV/dLT)p
Cp, CAL/ (G) (K)
GAMMAS
SON VEL,M/SEC

20.013
21. 294
17.528
21.276
13.946
21. 220
-1.03292 -1.00019 -1.08636 -1.00060 -1. 08730 -1.00194
l . 0054
2.6809
2.6458
1.6619
1. 0172
1.0556
1.8179
0.4667
4.2215
0.4987
4.9387
0.6036
1.1337
l . 2531
1.1194
1.1295
1.2062
1.2394
1421.4
1188.7
989.2
1262.1
984.2
972.2

MOLE FRACTIONS
*Ar
*CO
*C02
*H
*H2
H20
*N
*NO
*N2
*O
*OH
*02

0.00620
0.00018
0.00004
0.06014
0.14653
0.22436
0.00001
0.00573
0.51403
0.00765
0.03049
0.00463

0.00660
0.00016
0.00007
0.00062
0.14737
0.29510
0.00000
0.00001
0.54996
0.00000
0.00012
0.00000

0.00543
0.00017
0.00002
0.18240
0.13477
0.11320
0.00003
0.00928
0.44806
0.04197
0.05073
o. 01394

0.00659
0.00016
0.00007
0.00196
0.14674
0.29456
0.00000
0.00003
0.54950
0.00000
0.00039
0.00000

0.00432
0.00014
0.00000
0.39382
0.06283
0. 01486
0.00008
0.00737
0.35646
0.11820
0.03085
0.01.106

0.00658
0.00016
0.00007
0.00616
0.14483
0.29279
0.00000
0.00008
0.54803
0.00004
0.00124
0.00003

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONS
WERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONS
*C
*NH

116

HNO
N203

HN02
03

HN03

H02

EXAMPLE 2:
(a)
Assigned-temperature-and-volume (or density) problem (tv) .
(b)
Reactants are the same as in example 1.
(c) One temperature was taken from example 1 (t(k)=3000).
(d)
One mixture was taken from example 1 (phi,eq.ratio=l).
Note: For stoichiometric mixtures, phi = r = 1.
Densities (rho) were obtained from the results of example 1.
(e)
Composition and properties in examples 1 and 2 should match for
these input values.
(f)
'only' dataset is used to restrict possible products.
(g)
Transport properties are to be calculated (transport) .
reac
prob
only
outp
end

fuel=H2
wt\=100
oxid Air
wt\=100
case=Example-2 phi,eq.ratio=l, tv t(k)=3000
rho,g/cc=9.1864d-05,8.0877d-06,6.6054d-07
Ar c co C02 H H2 H20 HNO H02 HN02 HN03 N NH NO N2 N203 0 02 OH
transport calories

OPTIONS: TP=T
RKT•F FROZ=F
T,K

=

HP=F SP=F TV=T UV=F SV=F DETN=F SHOCK=F REFL=F
EQL=F IONS=F SIUNIT=F DEBUGF=F SHKDBG=F DETDBG=F

03

INCD=F
TRNSPT=T

3000.0000

TRACE= O.OOE+OO

S/R= O.OOOOOOE+OO

H/R= O.OOOOOOE+OO

U/R= O.OOOOOOE+OO

SPECIFIC VOLUME,M**3/KG = l.0885657E+Ol l.2364455E+02 l.5139129E+03
REACTANT
WT.FRAC
(ENERGY/R) ,K
EXPLODED FORMULA
F: H2
1.000000
O.OOOOOOE+OO
H 2.00000
0: Air
1.000000
O.OOOOOOE+OO
N 1. 56170 0 0.41959 AR 0.00937

TEMP,K

o.oo

DENSITY
0.0000

o.oo
c

0.0000
0.00032

SPECIES BEING CONSIDERED IN THIS SYSTEM
(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES)
1 6/88
1 7/88
tpis89
tpis78
111/89
1 4/90
tpis89

*Ar
*C02
HN02
*H2
*NH
N203
*02

111/88
1 6/94
1 4/90
1 8/89
tpis89
1 1/90
1 5/90

*C
*H
HN03
H20
*NO
*O
03

tpis79
112/89
1 5/89
1 6/88
tpis78
tpis78

*CO
HNO
H02
*N
*N2
*OH

SPECIES WITH TRANSPORT PROPERTIES
PURE SPECIES
Ar
H
H20
0
02

c

co

C02

H2
N
OH

NO

N2

117

BINARY INTERACTIONS

c
co
co
co

0

C02
N2
02
H2
H20
N2
02
H2

C02
C02
C02
C02
H
H
H
H
H2
H2
H2
H20
H20
N
N
N
N
NO
N2
N2
0

O/F

N

N2
0

H20
N2
02
N2
02
NO
N2
0

02
0

0

02
02

34.297046

INTERNAL ENERGY
(KG-MOL) (K) /KG

EFFECTIVE FUEL
u(2)/R
O.OOOOOOOOE+OO

EFFECTIVE OXIDANT
u(l)/R
O.OOOOOOOOE+OO

MIXTURE
uO/R
O.OOOOOOOOE+OO

KG-FORM.WT./KG
*H
*N
*O
*Ar
*C

bi(2)
0.99212255E+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO

bi(l)
O.OOOOOOOOE+OO
0.53915548E-01
0.14485769E-Ol
0.32348639E-03
O.ll047560E-04

bOi
0.28107807E-Ol
0.52388068E-Ol
0.14075373E-Ol
0.31432170E-03
0.10734572E-04

POINT ITN

T

H

N

0

AR

-11.767

-14.452

-17 .112

-27.077

-12.811

-15.668

-18.090

-29.507

-14.310

-16.920

-19.495

-32.012

c

118

l

13

2

5

3

5

3000.000
-25.140
3000.000
-26.387
3000.000
-27.378

THERMODYNAMIC EQUILIBRIUM PROPERTIES AT ASSIGNED
TEMPERATURE AND VOLUME
CASE

Example-2

REACTANT
FUEL
OXIDANT
O/F=

FRACTION
(SEE NOTE)

WT

1.0000000
1.0000000

H2

Air
34.29705

%FUEL=

2.833098

R,EQ.RATIO= 1.000000

ENERGY
CAL/MOL
0.000
0.000

TEMP
K

0.000
0.000

PHI,EQ.RATIO= 1.000000

THERMODYNAMIC PROPERTIES
P, ATM
T, K
RHO, G/CC
H, CAL/G
U, CAL/G
G, CAL/G
S, CAL/ (G) (K)

1.0000 0.10000 0.01000
3000.00 3000.00 3000.00
9.1864-5 8.0877-6 6.6054-7
658.92 1367.61 2655.91
395.30 1068.18 2289.29
-7973.51 -8615.20 -9379.92
2 .8775
3.3276
4. 0119

M, (l/n)
(dLV/dLP)t
(dLV/dLT)p
Cp, CAL/ (G) (K)
GAMMAs
SON VEL,M/SEC

22.615
19.910
16.261
-1.03437 -1.07935 -1. 07486
1.6948
2.5468
2.4145
3.4666
1. 6795
3. 7240
1.1311
1.1203
1.1318
1184.7
1117.0
1317.6

TRANSPORT PROPERTIES (GASES ONLY)
CONDUCTIVITY IN UNITS OF MILLICALORIES/(CM) (K) (SEC)
VISC,MILLIPOISE

0.93569

0.94006

0.94815

WITH EQUILIBRIUM REACTIONS
Cp, CAL/ (G) (K)

CONDUCTIVITY
PRANDTL NUMBER

1.6795
4.4242
0.3552

3.4666
9.6933
0.3362

3. 7240
8.8440
0.3992

0.4283
0.7269
0.5539

0.4369
0.8650
0.4789

WITH FROZEN REACTIONS
Cp, CAL/ (G) (K)
CONDUCTIVITY
PRANDTL NUMBER

0.4250
0.6289
0.6324

119

MOLE FRACTIONS
*Ar
*CO
*C02
*H
H02
*H2
H20
*N
*NO
*N2
*O
*OH
*02

0.00711
0.00017
0.00007
0.04069
0.00001
0.06708
0.20936
0.00001
0.01247
0.58613
0.01560
0.04205
0.01925

0.00626
0.00018
0.00003
0.14315
0.00001
0.08301
0.09741
0.00003
0.01389
0.51456
0.05864
0.05562
0.02721

0.00511
0.00017
0.00001
0.31984
0.00000
0.04144
0. 01193
0.00009
0.00974
0.42102
0.14381
0.03048
0.01637

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONS
WERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONS
*C
N203

HNO
03

HN02

HN03

*NH

NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS

120

EXAMPLE 3:
(a) Combustion or assigned-enthalpy-and-pressure problem (hp) .
(b)
Fuels are 'C7H8(L)' and 'C8H18(L),n-octa' at 298.15 K. The oxidant is
air at 700 K.
(c) Oxidant-to-fuel weight ratio is 17 (o/f =17). Weight fractions are
fractions of fuel relative to total fuel and fractions of oxidant
relative to total oxidant.
(d) Mixture enthalpy is calculated from reactant values given in
thermo.lib. This is because data for these species are given in
thermo.lib and the species names match exactly.
(e) Many species are omitted from the product data base ('omit' dataset).
Note: these species names must match those used in thermo.lib.
(f) Assigned pressures are 100, 10, and 1 bar (p(bar)=l00,10,1).
(g) Mixture properties are to be printed in SI units (siunits) .
(h) Mole fractions > 1.e-15 are to be in e-format (trace=l.e-15).
reac
t(k)=700.0
ox id Air wtfrac= 1
fuel C7H8(L)
wtfrac= .4
t(k)= 298.15
wtfrac= .6 t(k)= 298.15
fuel C8Hl8(L),n-octa
prob
case=Example-3
hp p(bar)=l00,10,1, o/f = 17
output siunits trace=l.e-15
omit CCN
CNC
C3H4,allene
C3H4,propyne
C3H6,propylene
C3H5,allyl
C3H60
C3H7,n-propyl
C302
C4
C4H4,1,3-cyclo- C4H6,butadiene
C4H8,tr2-butene C4HS,isobutene
(CH3COOH)2
C4H9,n-butyl
C4H9,t-butyl
C4H9,s-butyl
C4H10,n-butane
C4N2
C5H6,l,3cycloC5H8,cycloC5Hll,pentyl
C5Hl0,cycloC5Hl2,n-pentane CSH12,i-pentane
C6HSOH,phenol
C6H6
C6Hl2,l-hexene
C6Hl2,cycloC7H8
C7H7,benzyl
C7H14,1-heptene C7Hl5,n-heptyl
C8HlO,ethylbenz
C8H8,styrene
C8H18,isooctane
C8H17,n-octyl
Jet-A(L)
C6H6 (L)
end End all input for example 3
OPTIONS: TP=F
RKT=F FROZ=F
TRACE= 1.00E-15
P,BAR

=

C2N2
C3H4,cycloC3H6,cycloC3H7,i-propyl
C4H2
C4H6,2-butyne
C4H8,cycloC4H9, i-butyl
C4HlO,isobutane

cs
C5Hl0,l-pentene
C5Hll,t-pentyl
CH3C(CH3)2CH3
C6HlO,cycloC6Hl3,n-hexyl
C7H80,cresol-mx
C7Hl6,n-heptane
C8H16,1-octene
C8Hl8,n-octane
H20(s)

C20
C3
C3H3,propargyl
Jet-A(g)
C3H80,2propanol
C3H80,lpropanol
C4H6,cycloC4HB, l-butene
C4H8,cis2-buten
C3H8
ClOH21,n-decyl
Cl2HlO,biphenyl
Cl2H9,o-bipheny
C6H2
C6H5,phenyl
C6H50,phenoxy
ClOHS,azulene
ClOH8,napthlene
C9Hl9,n-nonyl
H20(L)

HP=T SP=F TV=F UV=F SV=F DETN=F SHOCK=F REFL=F
EQL=F IONS=F SIUNIT=T DEBUGF=F SHKDBG=F DETDBG=F
S/R= O.OOOOOOE+OO

100.000000

10.000000

H/R= O.OOOOOOE+OO

INCD=F
TRNSPT=F

U/R= O.OOOOOOE+OO

1.000000

121

(ENERGY/R) I K
REACTANT
WT.FRAC
EXPLODED FORMULA
1.000000
0.143092E+04
0: Air
N :' .. 561 70 0 0.41959 AR 0.00937
0.400000
0.146491E+04
F: C7H8 (L)
c 7.00000 H 8.00000
F: C8H18(L) ,n-octa 0.600000 -0.300992E+05
c 8.00000 H 18.00000

TEMP,K

c

DENSITY

700.00 0.0000
0.00032
298.15 0.0000
298.15

0.0000

SPECIES BEING CONSIDERED IN THIS SYSTEM
(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES)
1 6/88
111/89
110/92
tpis91
1 7/88
1 1/91
1 1/91
112/92
1 8/88
112/92
1 8/88
x 4/85
1 6/94
tpis89
112/89
1 5/89
1 8/88
1 8/88
111/89
tpis89
j12/64
1 5/90
1 7/88
1 4/90
1 1/90
1 5/90
x 4/83
O/F

=

*Ar
CH2
CH30
*CN
*C02
C2H
C2H2,acetylene
CH3CN
C2H40,ethylen-o
C2H5
C2H50H
C6H14,n-hexane
*H
HCCN
HNO
H02
HCOOH
(HCOOH)2
*NH
NH20H
N03
N2H2
N20
N205
*O
03
C(gr)

111/88
111/89
1 8/88
112/89
tpis91
1 6/89
1 5/90
1 6/96
1 8/88
1 8/88
112/92
xl0/85
1 7/88
111/92
tpis89
tpis78
1 8/89
1 6/88
112/89
tpis89
tpis78
tpis89
1 4/90
tpis89
tpis78
x 4/83

*C
CH3
CH4
CNN

COOH
CHCO,ketyl
CH2CO,ketene
CH3CO,acetyl
CH3CHO,ethanal
C2H6
CH30CH3
C7Hl6,2-methylh
HCN

HNC
HN02
*H2
H20
*N
NH2
*NO
*N2
NH2N02
N203
N3
*OH
C(gr)

*CH
CH20H
CH30H
*CO
*C2
C2H2,vinylidene
C2H3,vinyl
C2H4
CH3COOH
CH3N2CH3
C4H6,1-butyne
C10H8,naphthale
HCO
HNCO
HN03
HCHO,formaldehy
H202
NCO
NH3
N02
NCN
N2H4
N204
N3H
*02
C(gr)

17.000000

ENTHALPY
(KG-MOL) (K) /KG

EFFECTIVE FUEL
h(2)/R
-0.15173707E+03

KG-FORM.WT./KG
*N
*O
*Ar
*C
*H

bi(2)
0.00000000E+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
0.72408514E-01
0.12927489E+OO

122

tpis79
112/92
1 8/88
tpis79
tpis91
112/89
1 2/92
1 1/91
1 8/88
1 8/88
xl0/93
1 8/93
112/89
1 2/96
1 4/90
1 8/88
1 2/93
1 2/96
tpis89
1 7/88
112/89
1 5/90
tpis89
1 7/88
tpis89
x 4/83

EFFECTIVE OXIDANT
h(l)/R
0.49400444E+02

MIXTURE
hO/R
0.38226138E+02

bi (1)
0.53915548E-01
0.14485769E-01
0.32348639E-03
0.11047560E-04
0.00000000E+OO

bOi
0.50920240E-01
0.13681004E-01
0.30551493E-03
0.40331290E-02
0.71819385E-02

1

18

2

5

3

5

N

0

AR

c

-11.651

-14.247

-21.786

-21.401

-12.783

-15.355

-24.066

-21.672

-13.898

-16.426

-26.325

-22 .191

T

POINT ITN

H
2419.334
-11.891
2391.604
-12.538
2340.157
-13.247

THERMODYNAMIC EQUILIBRIUM COMBUSTION PROPERTIES AT ASSIGNED
PRESSURES
CASE

Example-3
REACTANT

OXIDANT
FUEL
FUEL
O/F=

Air
C7H8(L)
C8H18(L) ,n-octa
17.00000

\FUEL=

5.555556

WT FRACTION
(SEE NOTE)
1.0000000
0.4000000
0.6000000

ENERGY
KJ/KG-MOL
11897.374
12180.000
-250259.981

R,EQ.RATIO= 0.852074

TEMP
K

700.000
298.150
298.150

PHI,EQ.RATIO= 0.851848

THERMODYNAMIC PROPERTIES
P, BAR
T, K
RHO, KG/CU M
H, KJ/KG
U, KJ/KG
G, KJ/KG
s, KJ/ (KG) (K)

100.00
10.000
1.0000
2419.33 2391.60 2340.16
1. 4428 1 1.4565 0 1.4827-1
317.83
317.83
317.83
-375.27 -368.76 -356.61
-19443.2 -20795.8 -21891.3
8.1680
8.8282
9.4904

M, (1/n)
(dLV/dLP)t
(dLV/dLT)p
Cp, KJ/ (KG) (K)
GAMMAS
SON VEL,M/SEC

29.023
28.962
28.849
-1.00067 -1. 00157 -1.00322
1.0186
1.0442
1.0914
1.6068
1. 8127
2.2013
1. 2260
1.2064
1.1803
921.8
910.1
892.2

123

MOLE FRACTIONS
*Ar
*CN
*CO
*C02
COOH
*H
HCN
HCO
HNC
HNCO
HNO
HN02
HN03
H02
*H2
HCHO,formaldehy
HCOOH
H20
H202
*N
NCO
*NH
NH2
NH3
NH20H
*NO
N02
N03
*N2
N2H2
NH2N02
N20
N203
N204
N3
N3H
*O
*OH
*02
03

8.8668-3
5.454-14
l.6811-3
l.1537-l
5.1792-8
2.7692-5
9.662-12
7.579-10
l.024-12
l.229 -9
4.2385-7
1.8549-6
l.133 -9
7.8127-6
2.5156-4
l.723-11
6.485 -9
1.0288-1
1.0129-6
1.1572-8
8.645-11
2.9542-9
1.721 -9
3.909 -9
1.027-11
6.7922-3
2.3525-5
1.932-10
7.3550-1
5.207-13
2.449-15
3.6532-6
2.448-ll
3.ll0-15
1.241-12
3.876-13
1.5576-4
2.1257-3
2.6302-2
1.2251-8

8.8483-3
9.975-14
4.3275-3
1.1248-l
2.3423-8
l.2480-4
1.081-ll
9.191-lO
1.107-12
5.144-lO
2.0929-7
3.2796-7
6.656-ll
4.1701-6
6.6471-4
1.172-11
1.651 -9
l.0154-1
3.0297-7
2.7706-8
6.074-11
3.9044-9
1.291 -9
1.731 -9
1.461-12
6.5768-3
7.5946-6
1.962-11
7.3408-1
1.210-13
6.786-17
l.1174-6
7.760-13
3.306-17
3.029-13
5.282-14
4.3417-4
3.4565-3
2.7452-2
3.7798-9

8.8139-3
l.l06-l3
9.2288-3
l.0712-l
8.6875-9
4.5990-4
7.934-12
7.862-lO
7.601-13
l.646-lO
9.1839-8
5.7687-8
4.067-12
2.1216-6
l.4948-3
5.625-12
3.455-10
9.9280-2
8.6257-8
5.1386-8
3.090-11
3.9370-9
7.472-10
6.186-10
1.702-13
6.1768-3
2.4942-6
2.015-12
7.3142-l
2.129-14
1.669-18
3.3132-7
2.459-14
3.704-19
5.825-14
5.650-lS
1.0769-3
5.1814-3
2.9742-2
1.1377-9

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONS
WERE LESS THAN l.OOOOOOE-15 FOR ALL ASSIGNED CONDITIONS
*C
CH30
C2H
C2H3,vinyl
CH3CHO,ethanal
C2H50H
ClOH8,naphthale
N205

*CH
CH4
CHCO,ketyl
CH3CN
CH3COOH
CH30CH3
HCCN
C(gr)

