NASA
Reference
Publication
1311
June 1996

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

Bonnie J. McBride and Sanford Gordone~·'· ·~.~ ~~National Aeronautics andSpace Administration

lewis Research Center
Cleveland, Ohio 44135

NASA
Reference
Publication
1311

1996

Computer Program for Calculation ofComplex 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, Ohioat•

National Aeronautics andSpace Administration
Office of Management

SCientific and Technical
Information Program

Contents
Chapter
1. Introductionl

2. Description of Program Input
2.1 General Rules
2.1.1 File Names
2.1.2 Datasets
2.1.3 Keywords
2.1.4 Mandatory Keywords
2.1.5 Optional Keywords
2.1.6 Types of Variables
2.1.7 Delimiters
2.2 Specific Free-form Variables for CEA Datasets
2.3 Dataset reac
2.3.1 Identification and Order
2.3.2 Names of Reactants
2.3.3 Relative Amount of Reactant..
2.3.4 .Reactant Temperature
2.3.5 Assigned Enthalpy or Internal Energy
2.3.6 Exploded Chemical Formula2.3.7 Density of Reactant.
2.3.8 Option To Use thermo.lib
2.4 Dataset prob
2.4.1 Case Identification
2.4.2 Problem Type2.4.3 Fuel-Oxidant Mixture Values
2.4.4 Option To Include Ionized Species
2.4.5 Options for Rocket Problems
2.4.6 Options for Shock Problems
2.4.7 Temperature Schedule
2.4.8 Pressure Schedule
2.4.9 Specific Volume Schedule
2.4.10 Density Schedule
2.4.11 Assigned Enthalpy
2.4.12 Assigned Internal Energy
2.4.13 Assigned Entropy
2.4.14 Assigned Values for Shock Problems
2.4.15 Assigned Values for Rocket Problems
2.5 Dataset out.p
2.5.1 cal
2.5.2 deb (or dbg)
2.5.3 mass f
2.5.4 plot
2.5.5 short
2.5.6 t rae
2.5.7 tran
2.5.8 Examples of outp Datasets

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2.6 Options Involving Species To Be Considered
2.6.1 Dataset only
2.6.2 Dataset omi t
2.6.3 Dataset inse
2.7 Dataset end
2.8 Thermodynamic and Thermal Transport Property Data Bases

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3. Description of Program Output
3.1 Input Data
3.2 Intermediate Input Data
3.2.1 True/False Options
3.2.2 Schedules of Assigned Values
3.2.3 Reactant Information
3.2.4 Species Being Considered
3.2.5 Species With Thermal Transport Properties
3.2.6 Enthalpies and Relative Atoms Per Kilogram
3.3 Tables of Results
3.3.1 Thermodynamic Mixture Properties
3.3.2 Thermal Transport Mixture Properties
3.3.3 Rocket Performance Parameters
3.3.4 Shock Parameters
3.3.5 Chapman- J ouguet Detonation Parameters
3.4 Intermediate Output Data
3.4.1 Number of Iterations
3.4.2 Iteration Matrices and Compositions
3.4.3 Condensed-Phases Test
3.4.4 Derivative Matrices

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4. Modular Form and Modification of Program
4.1 Main Program and BLOCKDATA Module
4.2 General Input Module
4.3 Data-Preprocessing Module
4.4 Applications Module
4.5 Additional Input-Processing Module
4.6 Equilibrium Module
4.7 Transport Properties Module
4.8 Output Module
4.9 Modifications
4.9.1 PARAMETER Statements
4.9.2 Changing Number of Possible Reaction Products
4.9.3 Eliminating an Application
4.9.4 Adding an Application

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5. Routines
5.1 Main Program
5.2 BLOCKDATA
5.3 Subroutine CPHS
5.3.1 General.
5.3.2 Entry ALLCON
5.4 Subroutine DETON
5.5 Subroutine EFMT
5.6 Subroutine EQLBRM
5.7 Subroutine FROZEN
5.8 Subroutine GAUSS
5.9 Subroutine HCALC
S.lO Subroutine INFREE
5.11 Subroutine INPUT
5.12 Subroutine MATRIX

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5.13 Subroutine NEWOF
5.14 Subroutine OUTl
5.14.1 Entry OUT2
5.14.2 Entry OUT3
5.14.3 Entry OUT4
5.15 Subroutine REACT
5.16 Subroutine RKTOUT
5.17 Subroutine ROCKET
5.18 Subroutine SEARCH and Entry READTR
5.19 Subroutine SETEN
5.20 Subroutine SHCK
5.21 Subroutine THERMP
5.22 Subroutine TRANIN
5.23 Subroutine TRANP
5.24 Subroutine UTHERM
5.25 Subroutine UTRAN
5.26 Subroutine VARFMT
6. Error Messages

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6.1 DETON Message
6.2 EQLBRM Messages
6.3 FROZEN Message
6.4 HCALC Messages
6.5 INFREE Messages
6.6 INPUT Messages
6.7 REACT Messages
6.8 ROCKET Messages
6.9 SEARCH Messages
6.10 SHCK Messages
6.11 TRANIN Message
6.12 UTHERM Message
6.13 UTRAN Message
7. Example Problems
7.1 Examples I and 2
7.1.1 Example 1
7.1.2 Example 2
7.2 Examples 3 and 4
7.2.1 Example 3
7.2.2 Example 4
7.3 Example 5
7.4 Example 6
7.5 Example 7
7.6 Examples 8, 9, and 10
7.6.1 Example 8
7.6.2 Example 9
7.6.3 Example 10
7.7 Example 11
7.8 Example 12
7.9 Example 13
7.10 Example 14

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Appendixes
A. Format for Thermodynamic Data
Table A.l.~General Format for Nine-Constant Functional Form
B. Names of Species in Thermodynamic Data File (thermo.inp)
Table B.l.- Names of Gas-Phase Products in thermo.inp
Table B.2.-Names of Condensed-Phase Products in thermo.inp

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Table B.3.-Names of Reactants in thermo.inp
C. Thermodynamic and Density Data for Reactants
Table C.1.-Thermodynamic and Density Data for Reactants
Table C.2.-Reactant Thermodynamic Data in thermo.inp Format.
D. References for Reactant Data in Table C.I
Table D.l.-References for Reactant Data in Table C.I
E. Format and List of Species with Thermal Transport Property Data
Table E.1. - Format for Thermal Transport Property Data
Table E.2.- Viscosity and Thermal Conductivity Coefficientsin thermo.inp
F. COMMON Variables Used in Equilibrium Module
Table F.1.-COMMON Variables That Must Be Initialized Before
Entering Equilibrium Module
Table F.2.-COMMON Variables Calculated by Equilibrium Module
G. Example Problems

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ReferencesviChapter 1

Introduction
This is the second part of a two-part report describing the NASA Lewis ResearchCenter's computer program CEA (Chemical Equilibrium with Applications). The program isused to obtain chemical equilibrium compositions of complex mixtures with applications toseveral 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 mathematicalmethods 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 aI., 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 theirsignificance are discussed in chapter 6. Chapter 7 gives a number of examples that illustratevarious 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 thethermodynamic 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 datain the form of least-squares coefficients for reactants as well as for products. Some of thereactant 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. Mter 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 theyremain available for future use in running problems. Additional information on thethermo.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 databases thermo.inp and trans.inp use approximately 850 and 32 kilobytes, respectively; thebinary forms thermo.lib and trans.lih take approximately 425 and 20 kilobytes, respectively.
These storage requirements for the program and the data files may be easily adjusted as
di scussed in the following chapters.

Chapter 2

Description of Program Input
The CEA program requires two types of input. One type consists of files ofthermodynamic data (thermo.inp) and thermal transport property data (trans.inp), which arecommon 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 aI., 1994). Most of the material in this chapter describes thegeneral 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 weregenerated 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 firstpreprocess 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 ofvariables, 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 fileand the suffix .out. As an option, additional output files of columns of numbers can beobtained for plotting purposes. These files will also be given the same prefix and the suffix
.plt.

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2.1.2 Datasets
All useful program input is divided into sets of records called datasets. The firstrecord of each dataset starts with a keyword. Records that start with the symbols "#" and "1"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, omi t:., inse, out:.p, end, t:.her, and t.ran. Additional characters may be
used in the keywords but will be ignored by the program (e.g., problem is equivalent toprob). 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:
Keywordprob

Data
Problem type and associatedinput (see section 2.4)

reac

Reactant names and associatedinput (see section 2.3)

end

No data. Keyword signals theend of the problem.

2.1.5 Optional Keywords
There are four optional keywords for every problem. Three are always followed byproduct 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 0 species t at are the only
ones to be considered in the problem

omit

Set of names of species that are to beomitted as possible products

inse

Set of names of condensed species to betried (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 characterswill be ignored. The variables are as follows:ype
iteralCharacteri sties
First character is alphabetic.
All initial characters are lower case, with three
exceptions which follow:
Chemical element symbols start with upper-caseletters; the second letter may be either upper orlower 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 (seesection 2.4.1).
Sometimes the program checks for embedded
lower-case character strings as well as initialcharacter strings. For example, the symbol forpressure is p and the embedded string indicates theunits.
Examples:p,barsp(bars)pressure:bars
Numeric

Any legimate integer, decimal, or floating-point
numberSpecies names

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

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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 les (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:problemtpp,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 D atasets
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, andout.p are discussed 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 thereac dataset (see section 2.3.1). Also, any numerics associated with a literal variablemust 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 aI., 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

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subscripts), such as H20 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" formor formula and is discussed in section 2.3.6. Both forms are required in the CEA programand 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; andtemperatures, in section 2.3.4. As in the case for exploded formulas, enthalpies (or internalenergies) may be specified in the reac dataset or optionally obtained from thermo.lib. Somecomparisons 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 initialcharacters: 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
Initialcharacters
fu

Data
Fuel name a lowed by associated dataox

Oxidant name followed by associated datanaName and data of reactant not identified as afuel or oxidant. When name is used in any
particular dataset, all reactants must use thename 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 thisoption 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 dateof publication of this report but is often added to.) For example, Jet-A ( L) and Air

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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 j et-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 ofreactants are relative to total reactant. All values must follow a literal with one of the initialcharacters m orw defined here:
InitialcharacterDatamAmount given in moles. n a particular dataset, if
any reactant amount is given in moles, the otherreactants must be given in moles as well.

w

Amount given in weight fraction or weightpercent. 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 program.

Examples:reac name 02 mole3=.5, _name H2 moles=l, ...

reactant fuel CH4 wt%=30
fuel C6H6 wt%=70oxid Air wt%=10 0 ...
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 productor reactant thermodynamic data files. The temperature value follows a literal that starts with t.
Units are indicated by one of the following embedded characters:

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Em e dedcharacter

Temperature unitkKelvin (default unit if
not specified)rRankinec

CelsiusfFahrenheit

Example:reac fuel ...
oxidant

fuel= ...

t,f=212 ...
t,r=672t,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:
Imtia
character

a ue

h
u

Assigned internal energy

Embeddedcharactersc

Ent alpy orinternal energy unit
Calones per molekc

Kilocalories per molejJoules per mole (default unit
if not otherwise specified)kj

Kilojoules per mole

Examples:reac fuel AA
fuel BBoxid XXh,cal/mol=123.
t,k=445 ...
h,j/mol=-9996.3
t,r=lOOh, k j I rno 1 =556
t , r= 1000 ...

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 theircorresponding relative numbers (stoichiometric coefficients). This information must be partof 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 upperor lower case.
2. Relative numbers may be either integers or fractions.

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

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

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

reac name Water-vapor H20 1 _name Species-X Al 6 Si 4 0 9 ...
name Species-Y C 1 H 1.0769 ...
reac oxid Air N 1.56168 0 .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 isgiven for each reactant in the current prob dataset. (Note that this information is not stored
in the thermodynamic data library.) Each value follows a variz ble starting with the lettersrho, with possible embedded characters to indicate units as follows:
Em eddedcharacters

Density units

kg

ilograms per cubic metergGrams 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 eachreactant 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 thereactant name. If a search for a species in thermo.lib is successful, the exploded formula andenergy 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 Qx=02 wt%=30
Since 02 is in thermo.lib, the exploded formula will be taken from there.

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

reac

ox 02

wt%=30gives error message; a temperature must be specified.

reac

ox 02

wt%=30t,k=300

obtains exploded formula and enthalpy (ENERGY /R=6 . 53777 K) from thermo.lib.

reac

ox=02

wt%=30t,k=300h,j/mol=55

obtains exploded formula and enthalpy (ENERGY /R=6 • 53777 K) from thermo.lib. This isequivalent to 54.3584 J/mol. The value of h, j /mol = 55 in the reac dataset is overridden
because the exploded formula for O 2 was not given.

reacoxid 02

wt%=300 2t,k=300h,j/mol=55

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%=300 3

t,k=300

overrides the exploded formula (given intentionally incorrect as 0 3 in the above reac
dataset) and obtains the correct exploded formula 0 2 and ENERGY /R=6 • 53777 K fromthermo.lib .

reac

ox 02(L)

wt%=30t,k=88selects 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 10 K of the one thermo.lib temperature value of 90.17 K(see section 5.24).

reacoX=02(L)

wt%=30t,k=78gives 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, isrequired when the reactant is not contained in thermo.lib. Otherwise, unless there is somespecial 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.

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2.4 Dataset prob
The dataset prob includes all the input parameters associated with any problem withthe 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 TypeFor every problem one and only one problem type must be specified. The initialcharacters for various types of problems are as follows:
ImtIa
characterstp or pt12

ype of prob em
Assigned-temperature and -pressure
problem

hp or phAssigned-enthalpy and -pressure problem

sp or ps

Assigned-entropy and -pressure problem

tv or vt

Assigned-temperature and -volume (ordensity) problem

uv or vu

Assigned-internal-energy and -volume (ordensity) problem

sv or vsAssigned-entropy and -volume (or density)
problemro or rkt

Rocket problem

shShock problem

det

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:

Va ues

ImtIalcharacters%fPercent

f /0 orFuel-to-oxidant weight ratios

f/a

0/ f

Oxidant-to-fuel weight ratios

phiEquivalence ratios in termsof fuel-to-oxidant weightratios (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

ionscase=20_13

2.4.5 Options for Rocket Problems
The following options are available for rocket performance problems:
Imtla c aracters

fac

ption
Assumes a inite-area combustIOnchamber, f ac. If the area is not
given, the CEA program will default
to the infinite-area combustor
assumption, iac.

eq

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 thecolumn number for freezing
composition. Default is 1 (thecombustion point).

dbg or deb

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

Examples:Calculate rocket performance parameters assuming
both equilibrium compositions during
expansion and compositions frozen at the chambercomposition.
problemrocket equilibrium frozen _prob rkt fac dbg
2.4.6 Options for Shock Problems
The following options are available for shock problems:
Initialscharacters

Optioninc

Calcu ate incident shock parameters.

refCalculate reflected shock parameters.

eqAssume 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 shockincidentfrozenequil reflected _2.4.7 Temperature Schedule
Assigned values of temperature are required for tp or t v problems and for initialvalues 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 startingwith t, with one of the following embedded characters to indicate units:
emperature umt
Kelvin (t e de ault umt ifunits are not specified)rRankinec

CelsiusfFahrenheit

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

tp

problemt(r)=2500,2000 500 _detonationt=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:
Pressure umts

a tm

Atmospheres

ps i

Pounds per square inch absolute

mmhMillimeters of mercury

15

Examples:prob

tp p,bar=1,10,SO _problemrocket 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 typesof problems: tv, uv, or sv. This schedule follows the variable starting with v, with one of thefollowing embedded character strings for units:
Embed edcharacters

Volume umts

kg

ubic meters per kilogram

9

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

Examples:problemtv

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

problemtv

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 tv, 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 edcharacters

DenSIty units

kg

Kilograms per cubic meter9

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

Examples:problem tv rho,g/cc=9.e-OS, 8.e-06, 7.e-07 ...
problemtv

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 hlR (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 u v 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, internalenergies must be in units of ulR (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=1935_

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 siR [g-mole/(g of mixture)].
Example:prob sps/r=1.363 ...

2.4.14 Assigned Values for Shock Problems
Initial Mach numbers (mach) or incident shock velocities (u1) may be assigned forshock 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 anyone particular problem, either parameter may be assigned but notboth.
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 samelength as the u1 (or mach1) schedule, the last value of the t or p schedule will be used to fillin the missing values. Refer to example 7 in appendix G (or the first example below). For thiscase, seven u 1 values, no t schedule, and two pressures are given in the prob dataset. Withno t schedule, the temperature given with the reactants is used throughout. The first pressureis 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 pressureand velocity schedules. Again, if the t schedule is too short, the last t value will be used to fillin any missing values.
Examples:
EXAMPLE

7:.••

problem case=7 p,mmhg=10,20, shock u1=1000,1100,
1200,1250,1300,1350,1400, incd froz eql _17

prob case 21 shock incd eql mach1 = 3, 4, 5,
tlk=298,320,340, p1bar= .01,.02,.03
2.4.15 Assigned Values for Rocket Problems

A number of variables are involved in rocket (ra 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 thosefor 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:
Inittacharacterspvalueshamber pressure (see sectIon .4. )pi...pRatio of chamber pressure to exit pressure (Pinf/Pe or Pini/fe)'
not assignable for chamber and throat (1 to 22 values). (Notethat the second p in pi...p is embedded. For example, pip,
pi/p, pinj /pe, etc.)

sub

Subsonic area ratios (1 to 13 values)supSupersonic area ratios (l to 13 values)

mdot orrna

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

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

Option for freezing composition at the throat (nf z=2) or at asupersonic exit condition (nfz>2). The output table has
equilibrium properties through point nf z and frozen
thereafter. If nfz>2, only NeOL - nfz additional exit
points are allowed (where NeOL 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 benecessary only when a condensed species has been inserted in
an inse dataset and 3800 K is outside its temperature range.)t

Assigned chamber temperature, an option (see section 2.4.7)

Examples:probrocket pi/pe=3,lO,30,300, p,psia=3000, froz
tcest=llOO ...

probrocket p,bar=50, subsonic,ae/at=5,
supersonic,ae/at=lO,20,lOO, nfz=2
equilibrium frozen

problemrocket fac p,atm=50, ac/at=1.58,
supar=2S,SO,75, pi/pe=lO,lOO, _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 (ordbg), massf, 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 forthe output energy unit to be calories.

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

cal deb=5

output deb=1,4,6

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 massf
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 theoutp dataset now specifies that compositions in the final tables are to be given in massfractions.

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. Noalphabetic 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 moredata 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 (equilibriumonly), 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
InitIalcharacters

opertyp

Pressuret

Temperaturerho

DensityhEnthalpyuInternal energygGibbs energys

Entropym

Molecular weight (lin)(eq. (2.3a) in Gordon
and McBride, 1994)

mw

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

cp

Specific heatgam

Gamma(s)sonSonic velocity

2. Thermal transport properties
Initialcharacters
vis

Property
VIscosity

cond

Equilibrium thermal conductivity fromtable of equilibrium properties

cond... fz

Thermal conductivity from rocket
output tables assuming frozen
composition during expansion. (Notethat f z may be embedded anywhere
after initial cond.)

pran

Equilibrium Prandtl number from tableof equilibrium properties

pran ... f z

Frozen Prandtl number from rocket
output tables assuming frozen
composition during expansion. (Notethat f z may be embedded anywhere
after initial pran.)

21

3.

Rocket perlormance parameters-rocket problems only. The following codes are for datafrom 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 thecompositions at the equilibrium freezing point and are therefore not dumped. Whenrocket output tables are more than one page long, the combustion and throat values arerepeated for convenience on pages past the first. However, these repeated values areomitted in the (input prefix}.plt file.
ImtIa
characterspip

4.

Property
Pressure ratio, Pin/Pe for f ac
problems and Pinf/Pe for iac
problems

pi/pSame as pip

mach

Maeh number

aeArea ratio, A/At

cf

Coefficient of thrust, CF

ivac

Vacuum specific impulse, I, ac

isp

Specific impulse, I 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:
Initiacharactersson... 1

Sonic ve oeity

gam... 1

Gamma

h ... 1

Enthalpy

t ... 1

Temperature

p ... 1Pressure

Property

The following strings may be embedded
Embe edcharacters
vel

mach

22

Property
DetonatIon velocity(e.g., ctetvel)
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

t.rac

The option trac instructs the CEA program to print composItions of species withmole or mass fractions greater than or equal to the assigned trace value. When this option isused, 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

t.ran

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 out.p Datasets
Some examples of out.p datasets that use the information discussed in the previous
sections are as follows:

outputtrace=l.e-lO, calories transport short

outp debugcols=1,3
outputtransport

plot=p t C02 vis cond condfz

output trace=l.e-IS
gamfz
outp plot=tl hI
sonicvelplot pi/psonicl t hh ivac N2

Ar cpfz

detvel mach.number

2.6 Options Involving Species To Be Considered
The only, omi t., 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 ami t. datasets are included in the input for the current problem, allgaseous 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 ofcondensed species.) All three datasets must contain species names exactly as given in thethermodynamic 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 productthermodynamic 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

OR

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

C8R17,n-octyl C8H18,isooctane C8H18,n-octane
C9H19,n-nonyl

2.6.3 Dataset ins e
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 aparticular problem.

24

2.8 Thermodynamic and Thermal Transport
Property Data Bases
Inputs for thermodynamic and thermal transport properties are exceptions to the freeform. Generally, they are processed once before running particular problems, and theprocessed data are automatically saved for further use. The format for representing thethermodynamic 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 thesedata bases:
Keywordt.her

Data m succeedmg records
Unprocesse (ormatted) t ermodynamic data.
is input tie IS ca led
thermo.inp. CEA processes the data·from thermo.inp and then automaticallystores 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 processedagain. 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.

t.ran

Unprocessed (formatted) thermal transport property data. This input file iscalled trans.inp. CEA processes the data from this file and then automaticallystores 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 thermaltransport properties of the reaction mixture are desired. Mter tran has beencalled once, it need not be called again.

25

Chapter 3

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 pUfPOses, 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 processedby 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 re a c dataset
4. The out.p 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
datasels. 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 theout.p dataset. Intermediate data that are related to input are discussed in the following
subsections.

27

3.2.1 TruelFalse 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=O.OOOOO. The parameters include

1. Specifying the type of problem (TP, HP, SP, TV, UV, SV, DETN, SHOCK, or RKT), oneof which has been set to " t rue"
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 lor 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 procedurefor f ac 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 beprinted (DETDBG=T)
9. Specifying that thermal transport properties are to be calculated and printed in final tables(TRNSPT=T)
10. Specifying the value for the trace parameter for consideration of minor species. (Thedefault value, TRACE=O.OOOOO, 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, suchas schedules of temperatures and pressures. For rocket problems, a list of assigned values ofarea ratios and lor 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 tosimplify checking the data, if necessary. Some of this information is repeated in the final
output tables.

28

3.2.4 Species Being ConsideredThis 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 becontained in the current problem's chemical system. Each species in the list is preceded bysome identification, such as 112/65. The 1 (or j) refers to 1ANAF 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 forrather than five. If the original data are different, theidentification code will be different.

C;

3.2.5 Species With Thermal Transport Properties
If the option tran is included in the out.p dataset, a list of species is printed forwhich thermal transport property data are contained in the trans.lib file. Also printed arethose 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, fromthe 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. Mter 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
1. Heading
2. Case identification
3. Reactant data
4. Proportion of oxidant to fuel5. Density of reactant mixture if available
6. Thermodynamic mixture properties and derivatives
7. Thermal transport mixture properties (if tran is specified in the out.p 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 (lIn), (aln Vlaln p , (aln Vlaln P)1" c p , Ys' and a. The molecularweight 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 un it is specified in the au 't p dataset. The second set is a mixed set ofunits with energy in calories, temperature in kelvin, pressure in atmospheres, and velocity inmeters per second. This set is obtained when cal is specified in the outp dataset.

n3.3.2 Thermal Transport Mixture Properties
Thermal transport properties of the equilibrium mixture are optionally calculated andprinted if the out.p dataset contains the word tran. 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), theequilibrium 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.] ar d 3.3.2, the rocket problem(rkt or ro) lists the following rocket performance data: PinflPe (for the iac model) or
Pin/Pe (for the f ac model), Mach number, A/at, c*, CF , [vac' and [sp. For the f ac model, theparameters Pin/Pinf and eitherlAc or AclA 1are also listed. These parameters are discussed inchapter 6 in Gordon and McBride (1994).

m

3.3.4 Shock Parameters
In addition to the properties discussed in sections 3.3.] 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 M, u 1' u2' P21P 1, T21T1, M21M1, P2/Pl' and v 2 . For reflected shock waves,the parameters are us' P SIP 2, TsIT2 , M sIM2 , PS/P2' and u S+v 2 .

3.3.5 Chapman-Jouguet Detonation Parameters
In addition to the properties discussed in sections 3.3.1 and 3.3.2, this problem lists
the following properties: PIP I , TIT I , MIMI' p/PI' 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 (de b or dbg in the ou t.p dataset) is
provided primarily as a means of obtaining additional information for debugging. There isusually no point in using this option when the program is working well. We have used thisoption 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 of Iterations

The output discussed in this section is automatically printed for all problems (except
shock problems) unless short is included in the out.p 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 thechemical 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 thecolumns of data in the final tables. (One exception to this, for the f ac rocket. problem, isdiscussed 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 :l'ti (see section 2.3.1 ofGordon 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 ofexample 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 isprinted for each set of temperature and pressure estimates.
As mentioned earlier in this section, the f ac rocket problem is an exception to thestatement 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 datawith 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 forall points specified by the parameter debug in the out.p dataset as illustrated in example 14,
section 7.10 and appendix G. The option debug=5 given in the out.p 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 thewords SOLUTION VECTOR and is followed by a line containing the chemical names of thecurrent components. This line is followed by a line containing the solution vector to thematrix. The next line gives the current values of some parameters, that is, T, n (ENN), In n
(ENNL), P (PP), In(Pln) (LN PIN), and the control factor A (AMBDA). The next group of31

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 Aln nj only for gases but are Anj for condensed species. The
corrections for gases are obtained from the matrix solution and equation (2.18) (forassigned-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 theindividual species includes the chemical name or formula, nj , In nj , dimensionless enthalpy(HOj/RT= ltj IRI), dimensionless entropy (SOj/R=S; IR), dimensionless standard-state Gibbs
energy (GOj/RT=",,; IRT), and dimensionless Gibbs energy (Gj/RT=!-!JR7). Following this isadditional information pertaining to testing for condensed species, which is discussed in thenext section.

3.4.3 Condensed-Phases Test
The test for condensed phases is made after every convergence for equilibriumcompositions. Details of this convergence test are listed with other intermediate output as partof 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 thename, the temperature interval for which thermodynamic data exist, and the current numberof moles of the condensed species. For those species whose temperature interval bands thecurrent 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 thenotation [(GOj - SUM(Aij*Pli)]/M. After all condensed species have been tested, only thatspecies with the largest negative value as shown by MAX NEG UELTA G is included as apossible reaction species, and the iteration procedure is restarted. Dividing the quantity GOj SUM(Aij*Pli) 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) andtheir 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 withrespect to temperature follows the notation T DERIV MATRIX and is followed by thenotation 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 forthe 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 VIm, respectively.)32Chapter 4

Modular Form and Modificationof Program
To facilitate adding or deleting applications of the program, CEA was organized into
eight modules. These modules are concerned with general input, preprocessing ofthermodynamic 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 fromfigure 4.1, it is clear that, for example, the rocket application could be eliminated by omitting
subroutines ROCKET, 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

~

I

INPUT
INFREEREACT
SEARCHREADTR

Preprocess data-

UTHERM
UTRAN,
Additional input
processing

Applications(1) tp, hp, sp, tv, uv, sv
problems ~~THERMP(2) Rocket problems -ROCKETFROZENRKTOUT(3) Shock problems -SHCK(4) Detonation problems -DETON

-

--

~

NEWOF
SETEN
HCALC

-..

Output
OUT1
OUT2
OUT3
OUT4
EFMT
VARFMT

Transport
properties
TRANINTRANP

Figure 4.1.-Program modules.

34

Equilibrum
EQLBRMCPHS
ALLCONMATRIXGAUSSSEARCH (READTR)

INPUT

-E

UTHERMUTRAN
INFREEREACT
NEWOF

CPHS (ALLCON)
MATRIXGAUSSVARFMT
L-- EFMTE

EQLBRM - - - - - - - - - - .
THERMP
OUTl (OUT2, OUT3, OUT4)-----r--SETEN
TRANP ----------~r_ TRANIN
L - GAUSS
NEWOF
CPHS

E

EQLBRM - - - - - - - - - - .
SHCK--4--- HCALC

CPHS (ALLCON)
MATRIXGAUSSOUTl (OUT2, OUT3, OUT4) - - - - - . - VARFMT
L - EFMT
SETEN
TRANP
TRANINL - GAUSS

main-----------,r_

E

NEWOF
EQLBRM - - - - - - - - - - - . . . . ,DETON- + - - HCALC
OUTl (OUT2, OUT3, OUT4)CPHS (ALLCON)
MATRIXGAUSS-----C VARFMT
EFMT

SETEN
TRANP

- - - - - - - - - - r - TRANINNEWOFEQLBRM-E

L-- GAUSS

CPHS (ALLCON)
MATRIXGAUSSFROZENCPHS
ROCKET - - + - - RKTOUT - - . - - - - - - OUTl (OUT2, OUT3, OUT4) - , - - VARFMTL-VARFMT
L-EFMIT
SETEN
TRANP

- - . - - - - - - TRANIN
L - 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 tocharacter 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 thetrans.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 thethermodynamic 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 fromROCKET (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:
1. NEWOF-to adjust the initial variables that vary with assigned fuel-oxidant ratios. Thesevariables include values of biD , Po' T, and either uo'lR or haiR for each oxidant-to-fuelratio. (The variables are defined in Gordon and McBride, 1994.)

2. SETEN -to obtain initial estimates for composition and temperature for a current pointfrom a previously calculated point
3. HCALC-to calculate thermodynamic properties of the reactant mixture for shock anddetonation 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 aparticular point Npt. The module is controlled by subroutine EQLBRM, which calls threesubroutines and one entry:
1. 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:
1. Table Fl.-COMMON variables that must be initialized prior to entering the equilibrium
module2. 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 theequilibrium 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

lOSCH, 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 OUfI,with three entries, OUT2, OUT3, and OUT4. OUTI lists data given in the reac dataset as wellas olf, %F, r, and Po- OUT2 lists the properties P, T, p, h, s, (rJ In via In P)7' (0 In via In T)p' cp 'Ys' and a. (The variables are defined in Gordon and McBride, 1994.) OUT3 lists equilibriummole or mass fractions of the reaction species. OUT4 lists the transport mixture properties 11,
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 CI,A 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 thenumber 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 aredefined as follows:
Parameter
MAXNGC

Varia Ie or WhlC maximum number IS set
pecies t at can be considered In any pro em.
For condensed species, each temperature intervalof a species counts as a separate species.

MAXNG

Gaseous products that can be considered in any
problem

MAXNC

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

MAXTR

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

MAXEL

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 rinted on a pa e

The numbers to which these parameters are set depends to a large extent on the natureof the problems to which the CEA program is applied. Currently, for the large-scale computerversion of CEA, we are using slightly larger numbers than the largest number required in anyof 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

MAXNC

300

200

MAXTR

50

40

MAXEL

20

15

MAXMAT

50

40

MAXR

24

24

NCOL

13

7 or 839

The names and current assigned values of input/output units in the parameter
statements are as follows:
urrentvalue

File typeontents

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 numericalparameters dumped for plotting purposes

IOTRN

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 forthese parameters for the small-scale version (see previous section) accommodate mostproblems. 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
100 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 callingthe controlling subroutine (THERMP, ROCKET, SHCK, or DETON) and then removing thesubroutine (or subroutines) in the application module. The calling statements are near the endof 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 (110) unit numbers andcorresponding files for the entire program. The standard input file uses I/O unit 5. All
input data files are required to have the suffix .inp. The standard output file uses I/Ounit 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 tran is included in theout.p dataset. Thermal transport data are read in READTR from input/output unit
10TRN, 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.1
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 typefound in the prob dataset.

5.2 BLOCKDATABLOCKDATA 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 andfrom 1 to NCOL associated numbers. NCOL is set by a PARAMETER statement to be thenumber 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: Coef(j,i,l) for the temperature interval Tg(1) toTg(2); Coef(j,i,2) for the interval Tg(2) to Tg(3); and Coef(j,i,3) for the interval Tg(3) toTg(4). The index j (j=I,Ng) refers to the jth gaseous species among the Ng gaseous species
being considered in the current chemical system, and the index i (i=I,9) refers to the ithcoefficient. 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 theith coefficient, and ii is for the temperature interval (jj=I,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 in COMMON arrays Cp, HO, and S,
respecti vel y.

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 ortemperatures 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 equilibriumcompositions and mixture properties for point (output column) Npt. It is called from one of
the application routines THERMP, SHCK, DETON, or ROCKET. Subroutine EQLBRM, inturn, 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 ofcomposition. The COMMON variables that need to be set before entering EQLBRM aretabulated in appendix F (table F.l).
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 andthermodynamic properties for the following assigned theoretical rocket performance
conditions:43

1. Composition frozen at either combustion (Nfz=I), 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 ofGordon 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 arelisted.

5.8 Subroutine GAUSSSubroutine GAUSS is called from subroutine EQLBRM to solve the set ofsimultaneous linear iteration equations constructed by subroutine MATRIX. It is also calledfrom subroutine TRANP to solve the simultaneous linear equations needed to obtain the
mixture thermal transport properties. The simultaneous equations are solved by using amodified pivot technique to perform a Gauss reduction. In this modified pivot technique,only rows are interchanged. The row to be used for eliminating d variable is selected on thebasis 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 RCALC
Subroutine HCALC calculates thermodynamic properties for gaseous reactants inshock and detonation problems. It is called from subroutines SRCK and DETON only when
there is a t schedule in the prob dataset. If the reactants are species that are included in thefirst part of thermo.lib (containing data for products), the thermodynamic coefficients will
have already been stored in the common variable CoefU,i,k), and these coefficients will be
used to obtain the required thermodynamic properties. If the coefficients are in the last partof 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 Coefarray. The first index in this array indicates the species number. For the reactants thesenumbers are stored in the Jray array for future use. Subroutine RCALC also calculates theproperties of the reactant mixture. The mixture properties haiR, co/R, and solR (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 "#H or an "!". Character strings are formed byconcatenating 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 Iiteral.
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:
Variab e
Codeescription
Cin( 1) assumed to be the keyword

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

Cin

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

Ncin

Number of variables stored in Cin

Lcin

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 anegati ve sign.
2. If CinO) is numeric, Lein(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 thefree-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 areprocessed and stored as follows:
1. For the keywords only, inse, and omi t., species names are stored in the COMMON
variables Prod, Ensert, and Omi t, respectively.
2. For the keywords outp, reac, and prob, the dataset information stored by subroutine
INFREE in the Cin, Lcin, 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 reacdata.
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 ou'tp, 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 .plt.
7. For the keyword end, after some additional processing, control is transferred to the main
program.

5.12 Subroutine MATRIXSubroutine 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). Thesematrices 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. t p (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. tv (assigned temperature and volume or density) (Tp=. TRUE. ,Vol=. TRUE.)b. uv (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 isfalse for these three problems.
3. The matrix in table 2.3 corresponds to the equations for calculating derivatives withrespect 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=I,Npr). The appropriate contribution of eachspecies is summed into the matrix elements.

5.13 Subroutine NEWOF
Subroutine NEWOF combines the properties of total oxidant and total fuel (calculated
either in subroutine REACT or subroutine HCALC) for a particular oxidant-to-fuel ratio togive properties for the total reactant. NEWOF is called from either THERMP, ROCKEr,
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
McBride (1994). Values of b;2), bi1), and biD (eqs. (9.1) and (9.5» are printed for all
problems. For problems with an assigned pressure, values are printed out for h(2)IR, h(1)JR, andhaiR (eqs. (9.6) and (9.7) multiplied by 1). For problems with an assigned volume or density,
values are printed out for (u,)(2) JR, (u,)(l) /R, and u o' /R (eq~. (9.8) and (9.9) multiplied by 1).
The initial value of the Size variable discussed in section 3.2 of Gordon and McBride (1994)
is set in NEWOF. Adjusting Size for the value of Bratio is also done in this routine.