CH2
CH30H
C2H2,vinylidene
CH3CO,acetyl
C2H5
C4H6,1-butyne
(HCOOH) 2

CH3
CNN

C2H2,acetylene
C2H4
C2H6
C6H14,n-hexane
NCN

CH20H
*C2
CH2CO,ketene
C2H40,ethylen-o
CH3N2CH3
C7Hl6,2-rnethylh
N2H4

NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS

124

EXAMPLE 4:
(a) Assigned-internal-energy-and-density problem (uv) .
(b) Fuel, oxidant, and oxidant-to-fuel weight ratio are the same as in
example 3.
(c) Internal energy u was taken from col. 1 of the output of example 3.
However, input requires u/R, i.e., u = -375.27 kJ/kg and
u/R = -375.27/8.31451 = -45.1343 (kg-moll (K)/kg (u/r=-45.1343).
(d) units for density input are limited tog/cc and kg/m**3. From
example 3 point 1, rho = 14.428 kg/m**3 (rho,kg/m**3=14.428).
(e) Mixture properties are to be printed in SI units (default unit) .
(f) Mole fractions > 1.e-15 are to be in e-format (trace=1.e-15).
(g) Note that since all parameters for this example are the same as
those used for col. 1 of example 3, assigning u and rho from
this column should yield the same pressure and temperature assigned
for that point in example 3.
prob
output
reac

case=Example-4, o/f=17

uv

u/r=-45.1343, rho,kg/m**3=14.428

trace=1.e-15
oxid Air
wtfrac= 1
t(k)=700.0
fuel C7H8(L)
wtfrac= .4
t(k)= 298.15
fuel C8H18(L) ,n-octa wtfrac= .6 t(k)= 298.15

omit CCN CNC C2N2 C20 C3H4,allene C3H4,propyne C3H4,cyclo- C3
C3HS,allyl
C3H6,propylene C3H6,cycloC3H3,propargyl
C3H60
C3H7,n-propyl
C3H7,i-propyl
Jet-A(g)
C302
C4
C4H2
C3H80,2propanol
C4H4,1,3-cyclo- C4H6,butadiene C4H6,2-butyne
C3H80,lpropanol
C4HB,tr2-butene C4H8,isobutene C4H8,cycloC4H6,cyclo(CH3COOH)2
C4H9,n-butyl
C4H9,i-butyl
C4H8,1-butene
C4H9,s-butyl
C4H9,t-butyl
C4H10,isobutane C4HB,cis2-buten
C4H10,n-butane C4N2
CS
C3H8
CSH6,1,3cyclo- CSH8,cycloCSH10,1-pentene C10H21,n-decyl
CSH10,cycloCSH11,pentyl
CSH11,t-pentyl C12H10,biphenyl
CSH12,n-pentane CSH12,i-pentane CH3C(CH3)2CH3
C12H9,o-bipheny
C6H6
C6HSOH,phenol
C6H10,cycloC6H2
C6H12,1-hexene C6H12,cycloC6H13,n-hexyl
C6HS,phenyl
C7H7,benzyl
C7H8
C7H80,cresol-mx C6HSO,phenoxy
C7H14,1-heptene C7H15,n-heptyl C7H16,n-heptane C10H8,azulene
CBH8,styrene
CBHlO,ethylbenz C8H16,1-octene ClOHB,napthlene
CBH17,n-octyl
C8H18,isooctane C8H18,n-octane C9H19,n-nonyl
C7H8(L) C8H18(L) ,n-octa Jet-A(L) C6H6(L) H20(s)
H20(L)
end
OPTIONS: TP=F
RKT=F FROZ=F
TRACE= 1.00E-15

HP=T SP=F TV=F UV=T SV=F DETN=F SHOCK=F REFL=F
EQL=F IONS=F SIUNIT=T DEBUGF=F SHKDBG=F DETDBG=F
S/R= O.OOOOOOE+OO

SPECIFIC VOLUME,M**3/KG

H/R= O.OOOOOOE+OO

INCD=F
TRNSPT=F

U/R=-4.513430E+01

= 6.9309676E-02

125

(ENERGY/R} ,K
REACTANT
WT.FRAC
EXPLODED FORMULA
0.730917E+03
1.000000
0: Air
N 1. 561 70 0 0.41959 AR 0.00937
0.146491E+04
0.400000
F: C7H8 (L}
c 7.00000 H 8.00000
F: C8Hl8(L),n-octa 0.600000 -0.300992E+05
c 8.00000 H 18.00000

TEMP,K

c

DENSITY

700.00 0.0000
0.00032
298.15 0.0000
298.15

0.0000

SPECIES BEING CONSIDERED IN THIS SYSTEM
(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES}
1 6/88
111/89
110/92
tpis91
1 7/88
1 1/91
1 1/91
112/92
1 8/88
112/92
1 8/88
x 4/85
1 6/94
tpis89
112/89
1 5/89
1 8/88
1 8/88
111/89
tpis89
jl2/64
1 5/90
1 7/88
1 4/90
1 1/90
1 5/90
x 4/83
O/F

=

*Ar
CH2
CH30
*CN
*C02
C2H
C2H2,acetylene
CH3CN
C2H40,ethylen-o
C2H5
C2H50H
C6Hl4,n-hexane
*H
HCCN
HNO
H02
HCOOH
(HCOOH)2
*NH
NH20H
N03
N2H2
N20
N205
*O
03
C(gr}

*C
CH3
CH4
CNN

COOH
CHCO,ketyl
CH2CO,ketene
CH3CO,acetyl
CH3CHO,ethanal
C2H6
CH30CH3
C7Hl6,2-methylh
HCN

HNC
HN02
*H2
H20
*N
NH2
*NO
*N2
NH2N02
N203
N3
*OH
C(gr}

tpis79
112/92
1 8/88
tpis79
tpis91
112/89
1 2/92
1 1/91
1 8/88
1 8/88
xl0/93
1 8/93
112/89
1 2/96
1 4/90
1 8/88
1 2/93
1 2/96
tpis89
1 7/88
112/89
1 5/90
tpis89
1 7/88
tpis89
x 4/83

*CH
CH20H
CH30H
*CO
*C2
C2H2,vinylidene
C2H3,vinyl
C2H4
CH3COOH
CH3N2CH3
C4H6,l-butyne
C10H8,naphthale
HCO
HNCO
HN03
HCHO,formaldehy
H202
NCO
NH3
N02
NCN
N2H4
N204
N3H
*02
C(gr}

17.000000

INTERNAL ENERGY
(KG-MOL} (K} /KG
KG-FORM.WT./KG
*N
*O
*Ar
*C
*H

126

111/88
111/89
1 8/88
112/89
tpis91
1 6/89
1 5/90
1 6/96
1 8/88
1 8/88
112/92
xl0/85
1 7/88
111/92
tpis89
tpis78
1 8/89
1 6/88
112/89
tpis89
tpis78
tpis89
1 4/90
tpis89
tpis78
x 4/83

EFFECTIVE FUEL
u(2}/R
-0.15173707E+03
bi (2)
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
0.72408514E-01
0.12927489E+OO

EFFECTIVE OXIDANT
u(l)/R
0.25233905E+02
bi (1)
0.53915548E-01
0.14485769E-Ol
0.32348639E-03
0.11047560E-04
O.OOOOOOOOE+OO

MIXTURE
uO/R
-0.45134300E+02
bOi
0.50920240E-01
0.13681004E-Ol
0.30551493E-03
0.40331290E-02
0.71819385E-02

POINT ITN

T

N

0

-11.651

-14.247

AR

c

-21.786

-21.401

H

1

16

2419.335
-11.891

THERMODYNAMIC EQUILIBRIUM COMBUSTION PROPERTIES AT ASSIGNED
VOLUME
CASE

Example-4,
REACTANT

OXIDANT
FUEL
FUEL
O/F=

Air
C7H8 (L)
C8H18(L) ,n-octa
17.00000

%FUEL=

5.555556

WT FRACTION
(SEE NOTE)
1.0000000
0.4000000
0.6000000

ENERGY
KJ/KG-MOL
6077. 217
12180.000
-250259.981

R,EQ.RATIO= 0.852074

TEMP
K
700.000
298.150
298.150

PHI,EQ.RATIO= 0.851848

THERMODYNAMIC PROPERTIES
P, BAR
T, K
RHO, KG/CU M
H, KJ/KG
U, KJ/KG
G, KJ/KG
S, KJ/ (KG) (K)

100.00
2419.34
1.4428 1
317.83
-375.27
-19443.2
8.1680

M, (l/n)
(dLV/dLP)t
(dLV/dLT)p
Cp, KJ/ (KG) (K)
GAMMAS
SON VEL,M/SEC

29.023
-1.00067
1.0186
1.6068
1.2260
921.8

MOLE FRACTIONS
*Ar
*CN
*CO
*C02
COOH
*H
HCN
HCO
HNC
HNCO

8.8668-3
5.454-14
1.6811-3
1.1537-1
5.1793-8
2.7692-5
9.662-12
7.579-10
1.024-12
1.2290-9

127

HNO
HN02
HN03
H02
*H2
HCHO,formaldehy
HCOOH
H20
H202
*N
NCO
*NH
NH2
NH3
NH20H
*NO
N02
N03
*N2
N2H2
NH2N02
N20
N203
N204
N3
N3H
*O
*OH
*02
03

4.2385-7
1.8549-6
1.1332-9
7.8128-6
2.5156-4
1.723-11
6.4854-9
1.0288-1
1.0130-6
1.1572-8
8.645-11
2.9542-9
1. 7208-9
3.9091-9
1.027-11
6.7922-3
2.3525-5
1.932-10
7.3550-1
5.207-13
2.450-15
3.6532-6
2.448-11
3.110-15
1.241-12
3.876-13
1. 5576-4
2.1257-3
2.6302-2
l.2251-8

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONS
WERE LESS THAN 1.000000E-15 FOR ALL ASSIGNED CONDITIONS
*C
CH30
C2H
C2H3,vinyl
CH3CHO,ethanal
C2H50H
ClOH8,naphthale
N205

*CH
CH4
CHCO,ketyl
CH3CN
CH3COOH
CH30CH3
HCCN
C(gr)

CH2
CH30H
C2H2,vinylidene
CH3CO,acetyl
C2H5
C4H6,1-butyne
(HCOOH) 2

CH3
CNN
C2H2,acetylene
C2H4
C2H6
C6H14,n-hexane
NCN

CH20H
*C2
CH2CO,ketene
C2H40,ethylen-o
CH3N2CH3
C7Hl6,2-methylh
N2H4

NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS

128

EXAMPLE 5:
(a) Combustion problem (hp) for solid propellant with 5 ingredients.
(b) The assigned enthalpies and "exploded" formulas for four of the
components are to be taken from thermo.lib. However, data for
'CHOS-Binder' are not available in thermo.lib and thus the "exploded"
formula and enthalpy are given in the 'reac' dataset.
(c) The reactants are given in percent by weight (wt%= ... ). The
propellant components are not designated as fuel and oxidant - they
are labelled with the 'name' alternative. Weight fractions are
relative to the total reactant.
(d) Five pressures are given in units of psia (p,psia=S00,250,
125,50,5,).
(e) As with examples 3 and 4, many species in thermo.lib are omitted
as possible products by means of an 'omit' dataset.
(f) Energy units in the final tables are in calories (calories).
reac
name NH4CL04(I)
wt%= 72.06 t(k)=298.15
name CHOS-Binder C l H 1.86955 0 .031256 s .008415 wt%=18.58
h,cal=-2999.082 t(k)=298.15
t(k)=298.15
name AL(cr) wt%= 9.
name MgO(s) wt%= . 2
t(k)=298.15
name H20(L) wt%=.16
t(k)=298.15
prob
outp

case=S, hp

p,psia=500,250,125,SO,S,

calories

omit COOH C2 C2H CHCO,ketyl C2H2,vinylidene CH2CO,ketene C2H3,vinyl
CH3CO,acetyl C2H40,ethylen-o CH3CHO,ethanal CH3COOH
(HCOOH) 2
C2H5
C2H6
CH3N2CH3
CH30CH3
C2H50H
CCN
CNC
C2N2
C20
C3
C3H3,propargyl C3H4,allene
C3H4,propyne
C3H4,cycloC3HS,allyl
C3H6,propylene
C3H6,cycloC3H60
C3H7,n-propyl
C3H7,i-propyl
C3H8
C3H80,lpropanol C3H80,2propanol C302
C4
C4H2
C4H4,l,3-cyclo- C4H6,butadiene
C4H6,2-butyne
C4H6,cycloC4H8,l-butene
C4H8,cis2-buten
C4H8,tr2-butene C4H8,isobutene C4H8,cyclo(CH3COOH)2
C4H9,n-butyl
C4H9,i-butyl
C4H9,s-butyl
C4H9,t-butyl
C4Hl0,isobutane C4Hl0,n-butane C4N2
CS
CSH6,l,3cyclo- C5H8,cycloC5Hl0,l-pentene CSHlO,cycloCSHll,pentyl
C5Hll,t-pentyl CSH12,n-pentane CSH12,i-pentane
CH3C(CH3)2CH3
C6H2
C6HS,phenyl
C6HSO,phenoxy
C6H6
C6HSOH,phenol
C6Hl0,cycloC6Hl2,l-hexene
C6Hl2,cycloC6Hl3,n-hexyl
C7H7,benzyl
C7H8
C7H80,cresol-mx C7Hl4,l-heptene C7Hl5,n-heptyl C7Hl6,n-heptane
C8H8,styrene
CBHlO,ethylbenz C8Hl6,l-octene C8Hl7,n-octyl
C8Hl8,isooctane C8Hl8,n-octane C9Hl9,n-nonyl
ClOH8,naphthale
ClOH21,n-decyl Cl2H9,o-bipheny Cl2Hl0,biphenyl Jet-A(g)
HNCO
HNO HN02
HN03
HCCN
HCHO,formaldehy HCOOH
NH
NH2 NH20H NCN
N2H2 NH2N02
N2H4 H202
(HCOOH)2
C6H6(L) C7H8(L) CBH18(L),n-octa Jet-A(L) H20(s) H20(L)
end

129

OPTIONS: TP=F
RKT=F FROZ=F
TRACE= O.OOE+00
P,BAR

N:
N:
N:
N:
N:

=

HP=T SP=F TV=F UV=F SV=F DETN=F SHOCK=F REFL=F
EQL=F IONS=F SIUNIT=F DEBUGF=F SHKDBG=F DETDBG=F
S/R= O.OOOOOOE+OO

34.473652

H/R= O.OOOOOOE+OO

17.236826

WT.FRAC
(ENERGY/R) ,K
REACTANT
EXPLODED FORMULA
0.720600 -0. 355724E+05
NH4CL04(I)
N 1.00000 H 4.00000 CL 1.00000
0.185800 -0.150919E+04
CHOS-Binder
c 1.00000 H 1.86955 0 0.03126
0.090000
AL(cr)
0.496279E-05
AL 1.00000
MgO(s)
0.002000 -0. 723139E+05
MG 1.00000 0 1. 00000
0.001600 -0.343773E+05
H20(L)
H 2.00000 0 1.00000

U/R= O.OOOOOOE+OO

3.447365

8.618413

TEMP,K

INCD=F
TRNSPT=F

0.344737

DENSITY

298.15 0.0000
4.00000
298.15 0.0000
s 0.00841
298.15 0.0000

0

298.15

0.0000

298.15

0.0000

SPECIES BEING CONSIDERED IN THIS SYSTEM
(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES)
j 6/83
J 6/76
J12/79
J12/67
j12/79
J12/79
111/95
tpis91
x12/93
1 2/96
tpis91
1 8/88
112/89
tpis91
1 7/88
tpis91
tpis91
tpis91
tpis91
xl0/93
J 6/82
1 7/93
1 6/94
112/89
tpis89
1 8/89
J 9/83
J12/66
J12/75
J 9/83
tpis89

130

*AL
ALCL2
ALN

ALOH
ALS
AL20
CCL
CCL4
CHCL2
CH2CL
CH3CL
CH4
CNN
COCL2
*C02
C2CL
C2CL4
C2HCL3
C2H3CL
C4H6,1-butyne
CL
CL02
*H
HCO
HOCL
H20
Mg
MgH
MgOH
Mg2
NH3

J 6/63
J 9/79
J12/79
J12/79
J 6/79
J12/79
111/95
tpis79
1 6/95
tpis91
112/92
1 8/88
tpis79
tpis91
1 7/95
tpis91
tpis91
1 1/91
112/92
x 4/85
1 6/95
tpis89
J 3/64
tpis89
1 5/89
tpis89
J 3/66
J 3/64
J12/75
1 6/88
tpis89

ALC
ALCL3
ALO
AL02
AL2
AL202
CCL2
*CH
CHCL3
CH2CL2
CH20H
CH30H
*CO
COHCL

cs
C2CL2
C2CL6
C2H2,acetylene
CH3CN ·
C6H14,n-hexane
CLCN
CL2
HALO
HCL
H02
H2S
Mg CL
MgN
Mg02H2
*N
*NO

J 9/79
J 6/63
J 9/64
J12/68
J 9/79
111/88
x12/93
111/95
111/89
111/89
110/92
tpis91
tpis91
1 6/95
1 6/95
tpis91
tpis91
tpis91
1 1/91
xl0/85
tpis89
tpis89
1 7/88
111/92
tpis78
tpis89
J12/69
J12/74
J 9/77
1 2/96
1 5/95

ALCL
ALH

ALO CL
AL02H
AL2CL6
*C
CCL3
CHCL
CH2
CH3
CH30
*CN
COCL

cos
CS2
C2CL3
C2HCL
C2H2CL2
C2H4
C7H16,2-methylh
CLO
CL20
HCN
HNC
*H2
H2S04
MgCL2
MgO
MgS
NCO
NOCL

l 7/88
tpis78
tpis89
l 7/88
tpis89
J 6/78
tpis89
J 6/71
L 4/93
tpis89
tpis89
coda89
J 9/79
coda89
coda89
x 4/83
srd 93
J12/79
J12/65
J12/74
J12/75
L 7/76
BAR 73
tpis89
tpis89
J 6/78
J 6/78
O/F

=

N02
*N2
N204
N3H
*02
SCL
SN
S02CL2
S2CL2
S4
S7
AL(L)
ALCL3 (L)
AL203(a)
AL203 (L)
C(gr)
Mg(cr)
MgAL204(s)
MgCL2(s)
MgO(s)
Mg02H2(s)
MgS04(s)
NH4CL(a)
S(cr2)
S (L)
SCL2 (L)
S2CL2 (L)

(KG-MOL) (K)/KG
KG-FORM.WT./KG
*N
*H
CL
*O
*C
*AL
Mg

N02CL
N20
N205
*O
03
SCL2

so
S03
S20
SS
SB
ALCL3(s)
ALN(s)
AL203(a)
C(gr)
H2S04(L)
Mg(L)
MgAL204(L)
MgCL2(L)
MgO(s)
MgS(s)
MgS04(s)
NH4CL(b)
S(L)
S (L)
SCL2 (L)

j12/64
l 4/90
tpis89
tpis78
J 9/82
tpis89
tpis89
tpis89
tpis89
tpis89
coda89
J 9/79
J12/79
coda89
x 4/83
srd 93
J12/79
J12/66
J12/65
J12/74
J 9/77
L 7/76
tpis89
tpis89
tpis89
J 6/78

N03
N203
N3
*OH

s
SH
S02
S2
S3
S6
AL(cr)
ALCL3 (L)
ALN(s)
AL203 (a)
C(gr)
Mg(cr)
MgAL204(s)
MgC03(s)
MgCL2(L)
MgO(L)
MgS(s)
MgS04 (L)
S(crl)
S (L)
S (L)
S2CL2 (L)

0.000000

ENTHALPY

s

l 5/95
l 7/88
l 4/90
l 1/90
l 5/90
J 6/78
tpis89
tpis89
tpis89
tpis89
tpis89
J 9/79
J12/79
coda89
x 4/83
J 9/77
srd 93
J12/79
J12/65
J12/74
J 9/77
L 7/76
BAR 73
tpis89
tpis89
J 6/78

EFFECTIVE FUEL
h(2)/R
-0.24393994E+03
bi(2)
0.61333506E-02
0.48397025E-01
0.61333506E-02
0.25067832E-01
0.12669356E-Ol
0.10661263E-03
0.33356140E-02
0.49622374E-04

EFFECTIVE OXIDANT
h(l)/R
O.OOOOOOOOE+OO
bi(l)
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO

MIXTURE
hO/R
-0.24393994E+03
bOi
0.61333506E-02
0.48397025E-01
0.61333506E-02
0.25067832E-Ol
0.12669356E-01
0.10661263E-03
0.33356140E-02
0.49622374E-04

131

T

POINT !TN

s

2223.217
-13.211
-10.257
-16.675
ADD AL203(a)
2800.188
1
-1.3.61.8
7
-11.789
-1.7.41.8
PHASE CHANGE, REPLACE AL203 (a)
2724.464
-1.3.567
1
2
-1.7.289
-11. 563
2708.020
2
-1.3.903
3
-12.208
-17.473
2687.754
-1.4.237
3
3
-1.7.703
-12.840
2654.796
4
-14.675
3
-13.657
-18.073
2542.768
-15.754
5
4
-15.608
-1.9.236
1

CL

H

N

c
15

AL
-8. 721
-13.362

0

MG
-22.552
-21.039

-9.082
-20.821
-1.8.81.6
-21. 663
WITH AL203(L)
-9.031
-20.870
-1.9.670
-21..824
-9.369
-21.234
-19.750
-21. 884
-21. 603
-9.704
-1.9.850
-21.967
-10.143
-22.098
-20.01.8
-22.1.21.
-11. 231
-23.383
-20.635
-22.836

-21.610

-1.9.613

-19.869
-19.927
-19.999
-20.119
-20.548

THERMODYNAMIC EQUILIBRIUM COMBUSTION PROPERTIES AT ASSIGNED
PRESSURES
CASE

5
WT FRACTION
(SEE NOTE)
0.7206000
0.1858000
0.0900000
0.0020000
0.0016000

REACTANT
NAME
NAME
NAME
NAME
NAME
O/F=

NH4CL04(I)
CHOS-Binder
AL(cr)
MgO(s)
H20(L)
0.00000

%FUEL=

0.000000

ENERGY
CAL/MOL
-70690.009
-2999.082
0.000
-1.43703.308
-6831.5.026

R,EQ.RATIO= 1.947910

K

298.150
298.150
298.150
298.150
298.150

PHI,EQ.RATIO= 0.000000

THERMODYNAMIC PROPERTIES
P, ATM
T, K
RHO, G/CC
H, CAL/G
u, CAL/G
G, CAL/G
S, CAL/ (G) (K)

l. 7. 01.l.
34.023
8.5057
3.4023 0.34023
2724.46 2708.02 2687.75 2654.80 2542.77
3.5209-3 1.7681-3 8.8885-4 3.5874-4 3.7034-5
-484.76 -484.76 -484.76 -484.76 -484.76
-718.77 -717.76 -71.6.50 -714. 44 -707.24
-7370.89 -7490.69 -7598.71. -7721. 56 -7925.43
2.5275
2.5871.
2.6468
2. 7259
2.9262

M, (1/n)
MW, MOL WT
(dLV/dLP)t
(dLV/dLT)p
Cp, CAL/ (G) (K)
GAMMAS
SON VEL,M/SEC

23.136
23.096
22.970
22. 712
23.048
22.246
22.282
22.202
22.1.30
21..893
-1. 00263 -1.00342 -1..00438 -1..00590 -1.01098
1.0518
1.0686
1.2412
1.0892
1.1.228
0.5744
0.6051
0.6435
0.7082
0.9512
1.1890
1.1945
1.1828
1.1504
1.1738
1076.6
1081.. 4
1070.9
1.034.8
1062.l.