5.14 Subroutine OUTI
Subroutine OUTland entries OUT2, OUT3, and OUT4 write statements in the final
output tables that are common to all problems. They are called from subroutines THERMP,ROCKET, DETON, and SHCK. Subroutine OUTl writes the following information:
1. Case name or number
2. Reactant names and properties
3. Mixture values (oxidant-to-fuel ratio, percent fuel, and the two equivalence ratios definedin equations (9.18) and (9.19) of Gordon and McBride, 1994)
4. Reactant densities (if values are included in the input)

5.14.1 Entry OUT2
Entry OUT2 writes the final tables of the thermodynamic mixture properties andstores any requested plot data in the Phout array. These variables and their correspondinglabels are printed horizontally across the page with a variable format. Some format
adjustments are made by calling subroutines VARFMT and EFMT. The maximum number of47

columns of data on a page will vary depending on how the NCOL parameter is set in the
PARAMETER statements. For wider paper, NCOL=13 works well. For 8 1I2xl1-in. paper
NCOL=7 works well.
The data that are dumped into the PItout array are in the same units as the labeledlisted data. They are listed vertically, however, rather than horizontally and there is noalphabetic output. The columnar data are in the same order as requested in the outp dataset.
The PItout array is dimensioned for eight parameters, each with 100 values. Mole or massfractions may also be dumped into Pltout (see section 5.14.2).

5.14.2 Entry OUT3
Entry OUT3 writes product species names and equilibrium mole or mass fractions forthe final tables. If any product names are listed for plotting, their mole or mass fractions will
be dumped into the Pltout array in columns rather than in the horizontal form shown in thetables. All species are listed that have mole or mass fractions for at least some of the assigned
6conditions which are either greater than 5xl0- or greater than the trace value if trace isgiven in the outp dataset. Unless the short output option has been specified, the names ofthe species with mole or mass fractions less than this amount for all assigned conditions will
be listed at the end of the table. With the trace option, subroutine EFMT is called forprinting mole or mass fractions in an E-format in order to retain more figures.

5.14.3 Entry OUT4
Entry OUT4 writes the values of thermal transport mix' ure properties in the final
tables and also stores any of these properties that are requested for plotting purposes. The
comments in the last paragraphs of sections 5.14.1 and 5.14.2 pertaining to number ofcolumns and dumping for plotting purposes apply to transport properties as well.

5.15 Subroutine REACT
Subroutine REACT is called from subroutine INPUT to further process reactant data.
Subroutine REACT does the following for each reactant:1.

Searches the thermo.lib file for a species with the same name as the reactant if one of thefollowing is true:a. The exploded formula is missing.
b. An assigned enthalpy value is missing for a rocket or hp problem.
c. An assigned internal energy value is missing for a u v problem.
For the case where thermo.lib has data for only one temperature (usually a transition
point or 298.15 K), the temperature given in the input must be within 10 K of thethermo.lib value. Otherwise, the program will print a fatal error message. Some examples
are given in section 2.3.8.

2.

Calculates the enthalpy or internal energy from the coefficients in thermo.lib for (lb) or(Ic) above.

3.

For each new chemical element for the current problem, obtains the following data from
BLOCKDATA (section 5.2) and stores them in their corresponding arrays: chemical48

symbol in Elmt, atomic weight in Atwt, and valences in temporary storage. These valances
are then used to calculate plus-and-minus valances for both total fuel and total oxidantthat are stored in Vpls and Vmin (see eqs. (9.14) and (9.15) in Gordon and McBride,1994).
4.

Calculates the molecular weights of total oxidant lvI!) and total fuel tvf2) and stores values
in the Am array (see eq. (9.10) in Gordon and McBride, 1994).

5.

Determines if the reactant is labeled oxid, fu, or na. Reactants labeled na and fu aretreated alike during further processing. Program variables relating to oxidants or fuels areindexed 1 for oxidants and 2 for fuels.

6.

Adds the reactant contribution to the total oxidant or total fuel properties (see chapter 9of Gordon and McBride, 1994).

If there are several reactants labeled fu or na, their properties are combined into
properties of a total fuel by using the relative proportion of each fuel given in the reac
dataset. Labeled oxidant species are also combined. These total fuel and oxidant values arelater combined with oxidant-to-fuel ratio values in subroutine NEWOF to obtain total reactant
properties. Equation (9.12) in Gordon and McBride (1994) gives the density of total oxidantpO) (Rh( 1) and total fuel p(2) (Rh(2». H anyone of the densities used in equation (9.12) IS
zero, Rh(I)=Rh(2)=O.

5.16 Subroutine RKTOUT
Subroutine RKTOUT is called from ROCKET. It is the control program for wntmg
the final output tables for rocket problems. It calculates various rocket performanceparameters from previously calculated and stored thermodynamic mixture properties. It also
stores any requested plot data involving rocket performance in the PItout array. It calls
subroutine OUT 1 and entries OUT2 and OUT3 to write output common to all problems. The
rocket parameters are printed with the variable format Fmt described in section 5.2.

5.17 Subroutine ROCKET
Subroutine ROCKET is the control program for rocket performance calculations
described in chapter 6 of Gordon and McBride (1994). It is called from the main program if
the problem type rkt or ro is included in the prob dataset. Subroutine ROCKET selects
the appropriate iteration scheme for the assigned combustion chamber model f ac or iac. It
obtains the required thermodynamic properties for equilibrium performance by calling
subroutine EQLBRM. For frozen performance, subroutine ROCKET calls subroutine
FROZEN to obtain the required thermodynamic properties. It ·calls subroutine TRANP to
obtain thermal transport properties if trn or tran has been included in the ou'tp dataset.
The assignment of parameters for various points in the rocket problem is handled byvarious loops. An outer loop calls NEWOF for each new value of oxidant-to-fuel ratio.
Another loop assigns chamber pressures. Within this loop are other loops for assigned exit
conditions. For the exit conditions, assigned pressure ratios, if any, are processed first; then,assigned subsonic area ratios, if any; and finally, assigned supersonic area ratios, if any.
Subroutine RKTOUT is called for preparing output tables when either a page is filled(Npt=NCOL) or all exit points have been calculated for equilibrium compositions first andthen for frozen compositions.

49

5.18 Subroutine SEARCH and Entry READTR
Subroutine SEARCH is called from the main program to search the thermo.lib file forthermodynamic data of possible products appropriate for the current chemical system. Data
for all these species will be stored for consideration except for two situations:
1. When an only dataset specifies the species to be considered
2. When an ami t. dataset specifies the species to be omitted
For those selected species, the names are stored in the ProdU) array, where j is the
species index; the stoichiometric coefficients (index i) are stored in the A(i,j) array; and thethermodynamic coefficients (index i) are stored in the CoefU,i,k) array for gases (where k is
the temperature interval index) and in the CftU,i) array for condensed species. Since gases
precede condensed species in thermo.lib, their names come first in the Prod(j) array. These
names have a limit of 15 characters. The data for reactants only, which appear in thermo.lib
after the data for all the products, are not stored in subroutine SEARCH but are stored insubroutine REACT. For condensed species, the name (including the phase), as well as thethermodynamic coefficients, is stored for each temperature interval. The total number ofthese stored condensed species names or temperature intervals is Nc. Therefore, the total
number of stored names Ngc, including gases and condensed species, is Ngc=Ng + Nc. (Ngc
is also the total number of gaseous species and condensed-phase temperature intervals.) Since
the maximum values of Ng and Nc are MAXNG and JrIAXNC, respectively, thethermodynamic coefficients are dimensioned Coef(MAXNG,9,3) and Cft(MAXNC,9). If theshort option is not used, the names in the Prod array are listed along with the date code
stored with the data in thermo.lib.
If tran has been included as an option in the out.p dataset, entry READTR is calledfrom the main program to read thermal transport properties from trans. lib (stored on
input/output unit IOTRN). Data for species with the same names as contained in thethermodynamic property data (ProdO» are stored in a scratch file IOSCH (I/O unit 13) for
use in calculating mixture properties. Additional processing of thermal transport properties isdiscussed in section 5.22.

5.19 Subroutine SETEN
Subroutine SETEN is called from an application subroutine such as THERMP, SHCK,DETON, or ROCKET. It has several functions, all of which are concerned with saving some
information from a completed calculation for subsequent use in later calculations. The
primary purpose is to have reasonably good initial composition estimates for new points.
These estimates for the next point Npt come from either the point just completed Isv
or some other previous point. The flow of the routine is directed by Isv as follows:
1. Isv positive-transfers compositions for the point just completed for use as initial
estimates for the next point (transfer EnU,Isv) to EnU,Npt»
2. Isv negative-makes Isv positive and saves values of EnlnG) for gases and En(j,Isv) for
condensed phases in SInG), Enn in Ensave, Ennl in Enlsav, Ttt(Isv) in tsave, and Lsave inlsav. (These values are saved because they are to be used as initial estimates for somefuture point and they may be overwritten in the meantime.) Values in EnG,Isv) aretransferred to EnG,Npt). If the Isv point has two included condensed phases of the species,
the indices for these species will be Jliq (for the higher temperature phase) and Jsol (for50the lower temperature phase). For this situation, En(Jliq,Isv) is combined with En(Jsol,Isv)
and En(Jliq,Isv) is excluded. This procedure usually helps in obtaining convergence forthe next point and other future points that start with the saved estimates.
3. Isv zero~uses the data previously saved (as discussed in (2) above) as initial estimates forthe current point.

5.20 Subroutine SHCK
Subroutine SHCK is the application module for shock problems. It is called from themain program and calls the following subroutines: NEWOF, CPHS, EQLBRM, HCALC,
OUTI, OUI2, OUT3, OUT4, SETEN, and TRANP. When initial temperatures are given in the
prob dataset, subroutine HCALC is called to get the thermodynamic properties of the initial
mixture. It calculates the shock parameters discussed in chapter 7 of Gordon and McBride(1994). For every assigned mixture, subroutine SHCK calculates properties for as many as
NCOL assigned initial velocities or Mach numbers. NCOL is the number of columns in the
output listing- generally, 7 or 8 for 8 I/2x II-in. paper and 13 for wider computer paper.
Depending on the input options specified in the prob dataset, it calculates incident shockconditions based on equilibrium compositions after shock and/or based on compositions
frozen at initial conditions. It also calculates, on the basis of specified options, frozen and/or
equilibrium reflected shock conditions relative to the equilibrium and/or frozen incident
shock conditions.

5.21 Subroutine THERMP
Subroutine THERMP is called from the. main· program to execute tp, hp, sp, tv, uv,
and sv problems. Since EQLBRM calculates equilibrium compositions and mixture
properties for one point at a time (see sections 2.3 and 2.4 of Gordon and McBride, 1994),
THERMP sets up the necessary parameters for each point. This involves all combinations ofoxidant-to-fuel ratios for all problems; assigned pressures for t p, hp, and s p problems;
assigned volumes (or densities) for tv, UV, or sv problems; and either the estimated orassigned temperatures for all problems.
These parameters are assigned by means of three nested DO loops. The outermost
loop is the Nof array of oxidant-to-fuel ratios. For each of these ratios, subroutine NEWOF iscalled to obtain the reactant mixture properties. The next loop is for the Np assigned
pressures or volumes. Finally, the innermost loop is for temperature. For t p and tv
problems, there are Nt assigned temperatures. For hp~ sp, UV, and sv problems, Nt=I and
the initial temperature estimate for the first point is 3800 K. Succeeding initial estimates for
new points are taken from the results of previous points. Subroutine EQLBRM is called in thetemperature loop. Following the EQLBRM call, subroutine TRANP is called to calculate
thermal transport properties if the tran option was included in the outp dataset. The initial
estimate routine SETEN and the output routines OUT I , OUT2, OUT3, and OUT4 are calledat appropriate times.

5.22 Subroutine TRANIN
Subroutine TRANIN is called from subroutine TRANP for each point to perform thepreliminary steps for calculating thermal transport properties of the current mixture.

51

TRANIN first determines which species have the largest mole fractions. It next reads in theproperties for these largest individual species and binary interactions containing these species
from input/output unit lOSCH, estimates missing data, and eliminates species unimportant fortransport property calculations. Subroutine TRANP then solves the necessary equations to
obtain the thermal transport mixture properties.
Some processing accomplished in TRANIN is as follows:
1. For shock problems with the frozen composition option, mole fractions of the reactants
are calculated and their thermal transport data are stored.

2. The En array is searched for atomic gases and species whose mole fraction is greater thanll
IxlO- . The indices of the selected species are stored in the Ind array, with indices for theatomic gases stored first, followed by indices of other species stored generally in order oflargest species first. A maximum of MAXTR species is allowed, where the number for
MAXTR is set in a PARAMETER statement.
3. Mole fractions are recalculated by using only the compositions of the selected species.
4. Stoichiometric coefficients from the A array are copied into the Stc array in order toexpress them as a set of chemical reaction equations as required in equation (5.10) of
Gordon and McBride (1994).
5. Thermal transport properties from input/output unit IOSCH are read in for the selected setof species. IOSCH is a scratch unit with properties for specief', appropriate to the current
chemical system. IOSCH was written in entry READTR (subr )utine SEARCH).
6.

Estimates for thermal transport properties are made for those selected species for which
no data exist in IOSCH. For neutral species, the estimating formula is
-(22)
Q..
=In (50M/"~
1
]J

T .4

This formula is a slightly modified version of equation (39) of Svehla (1973). It is usedin equation (7c) in Svehla (1973) to obtain viscosity. For ionized species or ion-neutral
pairs, estimating formulas were taken from Gupta et al. (1990).

5.23 Subroutine TRANP
Subroutine TRANP calculates mixture thermal transport properties as described in
Gordon and McBride (1994). It is called only if the term tran has been included in theoutp dataset in the standard input file. In that case, it is called for every point from one of
the application routines, namely DETON, ROCKET, SHCK, or THERMP. Subroutine
TRANIN is called to read in or estimate thermal transport property data for pure species orpairs of species. The reaction contribution to thermal conductivity and heat capacity involves
solving sets of simultaneous linear equations. The matrix elements for these equations arecalculated in subroutine TRANP, and subroutine GAUSS is called to solve the equations.

52

5.24 Subroutine UTHERM
Subroutine UTHERM is called from subroutine INPUT after the keyword t.hermo isread. UTHERM reads thermodynamic data from thermo.inp, which is a formatted (text)
standard input file (i.e., input/output unit 5). For. the most part, the data are in the form ofleast-squares coefficients as discussed in section 4.2 of Gordon and McBride (1994).
Data are stacked in thermo.inp in the following order:
1. Keyword t.hermo
2. Temperature intervals for the gaseous species
3. Sets of data for the gaseous product species
4. Sets of data for the condensed product species
5. END PRODUCTS record
6. Data for reactants only
The format for these data is given in appendix A.When subroutine INPUT reads the
keyword t.hermo in the main program, it calls subroutine UTHERM to process thethermodynamic data that follow and to store them for further use in unformatted form in thethermo.lib file (input/output unit IOTHM). Input/output unit IOSCH is a scratch unit that isused in connection with the processing of the thermodynamic data. UTHERM sorts andcounts the number of species sets. The sorting process stores all gaseous species ahead of allcondensed species. The total number of gaseous species is stored in Ng, and the total numberof condensed-phase temperature intervals is stored in Nc. (Note that each condensed-phase
temperature interval is counted as a separate species.) The index Ngc contains the sum of theother two indices (i.e., Ngc=Ng + Nc). The current CEA program allows for threetemperature intervals for gaseous species and a variable number of intervals for condensed
phases. The standard set of gaseous species data that accompanies the CEA program isdivided into the following three temperature intervals: 200 to 1000 K, 1000 to 6000 K, and6000 to 20000 K. However, most gaseous products exist in negligible amounts above
6000 K, and therefore no thermodynamic data are provided for the highest temperatureinterval for most of the species. During the iteration process, to obtain equilibriumcompositions in the highest temperature interval,. it may be necessary to have the missing
thermodynamic data, at least temporarily, in order to obtain convergence. Subroutine
UTHERM estimates these missing data by means of a straight line for Cpo The equation forthe straight line is generated from the values of Cp at 6000 and 20 000 K, using the classicalvalue at infinity for the value at 20 000 K.
The data for reactants are stored after the data for gaseous or condensed products.
For some reactants, thermodynamic data (in the form of coefficients) are given over atemperature range. For other reactants, only one assigned enthalpy value is given at somespecified temperature (usually 298.15 K or some transition temperature). For example, for02(L), only one enthalpy value is given (at the boiling 'point of 90.17 K).
Any set of thermodynamic data needs to be:. read in and processed only once. Ifchanges are made to the data, by adding, removing or changing data for various species, the
new set will need to be read in. (However, data; for, one or more species may also be omitted
from consideration during any particular run without reading in a new dataset by the use of
the omi t. and only input datasets.)53

5.25 Subroutine UTRAN
Thermal transport property data (viscosity and thermal conductivity) are read asformatted data from standard input (i.e., input/output unit 5). The data are in the form ofleast-squares coefficients as discussed in chapter 5 of Gordon and McBride (1994).
Subroutine UTRAN processes these data and stores them for further use in unformatted formin the trans.lib file (input/output unit IOTRN). Input/output unit IOSCH is a scratch unit thatis also used in processing the transport property data. Subsequently, in entry READTR(subroutine SEARCH), transport data for the current chemical system under consideration are
stored in input/output unit IOSCH.

5.26 Subroutine VARFMT
Subroutine VARFMT (variable format) is called from entry OUT2 and subroutine
RKTOUT. It adjusts the number of decimal places printed in F-format in the variable format
Fmt according to the size of the number. It is used for Pinf/Pe or Pin/Pe. P, and Ae/A t. The
variable format is described in section 5.2.

54

Chapter 6

Error Messages
This chapter contains a list of error messages and warnings and some discussion
concerning them. The messages are grouped in alphabetical order within each subroutine inwhich they appear. The name of the subroutine is given in parentheses at the end of eachmessage.

6.1

DETON Message

CONSERVATION EQNS WERE NOT SATISFIED IN 8 ITERATIONS (DETON)
Fatal error. Conservation equations for the detonation problem usually converge inthree or four iterations. The program limits the number of iterations to eight, although wehave never run a problem that required this many iterations. Therefore, we have not yet seen
this message printed. If the message were to be' printed, the program would skip to the next
problem.

6.2 EQLBRM Messages
CALCULATIONS STOPPED AFfER POINT (number) (EQLBRM)
If a fatal error occurs in subroutine EQLBRM, this message will be printed, output
tables for any completed points will be printed, and control will be returned to the main
program, which continues with the next problem, if any.

(Number of) CONVERGENCES FAILED TO ESTABLISH SET OF CONDENSEDSPECIES (EQLBRM)
Fatal error. The CEA program will attempt to obtain the correct set of condensed
species up to 3 x Nlm times, where Nlm is the number of chemical elements in the system. If
the program is unsuccessful after this number of attempts, this message will be printed as wellas the previous message.

DERIVATIVEMATRIX SING ULAR (EQLBRM)
If singularities occur in the matrix solutions, they generally occur first in the iteration
matrices and the program does not get as far as the derivative matrices. However, it is possible
for the iteration matrix to just barely avoid being singular and for the derivative matrix to be55

singular. When this occurs, this message is printed, Dlvpt is set equal to -1, Dlvtp is set equal
to 1 (see appendix F for definitions), and the program continues.

DID NOT CONVERGE ON ELECTRON BALANCE (EQLBRM)
Fatal error. As discussed in section 3.7 of Gordon and McBride (1994), a special
iteration procedure is used for ions. For all problems tried, this procedure has been successful
in meeting the convergence criterion for ions. In the event convergence is not reached, thismessage is printed as well as the first EQLBRM message.

(Number of) ITERATIONS DID NOT SATISFY CONVERGENCE REQUIREMENTS
FOR THE POINT (Number) (EQLBRM)
Fatal error. The maximum number of iterations permitted to obtain convergence iseither 50 + Ns/2 if trace is included in the outp dataset or 50 otherwise. Generally,
convergence is obtained in considerably fewer iterations. The number 50 + Ns/2 wassomewhat arbitrarily selected to indicate that, if convergence has not been reached by that
number, the problem probably will not converge at all. This situation occurs rarely. When it
occurs, this message is printed, as well as the first EQLBRM message. If the cause ofnonconvergence is not obvious from the output, it may be helpful to rerun the problem withintermediate output. An examination of this output often pinpoints the source of the
difficul ty.

LOW TEMPERATURE IMPLIES A CONDENSED SPECIES ~HOULD HAVE BEEN
INSERTED. RESTART WITH inse rt DATASET (EQLBRM).
Fatal error. This message can occur only for an hp or uv problem. It occurs only
when the omission of an important condensed reaction product causes the program to seek a
combustion temperature that is unrealistically low (T < 100 K). When this occurs, the message
is printed as well as the first EQLBRM message.

REINSERTION OF (name of species) LIKELY TO CAUSE SINGULARITY (EQLBRM)
Fatal error. In the process of inserting and removing condensed species, the program
may attempt to insert a condensed species that it had just removed during the previous
iteration cycle. To prevent a possible infinite cycle, this message is printed as well as the first
EQLBRM message.

SINGULAR MATRIX, ITERATION (number) VARIABLE (number) (EQLBRM)
This message is printed whenever a singularity occurs during the matrix solution. As
discussed in section 3.6 of Gordon and McBride (1994), several procedures are used in
special singularity situations to obtain convergence. If none of the special techniques resolve
the problem, the first EQLBRM message is also printed.

THE TEMPERATURE = (degrees K) IS OUT OF RANGE FOR POINT (number)(EQLBRM)
Except for the shock problem, this message is printed whenever the converged
temperature for the indicated point is outside the temperature range read in on the second
record of the thermo.inp file. This temperature range, which at present is 200 to 20 000 K, isthe one over which some of the gas-phase thermodynamic data have been fitted. Generally,56

the thermodynamic data can be extrapolated a short distance without much loss in accuracy.
However, to prevent large errors due to extrapolation, the current temperature Tt is not
permitted to be less than a factor of 1.5 below the lowest temperature in the range or morethan a factor of 1.25 above the highest temperature in the range. If temperature is outsidethese limits, then after the above message has been printed, the first EQLBRM message is also
printed.

TRY REMOVING CONDENSED SPECIES (EQLBRM)
As discussed in section 3.6 of Gordon and McBride (1994), several techniques aretried to obtain convergence after a singularity has occurred. This message is printed under thefollowing circumstances: a singularity has occurred, the technique of adding small quantitiesof species to resolve the singularity has failed, and at least one condensed species is among
the species currently being considered in the calculations. The CEA program then removes
the first condensed species in the current array and makes another attempt at convergence.

WARNING! POINT (number of point) USES A REDUCED SET OF COMPONENTS.
SPECIES CONTAINING THE ELIMINATED COMPONENT ARE OMITTED. IT MAY
BE NECESSARY TO RERUN WITH INSERTED CONDENSED SPECIESCONTAINING COMPONENT (name of eliminated component) (EQLBRM)
After a component has been eliminated, it may be impossible to test for the possible
presence of other condensed species containing the eliminated component. For this situation,.
as suggested by the message, it may be desirable to rerun with an insert of the condensed
species to be considered.

WARNING!! RESULTS MAY BE WRONG FOR POINT (number) DUE TO LOW
MOLE FRACTION OF GASES (value of molar gas fraction) (EQLBRM)
As discussed in section 2.2 of Gordon and McBride (1994), the equation of state forgases is assumed to be correct even when small amounts of condensed species (up to several
percent by weight) are present. When the mole fraction of gases is less than 0.0001, theprogram prints this warning message and continues.

6.3 FROZEN Message
FROZEN DID NOT CONVERGE IN 8 ITERATIONS (FROZEN)
Rocket calculations based on frozen composition during expansion generally requirefrom one to four iterations to reach convergence for each assigned point. We have not yet
encountered a problem that required eight iterations. This error message was incl uded
primarily as a precaution to avoid infinite cycling of the iteration loop in the event of amachine error. The CEA program continues after printing this message.

57

6.4 BCALC Messages
COEFFICIENTS FOR (name of reactant) ARE NOT AVAILABLE (HCALC)
Fatal error. Reactant has thermodynamic data for only one temperature. Since shock
and detonation problems permit more than one temperature in the temperature schedule,
thermodynamic coefficients are needed to calculate thermodynamic properties. Control isreturned to the main program, which continues with the next problem, if any.

REACTANT (name of species) NOT FOUND IN thermo.lib (HCALC)
Fatal error. Reactant was not found in the thermodynamic library, thermo.lib. Checkfor possible errors in reactant name. If the data are not in the library, the problem may still be
run if all necessary infonnation is given in the reac dataset. Control is returned to the main
program, which continues with the next problem, if any.

REACTANTS MUST BE GASEOUS FOR THIS PROBLEM (ReALC)
Fatal error. Subroutine RCALC is used only for those detonation and shock problems
for which reactants must be gaseous. Control is returned to the main program, which
continues with the next problem, if any.

6.5

INFREE Messages

FATAL ERROR IN INPUT FORMAT (INFREE)
The CEA program was unable to decipher the line of input preceding this message. If
it occurs, control is returned to the main program, which terminates further calculations.

WARNING!! UNACCEPTABLE NUMBER (value of number) (INFREE)
An illegal numerical variable was found. Possibly alphabetical characters were mixed
with numbers. The variable is ignored and the program continues.

6.6

INPUT Messages

ERROR IN REACTANTS DATASET (INPUT)
Fatal error. This error, which is described in the printed message preceding this one in
the listing, occurred when the CEA program was trying to process data in subroutine REACT.
The following error message is also printed. Control is returned to the main program, which
continues with the next problem, if any.

58

FATAL ERROR IN DATASET (INPUT)
Fatal error. This error is described in the printed message preceding this one in thelisting.

MOLES AND WEIGHT PERCENTS SHOULD NOT BE MIXED (INPUT)
Fatal error. For each problem, reactant amounts should be given in terms of either allmoles (all number of moles, all mole fractions, or all mole percents) or all weights (all weightfractions or all weight percents), but not in both moles and weights. The second INPUT error
message is also printed, and control is returned to the main program, which continues with thenext problem, if any.

REACTANT AMOUNT MISSING (INPUT)
Fatal error. The amount of a reactant (moles or weight) is mlsslllg. The second
INPUT error message is also printed, and control is returned to the main program, which
continues with the next problem, if any.

REACTANT TEMPERATURE MISSING (INPUT)
Fatal error. A numerical value is not given following a literal that starts with the letterin the reac dataset. The second INPUT error message is also printed, and control isreturned to the main program, which continues with the next problem, if any.

t

TYPE OF PROBLEM NOT SPECIFIED (INPUT)
Fatal error. The variable indicating the type of problem in the prob dataset was notrecognized by the CEA program. The second INPUT error message is also printed, andcontrol is returned to the main program, which continues with the next problem, if any.

UNABLE TO PROCESS EQUIVALENCE RATIO = (number) (INPUT)
Fatal error. The program is unable to convert equivalence ratio to oxidant-to-fuelratio. Possibly, an oxidant is not labeled as an oxidant or a fuel is not labeled as a fuel. The
second INPUT error message is also printed, and control is returned to the main program,which continues with the next problem, if any.

WARNING!! A KEYWORD IS MISSING (INPUT)
Program continues.

WARNING!! DID NOT RECOGNIZE (name of variable) (INPUT)
A literal variable in the dataset just processed was not recognized by the CEA
program. The program ignores this variable and continues.

59

WARNING!! LITERAL EXPECTED FOR (name of variable) (INPUT)
A number was found instead of the literal that was expected for this variable in thereac dataset. This value is ignored and the program continues.

WARNING!! (atomic symbol) NOT RECOGNIZED (INPUT)
The program was unable to decipher the exploded chemical formula in the reac
dataset. The species is ignored and the program continues.

6.7 REACT Messages
AMOUNT MISSING FOR REACTANT NO. (reactant number) (REACT)
Fatal error. The amount of reactant in the reac dataset is missing. Control isreturned to the main program, which continues with the next problem, if any.

DATA FOR (name of reactant) NOT FOUND IN thermo.lib (REACT)
Fatal error. The CEA program was not able to match the name given in the reac
dataset with a name from thermo.lib. If the exploded chemical f'lrmula of a reactant is notincluded in the dataset or if a required enthalpy or internal energy value is missing, thethermodynamic 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 BLOCKDATA (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 andcorresponding temperature but no thermodynamic coefficients, the temperature given in thereac dataset must be within 10 K of the temperature in thermo.lib. Control is returned to themain 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 onl y 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 tobe 100% and continue.

60

6.8 ROCKET Messages
FATAL ERROR!! EITHER mdo1:/a or ac/a1: MISSING FOR THE fae PROBLEM(ROCKET)The f ac option for rocket performance calculations requires either the mass flowrate per unit chamber area mIA or the contraction area ratio AJA t 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 mdo1: / a = (value of liz fA) IS TOO LARGE. GIVESCONTRACTION RATIO ESTIMATE LESS THAN 1 (ROCKET)
Fatal error. In the rocket finite-area-combustor model f ac, an option is provided toassignIA. If this assigned value gives a contraction ratio less than 1, the error message isprinted and control is returned to the main program, which continues with the next problem,
if any.

m

WARNING!! AREA RATIO CALCULATION CANNOT BE DONE BECAUSEGAMMAs 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 isprinted 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 PIPe) IS NOT PERMITTED TO
BE LESS THAN PinjlPc = (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/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 / a1: (value of assigned A/A~ IS NOT PERMITTED
TO BE GREATER THAN acfat = (value of A/AJ. 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 thisincorrectly 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 to5. 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 t < 1.0001. The reason is that theconverged throat conditions do not correspond exactly to an area ratio of 1 (see eq. (6.16) ofGordon and McBride, 1994). If the number of iterations exceeds 10, the point is omitted andthe 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 thethroat, 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 WERE 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 thecalculations 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 WEREOMITTEDSINCEnfz 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 nf z > 1 (thethroat or some supersonic point), all subsonic area ratios are omitted and the calculations
continue.

62

WARNING!! FREEZING IS NOT ALLOWED AT A SUBSONIC PRESSURE RATIOFOR nfz GREATER THAN 1. FROZEN PERFORMANCE CALCULATIONS WEREOMITTED (ROCKET)For nfz > 1, throat conditions will be based on equilibrium compositions. For thissituation, 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 pageof the equilibrium output ,table. The reason is that a second page wipes out the informationfrom 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 andsupersonic) is greater than NCOL (the number of columns in the output listing) minus 2 (thenumber of columns for combustion and throat). In this situation, frozen performance isomitted and the program continues.

6.9 SEARCH Messages
INSUFFICIENT STORAGE FOR (number of) SPECIES (SEARCH)
Fatal error. This statement shows that for the chemical system under consideration, theprogram 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 thenext 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 (seesection 4.9.1). Secondly, an omit. dataset can be used. to eliminate the required number ofexcess 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 inthermo.lib. The species is ignored and the program continues.

6.10 SHCK Messages
WARNING!! ONLY (NCOL) ul OR machl VALUES ALLOWED (SHCK)The number of assigned values of u 1 or mach 1 in dataset prob exceeded the
maximum allowed. This maximum is NCOL (number of columns), which is set in a
PARAMETER statement. NeOL 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 u 1 = (value of u1). ANSWERS NOTRELIABLE, SOLUTION MAY NOT EXIST (SHCK)This message usually occurs when the assigned values of U 1, TH and P 1 do not have asolution. For example, for example 7 in section 7.5, no solution exists for values of shock U 1
less than approximately 1095 mls 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 shockproblem is higher than the highest T in the temperature range times 1.25 or if the assigned
temperature t 1 is less than the lowest T in 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. Mter themessage 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. Mter themessage is printed, the program terminates.

64Chapter 7

Example ProbleDlsFourteen 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 andthermal transport data are updated periodically, the answers given for these examples maychange 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 (orassigned 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 rkt. 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 thefeatures illustrated are the following:
1.

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

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

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

o/f: examples 3, 4, 8 to 10, and 12

11.

Chemical equivalence ratio r: examples I and 6iii. Fuel-air equivalence ratio <1>: example 2
iv. Percent fuel by weight, %fuel: example 13

65

2.

Exploded formulaa. Obtained directly from thermo.lib: 1 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 p rob 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 C 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. omi't: examples 3 to 5
7. only: examples 1 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 unitsa. 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 unitsa. Mass fractions: example 12b. 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, t p; andassigned-temperature and assigned-volume problems, tv. The same reactants are used in thetwo examples, and part of the output from example 1 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 (1, 0.1, and 0.01 atm) are specified, for a total of six
combinations. Each of these six combinations will be run for two equivalence ratios (r= 1 and
1.5). The exploded formulas for the fuel (H2) and oxidant (Air) are obtained automaticallyfrom 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 demonstrateinternal consistency in the CEA program for t p and t v problems. The combustion mixture
densities taken from example 1 output for the equivalence ratio of 1 and for 3000 K wereused as part of the input for example 2. It may be seen in the output of example 2 that thepressures of 1,0.1, and 0.01 atm, used as input in example I, are reproduced exactly. The
equivalence ratio was specified here in terms of <t> rather than r as in examplel. For
stoichiometric conditions, the two definitions give equal values (see discussion in chapter 9 ofGordon 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 thermaltransport property calculations Cp,equil is calculated by a different method from the moregeneral specific heat cp eg' When no condensed species are present, the two methods should
give the same numerical values of specific heat, except possibly for rounding errors. Thisagreement, which occurs here as well as in examples 6 and 11, confirms the accuracy of thecalculations.

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 theoutput 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. Threepressures 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 fueland oxidant do not have to be at the same initial temperature. In this problem, the air ispreheated to 700 K. The results of the enthalpy calculation for the oxidants may be seen inreactants 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 isaccomplished by using the trace option in the out.p dataset. In this example,
trace=1.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 ofproblem 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 thedensity 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 ofthe 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 density3
is 14.428 kg/m . The input for internal energy is required to be in the form of u/R, where u isinternal 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 initiallyconsiders onl y gaseous combustion products. An ini tial combustion temperature of2223.217 K was reached in 15 iterations. Thi s 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 AI 20 3(a)should be added. (The solid phase exists below the melting point of 2327 K.) With AI 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 liquidand 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 andgave a final combustion temperature of 2724.464 K.

68Had the keyword lnse followed by AL203(L) been used in the input, convergencewould 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 whichcondensed 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 thatthe program must then remove. The inse option may be used only for the first point. Mterthe first point the insertions and removals of condensed phases are all handled automaticallyby 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 madefor 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. Whentemperatures 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.., 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, s h. The input permits a schedule ofeither velocities u1 or Mach numbers mach1, but not both in the same input dataset. For thisexample, a set of velocities was assigned. Only the incident shock conditions were calculated.
To obtain reflected shock conditions, the prob dataset would have required re f leq forreflected shocks based on equilibrium incident conditions and/or re f 1 fr for reflected
shocks based on frozen incident conditions. The message that starts with WARNING!! NOCONVERGENCE 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, i ac, and a finite-area
combustor, f ac. All three examples are for the same propellant, chamber pressure, off 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 10, 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 (s ubar= 1 • 58) was assigned in order to compare theresults with those obtained when using the same assigned value of Ar/A I (the contraction ratio
assigned for examples 9 and 10). The outputs for examples 8 to 10 will be compared in thediscussion of examples 9 and 10.

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 NeOL (number of columns or points) was set to 8 in the program, output for the lastsupersonic 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 fac model. Two options are permitted with thismodel. The first option, assigning the contraction ratio AclA t (acat) is illustrated inexample 9. The second option, assigning the mass flow rate per unit arealAc (rna) is
illustrated in example 10. The results of example 9 for an assigned value of A c1Ar=1.58 werellsed to calculate a value ofIA c =1333.9. This value was used as input in example 10 inorder to verify the consistency of the results.

mm

7.6.3 Example 10
As mentioned in the previous section, example 10 is identical to example 9 except for
using a value of in lAc instead of A/At as input. The input value of ma=1333.9 forexample 10 was calculated from the results of example 9. As expected, the value of
A/At=1.5800 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 thef ac and i ac rocket models are extremely close for the same assigned area ratios. For
example, at an area ratio of 75, the i ac rocket model in example 8 gives a specific impulseof 4399.7 mIs, which compares closely with 4399.0 mls obtained for the f ac model ofexamples 9 and 10. The difference is only 0.02%.