132

TEMP

MOLE FRACTIONS
ALCL
ALCL2
ALCL3
ALO
ALO CL
ALOH
AL02H
*CO

cos
*C02
CL
*H
HCN
HCO
HCL
*H2
H20
H2S
Mg
Mg CL
MgCL2
Mg OH
Mg02H2
NH3
*NO
*N2
*O
*OH
*02

s
SH

so
S02
S2
AL203 (L)

0.00019
0.00014
0.00007
0.00000
0.00008
0.00001
0.00002
0.26445
0.00005
0.01779
0. 00168
0.00591
0.00001
0.00001
0.13214
0.32150
0.14659
0.00136
0.00002
0.00003
0.00104
0.00001
0.00001
0.00001
0.00003
0.06831
0.00001
0.00070
0.00000
0.00009
0.00062
0.00015
0.00006
0.00002
0.03691

0.00024
0.00013
0.00005
0.00000
0.00010
0.00002
0.00003
0.26396
0.00004
0.01783
0.00222
0. 00785
0.00000
0.00000
0.13144
0.32075
0.14594
0.00113
0.00004
0.00004
0.00101
0.00001
0.00000
0.00001
0.00003
0.06820
0.00001
0. 00092
0.00000
0.00013
0.00069
0.00023
0.00009
0.00003
0.03682

0.00030
0.00011
0.00003
0.00000
0.00012
0.00002
0.00003
0.26337
0.00003
0.01788
0.00290
0.01027
0.00000
0.00000
0.13055
0.31979
0.14516
0.00089
0.00007
0.00005
0.00096
0.00001
0.00000
0.00000
0.00004
0.06806
0.00002
0.00118
0.00000
0.00019
0.00073
0.00033
0. 00013
0.00004
0.03672

0.00037
0.00010
0.00002
0.00000
0.00015
0.00003
0.00004
0.26238
0.00002
0.01797
0.00401
0.01427
0.00000
0.00000
0.12912
0.31813
0.14391
0.00060
0.00013
0.00006
0.00088
0.00002
0.00000
0.00000
0.00005
0.06784
0.00005
0.00157
0.00001
0.00027
0.00071
0.00048
0.00019
0.00004
0.03655

0.00052
0.00005
0.00000
0.00001
0.00023
0.00004
0.00006
0.25895
0.00001
0.01841
0.00790
0.02829
0.00000
0.00000
0.12434
0.31176
0.13984
0.00018
0.00044
0.00008
0.00054
0.00002
0.00000
0.00000
0.00009
0. 06710
0.00016
0.00275
0.00003
0.00043
0.00049
0.00082
0.00036
0.00002
0.03606

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONS
WERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONS
*AL
ALS
*C
*CH
CH2CL
CH30

ALC
AL2
CCL
CHCL
CH2CL2
CH4

ALH

AL2CL6
CCL2
CHCL2
CH3
CH30H

ALN
AL20
CCL3
CHCL3
CH3CL
*CN

AL02
AL202
CCL4
CH2
CH20H
CNN

133

COCL
C2CL
C2HCL
CH3CN
CLCN
HALO
MgH
*N
N03
N3
SN
83
SB
ALN(s)
Mg(L)
MgCL2(L)
MgS04(s)
S(cr2)

COCL2
C2CL2
C2HCL3
C2H4
CLO
HNC
MgN
NCO
N20
N3H
S02CL2
84
AL(cr)
AL203(a)
MgAL204(s)
MgO(s)
MgS04(L)
S(L)

COHCL
C2CL3
C2H2,acetylene
C4H6,l-butyne
CL02
HOCL
MgO
NOCL
N203
03
S03
SS
AL(L)
C(gr)
MgAL204(L)
MgO(L)
NH4CL(a)
SCL2 (L)

cs
C2CL4
C2H2CL2
C6Hl4,n-hexane
CL2
H02
MgS
N02
N204
SCL
S2CL2
S6
ALCL3 (s)
H2S04(L)
MgC03(s)
Mg02H2(s)
NH4CL(b)
S2CL2 (L)

CS2
C2CL6
C2H3CL
C7Hl6,2-methylh
CL20
H2S04
Mg2
N02CL
N205
SCL2
S20
87
ALCL3 (L)
Mg(cr)
MgCL2(s)
MgS(s)
S (crl)

NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS

134

EXAMPLE 6:
(a)
Chapman-Jouguet detonation problem (detonation)
(b) The reactants are H2 and 02 gases. The mixture is
stoichiometric (r,e=l).
(c) The unburned gases are at 298.15 and 500 Kand pressures
l bar and 30 bars (t,k=298.l5,500, pbar=l,30)
(d)
Thermal transport properties are called for (transport) .
(e)
Energy units in the final tables are in calories (calories) .
reac

oxid 02
fuel H2

prob

detonation

output
end

=

t=298.l5,500, r,e=l, pbar=l,20

HP=F SP=F TV=F UV=F SV=F DETN=T SHOCK=F REFL=F
EQL=F IONS=F SIUNIT=F DEBUGF=F SHKDBG=F DETDBG=F

298.1500

TRACE= O.OOE+OO
P,BAR =

case=6

calories transport

OPTIONS: TP=F
RKT=F FROZ=F
T,K

t(k)=298.l5
t(k)=298.l5

wt%=100
wt\=100.

INCD=F
TRNSPT=T

500.0000
S/R= O.OOOOOOE+OO

1.000000

H/R= O.OOOOOOE+OO

U/R= O.OOOOOOE+OO

20.000000

REACTANT
WT.FRAC
EXPLODED FORMULA
0: 02
1.000000
0 2.00000
F: H2
1.000000
H 2.00000

(ENERGY/R), K

TEMP,K

DENSITY

-0.988319E-06

298.15

0.0000

-0.489101E-05

298.15

0.0000

SPECIES BEING CONSIDERED IN THIS SYSTEM
(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES)
1 6/94
1 8/89
tpis78
1 8/89

*H
H20
*OH
H20(s)

1 5/89
1 2/93
tpis89
1 8/89

H02
H202
*02
H20(L)

tpis78
1 1/90
1 5/90

*H2
*O
03

135

SPECIES WITH TRANSPORT PROPERTIES
PURE SPECIES
H
OH

H2
02

H20

0

BINARY INTERACTIONS
H2
0
H20
02
02
02

H
H
H2
H2
H20
0

O/F

7.936683

ENTHALPY
(KG-MOL) (K) /KG

EFFECTIVE FUEL
h(2)/R
-0.24262412E-05

KG-FORM.WT./KG
*O
*H

bi(2)
O.OOOOOOOOE+OO
0.99212255E+OO

POINT ITN
1
8

T
3609.250

-15.678

POINT ITN
1
3

T
3637.136

-15.600

POINT ITN
1
3

T
3680.926

-15.602

POINT ITN
2
1
2
5
2
3
2
3
2
2
6
3
3
3
3
3
3
2
4
5
4
3
4
3
2
4

T
3679.599
4147. 454
4219.559
4292.394
4290.262
3727.581
3669.044
3606. 911
3604. 962
4336.573
4267.642
4216.603
4216.063

-15.602
-14.591
-14.489
-14.492
-14.492
-15. 710
-15.808
-15.806
-15.806
-14.632
-14.689
-14.687
-14.687

136

0

0

0

0

EFFECTIVE OXIDANT
h(1)/R
-0.30886113E-07
bi (1)
0.62502344E-01
O.OOOOOOOOE+OO
H
-10.324
H
-10.241
H
-10.237
H
-10.237
-9.159
-9.047
-9.042
-9.042
-10.339
-10.446
-10.454
-10.454
-9.177
-9.242
-9.247
-9.247

MIXTURE
hO/R
-0.29892238E-06
bOi
0.55508435E-01
0 .1110168 7E+OO

DETONATION PROPERTIES OF AN IDEAL REACTING GAS
CASE

6
REACTANT
02
H2

OXIDANT
FUEL
O/F=

WT FRACTION
(SEE NOTE)
1.0000000
1.0000000

7.93668

%FUEL= 11.189834

R,EQ.RATIO= 1.000000

ENERGY
CAL/MOL
0.000
0.000

TEMP
K

298.150
298.150

PHI,EQ.RATIO= 1.000000

UNBURNED GAS
Pl, ATM
Tl, K
Hl, CAL/G
Ml, (1/n)
GAMMAl
SON VELl,M/SEC

0.9869
298.15
0.00
12.010
1. 4016
537.9

19.7385
298.15
0.00
12.010
1. 4016
537.9

0.9869
500.00
118.41
12.010
1.3858
692.6

19.7385
500.00
118.41
12.010
1.3858
692.6

BURNED GAS
P, ATM
T, K
RHO, G/CC
H, CAL/G
U, CAL/G
G, CAL/G
S, CAL/ (G) (K)

10.824
18.542
409.40
240.42
3679.60 4290.26 3604.96 4216.06
8.9087-4 1.7754-2 5.2196-4 1.0421-2
677. 36
752.70
758.96
837.29
194.25
173.32
256.74
278.61
-14642.7 -15416.7 -14599.2 -15431.0
3.7689
4.2603
4.1635
3.8587

M, (l/n)
(dLV/dLP)t
(dLV/dLT)p
Cp, CAL/ (G) (K)
GAMMAS
SON VEL,M/SEC

14.507
15.267
14.264
14.996
-1.08257 -1. 06066 -1.08950 -1.06761
1. 8752
2.5062
2.3666
1. 9883
3.9031
2.4578
4.3365
2.7278
1.1287
1.1436
1.1265
1.1421
1634.6
1542.8
1538.5
1633.9

TRANSPORT PROPERTIES (GASES ONLY)
CONDUCTIVITY IN UNITS OF MILLICALORIES/(CM) (K) (SEC)
VISC,MILLIPOISE

1.1411

1.2744

1.1243

1.2591

2.4578
5.9829
0.5235

4.3365
10.1413
0.4808

2. 7278
6.6951
0.5130

0.7939
1.4230
0. 7110

0. 7769
1.2844
0.6800

0.7923
1. 4190
0.7030

WITH EQUILIBRIUM REACTIONS
Cp, CAL/ (G) (K)
CONDUCTIVITY
PRANDTL NUMBER

3.9031
9.1690
0.4857

WITH FROZEN REACTIONS

Cp, CAL/ (G) (K)
CONDUCTIVITY
PRANDTL NUMBER

0. 7788
1.2925
0.6876

137

DETONATION PARAMETERS
P/Pl
T/Tl
M/Ml
RHO/RHOl
DET MACH NUMBER
DET VEL,M/SEC

18.788
12.341
1. 2079
1. 8388
5.2744
2836.9

20.741
14.390
1.2712
1.8322
5.5684
2995.1

10.968
7.210
1.1877
1. 8067
4. 0135
2779.7

12.180
8.432
1. 2486
1.8037
4.2551
2947.1

0.08098
0.00019
0.16234
0.53502
0.00002
0.03848
0.13460
0.04837

0.04765
0.00069
0.14401
0.61304
0.00017
0. 02411
0.13210
0.03823

0.09195
0.00015
0.16705
0.51045
0.00001
0.04330
0.13646
0.05063

0.05702
0.00058
0.15222
0.58216
0.00012
0.02868
0.13826
0.04096

MOLE FRACTIONS
*H
H02
*H2
H20
H202
*O
*OH
*02

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONS
WERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONS
03

H20(s)

H20(L)

NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS

138

EXAMPLE 7:
(a)
Shock tube problem (shock) .
(b)
Reactants are H2, 02, and Ar gases at 300 K. Note that for shock
problems reactants must be gaseous species in the thermodynamic
data base. The program calculates properties of the
reactants at the temperature given (300 K) using the thermo.lib
coefficients.
(c) Reactants are given in moles (moles= ... ) .
(d)
Initial gas pressures are 10 and 20 mm Hg (p,mmhg=l0,20,)
(e) Seven initial gas velocities are assigned (ul=l000,1100,1200,
1250,1300,1350,1400,). Note units of ul are always m/s.
(f)
Equilibrium calculations are to be performed for incident shock
conditions (incd eql).
(g)
Frozen calculations are to be performed for incident shock
conditions (incd froz) .
(h) No 'outp' dataset is given since the default values of the
the parameters have the desired values (e.g. SI units).
reac

name= H2
name= 02
name= Ar

moles= 0.050
moles= 0.050
moles= 0.900

t(k) 300.00
t (k) 300. 00
t(k) 300.00

problem case=7 p,mmhg=l0,20, shock ul=lOOO,ll00,1200,1250,1300,1350,1400,
incd froz eql
end
OPTIONS: TP=F
RKT=F FROZ=T
TRACE= O.OOE+OO
P,BAR =

HP=F SP=F TV=F UV=F SV=F DETN=F SHOCK=T REFL=F
EQL=T IONS=F SIUNIT=T DEBUGF=F SHKDBG=F DETDBG=F
S/R= O.OOOOOOE+OO

0.013332

H/R= O.OOOOOOE+OO

INCD=T
TRNSPT=F

U/R= O.OOOOOOE+OO

0.026664

REACTANT
MOLES
EXPLODED FORMULA
0.050000
N: H2
H 2.00000
N: 02
0.050000
0 2.00000
N: Ar
0.900000
AR 1.00000

(ENERGY/R) ,K

TEMP,K

DENSITY

0.641758E+Ol

300.00

0.0000

0.653777E+Ol

300.00

0.0000

0.462500E+Ol

300.00

0.0000

SPECIES BEING CONSIDERED IN THIS SYSTEM
(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES)
l 6/88
tpis78
1 1/90
1 5/90

*Ar
*H2
*O
03

6/94
l 8/89
tpis78
1 8/89
l

*H
H20
*OH
H20(s)

l 5/89
1 2/93

tpis89
l 8/89

H02
H202
*02
H20(L)

139

*** INPUT FOR SHOCK PROBLEMS ***
INCDEQ = T

REFLEQ = F

INCDFZ = T

REFLFZ

= F

Ul =

1.0000tOE+03 1.100000E+03 1.200000E+03 1.250000E+03 1.300000E+03
1.350000E+03 1.400000E+03

MACHl

O.OOOOOOE+OO O.OOOOOOE+OO O.OOOOOOE+OO O.OOOOOOE+OO O.OOOOOOE+OO
O.OOOOOOE+OO O.OOOOOOE+OO

O/F

0.000000

ENTHALPY
(KG-MOL) (K) /KG

EFFECTIVE FUEL
h(2)/R
0.12774941E+OO

EFFECTIVE OXIDANT
h(l) /R
O.OOOOOOOOE+OO

MIXTURE
hO/R
0.12774941E+OO

KG-FORM.WT./KG
*H
*O
*Ar

bi(2)
0.26557650E-02
0.26557650E-02
0.23901885E-01

bi(l)
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO

bOi
0.26557650E-02
0.26557650E-02
0.23901885E-Ol

SHOCK WAVE PARAMETERS ASSUMING
EQUILIBRIUM COMPOSITION FOR INCIDENT SHOCKED CONDITIONS
CASE

7
REACTANT

NAME
NAME
NAME
O/F=

H2
02
Ar
0.00000

INITIAL GAS (1)
MACH NUMBERl
Ul, M/SEC
P, BAR
T, K
RHO, KG/CU M
H, KJ/KG
U, KJ/KG
G, KJ/KG
s, KJ/ (KG) (K)
M,

MOLES

(l/n)

Cp, KJ/ (KG) (K)
GAMMAS
SON VEL,M/SEC

0.0500000
0.0500000
0.9000000
%-FUEL=

0.000000

R,EQ.RATIO= 0.500000

TEMP
K
300.000
300.000
300.000

PHI,EQ.RATIO= 0.000000

3.3528
3.6576
3.0480
3.8100
3.9624
4 .1148
4.2672
1000.00 1100.00 1200.00 1250.00 1300.00 1350.00 1400. 00
0.01333 0.02666 0.02666 0.02666 0.02666 0.02666 0.02666
300.00
300.00
300.00
300.00
300.00
300.00
300.00
2.0126-2 4.0252-2 4.0252-2 4.0252-2 4.0252-2 4.0252-2 4.0252-2
1.0622
1. 0622
1.0622
1.0622
1.0622
1. 0622
1.0622
-65.182 -65.182 -65.182 -65.182 -65.182 -65.182 -65.182
-1556.26 -1510.35 -1510.35 -1510.35 -1510.35 -1510.35 -1510.35
5.0380
5.1911
5.0380
5.0380
5.0380
5.0380
5.0380
37.654
0.5742
1.6249
328.1

37.654
0.5742
1.6249
328.1

37.654
0.5742
1.6249
328.1

37.654
0.5742
1. 6249
328.1

WARNING!!
NO CONVERGENCE FOR ul= 1000.0
ANSWERS NOT RELIABLE, SOLUTION MAY NOT EXIST (SHCK)

140

ENERGY
KJ/KG-MOL
53.359
54.358
38.455

37.654
0.5742
1. 6249
328.1

37.654
0.5742
1. 6249
328.1

37.654
0.5742
1. 6249
328.1

SHOCKED GAS (2)--INCIDENT--EQUILIBRIUM
U2, M/SEC
703.53
666.91
576.09
560.23
549.01
540.16
532.35
P, BAR
0.08449 0.21842 0.32803 0.37372 0.41964 0.46673 0.51561
1371.90 1528.10 1816.96 1932.22 2043.84 2152.73 2258.45
T, K
RHO, KG/CU M
2.8607-2 6.6391-2 8.3844-2 8.9812-2 9.5312-2 1.0060-1 1.0586-1
292.39
383.68
555.13
625.39
695.35
766.43
839.37
H, KJ/KG
U, KJ/KG
-2.9743
54.682
163.89
209.27
255.08
302.48
352.28
-7331.22 -7891.77 -9312.23 -9886.05 -10444.2 -10990.3 -11520.9
G, :XJ/KG
S, KJ/ (KG) (K)
5.5570
5.4155
5.4307
5.4401
5.4503
5.4613
5.4729
M,

(l/n)

(dLV/dLP)t
(dLV/dLT)p
Cp, KJ/ (KG) (K)
GAMMAa
SON VEL,M/SEC
P2/Pl
T2/Tl
M2/Ml
RH02/RH01
V2, M/SEC

38.619
38.619
38.614
38.608
38.597
38.580
38.552
-1.00000 -1.00000 -1.00005 -1.00010 -1.00021 -1.00040 -1.00072
1.0001
1.0002
1.0018
1.0037
1.0070
1.0123
1. 0207
0.5827
0.5869
0.6041
0.6187
0.6412
0.6747
0. 7226
1. 5861
1.5798
1.5570
1. 5397
1.5162
1.4857
l.4497
684.5
720.9
780.5
800.4
817.0
830.2
840.3
6.654
4.656
1. 0256
1.4214
296.47