7.7 Example 11
Example 11 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 toassign a schedule of points for expansion in a rocket that inel udes 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 subsonicand 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 theplot 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), theprogram will calculate the reactant mixture density. By including mas s f in the out.p
dataset, compositions are given as mass fractions. By including plot in the out.p dataset, adump 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 YST'
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,T 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 theerror caused by assuming zero volume of condensed species in the equation of state (eq.
(2.1a) in section 2.2 of Gordon and McBride, 1994). The second was to look at an exampleof 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 forfurther 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 werechosen 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 of3
3
mixture is calculated to be 4.5 cm , in contrast to 375 900 cm for the gases. Therefore, eventhough the mole fraction of the condensed species is about 25%, the relative volume of thecondensed 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 (egs. (2.1a) and (2.1b) in
Gordon and McBride, 1994) is valid for most practical purposes. For other problems withhigher 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, twovalues 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 weightsof the mixture would be the same for all points. This is indeed the case for the molecularweight 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 theassumptions incorporated in the equation of state (eq. (2.1) in Gordon and McBride, 1994).
The molecular weight M is obtained by means of equations (2.3a) or (2.3b), MW is given byequation (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=25.607xO.75319=19.287, which matches exactly the molecular weight of 19.287 givenin 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 andreactants. 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 theprocessed 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 A 1. 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) isalways zero. On record 3, only one number is given, the temperature of the assigned enthalpy
on record 2. Two examples are given. Example AI, for chlorine gas, illustrates the generalformat. Example A2, for liquid acetylene, illustrates the format for a condensed species withdata 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
canvenience.
TABLE A.I. -GENERAL FORtvlAT FOR NINE-CONSTANf FUNCTIONAL FORM
Constants
hHmat
Columns
RecordI
Species name or formula
A 2-+
I ~2-+
Comments (data source)
A5h
25-80
2

Number of T intervals
Optional identification code
Chemical formulas, symbols, and! numbers
Zero for gas and nonzero for condensed phasest\1olecular \veight
Heat of formation at 298. 15 K, J.. mol

12.:\65(:\2,Hl.2)
II
F13.5
F13.5

2
-+-9
II-SO
52
53-65
66-80

Temperature range
Numher of coefficients for C~) o. R

21;10.3
II

2-21
23

T exponents in empirical equation for L~ o . R

HI;5.12-+-6:~{H'(29KI5) - H'(O)}, .I mol

1:15.3M)-HO51)16.81-80iFirst fire coefficients for

C"a l?

l.ast three coefficients for C p 0 R
Intcgration constants h, and h~Rc )cat 3, -+, and 5 for cach interval

3D I (d~1~-+82D16.H-+<)-8073

Example A.I:
CL2
Chlorine gas. TPIS 1989, vI, pt2, pB8.
2 tpis89 CL 2.00
0.00
0.00
0.00
0.00 a70.90540
0.000
200.000 1000.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0
9181.110
3.46281724D+04 -5.54712949D+02 6.20759103D+00 -2.98963673D-03 3.17303416D~06-1.79363467D-09 4.26005863D-13 O.OOOOOOOOD+OO 1.53407075D+03 -9.43835303D+00
9181.110
1000.000 6000.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0
6.09256675D+06 -1.94962688D+04 2.85453491D+01 -1.44996828D-02 4.46388943D-06-6.35852403D-10 3.32735931D-14 O.OOOOOOOOD+OO 1.21211722D+05 -1.69077832D+02

Empirical equations for example A.I:
Heat capacity:

coIi' = ~ T- + a T- +a + a T + a T + a T + a T
P

2

3

2

1

2

3

4

5

6

4

7

Example A.2:
C2H2(L),acetyle
Acetylene. JANAF Prop.Ser.E,1/67. TRC a-3000,10/86.
a 1 3/95 C 2.00H 2.00
0.00
0.00
0.00 126.03788
207599.000
192.3574

AppendixB

Names of Species in Thermodynamic
Data File (thermo.inp)
The thermo.inp file is arranged with data for the products listed first, followed by data
for the reactants. Among the products. all gas-phase species data are listed first, followed bycondensed-phase species data (liquid and/or solid). The names of gas-phase products arelisted in table B.l; the names of condensed-phase products are listed in table B.2. No
subscripts are used and no phase is indicated for the gas phase. That is, 02 in thermo.inp is
gas-phase oxygen, 0ig), and 02(L) is liquid-phase oxygen, Oil). An upper case "L" isused to designate the liquid phase to avoid confusion between the lower case "I" and thenumber" I." Most of the reactant species are cryogenic fuels or oxidants. Reactant names
are listed in table B.3. Species that may be considered as either products or reactants (such as
H 2(g), CH4(g), or 02(g) and listed as H2, CH4, and 02) are generally included with the
products. Occasionally, additional information is added after the chemical formula forclarification. For example, two names start with C4HlO(L). One is followed by n-butan toindicate normal butane; the other is followed by isobuta to indicate isobutane. (A maximumof 15 characters is allowed for a name.)
As discussed in section 2.3.2, in order for the CEA program to use the data inthermo.inp for reactants. the names used in the reac dataset must match the names in thethermo.inp file exactly. The search for a reactant name starts at the beginning of the file, firstwith gaseous products, then with condensed produets, and finally with reactants.
A complete documentation of references for the thermodynamic data selected for
products was not available at the time of publication of this report. Some of the references are
given in McBride et al. (1993). Data for the reactants are given in tables C.I and C.2.
(References for the data in table C.1 are given in table 0.1.) At the time of publication of thisreport. the approximate number of species in the· thermo.inp file was 1340 reaction products
and 60 reactants. However, data for species are constantly being added to the file, so that thedata and the total number of species keep changing.

75

TABLE B.1.-NAMES OF GAS-PHASE PRODUCTS IN thermo.inp

e-

B-

AL

BCL
BCL+
BCLF
BCL2
BCL2+
BCL2BCL3

AL+

ALALB02

ALBr
ALBr3
ALC
ALCL
ALCL+
ALCLF
ALCLF+ALCLF2
ALCL2
ALCL2+
ALCL2ALCL2F
ALCL3
ALF
ALF+
ALF2
ALF2+
ALF2ALF20
ALF20ALF3
ALF4ALH
ALI
ALI3
ALN
ALO
ALO+
ALOALOCL
ALOF
ALOH
ALOH+
ALOHAL02
AL02AL02H
ALS
AL2
AL2Br6
AL2CL6
AL2F6
AL216
AL20
AL20+
AL202
AL202+
Ar
Ar+
B

B+

76

BF

BF2
BF2+
BF2BF3
BH
BHF2
BH2
BH3
BN
BO
BOCL
BOF
BOF2
B02
B02BS
B2
B2H6
B20
B202
B203
B303CL3
B303F3
B303H3
Ba
BaBr
BaBr2
BaCL
BaCL2
BaF
BaF+
BaF2
BaOH
BaOH+
Ba02H2
BaS
Be
Be+
Be++
BeB02
BeBr
BeBr2
BeCL
BeCL+
BeCLF
BeCL2
BeF

BeF2
BeH
BeH+
BeH2
Bel
BeI2
BeN
BEO
BeOH
BeOH+
Be02H2BeS
Be20
Be20F2
Be202
Be303
Be404
Be50S
Be606
Br
BrCL
BrF
BrF3
BrF5
BrO
Br2
C

C+
CCBr
CBr2
CBr3
CBr4

ceL
CCLBr3CCL2
CCL2Br2
CCL3
CCL3Br
CCL4
CF
CF+
CFBr3
CFCL
CFCLBr2
CFCL2
CFCL2Br
CFCL3
CF2
CF2+
CF2Br2
CF2CL
CF2CLBr
CF2CL2
CF3
CF3+

CF3Br
CF3CL
CF4
CH
CH+
CHBr3
CHCL
CHCLBr2
CHCL2
CHCL2Br
CHCL3
CHF
CHFBr2CHFCL
CHFCLBrCHFCL2CHF2CHF2BrCHF2CL
CHF3
CH2
CH2Br2
CH2CL
CH2CLBr
CH2CL2
CH2F
CH2FBr
CH2FCl
CH2F2
CH3
CH3Br
CH3CL
CH3F
CH20H
CH30
CH4
CH30H
Cl
CN
CN+
CNCNN
CO
CO+
COCL
COCL2
COF
COFCL
COF2
COHCL
COHF
COS
C02
C02+
COOH
CP

TABLE B.l.-Continued.
CS
CS2
C2
C2+
C2C2CL
C2CL2
C2CL3
C2CL4
C2CL6
C2F
C2FCL
C2FCL3
C2F2
C2F2CL2
C2F3
C2F3CL
C2F4
C2F6
C2H
C2HCL
C2HCL3C2HF
C2HFCL2C2HF2CL
C2HF3
CHCO,ketyl
C2H2,vinYlidene
C2H2,acetylene
C2H2CL2C2H2FCL
C2H2F2CH2CO,ketene
C2H3,vinyl
C2H3CL
C2H3F
CH3CN
CH3CO,acetyl
C2H4
C2H40,ethylen-o
CH3CHO,ethanal
CH3COOH
C2H5
C2H6
CH3N2CH3
C2H50H
CH30CH3
CCN
CNC
C2N2
C20
C3
C3H3,propargyl
C3H4,allene
C3H4,propyne
C3H4,cyclo-

C3H5,allyl
C3H6,propylene
C3H6,cycloC3H60,propyle-oC3H7,n-propyl
C3H7, i-propyl
C3H8
C3H80,lpropanol
C3H80,2propanol
C302
C4
C4H2
C4H4,l,3-cycloC4H6,butadiene
C4H6,1-butyne
C4H6,2-butyne
C4H6,cycloC4H8,1-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
C4HI0,isobutane
C4HIO,n-butane
C4N2
CS
CSH6,l,3cycloCSH8,cycloCSHI0,1-pentene
CSH10,cycloC5Hll,pentyl
CSHll,t-pentyl
CSH12,n-pentane
CSH12,i-pentane
CH3C(CH3)2CH3
C6H2
C6HS,phenyl
C60S,phenyl
C6HSO,phenoxy
C6H6
C6D6
C6HSOH,phenol
C6HI0,cycloC6H12,l-hexene
C6H12,cycloCGH13,n-hexyl
C6H14,n-hexane
C7H7,benzyl
C7H8
C7H80,cresol-rnx
C7H14,l-heptene

C7H15,n-heptyl
C7H16,2-rnethylh
C7H16,n-heptane
C8H8,styrene
C8HIO,ethylbenz
C8H16,l-octene
C8H17,n-octyl
C8H18,n-octane
C8H18,isooctane
C9H19,n-nonyl
CIOH8,naphthaie
CIOH21,n-decyl
C12H9,o-bipheny
C12D9,o-bipheny
C12HIO,biphenyl
C12DIO,biphenyl
Ca
Ca+
CaBr
CaBr2
CaCL
CaCL2
CaF
CaF2
Cal
Cal2
CaO
CaOH
CaOH+
Ca02H2
CaS
Ca2
CL
CL+
CLCLCN
CLF
CLF3
CLF5
CLO
CL02
CL2
CL20
Cr
CrN
CrO
Cr02
Cr03
Cs
Cs+
CsCL
CsF
CsO
CsOH
CsOH+
Cs2

Cs2CL2
Cs2F2
Cs20
Cs202H2
Cs2S04
Cu
Cu+
CuCL
CuF
CuF2
CuO
Cu2
Cu3CL3
D

D+
DDBr
DeL
DF
DOCL

002
002-

D2
D2+
02D20
D202
D2S
F

F+
FFCN
FO
F02
F2
F20
FS2F,fluorodisu
Fe
Fe+
FeFeC50S
FeCL
FeCL2
FeeL3
FeO
Fe(OH)2
Fe2CL4Fe2CL6
GeBr
GeBr2
GeBr3
GeBr4
GeCL
GeCL2
GeCL3
GeCL4

77

TABLE B.l.-Continued.
GeF
GeF2
GeF3
GeF4
Gel
GeO
Ge02
GeS
GeS2
Ge2
H

H+
HHALO
HBO
HBO+
HBOHB02
RBS

HBS+
HEr
HCN
HCO
HCO+
HCCN
HCL
HD
HD+

HDROO
HD02
HF
HI
lINC
lINCO
RNO
RN02
RN03

HOeL
HOF
H02
H02HPO
HS03F
H2
H2+
H2HCHO,formaldehy
HCOOH
H2F2
H20
H20+
H202
H2S
H2S04
H3B306

78

H3F3
H30+
(HCOOR)2
H4F4
H5F5
H6F6
H7F7
He
He+
Hg
HgBr2
I

IFS
IF?

12
K
K+

KB02
KCN
KCL
KF
KF2KH
KO
KOKOR
KOH+
K2
K2C2N2K2CL2
K2F2
K202H2
K2S04
Kr
Kr+
Li
Li+
LiALF4
LiB02
LiCL
LiF
LiFO
LiF2LiH
LiN
LiO
LiOLiOH
LiOH+
LiON
Li2
Li2CL2
Li2F2
Li20
Li202
Li202H2

Li2S04
Li3CL3
Li3F3
Mg
Mg+
MgBr
MgBr2
MgCL
MgCL+
MgCLF
MgCL2
MgF
MgF+
MgF2
MgF2+
MgH
MgI
MgI2
MgN
MgO
MgOH
MgOH+
Mg02H2
MgS
Mg2
Mg2F4
Mo03
Mo206
Mo309
Mo4012
Mo5015
N

N+

NNCO
NO

002
N03
NF
NF2
NF3

NH
NH+
NHF
NHF2

NH2
NH2F
NH3
NH20H

NH4+
NO
NO+
NOCL
NOF
NOF3
N02

N02N02CL
N02F
N03
N03N03F
N2
N2+
N2NCN
cis-N2D2
N2F2
N2F4
N2H2
NH2N02
N2H4
N20
N20+
N203
N204
N205
N3
N3H
Na
Na+
NaALF4
NaB02
NaBr
NaCN
NaCL
NaF
NaF2NaHNaI
NaO
NaONaOH
NaOH+
Na2
Na2C2N2
Na2CL2Na2F2
Na20
Na202H2
Na2S04
Nb
NbO
Nb02
Ne
Ne+
Ni
NiCL
NiCL2
NiO
NiS

o

TABLE B.l.-Concluded.

0+
000
00-

OH
OH+
OH02
02+
0203
P

P+
PCL
PCL2
PCL2PCL3
PCLS
PF
PF+
PFPFCLPFCLPFCL2
PFCL4
PF2
PF2PF2CL
PF2CL3PF3
PF3CL2
PF4CL
PF5
PH
PH2
PH2PH3
PN
PO

po-

POCL3
POFCL2POF2CL
POF3
P02
P02P$

P2
P203
P204
P205
P3
P4
P406
P4010
Pb

PbBr
PbBr2
PbBr3
PbBr4
PbCL+
PbCL2
PbCL2+
PbCL3
PbCL4
PbF
PbF2
PbF3
PbF4
PbI
Pbr2
PbI3
PbI4
PbO
Pb02
PbS
PbS2
Pb2
S

S+
SSCL
SCL2
SCL2+
SD
SF
SF+
SFSF2
SF2+
SF2SF3SF3+SF3SF4SF4+SF4SF5SF5+SFSSF6
SF6SH
SHSN
SO
SOSOF2S02802802CLF
S02CL2

S02F2
S03
82
S2S2F2,thiothiony
820
83
S4
85
S6
87
S8
Si
8i+
SiBr
SiBr2
SiBr3
SiBr4
SiC
SiC2
SiC4H12
SiCL
8iCL2
SiCL3
SiCL4
SiF
SiFCL
SiF2
SiF3
SiF4
SiH
SiH+
SiHBr3SiHCL
SiHCL3
SiHF
SiHF3
SiHI3
SiH2
SiH2Br2
SiH2CL2
SiH2F2SiH2I2SiH3SiH3Br
SiH3CL
SiH3F
SiH3I
SiH4

Sir
Sir2
SiN
Sio
Si02

SiS
SiS2

Si2
Si2C
Si2N
Si3
SnBr3
SnBr4
SnCL2
SnCL3
SnCL4
SnF2
SnF3
SnF4
8n02
SnS2
Sr
SrBr
SrCL
SrCL2
SrF
SrF+
SrF2
SrI2
SrO
SrOH
SrOH+
Sr02H2
SrS
Ta
Ta+
TaO
Ta02
Ti
Ti+
TiTieL
TiCL2
TiCL3
TiCL4
TiO
TiOCL
TiOCL2
Ti02
V

VCL4
VN

VO
V02
Xe
Xe+
Zn
Zn+
ZnZr
ZrN
ZrO
Zr02

79

TABLE B.2.-NAMES OF CONDENSED-PHASE PRODUCrS IN thermo.inp
Ag(cr)
Ag(L)
AL(er)AL(L)
ALBr3(s)ALBr3(L)ALCL3(s)ALCL3(L)ALF3(a)ALF3(b)
ALF3(L)
ALI3(s)
ALI3(L)
ALN(s)
AL203(a)AL203(L)
AL2SiOS(an)AL6Si2013 (s)
B(b)
B{L)
BN(s)
B203{L)
B303H3(er)Ba(er)
Ba(L)
BaBr2(s)BaBr2(L)BaCL2(a)BaCL2(b)BaCL2(L)BaF2{a)BaF2(b,e)
BaF2(L)
BaO(s)BaO(L)
Ba02H2(s)Ba02H2{L)BaS(s)
Be(a)
Be(b)
Be(L)
BeAL204(s)BeAL204(L)BeBr2{s)BeCL2{s)BeCL2(L)BeF2(Lqz)
BeF2 (hqz)
BeF2(L)BeI2(s)
BeI2(L)
BeO(a)
BeO(b)
BeO{L)
Be02H2(b)80

BeS(s)
Be2C(s)Be2C(L)Br2(er)Br2(L)
C(gr)
Ca(a}
Ca(b)
Ca(L}
CaBr2(s)CaBr2(L)CaC03(caL)
CaCL2(s)CaCL2(L)
CaF2(a}CaF2(b}
CaF2(L)
CaO(s)
CaO{L)
Ca02H2(s)CaSts)CaS04(s)Cd(er)
Cd(L)
Co{a)
Co(b)
Co{b)

Co(L)
Cr{er)Cr(cr)Cr(cr)Cr(L)
CrN(s)
Cr2N(s)
Cr203 (5)
Cr203 (L)Cs(er)Cs (L)
CsCL(a)CsCL(b)CsCL(L)CsF(s)CsF(L)
CsOH{a)CsOH(b)CsOH(e)CsOH(L)Cs2S04{II)Cs2S04{I)Cs2S04{L)Cuter}Cu(L)
CuF(s)
CuF2(s)CuF2(L)

CUO(s)
CU02H2(s)CUS04(s)Cu20(s)Cu20(L)
Cu205S(s)
Fe(a)
Fe{a)
Fe(e)
Fe(d)
Fe(L)
FeCS05(L)FeCL2(s)FeCL2(L)FeCL3(s)FeCL3(L)FeO(s)FeO(L)
Fe(OH)2(s)Fe{OH)3(s)FeS(a)
FeS(b)
FeS(c)FeS(L)
FeS04(s)FeS2(s)Fe203(s)Fe2S3012(s)Fe304(s)Ge{er)Ge(L)
H20(s)
H20(L)
H2S04(L)Hg{cr)Hg(L)
HgBr2(s)HgBr2(L)HgO(s)
12(er)
12{L)
K(cr)
K(L)
KCN(s)KCN(L)
KCL(s)KCL(L)KF(s)KF(L)
KHF2(a)KHF2(b)
KHF2(L)
KOH(a)
KOR(b)
KOH(L)

K02(s)
K2C03(s)K2C03(L)K20(s)
K202(s)K2S(1)
K2S(2)
K2S(3)
K2S(L)
K2S04(a)K2S04(b)K2S04(L)Li{er)
Li(L)
LiAL02(s)LiAL02(L)
LieL(s)LiCL(L)
LiF(s)
LiF(L)
LiH(s)
LiH(L)
LiOH(s)LiOH(L)
Li20(s)Li20(L)Li2S04(a}Li2S04(b)Li2S04(L)Li3N( s)Mg(cr)
Mg(L)
MgAL204(s)MgAL204{L)MgBr2(s}MgBr2(L)MgC03(s)MgCL2(s)MgCL2(L)
MgF2(s)MgF2(L)
MgI2(s)MgI2(L)MgO(s)
MgO(L}
Mg02H2(s)MgS(s)
MgS04(s)MgS04(L)MgSi03(I)
MgSi03(II)MgSi03(III)MgSi03(L)
MgTi03(s)MgTi03(L)TABLE B.2.-Conc1uded.

MgTi20S(s)MgTi20S(L)
Mg2Si04(s)Mg2Si04(L)Mg2Ti04(s)Mg2Ti04(L)
Mn(a)
Mn(b)
Mn(c)
Mn(d)
Mn(L)
Mo(er)
Mo(L)
NH4CL(a)NH4CL(b)NH4F(er)
NH4F(L)Na(er)Na(L)
NaAL02(a)NaAL02(b)NaBr(s)NaBr(L)
NaCN(s)NaCN(L)NaCL(s)
NaCL(L}NaF (s)NaF(L)
NaI(s)NaI(L)
NaOH(a}NaOH(L}
Na02(s)Na2C03(I)Na2C03(II)Na2C03(L)Na20(e}Na20(a)Na20(L)
Na202(a)Na202(b)Na2S(l)Na2S(2)
Na2S(L}Na2S04(V)Na2S04{IV)Na2S04(I}Na2S04(L}Na3ALF6(a)Na3ALF6(b)Na3ALF6(L)NaSAL3F14(s)NaSAL3F14{L)Nb(er)Nb(L)

NbO(s}
NbO(L}
Nb02(I)
Nb02{II)
Nb02(III)
Nb02{L)
Nb205(s}Nb205(L}Ni(er}Ni (er)Ni(L)NiS(b)
NiS(a)NiS(L)
NiS2(s)NiS2(L)Ni3S2(I}
Ni3S2(II)Ni3S2(L}Ni3S4(s}peer)
peL}
P4010(er)P4010(L}Pb(er}Pb(L}
PbBr2(s)PbBr2(L)PbCL2(s)PbCL2(L}PbF2 (II)PbF2(I)PbF2(L)PbI2(s)PbI2 (L)PbO (II-r)
PbO(I-y}PbO(L}
Pb02(s)
PbS{s)PbS(L)
Pb203(s}Pb304(s)Rb(er)Rb(L}
S(erl)
S(er2}S {L}

SCL2(L)S2CL2(L}Siler)Si(L)
SiC(b}
SiC(b}
SiC{L)
Si02(a-qz)

Si02 (b-qz)
Si02(b-ert}
Si02 (L)SiS(er)SiS(L}
SiS2(er)
SiS2(L)
Si2N20(s)Si3N4(er)Sneer}SneLl
SnBr2(s)SnBr2(L)SnBr4{s)SnBr4(L)SnCL2{s)SnCL2{L)SnCL4{L}SnCL4{L)SnF2{s)SnF2(L}SnI2(s)
SnI2(L)
SnI4(s)
SnI4(L}SnO(s)SnO(L}
Sn02(s)Sn02(L)
SnS(rh)SnS(eu)SnS(L)
SnS2(s}
Sr(a}
Sr(b)
Sr(L)
SrCL2(a}SrCL2(b}SrCL2(L)SrF2{s)SrF2(L)
SrO(s}
SrO(L)
Sr02H2(s)Sr02H2(L)
SrS(s)Ta(er)Ta(L}
TaC(s)
TaC{L}
Ta205(s)Ta20S(L)
Th{a}
Th(b)
Th(L)
Ti(a)

Ti(b)
Ti(L)
TiC(s)
TiC(L)TiCL2(s)TiCL3(s)TiCL4(L)TiN(s)
TiN(L)
TiO(a)
TiO(b)TiO(L)
Ti02(ru)
Ti02{L)Ti203(a)Ti203(b)Ti203(L)Ti305(a)Ti305 (b)Ti305(L)Ti407(s)Ti407(L)
U(a}
U(b)
U(e)
U(L)
Veer)
VeL)
VCL2(s)
VCL3(s)
VCL4(L)
VN(s)
VO{s)
VO(L)
V203{s)V203(L)
V204(I)
V204 (II)V204(L)
V205(s)V205(L)
Weer)
W(L)Zn(er)Zn(L)
ZnS04(a)ZnS04'(a)ZnS04(b)
Zr(a)
Zr(bl
Zr(L)
ZrN(s)
ZrN{L)
Zr02(a)Zr02(b)Zr02(L)81

TABLE B.3.-NAMES OF REACfANTS IN thermo.inp
Air
B2H6(L}B5H9 (L)(CH2)x (s)CH3N02{L)CH4{L)
CH30H{L)CH6N2(L)
C2H2(L),acetyle
CH3CN(L)
C2H4(L)C2H40(L),ethyle
C2H6(L}C2H50H(L)C2H8N2(L),UDMH
C2N2(L)C3H6 (L) ,propyle
C3H7N03(L)C3H8{L}
C4H8 (L) ,1-buten
C4HIO (L) ,n-buta
C4HIO(L),isobut
CSH12(L),n-pent
C6H6{L)C6H5NH2(L)C6H14{L),n-hexa
C7H8(L)
C7H16 (L) , n-hept
C8H18(L),n-octa
C8H18{L),isooct82

Jet-A(g)Jet-A(L)
CLF3(L)
CL03F
CL03F(L)
CL2{L)
F2{L)
F20(L)JP-4
JP-S
HN03 (L)
IRFNA
H2(L)
H202(L)
LiCL04(s)NF3(L)
NH3(L)
NH4CL04(I)NH4CL04(II)NH4N03 (IV)
NH4N03(III}
NH4N03 (II)NH4N03(I)NH4L03(L)
N2(L)
N2H4(L)
N204(L)
02(L)
03(L)

Appendix C

Thermodynamic and Density Datafor Reactants
Thermodynamic and density data for the reactants are given in tables C.1 and C.2.
Some reactants are in the condensed phase; others are in the gaseous phase. Density data are
given only for the condensed phase. For those reactants whose normal boiling points are
below 298.15 K, the following energy data in kilojoules per mole are given are given in table
C.l:

1.

Heat of formation of the gaseous phase at 298.] 5 K, f."H298.15 = H298.1S

2.

Sensible heat of the ideal state of the gas from 298.15 K to the boiling point, H298.15 - Hbp

3. Difference in enthalpy between ideal and real states of the gas at the normal boiling point,

Hbp - Hhp,re4.

Heat of vaporization at the normal boiling point f."Hvap = Hbp,re - H(C)bp

The assigned enthalpy of the condensed phase at the normal boiling point is calculated fromthese data by means of the formulaH( c )bp= H(g}z98.15 - (H298.15 - H bp) - (Hbp - H bp,re) - /),,/{vap(Note that in the thermodynamic enthalpy base in thermo.lib, the assigned value of enthalpy
at 298.15 K (H298.1S) is equal to the heat of formation at 298.15 K (i.e., H298.1S= f."H298.15; seeeg. (4.2) in Gordon and McBride, 1994). For those species for which the quantity (Hbp HbR,re) was unknown, it was taken as zero inasmuch as it is a relatively small quantity (say, 0.1
to u.s klImat). A blank in the temperature column indicates that the temperature is 298.15 K
and not a boiling point. References for the data in table C.I are given in table 0.1 inappendix D. Table C.2 gives the data and references for reactants in the format of thethermo.inp file (see table A.I). For some reactants, only one enthalpy value is given.; forothers, thermodynamic coefficients for heat capacity, enthalpy, and entropy are given for one
or more temperature intervals. Reactant species names used in reac datasets should match
those in tables B.1 to B.3.

83

TABLE C.l.-TIIERMODYNAMIC AND DENSITY DATA FOR REACTANTS
Phase
Boiling
Assigned
H 298IS H bp - HbP,re,/)"Hvap ,point,
enthalpy,
H bp '
kllmolkllmolK
kllmolkllmolAcetonitrile, C 2H 3N
L----------3 1.38
g
Acetylene, C 2H 2
0.172
16.242----------228 .2
4.187
L
192.35207.599.ag-----------.126
A Irg
Ammonia, NH 3
.222
2.042
23.351-----------45.940
L
239.72-71.555
I
Ammonium----------- 295.767
perchlorate,
NH4 CI04
Ammonium nitrate,IV-365.6
NH4N03
Aniline, C6 H sNH 2
31.5
LBenzene, C 6 H6L
49.08
Beryllium, Bes0gn-Butane, C4H IO-125.79
2.434
22.44
L
272.638-150.664g-134.99
3.374
21.30
L
261.361-159.664
-.54
2.563
g
22.07
266.92
L-25.173
Chlorine, Cl 2
g
0
1.968
.172
20.410L
239.12-22.550g-164.6Chlorine trifluoride,
.842
.414
27.53
CIF 3
L
284.89-193.386g
309.100
2.561
23.33
Cyanogen, C 2N 2
252.05283.209
L
g
36.6
.197
14.2635.695
L180.5916.445-83.852
5.267
14.70
g
L
184.559-103.819-277.51
Ethanol, C 2HsOH
L
g
4.865
.163
Ethylene, C2 H452.50
13.527
L
169.4233.945g-52.635
25.53
.676
L
283.65-78.841-25.6
Ethylene polymer,(CH 2).
6.66.078
Fluorine, F 2
g
o
6.353
85.02
-13.091
L
L-224.35
n-Heptane, C 7H 16-198.66
L
n- Hexane, C6 H14
L
Hydrazine, N 2H4
50.38
g
o
Hydrogen, H 2
8.043
.070
.899
L
20.27
-9.012
Hydrogen peroxide,-187.78
L
H 20
IRFNAbL-----------270.496
Species

let-A, C 12 H 23
a.
b.

c.

84

c

L

------------303.403

Density,g/cm

30.7793
.729

.6821
1.95

1.725
1.02173.873661.85-----------.06012-------_ ... --.5941-----------.6254------------

1.559------ -----1.850
.9577
.4371
.5465
.78509
.5690
.8824
.935

1.5021.67950.654841.0040.0709
1.4425
1.478.818

Air is based on the following molar percents: N2=78.084, O 2=20.9476, Ar=0.9365, CO 2 , 0.0319 (Gordon,
1982). The empirical formula for 1 mole of air is N 1.561680 A19S9Ar .00936SC .000319'
Inhibited red fuming nitric acid based on the following weight percents: HNOlL)=83.5, N20 4 (L)=14,
H 20(L)=2, HF(g)=0.5. (This gives the following empirical formula defined as 1 mole:
H 1.57216N 1.6294S04.69S0SF02499')
Typical jet fuel having the following properties: empirical formula defined as 1 mole is C 12 H 23 (equivalent to
H/C weight ratio of 0.16084); heat of combustion, 18500 Btu/lb.

SpeciesL

JP-4, RP-1
JP-5, ASTMA1
Lithium, Li

Phase

e

Lithium perchlorate,
LiCI04
Methane, CH4
Methanol, CH 30H
Monomethyl
hydrazine, CH 6 N2
Nitric acid, HN03
Nitrogen, N2
Nitrogen tetroxide,
N20 4
Nitrogen trifluoride,
NF3
Nitromethane, CH 3N0 2
n-Octane, CgH 18
i-Octane, CgH Ig
Oxygen, O 2
Oxygen difluoride, OF2
Ozone, 0 3
Pentaborane, BsH9n-Pentane, CSH 12
Perchloryl fluoride,
ClF0 3
Propane, C3Hg
Propylene, C3H6
Propyl nitrate, C3 H7N0 3
Toluene, C7 Hg
Unsymmetricaldimethyl hydrazine(UDMH), C2HgN2

L
s
L
s
g
L
L
L
g
L
g
L
g

TABLE C.l.-Concluded.
Boiling
Assigned
H298.1S point,
enthalpy,
H bP '
K
kJ/molkJ/mol--------- ....
-22.723----------- ...

_--------

f 453.69-------- .. --111.643--------------------- ...

----_ ...... _-------------

77.352-----------

Lg
144.09Lg
Lg
L

226.40L-----------

L------_ ... ---L---------------------------------------------------- ...

90.17-_ ........ -----128.40------- ... ---161.85------------------------------------------

231.076-- ...... _------

225.46

IiHvap ,Density,g/cm 3

kJ/mol0.773-22.183
0
7.187-380.7-74.6-89.233-238.9154.2-133.913-173.013
0-12.10711.111-17.549-131.7

L
L
L
L
g
L
g
L
g
L
L
L
g

H bp - HbP,re'kJ/mol-150.387-113.1-250.26-259.160-12.979
24.5
6.672
141.8
122.52742.84-173.49-23.8-47.436-104.68-128.228
20.00-2.704-214.5
12.18
48.9

.807
.534
.512
2.428
6.318

0.126

8.189

------------.4211.78664.874
39.1------------

1.5037
6.427

.103

5.577

.....

_----------

.8081
28.66

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

11.585- ... ----------

1.431
6.960

.142

1.537
1.1286.69854.68784
6.065

.094

6.820

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

6.608

.130

11.09

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

4.964

.113

14.196------- -----

1.149
1.518
1.449
.6183
.6213

4.306

19.33

-_ ...... --------

4.508

19.04

-- ...

4.284

18.42

-------- ... _--1.392---------

.5810
.6093
1.0538.86220.7914

Typical jet fuel having the following properties: H/C weight ratio, 0.163; heat of combustion, 18 640
Btu/lb (giving the following empirical formula defined as 1 mole: C1HI.9423)'
e. Typical jet fuel having the following properties: H/C weight ratio, 0.161; heat of combustion,
18600 Btu/lb (giving the following empirical formula defined as 1 mole: CIHI.918S)'
f. Melting point for Li.

d.