8.192
5.094
1.0256
1.6494
433.09

12.302
6.057
1. 0255
2.0830
623.91

14.016
6.441
1. 0253
2.2312
689. 77

15.738
6.813
1. 0251
2.3679
750.99

17.504
7.176
1.0246
2.4993
809.84

19.337
7.528
1.0238
2.6299
867.65

9.2307-1
6.3878-9
5.7290-9
3.2023-7
5.1272-2
2.311-10
3.3351-7
1.8151-5
2.5636-2

9.2306-1
7.1872-8
2.4000-8
1.8716-6
5.1248-2
9.754-10
2.0203-6
6.1566-5
2.5625-2

9.2294-1
4.2701-6
1.4081-7
3.5078-5
5.1025-2
4.623 -9
3.9781-5
4.2535-4
2.5530-2

9.2280-1
1.5520-5
2.4561-7
8.8322-5
5.0780-2
7.549 -9
1.0183-4
7.8035-4
2.5435-2

9.2255-1
4.7038-5
3.9562-7
1.9485-4
5.0378-2
1.149 -8
2.2822-4
1.3111-3
2.5293-2

9.2213-1
1.2367-4
5.9860-7
3.8722-4
4.9752-2
1.654 -8
4.6110-4
2.0550-3
2.5094-2

9.2146-1
2.8725-4
8.5747-7
7.0178-4
4.8831-2
2.266 -8
8.5170-4
3.0302-3
2.4835-2

MOLE FRACTIONS
*Ar

*H
H02

*H2
H20
H202

*O
*OH
*02

*

THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONS
WERE LESS THAN 5.000000E-09 FOR ALL ASSIGNED CONDITIONS

03

H20(s)

H20(L)

141

SHOCK WAVE PARAMETERS ASSUMING
FROZEN COMPOSITION FOR INCIDENT SHOCKED CONDITilONS
CASE

7
MOLES

REACTANT
H2

NAME
NAME
NAME
O/F=

0.0500000
0.0500000
0.9000000

02

Ar
0.00000

ENERGY
KJ/KG-MOL
53.359
54.358
38.455

%FUEL=

0.000000

R,EQ.RATIO= 0.500000

TEMP
K

300.000
300.000
300.000

PHI,EQ.RATIO= 0.000000

INITIAL GAS (1)
3.0480
3.3528
3.6576
3.8100
3.9624
4.1148
4.2672
MACH NUMBERl
1000.00 1100.00 1200.00 1250.00 1300.00 1350.00 1400.00
Ul, M/SEC
P, BAR
0.01333 0.02666 0.02666 0.02666 0.02666 0.02666 0.02666
300.00
300.00
300.00
300.00
300.00
300.00
300.00
T, K
2.0126-2 4.0252-2 4.0252-2 4.0252-2 4.0252-2 4.0252-2 4.0252-2
RHO, KG/CU M
1.0622
1.0622
1.0622
1.0622
1.0622
1.0622
1.0622
H, KJ/KG
-65.182
-65.182 -65.182 -65.182
-65.182
-65.182 -65.182
U, KJ/KG
-1556.26 -1510.35 -1510.35 -1510.35 -1510.35 -1510.35 -1510.35
G, KJ/KG
S, KJ/ (KG) (K)
5.1911
5.0380
5.0380
5.0380
5.0380
5.0380
5.0380
M,

(l/n)

Cp, KJ/ (KG) (K)
GAMMAS
SON VEL,M/SEC

37.654
0.5742
1. 6249
328.1

37.654
0.5742
1.6249
328.1

37.654
0.5742
1. 6249
328.1

37.654
0.5742
1.6249
328.1

37.654
0.5742
1.6249
328.1

37.654
0.5742
1.6249
328.1

37.654
0.5742
1.6249
328.1

SHOCKED GAS (2)--INCIDENT--FROZEN
349.41
358.06
366.89
375.87
U2, M/SEC
317.26
332.77
384.99
P, BAR
0.15074
0.36638 0.43752 0.47544 0.51494 0.55601 0.59865
T, K
1076.14 1247.03 1433.31 1532.25 1635.05 1741.69 1852.17
6.3438-2 1.3305-1 1.3824-1 1.4052-1 1.4263-1 1.4457-1 1.4637-1
RHO, KG/CU M
H, KJ/KG
450.75
550.72
660.02
718.21
778.76
841.67
906.95
213.13
275.36
343.52
379.87
417.72
457.08
497.97
U, KJ/KG
G, KJ/KG
-5354.24 -6039.09 -6975.05 -7475.96 -7998.88 -8543.88 -9111.04
S, KJ/ (KG) (K)
5.3943
5.2844
5.3478
5.3684
5.3888
5.3269
5.4088

Cp, KJ/ (KG) (K)
GAMMAS
SON VEL,M/SEC

37.654
0.5841
1.6078
618.1

37.654
0.5858
1.6049
664.8

37.654
0.5876
1.6019
712.0

37.654
0.5886
1.6005
735.9

37.654
0.5895
1.5989
759.8

37.654
0.5904
1.5974
783.8

37.654
0.5913
1.5960
807.9

P2/Pl
T2/Tl
M2/Ml
RH02/RH01
V2, M/SEC

11.307
3.587
1.0000
3.1520
682.74

13.740
4.157
1.0000
3.3056
767.23

16.408
4.778
1.0000
3.4344
850.59

17.831
5.108
1.0000
3.4911
891. 94

19.312
5.450
1. 0000
3.5433
933 .11

20.852
5.806
1.0000
3.5917
974.13

22.451
6.174
1.0000
3.6365
1015.01

0.05000
0.05000
0.90000

0.05000
0.05000
0.90000

0.05000
0.05000
0.90000

0.05000
0.05000
0.90000

0.05000
0.05000
0.90000

0.05000
0.05000
0.90000

0.05000
0.05000
0.90000

M,

(l/n)

MOLE FRACTIONS
*H2
*02

*Ar

142

#
#
#
#
#
#
#
#
#
#
#

EXAMPLE 8:
(a)
Rocket problem with infinite-area combustor (rocket iac by default) .
(b)
The fuel is H2(L) at 20.27 K; the oxidant is 02(L) at 90.17 K.
Both are in thermo.lib so that the enthalpies and "exploded" formulas
do not need to be given.
(c)
The oxidant-to-fuel ratio is 5.55157 (o/f=5.55157).
(d)
The chamber pressure is 53.3172 bars (p,bar=53.3172).
(e)
Calculations are with equilibrium chemistry only (equilibrium) .
(f)
For exit points there are three pressure ratios (pi/p=l0,100,1000),
one subsonic area ratio (subar=l.58), and three supersonic area
ratios (supar=25,50,75).

problem rocket equilibrium o/f=5.55157
p,bar=53.3172 subar=l.58,pi/p=l0,100,1000,supar=25,50,75
reactants
fuel= H2(L)
wt% 100.
t(k) 20.27
oxid = 02(L)
wt% 100.
t (k) 90.17
output siunits
end
case=8

OPTIONS: TP=F
RKT=T FROZ=F

HP=F SP=F TV=F UV=F SV=F DETN=F SHOCK=F REFL=F
EQL=T IONS=F SIUNIT=T DEBUGF=F SHKDBG=F DETDBG=F

TRACE= O.OOE+OO
Pc,BAR
Pc/P

S/R= O.OOOOOOE+OO

U/R= O.OOOOOOE+OO

53.317200

=

10.0000

100.0000

SUBSONIC AREA RATIOS =

1

1000.0000

1.5800

SUPERSONIC AREA RATIOS
NFZ=

H/R= O.OOOOOOE+OO

INCD=F
TRNSPT=F

25.0000

Mdot/Ac= O.OOOOOOE+OO

REACTANT
WT.FRAC
EXPLODED FORMULA
F: H2(L)
1.000000
H 2.00000
1.000000
0: 02 (L)
0 2.00000

50.0000

75.0000

Ac/At= O.OOOOOOE+OO
(ENERGY/R) I K

TEMP,K

-0.108389E+04

20.27

0.0000

-0.156101E+04

90.17

0.0000

DENSITY

143

SPECIES BEING CONSIDERED IN THIS SYSTEM
(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES}
1 6/94
1 8/89
tpis78
1 8/89
O/F =

1 5/89
1 2/93
tpis89
1 8/89

*H
H20
*OH
H20(s)

tpis78
1 1/90
1 5/90

H02
H202
*02
H20(L)

*H2
*O
03

5.551570

ENTHALPY
(KG-MOL) (K) /KG

EFFECTIVE FUEL
h(2}/R
-0.53767500E+03

EFFECTIVE OXIDANT
h(l)/R
-0.48783267E+02

KG-FORM.WT./KG
*H
*O

bi(2}
0.99212255E+OO
O.OOOOOOOOE+OO

bi(l)
0.00000000E+OO
0.62502344E-01

POINT ITN
T
3389.270
1
9
Pinf/Pt = 1. 737856
2
4
3190.532
Pinf/Pt = 1.739443
2
2
3190.207
2568.396
3
4
4
4
1759.119
1115.280
4
5
3360.178
6
3
3354.650
6
2
3353.978
6
2
3353.970
6
1
1441.190
7
5
7
2
1467.038
1241.429
8
3
1218.630
2
8

H
-9.266

0
-16.561

-9.433

-16.968

-9.434
-9.922
-10.454
-10.958
-9.291
-9.295
-9.296
-9.296
-10.682
-10.662
-10.845
-10.864

-16.968
-18.802
-23.533
-32.668
-16.616
-16.627
-16.628
-16.628
-26.980
-26.641
-30.099
-30.523

MIXTURE
hO/R
-0.12340534E+03
bOi
0.15143279E+OO
0.52962288E-01

THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pinj
CASE

773.3 PSIA
8
REACTANT

FUEL
OXIDANT
O/F=

144

H2 (L}
02 (L)
5.55157

%FUEL= 15.263517

WT FRACTION
(SEE NOTE)
1.0000000
1.0000000

ENERGY
KJ/KG-MOL
-9012.000
-12979.000

R,EQ.RATIO= 1.429629

TEMP
K

20.270
90.170

PHI,EQ.RATIO= 1.429628

CHAMBER
1.0000
53.317
3389.27
2.4071 0
-1026.05
-3241.04
-64259.7
18.6570

Pinf /P
P, BAR
T, K
RHO, KG/CU M
H, KJ/KG
U, KJ/KG
G, KJ/KG
S, KJ/ (KG) (K)
M,

(1/n)

(dLV/dLP)t
(dLV/dLT)p
Cp, Kil/ (KG) (K)
GAMMAS
SON VEL,M/SEC
MACH NUMBER

THROAT
1. 7394
30.652
3190.21
1.4848 0
-2210.09
-4274.40
-61729.8
18.6570

EXIT
10.000
5.3317
2568.40
3.2770-1
-5432.07
-7059.06
-53350.7
18.6570

EXIT
100.00
0.53317
1759.12
4.8139-2
-8564.25
-9671.81
-41384.1
18.6570

EXIT
1000.00
0.05332
1115.28
7.5938-3
-10623.5
-11325.7
-31431.3
18.6570

EXIT
1.1020
48.381
3353.97
2.2113 0
-1239.91
-3427.81
-63814.9
18.6570

EXIT
260.57
0.20462
1467.04
2.2155-2
-9535.06
-10458.6
-36905.6
18.6570

EXIT
655.41
0.08135
1218.63
1.0604-2
-10313.3
-11080.5
-33049.3
18.6570

12.723
12.849
13.125
13.206
13.207
12.746
13.207
13.207
-1.01996 -1.01459 -1.00317 -1.00005 -1.00000 -1.01897 -1.00000 -1.00000
1.0000
1.3627
1.2808
1. 0739
1.3482
1.0000
1.0017
1. 0001
2.9621
8.2837
7.4299
4.8447
3.4332
8.1390
3.2226
3.0413
1.1732
1.1472
1. 2254
1.2699
1.1451
1.2429
1.2610
1.1449
1538.9
944.3
1582.8
1592.4
1381. 6
1165.0
1071. 4
983.6
4.640
0.000
1.000
2.149
0.413
3.850
4.382
3.333

PERFORMANCE PARAMETERS
Ae/At
CSTAR, M/SEC
CF
Ivac, M/SEC
Isp, M/SEC

1.0000
2333.4
0.6595
2880.3
1538.9

2.3489
2333.4
1. 2722
3516.6
2968.5

12.225
2333.4
1.6640
4168.1
3882.8

68.680
2333.4
1. 8776
4541.5
4381.2

1. 5800
2333.4
0.2803
3999.5
654.0

25.000
2333.4
1.7679
4349.2
4125. 3

50.000
2333.4
1.8470
4487.8
4309.8

0.02683
0.00001
0.29373
0.65440
0.00000
0.00124
0.02271
0.00108

0.00797
0.00000
0.29695
0.69081
0.00000
0.00007
0.00413
0.00007

0.00019
0.00000
0.30040
0.69938
0.00000
0.00000
0.00003
0.00000

0.00000
0.00000
0.30052
0.69948
0.00000
0.00000
0.00000
0.00000

0.03265
0.00001
0.29398
0.63976
0.00001
0.00196
0.02998
0.00165

0.00001
0.00000
0.30051
0.69948
0.00000
0.00000
0.00000
0.00000

0.00000
0.00000
0.30052
0.69948
0.00000
0.00000
0.00000
0.00000

MOLE FRACTIONS
0.03390
0.00002
0.29410
0.63643
0.00001
0.00214
0.03162
0.00179

*H
H02

*H2
H20
H202
*O
*OH
*02

*

THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONS
WERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONS
H20(s)

03

H20(L)

NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS

3
3

3
2

1067.058
1087.734

-11. 004
-10.984

-33.815
-33.311

145

THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pinj
CASE

773.

~

PSIA

8
WT FRACTION
(SEE NOTE)
1.0000000
1.0000000

REACTANT
FUEL

OXIDANT
O/F=

H2(L)
02 (L)
5.55157

\FUEL= 15.263517

R,EQ.RATIO= 1.429629

Pinf/P
P, BAR
T, K
RHO, KG/CU M
H, KJ/KG
U, KJ/KG
G, KJ/KG
S, KJ/ (KG) (K)

CHAMBER
1.0000
53.317
3389.27
2.4071 0
-1026.05
-3241. 04
-64259.7
18.6570

M, (1/n)
(dLV/dLP)t
(dLV/dLT)p
Cp, KJ/ (KG) (K)
GAMMAS
SON VEL,M/SEC
MACH NUMBER

12.849
13.207
12. 723
-1. 01996 -1. 01459 -1.00000
1.3627
1. 2808
1.0000
7.4299
2.9409
8.2837
1.1472
1.2724
1.1449
933.4
1592.4
1538.9
4. 714
1. 000
0.000

PERFORMANCE PARAMETERS
Ae/At
CSTAR, M/SEC
CF
Ivac, M/SEC
Isp, M/SEC

MOLE FRACTIONS
*H
H02
*H2
H20
H202
*O
*OH
*02

0.03390
0.00002
0.29410
0.63643
0.00001
0.00214
0.03162
0.00179

THROAT
1.7394
30.652
3190.21
1. 4848 0
-2210.09
-4274.40
-61729.8
18.6570

ENERGY
KJ/KG-MOL
-9012.000
-12979.000

TEMP
K
20.270
90.170

PHI,EQ.RATIO= 1.429628

EXIT
1124.40
0.04742
1087.73
6.9247-3
-10704.9
-11389.6
-30998.7
18.6570

1.0000
2333.4
0.6595
2880.3
1538.9

75.000
2333.4
1.8856
4555.4
4399.7

0.02683
0.00001
0.29373
0.65440
0.00000
0.00124
0.02271
0.00108

0.00000
0.00000
0.30052
0.69948
0.00000
0.00000
0.00000
0.00000

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONS
WERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONS
03

H20(s)

H20(L)

NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS

146

#
#
#
#
#

EXAMPLE
(a)
(b)
(c)

9:
Rocket problem with a finite-area combustor (rocket fac) .
Contraction ratio of 1.58 (acat=1.58) is assigned.
Fuel, oxidant, and the remaining parameters are the same as in
example 8.

reac

fuel= H2(L) wt\=100. t,k= 20.27
oxid = 02(L) wt\=100. t,k= 90.17
problem o/f=5.55157 case=9 rocket fac p,bar=53.3172 acat=l.58
pi/p=l0,100,1000, supar=25,50,75
output siunits
end
OPTIONS: TP=F
RKT=T FROZ=F

HP=F SP=F TV=F UV=F SV=F DETN=F SHOCK=F REFL=F
EQL=T IONS=F SIUNIT=T DEBUGF=F SHKDBG=F DETDBG=F

TRACE= O.OOE+OO

S/R= O.OOOOOOE+OO

H/R= O.OOOOOOE+OO

INCD=F
TRNSPT=F

U/R= O.OOOOOOE+OO

53. 317200

Pc,BAR

10.0000

Pc/P =

100.0000

1000.0000

SUBSONIC AREA RATIOS =
25.0000

SUPERSONIC AREA RATIOS
NFZ=

1

Mdot/Ac= O.OOOOOOE+OO

WT.FRAC
REACTANT
EXPLODED FORMULA
1.000000
F: H2(L)
H 2.00000
1.000000
0: 02(L)
0 2.00000

50.0000

75.0000

Ac/At= 1.580000E+OO
(ENERGY/R) ,K

TEMP,K

DENSITY

-0.108389E+04

20 .27

0.0000

-0.156101E+04

90.17

0.0000

SPECIES BEING CONSIDERED IN THIS SYSTEM
(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES)
1 6/94
1 8/89
tpis78
1 8/89
O/F =

*H
H20
*OH
H20(s)

1 5/89
1 2/93

tpis89
1 8/89

H02
H202
*02
H20(L)

tpis78
1 1/90
1 5/90

*H2
*O
03

5.551570

ENTHALPY
(KG-MOL) (K) /KG

EFFECTIVE FUEL
h(2)/R
-0.53767SOOE+03

EFFECTIVE OXIDANT
h(l)/R
-0.48783267E+02

KG-FORM.WT./KG
*H
*O

bi(2)
0.99212255E+OO
O.OOOOOOOOE+OO

bi(l)
0.00000000E+OO
0.62502344E-01

MIXTURE
hO/R
-0.12340534E+03
bOi
0.15143279E+OO
0.52962288E-01

147

H
POINT ITN
T
-9.266
3389.270
1
9
3381.326
-9.303
2
3
Pinf/Pt = 1. 7::: 7476
-9.471
3134.432
4
3
Pinf/Pt = 1.739009
-9.471
2
3184.121
3
3352.506
-9.328
4
3
-9.332
4
2
3347.029
3346.363
-9.333
4
2
-9.333
4
3346.355
1
-9.303
3381.345
2
1
Pinf /Pt = 1. 737477
-9.471
3184.446
4
3
Pinf /Pt = 1.739010
-9.471
2
3184.135
3
-9.327
3352.524
4
3
3347.047
-9.332
4
2
-9.333
4
2
3346.381
3346.373
-9.333
1
4
END OF CHAMBER ITERATIONS
-9.941
2596.353
4
5
-10.478
4
1786.498
5
-10.981
1135.439
4
6
1442.273
-10. 724
7
5
-10.704
7
2
1468.448
1242.967
-10.885
8
3
-10.905
1219.873
2
8

0

-16.561
-16.578
-16.983
-16.984
-16.634
-16.644
-16.645
-16.645
-16.578
-16.983
-16.984
-16.634
-16.644
-16.645
-16.645
-18.697
-23.297
-32.218
-26.966
-26.623
-30. 071
-30.499

THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM FINITE AREA COMBUSTOR
Pinj =
773.3 PSIA
Ac/At = 1.5800
CASE = 9

Pinj/Pinf

REACTANT
FUEL
OXIDANT
O/F=

148

H2 {L)

02 {L)
5.55157

tFUEL= 15.263517

1. 084780

WT FRACTION
(SEE NOTE)
1.0000000
1.0000000

ENERGY
KJ/KG-MOL
-9012.000
-12979.000

R,EQ.RATIO= 1.429629

TEMP
K

20.270
90.170

PHI,EQ.RATIO= 1.429628

COMB END THROAT
1.8864
1.1954
28.263
44.602
3346.37 3184.14
2.0416 0 1. 3709 0
-1239.49 -2207.90
-3424.10 -4269.63
-63850.8 -61783.7
18. 7102 18. 7102

EXIT
10.000
5.3317
2596.35
3.2390-1
-5294.68
-6940.78
-53873. 0
18.7102

EXIT
100.00
0.53317
1786.50
4.7400-2
-8469.93
-9594.77
-41895.7
18.7102

EXIT
1000.00
0.05332
1135.44
7.4589-3
-10563.7
-11278. 5
-31808.0
18. 7102

EXIT
282.15
0.18897
1468.45
2.0441-2
-9530.50
-10455.0
-37005.5
18. 7102

Pinj/P
P, BAR
T, K
RHO, KG/CU M
H, KJ/KG
u, KJ/KG
G, KJ/KG
S, KJ/ (KG) (K)