85

TABLE C.2.-REACI'ANT THERMODYNAMIC DATA IN thermo.inp l::'ORMAT

Air
Mole%:N2 78.084,02 20.9476,Ar .9365,C02 .0319.NASA TPl906 1982
2 1 9/95 N 1.56170 .41959AR.00937C .00032.00000 028.9651785-125.530
200.000
1000.0007 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0
8649.264
1.009950160+04 -1.968275610+02 5.009155110+00 -5.761013730-03 1.066859930-05-7.940297970-09 2.185231910-12 0.000000000+00 -1.767967310+02 -3.921500980+00
1000.000
6000.0007 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0
8649.264
2.415214430+05 -1.25787460D+03 5.144558670+00 -2.138541790-04 7.065227840-08-1.071483490-11 6.577800150-16 0.000000000+00 6.462263190+03 -8.147408660+00
B2H6(L)
Diborane. JANAF Prop.Ser.E,l/67. TPIS v.III,1981.
16445.000
o 1 4/95 B 2.00H 6.00
0.00
0.00
0.00 127.66964
180.59
B5H9(L)Pentaborane. JANAF June 1963 p300.
42840.000
63.12646
o j 6/63 B 5.00H 9.00
0.00
0.00
0.00 1
298.15(CH2 )x(s)Ethylene polymer. Est. from paraffin HC series,TRC p-2500,4/88.
0.00
0.00
0.00 114.02688-25600.000
o 1 4/95 C 1.00H 2.00
298.15
CH3N02(L}Nitromethane. TRC p-9520,12/91.
61.04036-113100.000
o x12/91 C 1.aOH 3.00N 1.000 2.00
0.00 1
298.15
CH4(L}
Methane. TRC m-1350,10/93. JANAF Prop.Ser.E,l/67.
o 1 4/95 C 1.00H
4.00
0.00
0.00
0.00 I
16.04276-89233.000
111. 643
CH30H(L}Methanol. TRC p-5000,12/87; tc,uc,vc-5031-3,12/84.
-238910.000
1 x12/84 C
1.00H
4.000
1.00
0.00
0.00 132.04216
18995.000
175.610390.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 {.O 0.0-1.302005180+06 3.16698523D+04 -3.031243150+02 1.60223163D+00 -4.59450874D-03
6.990180370-06 -4.207390190-09 0.000000000+00 -1.65616865D+05 1.51434714D+03
CH6N2(L)Monomethyl Hydrazine. TRC p-9220,12/93.
54200.000
o x12/93 C 1.00H 6.00N 2.00
0.00
0.00 146.07212298.15
C2H2(L),acetyle
Acetylene. Dens:JANAF Prop.Ser.E,I/67. B.P.:TRC a-3000,10/86.
a 1 3/95 C
2.00H
2.00
0.00
0.00
0.00 126.03788
207599.000
192.35
Ethanenitrile (Acetonitrile). JPCRO vll,Sup.2,1982.
CH3CN{L)31380.
2.00H
3.00N
1.00
0.00
0.00 141.05256o 1 3/95 C
298.15
C2H4(L}
Ethylene. TRC m-2600,10/93.
28.05376
33945.000
o 1 4/95 C
2.00H
4.00
0.00
0.00
0.00 1
169.42
C2H40(L),ethyleEthylene oxide (Oxirane). TRC m-6150,6/94.
-78841.000
o 1 4/95 C 2.00H 4.000 1.00
0.00
0.00 144.05316
283.65
Ethane. TRC m-1350, 10/93.
C2H6(L)30.06964-103819.000
0.00
0.00
0.00 1o 1 4/95 C 2.00H 6.00
184.559
C2HSOH(L)TRC p-5000,12/31/87; tc,uc,vc-5031-3,12/31/84.
I x12/84 C
2.00H
6.000
1.00
0.00
0.00 I
46.06904-277510.000
159.000
390.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0
24082.000
4.501115940+05 -1.02082899D+04 1.014266780+02 -3.874672610-01 7.121392610-04-1.857071450-07 -2.037622570-10 0.000000000+00 7.448557900+03 -5.04425552D+02
C2H8N2{L},UDMH
Unsymmetrical Dimethyl Hydrazine. TRC p9220,12/93.
48900.000
o 1 4/95 C
2.00H
8.00N
2.00
0.00
0.00 160.099298.15Cyanogen. Hdbk C&P Ed.73,1992-3.
C2N2(L)52.03548
283209.000
0.00
0.00
0.00 1o 1 3/95 C 2.00N 2.00
252.0586

TABLE C.2. -Continued.
C3H6(L),propyle
Propylene. TRC m2600,10/93.
o 1 4/95 C 3.00H 6.00
0.00
0.00
42.08064
0.00 1-2704.000
225.46C3H7N03(L)Propyl Nitrate. Pedley, Naylor, Kirby, 1986,p178.
o 1 4/95 C 3.00H 7.00N 1.000 3.00
0.00 1105.09352-214500.000
298.15
C3H8(L)
Propane. TRC m1350,1o/93.
o 1 4/95 C 3.00H
8.00
0.00
0.00
0.00 144.09652-128228.000
231. 076
C4H8(L),1-buten
I-Butene. TRC m-2600,10/93. p-2600,4/88.
o 1 3/95 C 4.00H
8.0
0.00
0.00
0.00 156.10752-25173.000
266.92
C4H10(L),n-buta
n-Butane. TRC m-1350,10/93.
o 1 3/95 C 4.00H 10.0
0.00
0.00
58.12340
0.00 1-150664.000
272.638
C4HI0(L),isobut
Isobutane(2-methyl propane). TRC m-1350,10/93.
o 1 3/95 C 4.00H 10.0
0.00
0.00
0.00 1
58.12340-159664.000
261.361
C5H12 (L),n-pentn-Pentane. TRC p-1350,4/85.
o 1 4/85 C 5.00H 12.0
0.00
0.00
72.15028-173490.000
0.00 1
298.15
C6H6(L)Benzene. TRC tc,uc,vc-3201,10/31/86; p-3200,4/30/83.
1 xl0/86 C
6.00H
6.00
0.00
0.00
0.00 178.11364
49080.000
278.680
500.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.030110.000-2.560137100+06 4.136745880+04 -2.12297357D+02 3.72357902D-Ol 7.561068870-04-3.077215090-06 2.78750625D-09 0.000000000+00 -1.93546778D+OS 1.231845750+03
C6H5NH2(L)Aniline. TRC p9370 6/30/90. TRC tc,uc,vc-9370 12/31/88
1 x12/88 C
6.00H
7.00N
1.00
0.00
0.00 1
93.12832
31500.000
267.130460.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0
34020.000
6.267734410+07 -8.947510400+05 5.06761571D+03 -1.402163200+01 1.899635910-02-9.316664840-06 -1.238222490-09 0.000000000+00 4.27541061D+06 -2.807774080+04
C6H14(L),n-hexa
n-hexane. TRC p,tc,uc,vc-1440-1,4/85.
1 x 4/85 C
6.00H 14.00
0.00
0.00
0.00 186.17716-198660.000
177.860
300.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.046920.000
7.730917160+06 -2.25189247D+05 2.719902840+03 -1.69986707D+01 5.912397590-02-1.07540944D-04 8.030437090-08 O.OOOOOOOOD+OO 8.819466380+05 -1. 294138410+04
C7H8(L)TRC tc,uc,vc-3200-1,10/31/86; p-3200,4/30/83.
1 x10/86 C
7.00H
8.00
0.00
0.00
0.00 192.14052
12180.000
178.150
500.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0
33470.000-3.71356003D+06 7.77255072D+04 -6.31228799D+02 2.724399B6D+00 -6.10355386D-03
7.022445240-06 -3.113727500-09 O.OOOOOOOOD+OO -3.452125050+05 3.26599001D+03
C7H16(L),n-hept
TRC m-1460,4/93; tc,uc,vc-1460,lO/31/7S.
1 xl0/75 C
7.00H 16.00
0.00
0.00
0.00 1
100.20404-224350.000
182.580
380.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0
52640.000
1.760036000+06 -3.749601730+04 3.963259800+02 -2.11792498D+00 6.82851971D-03-1.131901770-05 7.737098830-09 0.000000000+00 1.26916032D+05 -1.921784190+03
C8H18(L),n-octa
TRC tables tc,uc,vc-1491-2. Hf298: p-1010,Oct.31,1984.
1 x10/76 C
8.00H 18.00
0.00
0.00
0.00 1114.23092-250260.000
216.370
310.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.061490.000-2.322825010+07 4.846535450+05 -4.084818230+03 1.82081928D+01 -4.465662900-02
5.814101340-05 -3.149603340-08 O.OOOOOOOOD+OO -2.166270480+06 2.091659730+04
C8H18(L),isooct
TRC tables tc,uc,vc-1491-2. Hf298: p-1490,Oct.31,1982.
1 x10/76 C
8.00H 18.00
0.00
0.00
0.00 1114.23092-259160.000
165.790380.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.050190.000
4.78104766D+06 -1.126911380+05 1.096521770+03 -5.34411704D+00 1.460037240-02-2.028719990-05 1.13340043D-08 0.000000000+00 4.43284874D+05 -5.45790515D+03
CLF3(L)JANAF Prop.SerD,3/66. TRC k-140,12/73.
o 1 3/95 CL 1.00F 3.00
0.00
0.00
0.00 192.44791-193386.000
284.8987

TABLE C.2.-Continued.
CL03F
Perchloryl Fluoride. JPCRD v22 sup2,1982. JANAF 3/61.
2 1 5/95 CL 1.000
3.00F
1.00
0.00
0.00 0102.44930-23800.000
200.000 1000.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0
13298.823
4.460877700+04 -5.892084080+02 3.558713370+00 2.809620190-02 -3.610924770-05
2.27336016D-08 -5.71680272D-12 0.000000000+00 -1.388798110+03 4.59151362D+00
1000.0DO 6000.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0
13298.823-3.910413440+05 -1.193259020+03 1.388663300+01 -3.54168398D-04 7.82659835D-08-8.97991688D-12 4.164698430-16 o.nOOOOOOOO+OO -1.27485199D+03 -5.10649344D+01
CL03F{L)Perchloryl Fluoride. Hdbk C&P,ED.73,1992-3.
o 1 4/95 CL 1.000
3.00F
1.00
0.00
0.00 1102.44930-47436.000
226.40CL2(L)
Chlorine. HdbkC&P Ed.73,1992-3. JANAF Prop.Ser.E,I/67
o 1 4/95 CL 2.00
0.00
0.00
0.00
0.00 I
70.90540-22550.000
239.12F2(L)Fluorine. Hdbk C&P Ed.73 1992-3. JANAF Prop.Ser.0,3/66.
o 1 4/95 F 2.00
0.00
0.00
0.00
0.00 137.99681-13091.000
85.02
F20(L)
Oxygen Difluoride.Hdbk C&P Ed.73 t 1992-3.JANAF Prop.Ser.E,1/67.
o 1 4/95 F 2.000' 1.00
0.00
0.00
0.00 153.99621
6672.000
128.40
HN03(L)
Nitric Acid. Hdbk C&P Ed.73,1992-3,p6-102.
a 1 4/95 H l.OON 1.000 -3.00
0.00
0.00 163.01288-173013.000
298.15H2{L)Hydrogen. JANAF Prop.Ser.D,3/66.
o jp3/66 H 2.00
0.00
0.00
0.00
0.00 12.01588-9012.000
20.27
H202{L)
Hydrogen Peroxide Liquid.TPIS,1989.
1 tpis89 H
2.000
2.00
0.00
0.00
0.00 134.01468-187780.000
272.740 6000.000 1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
22949.000
1.074386830+01 0.000000000+00 0.000000000+00 O.OOOOOOOOD+OO 0.000000000+00
0.000000000+00 0.000000000+00 O.OOOOOOOOD+OO -2.57878985D+04 -4.803221290+01
IRFNA
Wt%: HN03(L) 83.5; N204(L) 14.; H20(L) 2.; HF(g) .5.
a 1 4/95 H 1.5722N 1.62940 4.6950F .02499
1
100.
-270496.000
298.15JP-4
18640.BTU/i
Also RP-1. NASA RP-1311, Part II, 1996. Hcombo 1 5/95 C I.OOH 1.9423
1
13.96872-22723.000
298.1518600.BTU/i
JP-5
Also ASTMA1. NASA RP-1311, Part II, 1996. Hcomb-22183.000
o 1 5/95 C
1.00H 1.9185
1
13.94473
298.15
Jet-A(L)NASA TM-101475,1988. Hcomb=18500 BTU/#:NASA CR-72951,1971.
1 1 2/96 C 12.00H 23.00
0.00
0.00
0.00 1167.31462-303403.000
220.000
550.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0
0.000-4.2184673400+05-5.5762348400+03 1.5220943350+02-8.6100961400-01 3.0716409260-03-4.7027661200-06 2.743009309D-09 0.0000000000+00-3.2385353500+04-6.780954740D+02
Jet-A(g)NASA TM-101475,1988. NASA CR-72951,1971.
2 1 2/96 C 12.00H 23.00
0.00
0.00
0.00 0167.31462-249657.000
273.150 1000.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0
0.000-6.0686992800+05 8.3282642200+03-4.3123235500+01 2.572391032D-01-2.629316827D-04
1.6449894910-07-4.6453366900-11 0.0000000000+00-7.6069650400+04 2.7943072290+02
1000.000 5000.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0
0.000
1.541871660D+07-7.4338690200+04 1.4686453800+02-1.297042936D-02 2.1591401960-06-1.8871836420-10 6.6045595400-15 0.0000000000+00 3.9963233400+05-9.266674660D+02
LiCL04{s)Lithium Perchlorate. JANAF, March, 1964.
o j 3/64 LI 1.0QCL 1.000 4.00
0.00
0.00 1106.3913-380700.000
298.15
NF3(L)
Nitrogen trifluoride. JANAF Prop.Ser.E,1/67.
o 1 3/95 N 1.00F
3.00
0.00
0.00
0.00 171.001950-150387.000
144.0988

TABLE C.2. -Concluded.

NH3(L)
Ammonia. TRC m-500,6/56,B.P.a-500 12/63. JANAF Prop.Ser.E 1/67
a 1 3/95 N 1.00H 3.00
0.00
0.00
0.00 117.03056-71555.000
239.72NH4CL04(I)Ammonium Perchlorate. JANAF Oec.1962.
1 j12/62 N
1.00H
4.00CL 1.000
4.00
0.00 1117.48880-295767.000
25238.000
100.000
513.150 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0-3.075345570+03 -2.136505940+02 1.021583070+01 1.659463750-02 1.66526642D-05-2.306096050-08 1.543657320-11 0.000000000+00 -3.825767260+04 -4.230254270+01
NH4CL04(II)Ammonium Perchlorate. JANAF Dec.1962.
1 j12/62 N
1.00H
4.00CL 1.000
4.00
0.00 2117.48880-295767.000
513.150 1500.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.025238.000
4.296999480+07 -3.178417800+05 9.591437550+02 -1.439881370+00 1.222673650-03-5.215401620-07 8.803612760-11 O.OOOOOOOOD+OO 1.687446300+06 -5.889478160+03
NH4N03(IV)Ammonium Nitrate Rhombic Crystal (IV) . TPIS,1989.
2 tpis89 N
2.00H
4.000
3.00
0.00
0.00 180.04344-365600.000
256.200
298.150 6 -2.0 -1.0 0.0 1.0 2.0 3.0 0.0 0.0
23662.000-1.626679000+07 2.614603390+05 -1.680046300+03 5.448971540+00 -8.587849850-03
5.343277780-06 0.000000000+00 O.OOOOOOOOD+OO -1.26419517D+06 9.08569617D+03
298.150305.380 2 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0
23662.000
5.865649330+00 3.643028870-02 0.000000000+00 O.OOOOOOOOD+OO O.OOOOOOOOD+OO
O.OOOOOOOOD+OO O.OOOOOOOOD+OO O.OOOOOOOOD+OO -4.73393723D+04 -2.61436244D+Ol
NH4N03(III)Ammonium Nitrate Rhombic Crystal (III) . TPIS,1989.
1 tpis89 N
2.00H
4.000
3.00
0.00
0.00 380.04344-365600.000
305.380
357.250 2 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0
23662.000
7.233138210+00 2.33327039D-02 O.OOOOOOOOD+OO O.OOOOOOOOD+OO O.OOOOOOOOD+OO
O.OoOOOOOOD+OO O.OOOOOOOOD+OO O.OOOOOOOOD+OO -4.69417938D+04 -2.92985169D+Ol
NH4N03(II)Ammonium Nitrate Tetragonal Crystal(II). TPIS,1989.
1 tpis89 N
2.00H
4.000
3.00
0.00
0.00 480.04344-365600.000
357.250
399.000 3 0.0 1.0 3.0 0.0 0.0 0.0 0.0 0.0
23662.000
6.02320522D+01 -1.76799354D-Ol 4.52882972D-07 O.OOOOOOOOD+OO O.OOOOOOOOD+OO
O.OOOOOOOOD+OO O.OOOOOOOOD+OO O.OOOOOOOOD+OO -5.47863351D+04 -2.757806210+02
NH4N03(I)Ammonium Nitrate Cubic Crystal(I). TPIS,1989.
-365600.000
1 tpis89 N
2.00H
4.000
3.00
0.00
0.00 580.04344
23662.000
399.000
442.850 2 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0
1.29532588D+Ol 1. 56353171D-02 0.000000000+00 O.OOOOOOOOD+OO O.OOOOOOOOD+OO
O.OOOOOOOOD+OO O.OOOOOOOOD+OO O.OOOOOOOOD+OO -4.78370128D+04 -5.84851082D+01
NH4N03(L)Ammonium Nitrate Liquid. TPIS,1989.
1 tpis89 N
2.00H
4.000
3.00
0.00
0.00 680.04344-365600.000
442.850 6000.000 1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
23662.000
1.936373880+01 0.000000000+00 O.OOOOOOOOD+OO O.OOOOOOOOD+OO O.OOOOOOOOD+OO
O.OOOOOOOOD+OO O.OOOOOOOOD+OO O.OOOOOOOOD+OO -4.84379330D+04 -B.90300528D+Ol
N2(L)
Nitrogen. TRC k-460,6/60, m-470,6/56. JANAF Prop.Ser.D,3/66.
o 1 4/95 N
2.00
0.00
0.00
0.00
0.00 128.01348-12107.000
77.352
N2H4(L)
Hydrazine. Hf298: TPIS89. Props: JANAF 12/65.
1 j12/65 N
2.00H
4.00
0.00
0.00
0.00 132.04524
50380.000
100.000
800.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0
0.000
2.08096574D+04 -7.41816770D+02 1.91656919D+Ol -4.539330140-02 1.34202426D-04-1.47087394D-07 6.05628828D-11 O.OOOOOOOOD+OO 5.73540821D+03 -8.820213970+01
N204(L)
Dinitrogen tetroxide. Hvap: JANAF Prop.Ser.C,4/65.
-17549.000
o 1 4/95 N 2.000 4.00
0.00
0.00
0.00 192.01108298.1502 (L)
Oxygen. Hvap: TRC m-10,12/63. JANAF Prop.Ser.D,3/66.
o 1 4/95 0 2.00
0.00
0.00
0.00
0.00 131.99880-12979.000
90.17
03(L)
Ozone. Hvap: TRC m-10 t 12/63. JANAF Prop.Ser.E,1/67.
o 1 4/95 0 3.00
122527.000
0.00
0.00
0.00
0.00 147.99820
161. 85tt

89

AppendixD

References for Reactant Data
in Table e.l
References given in this appendix correspond to the data in table C.l. The references,
given at the end of this appendix, are indicated in table D.l by the following brief codes:
ode
AUTH

Authors

Abbreviated reference

FAITH

Faith: NASA CR-72951

GRACIA

Gracia: NASA TM-IOI475

HI

Lide: Handbook of Chern. & Phys., 73rd Ed

H2

Weast: Handbook of Chern. & Phys., 65th Ed.

J

Chase: JANAF Thermochemical Table

JCS

Banks: J. Chern. Soc.

JPR

Stull: JANAF Thermo. Data (Propellants)

MARK

Mark: Encyclopedia of Polymer Science

PED

Pedley: Thermo. Data of Organic Compounds

RD 1

Pamidimukkala: JPCRD, Vol. 11, No. 1

RDS2

Wagman: JPCRD, Vol. 11, Supp. 2

SP273

Gordon: NASA SP-273, Interim Revision

TP81

Gurvich: TPIS, Vol. 3, Pts. 1 & 2, 1981

TP82

Gurvich: TPIS. Vol. 4, Pts. 1 & 2, 1982

TP89:

Gurvich: TPIS, Vol. 1, Pts. 1 & 2, 1989

TP91:

Gurvich: TPIS, Vol. 2, Pts. 1 & 2, 1991

X

TRC Thermodynamic Tables

91

Page numbers follow all codes except AlITH and JPR. Following JPR is a series code,
either A, B, C, D, or E (examples: X w-3040 refers to reference X, page w-3040; JPR E refers
to reference JPR, series E). The data from TPSl, TPS2, TPS9, and TP91 are often found inboth parts 1 and 2 of these references. In this situation the page numbers refer to part 1 with afew exceptions.
TABLE 0.1. - REFERENCES FOR REACTANT DATA IN TABLE C.lSpeciesPhase
Boiling
Assigned
Hhp~
H Z98 15 !1Hvap ,point,
enthalpy,
Hbp 'Hbp,rc'kllmolkllmalkllmolK
kllmol------------Acetonitrile, C zII3 N
L
RDS22-103
X w-3040
Acetylene, C2I-~
g
AU11I
lPRE
lPRE
-----_ .... _----X a-3000
AUfH
L------------Air
AUrH
gAmmonia, NH}
TP89354
Alm-I
g
JPRE
X m-500
L
X a-500
AlITH--- ---------Ammonium
J 747
I
perchlorate,
NH4 ClO 4
Ammonium nitrate,
IV
TP89371
NH4 N)3
L
X p-9370
Aniline, C61-4NH2------------Benzene, C6I-J"
X p-3200
L------------Beryllium, Be
sref. element------------n-Butane, C 4 H 1Og
X w-1350
AUfH
X m-1350
X m-1350
L
AUrIl
i-Butane, C4 H1O
X w-1350g
AUfH
X m-1350
X m-1350
AUTH
Lg
X w-2600
I-Butene, C4I-~
AlTTH
X m-2600
L
X m-2600
AUIH------------Chlorine, el zref. elementg
JPRE
HI 6-101
AUfH------------X k-120
AUI11
L
Chlorine trifluoride,
TPR9 194
AlTTH
JPRD
HI 6-101g
CIFj
L
X a-140
AlnH-----------Cyanogen, C 2 N2g
TP91 225
HI 6-104
AUIH
L
AUIII
HI 6-104-----------Diborane, B)-J"
TP81 35
JPRE
JPRE
g
AlITH
L
lPRE
AlITH
-----------Ethane, C 2 l:-\,X m-1350
RD185
g
AUrH
X m-1350
ALTTH
L-----------------------L
X p-5000
Ethanol, CzI-IsOH-----------Ethylene, C 2H4
X w-2600g
AlITH
JPRE X m-2600
X m~2600
AUTH
L
Ethylene oxide,
J 662
AUfI-!
X m-6I50
g
C zI-I4O------------L
X m-6150
AtTTH-----------Ethylene polymer,s
Alm-f(CH 2 ),
Fluorine, F2
ref. element
g
AurH
lPRD
HI 6-102------------L
III 6-102
AUrH-----------------------n-Heptane, C 7 H16
X p-lOlO
L-----------------------X p-I440
L
n-Hexane, Cr,H'4-----------------------TP89361
L
Hydrazine, NJ~-----------ref. element
Hydrogen, H2
g
JPRE
lPRE
lPRE
------------JPRE
L
Aln'H-------~-----HI 15--43-----------~-----~----~----------~------------~------~---------------~-----------------~--------------~------~-----------------~-------~-------~----~---------------~---------~--------------~~----------~---------------~------~~-----------------~-------~---------------~---------~---------~-----------~-----~-------~---~-~-------~--------

92

Density,
g/cm3

lPRE
---------------------------

H2 B-365
HI 4-38

HI 4-39
HI 3-37
X d-3200
HI 4-43~------------~

X d-1350--------------

X d-1350--------------

X d-2500---~----~-----

X d-I20--------------

lCS50 191~-~-------~---

HI 4-58--------------

lPRE--------~-----

X d-I350
X a-5030---------~~---

X d-2500~------------

HI 3-243

MARK--~----------Xd-90
X d-I460
X a-lOlO
X a-500-~-----------JPRD

Species

Hydrogen peroxide,
~Oz

IRFNA
let-A
lP-4, RP-l
JP~5, ASTMAI
Lithium, Li
Lithium perchlorate,
LiCI04
Methane, CH4
Methanol, CH30H
Monomethyl
hydrazine, CH6 Nz
Nitric acid, HN0 3
Nitrogen, N z
Nitrogen tetroxide,
NZ0 4
Nitrgen trifluoride,

Phase

L

L
L
L
L
s
L

TABLE 0.1- Continued.
Assigned
Boiling
HZ98 IS point,
enthalpy,
Hbp'kl/malK
kl/mal-----------X p~30------------~---------------------~--------~--------------TP82286------------

g
L
L
L

--- ------ ---X m-lOlO~-----~-------------------

g
L
g
L
g

---- .... --------------------------------

Lg-------------

X k-460------------~~---~--~--_

... -

Hbp~

Hbp,re'kl/molAUI'H
GRACIA
AUIl-I
AUfH
ref. element
TP82286l763
TP9l46AUTH
X p-5000
X p-9220
TP89231
AUIH
ref. element
AUfH
TP89212
AUi'll
TP89376

l1fL,ap'
kl/mol-------------

Xd-30-------------

AUfl-I
FAITH
SP273
SP273
HI 4--69
SP273
HI 4---469--------------------------~-------------------------~---------------~------

AUfH

JPRE

Xm-1350--------------------------------------

X d-lOlO
X a-5030
HI 3-283

HI 6-102--------------------------

AUnI

lPRD

Density,g/cm3-------------

X a-51O

X m-470-------------

HI 4--79-------------

JPRC~------------

JPRC-------------

AllTH

.TPRE

JPRE

~---------~--

NF3

Nitromethane,Cl-[3:l'-.D z
n~Octane, C g H l8
i-Octane, CgH lg
Oxygen,Oz
Oxygen di11uoridc,
OFz
Ozone, 03
Pentaborane, BsH;
n -Pentane, CSH lZ
Perchloryl fluoride,
CIF03
Propane, CJig
Propylene, C31~
Propyl nitrate,
C 3H7:l'-.DJ
Toluene, C 7Hg
Unsymmetricaldimethyl hydrazine(UDMH), C zllgN2

L

X a-520

L-------------

L
L
g
L
g

L
g
L
L

L
g
L
g
L
g
L
L
L
L

AUfH
X p~9520----~--~--~~~-------------

X p-lOlO
X p-1490
ref. element
AUfH
TP89 162

AUfl-IlPRE--- ----------

AUTll
TP89 103

AUTI-lJPRFi--------------------------------------X m-IO-------------

HI 6-102------------._------------

AUnl

lPRD

Xm-lO
HI 6-102

X m-lO

AUTH-------------J 300
X p-1350
RDS22-49-------------

HI 6-101

AUfH
X w-1350
AUrI-I
X w-2600
AUfH
PED 178-------~-~---

X m-2600---------------------~----------------

X p-3200
X p-9220------------~

HI 4-80----~~~------

Xd-90-------------

X m-IO

X m-1350

X d~I490
X d-1493---------------------------------------------------------------

HI 4--79
HI 15--47~------------AUfH

HI 6-101

AlITI-l

X m-1350

AUIH

X m~2600------------~

lPRE
JPRA
X a-lOlO--------~----

HI 4-53---------~----------------------------------------------------~----------~~--~-- -~----~~-

X d~1350-~---------~-

X d-2600
Hi 3-427
X a-3200
HI 3-283

93

TABLE D.1.-Concluded.
References:
AUTH: Calculated by the authors (assigned enthalpy either from the equation in appendix C or from heats of
combustion for jet fuels; sensible heat from molecular data).
FAITH: Faith, L.E., Ac~erman, G.H., and Henderson, H.T., 1971, "Heat Sink Capability of Jet A Fuel: Heat
Transfer and Coldng Studies," NASA CR-72951.
GRACIA: Gracia-Salcedo, C.M., Brabbs, T.A., and McBride, B.1., 1988, "Experimental Verification of the
Thermodynamic Properties for a Jet-A Fuel," NASA TM-IOI475.
HI: Lide, D.R, ed., 1992, CRe Handbook of Chemistry andPhysics, 73th Ed., CRC Press, Inc., Boca Raton, FL.
H2: Weast, RC., ed., 1984, CRC Handbook of Chemistry andPhysics, 65th Ed., CRC Press, Inc. Boca Raton, FL.
J: Chase, M.W., Jr., ed., 1985, "JANAFThermochemical Tables," Third Ed., Pts. 1 & 2, J. Phys. and Chern. Ref.
DaJa, Vol. 14, Supp!. 1.
JCS: Banks, A.A.; and Rudge, A.J., 1950, "The Determination of the Liquid Density of Chlorine Trifluoride,".
J. Chem. Soc., Pt. I, pp. 191-193.
JPR: Joint Anny-Navy-Air Force Thermochemical Panel, "JANAF Thermochemical Data," Dow Chemical Co.,
Midland, MI, Ser. A,June 1963; Ser. B, Jan. 2,1964; Ser. C, Apr. 1965; Ser. D, Mar. 1%6; Ser. E, Jan.
1967.
.
MARK: Mark, H.F., Gaylord, N.G., and Bikales, N.M., eds., 1967, Encyclopedia of Polymer Science andTechnology, Vol. 6. Interscience Publishers, New York, p. 304.
PED: Pedley, l.B., Naylor, RD., and Kirby, S.P., 1986, Thermochemical Data of Organic Compounds, Second
Ed., Chapman and Hall, London.
RDl: Pamidimukkala, KM., Rogers, D., and Skinner, G.B., 1982, "Ideal Gas Thermodynamic Properties of CI-I3 ,CD)' CD4 , C 2D2, C 2 D4 , C 2 D6 , C 2 H6 , C~N2aI3'''J. Phys. andChem. Ref. Data, Vol. II. No.1, pp. 83-99.
RDS2: Wagman, D.D., et aI., 1982, "The NBS Tables of Chemical Thermodynamic Properties, Selected Values For
Inorganic and C 1 andC 2 Organic Substances in SI Units," J. Phys. Chem. Ref. Da1a, Vol. 11, Supp!. 2.
SP273: Gordon, S., and McBride, B.l., 1976, Computer Program for Calculation of Complex Chemical
Equihbrium Compositions, Rocket Performance, Incident and Reflected Shocks, and Chapman-Jouget
Detonations, NASASP-273 (Interim Revision).
TP81: Gurvich, L.V., et aI., 1981, Thermodynamic Properties of Individual Substances, Vol. III, Pts. 1-2, Nauka,
Moscow, U.S.S.R.
TP82: Gurvich, L.V., et aI., 1982, Thermodynamic Properties of Individual Substances, Vol. IV, Pts. 1-2, Nauka,
Moscow, U.S.S.R
TP89: Gurvich, L.V., Veyts, LV., and Alcock, C.R, 1989, Thermodynamic Properties of Individual Substances,
Fourth Ed., Vol. 1, Pts. 1 & 2, Hemisphere Publishing Corp., Washington, DC.
TP91: Gurvich, L.V., Veyts, LV., and Alcock, C.R, 1991, Thermodynamic Properties of Individual Substances,
Fourth Ed., Vol. 1, Pts. 1 & 2, Hemisphere Publishing Corp., Washington, DC.
X: Anon., 1985-1986, TRC Thermodynamic Tables, Nonhydrocarbons; or TRC Thermodynamic Tables,
Hydrocarbons. Thermodynamics Research Center, Texas A&M University, College Station, TX. (Looseleaf
Tables.)94

AppendixE

Format and List of Species With
Thermal Transport Property Data
Most of the library of thennal transport property data in the form of least-squares
coefficients (trans.inp) are taken from Svehla (1995). However, since the publication of his
report, Mr. Svehla has revised some of the data (Svehla, 1996). At present, this library
contains data for 65 reaction products and 42 binary interaction parameters. However, as data
for species or interactions are added, revised, or deleted, these numbers may change. The
format for the functional form used in trans.inp is given in table E.1. The current set of leastsquares coefficients in trans.inp is given in table E.2. This set replaces the set given intable III of SveWa (1995). The last column in table E.2 indicates whether the coefficientswere taken from Svehla (1995) or Svehla (1996). Chapter 1 and section 5.25 discuss
processing the trans.inp data and storing the processed data in trans.lib for subsequent use in
the CEA program.

95

1a

TABLE E.1.-FORMAT FOR THERMAL TRANSPORT PROPERTY DATA
Records
Contents
FormatColumns
Species name
A 15
1-15

Any numberbfrom 1 to 6

Second species name if binary interaction (blankfor pure species)

A15

17-31

V if there are viscosity coefficientsAl

35

Temperature intervals for viscosity (0. 1.2, or 3)

II

36

C if there are thermal conductivity coefficientsAl

37

Temperature intervals for thermal conductivity(0, 1, 2, or 3)

It

38

Comments (references, date, etc.)

A40

41-80

V if coefficients are for viscosityAl

2

C if coefficients are for thermal conductivity

Al

2First and last temperatures of temperature interval

2F9.2

3-20

Four coefficients in equations belowc

4E 15. 8

21 ~80a. Header record for each pure species or binary interaction.
b. The number of records for each pure species or binary interaction equals the sum of thenumber of temperature intervals for both viscosity and thermal conductivity (sum of
numbers in columns 36 and 38 of header record). Temperature intervals must be inincreasing order. Viscosity or thermal conductivity order is immaterial. Any numberof species is permitted between the first record (tran) and the last record (end).
c. The empirical equations follow (coefficients are different for each property):

96

Viscosity:

In 'Y/

Thermal conductivity:

In A

Interaction parameter:

In 'YJ(i,j)=

B C
AInT+-+-+D
2

T T

TABLE E.2.~ VISCOSITY AND TlffiRMAL CONDUCflVITY COEFFICIENTS IN trans.inp
trans.inp Filetransport property coefficientsAr
V3C3 BICR ET AL (1990)
V 200.0
O.61205763E OO-O.67714354E 02 0.19040660E 03 0.21588272E 01
1000.0V 1000.0
5000.00.69357334E 00 0.70953943E 02-0.28386007E 05 0.14856447E 01
15000.0
V 5000.0
0.76608935E+oO 0.67867215E+03-0.84991417E+06 0.77935167E+00
C 200.0
1000.00.60968928E OO-0.70892249E 02 0.58420624E 03 0.19337152E 01
5000.0C 1000.0
0.69075463E 00 0.62676058E 02-0.25667413E 05 0.12664189E 01
C 5000.0 15000.0
0.76269502E+OO 0.62341752E+03-0.71899552E+06 0.56927918E+00
BCL3
V2C2 SVEHLA (1962)
V 300.0
1000.00.52572590E OO-0.27B03504E 03 0.19159256E 05·0.24373790E 01
V 1000.0
5000.00.62929553E OO-0.60723560E 02-0.37711618E 05 0.15615047E 01
C 300.0
0.41518585E OO-0.48149960E 03 0.30788060E 05 0.33168239E 01
1000.0C 1000.0
5000.00.61148589E OO-0.18167042E 03-0.20976969E as 0.17127671E 01
BF3
V2C2 SVEHLA (1962,1994)
V 300.0
1000.00.58778079E OO-0.96213686E 02-0.37660007E 03 0.21035273E 01
V 1000.0
5000.00.64430285E 00 0.73362845E 01-0.23890605E 05 0.16330508E 01
C 300.0
1000.00.3928B181E OO-0.53781426E 03 0.39023491E 05 0.4228700GE 01
C 1000.0
5000.00.60695214E OO-0.19889031E 03-0.23403767E 05 0.24734586E 01
Br2
V2C2 SVEHLA (1962,1994)
V
300.0
1000.00.45241871E OO-0.52542766E.03 0.61354230E 05 O.35322870E 01
V 1000.0
5000.00.60111079E OO-0.22499274E 03-0.14517179E 05 O.22805949E 01
1000.0C 300.0
0.13579199E OO-0.80137295E 03 0.83046621E 05 O.48052172E 01
o. 13602376E OO-0.21904601E 04 0.77769913E 06 O.54980508E 01
C 1000.0
5000.0C
V2C2 BIOLSI (1982)
V 1000.0
5000.0O.80124735E+OO 0.17261643E+03-0.69940019E+05 0.88364870E-01
V 5000.015000.0
0.10344416E+Ol O.31310924E+04-0.45512020E+07-0.23102402E+01
C 1000.0
5000.00.80224051E+OO 0.17739617E+03-0.72350849E+05 0.10329911E+01
C 5000.0 15000.0
O.10355137E+Ol 0.31489830E+04-0.45854028E+07-0.13676372E+01
C
0
V1CD CAPITELLI & FICOCELLI (1973)
V 4000.0 15000.00.12635466E+Ol 0.46866S28E+04-0.59789292E+07-0.43066246E+01
CCLF3
V2C2 SVEHLA (1994)
V 300.0
0.57775962E 00-0.11595656E 03 O.13894846E 04 0.20719367E 01
1000.0V 1000.0
5000.00.64278913E 00 0.lB533422E 01-0.2500077SE 05 O.15313091E 01
1000.0O.30701673E 00-0.5B621120E 03 O.37562739E 05 O.45977739E 01
C 300.0
C 1000.0
5000.00.59447897E 00-O.25405493E 03 0.15214514E 05 O.23022470E 01
CCL2F2
V2C2 SVEHLA (1994)
V 300.0
O.551B8576E 00-0.18084616E 03 0.74399094E 04 0.220B9157E 01
1000.0V 1000.0
5000.0O.63820813E 00-0.16395245E 02-0.31624406E 05 0.14872353E 01
1000.0O.37505967E OO-0.4597533BE 03 O.13246268E as 0.38355232E 01
C 300.0
C 1000.0
5000.0O.59226968E 00-0.2598B712E 03 0.2191697BE 05 o .21265S25E 01
CCL3F
V2C2 SVEHLA (1994)
V 300.0
1000.00.52599241E 00-0.27466441E 03 O.18699061E 05 0.23965367E 01
V 1000.0
5000.0O.62963969E OO-0.58775545E 02-0.374216B9E as 0.1520798GE 01
1000.00.25082525E 00-0.69236016E 03 O.58465610E 05 0.46480202E 01
C 300.0
0.58847038E OO-0.29613903E 03 0.29176214E 05 0.194B7185E 01
C 1000.0
5000.0
CCL4
V2C2 SVEHLA (1994)
V
300.0
1000.00.52914726E 00-0.26173707E 03 0.16983586E 05 0.22508228E 01
5000.00.63117223E 00-O.508739B7E 02-0.37435436E 05 0.13 896152E 01
V 1000.0
1000.00.39796301E OO-0.45970713E 03 0.25887539E 05 0.321B2809E 01
C 300.0
O.60345477E 00-0.22665258E 03 0.12105253E 05 0.15795218E 01
C 1000.0
5000.0
V2C2 BOUSHEHRI ET AL (1987)
CF4
SVEHLA (1994)
V 300.0
0.G2364242E 00-O.15734540E 02-0.11268526E 05 0.17826560E 01
1000.0V 1000.0
5000.00.52895824E OO-0.34441290E 03 O.10572786E 06 0.26483931E 01
O.29102001E OO-0.62544847E 03 0.40137545E 05 O.50559989E 01
C 300.0
1000.05000.00.46958735E 00-O.71864138E 03 0.17601542E 06 O.37798145E 01
C 1000.0

Ref.

a

a
b
a
a
b

a
a
a
a
a
a
a
a
a
a
a
a
b
b
b

b
b

a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a

97

TABLE E.2.-Continued.
CHCLF2
V 300.0
V 1000.0
C 300.0
C 1000.0
CHCL2FV 300.0
V 1000.0
C 300.0
C 1000.0
CHCL3
V 300.0
V 1000.0
C 300.0
C 1000.0
CHF3
V 300.0
V 1000.0
C 300.0
C 1000.0
CH2CL2V
300.0
V 1000.0
C 300.0
C 1000.0
CH3CL
V
300.0
V 1000.0
C 300.0
C 1000.0
CH4
V 200.0
V 1000.0
C 200.0
C 1000.0
CH4
V 300.0
V 1000.0
CH30H
V 300.0
V 1000.0
C 300.0
C 1000.0

1000.05000.01000.05000,.0
1000.05000.01000.05000.01000.05000.01000.05000.01000.05000.01000.05000.01000.05000.01000.05000.01000.05000.01000.05000.01000.05000.01000.05000.002
1000.05000.01000.05000.01000.05000.0

CO
V

200.0

V 1000.0

V 5000.0
C 200.0
C 1000.0
C 5000.0
COV 300.0
V 1000.0
V 5000.0

98

1000.05000.015000.0
1000.05000.015000.0CO21000.05000.010000.0

V2C2 SVEHLA (1994)
OO-O.19151112E 03 0.92302454E 04 0.22465942E 01
00-0.18642363E 02-0.35632589E 05 0.15442566E 01
OO-0.40344356E 03 0.76841854E 04 O.26855196E 01
OO-O.42144805E 03 0.17313314E 05 0.26B52328E 01
V2C2 SVEHLA (1994)
0.54261029E 00-0.23693132E 03 0.14722387E 05 0.22950603E 01
0.63322050E OO-0.43091499E 02-0.36892355E as 0.15269221E 01
0.64554399E 00-0.29614334E 03-0.34305973E 04 0.18524599E 01
0.58133799E 00-O.38461009E 03 0.86999769E 04 0.23723154E 01
V2C2 SVEHLA (1962,1994)
O.52563815E 00-0.28025371E 03 0.19479241E 05 O.23475804E 01
0.62913497E 00-0.61794789E 02-0.38001753E 05 0.14716717E 01
0.43704658E OO-0.53648192E 03 O.29187663E 05 0.32672103E 01
0.55383193E 00-0.51059645E 03 0.74636570E 05 0.23891512E 01
V2C2 SVEHLA (1994)
0.58092199E 00-0.11862927E 03 0.25039931E 04 0.20948315E 01
0.64363521E 00-0.70920001E OO-0.25099472E 05 0.15713073E 01
0.73882642E 00-0.170S8713E 03-0.32698111E 05 0.16126977E 01
0.58787951E 00-0.35203256E 03-0.17448254E 05 0.28215977E 01
V2C2 SVEHLA (1994)
0.57185884E 00-0.34599168E 03 0.32975791E 05 0.21786059E 01
0.60922943E 00-0.18784625E 03-0.27411214E 05 0.18227006E 01
0.25979341E 00-0.105100418 04 0.11078850E 06 0.51956543E 01
0.48080771E 00-0.95120530E 03 0.17139452E 06 0.35085367E 01
V2C2 MONCHICK & MASON (1961) SVEHLA (1994)
0.58181268E OO-0.30714376E 03 0.27516618E 05 0.20941516E 01
0.61479454E 00-0.16327574E 03-0.27926072E 05 0.17778956E 01
0.43048390E 00-0.96586387E 03 0.91616260E 05 0.44424192E 01
0.44418462E 00-0.11573896E 04 0.19422838E 06 0.44366915E 01
V2C2 BOUSHEHRI ET AL (1987) SVEHLA (1994)
O.57643622E 00-0.93704079E 02 0.86992395E 03 0.17333347E 01
O.66400044E 00 0.10860843E 02-0.76307841E 04 0.10323984E 01
0.10238177E 01-0.31092375E 03 0.32944309E 05 0.67787437E 00
0.77485028E 00-0.40089627E 03-0.46551082E 05 0.25671481E 01
V2CO SVEHLA (1994)
0.68971658E 00-0.82884483E 00-0.47557575E 04 0.11497470E 01
0.69426262E 00-0.17685146E 02 0.59452784E 04 0.11244994E 01
V2C2 MONCHICK & MASON (1961) SVEHLA (1994)
0.58408390E 00-0.30677174E 03 0.27569892E 05 0.19794348E 01
0.61454903E 00-0.16540203E 03-0.27881995E 05 0.16830713E 01
0.33374512E 00-0.11617154E 04 0.10894211E 06 0.57684124E 01
0.42733576E OO-0.12682528E 04 0.20900463E 06 0.51283860E 01
V3C3 SVEHLA (1994)
0.62526577E 00-0.31779652E 02-0.16407983E 04 0.17454992E 01
0.87395209E 00 0.56152222E 03-0.17394809E 06-0.39335958E 00
0.88503551E+00 0.90902171E+03-0.73129061E+06-0.53503838E+00
0.85439436E+00 0.10573224E+03-0.12347848E+05 0.47793128E+00
0.88407146E+00 0.13357293E+03-0.11429640E+05 0.24417019E+00
0.24175411E+Ol 0.80462671E+04 0.31090740E+07-0.14516932E+02
V3CO SVEHLA (1995)
0.68926185E 00-0.13796096E 01-0.46847568E 04 O.13060681E 01
0.69417954E 00-0.18021840E 02 0.60950694E 04 0.12779603E 01
0.61979004E+00-O.79830067E+03 0.11130858E+07 0.20233248E+Ol

O.55518512E
O.63832814E
0.57111784E
O.57237181E

a
a
a
a
a
a
a
a
a
a
a
a
a

a
a
a
a

a
a

a
a
a
a

a
a
a
a
a

a
a
a
a
a
a
a
a
b
b
b
b
b
b
b

TABLE E.2.-Continued.

coN2
V 200.0
1000.0V 1000.0
5000.0V 5000.0 15000.0
CO02
V 300.0
1000.0V 1000.0
5000.0V 5000.0 15000.0
COS
V 300.0
1000.0V 1000.0
5000.0C 300.0
1000.0C 1000.0
5000.0
CO2
V 200.0
1000.0V 1000.0
5000.0V 5000.0 10000.0
C 200.0
1000.0C 1000.0
5000.0C 5000.0 10000.0
CO2
H2V 300.0
1000.0V 1000.0
5000.0V 5000.0 10000.0
CO2
H2O
V 300.0
1000.0V 1000.0
5000.0V 5000.0 10000.0
CO2N2
V 300.0
1000.0V 1000.0
5000.0V 5000.0 10000.0
CO202
V 300.0
1000.0V 1000.0
5000.0V 5000.0 10000.0
CS2
V 300.0
1000.0V 1000.0
5000.01000.0C 300.0
C 1000.0
5000.0C2H2,acetylene
V 300.0
1000.0V 1000.0
5000.0C 300.0
1000.0C 1000.0
5000.0
C2H4
V 200.0
1000.0V 1000.0
5000.0C 200.0
1000.0C 1000.0
5000.0
C2H6
V 200.0
1000.0V 1000.0
5000.0C 200.0
1000.05000.0C 1000.0

V3CO SVEHLA (1994)
0.62526577E OD-0.31779652E 02-0.16407983E 04 0.17454992E 01
D.87395209E 00 0.56152222E 03-0.17394809E 06-0.39335958E 00
D.88503551E+OO 0.90902171E+03-0.73129061E+06-0.53503838E+OO
V3CO SVEHLA (1994)
0.70122551E 00 0.51717887E 01-0.14240838E 04 0.12895991E 01
0.66744478E OO-0.86348036E 02 0.27445341E 05 0.15855986E 01
O.21151565E+00-0.91881544E+04 0.18253525E+08 0.65600002E+01
V2C2 SVEHLA (1962)
0.52573161E 00-0.27668290E 03 0.18982511E 05 0.25359860E 01
0.62947137E 00-0.59744762E 02-0.37616630E 05 0.16590382E 01
0.56172985E 00-0.42167958E 03 0.28198920E 05 0.26921796E 01
0.65503267E 00-0.17103349E 03-0.50472397E 05 0.18756918E 01
V3C3 BOUSHEHRI ET AL (1987) SVEHLA (1994)
0.51137258E 00-0.22951321E 03 0.13710678E 05 0.27075538E 01
0.63978285E 00-0.42637076E 02-0.15522605E 05 0.16628843E 01
0.72150912E+00 0.75012895E+03-0.11825507E+07 0.85493645E+00
0.48056568E+00-0.50786720E+03 0.35088811E+05 0.36747794E+01
0.69857277E+00-0.11830477E+03-0.50688859E+05 0.18650551E+01
0.10518358E+01-0.42555944E+04 0.14288688E+08-0.88950473E+OO
V3CO SVEHLA (1994)
0.66101867E 00-0.40651732E 02-0.42877325E 04 0.74444661E 00
0.70351908E 00 0.19946369E 02-0.13336698E 05 0.39931502E 00
0.66401272E+00-0.33671205E+03 0.41670634E+06 0.78993145E+00
V3CO SVEHLA (1994)
0.56499100E 00-0.32219550E 03 0.26301733E OS 0.26351165E 01
0.68455483E 00-0.33114757E 02-0.s8456473E 05 0.16048763E 01
0.70748069E+00 0.11586070E+03-0.22772841E+06 0.13865863E+01
V3CO SVEHLA (1994)
0.689261858 00-0.13796096E 01-0.46847568E 04 0.13060681E 01
0.69417954E 00-0.18021840E 02 0.60950694E 04 0.12779603E 01
0.619790048+00-0.79830067E+03 0.11130858E+07 0.20233248E+01
V3CO SVEHLA (1994)
0.55753165E 00-0.17140020E 03 0.72594450E 04 0.24603725E 01
0.66011947E 00 0.25362441E 02-0.39828007E 05 0.16020458E 01
0.66564107E+00 0.13062608E+03-0.27519463E+06 0.15433736E+01
V2C2 SVEHLA (1962)
0.54573740E 00-0.36042852E 03 0.33177885E 05 0.23235206E 01
0.614277878 00-0.15337427E 03-0.36078656E 05 0.17122621E 01
0.52603181E 00-0.50780062E 03 0.41502601E 05 0.26684257E 01
0.66331137E 00-0.15058989E 03-0.68462565E 05 0.14728865E 01
V2C2 SVEHLA (1962,1994)
0.56299896E 00-0.15304865E 03 0.46019734E 04 0.18854528E 01
0.64038318E OO-0.72360229E 01-0.29612277E 05 0.12393032E 01
0.84030505E 00-O.10051610E 03-0.26171483E 05 0.11926036E 01
0.62672572E 00-0.58147342E 03 0.10751724E 06 0.30152260E 01
V2C2 BOUSHEHRI ET AL (1987) SVEHLA (1994)
0.59136053E 00-0.14088938E 03 0.30012800E 04 0.17018932E 01
0.66000894E 00 0.39114999E 02-0.52676489E 05 0.11033601E 01
0.24736650E 00-0.10589987E 04 O.89911568E 05 0.64456092E 01
0.51616035E 00-0.92486351E 03 0.15723887E 06 0.43873845E 01
V2C2 BOUSHEHRI ET AL (1987) SVEHLA (1994)
0.59089348E 00-0.13994405E 03 0.29868374E 04 0.15988866E 01
0.66061323E 00 O.41062220E 02-0.52656212E 05 0.99191640E 00
0.70867490E OO-O.63016563E 03 0.50951026E 05 0.29508724E 01
0.57947247E 00-0.64990228E 03-0.37806714E 04 O.39178395E 01

a
a
b

a
a
b

a
a
a
a
a
a
b
b

b
b
a
a
b

a
a
b
a
a
b

a
a
b

a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a

99

TABLE E.2, - Continued.
C2H50HV 300.0
V 1000.0
C 300.0
C 1000.0
C2N2
V
300.0
V 1000.0
C 300.0
C 1000.0
CL2
V 300.0
V 1000.0
C 300.0
C 1000.0'D2
V 200.0
V 1000.0
C 200.0
C 1000.0
D20
V 300.0
V 1000.0
C 300.0
C 1000.0
eV 2000.0
C 2000.0

eV 2000.0
V 8000.0
eV 1000.0
V 8000.0
eV 5000.0
V10000.0

eV 2000.0
V 6000.0
eV 5000.0

V10000.0

eV 2000.0
V 6000.0
eV 2000.0
V 6000.0
F2V
200.0
V 1000.0
C 200.0
C 1000.0100

1000.05000.01000.05000.01000.05000.01000.05000.01000.05000.01000.05000.01000.05000.01000.05000.01000.05000.01000.05000.05000.05000.0H

8000.015000.0
H2
8000.015000.0N10000.015000.0NO
6000.015000.0N210000.015000.0o6000.015000.002
6000.015000.0
1000.05000.01000.05000.0

V2C2 SVEHLA (1994)a00-0.31382676E 03 0.26089200E 05 O.21078504E 01
a00-0.11935847E 03-0.34285357E 05 0.14645259E 01
a00-0.12251941E 04 0.11716632E 06 0.65571580E 01
a
OO-0.12128199E 04 0.21462928E 06 0.50153152E 01
V2C2 SVEHLA (1962)a0.52471007E 00-0.28839713E 03 0.20625913E 05 0.23625791E 01
a0.62832879E 00-0.66440897E 02-0.38542772E 05 0.14840188E 01
a0.76361743E 00-0.24078764E 03 0.11152243E 05 0.13726624E 01
a0.66495585E OO-0.19733792E 03-0.59902201E 05 0.20817971E 01
V2C2 SVEHLA (1994)a0.53516134E OO-0.23624735E 03 0.13738454E 05 0.24970463E 01
a0.63348430E 00-0.38786240E 02-0.35830615E 05 0.16699633E 01
a0.34156262E 00-0.46059166E 03 0.34712872E 05 0.37412367E 01
a0.8739252'68 00 0.19876120E 03-0.28784264E 05-0.53204988E 00
V2C2 SVEHLA (1994)a0.74566381E 00 0.43611949E 02-0.32396252E 04 0.48064872E 00
aO.96835229E 00 0.68241861E 03-0.21129775E 06-0.14883773E 01
a0.11180891E 01 0.29771761E 03-0.23323095E 05 0.94208300E-Ola0.10670411E 01 0.49811245E 03-0.14904299E 06 0.37216028E 00
V2C2 MATSUNAGA & NAGASHlMA(1983) SVEHLA(1994)a0.51773336E OO-0.66413680E 03 O.82973607E 05 0.29575078E 01
aO.58703537E OO-O.55101540E 03 0.61063786E 05 O.23875750E 01
a0.74656939E OO-0.10592831E 04 O.17838377E 06 O.26602773E 01
a0.50642285E OO-0.16925317E 04 O.37493403E 06 O.47558493E 01
VIC1 MASON ET AL (1967)a0.59319174E 01 0.56594215E 04-0.22576125E 07-0.53458874E 02
a0.59320964E 01 0.56601476E 04-0.22577332E 07-0.42512600E 02
V2CO CAPITELLI ET AL (1976)b0.12996657E+Ol 0.29049200E+04-0.19315880E+07-0.96081497E+Olb0.13439163E+Ol 0.62981265E+04-0.140B8393E+08-0.10240040E+02
V2CO CAPITELLI ET AL (1976)b0.13682927E+Ol 0.70665102E+04-0.56748561E+07-0.10480386E+02b0.20875514E+Ol 0.27345700E+05-0.63775336E+08-0.18571585E+02
V2CO CAPITELLI & DEVOTO (1973)
0.14373966E+01 0.18230345E+05-0.27492090E+08~0.96279246E+Ol bb
0.22566004E+01 0.48916050E+05-0.13996043E+09-0.19116958E+02
V2CO GUPTA ET AL (1990)b
0.61252493E+OO 0.46768585E+04-0.30292080E+07-0.30467956E+01b-0.31058569E+01-0.69841I16E+05 O.15359384E+09 0.37370344E+02
V2CO CAPITELLI & DEVOTO (1973)b0.22167522E+01 0.22078280E+05-0.26142843E+08-0.18975334E+02b0.14276153E+Ol O.81306835E+04 0.41382925E+07-0.10615166E+02
V2CO GUPTA ET AL (1990)b-0.36876460E+00-0.19261587E+04 0.72235159E+06 0.82699294E+01b0.12858415E+00 0.88173340E+04-0.22555849E+08 0.27992711E+Ol
V2CO GUPTA ET AL (1990)b-0.12686144E+01-0.64961158E+04 0.37615998E+07 0.15676996E+02b
O.44642126E+01 0.65553833E+05-0.10919736E+09-0.43066392E+02
V2C2 SVEHLA (1962,1994)a0.61198519E 00-0.396479608 02-0.17294474E 04 0.21237710E 01
a0.64406091E 00-0.58273377E 00-0.52243255E 04 0.18666294E 01
a0.46767823E OO-0.26624115E 03 0.18169657E 05 0.36165585E 01
a-0.19981248E 00-0.25129092E 04 0.80775379E 06 O.96845049E 01
0.54586031E
0.61957901E
0.22185435E
0.42915840E

TABLE E.2. - Continued.
H

V 1000.0
V 5000.0
C 1000.0
C 5000.0
H

V 2000.0
V 8000.0
H

V 1000.0
V 5000.0
H

V 1000.0
V 5000.0
H
V 1000.0

V 6000.0
H

V

600.0

V 3000.0
H

V 1000.0
V 5000.0
HBr
V 300.0
V 1000.0
C 300.0
C 1000.0
HCN
V
300.0
V 1000.0
C 300.0
C 1000.0
HCL
300.0
V
V 1000.0
C 300.0
C 1000.0
HF
V

300.0
1000.0C 300.0
C 1000.0
HF
V 300.0
V 1000.0
HI
300.0
V
V 1000.0
C 300.0
C 1000.0
V

V2C2 VANDERSLICE ET AL (1962)
0.74226149E+00-0.40132865E+03 0.18554165E+06 0.46741844E-01
0.87486623E+00-0.25022902E+04 0.709550488+07-0.938884558+00
0.74166119E+00-0.40487203E+03 0.18775642E+06 0.34843121E+01
0.87447639E+00-0.25089452E+04 0.71081294E+07 0.24970991E+01
V2CO CAPITELLI ET AL (1976)
0.65497943E+00 0.43620326E+03-0.20032290E+06-0.15933989E+01
0.35775595E+00-0.56298406E+04 0.14552701E+08 0.16055465E+01
V2CO TANG & WEI (1974)
SVEHLA (1994)
0.91735768E+00 0.22052887E+03-0.57464994E+05-0.93741490E+00
0.94056210E+00-0.17266834E+02 0.82707957E+06-0.11228741E+01
Li
V2CO KRUPENI8 ET AL (1963)
5000.00.88870800E+00 0.25460216E+03-0.71635951E+05-0.24355021E+01
10000.0
0.96451195E+00 O.78151762E+03-0.44137515E+06-0.31717326E+Ol
V2CO STALLCOP ET AL (1992b)
N
6000.00.75455738E+00-0.15697085E+03 0.97258456E+05-0.48331565E-01
16000.0
0.15653364E+01 0.87404680E+04-0.12001036E+08-0.82485581E+Ol
N2V2CO STALLCOP ET AL (1992b)
3000.00.10228384E+01 0.53349114E+03-0.11365313E+06-0.23880331E+01
10000.0
0.13275932E+01 0.14701554E+04-0.14725296E+06-0.51365002E+01
V2CO KRUPENIE ET AL (1963)o5000.00.85479480E+00 O.18680077E+03-0.46790687E+05-0.11272657E+01
10000.0
0.88515794E+00 0.64127280E+02 0.63943230E+06-0.13887887E+01
V2C2 ZELEZNIK & SVEHLA (1970) SVEHLA (1994)
1000.00.54286515E 00-0.32909036E 03 0.28143861E 05 0.29266732E 01
5000.0O.61904039E 00-0.12370443E 03-0.36461217E 05 0.22596924E 01
1000.00.91269760E OO-O.15456150E 03 0.21177636E 05-0.43914664E 00
5000.00.63722B27E 00-0.35434488E 03-0.16663585E 05 0.17013527E 01
V2C2 ZELEZNIK & SVEHLA (1970) SVEHLA (1994)
1000.00.94863717E 00-0.14891490E 03 0.15258721E 05-0.72592817E 00
0.57370725E 00-0.85239973E 03 0.17953641E 06 0.24032031E 01
5000.01000.00.11749061E 01-0.19100307E 03 0.15714065E 05-0.13488014E 01
5000.00.50543688E 00-0.13891056E 04 0.28003144E 06 0.42095130E 01
V2C2 SVEHLA (1994)
1000.00.54302009E 00-0.27882979E 03 0.20927618E 05 0.25895500E 01
5000.00.626739068 00-0.81516979E 02-0.35869154E 05 0.18707238E 01
1000.00.90670645E 00-0.13561693E 03 0.18563886E 05 0.60312859E-01
5000.00.6252113BE OO-0.43742347E 03 0.28720932E 05 0.22964614E 01
V2C2 SVEHLA (1994)
1000.00.81674828E 00-0.23635428E 03 0.22759084E 05 0.70625888E 00
5000.00.58742532E 00-0.55543347E 03 0.67637899E 05 0.25645661E 01
1000.00.12590294E 01 0.11896441E 01-0.47558763E 03-0.19367617E 01
5000.00.51518587E 00-0.14932469E 04 0.37482086E 06 0.43206676E 01
H6F6
V2CO SVEHLA (1994)
1000.00.52633473E 00-0.32896634E 03 0.26842682E 05 0.22132195E 01
5000.00.62213454E 00-0.10239431E 03-0.38543254E 05 0.13902717E 01
V2C2 SVEHLA (1962)
1000.00.53718504E 00-0.22504609E 03 0.12416876E 05 0.27888146E 01
0.63448421E OO-0.33714923E 02-0.34599137E 05 0.19723806E 01
5000.01000.00.83653272E OO-O.10434645E 03 0.90075923E 04-0.38982280E 00
5000.00.65866010E 00-0.18846822E 03-0.37866478E 05 0.96987360E 00

5000.015000.0
5000.015000.0
H+
8000.015000.0
H2
5000.015000.0

b
b
b

b
b
b
b
b
b
b
b

b
b
b
b
b

a

a
a
a
a
a
a
a
a

a
a
a
a
a
a
a
a
a
a
a
a
a

101

TABLE E.2.-Continued.
H2

v

200.0
v 1000.0v 5000.0
c 200.0c 1000.0
C 5000.0
H2
V 300.0
V 1000.0
V 5000.0
H2
V 300.0
V 1000.0
V 5000.0
H2V
300.0
V 1000.0
V 5000.0
H20
V 373.2
V 1073.2
V 5000.0
C 373.2
C 1073.2
C 5000.0
H20
V 300.0
V 1000.0
V 5000.0
H20
V 300.0
V 1000.0
V 5000.0
H2S
V 300.0
V 1000.0
C 300.0
C 1000.0
H6F6
V 300.0
V 1000.0
C 300.0
C 1000.0
HeV
200.0
V 1000.0
V 5000.0
C 200.0
C 1000.0
C 5000.0
He

V 300.0
V 1000.0
V 5000.0102

V3C3 ASSAEL ET AL (1986)
SVEHLA (1994)
1000.00.74553182E 00 0.43555109E 02-0.32579340E 04 0.135562438 00
5000.0O.96730605E 00 0.67931897E 03-0.21025179E 06-0.182516978 01
15000.0
0.10126129E+01 0.14973739E+04-0.14428484E+07-0.23254928E+01
1000.00.10059461E+Ol 0.27951262E+03-0.29792018E+05 0.11996252E+01
5000.0O.10582450E+01 0.24875372E+03 0.11736907E+05 0.82758695E+00
15000.0 -0.22364420E+00-0.69650442E+04-0.77771313E+05 0.13189369E+02
H20
V3CO SVEHLA (1964)
1000.0O.60085490E 00-O.67691161E 02-0.21319326E 04 O.14199776E 01
5000.00.64550551E 00 0.10165601E 02-0.18735061E 05 0.10502885E 01
10000.0
O.66153255E+00 0.22389456E+03-0.37073622E+06 0.88511419E+00
N2
V3CO SVEHLA (1994)
1000.00.66038264E 00 0.35574798E 01-0.95778014E 03 0.70536614E 00
5000.00.62938039E 00-0.69072207E 02 0.19855881E 05 0.97133819E 00
8000.0 -0.77818660E-01-0.82764842E+04 0.11699769E+08 0.81689807E+Ol
02
V3CO SVEHLA (1994)
1000.00.69018087E 00-0.23876092E 00-0.48432502E 04 0.66856355E 00
5000.00.69427291E 00-0.17583177E 02 0.58748504E 04 0.64692305E 00
10000.0
O.62089983E+00-0.78264233E+03 O.10864044E+07 0.13816401E+01
V3C3 SENGERS & WATSON (1986) SVEHLA (1994)
1073.2O.50019557E+00-0.69712796E+03 0.88163892E+05 0.30836508E+01
5000.00.58988538E+OO-O.53769814E+03 0.54263513E+05 0.23386375E+01
15000.0
0.64330087E+OO-0.95668913E+02-0.37742283E+06 0.18125190E+Ol
1073.2
O.10966389E+01-D.55513429E+03 0.10623408E+06-0.24664550E+00
5000.00.39367933E+00-0.22524226E+04 0.61217458E+06 0.58011317E+01
15000.0 -0.41858737E+00-0.14096649E+OS 0.19179190E+08 0.14345613E+02
N2
V3CO SVEHLA (1994)
1000.00.57304553E OO-0.14853813E 03 O.39029324E 04 O.23462780E 01
5000.00.64243064E 00 0.25018380E 01-0.36924430E 05 O.17567700E 01
10000.00.64420052E+OO O.10592615E+OI-0.34300588E+05 O.17418827E+01
02
V3CO SVEHLA {1994}
1000.00.64727375E 00-0.42110733E 01-0.45255490E 04 0.16510807E 01
5000.00.65299406E 00-0.17723412E 02 0.50906530E 04 0.16154623E 01
10000.0
O.60614671E+DO-0.45218012E+03 0.56149352E+06 0.20791053E+01
V2C2 ZELEZNIK & SVEHLA (1970) SVEHLA (1994)
1000.0O.54078516E OO-0.30304377E 03 0.24073168E 05 0.24952022E 01
5000.00.62320319E OO-O.98355396E 02-0.37061803E 05 0.17823252E 01
1000.00.99442135E 00-0.19849376E 03 0.18380943E 05-0.19947763E 00
5000.00.60597875E 00-O.56357581E 03 0.67027311E 04 0.28605490E 01
V2C2 SVEHLA (1994)
1000.00.59712969E 00-0.36775006E 03 0.38256100E 05 0.15811495E 01
5000.0O.60263706E 00-0.23619918E 03-0.24765049E 05 0.14745761E 01
1000.00.82019209E 00-0.29783007E 03 0.17372752E 05 0.94706680E 00
5000.00.53249125E OO-0.75921725E 03 0.10421649E 06 0.33089772E 01
V3C3 BIeH ET AL (1990)
1000.00.75015944E 00 0.35763243E 02-0.22121291E 04 0.92126352E 00
5000.00.83394166E 00 0.22082656E 03-0.52852591E 05 0.20809361E 00
15000.0
O.86316349E+00 O.96205176E+03-0.12498705E+07-0.14115714E+00
1000.00.75007833E 00 O.36577987E 02-0.23636600E 04 0.29766475E 01
5000.00.83319259E 00 0.22157417E 03-0.53304530E 05 O.22684592E 01
15000.00.85920953E+00 0.89873206E+03-0.11069262E+07 0.19535742E+01
N2V3CO SVEHLA (1994)
1000.00.70332377E 00 D.77412205E 01-0.17715400E 04 O.11440787E 01
5000.0O.66785742E OO-O.84659628E 02 0.26695708E 05 0.14530051E 01
15000.0
0.16804077E+01 0.15615203E+05-0.28112833E+08-0.91877596E+01

a
a
b
b
b
b

a
a
b
a
a
b

a
a
b
b
b
b
b
b
b

a

a
b

a
a
b

a
a
a
a

a
a
a
a

a
a
b

a
a
b
b
b

b

TABLE E.2.-Continued.
12
V
300. aV 1000.0
300.0CC 1000.0

1000.05000.01000.05000.0Kr

V 200.0
V 1000.0
V 5000.0

C

200.0

C 1000.0
C 5000.0

1000.05000.015000.0
1000.05000.015000.0

Li
V 1000.0
V 3000.0
C 1000.0
C 3000.0
N
V
V
C
C
N
V

1000.05000.01000.05000.01000.0V 5000.0

N

V 1000.0
V 5000.0
N
V 1000.0

V 5000.0
N
V 1000.0

V 5000.0
N
V 1000.0
V 5000.0
N

V 1000.0

V 5000.0
N+
V 1000.0

V 5000.0

3000.010000.0
3000.010000.0
5000.015000.0
5000.015000.0N+
5000.015000.0
NO
5000.015000.0
N25000.015000.0o5000.015000.00+5000.015000.002
5000.015000.0o5000.015000.0

NH3
V
200.0
V 1000.0
C 200.0
C 1000.0

1000.05000.01000.05000.0NO
V
200.0
V 1000.0
V 5000.0

200.0
C 1000.0
C 5000.0C

1000.05000.015000.0
1000.05000.015000.0

V2C2 SVEHLA (1962)
OO-0.36186119E 03 0.33655931E 05 0.26154108E 01
00-0.15938416E 03-0.35539572E 05 0.20394438E 01
00-O.62470054E 03 0.63289228E 05 O.30234067E 01
00-O.28843448E 04 0.96629457E 06 0.75135419E 01
V3C3 BICH ET AL (1990)
0.58597795E 00-0.12924832E 03 O.47495759E 04 0.25793650E 01
0.68985845E 00 O.56296306E 02-0.36082600E 05 0.17170715E 01
0.76582939E+00 0.68610377E+03-0.82537190E+06 0.97565128E+00
0.58008139E OO-0.13792556E 03 0.60771460E 04 0.16420039E 01
0.68859431E 00 O.51765647E 02-0.34512131E 05 O.74332130E 00
0.76365443E+00 0.65175847E+03-0.73589800E+06 0.12112126E-01
V2C2 HOLLAND ET AL (1986)
0.11808900E+Ol 0.10427008E+04-0.42642819E+06-0.40060038E+01
O.13061758E+01 0.10446775E+04 0.13439272E+06-0.50720601E+01
0.11802957E+Ol 0.10408710E+04-0.42655445E+06-0.24982084E+Ol
0.13086032E+01 O.10695497E+04 0.10781083E+06-0.35944181E+01
V2C2 LEVIN ET AL (1990)
0.83724737E+00 0.43997150E+03-0.17450753E+06 0.10365689E+00
0.89986588E+00 0.14112801E+04-0.18200478E+07-0.55811716E+00
0.83771661E+00 0.44243270E+03-0.17578446E+06 0.89942915E+00
0.90001710E+00 0.14141175E+04-0.18262403E+07 0.24048513E+00
V2CO STALLCOP ET AL (1991)
0.81904143E+00-0.59239089E+02 0.21722555E+05-0.14759287E+00
O.14065434E+01 0.52447258E+04-0.58944155E+07-0.59756079E+01
V2CO CUBLEY & MASON (1975)
0.79891098E+00 0.16929386E+03-0.49068896E+05 0.47986716E+00
0.85695322E+00 0.70223546E+03-0.65589491E+06-0.96805084E-01
V2CO CUBLEY & MASON (1975)
O.84730498E+00 O.22158858E+03-0.65003723E+05 0.51991532E-01
0.92821273E+00 0.97122155E+03-0.92773923E+06-0.75253261E+00
V2CO LEVIN ET AL (1990)
0.70857405E+00-O.14025530E+03 0.76739975E+05 0.13001914E+01
0.98622236E+00 0.23653200E+04-0.27165945E+07-0.14539746E+01
V2CO PARTRIDGE ET AL (1991)
0.71806621E+00-0.22692123E+03 0.63051343E+03 0.88739853E+00
0.12913413E+01 0.49522731E+04-0.57814165E+07-0.47998532E+01
V2CO CUBLEY & MASON (1975)
0.76538325E+00 0.13624746E+03-0.39083438E+05 0.80110069E+00
0.81011289E+00 0.54373468E+03-0.49868094E+06 0.35701613E+00
V2CO PARTRIDGE ET AL (1991)
0.11462863E+01 O.12410378E+04-0.56794094E+06-0.29071183E+01
0.10155522E+01-0.32731184E+03 O.17187573E+07-0.15714289E+01
V2C2 ZELEZNIK & SVEHLA (1970)
SVEHLA (1994)
0.56652403E 00-0.36718083E 03 0.31663844E 05 0.22647443E 01
0.59761003E 00-0.28027339E 03 0.37532457E 04 0.19910129E 01
0.17498387E 01 O.29195254E 03-0.33033738E 05-0.50944985E 01
0.64477673E 00-O.91294723E 03 O.16890182E 05 0.36939751E 01
v3C3 BOUSHEHRI ET AL (1987)
SVEHLA (1994)
0.60262029E 00-O.62017783E 02-0.13954524E 03 O.20268332E 01
0.78009050E 00 0.30486891E 03-0.94847722E 05 O.52873381E 00
0.80580582E+QO 0.62427878E+03-0.57879210E+06 0.26516450E+00
0.9S028758E+OO 0.76667058E+02-0.99894764E+04-0.62776717E-02
0.86215238E+00 O.44568223E+03-0.23856466E+06 O.46209876E+00-0.10377865E+01-0.34486864E+05 0.67451187E+08 0.20928749E+02

0.54929498E
0.61338027E
O.29817264E-0.15544742E

a
a
a
a
a
a
b
a
a
b
b

b
b
b
b

b
b

b
b
b
b

b
b
b
b
b
b
b
b
b

b

b
a
a
a
a
a
a
b
b
b
b

103

TABLE E.2. - Continued.
NO
V 1000.0
V 5000.0
NOCL
V 300.0
V 1000.0
C 300.0
C 1000.0
N02
V 300.0
V 1000.0
C 300.0
C 1000.0
N2
V 200.0
V 1000.0
V 5000.0
C 200.0
C 1000.0
C 5000.0
N2
V 1000.0
V 5000.0
N2
V 300.0
V 1000.0
V 5000.0o5000.015000.0
1000.05000.01000.05000.01000.05000.01000.05000.01000.05000.015000.0
1000.05000.015000.0o5000.015000.002
1000.05000.015000.0

N20

V 200.0
V 1000.0
C 200.0
C 1000.0
N204
V 300.0
V 1000.0
C 300.0
C 1000.0

1000.05000.01000.05000.01000.05000.01000.05000.0Na

V 500.0
V 2000.0
C 500.0
C 2000.0
Ne
V 200.0
V 1000.0
V 5000.0
C 200.0
C 1000.0
C 5000.0

2000.010000.0
2000.010000.0
1000.05000.015000.0
1000.05000.015000.0o
V 1000.0
V 5000.0
C 1000.0
C 5000.0