INJECTOR
1.0000
53.317
3389.27
2.4071 0
-1026.05
-3241. 04
-64259.7
18.6570

EXIT
709. 71
0.07513
1219.87
9.7824-3
-10309.5
-11077.5
-33133.6
18. 7102

M, (l/n)
(dLV/dLP) t
(dLV/dLT)p
Cp, KJ/ (KG) (K)
GAMMAS
SON VEL,M/SEC
MACH NUMBER

12.841
13.205
13.207
12. 723
12.736
13.114
13.207
13.207
-1.01996 -1. 01940 -1.01495 -1.00361 -1. 00007 -1.00000 -1.00000 -1.00000
1.2882
1.0834
1.0022
1.0000
1. 0001
1. 3627
1. 3567
1.0000
7.5303
4.9862
3.4569
2.9777
3.2237
8.2837
8.2508
3.0422
1.1465
1.1445
1.1705
1. 2238
1.2681
1. 2609
1.1449
1. 2428
1537.4
1388.1
952.l
1071. 9
1592.4
1581.2
1173.3
984.0
1.000
2.105
4.587
0.000
0.413
3.289
3.848
4.379

PERFORMANCE PARAMETERS
Ae/At
CSTAR, M/SEC
CF
Ivac, M/SEC
Isp, M/SEC

1.5800
2332.l
0.2802
3997.0
653.4

1.0000
2332.l
0.6593
2878.5
1537.4

2.2270
2332.1
1.2529
3485.2
2921. 9

11. 524
2332.1
1. 6545
4150.0
3858.5

64.695
2332.1
1. 8728
4531. 2
4367.5

25.000
2332.1
1.7685
4348.3
4124.2

50.000
2332.1
1. 8477
4487.2
4308.9

0.03336
0.00001
0.29384
0.63858
0.00001
0.00204
0.03045
0.00172

0.02747
0.00001
0.29358
0.65337
0.00000
0.00130
0.02314
0.00113

0. 00893
0.00000
0.29659
0.68952
0.00000
0.00009
0.00477
0.00009

0.00024
0.00000
0.30037
0.69935
0.00000
0.00000
0.00004
0.00000

0.00000
0.00000
0.30052
0.69948
0.00000
0.00000
0.00000
0.00000

0.00002
0.00000
0.30051
0.69948
0.00000
0.00000
0.00000
0.00000

0.00000
0.00000
0.30052
0.69948
0.00000
0.00000
0.00000
0.00000

MOLE FRACTIONS
0.03390
0.00002
0.29410
0.63643
0.00001
0.00214
0.03162
0.00179

*H
H02
*H2
H20
H202
*O
*OH
*02

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONS
WERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONS
03

H20(L)

H20(s)

NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS

4

4

3
2

1067.940
1088.883

-11. 046
-11.025

-33.793
-33.283

149

THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM FINITE AREA COMBUSTOR
Pinj =
773.3 PSIA
Ac/At = 1.580U
Pinj/Pinf
CASE = 9
REACTANT
FUEL
OXIDANT
O/F=

H2(L)
02 (L)
5.55157

%FUEL= 15.263517

1.084780
WT FRACTION
(SEE NOTE)
1.0000000
1.0000000

R,EQ.RATIO= 1.429629

COMB END THROAT
1.1954
1.8864
28.263
44.602
3346.37 3184.14
2.0416 0 1.3709 0
-1239.49 -2207.90
-3424.10 -4269.63
-63850.8 -61783.7
18. 7102 18.7102

RHO, KG/CU M
H, KJ/KG
U, KJ/KG
G, KJ/KG
S, KJ/ (KG) (K)
M, (1/n)
(dLV/dLP)t
(dLV/dLT)p
Cp, KJ/ (KG) (K)
GAMMAS
SON VEL,M/SEC
MACH NUMBER

12.841
13.207
12.723
12.736
-1.01996 -1.01940 -1.01495 -1.00000
1.2882
1.0000
1. 3627
1.3567
7.5303
2.9418
8.2837
B.2508
1.1449
1.1445
1.1465
1. 2723
1592.4
1581.2
1537.4
933.9
0.000
0.413
1.000
4. 710

T, K

PERFORMANCE PARAMETERS
Ae/At
CSTAR, M/SEC
CF
Ivac, M/SEC
Isp, M/SEC
MOLE FRACTIONS
*H
H02
*H2
H20
H202
*O
*OH
*02

0.03390
0.00002
0. 29410
0.63643
0.00001
0.00214
0.03162
0.00179

TEMP
K

20.270
90.170

PHI,EQ.RATIO= 1.429628

EXIT
1217.53
0.04379
1088.88
6.3882-3
-10701.5
-11387.0
-31074.7
18.7102

INJECTOR
1.0000
53.317
3389.27
2. 4071 0
-1026.05
-3241.04
-64259.7
18.6570

Pinj/P
P, BAR

ENERGY
KJ/KG-MOL
-9012.000
-12979.000

1.5800
2332.1
0.2802
3997.0
653.4

1.0000
2332.1
0.6593
2878.5
1537.4

75.000
2332.1
1. 8863
4554.8
4399.0

0.03336
0.00001
0.29384
0.63858
0.00001
0.00204
0.03045
0.00172

0.02747
0.00001
0.29358
0.65337
0.00000
0.00130
0.02314
0.00113

0.00000
0.00000
0.30052
0.69948
0.00000
0.00000
0.00000
0.00000

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONS
WERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONS
03
H20(s)
H20(L)
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS

150

#
#
#
#
#
#
#

EXAMPLE 10:
(a) Rocket problem with a finite-area combustor (rocket fac) .
(b) A ratio of mass flow rate to chamber area of 1333.9 (ma=1333.9)
is assigned. This value was calculated from the results
of example 9 where a contraction ratio of 1.58 was assigned.
(c)
Fuel, oxidant, and the remaining parameters are the same as in
examples B and 9.

reac

fuel= H2(L)
t,k= 20.27
oxid = 02(L)
t,k= 90.17
problem o/f=5.55157 case=lO rocket fac p,bar=53.3172 ma=l333.9
pi/p=l0,100,1000, sup-ae/at=25,50,75
output short
end
WARNING!! AMOUNT MISSING FOR REACTANT 1.
PROGRAM SETS WEIGHT PERCENT = 100. (REACT)
WARNING!! AMOUNT MISSING FOR REACTANT 2.
PROGRAM SETS WEIGHT PERCENT = 100. (REACT)

151

THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM FINITE AREA COMBUSTOR
Pinj =
773.3 PSIA
MDOT/Ac
1333.SOO (KG/S)/M**2
CASE = 10
REACTANT
FUEL
OXIDANT
O/F=

1.084780

WT FRACTION
(SEE NOTE)
1.0000000
1.0000000

H2 (L)
02 (L)
5.55157

Pinj/Pinf

\FUEL= 15.263517

ENERGY
KJ/KG-MOL
-9012.000
-12979.000

R,EQ.RATIO= 1.429629

PHI,EQ.RATIO= 1.429628

RHO, KG/CU M
H, KJ/KG
U, KJ/KG
G, KJ/KG
S, KJ/ (KG) (K)
M, (l/n)
(dLV/dLP)t
(dLV/dLT)p
Cp, KJ/ (KG) (K)
GAMMAS
SON VEL,M/SEC
MACH NUMBER

12.723
12.736
12.841
13.114
13.205
13.207
13.207
13.207
-1.01996 -1.01940 -1.01495 -1.00361 -1.00007 -1.00000 -1.00000 -1.00000
1. 3627
1.3567
1.2882
1. 0834
1. 0022
1.0000
1. 0001
1.0000
8.2837
8.2508
7.5303
4.9862
3.4569
2.9777
3.2237
3.0422
1.1449
1.1445
1.1465
1.1705
1.2238
1. 2681
1.2428
1. 2609
1537.4
1592.4
1173.3
952.1
1071. 9
1388.1
984.0
1581.2
0.000
4.587
0.413
1.000
2.105
3.289
3.848
4.379

T, K

PERFORMANCE PARAMETERS
Ae/At
CSTAR, M/SEC
CF
Ivac, M/SEC
Isp, M/SEC

MOLE FRACTIONS
*H
H02
*H2
H20
H202
*O
*OH
*02

*

0.03390
0.00002
0.29410
0.63643
0.00001
0.00214
0.03162
0.00179

EXIT
10.000
5.3317
2596.35
3.2390-1
-5294.68
-6940.78
-53873.0
18.7102

K

20.270
90.170

INJECTOR
1.0000
53.317
3389.27
2.4071 0
-1026.05
-3241.04
-64259.7
18.6570

Pinj/P
P, BAR

COMB END THROAT
1.1954
1.8864
44.602
28.263
3346.37 3184.14
2.0417 0 1.3709 0
-1239.48 -2207.90
-3424.09 -4269.63
-63850.8 -61783.7
18.7102 18.7102

TEMP

EXIT
100.00
0.53317
1786.50
4.7400-2
-8469.93
-9594.77
-41895.7
18.7102

EXIT
1000.00
0.05332
1135.44
7.4589-3
-10563.7
-11278.5
-31808.0
18.7102

EXIT
282.15
0.18897
1468.45
2.0441-2
-9530.50
-10455.0
-37005.5
18.7102

1.5800
2332.1
0.2802
3997.1
653.3

1.0000
2332.1
0.6593
2878.5
1537.4

2.2270
2332.l
1.2529
3485.2
2921. 9

11. 524
2332.1
1. 6545
4150.0
3858.5

64.695
2332.1
1.8728
4531. 2
4367.5

25.000
2332.1
1.7685
4348.3
4124.2

50.000
2332.1
1. 8477
4487.2
4308.9

0.03336
0.00001
0.29384
0.63858
0.00001
0.00204
0.03045
0.00172

0.02747
0.00001
0.29358
0.65337
0.00000
0.00130
0.02314
0.00113

0.00893
0.00000
0.29659
0.68952
0.00000
0.00009
0.00477
0.00009

0.00024
0.00000
0.30037
0.69935
0.00000
0.00000
0.00004
0.00000

0.00000
0.00000
0.30052
0.69948
0.00000
0.00000
0.00000
0.00000

0.00002
0.00000
0.30051
0.69948
0.00000
0.00000
0.00000
0.00000

0.00000
0.00000
0.30052
0.69948
0.00000
0.00000
0.00000
0.00000

THERMODYNAMIC PROPERTIES FITTED TO 20000.K

NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS

152

EXIT
709.71
0.07513
1219.87
9.7824-3
-10309.5
-11077.5
-33133.6
18.7102

THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM FINITE AREA COMBUSTOR
Pinj =
773.3 PSIA
MDOT/Ac
1333.900 (KG/S)/M**2
CASE = 10

O/F=

H2(L)
02 (L)
5.55157

Pinj/P
P, BAR
T, K

RHO, KG/CU M
H, KJ/KG
U, KJ/KG
G, KJ/KG
S,

KJ/ (KG)

(K)

M, (1/n)
(dLV/dLP)t
(dLV/dLT)p
Cp, KJ/ (KG) (K)
GAMMAS
SON VEL,M/SEC
MACH NUMBER

\FUEL= 15.263517
INJECTOR
1.0000
53.317
3389.27
2.4071 0
-1026.05
-3241. 04
-64259.7
18.6570
12. 723

R,EQ.RATIO= 1.429629

COMB END THROAT
1.1954
1. 8864
44.602
28.263
3346.37 3184.14
2.0417 0 1.3709 0
-1239.48 -2207.90
-3424.09 -4269.63
-63850.8 -61783.7
18. 7102 18. 7102
12.736

ENERGY
KJ/KG-MOL
-9012.000
-12979.000

12.841

TEMP
K

20.270
90.170

PHI,EQ.RATIO= 1.429628

EXIT
1217.53
0.04379
1088.88
6.3882-3
-10701.5
-11387.0
-31074.7
18. 7102
13.207

-1. 01996 -1.01940 -1.01495 -1.00000
1. 3627
1.3567
1.2882
1.0000

8.2837
1.1449
1592.4
0.000

PERFORMANCE PARAMETERS
Ae/At
CSTAR, M/SEC
CF
Ivac, M/SEC
Isp, M/SEC

MOLE FRACTIONS
*H
H02
*H2
H20
H202
*O
*OH
*02

1.084780

WT FRACTION
(SEE NOTE)
1.0000000
1.0000000

REACTANT
FUEL
OXIDANT

Pinj/Pinf

0.03390
0.00002
0.29410
0.63643
0.00001
0.00214
0.03162
0.00179

8.2508
1.1445
1581.2
0.413

7.5303
1.1465
1537.4
1.000

2.9418
1.2723
933.9
4.710

1.5800
2332.1
0.2802
3997.1
653.3

1. 0000

2332.1
0.6593
2878.5
1537.4

75.000
2332.1
1. 8863
4554.8
4399.0

0.03336
0.00001
0.29384
0.63858
0.00001
0.00204
0.03045
0.00172

0.02747
0.00001
0.29358
0.65337
0.00000
0.00130
0.02314
0.00113

0.00000
0.00000
0.30052
0.69948
0.00000
0.00000
0.00000
0.00000

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS

153

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#

EXAMPLE 11:
(a) Rocket problem with an infinite-area combustor (rocket) .
(b) Reactants are Li(cr) at 298.15 Kand F2(L) at 85.02 K.
Enthalpies and "exploded" formulas are to be taken from
thexmo.lib. Thus this information is not given.
(c) Relative amounts of reactants are given as moles.
(d) Chamber pressure is 1000 psia (p,psia =1000) .
(e)
Ionized species are to be included in the products (ions) .
(f) Only equilibrium calculations are to be performed (equilibrium) .
(g)
For exit points, one pressure ratio (pi/p=68.0457), one
subsonic area ratio (sub,ae/at=lO), and three supersonic area ratios
(sup,ae/at=l0,20,100) are to be included.

fuel= Li(cr) moles=
1.
oxid = F2(L)
moles= .5556
case=ll rocket equilibrium
prob
pi/p=68.0457, sub,ae/at=lO,
output siunits transport
end
reac

OPTIONS: TP=F
RKT=T FROZ=F

HP=F SP=F TV=F UV=F SV=F DETN=F SHOCK=F REFL=F
EQL=T IONS=T SIUNIT=T DEBUGF=F SHKDBG=F DETDBG=F

TRACE= O.OOE+OO
Pc,BAR
Pc/P

S/R= O.OOOOOOE+OO

=

10.0000

1

10.0000

Mdot/Ac= O.OOOOOOE+OO

REACTANT
MOLES
EXPLODED FORMULA
F: Li (er)
1.000000
LI 1.00000
0: F2 (L)
0.555600
F 2.00000

20.0000

INCD=F
TRNSPT=T

U/R= O.OOOOOOE+OO

68.0457

SUPERSONIC AREA RATIOS

154

H/R= O.OOOOOOE+OO

68.947304

SUBSONIC AREA RATIOS

NFZ=

t(k)=29B.15
t(k)=B5.02
p,psia=lOOO ions
sup,ae/at=l0,20,100

100.0000

Ac/At= O.OOOOOOE+OO
(ENERGY/R) ,K

TEMP,K

DENSITY

-0.298149E-06

298.15

0.0000

-0.157448E+04

85.02

0.0000

SPECIES BEING CONSIDERED IN THIS SYSTEM
(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES)
1 6/88
J 6/82
Jl2/83
Jl2/83
tpis82
Jl2/68

J 6/82
tpis89
J12/68
Jl2/68
tpis82
Jl2/68

*eF*Li+
Li2
Li (er)
LiF(s)

F
F2
LiF
Li2F2
Li(cr)
LiF(s)

J 6/82
Jl2/83
Jl2/68
Jl2/68
tpis82
Jl2/68

F+
*Li
LiF2Li3F3
Li(L)
LiF(L)

SPECIES WITH TRANSPORT PROPERTIES
PURE SPECIES

e-

Li

F2
BINARY INTERACTIONS

O/F

3.041496

ENTHALPY
(KG-MOL) (K) /KG

EFFECTIVE FUEL
h(2)/R
-0.42954723E-07

KG-FORM.WT./KG
*Li
F
*e-

bi(2)
0.14407146E+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO

POINT ITN
T
10
1
5685.658
Pinf/Pt = 1.760223
2
4
5334.399
Pinf/Pt = 1.756026
2
2
5335.817
6
3508.754
3
2
4
5683.383
2
4
5684.563
2
4
5684.330
4
1
5684.303
4
1
5684.303
5
6
3414.068
3
3468.547
5
1
3468.466
5
2926.255
6
4
2916.483
6
2
1925. 971
7
6
7
3
1952.523
7
2
1952.608

EFFECTIVE OXIDANT
h(l)/R
-0.41437073E+02
bi(l)
O.OOOOOOOOE+OO
0.52636003E-01
O.OOOOOOOOE+OO

LI
-16.270

F
-19.916

E
-9.127

-16.596

-20.296

-9.760

-16.595
-19.880
-16.272
-16.271
-16.271
-16.271
-16. 271
-20.203
-20.014
-20.015
-22.339
-22.391
-30.675
-30.334
-30.333

-20.294
-22.630
-19.918
-19.917
-19.917
-19.917
-19.917
-22.691
-22.658
-22.658
-22.741
-22.738
-22.338
-22.334
-22.334

-9.757
-15.648
-9.131
-9.129
-9.129
-9.129
-9.129
-16.205
-15.879
-15.880
-19.920
-20. 011
-34.299
-33.731
-33.729

MIXTURE
hO/R
-0.31184169E+02
bOi
0.35648050E-01
0.39612113E-Ol
O.OOOOOOOOE+OO

155

THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pinj
CASE

1000.0 PSIA
11

REACTANT
FUEL
OXIDANT
O/F=

Li {er)
F2(L)
3.04150

l.0000000
0.5556000

%FUEL= 24.743311
CHAMBER

Pinf/P
P, BAR
T, K

RHO, KG/CUM
H, KJ/KG
U, KJ/KG
G, KJ/KG
S, KJ/ (KG) (K)
M,

(l/n)

(dLV/dLP)t
(dLV/dLT)p
Cp, KJ/ (KG) (K)
GAMMAS

SON VEL,M/SEC
MACH NUMBER

1.0000
68.947
5685.66
3.1988 0
-259.28
-2414.71
-64713.0
11.3362

ENERGY
KJ/KG-MOL

MOLES

THROAT
1.7560
39.263
5335.82
1.9836 0
-1422.40
-3401.82
-61910.3
11.3362

EXIT

EXIT

68.046
l. 0021
l.0132
68.804
3508.75 5684.30
8.6962-2 3.1931 0
-7051.17 -263.77
-8216.33 -2418.51
-46827.l -64702.2
11.3362 11.3362

K

298.150
85.020

0.000
-13091. 000

R,EQ.RATIO= 0.899928

TEMP

PHI,EQ.RATIO= 0.899928
EXIT

73.493
0.93814
3468.47
8.1552-2
-7140.33
-8290.70
-46459.6
ll.3362

EXIT
188.51
0.36576
2916.48
3.8114-2
-8135.15
-9094.79
-41197.0
11.3362

EXIT
1585.57
0.04348
1952.61
6.9320-3
-9782.87
-10410.2
-31918.0
11.3362

21.932
22.413
25.038
21.934
25.069
25.269
25.881
-1.08286 -1.07324 -1.00885 -1.08283 -1.00782 -1.00183 -1.02364
2.0665
1.9980
1.1726
2.0663
1.1530
1.0248
1.3639
6.8472
6.6601
2.6365
6.8467
2. 5114
l. 6054
3.2529
1.1814
1.1752
l.1967
l.1814
l.2016
l. 2714
1.1906
1525.2
1595.8
1180.8
1595.5
1175. 7
1104. 6
864.2
0.000
l. 000
3.121
0.059
3.155
3.593
5.050

TRANSPORT PROPERTIES (GASES ONLY)
CONDUCTIVITY IN UNITS OF MILLIWATTS/(CM) (K)
VISC,MILLIPOISE

1.3862

1.0809

1.4390

1.0729

0.95570

0.72997

WITH EQUILIBRIUM REACTIONS
Cp, KJ/(KG) (K)
6.8472
6.6601
CONDUCTIVITY
14.6729 13.8861
PRANDTL NUMBER
0.6716
0.6648

2.6365
4.3181
0.6599

6.8467
14.6703
0. 6716

2. 5114
4.0680
0.6624

l . 6054
2.1692
0.7073

3.2529
2.7591
0.8606

WITH FROZEN REACTIONS
Cp, KJ/ (KG) (K)
l. 5912
2.9867
CONDUCTIVITY
PRANDTL NUMBER
0.7668

1.5704
2.8786
0.7562

1.4855
2.2503
0. 7135

1.5912
2.9863
0.7667

1.4844
2.2332
0.7132

l. 4713
1.9786
0.7107

l. 4523
1.4809
0. 7158

1.0000
2279.0
0.6692
2823.0
1525.2

9.4392
2279.0
1.6172
4001.8
3685.6

10.000
2279.0
0.0416
22837.2
94.7

10.000
2279.0
l.6278
4019.8
3709.7

20.000
2279.0
1.7415
4210.6
3968.8

100.00
2279.0
1.9150
4508.0
4364.3

l.4392

PERFORMANCE PARAMETERS
Ae/At
CSTAR, M/SEC
CF
Ivac, M/SEC
Isp, M/SEC

156

MOLE FRACTIONS
*eF
FF2
*Li
*Li+
LiF
Li2
Li2F2
Li3F3

0.00292
0.21188
0.00465
0.00002
0.12161
0.00758
0.65001
0.00022
0.00109
0.00000

0.00235
0.19608
0.00365
0.00001
0.10469
0.00601
0.68614
0.00011
0.00096
0.00000

0.00009
0.10774
0.00028
0.00000
0.00840
0.00038
0.88242
0.00000
0.00068
0.00000

0.00292
0 .21183
0.00465
0.00002
0.12155
0.00757
0.65015
0.00022
0.00109
0.00000

0.00008
0.10670
0.00026
0.00000
0.00725
0.00034
0.88468
0.00000
0.00070
0.00000

0.00000
0.10058
0.00004
0.00000
0.00041
0.00004
0.89754
0.00000
0. 00140
0.00000

0.00000
0.10259
0.00000
0.00000
0.00000
0.00000
0.87248
0.00000
0.02465
0.00028

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONS
WERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONS
F+
LiF(L)