104

5000.015000.0
5000.015000.0

V2CO CUBLEY & MASON (1975)
0.75990752E+OO 0.13133851E+03-0.37679635E+05 0.87807540E+00
O.80259080E+OO O.51991196E+03-0.47557226E+06 O.45433467E+OO
V2C2 SVEHLA (1994)
0.60503640E OO-0.30599542E 03 O.28616290E 05 O.20637208E 01
O.60958727E 00-0.19972327E 03-0.22243863E 05 0.19768724E 01
0.52036442E 00-O.53758642E 03 O.52600561E 05 0.29380096E 01
0.92835992E 00 0.13511240E 03-0.79751817E 05-0.42066992E 00
V2C2 SVEHLA (1966)
0.57379100E OO-0.12636034E 03 0.21566823E 04 0.22287492E 01
0.64239645E 00 0.60012144E 00-0.27020876E 05 0.16570566E 01
0.48574998E 00-0.50702110E 03 0.46605820E 05 0.36444556E 01
0.97660465E 00 0.72760751E 03-0.32527989E 06-0.60899123E 00
V3C3 BOUSHEHRI ET AL (1987) SVEHLA (1994)
O.62526577E OO-0.31779652E 02-0.16407983E 04 0.17454992E 01
0.87395209E 00 O.56152222E 03-0.17394809E 06-0.39335958E 00
O.88503551E+OO 0.90902171E+03-O.73129061E+06-0.53503838E+OO
O.85439436E+OO O.10573224E+03-0.12347848E+05 0.47793128E+OO
0.88407146E+00 0.13357293E+03-0.11429640E+05 O.24417019E+00
0.24176185E+01 0.80477749E+04 0.31055802E+07-0.14517761E+02
V2CO CUBLEY & MASON (1975)
0.79176378E+OO 0.16226176E+03-0.47001647E+05 0.58989646E+OO
0.84676036E+00 0.66685159E+03-0.62101896E+06 0.43522696E-01
V3CO SVEHLA (1994)
0.70122551E 00 0.51717887E 01-0.14240838E 04 O.12895991E 01
0.66744478E OO-0.86348036E 02 0.27445341E 05 0.15855986E 01
0.21151565E+OO-O.91881544E+04 0.18253525E+08 0.65600002E+01
V2C2 BOUSHEHRI ET AL(1987) URIBE ET AL(1990)
0.58959112E 00-0.15565178B 03 0.37630431E 04 O.21223853E 01
0.64571469E OO-0.88806585E 01-0.41560559E 05 0.16332498E 01
O.65165376E 00-0.34373058E 03 0.15090399E 05 0.24242359E 01
0.64720604E OO-0.78680195E 02-0.11965729E 06 O.23246569E 01
V2C2 SVEHLA (1966)
O.52508683E OO-0.28652689E 03 0.20354406E 05 0.25287873E 01
0.62841605E 00-O.65798081E 02-0.38345315E 05 0.16529852E 01
O.33364942E OO-O.68702644E 03 0.52625318E 05 0.47685793E 01
O.59441359E OO-0.26239268E 03-0.29309960E 05 0.26245858E 01
V2C2 HOLLAND & BIOLSI (1987)
O.91803855E+OO O.22790517E+03-0.63721828E+05-0.12813410E+01
0.11882599E+01 O.48628768E+03 0.21833835E+06-0.35349734E+01
0.91834808E+00 0.22837346E+03-0.63906051E+05-0.97901956E+OO
O.11900946E+01 O.49842922E+03 0.20953120E+06-0.32479254E+01
V3C3 BICH ET AL (1990)
O.68398511E 00 0.18732366E 02-0.23663189E 04 O.18284755E 01
0.72333495E 00 0.10420872E 03-0.25429545E 05 0.14942434E 01
O.77549350E+OO 0.59414850E+03-0.69670786E+06 O.97885712E+00
0.68509965E 00 0.19794924E 02-0.24525539E 04 0.22s86136E 01
O.72278122E 00 0.10528290E 03-0.26355706E OS 0.19367337E 01
O.77589413E+OO O.61283778E+03-0.74015705E+06 0.14114011E+01
V2C2 LEVIN ET AL (1990)
0.77269241E+00 O.83842977E+02-0.S8502098E+OS 0.85100827E+00
0.87669586E+OO O.10158420E+04-0.10884566E+07-0.18001077E+OO
O.77271664E+00 O.83989100E+02-0.58580966E+05 O.15179900E+01
0.87676666E+OO 0.10170744E+04-0.10906690E+07 0.48644232E+OO

b
b

a
a
a
a
a
a
a
a
a

a
b
b
b

b
b

b
a
a
b

a
a
a
a
a
a
a

a
b
b

b
b
a
a
b

a

a
b
b
b

b
b

TABLE E.2. -Concluded.

o
V 1000.0
V 5000.0o
V 1000.0
V 5000.0
OH
V 1000.0
V 5000.0
C 1000.0
C 5000.002
V 200.0
V 1000.0
V 5000.0
C 200.0
C 1000.0
C 5000.0
SF6
V 300.0
V 1000.0
C 300.0
C 1000.0
S02
V 300.0
V 1000.0
C 300.0
C 1000.0
SiCL4
V 300.0
V 1000.0
C 300.0
C 1000.0
SiF4
V 300.0
V 1000.0
C 300.0
C 1000.0
SiH4
V 300.0
V 1000.0
C 300.0
C 1000.0

0+5000.015000.002
5000.015000.0
5000.015000.0
5000.015000.0
1000.05000.015000.0
1000.05000.015000.0
1000.05000.01000.05000.01000.05000.01000.05000.01000.05000.01000.05000.01000.05000.01000.05000.01000.05000.01000.05000.0UF6

V 300.0
V 1000.0

1000.05000.0Xe
V 200.0
V 1000.0
V 5000.0
C 200.0
C 1000.0
C 5000.0enda.
b.

1000.05000.015000.0
1000.05000.015000.0

V2CO STALLCOP ET AL (1991)
0.96270522E+00 0.57916036E+03-0.28549938E+06-0.12297154E+01
0.99113919E+00-0.80815595E+02 0.17198651E+07-0.14201124E+Ol
V2CO CUBLEY & MASON (1975)
0.73493993E+00 0.10911663E+03-0.31057767E+05 0.10998186E+Ol
0.76924754E+00 0.42004937E+03-0.37954441E+06 O.75936688E+OO
V2C2 SVEHLA (1994)
0.59711536E+OO-0.46100678E+03 0.37606286E+05 O.24041761E+01
0.64287721E+00-0.18173747E+03-0.88543767E+05 O.19636057E+01
0.68627561E+00-0.74033274E+03 0.27559033E+05 0.28308741E+Ol-0.47918112E+00-O.93769908E+04 0.70509952E+07 0.14203688E+02
V3C3 BOUSHEHRI ET AL (1987) SVEHLA (1994)
0.60916180E 00-O.52244847E 02-0.59974009E 03 0.20410801E 01
0.722164868 00 0.17550839E 03-0.579748168 05 O.10901044E 01
0.73981127E+00 0.39194906E+03-0.37833168E+06 0.90931780E+00
0.77229167E+00 0.68463210E+01-0.58933377E+04 0.12210365E+01
0.90917351E+00 0.29124182E+03-0.79650171E+05 0.64851631E-01-0.11218262E+01-0.19286378E+05 0.23295011E+08 0.20342043E+02
V2C2 BOUSHEHRI ET AL (1987)
SVEHLA (1994)
0.49748474E 00-0.21864084E 03 0.14509989E 05 0.27631958E 01
0.60769589E 00-0.14230978E 03 0.31449312E 05 0.19086137E 01
O.41857258E 00-O.19733612E 03-0.25661949E 05 O.34555207E 01
0.60633905E 00 0.44458129E 02-0.52676509E 05 0.19436963E 01
V2C2 ZELEZNIK & SVEHLA (1970) SVEHLA (1994)
O.531570B4E 00-0.29589873E 03 0.21224840E 05 0.25975549E 01
0.60783098E 00-0.19283581E 03 0.78232002E 04 0.19811072E 01
0.61476551E 00-0.56409295E 03 0.49580787E 05 0.23940064E 01
0.53617558E 00-0.69413085E 03 0.75304908E 05 0.30412002E 01
V2C2 SVEHLA (1994)
0.52724861E 00-0.26992512E 03 0.18062726E 05 0.22413435E 01
0.63025696E 00-0.55616232E 02-0.37587506E 05 0.13711284E 01
0.48928637E 00-0.34031669E 03 0.15336652E 05 0.23608171E 01
0.62189282E 00-0.14644974E 03-0.15293955E 05 0.12815679E 01
V2C2 SVEHLA (1962,1994)
0.59609697E 00-0.79178529E 02-0.15915012E 04 0.19580540E 01
0.64527457E 00 0.10348180E 02-0.21766101E 05 0.15489951E 01
0.44281914E 00-0.38082561E 03 0.16794039E 05 0.35456135E 01
0.62544021E 00-0.11192686E 03-0.26345285E 05 0.20583524E 01
V2C2 SVEHLA (1962)
0.57519423E 00-0.12326162E 03 0.18824028E 04 0.lB761319E 01
0.64257687E 00 0.12846016E 01-0.26699436E 05 0.13147047E 01
0.55408670E 00-0.64339630E 03 0.55747611E 05 0.37641386E 01
0.56234379E 00-0.44931035E 03-0.37165926E 05 0.36059282E 01
V2CO SVEHLA (1962)
O.56019928E 00-0.15978215E 03 0.52866529E 04 0.24249812E 01
0.63981806E 00-0.95366264E 01-0.30026765E 05 0.17600620E 01
V3C3 BrCH ET AL (1990)
O.57988418E OO-0.18806666E 03 0.10508723E 05 0.26502107E 01
O.68506945E 00 0.47671749E 02-0.54767718E 05 0.17531546E 01
O.75436414E+00 0.69100248E+03-0.75140593E+06 0.10621747E+Ol
0.57308328E 00-0.19991432E 03 0.12872027E 05 0.12718931E 01
O.68319650E 00 0.40020092E 02-0.52038474E 05 0.336234078 00
0.75593640E+00 0.72923858E+03-0.82407834E+06-0.39025477E+00

b
b
b
b
b
b
b
b

a
a
b
b

b
b

a
a
a
a

a
a
a
a

a
a
a
a

a
a
a
a

a
a
a
a
a
a

a
a
b

a
a
b

Svehla, R.A., 1995, "Transport Coefficients for the NASA Lewis Chemical
Equilibrium Program,· NASA TM-4647.
Svehla, R.A., 1996, Private communication.

105

AppendixF•
COMMON Variables Used In
Equilibrium ModuleThis appendix contains two tables. Table F.l is entitled "COMMON Variables That
Must Be Initialized Before Entering Equilibrium Module". It gives the following
information:
1. The name of the variable
2. Its dimension
3. The type of variable, such as R*8 or L*4
4. The COMMON label
5. The subroutine where the variable is set
6. Whether the variable can be reset within the module
7. Information describing the variable, such as its symbol and the equation number in
Gordon and McBride (1994)
Table F.2, entitled "COMMON Variables Calculated by Equilibrium Module", gives
information similar to that described above.

107

Variable

A

Atwt
BO
BOp
BratioCft

TABLE F.l.-COMMON VARIABLES THAT MUST BE INITIALIZEDUILIBRIUM MODULE
BEFORE ENfERING
Where set
Dimension
Type
COMMON
Reset?
Description (symbols andlabel
equations from Gordon and
McBride, 1994)
MAXEL,R*8MISCRSEARCHYes
aij , eq. (2.7a)
MAXNGC
R*8
MISCR
REACr
Yes
Atomic weight of elements
rvtAXEL
SEARCH
R*8
MISCR
NEWOF
Yes
MAXEL
b,o, eg. (9.5)
R*8MAXEL,2
INIT
REACT
Yes
b/ kl t eq. (9.1)
R*4
INIT
NEWOF
No
Bratio is discussed in sec. 3.2.
'fHERM
MAXNC,9R*8
SEARCHNo
a y t eqs. (4.9) to (4.11) for-------~---------

condensed species and eachtemperature interval
a y t eqs. (4.9) to (4.11) for gases

Coef

MAXNG,9,3

R*8

THERM

SEARCH

No

Debug

NCOL

L*4

MISCL

INPUr

No

Elmt

MAXEL

En

C*2
R*8

CDATA
COMP

R*8

CaMP

Yes

In n iEnn-----------------

R*8

COMP

Yes

11, eg. (2.1a)Ennl-~~--------------

R*8

CaMP

Yes

In n

Gonly

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

L*4

MISCL

REACT
Main
SETEN
Main
SEfEN
Main
SEfEN
Main
SEfEN
Main

Yes
Yes

Enln

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

Yes

Hp

-----~-~-----~--

L*4

MISCL

No

HsubO

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

R*8

MISCR

lfz

MAXNC

1*4

INDX

Main
DETON
INPUf
ROCKErSHCK
THERMP
DEfON
HCALC
NEWOF
INPUf
SHCK
REACT
SEARCH

If true, all product species aregaseous.
If true, either enthalpy andpressure or internal energy andvolume (or density) have been
assigned.

L*4

MISCL

INPUT

No

Ions

--------~-------

No

haiR, assigned specific enthalpyof mixture divided by universal
gas constant, eq. (9.7)

No

Positive integer numbering
condensed phases of a species
starting with 1 and increasing
with temperature ranges
If true, ionic species are to beconsidered.
Indices of species currently used
as components (usuallymonatomic gases)
Indices of condensed species
currentl bein considered

Jcm

MAXEL

1*4

TRNP

SEARCH

Yes

Jcond

45

1*4

INDX

t\!lain
SErEN

Yes

108

Variable

Dimension

Type

TABLE F.1. -Continued.
Reset?
Where set
COMMONlabel

Jliq----------------

1*4

MISCI

NEWOF
SEfEN

Yes

Jsol

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

1*4

MISCr

Yes

Jx
Lsave

MAXEL

1*4
1*4

INDX
MISCr

NEWOF
SETEN
SEARCH
INPUT
SEfEN

Description (symbols andequations from Gordon and
McBride, 1994)
Index of condensed species thatis included simultaneouslywith another condensed phaseof same species. Jeol is forthe adjacent species; Jliq is
for the higher temperatureinterval.
See Jliq.

Yes
Yeso when processing input; Nlm+ 1

No----------------

Mw'

MAXNGC

R*8

THERM

No

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

1*4

INDX

HCALC
SEARCHSEARCH

Ng----------------

1*4

INDX

SEARCH

Yes

1*4
1*4
1*4

INDX
INDX

SEARCHSEARCH
Main
REACT
Main
SEARCH
DEfON
NEWOF
ROCKETSHCKTHERMP
SEARCH

No
No
Yes

Ngc
Ngpl
Nlm

----~-------------~--~---~----------------------

INDX

Npr

------------~---

1*4

INDX

Npt

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

1*4

INDX

Nspx

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

1*4

INDX

Pp

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

R*8

MISCR

Prod

O:MAXNGC

Rr----------------

C*15
R*8

CDATA
MISCR

so

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

R*8

Shock
Short

-----

~----- -~~---------~~--~~-~~

No

Yes
No

No

DillONROCKET
SHCK
Tl..IERMPSEARCH
BIJ)(]{])ATA

Yes

MISCR

INPUr
ROCKEr

No

L*4
L*4

MISCL
MISCL

INPUT
INPUT

No
No

INPlD'NEWOF
INPUTROCKEI'
Main
SEfEN
SEARCHYes

Size----------------

R*8

MISCR

sp

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

L*4

MISCL

Sumn

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

R*8

CaMP

Temp

2,MAXNC

R*8

THElTh:l

No
No

No
Yes
No

Indices of monatomic gases

in EQLBRM afterconvergence when ionicspecies are included as
products, and Nlm when they
are not
Molecular weight of productspeciesNumber 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:=:Npt:=NCOL)

Ngc plus number of monatomic
gases without thermo data
Assigned pressure in bars for
current point
Species names
Universal gas constant,
8314.51 J/(kg-mol)K
sol R, assigned specific entropyof mixture divided byuniversal gas constantIf true, shock problem.
If true, listed output isabbrev iated.
SIZE as discussed in sec. 3.2 ofGordon and McBride (1994)
If true, entropy and pressure (orvolume) have been assigned.
Value of summation in eq. (2.2)
Temperature ranges forthermodynamic properties of
all condensed roducts

109

Variable

Dimension

Type

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

Tg

4

R*8

THERM

SEARCHNo

Tp------- ---------

L*4

MISCL

No

Trace

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

R*8

MISCR

DEI'ONINPUTROCKEr
SHCK
INPUT
SHCK

Tt

-~--

---------~~-

R*8

MISCR

Yes

Vol

----~-----------

L*4

MISCL

DillONROCKEr
SETEN
SHCK
Trn:;J{MP
INPUT

Vv

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

R*8

MISCR

THERMP

No

Variable
Cp
Cpr
Dlvpt
Dlvtp
Gammas
HO
Hsum
Mu
Ppp
S
Ssum
Totn
Ttt
Vim
Wm

110

No

No

Description (symbols andequations from Gordon and
McBride, 1994)
Temperature ranges forthermodynamic properties ofgases
If true, temperature and pressure(or volume) have been
assigned.
IfTrace>O, print mole (ormass) fractions::: Trace in
special E-format
Current temperature in kelv in

If true, volume has been
assigned.
Assigned specific volume times
10-5 , (m3 /k )I 0-5 , . (2.1a)

TABLE F.2. -COMMON VARIABLES CALCULATED BY EQUILIBRIUM MODULECOMMON
Where set
Dimension Type
Description (symbols and equations fromlabel
Gordon and McBride, 1994)
CPHS
Molar heat capacity for species divided by
MAXNGC
R*8
THERM
universal gas constant, eq. (4.9)
R*8
PRTOUTEQLBRM
Specific heat of mixture divided by universal gas
NCOL
constant, eq. (2.59)
EQLBR!v1
PRTOurDerivative defined by eq. (2.51)
NeOL
R*8[)crivative defined by eq. (2.50)
NCOL
R*8
PRTOurl-~LBRM
NffiL
R*8PRTOUrEQLBRM
Isentropic exponent, eqs. (2.71)
CPHS
MAXNGC
R*8
THERM
Molar standard-state enthalpy of species divided
by universal gas constant, eq. (4.10)
PRTOUr
MATRIX
Specific enthalpy of mixture divided by
NCOL
R*8universal gas constant, eq. (2.14)
MATRIXMAXNGC
R*8
THERM
Molar Gibbs energy for each species
PRTourEQLBRM
Static pressure in bars stored for output
NCOL
R*8
R*8
TI·!ERM
CPHS
Molar standard-state entropy of species divided
MAXNGCby universal gas constant, eq. (4.11)
NeOL
R*8
PRTOUrEQLBRM
Specific entropy of mixture divided by lUliversal
gas constant, eq. (2.16)
R*8
PRTOurEQLBRM
Totn(i)=sum of EnU,Npt) for all species,
NCOL
denominator of eq. (2.4a)
PRTOUrEQLBRM
Temperature in kelvin stored for output
R*8
NeOL
Specific volume times 10 5 , (m3 /kg) 10. 5 ,PRTOUTEQLBRM
NffiL
R*8
eq. (2.1a)
PRTOlJI'NeOL
R*8
E LBRM
Molecular wei ht of mixture, e . (2.3a)

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 GORDONREFS: NASA RP-1311, PART I, 1994 AND NASA RP-1311, PART II, 1996*******************************************************************************SAMPLE PROBLEMS

EXAMPLE I:(a)
Assigned-temperature-and-pressure problem (tp).
(b)
Reactants are H2 and Air. Since "exploded ll 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 =1,1.5) .
(d)Assigned pressures are I, 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)=1,.l,.01,t(k)=3000,2000,
r,eq.ratio=1,1.5'reactants' dataset:
reac1.
fuel= H2 molesoxid= Air moles
1.
'only' dataset:
H2
H20 HNO
H02
HN02
HN03
only ArC
CO C02 H
NO
N2N203 o 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=FTRNSPT=F

2000.0000

SiR: O.OOOOOOE+OO

1.013250

0.101325

H/R: O.OOOOOOE+OO

U/R= O.OOOOOOE+OO

0.010132

REACTANT
MOLES(ENERGY/R) ,K
EXPLODED FORMULA
F: H2
1.000000O.OOOOOOE+OO
H 2.00000
0: Air1.000000O.OOOOOOE+OO
1. 56170
00.41959 AR 0.00937
N

112

N

TEMP,KDENSITY

0.00

0.0000C

0.00 0.0000
0.00032

SPECIES BEING CONSIDERED IN THIS SYSTEM(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES}*Ar

1 6/88
1 7/88
tpis89tpis78111/89
1 4/90tpis89OfF

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

*C02
HN02
*H2

*NH
N203
*02

*c
*H

tpis79112/89
1 5/891 6/88
tpis78
tpis78

HN03
H2O
*NO
*0
03

*CO
HNO
H02
*N
*N2
*OH

34.297046
EFFECTIVE FUELh(2)/RO.OOOOOOOOE+OO

ENTHALPY(KG-MOL) (K}/KG
KG-FORM.WT./KG
*H
*N
*0

*Ar

*c

POINT ITN
1

13

2

6

3

5

4

7

5

6

6

8

EFFECTIVE OXIDANTh(l)/RO.OOOOOOOOE+OO

MIXTUREhO/R
O.OOOOOOOOE+OO

bi (2)bi(l)O.9921225SE+00
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO

O.OOOOOOOOE+OO
0.53915548E-01
0.14485769E-01
0.32348639E-03
0.11047560E-04

bOi
0.28107807E-01
0.5238806BE-01
0.14075373E-01
0.31432170E-03
0.10734572E-04

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

H

N

0

AR

-11. 767-14.452-17.112-27.077-12.631-13.684-17.810-26.104-12.811-15.668-18.090-29.507-13.414-14.837-18.560-28.409-14.310-16.920-19.495-32.012-14.202-15.991-19.318-30.716113

THERMODYNAMIC EQUILIBRIUM PROPERTIES AT ASSIGNEDTEMPERATURE AND PRESSURE
CASE

Example-1
REACTANT
H2
Air

FUEL
OXIDANT

O/F=

34.29705

ENERGY
CAL/MOL
0.000
0.000

MOLES
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, CALI (G) (K)M, (lIn)(dLV/dLP)t(dLV/dLT)p
Cp, CAL/ (G) (K)GAMMAsSON VEL,M/sEC

1.00001.0000 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
2.54333.32762.73522.87754.01192.935524.601
16.26124.41722.61519.91024.547-1.03437 -1. 00062 -1. 07935 -1.00143 -1. 07486 -1.00352
2.4145
1. 69481.02002.54681.0452
1.10901. 6795
0.45393.46660.51873.72400.68011.13181.13111.2263
1. 2035
1.16771.12031317.61117.0910.4
1184.7902.9891. 8MOLE FRACTIONS
*Ar
*CO
*C02
*H
H02
*H2
H2O
*N
*NO
*N2
*0
*OH
*02

0.007110.000170.000070.040690.00001
0.067080.209360.00001
0.01247
0.586130.01560
0.04205
0.01925

0.007730.00001
0.000250.00009
0.00000
0.00304
0.342160.00000
0.000490.644160.000020.00100
0.00104

0.006260.000180.000030.143150.00001
0.08301
0.097410.00003
0.013890.51456
0.058640.055620.027210.00772
0.000020.000240.000410.00000
0.00633
0.337360.00000
0.00073
0.642610.000100.002160.00232

0.005110.000170.00001
0.31984
0.00000
0.041440.011930.000090.00974
0.421020.143810.030480.01637

0.007670.00004
0.000220.001850.00000
0.01309
0.326830.00000
0.00108
0.639030.000470.00460
0.00510* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONSWERE LESS THAN 5.000000&-06 FOR ALL ASSIGNED CONDITIONS
*C
N203

114

RNO
03

HN02

RN03

*NH

OIF

22.853060

ENTHALPY(KG-MOL) (K) /KG

EFFECTIVE FUELEFFECTIVE OXIDANTh(2)/Rh{l)/R

ho/R

O.OOOOOOOOE+OO

O.OOOOOOOOE+OO

O.OOOOOOOOE+OObi(2)bi (I)

bOi

O.99212255E+00
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO

O.OOOOOOOOE+OO
O.53915548E-Ol
0.14485769E-01
0.32348639E-03
0.11047560E-04

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

KG-FORM. WT. IKG

*H
*N
*0

*Ar

*c

POINT 1TNMIXTURE

T

H

N

0

AR

-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

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
2000.000-25.879115

THERMODYNAMIC EQUILIBRIUM PROPERTIES AT ASSIGNEDTEMPERATURE AND PRESSURE
CASE

Example-·1
REACTANTFUELH2OXIDANT

Air

O/F=

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
1.00003000.00 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 1.2930-6
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
3.17692.85493.69663.0721
4.5471
3.2944M,

21. 29417.528
21. 276
13.94621.22020.013-1. 03292 -1.00019 -1.08636 -1.00060 -1.08730 -1.00194
2.68092.64581.66191. 0054
1. 0172
1. 0556
1.81790.46674.22150.49874.93870.6036
1.13371.2531
1.1194
1.23941.12951.20621188.71421.4972.2
989.2
1262.1984.2(l/n)(dLV/dLP)t(dLV/dLT)p
Cp, CAL/ (G) (K)GAMMAsSON VEL,M/SEC

MOLE FRACTIONS
*Ar
*CO
*C02
*H
*H2
H2O
*N
*NO
*N2
*0
*OH
*02

0.006200.000180.00004
0.060140.146530.224360.00001
0.00573
0.51403
0.007650.030490.00463

0.00660
0.000160.000070.000620.14737
0.295100.00000
0.00001
0.549960.00000
0.000120.00000

0.005430.000170.000020.182400.13477
0.113200.000030.009280.44806
0.04197
0.05073
0.01394

0.006590.000160.000070.001960.14674
0.294560.00000
0.000030.549500.00000
0.000390.00000

0.00432
0.000140.00000
0.39382
0.062830.014860.00008
0.00737
0.356460.118200.030850.01106

0.00658
0.000160.000070.006160.14483
0.292790.00000
0.00008
0.548030.00004
0.001240.00003* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONSWERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONS
*C
*NH

116

RNO
N203

HN02
03

RN03

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.
(e)Densities (rho) were obtained from the results of example 1.
Composition and properties in examples 1 and 2 should match forthese input values.
(f)'only' dataset is used to restrict possible products.
(g)Transport properties are to be calculated (transport).
reac
prob
only
outp
end

fue1=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 RNO 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=FTRNSPT=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 = 1.0885657E+Ol 1.2364455E+02 1.5139129E+03(ENERGY/R),K
REACTANTWT • FRACEXPLODED FORMULA
F: H2
1.000000O.OOOOOOE+OO
H 2.00000
0: Air1.000000O.OOOOOOE+OO
N 1.56170 0 0.41959 AR 0.00937

TEMP,KDENSITY

0.00

0.0000C

0.00 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
tpiS78111/89
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
RN03
H2O
*NO
*0
03

tpis79112/89
1 5/891 6/88
tpis78
tpis78

*CO
RNO
H02
*N
*N2
*OH

SPECIES WITH TRANSPORT PROPERTIES
PURE SPECIES
Ar
H
H2O
0
02

C
H2
N
OR

CO

C02

NO

N2

117

BINARY INTERACTIONS

o

C

CO
CO
CO

C02

N2
02
H2
H20
N2
02

C02
C02
C02
C02
H
H
H
H

H2
N

H2

H20
N2

N2

o

H2
H2

02
N2
02
NO
N2

H20
H20
N
N
N
N

o
02

NO

o

N2

o

N2

02
02

o
OfF

34.297046

INTERNAL ENERGY(KG-MOL) (K) /KG
KG-FORM.WT./KG
*H
*N
*0

*Ar
*C

POINT ITN

EFFECTIVE FUELEFFECTIVE OXIDANTu(2)/Ru(l)/RMIXTUREuO/Ro.oooooaOOE+Oo

O.OOOOOOOOE+OO

O.OOOOOOOOE+OO

bi(2)

bi(l)

bOi

O.9921225SE+OO
o.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO

O.OOOOOOOOE+OO
O.53915548E-01
0.14485769E-01
0.32348639E-03
O.11047560E-04

O.28107807E-Ol
0.52388068E-Ol
0.14075373E-Ol
O.31432170E-03
O.10734572E-04

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

1

13

2

5

3

5

3000.000-25.140
3000.000-26.387
3000.000-27.378

THERMODYNAMIC EQUILIBRIUM PROPERTIES AT ASSIGNEDTEMPERATURE AND VOLUME
CASE

Example-2
WT FRACTION(SEE NOTE)
1.0000000
1.0000000

REACTANTFUELH2OXIDANTAir

O/F=

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
2.87753.32764.0119M,

22.61519.91016.261-1. 03437 -1. 07935 -1.07486
1. 69482.54682.41453.4666
1.67953.72401.13111.1203
1.13181184.71117.01317.6(l/n)(dLV/dLP)t(dLV/dLT)p
Cp, CAL/ (G) (K)GAMMAsSON VEL,M/SEC

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

1.67954.42420.3552

3.46669.69330.33623.72408.84400.39920.42830.72690.55390.43690.86500.4789WITH FROZEN REACTIONS

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

0.42500.62890.6324119

MOLE FRACTIONS
*Ar
*CO
*C02
*H
H02
*H2
H2O

*N
*NO
*N2
*0
*OH
*02

0.007110.000170.000070.040690.00001
0.067080.209360.00001
0.01247
0.586130.01560
0.04205
0.01925

0.006260.000180.000030.143150.00001
0.08301
0.097410.00003
0.013890.51456
0.058640.055620.027210.005110.000170.00001
0.31984
0.00000
0.041440.011930.000090.00974
0.421020.143810.030480.01637* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONSWERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONS
*C
N203

RNO

HN02

HN03

*NH

03

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 'CBH18(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 inthermo. lib. This is because data for these species are given inthermo. 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)=100,lO,1).
(g)
Mixture properties are to be printed in 8I units (siunits).
(h)Mole fractions> I.e-IS are to be in e-format (trace=1.e-15).
reacoxid Air wtfrac= 1t(k)=700.0
fuel C7H8(L)wtfrac=.4t(k)= 298.15
fuel C8HI8(L),n-octa
wtfrac=.6 t(k)= 298.15
prob
case=Example-3
hp p(bar)=lOO,lO,l, olf = 17
output siunits trace=1.e-15
omit CCN
CNC
C3H4,allene
C3H4,propyne
C3H5,allyl
C3H6,propylene
C3H60
C3H7,n-propyl
C302
C4
C4H4,l,3-cyclo- C4H6,butadiene
C4H8,tr2-butene C4H8,isobutene(CH3COOH)2
C4H9,n-butyl
C4H9,s-butyl
C4H9,t-butyl
C4HIO,n-butane
C4N2
CSH6,l,3cycloC5H8,cycloCSHIO,cycloC5Hl1,pentyl
CSH12,n-pentane CSH12,i-pentane
C6H6
C6HSOH,phenol
C6H12,1-hexene
C6H12,cycloC7H7,benzyl
C7H8
C7H14,1-heptene C7H15,n-heptyl
C8H8,styrene
C8HIO,ethylbenz
C8H17,n-octyl
C8H18,isooctane
Jet-A(L)C6H6 (L)end End all input for example 3
OPTIONS: TP=F
RKT=F FROZ=F
TRACE= 1.00E-IS

P,BAR =

C2N2
C3H4,cycloC3H6,cycloC3H7,i-propyl
C4H2
C4H6,2-butyne
C4H8,cycloC4H9,i-butyl
C4HIO,isobutane
C5
C5HIO,1-pentene
C5H11,t-pentyl
CH3C(CH3)2CH3
C6HIO,cycloC6H13,n-hexyl
C7H80,cresol-mx
C7H16,n-heptane
C8H16,l-octene
C8H18,n-octane
H20{s)

C20
C3
C3H3,propargyl
Jet-A{g)C3H80,2propanol
C3HBO,lpropanol
C4H6,cycloC4HB,l-butene
C4HB,cis2-buten
C3H8
CIOH21,n-decyl
C12HIO,biphenyl
C12H9,o-bipheny
C6H2
C6H5,phenyl
C6HSO,phenoxy
ClOH8,azulene
CI0H8,napthlene
C9H19,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=FTRNSPT=F

u/R= O.OOOOOOE+OO

1.000000

121

(ENERGY/R) , K
WT.FRACREACTANTEXPLODED FORMULA
0.143092E+04
1.000000
0: Air
N ;'.. 56170 0 0.41959 AR 0.00937
0.146491£+040.400000
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,KDENSITY

700.00 0.0000
C 0.00032
298.15 0.0000
29B.150.0000

SPECIES BEING CONSIDERED IN THIS SYSTEM(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES)
1 6/88111/89110/92
tpiS91
1 7/88
1 1/91
1 1/91
112/92
1 8/88112/92
1 8/88x 4/85
1 6/94
tpis89112/89
1 5/89
1 8/88
1 8/88111/89tpis89j12/64
1 5/90
1 7/88
1 4/901 1/90
1 5/90x 4/83
OfF =

*Ar
CH2
CH30
*CN
*C02
C2H
C2H2,acetylene
CH3CN
C2H40,ethylen-o
C2H5
C2H50HC6H14,n-hexane
*H
HCCN
RNO

H02
HCOOH
(HCOOH) 2

*NH
NH20H
N03
N2H2
N20
N205
*0
03
C(gr)

111/88111/89
1 8/88112/89tpis91
1 6/89
1 5/90
1 6/96
1 8/88
1 8/88112/92x10/85
1 7/88111/92
tpis89tpis78
1 8/891 6/88112/89tpis89
tpiS78
tpis89
1 4/90tpis89tpis7Bx 4/83

*C
CH3
CH4
CNN
COOH
CHCO,ketyl
CH2CO,ketene
CH3CO,acetyl
CH3CHO,ethanal
C2H6
CH30CH3
C7H16,2-methylh
HCN

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

tpis79112/92
1 8/88
tpis79tpis91
112/89
1 2/92
1 1/91
1 8/88
1 8/88x10/93
1 8/93
112/89
1 2/96
1 4/90
1 8/88
1 2/93
1 2/96
tpis891 7/88112/89
1 5/90tpis891 7/88
tpis89x 4/83

*CH
CH20H
CH30H
*Co
*C2
C2H2,vinylidene
C2H3,vinyl
C2H4
CH3COOH
CH3N2CH3
C4H6,1-butyne
C10H8,naphthale
HCO

lINeo
HN03
HCHO,formaldehy
H202
NCO
NH3
N02
NCN
N2H4
N204
N3H
*02
C(gr)

17.000000

ENTHALPY(KG-MOL) (K) /KG

EFFECTIVE FUELh(2}/R-0.15173707E+03

EFFECTIVE OXIDANTh(l)/R
0.49400444E+02

MIXTURE
hO/R
0.38226138E+02

KG-FORM.WT./KG
*N
*0
*Ar
*C
*H

bi(2)
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
0.72408514E-01
0.12927489E+00bi(l)0.53915548E-Ol
0.14485769E-01
0.32348639E-03
0.11047560£-04
O.OOOOOOOOE+OO

hOi
0.50920240E-01
0.13681004E-01
0.30551493E-03
0.40331290E-02
0.71819385£-02

122

T

POINT ITN
1

18

2

5

3

5

H
2419.334-11. 891
2391.604-12.538
2340.157-13.247

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

THERMODYNAMIC EQUILIBRIUM COMBUSTION PROPERTIES AT ASSIGNEDPRESSURES
CASE

Example-3
REACTANTOXIDANT
FUEL

FUEL

O/F=

WT FRACTION

Air
C7H8 (L)C8H18(L) ,n-acta
17.00000%FUEL=

5.555556(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)

100.0010.0001.00002419.33 2391.60 2340.16
1.4428 1 1.4565 0 1.4827-1
317.83317.83317.83-375.27 -368.76 -356.61-19443.2 -20795.8 -21891. 3
8.16808.82829.4904M, (l/n)(dLV/dLP)t(dLV/dLT)pCp, KJ/ (KG) (K)28.96229.02328.849-1.00067 -1. 00157 -1. 00322
1. 0186
1.0442
1.09141.6068
1. 81272.2013
1. 2260
1. 20641.1803
921.8
910.1
892.2