LiF2-

Li (er)

Li (L)

LiF(s)

157

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#

EXAMPLE 12:
(a)
Infinite-area rocket problem (rocket).
(b) The fuel is monomethyl hydrazine (CH6N2(L)) and the oxidant is
nitrogen tetroxide (N204(L)) at 298.15 K. Enthalpies and
"exploded" formulas are to be taken from thermo.lib.
(c) The density of the reactant mixture is desired. This requires
the individual densities be given with the reactant data
(rho,g/cc = .874 and rho,g/cc == 1.431).
(d) The oxidant-to-fuel weight ratio is 2.5 (o/f=2.5).
(e)
Chamber pressure is 1000 psia (p,psia=lOOO).
(f) Equilibrium and frozen calculations are to be performed with
freezing at the throat (nfz=2) .
(g) For exit points one pressure ratio (pi/p=68.0457) and four
supersonic area ratios (supersonic=l0,50,100,200) are given.

reac fuel= CH6N2(L)
rho,g/cc = .874
oxid = N204(L)
rho,g/cc = 1.431
prob rocket case=12 p,psia =1000, pi/p=68.0457, eql frozen nf z=2
supersonic=5,10,25,50,75,100,150,200, o/f= 2.5,
only CO
C02
H
HNO HN02 H02
H2
H20
H202 N
NO
N02
N2
N20
0 OH 02
HCO
NH
CH4 NH2 NH3 H20 (L)
C (gr)
output siunits massf plot aeat t p ivac isp mach cf
end
OPTIONS: TP=F
RKT=T ·FROZ=T

HP=F SP=F TV=F UV=F SV=F DETN=F SHOCK=F REFL=F
EQL=T IONS=F SIUNIT=T DEBUGF=F SHKDBG=F DETDBG=F

TRACE= O.OOE+OO
Pc,BAR

S/R= O.OOOOOOE+OO

H/R= O.OOOOOOE+OO

INCD=F
TRNSPT=F

U/R= O.OOOOOOE+OO

68.947304
68.0457

Pc/P =

SUBSONIC AREA RATIOS
SUPERSONIC AREA RATIOS
100.0000
150.0000
NFZ=

2

5.0000
200.0000

Mdot/Ac= O.OOOOOOE+OO

10.0000

25.0000

Ac/At= 0.000000E+OO

WARNING!! AMOUNT MISSING FOR REACTANT 1.
PROGRAM SETS WEIGHT PERCENT = 100. (REACT)
WARNINGll AMOUNT MISSING FOR REACTANT 2.
PROGRAM SETS WEIGHT PERCENT = 100. (REACT)
REACTANT
WT.FRAC
(ENERGY/R) ,K
EXPLODED FORMULA
F: CH6N2(L)
1.000000
0.651872E+04
C 1.00000 H 6.00000 N 2.00000
0: N204(L)
1.000000 -0.211065E+04
N 2.00000 0 4.00000

158

TEMP,K

DENSITY

298.15

0.8740

298.15

1.4310

50.0000

75.0000

SPECIES BEING CONSIDERED IN THIS SYSTEM
(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES)
1 8/88
1 6/94
tpis89
1 8/89
111/89
tpis89
1 7/88
tpis89
x 4/83
O/F

=

tpis79
112/89
1 5/89
1 2/93
112/89
1 7/88
1 1/90
x 4/83
1 8/89

CH4
*H
HN02
H20
*NH
*NO
N20
*02
C(gr)

1 7/88
112/89
tpis78
1 6/88
tpis89
tpis78
tpis78
x 4/83

*CO
HCO
H02
H202
NH2
N02
*O
C(gr)
H20(L)

*C02
HNO
*H2
*N
NH3
*N2
*OH
C(gr)

2.500000

ENTHALPY
(KG-MOL) (K) /KG
KG-FORM.WT./KG

c
*H
*N
*O
POINT ITN

T

3386.569
10
l
Pinf/Pt = 1.733517
3207.237
2
3
Pinf/Pt = 1.731796
3207.551
2
2
2173.122
3
5
2400.051
4
4
2422.435
4
3
2422.478
1
4
2171.383
4
5
2175.478
2
5
1843.631
4
6
1840.505
2
6
1580.708
4
7
1583.036
7
2
1440.447
8
3
1438.100
2
8

EFFECTIVE FUEL
h(2)/R
0.14148957E+03

EFFECTIVE OXIDANT
h(l)/R
-0.22939058E+02

MIXTURE
hO/R
0.24040550E+02

bi (2)
0.2170510lE-01
0.13023060E+OO
0.434l020lE-Ol
O.OOOOOOOOE+OO

bi(l)
O.OOOOOOOOE+OO
0.00000000E+OO
0.2l736513E-Ol
0.43473025E-01

bOi
0.62014573E-02
0. 37208744E-01
0.27928995E-01
0.31052l61E-Ol

c

H

N

0

-17.018

-10.171

-12.866

-15.018

-17.495

-10.420

-13.029

-15.222

-17.494
-21. 717
-20.495
-20.386
-20.386
-21.727
-21.703
-24.075
-24.102
-27.097
-27.061
-29.620
-29.669

-10.420
-12.457
-11. 908
-11. 858
-11. 858
-12.462
-12.451
-13.429
-13.439
-14.543
-14.530
-15.403
-15.419

-13.029
-14.122
-13.886
-13.861
-13.861
-14.124
-14.120
-14.421
-14.424
-14.630
-14.628
-14.741
-14.743

-15.222
-17.057
-16.543
-16.496
-16.496
-17.061
-17.051
-17.925
-17.934
-18.600
-18.595
-18.819
-18.822

159

THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pinj
CASE

1000.0
12

~~IA

WT FRACTION
(SEE NOTE)
1.0000000
1.0000000

REACTANT
FUEL

OXIDANT

CH6N2(L)
N204 (L)

ENERGY
KJ/KG-MOL
54200.000
-17549.000

TEMP
K
298.150
298.150

REACTANT DENSITY= 1210.57 KG/CUM
O/F=

2.50000

%FUEL= 28.571429

R,EQ.RATIO= 0.998555
EXIT
68.046
1. 0132
2173.12
1.4329-1
-3713.93
-4421.09
-27505.l
10.9479

EXIT
27.260
2.5292
2422.48
3.1771-1
-3026.58
-3822.66
-29547.7
10.9479

PHI,EQ.RATIO= 0.998555

EXIT
67.469
1.0219
2175.48
1.4434-1
-3707.90
-4415.88
-27524.9
10.9479

EXIT
219.62
0.31394
1840.51
5.2779-2
-4476.65
-5071.46
-24626.4
10.9479

EXIT
537.92
0.12817
1583.04
2.5095-2
-4971.56
-5482.31
-22302.5
10.9479

EXIT
910.15
0.07575
1438.10
1.6331-2
-5227.72
-5691.60
-20971.9
10.9479

RHO, KG/CU M
H, KJ/KG
U, KJ/KG
G, KJ/KG
S, KJ/ (KG) (K)

CHAMBER
THROAT
1.0000
1.7318
68.947
39.813
3386.57 3207.55
5.8414 0 3.6029 0
199.89 -427.33
-980.43 -1532.34
-36876.0 -35543.4
10.9479 10.9479

M, (l/n)
(dLV/dLP)t
(dLV/dLT)p
Cp, KJ/ (KG) (K)
GAMMAS
SON VEL,M/SEC
MACH NUMBER

23.856
24.135
25.551
25.301
25.549
25.727
25.770
25.776
-1.02415 -1.02080 -1.00301 -1.00625 -1.00304 -1.00071 -1.00012 -1.00003
1.4608
1.4206
1.0916
1.1700
1.0922
1.0253
1.0051
1.0012
5.1203
4.9690
2.7893
3.4486
2.7952
2.1078
1.8208
1.7311
1.1352
1.1572
1.1912
1.2179
1.2297
1.1574
1.1418
1.1378
905.1
788.7
1158.9
1120.0
904.7
953.4
841.7
755.3
3.093
1.000
2.664
3.089
3.633
4.078
4.362
0.000

Pinf/P
P, BAR
T, K

PERFORMANCE PARAMETERS
Ae/At
CSTAR, M/SEC
CF
Ivac, M/SEC
Isp, M/SEC

160

1.0000
1708.6
0.6555
2106.6
1120. 0

10.066
1708.6
1.6375
3050.5
2797.8

5.0000
1708.6
1. 4868
2853.6
2540.3

10.000
1708.6
1.6362
3048.9
2795.6

25.000
1708.6
1.7899
3252.8
3058.3

50.000
1708.6
1.8823
3374.8
3216.0

75.000
1708.6
1.9283
3435.5
3294.7

MASS FRACTIONS
0.07696
0.15200
0.00044
0.00002
0.00001
0.00014
0.00314
0.28566
0.00002
0.00001
0.02214
0.00005
0.38082
0.00001
0.00515
0.03288
0.04055

*CO
*C02
*H
HNO
HN02
H02
*H2
H20
H202
*N
*NO
N02
*N2
N20
*O
*OH
*02

*

0.06751
0.16686
0.00034
0.00001
0.00000
0.00009
0.00268
0.29378
0.00001
0.00000
0.01774
0.00003
0.38289
0.00001
0.00387
0.02709
0.03708

0.01018
0.25693
0.00001
0.00000
0.00000
0.00000
0.00044
0.32967
0.00000
0.00000
0.00163
0.00000
0.39043
0.00000
0.00011
0.00267
0.00792

0.02136
0.23936
0.00005
0.00000
0.00000
0.00000
0.00085
0.32385
0.00000
0.00000
0. 00373
0.00000
0.38945
0.00000
0.00042
0.00621
0. 01471

0.01026
0.25680
0.00001
0.00000
0.00000
0.00000
0.00045
0.32962
0.00000
0.00000
0.00164
0.00000
0.39043
0.00000
0.00011
0.00269
0.00798

0.00214
0.26956
0.00000
0.00000
0.00000
0.00000
0.00012
0.33382
0.00000
0.00000
0.00036
0.00000
0.39103
0.00000
0.00001
0.00052
0.00243

0.00028
0.27249
0. 00000·
0.00000
0.00000
0.00000
0.00002
0.33493
0.00000
0.00000
0.00009
0.00000
0.39115
0.00000
0.00000
0.00009
0.00095

0.00005
0.27285
0.00000
0.00000
0.00000
0.00000
0.00000
0.33511
0.00000
0.00000
0.00004
0.00000
0. 39118
0.00000
0.00000
0.00003
0.00075

THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MASS FRACTIONS
WERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONS
HCO
H20(L)

CH4
C(gr)

NH2

*NH

NH3

NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS

3
3
4
4
5
5

3
2
3
2
3
2

1337.947
1340.166
1212.262
1210.175
1121. 722
1123.659

-31. 974
-31. 918
-35.486
-35.551
-38.528
-38.458

-16.184
-16.166
-17.337
-17.358
-18.328
-18.305

-14.826
-14.824
-14.938
-14.940
-15.025
-15.023

-18.919
-18.918
-19.025
-19.027
-19.105
-19.103

THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR

Pinj
CASE

FUEL
OXIDANT

1000.0 PSIA
12
REACTANT
CH6N2 (L)
N204 (L)

REACTANT DENSITY= 1210.57 KG/CUM
O/F=
2.50000 %FUEL= 28.571429

WT FRACTION
(SEE NOTE)
1.0000000
1.0000000

ENERGY
KJ/KG-MOL
54200.000
-17549.000

R,EQ.RATIO= 0.998555

TEMP
K
298.150
298.150

PHI,EQ.RATIO= 0.998555

161

Pinf/P
P, BAR
T, K
RHO, KG/CU M
H, KJ/KG
U, KJ/KG
G, KJ/KG
S, KJ/(KG) (K)
(l/n)
(dLV/dLP)t
(dLV/dLT)p
Cp, KJ/ (KG) (K)

M,

GAMMAS

SON VEL,M/SEC
MACH NUMBER

CHAMBER
THROAT
1.0000
1.7318
68. 947
39.813
3386.57 3207.55
5.8414 0 3.6029 0
199.89 -427.33
-980.43 -1532.34
-36876.0 -35543.4
10.9479 10.9479

*

EXIT
2238.43
0.03080
1210.17
7.8911-3
-5611.41
-6001.74
-18860.3
10.9479

EXIT
3253.04
0. 02119
1123.66
5.8480-3
-5752.06
-6114.49
-18053.8
10.9479

23.856
24.135
25.778
25.778
25.778
-1.02415 -1.02080 -1.00001 -1.00000 -1.00000
1. 0000
1.4608
1.4206
1. 0004
1.0001
1. 6099
5.1203
1. 6891
1. 6415
4.9690
1.2446
1.2506
1.1378
1.1352
1. 2362
673.2
1158. 9
697.0
1120 .0
731. 0
5.125
0.000
1. 000
4.576
4.891

PERFORMANCE PARAMETERS
Ae/At
CSTAR, M/SEC
CF
Ivac, M/SEC
Isp, M/SEC
MASS FRACTIONS
*CO
*C02
*H
HNO
HN02
H02
*H2
H20
H202
*N
*NO
N02
*N2
N20
*O
*OH
*02

EXIT
1322.19
0.05215
1340.17
1.2063-2
-5395.00
-5827.27
-20067.0
10.9479

0. 07696
0.15200
0.00044
0.00002
0.00001
0.00014
0.00314
0.28566
0.00002
0.00001
0.02214
0.00005
0.38082
0.00001
0.00515
0.03288
0.04055

1.0000
1708.6
0.6555
2106.6
1120. 0

100.00
1708.6
1. 9578
3474.3
3345.l

150.00
1708.6
1. 9953
3523.7
3409.2

200.00
1708.6
2.0193
3555.2
3450.2

0.06751
0.16686
0.00034
0.00001
0.00000
0.00009
0.00268
0.29378
0.00001
0.00000
0.01774
0.00003
0.38289
0.00001
0.00387
0.02709
0.03708

0.00001
0.27291
0.00000
0.00000
0.00000
0.00000
0.00000
0.33515
0.00000
0.00000
0.00002
0.00000
0. 39118
0.00000
0.00000
0.00001
0.00072

0.00000
0.27292
0.00000
0.00000
0.00000
0.00000
0.00000
0.33516
0.00000
0.00000
0.00001
0.00000
0.39119
0.00000
0.00000
0.00000
0. 00071

0.00000
0.27292
0.00000
0.00000
0.00000
0.00000
0.00000
0.33516
0.00000
0.00000
0.00000
0.00000
0.39119
0.00000
0.00000
0.00000
0.00072

THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MASS FRACTIONS
WERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONS

CH4
C(gr)

HCO
H20(L)

*NH

NH2

NH3

NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS

162

THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
AFTER POINT 2
Pinj
CASE

1000.0 PSIA
12
REACTANT

FUEL

OXIDANT

WT FRACTION
(SEE NOTE)
1.0000000
1.0000000

CH6N2(L)
N204 (L)

ENERGY
KJ/KG-MOL
54200.000
-17549.000

TEMP
K
298.150
298.150

REACTANT DENSITY= 1210.57 KG/CUM
O/F=

2.50000

Pinf/P
P, BAR
T, K

RHO, KG/CU M
H, KJ/KG
U, KJ/KG
G, KJ/KG
S, KJ/ (KG) (K)
M,

(l/n)

Cp, KJ/ (KG) (K)
GAMMAs

SON VEL,M/SEC
MACH NUMBER

%FUEL= 28.571429
CHAMBER
THROAT
1.0000
1.7318
68.947
39.813
3386.57 3207~55
5.8414 0 3.6029 0
199.89 -427.33
-980.43 -1532.34
-36876.0 -35543.4
10.9479 10.9479
23.856
5.1203
1.1378
1158.9
0.000

R,EQ.RATIO= 0.998555

PHI,EQ.RATIO= 0.998555

EXIT
68.046
1.0132
1630.44
1.8039-1
-3393.03
-3954.71
-21243.0
10.9479

EXIT
33.323
2.0691
1871.65
3.2089-1
-2962.89
-3607.68
-23453.6
10.9479

EXIT
87.244
0.79028
1552.50
1.4776-1
-3529.26
-4064.10
-20525.9
10.9479

EXIT
302.39
0.22801
1204.85
5.4932-2
-4117.22
-4532.30
-17307.9
10.9479

EXIT
768.78
0.08968
985.62
2.6413-2
-4468.39
-4807.94
-15258.9
10.9479

EXIT
1327.00
0.05196
872.37
1.7288-2
-4642.93
-4943.46
-14193.6
10.9479

24.135
4.9690
1.1352
1120.0
1.000

24.135
1.7572
1.2439
835.9
3.207

24.135
1.8076
1.2355
892.5
2.818

24.135
1. 7386
1.2471
816.7
3.344

24.135
1.6393
1.2661
4.053

24.135
1.5626
1. 2828
660.0
4.630

24.135
1. 5194
1.2932
623.4
4.992

1.0000
1708.6
0.6555
2106.6
1120.0

8.3449
1708.6
1. 5689
2890.2
2680.6

5.0000
1708.6
1.4720
2771.4
2515.1

10.000
1708.6
1. 5984
2926.8
2731. 0

25.000
1708.6
1.7198
3079.7
2938.4

50.000
1708.6
1.7884
3166.7
3055.6

75.000
1708.6
1.8215
3208.7
3112. 2

724. 9

PERFORMANCE PARAMETERS
Ae/At
CSTAR, M/SEC
CF
Ivac, M/SEC
Isp, M/SEC
MASS FRACTIONS
0.06751
0.00001
0.29378
0.00003
0.00387

*CO
HNO
H20
N02
*O

*C02
H02
H202
*N2
*OH

0.16686
0.00009
0.00001
0.38289
0.02709

0.00034
0.00268
0.01774
0.00001
0.03708

*H
*H2
*NO
N20
*02

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MASS FRACTIONS
WERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONS
CH4
C(gr)

HCO
H20(L)

*NH

NH2

NH3

NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS

163

THEORETICAL ROCKET PERFORMANCE ASSUMING FROZEN COMPOSITION
AFTER POINT 2
Pinj
CASE

FUEL
OXIDANT

1000. 0 PSIA
12
REACTANT

WT FRACTION
(SEE NOTE)
1.0000000
1.0000000

CH6N2 (L)
N204 (L)

ENERGY
KJ/KG-MOL
54200.000
-17549.000

TEMP
K

298.150
298.150

REACTANT DENSITY= 1210.57 KG/CUM
O/F=

2.50000

Pinf /P
P, BAR
T, K
RHO, KG/CU M
H, KJ/KG
u, KJ/KG
G, KJ/KG
s, KJ/ (KG) (K)
M, (l/n)
Cp, KJ/ (KG) {K)
GAMMAS
SON VEL,M/SEC
MACH NUMBER

%FUEL= 28.571429
CHAMBER
THROAT
1.0000
1.7318
68.947
39.813
3386.57 3207.55
5.8414 0 3.6029 0
199.89 -427.33
-980.43 -1532.34
-36876.0 -35543.4
10.9479 10.9479
23.856
5.1203
1.1378
1158. 9
0.000

PERFORMANCE PARAMETERS
Ae/At
CSTAR, M/SEC
CF
Ivac, M/SEC
Isp, M/SEC
MASS FRACTIONS
*CO
HNO
H20
N02
*O

0.06751
0.00001
0.29378
0.00003
0.00387

R,EQ.RATIO= 0.998555
EXIT
1955.79
0. 03525
798.24
1.2819-2
-4754.49
-5029.48
-13493.5
10.9479

EXIT
3382.76
0.02038
702.08
8.4269-3
-4895.92
-5137.79
-12582.3
10.9479

24.135
4.9690
1.1352
1120.0
1.000

24.135
1.4902
1.3007
598.1
5.263

24.135
1. 4516
1. 3112
563.1
5.669

1.0000
1708.6
0.6555
2106.6
1120.0

100.00
1708.6
1.8423
3235.2
3147.8

150.00
1708.6
1. 8685
3268.2
3192.4

*C02
H02
H202
*N2
*OH

0.16686
0.00009
0.00001
0.38289
0.02709

PHI,EQ.RATIO= 0.998555

EXIT
4995.07
0.01380
639.53
6.2651-3
-4985.94
-5206.26
-11987.4
10.9479
24.135
1. 4264
1. 3184

539.0
5.975

200.00
1708.6
1. 8849
3288.9
3220.5

*H
*H2
*NO
N20
*02

0.00034
0.00268
0.01774
0.00001
0.03708

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MASS FRACTIONS
WERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONS
CH4
C(gr)

HCO
H20(L)

*NH

NH2

NH3

NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS

164

tEXAMPLE 13:
(a) Rocket problem with an infinite-area combustor (rocket). This
problem was selected to show some unusual derivatives.
(b) Tripropellant. Fuels are N2H4(L) and Be(L) and oxidant is H202(L),
all at 298.15 K.
(c)
Reactant mixture is given as 67\ fuel by weight (\fuel=67.).
(d) Chamber pressure is 3000 psia (p,psia=3000) .
(e) Calculations are to be for equilibrium conditions only (equilibrium) .
(f)
Four exit pressure ratios are assigned (pi/p=3,10,30,300).
(g)
BeO(L) is included as possible combustion product for the first
point (insert).
(h) Mole fractions > l.e-10 are to be in e-format (trace=l.e-10).
(i) Units in final tables to be non-SI (calories) .

N2H4(L)
reac fuel
Be(a)
fuel
H202 (L)
ox id
prob rocket case=l3

wt\= 80
t=298.15
wt\= 20
t=298.15
wt\=100
t=298.15
p,psia=3000, pi/p=3,10,30,300,equilibrium

%fuel

67.

outp trace= l.e-10 calories
insert BeO(L)
end
OPTIONS: TP=F
RKT=T FROZ=F

HP=F SP=F TV=F UV=F SV=F DETN=F SHOCK=F REFL=F
EQL=T IONS=F SIUNIT=F DEBUGF=F SHKDBG=F DETDBG=F

TRACE= l.OOE-10

S/R= O.OOOOOOE+OO

Pc,BAR

206.841913

Pc/P =

3.0000

10.0000

H/R= O.OOOOOOE+OO

30.0000

INCD=F
TRNSPT=F

U/R= O.OOOOOOE+OO

300.0000

SUBSONIC AREA RATIOS
SUPERSONIC AREA RATIOS
NFZ=

1

Mdot/Ac= O.OOOOOOE+OO

Ac/At= 0.000000E+OO

REACTANT
WT.FRAC
(ENERGY/R) I K
EXPLODED FORMULA
F: N2H4(L)
0.800000
0. 605929E+04
N 2.00000 H 4.00000
F: Be(a)
0.200000 -0.l30953E-05
BE 1.00000
0: H202 (L)
l.000000 -0.225846E+05
H 2.00000 0 2.00000

TEMP,K

DENSITY

298.15

0.8740

298.15

1. 4310

298.15

0.0000

165

SPECIES BEING CONSIDERED IN THIS SYSTEM
(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES)
1 6/94
j 6/63
j12/75
j 9/63
j 9/63
tpis89
tpis78
1 6/88
tpis89
1 7/88
1 5/90
1 7/88
1 4/90
1 1/90
1 5/90
srd 93
coda89
J12/75
BeO(L)
O/F

=

*Be
BeN
Be02H2
Be303
Be606
HN02
*H2
*N
NH3
N02
N2H2
N20
N205
*O
03
Be(b)
BeO(a)
Be02H2(b)
INSERTED

j12/60
j12/75
j 9/63
j 9/63
112/89
1 5/89
1 2/93
112/89
tpis89
tpis78
1 5/90
tpis89
1 7/88
tpis89
srd 93
coda89
coda89
1 8/89

BeH
*BEO
Be20
Be404
*H
HN03
H20
*NH
NH20H
N03
NH2N02
N203
N3
*OH
Be(a)
Be(L)
BeO(b)
H20(s)

BeH2
BeOH
Be202
Be505
HNO
H02
H202
NH2
*NO
*N2
N2H4
N204
N3H
*02
Be(a)
BeO (a)
BeO(L)
H20 (L)

0.492537

ENTHALPY
(KG-MOL) (K) /KG
KG-FORM.WT./KG
*N
*H
*Be
*O
POINT ITN
T
3015.477
l
13
Pinf /Pt = l.743807
2802.203
2
4
ADD BeO(b)
2
4
2851.000
Pinf/Pt = l.630416
2851.000
4
2
Pinf /Pt = 1.626685
2
2
2851.000
3
5
2604.969
PHASE CHANGE, REPLACE
3
4
2922.003
ADD BeO(L)
3
4
2851.000
4
5
2204.200
PHASE CHANGE, REPLACE
4
2451.195
4
PHASE CHANGE, REPLACE
4
2
2451.586
5
2061. 574
5
PHASE CHANGE, REPLACE
5
2
2067 .118
6
5
1396.587

166

tpis81
j 12/74
j 9/63
j 9/63
1 6/94
1 4/90
1 8/89
111/89
tpis89
j12/64
tpis89
1 4/90
tpis89
tpis78
srd 93
srd 93
coda89
1 8/89

EFFECTIVE FUEL
h(2)/R
0.15126831E+03
bi(2)
0.49929412E-01
0.99858825E-01
0.22192184E-01
O.OOOOOOOOE+OO

EFFECTIVE OXIDANT
h(1)/R
-0.66396668E+03
bi(l)
O.OOOOOOOOE+OO
0.58798142E-01
O.OOOOOOOOE+OO
0.58798l42E-Ol

MIXTURE
hO/R
-0.ll775924E+03
bOi
0.33452706E-01
0.86308799E-01
0.14868763E-Ol
O.l9403387E-Ol

N
-12.175

H
-7.991

BE
-13.104

0
-20.398

-12.317

-8.137

-13.670

-21. 009

-12.349

-8.168

-13.530

-20.860

-12.315

-8 .135

-13.530

-20.860

-12.314
-12.455
BeO(L)
-12.667

-13.530
-8.133
-14.318
-8.281
WITH BeO(b)
-13.245
-8.486

-20.860
-21.678

-12.621
-12.760
BeO(L)
-12.948
BeO(a)
-12.948
-13.195
BeO(b)
-13.199
-13. 721

-13.530
-8 .441
-16.149
-8.601
WITH BeO(a)
-15.487
-8.779
WITH BeO(b)
-15.484
-8.779
-18.232
-9.042
WITH BeO(a)
-18.191
-9.046
-27.072
-9.603

-20.859
-23.464

-20.656

-22.276
-22.274
-24.282
-24.247
-30.583

THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM
COMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pinj
CASE

3000.0 PSIA
13
WT FRACTION
(SEE NOTE)
0.8000000
0.2000000
1.0000000

REACTANT
N2H4(L)
Be(a)
H202 (L)

FUEL
FUEL

OXIDANT
O/F=

0.49254

Pinf/P
P, ATM
T, K

RHO, G/CC

H, CAL/G
U, CAL/G
G, CAL/G
s I CAL/ (G) (K)
M, (1/n)
MW, MOL WT

(dLV/dLP)t
(dLV/dLT)p
Cp, CAL/ (G) (K)

GAMMAs
SON VEL,M/SEC
MACH NUMBER

%FUEL= 67.000000

ENERGY
CAL/MOL
12041.109
0.000
-44880.497

R,EQ.RATIO= 2.990363

TEMP
K

298.150
298.150
298.150

PHI,EQ.RATIO= 4.980725

CHAMBER
THROAT
EXIT
EXIT
EXIT
EXIT
1.0000
1.6267
3.0000
10.000
30.000
300.00
204.14
125.49
68.046
20.414
6.8046 0.68046
3015.48 2851.00 2851.00 2451.59 2067.12 1396.59
1.3715-2 8.9279-3 4.8341-3 1.6916-3 6.6969-4 9.9159-5
-234.01 -403.86 -612.35 -997.47 -1292.67 -1762.88
-594.46 -744.26 -953.24 -1289.71 -1538.74 -1929.07
-10112.8 -9743.85 -9952.34 -9028.96 -8064.63 -6338.16
3.2760
3.2760
3.2760
3.2760
3.2760
3.2760
16.644
16.625
16.620
16.670
16.700
16.694
13.361
13.376
13.372
13.378
13.376
13.370
-1.00283 -1.00209 -1.00262 -1.00098 -1.00023 -1.00002
1.0465
0.0000
0.0000
1.0209
1.0053
1.0001
0.9575
0.0000
0.0000
0.7984
0.7448
0.6649
0.9979
1.1546
0.9974
1.1829
1.1923
1.2180
1192.2
1192.7
1202.7
1319.6
1108. 0
920.3
1.000
0.000
1.492
2.102
2.686
3.887

PERFORMANCE PARAMETERS
Ae/At
CSTAR, FT/SEC
CF
Ivac,LB-SEC/LB
Isp, LB-SEC/LB

1.0000
6375.8
0.6135
243.4
121.6

1.2374
6375.8
0.9156
263.2
181.4

2.4894
6375.8
1.3006
307.1
257.7

5.3398
6375.8
1. 5316
338.8
303.5

30.010
6375.8
1.8405
384.6
364.7

167

MOLE FRACTIONS
*Be
BeH
BeH2
BeN
*BEO
BeOH
Be02H2
Be20
Be202
Be303
Be404
Be505
Be606
*H
HNO
HN02
H02
*H2
H20
H202
*N
*NH
NH2
NH3
NH20H
*NO
N02
*N2
N2H2
N20
N3H
*O
*OH
*02
BeO(a)
BeO(b)
BeO(L)

8.681 -6
1.104 -6
1.171 -5
4.457 -8
3.551 -7
1.240 -4
2.9966-3
7.060 -7
3.894 -7
7.665 -7
2.173 -7
6.079 -9
3.717-10
7.4008-3
9.938 -8
2.406-10
2.553 -9
5.1230-1
5.7363-2
5.504 -9
4.529 -7
2.470 -6
1.921 -5
3.0252-4
2.905 -9
1.860 -5
1.236-10
2.2349-1
7.477 -9
9.032 -9
1.480-10
2.448 -6
2.7768-4
1.083 -7
0.0000 0
0.0000 0
1.9567-1

3.857 -6
3.684 -7
5.070 -6
1.236 -8
1.342 -7
6.727 -5
2.5056-3
2.511 -7
1.728 -7
4.787 -7
1.434 -7
4.184 -9
2.827-10
5.5693-3
4.355 -8
9.046-11
1.015 -9
5.1354-1
5.7964-2
2.426 -9
1.904 -7
1.086 -6
9.841 -6
2.1058-4
1.107 -9
1.087 -5
4.605-11
2.2362-1
2.733 -9
4.103 -9
4.527-11
1.245 -6
1.8428-4
5.610 -8
0.0000 0
1.3853-2
1.8245-1

7.lll -6
4.994 -7
5.054 -6
1.677 -8
2.476 -7
9.125 -5
2.5000-3
4.630 -7
3.188 -7
8.831 -7
2.646 -7
7.718 -9
5.216-10
7.5542-3
4.349 -8
9.038-ll
1.379 -9
5.1214-1
5.7835-2
2.422 -9
2.585 -7
1.084 -6
7.222 -6
1.1363-4
5.975-10
1.476 -5
6.258-11
2.2342-1
1.476 -9
4.101 -9
2.447-11
2.297 -6
2.5007-4
1.036 -7
0.0000 0
l.5511-1
4.0950-2

2.586 -7
8.737 -9
2.194 -7
l.685-10
5.763 -9
6.858 -6
7.9244-4
4.580 -9
6.143 -9
2.536 -8
4.831 -9
8.580-11
4.205-12
2.8642-3
3.791 -9
4.939-12
7.839-11
5.1486-1
5.9767-2
2.117-10
1.721 -8
9.309 -8
1.113 -6
4.9681-5
4.397-11
2.620 -6
2.930-12
2.2360-1
9.647-11
3.946-10
9.231-13
2.389 -7
6.4898-5
1.142 -8
0.0000 0
1.9799-1
0.0000 0

l.859 -9
3.040-11
3.305 -9
2.807-13
2.341-11
1.620 -7
1.6333-4
5.497-12
l.750-11
1.184-10
1.201-11
l.070-13
3.317-15
6.2153-4
l.498-10
1.004-13
1.296-12
5.1624-1
6.0485-2
7.944-12
3.711-10
3.580 -9
1.197 -7
2.7432-5
2.287-12
2.002 -7
3.760-14
2.2372-1
4.461-12
1.757-11
2.001-14
7.057 -9
8.1758-6
3.535-10
1.9873-1
0.0000 0
0.0000 0

l.351-16
4.032-19
7.002-15
3.873-22
3.240-19
7.729-13
1.1620-6
1.278-21
5.868-20
1.538-18
2.030-20
1.914-23
1.280-25
3.5990-6
8.418-15
7.126-19
2.695-18
5.1664-1
6.0664-2
3.489-16
l.810-15
l.671-13
2.226-10
1.3148-5
9.065-16
4.479-ll
3.713-20
2.2376-1
1.288-15
l.410-15
5.124-19
5.241-14
8.2744-9
2.936-15
1.9892-l
0.0000 0
0.0000 0

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONS
WERE LESS THAN l.OOOOOOE-10 FOR ALL ASSIGNED CONDITIONS
HN03
N204
Be(b)

N03
N205
Be(L)

NH2N02
N3
Be02H2(b)

N2H4
03
H20(s)

N203
Be(a)
H20(L)

NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS

168

EXAMPLE 14:
(a) Output from this case is used 1) to illustrate the effect of
condensed species on volume and molecular weight (see sec.2.2,part I)
(b) Assigned-temperature-and-pressure problem (tp) .
(c) Reactants are H2(L) and 02(L) and amounts are specified in moles.
(d) The "exploded" formulas are given to save the program looking them
up. Reactant enthalpies are not needed for assigned temperature
problems.
(e) Assigned pressure in atmospheres is p,atm =.05.
(f) Assigned temperatures in kelvin are t,k =1000,500,351,305,304.3,
304, 300.
(g)
Print intermediate output for the fifth point with debug = 5.
name H2(L) moles=lOO
name 02(L) moles=60

reac

H 2

0 2

prob

tp p,atm=.05 case=l4
t,k = 1000,500,350,305,304.3,304.2,304,300,

output

siunits

debug = 5

end
OPTIONS: TP=T
RKT=F FROZ=F
T, K =

1000 .. 0000

TRACE='. 0. OOE+·oo
P,BAR

HP=F SP=F TV=F UV=F SV=F DETN=F SHOCK=F REFL=F
EQL=F IONS=F SIUNIT=T DEBUGF=F SHKDBG=F DETDBG=F

=

500.0000

350.0000

S/R= 0. OOOOOOE+OO

305.0000

304.3000

H/R= 0. OOOOOOE+OO

INCD=F
TRNSPT=F

304.2000

304.0000

30

U/R= 0. OOOOOOE+OO

0.050663

REACTANT
MOLES
EXPLODED FORMULA
100.000000
N: H2(L)
H 2.00000
60.000000
N: 02 (L)
0 2.00000

(ENERGY /R) , K

TEMP,K

O.OOOOOOE+OO

0.00

0.8740

-0.156101E+04

90.17

1.4310

DENSITY

SPECIES BEING CONSIDERED IN THIS SYSTEM
(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES)
1 6/94
1 8/89
tpis78
1 8/89

*H
H20
*OH
H20(s)

1 5/89
1 2/93
tpis89
1 8/89

H02
H202
*02
H20(L)

tpis78
1 1/90
1 5/90

*H2
*O
03

169

O/F

0.000000

ENTHALPY
(KG-MOL) (K)/KG

EFFECTIVE FUEL
h(2)/R
-0.44147845E+02

KG-FORM.WT./KG
*H
*O

bi(2)
0.94272209E-01
0.56563325E-01

POINT ITN
1
10
2
3
3
1
4
1

H
-20.527
-34.596
-46.944
-53.061

T
1000.000
500.000
350.000
305.000

ITERATION 1
MATRIX
0.188544E+OO
0.942722E-01
0.942722E-01
0.659905E-01
0. 942 722E- 01
0.565633E-01

EFFECTIVE OXIDANT
h(l)/R
O.OOOOOOOOE+OO

MIXTURE
hO/R
-0.44147845E+02

bi(l)
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO

bOi
0.94272209E-01
0.56563325E-Ol

0
-15.973
-15.230
-15.049
-15.028

0.942722E-01
0.565633E-01
O.OOOOOOE+OO

-0.114417E+02
-0 .'600419E+Ol
-0.586253E+Ol

SOLUTION VECTOR
H

0

-0.531707E+02

-0.150274E+02

O.OOOOOOE+OO

T= 0.30430000E+03 ENN= 0.51849715E-01 ENNL=-0.29594058E+Ol PP= 0.50662500E-Ol
LN P/N=-0.23163446E-Ol AMBDA= O.lOOOOOOOE+Ol
LN Nj
DEL LN Nj
HOj/RT
SOj/R
GOj/RT
Gj/RT
O.OOOOOOE+OO -0.125204E+03 -0.307497E+OO
0.862123E+02
0.138484E+02
0.723640E+02 -0.528633E+02
O.OOOOOOE+OO -0.604867E+02 -0.121044E+OO
0.504603E+Ol
0.276408E+02 -0.225947E+02 -0.831046E+02
O.OOOOOOE+OO -0.903810E+02 -0.219421E+OO
0.701441E-01
0.157881E+02 -0.157179E+02 -0.106122E+03
0.471361E-01 -0.305472E+Ol
0.177636E-14 -0.954977E+02
0.227933E+02 -0.118291E+03 -0.121369E+03
O.OOOOOOE+OO -0.541943E+02 -0.956804E-Ol -0.537719E+02
0.283113E+02 -0.820832E+02 -0.136301E+03
O.OOOOOOE+OO -0.938907E+02 -0.226071E+OO
0.985373E+02
0.791125E+02 -0.148014E+02
0.194248E+02
O.OOOOOOE+OO -0.614818E+02 -0.145407E+OO
0.156242E+02
0.221720E+02 -0.654785E+Ol -0.680528E+02
0.471361E-02 -0.535730E+Ol -0.639488E-13
0.714483E-Ol
0.247458E+02 -0.246744E+02 -0.300549E+02
O.OOOOOOE+OO -0.722284E+02 -0.128601E+OO
0.561412E+02
0.288433E+02
0.272979E+02 -0.449537E+02
O.OOOOOOE+OO
O.OOOOOOE+OO
O.OOOOOOE+OO -0.115317E+03
0.550772E+Ol -0.120825E+03 -0.172966E+03
O.OOOOOOE+OO
O.OOOOOOE+OO
O.OOOOOOE+OO -0.112509E+03
0.861762E+Ol -0.121126E+03 -0.230622E+03
304.300
-53.171
-15.027
Nj

*H
H02
*H2
H20
H202
*O
*OH
*02
03
H20 (s)
H20{L)
5

170

l

200.000

H20(s)

273.150

O.OOOOOOOE+OO

H20(L)
273.150
600.000
[GOj-SUM(Aij*Pii)]/Mj = -0.9021700E-03
ADD H20(L)
MATRIX
ITERATION 0
0.942722E-Ol
0.188544E+OO
0.659905E-Ol
0. 942722E-Ol
O.lOOOOOE+Ol
0.200000E+Ol
0.565633E-Ol
0. 942722E-01

O.OOOOOOOE+OO
MAX NEG DELTA G

0.200000E+Ol
O.lOOOOOE+Ol
O.OOOOOOE+OO
O.OOOOOOE+OO

0.942722E-01
0.565633E-01
O.OOOOOOE+OO
0.770217E-15

0.842705E-02

-0.162528E+OO

-0.9021700E-03

-0.114417E+02
-0.600419E+Ol
-0.121385E+03
-0.586253E+Ol

SOLUTION VECTOR
H

-0.532195E+02

0

-0.149462E+02

T= 0.30430000E+03. ENN= 0.51849715E-01 ENNL=-0.29594058E+Ol PP= 0.50662500E-Ol
LN P/N=-0.23163446E-01 AMBDA= O.lOOOOOOOE+Ol

Nj
*H

O.OOOOOOE+OO

H02

O.OOOOOOE+OO

*H2

O.OOOOOOE+OO

H20

0.471361E-01

H202

O.OOOOOOE+OO

*O

O.OOOOOOE+OO

*OH

O.OOOOOOE+OO

*02

0.471361E-02

03

O.OOOOOOE+OO

H20(s)

O.OOOOOOE+OO

H20(L)

O.OOOOOOE+OO

ITERATION 1
MATRIX
0.157678E+OO
0.788388E-01
0.788388E-Ol
0.582738E-01
0.200000E+01
O.lOOOOOE+Ol
0.788388E-Ol
0.488466E-01