GAMMAsSON VEL,M/SEC

123

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

8.8668-3 8.8483-3 8.8139-3
5.454-14 9.975-14 1.106-13
1.6811-3 4.3275-3 9.2288-3
1.1537-1 1.1248-1 1.0712-1
5.1792-8 2.3423-8 8.6875-9
2.7692-5 1.2480-4 4.5990-4
9.662-12 1.081-11 7.934-12
7.579-10 9.191-10 7.862-10
1.024-12 1.107-12 7.601-13
1.229 -9 5.144-10 1.646-10
4.2385-7 2.0929-7 9.1839-8
HNO
1.8549-6 3.2796-7 5.7687-8
HN02
RN03
1.133 -9 6.656-11 4.067-12
7.8127-6 4.1701-6 2.1216-6
H02
2.5156-4 6.6471-4 1.4948-3*H2
HCHO,formaldehy 1.723-11 1.172-11 5.625-12
HCOOH
6.485 -9 1.651 -9 3.455-10H20
1.0288-1 1.0154-1 9.9280-2
1.0129-6 3.0297-7 8.6257-8
H202
1.1572-8 2.7706-8 5.1386-8*N
8.645-11 6.074-11 3.090-11
NCO
2.9542-9 3.9044-9 3.9370-9*NH
1.721 -9 1.291 -9 7.472-10
NH2
3.909 -9 1.731 -9 6.186-10
NH3
1.027-11 1.461-12 1.702-13
NH20H
6.7922-3 6.5768-3 6.1768-3*NO
2.3525-5 7.5946-6 2.4942-6
N02
1.932-10 1.962-11 2.015-12N037.3550-1 7.3408-1 7.3142-1*N2
5.207-13 1.210-13 2.129-14
N2H2
2.449-15 6.786-17 1.669-18
NH2N023.6532-6 1.1174-6 3.3132-7N20
2.448-11 7.760-13 2.459-14N203
3.110-15 3.306-17 3.704-19
N204
1.241-12 3.029-13 5.825-14
N3
3.876-13 5.282-14 5.650-15
N3H
1.5576-4 4.3417-4 1.0769-3*02.1257-3 3.4565-3 5.1814-3*OH
2.6302-2 2.7452-2 2.9742-2*02031.2251-8 3.7798-9 1.1377-9* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONSWERE LESS THAN 1.000000E-15 FOR ALL ASSIGNED CONDITIONS
*CH
*C
CH30
CH4
C2H
CHCO,ketyl
CH3CN
C2H3,vinyl
CH3CHO,ethanal CH3COOH
C2H50H
CH30CH3
C10H8,naphthale HCCN
C(gr)
N205

CH2
CH3
CH30H
CNN
C2H2,vinylidene C2H2,acetylene
CH3CO,acetyl
C2H4
C2H6
C2H5
C4H6,1-butyne
C6H14,n-hexane(HCOOH) :2
NCN

CH20H
*C2
CH2CO,ketene
C2H40,ethylen-oCH3N2CH3
C7H16,2-methylh
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).
Fuel, oxidant, and oxidant-to-fuel weight ratio are the same as in(b)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 andu/R = -375.27/8.31451 = -45.1343 (kg-mol) (K)/kg (u/r=-45.1343).
(d) Units for density input are limited to g/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 81 units (default unit) .
(f) Mole fractions> I.e-IS are to be in e-format (trace=l.e-lS).
(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 fromthis column should yield the same pressure and temperature assigned
for that point in example 3.
prob

case=Example-4, 0/f=17uv

u/r=-4S.1343, rho,kg/m**3=14.428

outputtrace=l.e-15

reacoxid Air
wtfrac= 1t(k)=700.0
fuel C7H8(L)wtfrac=.4t(k)= 298.15
fuel C8HI8(L) ,n-octa wtfrac= .6 t(k)= 298.15

omit CCN CNC C2N2 C20 C3H4,allene C3H4,propyne C3H4,cyclo- C3C3HS,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
C4H8,tr2-butene C4H8,isobutene C4H8,cycloC4H6,cyclo(CH3COOH)2
C4H9,n-butyl
C4H9,i-butyl
C4H8,l-butene
C4H9,s-butyl
C4H9,t-butyl
C4HI0,isobutane C4HB,cis2-buten
C4HI0,n-butane C4N2C5C3H8C5H6,l,3cyclo- C5H8,cycloC5HI0,l-pentene CIOH21,n-decyl
CSHI0,cycloCSHll,pentyl
C5Hll,t-pentyl C12HI0,biphenyl
CSH12,n-pentane CSH12,i-pentane CH3C(CH3)2CH3
C12H9,o-bi~heny
C6H6
C6HSOH,phenol
C6HI0,cycloC6H2
C6H12,l-hexene C6H12,cycloC6H13,n-hexyl
C6H5,phenyl
C7H7,benzyl
C7H8
C7H80,cresol-mx C6H50,phenoxy
C7H14,1-heptene C7H15,n-heptyl C7H16,n-heptane CIOH8,azulene
C8H8,styrene
C8HI0,ethylbenz C8R16,1-octene CI0H8,napthlene
C8H17,n-octyl
C8H18,isooctane CBR18,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-IS

HP=T 8P=F TV=F UV=T SV=F DETN=F SHOCK=F REFL=F
EQL=F 10NS=F 8IUNIT=T DEBUGF=F SHKDBG=F DETDBG=F
S/R= O.OOOOOOE+OO

H/R= O.OOOOOOE+OO

INCD=FTRNSPT=F

U/R=-4.S13430E+Ol

SPECIFIC VOLUME,M**3/KG = 6.9309676E-02

125

(ENERGY/R) t K
REACTANTWT.FRACEXPLODED FORMULA
0.730917E+03
1.000000
0: AirN 1. 56170 0 0.41959 AR 0.00937
0.146491E+04
0.400000
F: C7HB (L)C 7.00000 H 8.00000
F: C8H18(L),n-octa 0.600000 -0.300992E+05
C 8.00000 H 18.00000

TEMP,KDENSITY

700.00 0.0000
C 0.00032
298.15 0.0000
298.150.0000

SPECIES BEING CONSIDERED IN THIS SYSTEM(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES)
1 6/88111/89110/92
tpis91
1 7/88
1 1/91
1 1/91
112/92
1 8/88112/92
1 8/88x 4/85
1 6/94
tpis89112/89
1 5/89
1 8/88
1 8/88111/89
tpiS89j12/64
1 5/90
1 7/88
1 4/901 1/90
1 5/90x 4/83
OfF =

*Ar
CH2
CH30
*CN
*C02
C2H
C2H2,acetylene
CH3CN
C2H40,ethylen-o
C2H5
C2H50HC6H14,n-hexane
*H
HCCN
lINO

H02
HCOOH
(HCOOH) 2
*NH
NH20H
N03
N2H2
N20
N205
*0
03
C(gr)

KG-FORM.WT./KG
*N
*0
*Ar

126

*C
CH3
CH4

112/89CNN

tpis91
1 6/89
1 5/90
1 6/96
1 8/88
1 8/88112/92x10/85
1 7/88111/92
tpiS89tpis78
1 8/891 6/88112/89tpis89tpis78
tpis89
1 4/90tpis89
tpiS78x 4/83

COOH
CHCO ketyl
CH2CO,ketene
CH3CO,acetyi
CH3CHO,ethana1
C2H6
CH30CH3
C7H16,2-methylh
t

HCN

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

tpiS79112/92
1 8/88
tpiS79tpis91
112/89
1 2/92
1 1/91
1 8/88
1 8/88x10/93
1 8/93
112/89
1 2/96
1 4/90
1 8/88
1 2/93
1 2/96
tpis891 7/88112/89
1 5/90
tpiS891 7/88
tpis89x 4/83

*CH
CH20H
CH30H
*CO
*C2
C2H2,vinylidene
C2H3,vinyl
C2H4
CH3COOH
CH3N2CH3
C4H6,1-butyne
C10H8,naphtha1e
HCO
HNCO
HN03
HCHO,formaldehy
H202
NCO
NH3
N02
NCN
N2H4
N204
N3H
""02
C(gr)

17.000000

INTERNAL ENERGY(KG-MOL) (K) IKG*c*H

111/88111/89
1 8/88

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

EFFECTIVE OXIDANTu(l)/R
0.2523390SE+02

MIXTURE
uO/R-0.45134300E+02

hi (2)bi(l)0.53915548E-01
0.14485769E-01
0.32348639E-03
0.11047560E-04
O.OOOOOOOOE+OO

hOi
0.50920240E-01
0.13681004E-01
0.30551493E-03
O.40331290E-02
0.71819385E-02

O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
0.72408514E-01
0.12927489E+00

POINT ITN

N

o

AR

c

~11.651-14.247-21.786-21. 401

T
H

16

1

2419.335-11. 891

THERMODYNAMIC EQUILIBRIUM COMBUSTION PROPERTIES AT ASSIGNEDVOLUME
CASE

Example-4,
REACTANTOXIDANT
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,

KJI (KG) (K)M, (lin)(dLv/dLP)t(dLV/dLT)pCp, KJ/ {KG} (K)GAMMAsSON VEL,M/SEC

100.002419.34
1.4428 1
317.83-375.27-19443.2
8.168029.023-1.00067
1.01861.6068
1. 2260
921. 8MOLE 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

RNO
4.2385-7
HN02
1. 8549-6
RN03
1.1332-9H02
7.8128-6*H2
2.5156-4
HCHO,formaldehy 1.723-11
HCOOH
6.4854-9H20
1.0288-1
H202
1. 0130-6*N
1.1572-8NCO
8.645-11
2.9542-9*NH1.7208-9
NH2NIB
3.9091-9
NH20H
1.027-11*NO
6.7922-3N022.3525-5N03
1.932-10*N2
7.3550-1
N2H2
5.207-13
NH2N022.450-15
3.6532-6N20
2.448-11N203
3.110-15
N204
1. 241-12N3
3.876-13
N3H
1.5576-4*02.1257-3*OH
2.6302-2*02031.2251-8* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONSWERE LESS THAN 1.000000E-15 FOR ALL ASSIGNED CONDITIONS
*CH
*C
CH4
CH30
C2H
CHCO,ketyl
C2H3,vinyl
CH3CN
CH3CHO,ethanal CR3CaOH
CH30CH3
C2H50H
CIOH8,naphthale HCCN
C(gr)
N205

CH2
CH3
CH30H
CNN
C2H2,vinylidene C2H2,acetylene
CH3CO,acetyl
C2H4
C2H6
C2H5
C4H6,l-butyne
C6H14,n-hexane(RCaOH) 2
NCN

CH20H
*C2
CH2CO,ketene
C2H40,ethylen-oCH3N2CH3
C7H16,2-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 thecomponents 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=SOO,2S0,
125,50 15, ) •(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).
reacname NH4CL04{I}
wt%= 72.06 t(k)=298.15
name CHOS-Binder C 1 H 1.86955 0 .031256 S .008415 wt%=18.58
h,cal=-2999.082 t(k)=298.15
name AL(cr) wt%= 9.
t(k)=298.15
name MgO(s) wt\= .2t(k)=298.15
name H20(L) wt%=.16
t(k)=298.15
prob

case=5, hp

outp

caloriesp,psia=500,250,125,SO,5,

omit COOH C2 C2H CHCO,ketyl C2H2,vinylidene CH2CO,ketene C2H3,vinyl
CH3CO, acetyl C2H40,ethylen-o CH3CHO,ethanal CH3COOH(HCOOH)2
CH3N2CH3
CH30CH3C2HS
C2H6
C2HSOH
CCN
CNC
C2N2
C20
C3
C3H3,propargyl C3H4,allene
C3H4,propyne
C3H4,cycloC3H5,allyl
C3H6,propylene
C3H6,cycloC3H60
C3H7,n-propyl
C3H7,i-propyl
C3H8
C3HBO,lpropanol C3H80,2propanol C302
C4H4,l,3-cyclo- C4H6,butadiene
C4
C4H2
C4H6,2-butyne
C4H6,cycloC4H8,l-butene
C4HB,cis2-buten
C4H8,tr2-butene C4H8,isobutene C4H8,cyclo(CH3COOH)2
C4H9,n-butyl
C4H9, i-butyl
C4H9,s-butyl
C4H9,t-butyl
C4HIO,isobutane C4H10,n-butane C4N2
C5
CSH6,l,3cyclo- CSH8,cycloC5H10,1-pentene CSHIO,cycloCSHll,pentyl
CSHll,t-pentyl CSH12,n-pentane C5H12,i-pentane
CH3C(CH3)2CH3
C6H2
C6HS,phenyl
C6HSO,phenoxy
C6H6
C6HSOH,phenol
C6HIO,cycloC6H12,l-hexene
C6H12,cycloC6H13,n-hexyl
C7H7,benzyl
C7HB
C7H80,cresol-rnx C7H14,1-heptene C7H1S,n-heptyl C7H16,n-heptane
C8H8,styrene
C8HIO,ethylbenz C8H16,l-octene C8H17,n-octyl
C8H18,isooctane C8H18,n-octane C9H19,n-nonyl
CIOHB,naphthaleCIOH21,n-decyl C12H9,o-bipheny C12HIO,biphenyl Jet-A(g)HNCO
HNO HN02
RN03
HceN
HCHO,formaldehy HCOOH
NH
NH2 NH20H NCN
N2H2 NH2N02
N2H4 H202(HCOOH)2
C6H6(L) C7H8(L)CBHIB(L),n-octa Jet-A(L)H20(s) H20(L)
end

129

OPTIONS: TP=F
RKT=F FROZ=F
TRACE= 0.00E+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

17.236826

H/R= O.OOOOOOE+OO
8.618413

WT.FRAC(ENERGY/R) ,K
REACTANTEXPLODED 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
AL(cr)
0.090000
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)0
H 2.00000
1.00000

V/R= O.OOOOOOE+OO

3.447365
TEMP,K

INCD=FTRNSPT=F

0.344737

DENSITY

298.15 0.0000
4.00000
298.15 0.0000
S 0.00841
298.15 0.0000

029B.150.0000298.150.0000

SPECIES BEING CONSIDERED IN THIS SYSTEM(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES)
j 6/83
J 6/76
J12/79J12/67
j12/79J12/79111/95
tpis91
X12/93
1 2/96
tpis91
1 8/88112/89tpis91
1 7/88
tpis91
tpis91
tpis91
tpis91
X10/93
J 6/82
1 7/93
1 6/94
112/89tpis89
1 8/89J 9/83
J12/66
J12/75
J 9/83
tpis89

130

*AL

ALCL2
ALN

ALOH
ALB
AL20
CCL
CCL4
CHCL2
CH2CL
CH3CL
CH4
CNN
COCL2
*C02
C2CL
C2CL4
C2HCL3C2H3CL
C4H6,1-butyne
CL
CL02
*H
HCO
HOCL
H2O
Mg
MgH
MgOH
Mg2
NH3

J 6/63
J 9/79J12/79J12/79J 6/79J12/79111/95
tpis79
1 6/95
tpis91
112/92
1 8/88
tpis79tpis91
1 7/95
tpiS91
tpiS91
1 1/91
112/92x 4/85
1 6/95

tpis89J

3/64

tpiS89
1 5/89tpis89J 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
CB
C2CL2
C2CL6
C2H2,acety1ene
CH3CN'C6H14,n-hexane
CLCN
CL2
HALO
HCL
H02
H2S
MgCL
MgN
Mg02H2*N*NO

J 9/79J 6/63
J 9/64
J12/6BJ 9/79111/88x12/93111/95111/89111/89110/92
tpis91
tpis91
1 6/95
1 6/95
tpis91
tpis91
tpis91
1 1/91x10/85
tpis89tpis891 7/88111/92
tpis78tpisB9J12/69J12/74
J 9/77
1 2/96
1 5/95

ALCL
ALH

ALOCL
AL02H
AL2CL6
*C
CCL3
CHCL
CH2
CH3
CH30
*CN
COCL
COS
CS2
C2CL3
C2HCL
C2H2CL2
C2H4
C7H16,2-methylh
CLO
CL20
HCN
HNC
*H2
H2SO4
MgCL2
MgO
MgS
NCO
NoeL

1 7/88
tpiS78tpisB91 7/88
tpiS89J 6/78
tpiS89J 6/71
L 4/93
tpiS89tpis89coda89J 9/79coda89coda89x 4/83srd 93
J12/79J12/65
J12/74
J12/75
L 7/76
BAR 73
tpis89tpis89J 6/78
J 6/78

N02
*N2
N204
N3H
*02
SCL
SN
802CL2
82CL2
S4
87
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)SeLl
SCL2 (L)S2CL2(L)OfF =0.000000ENTHALPY(KG-MOL) (K)/KG
KG-FORM.WT./KG
*N
*H
CL
*0
*C
S

*AL
Mg

1
1
1
1
1

5/95
7/88
4/90
1/90
5/90
J 6/78
tpia89tpia89tpia89tpis89tpia89J 9/79J12/79coda89x 4/83
J 9/77srd 93
J12/79J12/65
J12/74
J 9/77
L 7/76
BAR 73
tpiS89
tpiS89J 6/78

N02CL
N20
N205
*0
03
SCL2
SO
S03
S20
S5
S8
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
1 4/90tpis89tpis78J 9/82
tpisB9tpisB9tpisB9tpis89tpis89coda89J 9/79J12/79coda89x 4/83srd 93
J12/79J12/66
J12/65
J12/74
J 9/77
L 7/76
tpis89tpis89tpia89J 6/78

N03
N203
N3
*OH
5
SH
S02
82
S3
56
AL (cr)
ALCL3 (L)
ALN(s)
AL203(a)C(gr)
Mg (cr)MgAL204(s)MgC03(s)MgCL2(L)MgO (L)MgS (a)MgS04 (L)S (cr1)
S (L)
S (L)S2CL2 (L)EFFECTIVE FUELh(2)/R-0.24393994E+03

EFFECTIVE OXIDANT
h(1)/RO.OOOOOOOOE+OO

MIXTURE
hO/R-0.24393994E+03bi(2)0.61333506E-02
0.48397025E-01
0.61333506E-02
0.25067832E-01
0.12669356E-01
0.10661263E-03
0.33356140E-02
0.49622374E-04

bi(1}O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO

bOi
0.61333506E-02
0.48397025E-01
0.61333506E-02
0.25067832E-01
0.12669356E-01
0.10661263E-03
0.33356140E-02
0.49622374E-04

131

T

POINT ITNS

2223.217-13.211-10.257-16.675
ADD AL203{a)172800.188-13.618-11.789-17.418
PHASE CHANGE, REPLACE AL203(a)122724.464-13.567-11.563-17.2892
32708.020-13.903-12.208-17.4733
32687.754-14.237-12.840-17.7034
32654.796-14.675-13.657-18.073542542.768-15.754-15.608-19.236
15

1

CL

o

MG
-22.552-21.039-21.610

H

N

C

AL
-8.721-13.362-9.082-20.821-18.816-21.663
WITH AL203(L)-9.031-20.870-19.670-21.824-9.369-21.234-19.750-21.884-9.704-21.603-19.850-21.967-10.143-22.098-20.018-22.121-11.231-23.383-20.635-22.836-19.613-19.869-19.927-19.999-20.119-20.548

THERMODYNAMIC EQUILIBRIUM COMBUSTION PROPERTIES AT ASSIGNEDPRESSURES
CASE

5WT 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

ENERGYCAL!MOL-70690.009-2999.082
0.000-143703.308-68315.026

R,EQ.RATIO= 1.947910

PHI,EQ.RATIO~ 0.000000

THERMODYNAMIC PROPERTIES
P, ATM
T, K
RHO, G!CCH, CAL!GU, CAL!G
G, CAL/G
S, CAL! (G) (K)34.02317.0118.50573.4023 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 -716.50 -714.44 -707.24-7370.89 -7490.69 -7598.71 -7721.56 -7925.43
2.5871
2.52752.64682.72592.9262

M,

23.09623.04823.13622.97022.71222.24622.28222.202
21. 89322.130-1.00263 -1.00342 -1.00438 -1.00590 -1. 01098
1.05181.06861.0892
1. 2412
1.12280.57440.60510.64350.95120.7082
1.18901.19451.18281.15041.17381076.61081.41070.91034.81062.1(lIn)

MW, MOL WT(dLV/dLP)t(dLV/dLT)p
Cp, CAL/ (G) (K)GAMMAsSON VEL,M/SEC

132

TEMP
K
298.150
298.150
298.150
298.150
298.150

MOLE FRACTIONS
ALCL
ALCL2
ALCL3
ALO
ALOCL
ALOR
AL02H
*CO
COS
*C02
CL
*R
BCN
BCO
BCL
*H2
H2O
B2S
Mg
MgCL
MgCL2
MgOH
Mg02H2
NH3
*NO
*N2
*0
*OH
*02
S
SH
SO
S02
82
AL203 (L)

0.000190.000140.000070.00000
0.00008
0.00001
0.000020.264450.00005
0.017790.00168
0.00591
0.00001
0.00001
0.132140.321500.146590.001360.000020.000030.00104
0.00001
0.00001
0.00001
0.00003
0.068310.00001
0.000700.00000
0.00009
0.000620.000150.00006
0.00002
0.03691

0.000240.000130.00005
0.00000
0.000100.000020.00003
0.263960.00004
0.01783
0.002220.007850.00000
0.00000
0.13144
0.320750.145940.001130.00004
0.00004
0.00101
0.00001
0.00000
0.00001
0.00003
0.068200.00001
0.000920.00000
0.000130.000690.000230.00009
0.00003
0.036820.000300.000110.000030.00000
0.000120.000020.00003
0.263370.00003
0.01788
0.002900.010270.00000
0.00000
0.13055
0.319790.145160.000890.000070.00005
0.000960.00001
0.00000
0.00000
0.00004
0.06806
0.000020.001180.00000
0.000190.000730.00033
0.000130.00004
0.03672

0.000370.000100.000020.00000
0.000150.000030.00004
0.262380.000020.01797
0.00401
0.014270.00000
0.00000
0.129120.318130.14391
0.00060
0.000130.00006
0.00088
0.000020.00000
0.00000
0.00005
0.06784
0.00005
0.00157
0.00001
0.000270.000710.000480.000190.00004
0.03655

0.000520.00005
0.00000
0.00001
0.000230.00004
0.00006
0.25895
0.00001
0.018410.007900.028290.00000
0.00000
0.12434
0.311760.13984
0.000180.000440.00008
0.000540.000020.00000
0.00000
0.00009
0.067100.000160.002750.000030.000430.000490.000820.000360.00002
0.03606* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONSWERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONS
*AL
ALS
*C
*CH
CH2CL
CH30

ALC
AL2
CCL
CHCL
CH2CL2CH4ALH

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
S8
ALN(s)Mg(L)
MgCL2(L}MgS04(S)S(cr2)COCL2
C2CL2
C2HCL3
C2H4
CLO
HNC
MgN
NCO
N20
N3H
S02CL2
S4
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
85
AL(L)
C(gr)
MgAL204(L)
MgO (L)
NH4CL(a)SCL2(L)CS
C2CL4
C2H2CL2
C6H14,n-hexane
CL2
H02
MgS
N02
N204
SCL
82CL2
86
ALCL3(s)H2804(L)MgC03(s)Mg02H2(s}NH4CL(b}82CL2(L)CS2
C2CL6
C2H3CL
C7H16,2-methylh
CL20
H2SO4
Mg2
N02CL
N205
8CL2
820
87
ALCL3 (L)Mg (cr)MgCL2(S)MgS(s)
8(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 K and pressures
1 bar and 30 bars (t,k=298.15,500, pbar=1,30)(d)Thermal transport properties are called for (transport).
(e)Energy units in the final tables are in calories (calories).
reacoxid 02
fuel H2

wtt=100
wtt=100.

prob

detonation

outputend

calories transport

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

case=6

t=298.1S,500, r,e=l, pbar=I,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

t(k)=298.15
t(k)=298.15

INCD=FTRNSPT=T

500.0000
S/R= O.OOOOOOE+OO

1.000000

H/R= O.OOOOOOE+OO

U/R= O.OOOOOOE+OO

20.000000

WT.FRACREACTANTEXPLODED FORMULA
0: 02
1. 000000
02.00000
F: H2
1.000000
H 2.00000(ENERGY/R),K

TEMP,KDENSITY-0.988319E-06

298.150.0000-0.489101E-05

298.150.0000

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
*0
03

135

SPECIES WITH TRANSPORT PROPERTIES
PURE SPECIES
H2
02

H

OR

o

H20

BINARY INTERACTIONS
H

H2

H

o

H2
H2
H20

H20
02
02
02

o
OIF

7.936683

ENTHALPY(KG-MOL) (K) /KG
KG-FORM.WT./KG*0*H

EFFECTIVE FUELh(2)/R-O.24262412E-OS

EFFECTIVE OXIDANTh(l)/R-O.30886113E-07

MIXTURE
hO/R-O.29892238E-06

bi(2)O.OOOOOOOOE+OO
O.99212255E+OO

bi (1)
0.62502344E-Ol
O.OOOOOOOOE+OO

bOi
O.55508435E-01
O.11101687E+00

POINT ITN
81

T3609.2500H-15.678-10.324

POINT ITN
1
3

T3637.136aH-15.600-10.241

POINT ITN
1
3

T3680.9260H-15.602-10.237

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
4
2

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

0H-15.602-14.591-14.489-14.492-14.492-15.710-15.808-15.806-15.B06-14.632-14.689-14.687-14.687-10.237-9.159-9.047-9.042-9.042-10.339-10.446-10.454-10.454-9.177-9.242-9.247-9.247136

DETONATION PROPERTIES OF AN IDEAL REACTING GASCASE6REACTANT02
H2

OXIDANTFUELO/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

PI, ATM
T1, K
HI, CAL/G
Ml, (l/n)
GAMMA1SON VEL1,M/SEC

0.9869298.150.00
12.0101.4016537.9

19.7385298.150.00
12.0101. 4016537.9

0.9869500.00118.4112.0101.3858692.6

19.7385
500.00118.4112.0101. 3858692.6

BURNED GASP, ATM
T, K
RHO, G/CC
H, CAL/G
U, CAL/G
G, CAL/G
S, CAL/ (G) (K)10.82418.542409.40240.423679.60 4290.26 3604.96 4216.06
8.9087-4 1.7754-2 5.2196-4 1.0421-2
752.70758.96677.36837.29173.32
194.25256.74278.61-14642.7 -15416.7 -14599.2 -15431.0
4.16353.76894.26033.8587M, (l/n)(dLV/dLP)t(dLV/dLT)p
Cp, CAL/ (G) (K)GAMMAsSON VEL,M/SEC

14.50715.267
14.26414.996-1.08257 -1.06066 -1.08950 -1.06761
1.87522.50622.3666
1. 9883
2.45784.33653.90312.72781.1287
1.1436
1.1265
1.14211542.81634.6
1538.51633.9TRANSPORT PROPERTIES (GASES ONLY)CONDUCTIVITY IN UNITS OF MILLICALORIES/(CM) (K) (SEC)
VISC,MILLIPOISE

1.14111.2744

1.1243

1. 2591

2.45785.98290.52354.336510.14130.48082.72786.69510.51300.79391.42300.71100.77690.7923

1. 2844

1. 41900.68000.7030

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

3.9031
9.16900.4857

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

0.77881.29250.6876137

DETONATION PARAMETERS
P/P1
T/T1
M/M1
RHO/RH01
DET MACH NUMBER
DET VEL,M/SEC

18.78812.3411.2079
1. 83885.27442836.920.741
14.3901. 27121.83225.56842995.110.9687.210
1.1877
1. 8067
4.01352779.712.1808.432
1.24861.80374.25512947.10.08098
0.00019
0.16234
0.535020.00002
0.038480.13460
0.048370.047650.00069
0.14401
0.61304
0.000170.024110.132100.03823

0.09195
0.000150.167050.510450.00001
0.043300.136460.05063

0.057020.00058
0.152220.582160.000120.02868
0.138260.04096

MOLE FRACTIONS
*H
H02
*H2
H2O
H202
*0
*OH
*02

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONSWERE 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 shockproblems reactants must be gaseous species in the thermodynamic
data base.
The program calculates properties of thereactants 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=10,20,)(e)Seven initial gas velocities are assigned (ul=1000,1100,1200,
1250,1300,1350,1400,). Note units of u1 are always m/s.
(f) Equilibrium calculations are to be performed for incident shockconditions (incd eql).
(g)
Frozen calculations are to be performed for incident shockconditions (incd froz).
(h)No 'outp' dataset is given since the default values of thethe parameters have the desired values (e.g. SI units) .
reac

name= H2
name= 02
name= Ar

moles= 0.050
moles= 0.050
moles= 0.900t(k) 300.00
t(k) 300.00
t(k) 300.00

problem case=7 p,mmhg=10,20, shock ul=1000,1100,1200,1250,1300,1350,1400,
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=TTRNSPT=F

U/R: O.OOOOOOE+OO

0.026664

REACTANTMOLESEXPLODED FORMULA
0.050000
N: H2
H 2.00000
0.050000
N: 02
0 2.00000
N: Ar
0.900000
AR 1.00000(ENERGY/R) , K

TEMP,KDENSITY

0.641758E+01

300.000.00000.653777E+01

300.000.00000.462500E+Ol

300.000.0000

SPECIES BEING CONSIDERED IN THIS SYSTEM(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES)

1 6/88
tpis78
1 1/90
1 5/90

*Ar
*H2
*0
03

1 6/94

1 8/89tpis78
1 8/89*H
H20*OH
H20 (s)

1 5/89
1 2/93

tpis89
1 8/89

H02
H202
*02
H20(L)

139

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

REFLEQ = F

INCDFZ = T

REFLFZ = F

U1 =1.0000tOE+03 1.100000E+03 1.200000E+03 1.250000E+03 1.300000E+03
1.350000E+03 1.400000E+03

MACHI

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

OfF

0.000000ENTHALPY(KG-MOL) (K)/KG
KG-FORM.WT./KG

*H
*0
*Ar

EFFECTIVE FUELh(2)/R
O.12774941E+00

EFFECTIVE OXIDANTh(l) /R
O.OOOOOOOOE+OO

MIXTURE
hO/R
O.12774941E+00

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-01

SHOCK WAVE PARAMETERS ASSUMING
EQUILIBRIUM COMPOSITION FOR INCIDENT SHOCKED CONDITIONS
CASE

7
MOLES

REACTANT
NAME
NAME
NAME

H2
02
Ar

O/F=

0.00000

ENERGY
KJ/KG-MOL
53.35954.35838.4550.0500000
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

INITIAL GAS (1)3.35283.65763.04803.81003.96244.11484.2672
MACH NUMBER1
1000.00 1100.00 1200.00 1250.00 1300.00 1350.00 1400.00
Ul, M/SEC
0.01333 0.02666 0.02666 0.02666 0.02666 0.02666 0.02666
P, BAR
300.00300.00300.00300.00T, K
300.00300.00300.00
RHO, KG/CU M
2.0126-2 4.0252-2 4.0252-2 4.0252-2 4.0252-2 4.0252-2 4.0252-2
H, KJ/KG
1.0622
1.0622
1.0622
1. 06221.0622
1.0622
1.0622-65.182 -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
5.19115.03805.0380S, KJ/ (KG) (K)5.03805.03805.03805.0380M, (l/n)Cp, KJ/ (KG) (K)GAMMAsSON VEL,M/SEC

37.6540.5742
1.6249328.1

37.6540.5742
1.6249328.1

37.6540.5742
1.6249328.1

37.6540.5742
1. 6249
328.1

WARNING! ! NO CONVERGENCE FOR u1= 1000.0
ANSWERS NOT RELIABLE, SOLUTION MAY NOT EXIST (SHCK)

140

37.6540.5742
1. 6249328.1

37.6540.5742
1. 6249328.1

37.6540.5742
1. 6249
328.1

SHOCKED GAS (2)--INCIDENT--EQUILIBRIUM
703.53666.91576.09532.35560.23
U2, M/SEC
549.01
540.16
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
2.8607-2 6.6391-2 8.3844-2 8.9812-2 9.5312-2 1.0060-1 1.0586-1
RHO, KG/CU M
292.39383.68555.13625.39766.43
839.37
H, KJ/KG
695.35-2.9743
54.682163.89U, KJ/KG
209.27255.08302.48352.28-7331.22 -7891.77 -9312.23 -9886.05 -10444.2 -10990.3 -11520.9
G, :KJ/KG
5.55705.4155
5.4307
S, KJ/(KG) (K)5.44015.47295.45035.4613M,(l/n)(dLV/dLP) t(dLV/dLT)pCp, KJ/(KG) (K)GAMMAsSON VEL,M/SEC
P2/P1
T2/T1
M2/M1
RH02/RH01
V2, M/SEC

38.61938.61938.61438.60838.59738.55238.580-1.00000 -1. 00000 -1.00005 -1.00010 -1.00021 -1.00040 -1.00072
1. 0001
1.00021.00181. 0037
1.0123
1.00701. 02070.5827
0.58690.60410.61870.67470.64120.7226
1. 5861
1.57981.55701.5397
1. 5162
1. 4857
1.4497
684.5
720.9
780.5
800.4
817.0
830.2
840.3
6.654
4.656
1. 0256
1.4214296.47

8.192
5.094
1.02561.6494433.0912.3026.057
1. 0255
2.0830623.9115.7386.813
1.02512.3679750.9917.504
7.176
1.02462.4993809.8419.3377.528
1. 0238
2.6299867.659.2307-1 9.2306-1 9.2294-1 9.2280-1 9.2255-1
6.3878-9 7.1872-8 4.2701-6 1.5520-5 4.7038-5
5.7290-9 2.4000-8 1.4081-7 2.4561-7 3.9562-7
3.2023-7 1.8716-6 3.5078-5 8.8322-5 1.9485-4
5.1272-2 5.1248-2 5.1025-2 5.0780-2 5.0378-2
2.311-10 9.754-10 4.623 -9 7.549 -9 1.149 -8
3.3351-7 2.0203-6 3.9781-5 1.0183-4 2.2822-4
1.8151-5 6.1566-5 4.2535-4 7.8035-4 1.3111-3
2.5636-2 2.5625-2 2.5530-2 2.5435-2 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 -88.5170-4
3.0302-3
2.4835-2

14.016
6.441
1. 0253
2.2312689.77MOLE FRACTIONS

*Ar
*H
H02

*H2
H20
H202
*0

*OH
*02

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONSWERE LESS THAN 5.000000E-09 FOR ALL ASSIGNED CONDITIONS
03

H20(s)

H20(L)

141

SHOCK WAVE PARAMETERS ASSUMINGFROZEN COMPOSITION FOR INCIDENT SHOCKED CONDITI10NS
CASE = 7
REACTANT
H2

NAME
NAME
NAME
O/F=

0.0500000
0.0500000
0.9000000

02Ar
0.00000

ENERGY
KJ/KG-MOL
53.35954.35838.455MOLES%-FUEL=

0.000000

R,EQ.RATIO= 0.500000

TEMP
K

300.000
300.000
300.000

PHI,EQ.RATIO= 0.000000

INITIAL GAS (1)4.11483.65763.04803.35283.81003.96244.2672
MACH NUMBER1
Ul, M/SEC
1000.00 1100.00 1200.00 1250.00 1300.00 1350.00 1400.00
P, BAR
0.01333 0.02666 0.02666 0.02666 0.02666 0.02666 0.02666
300.00300.00300.00300.00300.00300.00300.00
T, K
RHO, KG/CU M
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. 06221.0622
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
5.03805.03805.03805.03805.03805.19115.0380S, KJ/ (KG) (K)

M,

(l/n)

Cp, KJ/ (KG) (K)GAMMAsSON VEL,M/SEC

37.6540.5742
1.6249328.1

37.6540.5742
1. 6249328.1

37.6540.5742
1.6249328.1

37.6540.5742
1.6249328.1

37.6540.5742
1.6249328.1

37.6540.5742
1.6249328.1

37.6540.5742
1.6249328.1

SHOCKED GAS (2)--INCIDENT--FROZEN
375.87366.89317.26332.77349.41358.06384.99U2, M/SEC
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
RHO, KG/CU M
6.3438-2 1.3305-1 1.3824-1 1.4052-1 1.4263-1 1.4457-1 1.4637-1
778.76550.72660.02718.21841. 67
H, KJ/KG
450.75906.9,5
417.72U, KJ/KG
213.13275.36343.52379.87457.08497.97
G, KJ/KG-5354.24 -6039.09 -6975.05 -7475.96 -7998.88 -8543.88 -9111. 04
S, KJ/ (KG) (K)5.34785.36845.38885.40885.39435.28445.3269M, (l/n)Cp, KJ/ (KG) (K)SON VEL,M/SEC

37.6540.5841
1. 6078618.1

37.6540.58581.6049664.8

37.654
0.58761.6019712.0

37.654
0.58861.6005735.9

37.654
0.58951.5989759.8

37.6540.5904
1. 5974
783.8.