LN Nj

DEL LN Nj
HOj/RT
SOj/R
GOj/RT
Gj/RT
-0.125512E+03 -0.211287E+OO
0.862123E+02
0.138484E+02
0.723640E+02 -0.531707E+02
-0.606077E+02 -0.487585E-01
0.504603E+Ol
0.276408E+02 -0.225947E+02 -0.832256E+02
-0.906004E+02 -0.260046E+OO
0.701441E-Ol
0.157881E+02 -0.157179E+02 -0.106341E+03
-0.305472E+Ol -0.178781E+OO -0.954977E+02
0.227933E+02 -0.118291E+03 -0.121369E+03
-0.542900E+02 -0.975171E-01 -0.537719E+02
0.283113E+02 -0.820832E+02 -0.136396E+03
-0.941168E+02 -0.812642E-Ol
0.985373E+02
0.194248E+02
0.791125E+02 -0.150274E+02
-0.616272E+02 -0.130023E+OO
0.156242E+02
0.221720E+02 -0.654785E+Ol -0.681982E+02
-0.535730E+Ol
0.124345E-12
0.7144838-01
0.247458E+02 -0.246744E+02 -0.300549E+02
-0.723570E+02
0.812642E-Ol
0.561412E+02
0.288433E+02
0.272979E+02 -0.450823E+02
O.OOOOOOE+OO
O.OOOOOOE+OO -0.115594E+03
0.549580E+Ol -0.121090E+03 -0.172966E+03
O.OOOOOOE+OO
0.842705E-02 -0.112788E+03
0.859679E+Ol -0.121385E+03 -0.121385E+03

0.200000E+01
0.100000E+01
O.OOOOOOE+OO
O.OOOOOOE+OO

0.788388E-01
0.488466E-01
O.OOOOOOE+OO
0.611676E-04

-0.122861E-02

0.131474E-01

-0.957128E+Ol
-0.506744E+Ol
-0.121385E+03
-0. 492589E+Ol

SOLUTION VECTOR
H

-0.532162E+02

0

-0.149527E+02

171

T= 0.30430000E+03 ENN= 0.44071839E-01 ENNL=-0.31219343E+Ol PP= 0.50662SOOE-01
LN P/N= 0.13936499E+OO AMBDA= O.lOOOOOOOE+Ol
Nj

*H

O.OOOOOOE+OO

H02

O.OOOOOOE+OO

*H2

O.OOOOOOE+OO

H20

0.394194E-Ol

H202

O.OOOOOOE+OO

*O

O.OOOOOOE+OO

*OH

0.000000E+OO

*02

0.471361E-02

03

O.OOOOOOE+OO

H20(s)

O.OOOOOOE+OO

H20(L)

0.842705E-02

ITERATION 2
MATRIX
0.159764E+OO
0.798822E-01
0.798822E-01
0.587955E-01
0.200000E+Ol
O.lOOOOOE+Ol
0.798822E-01
0.493683E-01

HOj/RT
LN Nj
DEL LN Nj
Gj/RT
SOj/R
GOj/RT
0.862123E+02
-0.125723E+03
0.164343E-01
0.723640E+02 -0.532195E+02
0.138484E+02
-0.606565E+02
0.328686E-02
0.504603E+Ol
0.276408E+02 -0.225947E+02 -0.831118E+02
0.701441E-01
-0.908604E+02
0.197211E-01
0.157881E+02 -0.157179E+02 -0.106439E+03
-0.3233SOE+Ol
0.131474E-01 -0.954977E+02
0.227933E+02 -0.118291E+03 -0.121385E+03
-0.54387SE+02
0.657371E-02 -0.537719E+02
0.283113E+02 -0.820832E+02 -0.136331E+03
-0.941980E+02
0.657371E-02
0.985373E+02
0.19424BE+02
0.791125E+02 -0.149462E+02
-0.617572E+02
0.986057E-02
0.156242E+02
0.221720E+02 -0.654785E+Ol -0.681657E+02
-0.535730E+Ol -0.127898E-12
0.714483E-01
0.247458E+02 -0.246744E+02 -0.298923E+02
-0.722758E+02 -0.657371E-02
0.561412E+02
0.272979E+02 -0.448385E+02
0.288433E+02
O.OOOOOOE+OO
0.000000E+OO -0.115594E+03
0.549580E+Ol -0.121090E+03 -0.172966E+03
O.OOOOOOE+OO -0.122861E-02 -0.112788E+03
0.859679E+Ol -0.121385E+03 -0.12138SE+03

0.200000E+Ol
O.lOOOOOE+Ol
O.OOOOOOE+OO
O.OOOOOOE+OO

0.798822E-01
0.493683E-Ol
O.OOOOOOE+OO
-0.403867E-06

0.126035E-13

-0.856736E-04

SOLUTION VECTOR
H

-0.532162E+02

172

0

-0.149527E+02

-0.969652E+Ol
-0.51301BE+Ol
-0.12138SE+03
-0.498922E+Ol

T= 0.30430000E+03 ENN= 0.44655096E-01 ENNL=-0.31087869E+Ol PP= 0.50662500E-01
LN P/N= 0.12621757E+OO AMBDA= O.lOOOOOOOE+Ol
Nj
*H

O.OOOOOOE+OO

H02

O.OOOOOOE+OO

*H2

O.OOOOOOE+OO

H20

0.399411E-01

H202

O.OOOOOOE+OO

*O

O.OOOOOOE+OO

*OH

O.OOOOOOE+OO

*02

0.471361E-02

03

O.OOOOOOE+OO

H20(s)

O.OOOOOOE+OO

H20(L)

0. 719845E-02

ITERATION 3
MATRIX
0.798753E-01
0.159751E+OO
0.587921E-Ol
0.798753E-01
O.lOOOOOE+Ol
0.200000E+Ol
0.493649E-01
0.798753E-01

HOj/RT
LN Nj
DEL LN Nj
Gj/RT
SOj/R
GOj/RT
0.862123E+02
-0.125706E+03 -0.107092E-03
0.138484E+02
0.723640E+02 -0.532162E+02
0.504603E+Ol
-0.606532E+02 -0.214184E-04
0.276408E+02 -0.225947E+02 -0.831217E+02
0.701441E-01
-0.908407E+02 -0.128510E-03
0.157881E+02 -0.157179E+02 -0.106432E+03
-0.322035E+Ol -0.856736E-04 -0.954977E+02
0.227933E+02 -0.118291E+03 -0.121385E+03
-0.543809E+02 -0.428368E-04 -0.537719E+02
0.283113E+02 -0.820832E+02 -0.136338E+03
-0.941915E+02 -0.428368E-04
0.985373E+02
0.791125E+02 -0.149527E+02
0.194248E+02
-0.617473E+02
0.156242E+02
-0.642552E-04
0.221720E+02 -0.654785E+Ol -0.681690E+02
0.714483E-01
-0.535730E+Ol -0.284217E-13
0.247458E+02 -0.246744E+02 -0.299055E+02
0.561412E+02
-0.722823E+02
0.428368E-04
0.272979E+02 -0.448582E+02
0.288433E+02
O.OOOOOOE+OO
O.OOOOOOE+OO -0.115594E+03
0.549580E+Ol -0.121090E+03 -0.172966E+03
O.OOOOOOE+OO
0.126035E-13 -0.112788E+03
0.859679E+Ol -0.121385E+03 -0.121385E+03

0.200000E+Ol
O.lOOOOOE+Ol
O.OOOOOOE+OO
O.OOOOOOE+OO

0.798753E-Ol
0.493649E-Ol
O.OOOOOOE+OO
-0.172989E-10

-0.757420E-14

-0.367002E-08

-0.969568E+Ol
-0.512976E+Ol
-0.121385E+03
-0.498880E+Ol

SOLUTION VECTOR
H

-0.532162E+02

0

-0.149527E+02

T= 0.30430000E+03 ENN= 0.44651270E-Ol ENNL=-0.31088725E+Ol PP= 0.50662500E-01
LN P/N= 0.12630324E+OO AMBDA= O.lOOOOOOOE+Ol

173

LN Nj
HOj/RT
DEL LN Nj
SOj/R
GOj/RT
Gj/RT
0.862123E+02
O.OOOOOOE+OO -0.125707E+03 -0.458755E-08
0.138484E+02
0.723640E+02 -0.532162E+02
O.OOOOOOE+OO -0.606532E+02 -0.917481E-09
0.504603E+Ol
0.276408E+02 -0.225947E+02 -0.831216E+02
O.OOOOOOE+OO -0.908408E+02 -0.550507E-08
0.701441E-Ol
0.157881E+02 -0.157179E+02 -0.106432E+03
0.399377E-Ol -0.322044E+Ol -0.367004E-08 -0.954977E+02
0.227933E+02 -0.ll8291E+03 -0.121385E+03
O.OOOOOOE+OO -0.543810E+02 -0.183496E-08 -0.537719E+02
0.283113E+02 -0.820832E+02 -0.136338E+03
O.OOOOOOE+OO -0.941915E+02 -0.183497E-08
0.985373E+02
0.194248E+02
0.791125E+02 -0.149527E+02
O.OOOOOOE+OO -0.617474E+02 -0.275250E-08
0.156242E+02
0.221720E+02 -0.654785E+Ol -0.681689E+02
0.471361E-02 -0.535730E+Ol
0.746070E-13
0.714483E-Ol
0.247458E+02 -0.246744E+02 -0.299054E+02
O.OOOOOOE+OO -0.722823E+02
0.183512E-08
0.561412E+02
0.288433E+02
0.272979E+02 -0.448581E+02
O.OOOOOOE+OO
O.OOOOOOE+OO
O.OOOOOOE+OO -0.ll5594E+03
0.549580E+Ol -0.121090E+03 -0.172966E+03
0.719845E-02
O.OOOOOOE+OO -0.757420E-14 -O.ll2788E+03
0.859679E+Ol -0.121385E+03 -0.121385E+03
304.300
-53.216
-14.953
Nj

*H
H02
*H2
H20
H202
*O
*OH
*02
03
H20(s)
H20(L)
5

3

H20(s)

200.000

273.150

O.OOOOOOOE+OO

H20(L)

273.150

600.000

0.7198445E-02

T DERIV MATRIX
0.159751E+OO
0.798753E-Ol
0.200000E+Ol
0.798753E-Ol

0.798753E-Ol
0.587921E-Ol
O.lOOOOOE+Ol
0.493649E-Ol

0.200000E+Ol
O.lOOOOOE+Ol
O.OOOOOOE+OO
O.OOOOOOE+OO

0.798753E-Ol
0.493649E-Ol
O.OOOOOOE+OO
O.OOOOOOE+OO

-0.930373E+02

0
0.732862E+02

0.654145E+Ol

-0.146501E+03

P DERIV MATRIX
0.159751E+OO
0.798753E-Ol
0.200000E+Ol
0.798753E-01

0.798753E-Ol
0.587921E-Ol
O.lOOOOOE+Ol
0.493649E-Ol

0.200000E+Ol
O.lOOOOOE+Ol
O.OOOOOOE+OO
O.OOOOOOE+OO

0.798753E-01
0.493649E-Ol
O.OOOOOOE+OO
O.OOOOOOE+OO

0
0.473642E+Ol

0.378323E+OO

-0.847284E+Ol

-0.762791E+Ol
-0.381328E+Ol
-0.112788E+03
-0.381362E+Ol

SOLUTION VECTOR
H

SOLUTION VECTOR
H

-0.236821E+Ol

POINT= 5
P= 0.506625E-Ol
T= 0.304300E+03
H/R=-0.140755E+04
S/R= 0.123707E+Ol
M= 0.223958E+02
CP/R= 0.113349E+03
DLVPT=-0.947284E+Ol
DLVTP= 0.147501E+03
GAMMA(S)= 0.110818E+Ol
V= 0.222990E+07

174

0.798753E-Ol
0.493649E-Ol
O.OOOOOOE+OO
0.446513E-Ol

6
7
8

304.200
304.000
300.000

3
4
6

-53.247
-53.305
-54.288

-14. 929
-14.886
-14.426

THERMODYNAMIC EQUILIBRIUM PROPERTIES AT ASSIGNED
TEMPERATURE AND PRESSURE
CASE

14
REACTANT

MOLES

H2 (L)
02 (L)

NAME
NAME

ENERGY
KJ/KG-MOL
0.000
-12979.000

100.0000000
60.0000000

TEMP
K

0.000
90.170

REACTANT DENSITY= 1349.29 KG/CUM
O/F=

0.00000

\FUEL=

0.000000

R,EQ.RATIO= 0.833333

PHI,EQ.RATIO= 0.000000

THERMODYNAMIC PROPERTIES
P, BAR
T, K

RHO, KG/CU M
H, KJ/KG
U, KJ/KG
G, KJ/KG
S, KJ/(KG) (K)
M,

(l/n)

MW, MOL WT
(dLV/dLP)t
(dLV/dLT)p
Cp, KJ/ (KG) (K)
GAMMAS
SON VE:f.,,M/SEC

0.05066
1000.00
1.1752-2
-10066.0
-10497.1
-23601.6
13.5356

0.05066
500.00
2.3504-2
-11043.6
-11259.2
-17139.8
12.1924

0.05066
350.00
3.3577-2
-11309.l
-11460.0
-15355.8
11.5619

0.05066
305.00
3.8530-2
-11386.9
-11518.4
-14840.7
11.3239

0.05066
304.30
4.4845-2
-11703.l
-11816.0
-14833.0
10.2856

0.05066
304.20
4.7014-2
-11792.8
-11900.5
-14831.9
9.9907

0.05066
304.00
5.1325-2
-11948.7
-12047.4
-14830.0
9.4781

0.05066
300.00
1.3024-1
-12988.1
-13027.0
-14801.2
6.0435

19.287
19.287
19.287
25.607
22.396
64.125
19.287
23 .471
19.287
19.287
19.287
19.287
19.287
19.287
19.287
19.287
-1.00000 -1.00000 -1.00000 -1.00000 -9.47284 -9.03875 -8.28504 -3.30842
1.0000
1. 0000
1.0000
1.0000 147.5009 140.0542 127.1235 41.6525
2.1108
1.8069
1.7370
1.7233 942.4445 854.1858 711.2554 96.0625
1.3133
1.3301
1.2567
1. 3336
1.1082
1.1061
1.1019
1. 0345
736.0
532.1
448.0
418.8
353.8
345.2
329.8
200.6

MOLE FRACTIONS
H20
*02
H20(L)

0.90909
0.09091
0.00000

0.90909
0.09091
0.00000

0.90909
0.09091
0.00000

0.90909
0.09091
0.00000

0.77026
0.09091
0.13883

0.73080
0.09091
0.17830

0.66228
0.09091
0.24681

0.20986
0.09091
0.69923

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONS
WERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONS
*H
*OH

H02
03

*H2
H20(s)

H202

*O

175

References
Anon., 1995, "Atomic Weights of the Elements, 1993," Journal of Physical and Chemical Reference Data, Vol.
24, No. 4, pp. 1561-1576.
Chase, M.W., Jr., ed., 1985, JANAFThermochemical Tables, 3rd Ed., Pts. 1 & 2. (Also, Journal of Physical and
Chemical Reference Data, Vol. 14, Suppl. 1, 1985).
Cohen, E.R. and Taylor, B.N., 1987, "The 1986 CODATA Recommended Values of the Fundamental Physical
Constants," NationalBureauo/StandardsJournalo/Research, Vol. 92, Mar.-Apr., pp. 85-95.
Gordon S., 1970, "Calculation of Theoretical Equilibrium Nozzle Throat Conditions When Velocity of Sound Is
Discontinuous," American Institute of Aeronautics and A~tronautics Journal, Vol. 9, No. l, pp. 179-182.
Gordon S. and McBride, B.J., 1976, Computer Program for Calculation of Complex Chemical Equilibrium
Compositions, Rocket Performance, Incident and Reflected Shocks, and Chapman-Jouguet Detonations, NASA
SP-273, Interim Revision.
Gordon, S., 1982, "Thermodynamic and Transport Combustion Properties of Hydrocarbons With Air. I-Properties
in SI Units," NASATP-1906.
Gordon, S. and McBride, B.J., 1988, "Finite Area Combustor Theoretical Rocket Performance," NASA TM100785.
Gordon S. and McBride, B.J., 1994, Computer Program for Calculation of Complex Chemical Equilibrium
Compositions andApplications. I. Analysis, NASARP-1311.
Gupta, R.N., Yos, J.M., Thompson R.A., and Lee, KP., 1990, A Review of Reaction Rates and Thermodynamic
and Transport Properties/or an 11-Species Air Model for Chemical and Thermal Nonequilibrium Calculations to
30 000 K, NASARP-1232.
Lide, D.R., ed., 1992-1993, CRC Handbook of Chemistry and Physics, 73rd Ed., CRC Press, Inc., Boca Raton,
FL, pp. 6-12.
McBride, B.J. and Gordon, S., 1992, Computer Program/or Calculating and Fitting Thermodynamic Functions,
NASARP-1271.
McBride, B.J., Gordon, S., and Reno, M.A., 1993, "Coefficients for Calculating Thermodynamic and Transport
Properties of Individual Species," NASA TM-4513.
McBride, B.J., Reno, M.A., and Gordon, S., 1994, "CET93 and CETPC: An Interim Updated Version of the NASA
Lewis Computer Program for Calculating Complex Chemical Equilibria With Applications," NASA TM-4557.
Svehla, R.A. and McBride, H.J., 1973, "FORTRAN IV Computer Program for the Calculation of Thermodynamic
and Transport Properties of Complex Chemical Systems," NASA TN D-7056.
Svehla, R.A., 1995, "Transport Coefficients for the NASA Lewis Chemical Equilibrium Program," NASA TM4647.
Svehla, RA., 1996, Private communication.

177

REPORT DOCUMENTATION PAGE

I

Form Approved
OMB No. 0704-0188

Public reporting burden for this collection of Information is estimated to average 1 hour per response. Including the time for revlewln~ Instructions, searching existing data sources,
gathering and malntainln~ the data needed, and corrpletlng and reviewing the collection of Information. Send comments regarding t Is burden estimate or any other aspect of this
collection of Information, ncludlng sug'{iestlons for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports 1215 Jetterson
Davis Highway, Suite 1204, Arlington, A 22202-4302, and to the Ottlce of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, oC 20503.

1. AGENCY USE ONLY (Leave blanl<)

12. REPORTDATE

13. REPORT TYPE AND DATES COVERED

June 1996

Reference Publication

4. TITLE AND SUBTITLE

5. FUNDING NUMBERS

Computer Program for Calculation of Complex Chemical Equlibrium
Compositions and Appl; cations
II. Users Manual and Prog1 ill1 Description

WU-505-62-52

6. AUTHOR(S)

Bonnie J. McBride and Sanford Gordon

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

8. PERFORMING ORGANIZATION
REPORT NUMBER

National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135-3191

E-8017-1

10. SPONSORING/MONITORING
AGENCY REPORT NUMBER

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration
Washington, D.C. 20546-0001

NASA RP-1311

11. SUPPLEMENTARY NOTES

Bonnie J. McBride, NASA Lewis Research Center, and Sanford Gordon, Sanford Gordon and Associates, Cleveland,
Ohio. Responsible person, Bonnie J. McBride, organization code 2670, (216) 433-5870.
12b. DISTRIBUTION CODE

12a. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified -Unlimited
Subject Categories 20 and 25
Tiris publication is available from the NASA Center for AeroSpace Information, (301) 621-0390.
13. ABSTRACT (Maximum 200 words)

This users manual is the second part of a two-part report describing the NASA Lewis CEA (Chemical Equilibrium with
Applications) program. The program obtains chemical equilibrium compositions of complex mixtures with applications
to several types of problems. The topics presented in this manual are (1) details for preparing input data sets; (2) a
description of output tables for various types of problems; (3) the overall modular organization of the program with
information on how to make modifications; (4) a description of the function of each subroutine; (5) error messages and
their significance; and (6) a number of examples that illustrate various types of problems handled by CEA and that cover
many of the options available in both input and output. Seven appendixes give information on the thermodynamic and
thermal transport data used in CEA; some information on common variables used in or generated by the equilibrium
module; and output tables for 14 example problems. The CEA program was written in ANSI standard FORTRAN 77.
CEA should work on any system with sufficient storage. There are about 6300 lines in the source code, which uses about
225 kilobytes of memory. The compiled program takes about 975 kilobytes.

15. NUMBER OF PAGES

14. SUBJECT TERMS

Chemical equilibrium; Combustion products; Combustion temperatures; Computer
program; Thermodynamic mixture properties; Thermal transport properties; Rocket
nerformance
17. SECURITY CLASSIFICATION
OF REPORT

Unclassified
NSN 7540-01-280-5500

18. SECURITY CLASSIFICATION
OF THIS PAGE

Unclassified

19. SECURITY CLASSIFICATION
OF ABSTRACT

178
16. PRICE CODE

A09
20. LIMITATION OF ABSTRACT

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