37.654
0.5913
1.5960
807.9

P2/P1
T2/Tl
M2/Ml
RH02/RH01
V2, M/SEC

11.3073.587
1. 0000
3.1520682.7413.7404.157
1.00003.3056767.2316.4084.778
1.00003.4344850.5917.8315.108
1.00003.4911891.9419.3125.450
1.00003.5433933.1120.8525.806
1.00003.5917974.1322.451
6.174
1. 0000
3.63651015.010.05000
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

GAMMAsMOLE 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=10,100,1000),
one subsonic area ratio (subar=1.58), and three supersonic area
ratios (supar=25,SO,75).

problem rocket equilibrium 0/f=5.55157
p,bar=53.3172 subar=1.SB,pi/p=10,100,1000,supar=25,SO,75
reactants
fuel = H2{L)
wt% 100.
t(k) 20.27
t (k) 90.17
oxid = 02{L}
wt% 100.
output siunitsendcase=8OPTIONS: 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

S/R= O.OOOOOOE+OO

U/R= O.OOOOOOE+OO

53.317200

Pc/p ""

10.0000

100.0000

1000.0000

SUBSONIC AREA RATIOS =1.5800SUPERSONIC AREA RATIOS

25.0000

NFZ=

H/R= O.OOOOOOE+OO

INCD=FTRNSPT=F

1

Mdot/Ac= O.OOOOOOE+OO

REACTANTWT.FRACEXPLODED FORMULA
F: H2 (L)
1.000000
H 2.00000
0: 02 (L)
1.000000
0 2.00000

50.0000

75.0000

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

TEMP,KDENSITY-0.108389E+04

20.27

0.0000-0.156101E+04

90.17

0.0000143

SPECIES BEING CONSIDERED IN THIS SYSTEM(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES)
1 6/94
1 8/89
1 8/89*H
H2O*OH
H20(s}

OfF =5.551570

tpis78

1 5/89
1 2/93

tpis89
1 8/89ENTHALPY(KG-MOL) (K)/KG
KG-FORM.WT./KG*H*0

POINT ITNT
3389.270
1
9
Pinf/Pt = 1.737856
243190.532
Pinf/Pt '" 1.739443
23190.2072
2568.396
4
3
41759.1194
1115.280453360.1786
33354.650
623353.978623353.970
6
1
71441.190571467.0382
1241.42983:21218.630
8

tpis78

H02
H202
*02
H20(L}*H2*003

1 1/90
1 5/90EFFECTIVE FUEL
h(2) /R-O.53767500E+03

EFFECTIVE OXIDANTh(l}/R-0.48783267E+02

MIXTURE
hO/R-0.12340534E+03bi(2)0.99212255E+OO
O.OOOOOOOOE+OO

bi(l)O.OOOOOOOOE+OO
0.62502344E-01

bOi
0.1S143279E+00
0.52962288E-01

H0-9.266-16.561-9.433-16.968-9.434-9.922-10.454-10.958-9.291-9.295-9.296-9.296-10.682-10.662-10.845-10.864-16.968-18.802-23.533-32.668-16.616-16.627-16.628-16.628-26.980-26.641-30.099-30.523

THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUMCOMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pinj
773.3 PSIA
CASE = 8
REACTANTFUELOXIDANT
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

TEMPK

20.27090.170

PHI,EQ.RATIO'" 1.429628

EXIT
EXIT
EXIT
EXIT
1000.00
655.411.1020260.57
0.05332
48.381 0.20462 0.08135
1115.28 3353.97 1467.04 1218.63
7.5938-3 2.2113 0 2.2155-2 1.0604-2-10623.5 -1239.91 -9535.06 -10313.3-11325.7 -3427.81 -10458.6 -11080.5-31431.3 -63814.9 -36905.6 -33049.3
18.6570 18.6570 18.6570 18.6570

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

THROATEXIT
EXIT
CHAMBER
1.739410.000100.001.000030.6525.3317 0.53317
53.3173389.27 3190.21 2568.40 1759.12
2.4071 0 1. 4848 0 3.2770-1 4.8139-2-1026.05 -2210.09 -5432.07 -8564.25-3241.04 -4274.40 -7059.06 -9671. 81-64259.7 -61729.8 -53350.7 -41384.1
18.6570 1B.6570 18.6570 18.6570

M, (l/n)(dLV/dLP)t(dLV/dLT)pCp, KJ/ (KG) (K)GAMMAsSON VEL,M/SEC
MACH NUMBER

13.12513.20712.74613.20712.84913.20613.20712.723-1.01996 -1. 01459 -1.00317 -1.00005 -1. 00000 -1. 01897 -1. 00000 -1. 00000
1. 2808
1.07391. 0000
1.3482
1. 3627
1. 0001
1. 0000
1.00172.9621
7.42993.22268.28374.84473.4332
8.13903.0413
1.1732
1. 2699
1. 2429
1.14491.1472
1. 2254
1.1451
1.26101538.91381. 6944.3
1582.8983.61165.01071. 4
1592.4
1. 000
2.149
4.640
0.413
0.000
3.850
4.382
3.333

PERFORMANCE PARAMETERS
1. 0000

Ae/At
CSTAR, M/SEC
CF
Ivac, M/SEC
lap, M/SEC

2333.40.65952880.31538.92.34892333.4
1. 27223516.62968.512.2252333.4
1. 6640
416B.13882.868.6802333.4
1. 87764541. 54381.21.58002333.40.28033999.5654.0

25.0002333.4
1. 76794349.24125.350.0002333.4
1. 84704487.84309.80.026830.00001
0.293730.654400.00000
0.00124
O. 02271
0.00108

0.007970.00000
0.29695
0.690B1
0.00000
0.000070.004130.000070.000190.00000
0.300400.699380.00000
0.00000
0.000030.00000

0.00000
0.00000
0.30052
0.699480.00000
0.00000
0.00000
0.00000

0.032650.00001
0.29398
0.639760.00001
0.001960.02998
0.001650.00001
0.00000
0.30051
0.699480.00000
0.00000
0.00000
0.00000

0.00000
0.00000
0.30052
0.699480.00000
0.00000
0.00000
0.00000

MOLE FRACTIONS
0.033900.000020.294100.636430.00001
0.002140.031620.00179

*H
H02
*H2
H2O
H202
*0
*OH
*02

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONSWERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONS
H20 (8)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. 004-10.984-33.815-33.311145

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

773.~

PSIA

8
WT FRACTION(SEE NOTE)
1.0000000
1.0000000

REACTANTFUELOXIDANT
O/F=="

H2 (L)
02 (L)
5.55157

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

M,

(lin)

(dLV/dLP) t(dLV/dLT)pCp, KJ/ (KG) (K)GAMMAsSON VEL,M/SEC
MACH NUMBER%FUEL== 15.263517

R,EQ.RATIO== 1.429629

TEMPK

20.27090.170

PHI,EQ.RATIO~ 1.429628

CHAMBERTHROAT
EXIT
1.00001.7394 1124.40
53.31730.652 0.04742
3389.27 3190.21 1087.73
2.4071 0 1. 4848 0 6.9247-3-1026.05 -2210.09 -10704.9-3241.04 -4274.40 -11389.6-64259.7 -61729.8 -30998.7
18.6570 18.6570 18.6570
12.84913.20712.723-1.01996 -1. 01459 -1.00000
1. 2808
1.00001.36272.94098.28377.42991.2724
1.1472
1.1449933.4
1592.4
1538.94.714
1. 0000.000

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

MOLE FRACTIONS
*H
H02
*H2
H2O
H202
*0
*OH
*02

ENERGY
KJ/KG-MOL-9012.000-12979.000

0.033900.000020.294100.636430.00001
0.002140.031620.00179

1. 0000

2333.40.65952880.31538.975.0002333.4
1. 88564555.44399.70.026830.00001
0.293730.654400.00000
0.001240.022710.00108

0.00000
0.00000
0.30052
0.699480.00000
0.00000
0.00000
0.00000* THERMODYNAMIC PROPERTIES FITTED TO 20000.K

PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONSWERE 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 9 :Rocket problem with a finite-area combustor (rocket fac) .
(a)(b)
Contraction ratio of 1.58 (acat=1.58) is assigned.
Fuel, oxidant, and the remaining parameters are the same as in(c)example 8.

reacfuel = H2(L} wt%=lo0. 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=1.58
pi/p=10,100,1000, supar=25,50,75
output aiunits
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

H/R= O.OOOOOOE+OO

U/R= O.OOOOOOE+OO

53.317200

Pc, BAR
PC/P

S/R= O.OOOOOOE+OO

INCD=FTRNSPT=F=

10.0000

100.0000

1000.0000

SUBSONIC AREA RATIOS =25.0000

SUPERSONIC AREA RATIOS
NFZ=

1Mdot/Ac= O.OOOOOOE+OO

REACTANTWT.FRACEXPLODED FORMULA
1.000000
F: H2(L}H 2.00000
1.000000
0: 02 (L)02.00000

50.0000

75.0000

Ac/At= 1.580000E+00(ENERGY /R) ,K

TEMP,KDENSITY-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
1 8/89*H
H20*OH
H20(s)

OfF =5.551570

tpiS78

1 5/89
1 2/93

tpis89
1 8/89

H02
H202
*02
H20 (L)

tpis78
1 1/90
1 5/90*H2*003

ENTHALPY(KG-MOL) (K)/KG

EFFECTIVE FUELh(2)/R-0.53767500E+03

EFFECTIVE OXIDANTh(l)/R-0.487832678+02

MIXTURE
hO/R-0.12340534E+03

KG-FORM.WT./KG
*H
*0

bi(2)
0.99212255E+00
O.OOOOOOOOE+OO

bi(l)O.OOOOOoOOE+OO
0.625023448-01

bOi
0.15143279E+00
0.52962288E-01

147

H
POINT ITN
T
-9.2663389.27019-9.3033381. 326
2
3
Pinf/pt = 1. 737476-9.4713134.432
43
pinf/Pt = 1.739009
3184.121-9.4712
33352.506-9.3284
3-9.3324
23347.029-9.3333346.363
423346.355-9.3334
13381.345-9.303
2
1
Pinf/Pt = 1.737477
3184.446-9.471
4
3
pinf/Pt = 1.739010-9.4713184.1352
33352.524-9.327433347.047-9.3324
2
43346.381-9.33323346.373-9.333
4
1
END OF CHAMBER ITERATIONS-9.941
42596.353
5
1786.498-10.4785
4-10.9816
41135.439
1442.273-10.7247
5
71468.448-10.70421242.967-10.8858
3-10.905
1219.87382

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 EQUILIBRIUMCOMPOSITION DURING EXPANSION FROM FINITE AREA COMBUSTOR
773.3 PSIA
Pinj =
Ac/At = 1. 5800
CASE = 9

Pinj/pinf

REACTANTFUELOXIDANT
O/F=

148

H2(L)
02 (L)

5.55157%FUEL= 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

TEMPK

20.27090.170

PHI,EQ.RATIO= 1.429628

EXIT
EXIT
INJECTOR COMB END THROAT
1. 8864100.0010.0001. 0000
1.195428.2635.3317 0.53317
53.31744.6023389.27 3346.37 3184.14 2596.35 1786.50
2.4071 0 2.0416 0 1.3709 0 3.2390-1 4.7400-2-1026.05 -1239.49 -2207.90 -5294.68 -8469.93-3241.04 -3424.10 -4269.63 -6940.78 -9594.77-64259.7 -63850.8 -61783.7 -53873.0 -41895.7
18.6570 18.7102 18.7102 18.7102 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)
M,

(l/n)

(dI:,v /dLP) t(dLV/dLT)pCp, KJ/ (KG) (K)GAMMAsSON VEL,M/SEC
MACH NUMBER

EXIT
EXIT
1000.00
282.150.05332 0.18897
1135.44 1468.45
7.4589-3 2.0441-2-10563.7 -9530.50-11278.5 -10455.0-31808.0 -37005.5
18.7102 18.7102

EXIT
709.710.075131219.87
9.7824-3-10309.5-11077.5-33133.6
18.710213.20712.841
13.11413.20513.20713.20712.73612.723-1.01996 -1. 01940 -1. 01495 -1.00361 -1.00007 -1.00000 -1.00000 -1.00000
1.08341.0001
1. 2882
1. 0000
1.3627
1. 3567
1. 00221.00007.5303
2.97778.25084.98623.45693.22373.04228.2837
1. 2238
1. 26811.2609
1.14651.14491.1445
1.1705
1. 2428
1537.41388.11173.3952.1
1071. 9984.0
1592.4
1581. 2
1.000
2.105
4.587
3.848
0.000
0.413
3.289
4.379

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

1.58002332.10.28023997.0653.4

1.00002332.10.65932878.51537.42.22702332.1
1. 25293485.22921. 911.5242332.1
1. 6545
4150.03858.564.6952332.1
1.87284531.24367.525.0002332.1
1. 76854348.34124.250.0002332.1
1. 84774487.24308.90.033360.00001
0.29384
0.63858
0.00001
0.00204
0.030450.00172

0.027470.00001
0.29358
0.653370.00000
0.00130
0.023140.001130.008930.00000
0.29659
0.689520.00000
0.000090.004770.00009

0.000240.00000
0.30037
0.699350.00000
0.00000
0.00004
0.00000

0.00000
0.00000
0.30052
0.699480.00000
0.00000
0.00000
0.00000

0.000020.00000
0.30051
0.699480.00000
0.00000
0.00000
0.00000

0.00000
0.00000
0.30052
0.699480.00000
0.00000
0.00000
0.00000

MOLE FRACTIONS
0.033900.000020.294100.636430.00001
0.002140.031620.00179

*H
H02
*H2
H2O
H202
*0
*OH
*02

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONSWERE 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. 025-33.793-33.283149

THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUMCOMPOSITION DURING EXPANSION FROM FINITE AREA COMBUSTOR
773.3 PSIA
Pinj =
Pinj/Pinf
Ac/At = 1.580U
CASE = 9
REACTANTFUELOXIDANT
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
1.8864
1.195428.26344.6023346.37 3184.14
2.0416 0 1.3709 0-1239.49 -2207.90-3424.10 -4269.63-63850.8 -61783.7
18.7102 18.7102

TEMPK
20.27090.170

PHI,EQ.RATIO= 1.429628

EXIT
1217.53
0.043791088.88
6.3882-3-10701.5-11387.0-31074.7
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
1.000053.3173389.27
2.4071 0-1026.05-3241.04-64259.7
18.6570

M, (lin)(dLV/dLP)t(dLV/dLT)pCp, KJ/ (KG) (K)GAMMAsSON VEL,M/sEC
MACH NUMBER

12.72312.841
13.20712.736-1.01996 -1. 01940 -1.01495 -1.00000
1. 3567
1. 2882
1. 0000
1. 3627
2.94188.28378.25087.53031.14491.1445
1.14651.2723933.9
1592.4
1581. 21537.4
0.413
4.710
0.000
1. 000PERFORMANCE PARAMETERS
Ae/At
CSTAR, M/SEC
CF
Ivac, M/SEC
Isp, M/SEC

1.58002332.10.28023997.0653.4

1.00002332.10.65932878.51537.475.0002332.11.88634554.84399.0MOLE FRACTIONS
*H
H02
*H2
H2O
H202
*0
*OH
*02

0.033360.00001
0.29384
0.63858
0.00001
0.00204
0.030450.00172

0.027470.00001
0.29358
0.653370.00000
0.00130
0.023140.001130.00000
0.00000
0.30052
0.699480.00000
0.00000
0.00000
0.00000

0.033900.000020.294100.636430.00001
0.002.14
0.031620.00179

ENERGY
KJ/KG-MOL-9012.000-12979.000* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONSWERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONS03
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 resultsof example 9 where a contraction ratio of 1.58 was assigned.
(c)Fuel, oxidant, and the remaining parameters are the same as inexamples 8 and 9.

reacfuel = H2(L}t,k= 20.27
oxid = 02(L)t,k= 90.17
problem 0/f=5.55157 case=10 rocket fac p,bar=53.3172 ma=1333.9
pi/p=10,100,1000, sup-ae/at=25,50,75
output shorteoo
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 EQUILIBRIUMCOMPOSITION DURING EXPANSION FROM FINITE AREA COMBUSTOR

Pinj

=:

MDOT/Ac
CASE =: 10773.3 P8IA
1333.S00 (KG/S)/M**2

Pinj/Pinf

WT FRACTION(SEE NOTE)
1.0000000
1.0000000

REACTANTFUELOXIDANTO/F-

H2 (L)
02 (Ll5.55157

Pinj/P
P, BAR
T, K

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

(l/n)

(dLV/dLP)t(dLV/dLT)pCp, KJ/ (KG) (K)GAMMAsSON VEL,M/SEC
MACH NUMBER%FUEL= 15.263517

ENERGY
KJ/KG-MOL-9012.000-12979.000

R,EQ.RATIO= 1.429629

INJECTOR COMB END THROAT
1. 0000
1.1954
1. 886453.31744.60228.2633389.27 3346.37 3184.14
2.4071 0 2.0417 a 1.3709 0-1026.05 -1239.48 -2207.90-3241.04 -3424.09 -4269.63-64259.7 -63850.8 -61783.7
18.6570 18.7102 18.7102

TEMPK

20.27090.170

PHI,EQ.RATIO= 1.429628

EXIT
EXIT
100.0010.0005.3317 0.53317
2596.35 1786.50
3.2390-1 4.7400-2-5294.68 -8469.93-6940.78 -9594.77-53873.0 -41895.7
18.7102 18.7102

EXIT
1000.00
0.05332
1135.447.4589-3-10563.7-11278.5-31808.0
18.7102

EXIT
282.150.18897
1468.452.0441-2-9530.50-10455.0-37005.5
18.7102

0.033900.000020.294100.636430.00001
0.002140.031620.00179

1. 5800

1. 0000

2332.10.28023997.1653.32332.10.65932878.51537.42.22702332.1
1. 25293485.22921.911.5242332.1
1. 6545
4150.03858.564.6952332.1
1.87280.033360.00001
0.29384
0.63858
0.00001
0.00204
0.030450.027470.00001
0.29358
0.653370.00000
0.00130
0.023140.001130.008930.00000
0.29659
0.689520.00000
0.000090.004770.00009

0.000240.00000
0.30037
0.699350.00000
0.00000
0.00004
0.00000

0.001

n4367.525.0002332.1
1.76854348.34124.250.0002332.1
1. 84774487.24308.90.00000
0.00000
0.30052
0.699480.00000
0.00000
0.00000
0.00000

0.000020.00000
0.30051
0.699480.00000
0.00000
0.00000
0.00000

0.00000
0.00000
0.30052
0.699480.00000
0.00000
0.00000
0.00000

4531. 2

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

152

EXIT
709.710.075131219.87
9.7824-3-10309.5-11077.5-33133.6
18.710212.72312.73612.841
13.11413.20513.207
13 .20713 .207-1.01996 -1. 01940 -1.01495 -1.00361 -1. 00007 -1. 00000 -1. 00000 -l.00000
1.3627
1. 3567
1.2882
1.0834
1. 00221.00001.00011.00008.28378.25087.53034.98623.45692.9777
3.22373.0422
1.14491.1445
1.1465
1.1705
1. 2238
1.2681
1. 2428
1. 2609
1592.41173.3952.1
1537.4
1581.21388.1
1071. 9
984.0
0.000
1.000
4.587
0.413
2.105
3.848
4.379
3.289

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

MOLE FRACTIONS
*H
H02
*H2
H20
H202
*0
*OH
*02

1. 084780

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

O/F=

H2 (L)
02 (L)
5.55157

Pinj/P
P, BAR
T, K
RHO, KG/CU M
H, K;I/KG
U, K;I/KG
G, KJ/KG
S, KJ/ (KG) (K)M, (lIn)(dLV/dLP)t(dLV/dLT)pCpt KJ/ (KG) (K)GAMMAsSON VEL,M/SEC
MACH NUMBER

1.084780

WT FRACTION(SEE NOTE)
1.0000000
1.0000000

REACTANTFUELOXIDANT

Pinj/Pinf%FUEL= 15.263517

ENERGY
KJ/KG-MOL-9012.000-12979.000

R,EQ.RATIO= 1.429629

TEMPK

20.27090.170

PHI,EQ.RATIO= 1.429628

INJECTOR COMB END THROAT
EXIT
1.00001.1954
1.8864 1217.53
53.31744.60228.263 0.04379
3389.27 3346.37 3184.14 1088.88
2.4071 0 2.0417 0 1.3709 0 6.3882-3-1026.05 -1239.48 -2207.90 -10701.5-3241.04 -3424.09 -4269.63 -11387.0-64259.7 -63850.8 -61783.7 -31074.7
18.6570 18.7102 18.7102 18.7102
12.72312.73612.841

13.207-1. 01996 -1.01940 -1.01495 -1.00000

1.36278.28371.14491592.40.000

1.35678.25081.14451581. 20.413

1.28827.5303
1.14651537.41.000

1.00002.94181.2723933.9
4.710

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

1. 5800
2332.10.28023997.1653.3

1.00002332.10.65932878.51537.475.0002332.11.88634554.84399.0MOLE FRACTIONS
*H
H02
*H2
H2O
H202
*0
*OH
*02

0.033360.00001
0.29384
0.63858
0.00001
0.00204
0.030450.00172

0.027470.00001
0.29358
0.653370.00000
0.00130
0.023140.001130.00000
0.00000
0.30052
0.699480.00000
0.00000
0.00000
0.00000

0.033900.000020.294100.636430.00001
0.002140.031620.00179* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
NOTE. WEIGHT FRACTION OF FUEL IN TOTAL FUELS AND OF OXIDANT IN TOTAL OXIDANTS

153

#
#
#.

#
#
#
#
#.
#

#
#.
#

EXAMPLE 11:(a)
Rocket problem with an infinite-area combustor (rocket).
(b)
Reactants are Li(cr) at 298.15 K and F2(L) at 85.02 K.
Enthalpies and "exploded" formulas are to be taken fromthermo. 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=10), and three supersonic area ratios(sup,ae/at=10,20,100) are to be included.

reacfuel = Li(cr) moles:
1.
oxid = F2(L)moles= .5556
prob
case=11 rocket equilibrium
pi/p=68.0457, sub,ae/at=10,
output siunits transport
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=T SIUNIT=T DEBUGF=F SHKDBG=F DETDBG=F

TRACE= O.OOE+OO

S/R= O.OOOOOOE+OO

PC/p =

10.0000

SUPERSONIC AREA RATIOS
1

10.0000

Mdot/Ac= O.OOOOOOE+OO

REACTANTMOLESEXPLODED FORMULA
F: Li(cr)1.000000
LI 1. 00000
0: F2 (L)0.555600
F 2.00000

20.0000

INCD=FTRNSPT=T

U/R= O.OOOOOOE+OO

68.0457

SUBSONIC AREA RATIOS154

H/R= O.OOOOOOE+OO

68.947304

PC,BAR

NFZ=

t(k)=298.15
t(k)=B5.02
p,psia=1000 ionssup,ae/at=10,20, 100

100.0000

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

TEMP,KDENSITY-0.298149E-06

298.150.0000-0.157448E+04

85.02

0.0000SPECIES BEING CONSIDERED IN THIS SYSTEM(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES)
1 6/88J 6/82
J12/83
J12/83
tpis82
J12/68J 6/82
tpis89J12/68J12/68
tpis82
J12/68*eF*Li+Li2
Li (cr)
LiF(s)

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

J 6/82
J12/83
J12/68J12/68
tpiS82
J12/68F+*Li
LiF2Li3F3
Li(L)
LiF{L)

SPECIES WITH TRANSPORT PROPERTIES
PURE SPECIES

e-

Li

F2
BINARY INTERACTIONS

OfF

3.041496

ENTHALPY(KG-MOL) (K) /KG
KG-FORM.WT./KG*Li
F*ePOINT ITN
T
1
105685.658
Pinf/Pt = 1.760223
25334.399
4
Pinf/Pt = 1.756026
25335.8172
3
63508.754425683.383
425684.563
425684.3304
15684.303
4
15684.30353414.0686
3468.5475
33468.4665162926.2554
62916.483
2·6
7
1925.971
7
1952.523
3
7:2
1952.608

EFFECTIVE FUELh(2}/R-O.42954723E-07

EFFECTIVE OXIDANTh(1}/R-0.41437073E+02

MIXTURE
hO/R-0.31184169E+02bi(2}0.14407146E+OO
O.OOOOOOOOE+OO
O.OOOOOOOOE+OO

bi(l)O.OOOOOOOOE+OO
0.52636003E-Ol
O.OOOOOOOOE+OO

bOi
0.35648050E-Ol
0.39612113E-01
O.OOOOOOOOE+OO

LI-16.270F-19.916E-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

155

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

1000.0 PSIA
11
REACTANT
Li (cr)FUELOXIDANT
O/F~

3.04150(l/n)(dLV/dLP) t(dLV/dLT)pCp,1.0000000
0.5556000

F2 (L)

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

MOLES

KJ/ (KG) (K)GAMMAsSON VEL,M/SEC
MACH NUMBER

ENERGY
KJ/KG-MOL
0.000-13091.000%FUEL= 24.743311

R,EQ.RATIO= 0.899928

CHAMBER
1.000068.9475685.66
3.1988 0-259.28-2414.71-64713.0
11.3362

EXIT
EXIT
68.046
1. 0021
1. 0132
68.8043508.75 5684.30
8.6962-2 3.1931 0-7051.17 -263.77-8216.33 -2418.51-46827.1 -64702.2
11. 3362 11.3362

THROAT
1.756039.2635335.82
1. 9836 0-1422.40-3401. 82-61910.3
11.3362

TEMP
K

298.15085.020

PHI,EQ.RATIO= 0.899928

EXIT
73.4930.938143468.47
8.1552-2-7140.33-8290.70-46459.6
11.3362

EXIT
188.510.365762916.483.8114-2-8135.15-9094.79-41197.0
11.3362

EXIT
1585.57
0.04348
1952.616.9320-3-9782.87-10410.2-31918.0
11.3362

21.93222.41325.03821.93425.06925.26925.881-1.08286 -1.07324 -1.00885 -1.08283 -1. 00782 -1.00183 -1.02364
1. 9980
2.0665
1.17262.0663
1.15301.0248
1. 36396.84726.66012.63656.84672.5114
1. 6054
3.25291.1752
1.1814
1.19671.1814
1. 2016
1. 27141.19061180.81525.21595.81175.71104.61595.5864.2
0.000
1. 000
3.121
0.059
3.155
3.593
5.050

TRANSPORT PROPERTIES (GASES ONLY)CONDUCTIVITY IN UNITS OF MILLIWATTS/(CM) (K)
1. 38621.08091.43901.07290.955700.72997

WITH EQUILIBRIUM REACTIONS
6.84726.6601CONDUCTIVITY
14.6729 13.8861
PRANDTL NUMBER
0.6716
0.66482.63654.31810.65996.846714.6703
0.67162.51144.06800.6624

1. 6054
2.16920.70733.25292.75910.8606

WITH FROZEN REACTIONS
1.5912CONDUCTIVITY
2.9867PRANDTL NUMBER
0.76681.57042.87860.75621.48552.25030.7135

1. 59122.98630.76671.48442.23320.7132

1. 4713

1. 4523

1.97860.71071.48090.71581.00002279.00.66922823.01525.29.43922279.01. 6172
4001. 83685.610.0002279.00.041622837.2
94.7

10.0002279.01.62784019.83709.720.0002279.01.74154210.63968.8100.002279.01.91504508.04364.3

VISC,MILLIPOISE

1. 4392

Cp, KJ/ (KG) (K)Cp, KJ/ (KG) (K)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
0.211880.004650.000020.12161
0.007580.65001
0.000220.00109
0.00000

0.00235
0.19608
0.003650.00001
0.10469
0.00601
0.686140.000110.000960.00000

0.00009
0.107740.000280.00000
0.008400.00038
0.882420.00000
0.000680.00000

0.00292
0.211830.004650.000020.12155
0.007570.650150.000220.00109
0.00000

0.00008
0.106700.000260.00000
0.007250.00034
0.884680.00000
0.000700.00000

0.00000
0.10058
0.00004
0.00000
0.000410.00004
0.897540.00000
0.001400.00000

0.00000
0.102590.00000
0.00000
0.00000
0.00000
0.872480.00000
0.024650.00028* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONSWERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONSF+
LiF(L)

LiF2-

Li (cr)

Li(L)

LiF{s)

157

#
#
#
#
#
#
#
#
#
#
#
#
#
#

EXAMPLE 12:(a)
Infinite-area rocket problem (rocket).
(b)
The fuel is monomethyl hydrazine (CH6N2(L»and the oxidant isnitrogen 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 (0/f:2.5).
(e)Chamber pressure is 1000 psia (p,psia=1000).
(f)
Equilibrium and frozen calculations are to be performed withfreezing at the throat (nfz=2).
(g)
For exit points one pressure ratio (pi/p==68.0457) and four
supersonic area ratios (supersonic=10,50,100,200) are given.

reac fuel == CH6N2(L)rho,g!cc == .874
oxid == N204(L)rho/g/ee = 1.431
prob rocket case=12 p,psia =1000, pi/p=68.0457,
eql frozen nfz=2
supersonic=5,10,25,50,75,100,150,200, o/f= 2.5,
only COC02
H
RNO HN02 H02
H2
H20
H202 NNO
N02
C (gr)
N2
N20
0
OH 02
HCO
NH
CH4 NH2 NH3 H20 (L)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
Pc/p

S/R= O.OOOOOOE+OO

H/R= O.OOOOOOE+OO

INCD=FTRNSPT=F

U/R= O.OOOOOOE+OO

68.947304
68.0457=

SUBSONIC AREA RATIOSSUPERSONIC AREA RATIOS
100.0000
150.0000
NFZ=

25.0000200.0000

Mdot/Ae= O.OOOOOOE+OO

10.0000

25.0000

Ae/At= O.OOOOOOE+OO

AMOUNT MISSING FOR REACTANT 1.
WARNING!!
PROGRAM SETS WEIGHT PERCENT = 100. (REACT)WARNING!!
AMOUNT MISSING FOR REACTANT 2.
PROGRAM SETS WEIGHT PERCENT = 100. (REACT)
REACTANTWT.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,KDENSITY

298.150.8740298.151.431050.0000

75.0000

SPECIES BEING CONSIDERED IN THIS SYSTEM(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES)
tpis79112/89
1 5/89
1 2/93
112/891 7/881 °1/90x 4/83
1 8/89

1 8/88
1 6/94
tpis89
1 8/89111/89
tpiS891 7/88
tpis89X 4/83

CH4
*H
HN02
H2O
*NH
*NO
N20
*02
C(gr)

=

2.500000

OIF

*Co
HCO
H02
H202
NH2
N02
*0
C(gr)
H20(L)

1 7/88112/89tpis78
1 6/88
tpis89tpis78
tpis78x 4/83

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

ENTHALPY(KG-MOL) (K) /KG

EFFECTIVE FUELh(2)/R
0.14148957E+03

EFFECTIVE OXIDANTh(l}/R-O.22939058E+02

MIXTURE
hO/R
0.24040550E+02

KG-FORM.WT./KG
C
*H
*N
*0

bi(2)
0.21705101E-Ol
0.13023060E+OO
0.43410201E-01
O.OOOOOOOOE+OO

bi(l)O.OOOOOOOOE+OO
O.OOOOOOOOE+OO
0.21736513E-01
O.43473025E-01

boi
0.62014573E-02
0.37208744E-01
O.27928995E-01
0.31052161E-01

POINT ITN

T

1
103386.569
Pinf/Pt = 1.733517
3207.237
2
3
Pinf/Pt = 1.731796
3207.551222173.122
3
52400.051442422.435
4
3
12422.47842171. 383542175.4785241843.631
62
61840.505471580.708
7
1583.0362
1440.4478321438.100
8

C

H

N

a

-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.B86-13.861-13.861-14.124-14.120-14.421-14.424-14.630-14.628-14.741-14.743-15.222-17.057-16.543-16.496-16.496-17.061-17.051-17.925-17.934-18.600-18.595-18.819-18.822

159

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

1000.0 P,UA12
WT FRACTION(SEE NOTE)
1.0000000
1.0000000

REACTANTFUELOXIDANT

CH6N2(L)N204 (L)ENERGY
KJ/KG-MOL
54200.000-17549.000

TEMPK
298.150
298.150

REACTANT DENSITY= 1210.57 KG/CU M
O/F=

2.50000

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

(l/n)

(dLV!dLP)t(dLV/dLT)pCp, KJ/ (KG) (K)GAMMAsSON VEL,M/SEC
MACH NUMBER%FUEL= 28.571429

R,EQ.RATIO= 0.998555

PHI,EQ.RATIO= 0.998555

EXIT
CHAMBEREXIT
EXIT
THROAT
EXIT
67.469219.621.00001.731868.04627.26068.9472.5292
1. 0219 0.31394
39.8131.01323386.57 3207.55 2173.12 2422.48 2175.48 1840.51
5.8414 a 3.6029 a 1.4329-1 3.1771-1 1.4434-1 5.2779-2
199.89 -427.33 -3713.93 -3026.58 -3707.90 -4476.65-980.43 -1532.34 -4421.09 -3822.66 -4415.88 -5071.46-36876.0 -35543.4 -27505.1 -29547.7 -27524.9 -24626.4
10.9479 10.9479 10.9479 10.9479 10.9479 10.9479

EXIT
537.920.128171583.04
2.5095-2-4971.56-5482.31-22302.5
10.9479EXIT
910.150.07575
1438.101.6331-2-5227.72-5691.60-20971.9
10.947925.30123.85625.55125.54925.72725.77025.77624.135-1.02415 -1. 02080 -1. 00301 -1.00625 -1.00304 -1. 00071 -1. 00012 -1.00003
1.0916
1. 0253
1.00121.4206
1.17001.0922
1. 00511.46082.79524.96902.78933.4486
2.1078
1. 82085.1203
1.73111.1572
1. 2297
1.13781.1352
1.15741.14181.1912
1. 2179
1158.91120.0
904.7
953.4
905.1
841.7
788.7
755.3
3.093
4.078
0.000
1. 000
2.664
3.089
3.633
4.362

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

160

1.00001708.60.65552106.61120.010.066
1708.6
1.63753050.52797.85.00001708.61.48682853.62540.310.0001708.6
1. 63623048.92795.625.0001708.6
1. 78993252.83058.350.0001708.61.88233374.83216.075.0001708.6
1. 92833435.53294.7

MASS FRACTIONS
0.076960.15200
0.000440.000020.00001
0.000140.003140.28566
0.000020.00001
0.022140.00005
0.380820.00001
0.00515
O. 03288
O. 04055

*CO
*C02
*H
RNO
HN02
H02
*H2
H2O
H202
*N
*NO
N02
*N2
N20
*0
*OH
*02

0.06751
0.166860.000340.00001
0.00000
0.00009
0.002680.293780.00001
0.00000
0.017740.00003
0.382890.00001
0.00387
0.02709
0.037080.01018
0.256930.00001
0.00000
0.00000
0.00000
0.00044
0.329670.00000
0.00000
0.001630.00000
0.390430.00000
0.000110.00267
0.00792

0.02136
0.239360.00005
0.00000
0.00000
0.00000
0.000850.323850.00000
0.00000
0.003730.00000
0.389450.00000
0.000420.006210.014710.01026
0.256800.00001
0.00000
0.00000
0.00000
0.000450.329620.00000
0.00000
0.001640.00000
0.390430.00000
0.000110.00269
0.00798

0.002140.269560.00000
0.00000
0.00000
0.00000
0.000120.333820.00000
0.00000
0.000360.00000
0.391030.00000
0.00001
0.00052
0.002430.00028
0.272490.00000'
0.00000
0.00000
0.00000
0.000020.334930.00000
0.00000
0.00009
0.00000
0.391150.00000
0.00000
0.00009
0.00095

0.00005
0.272850.00000
0.00000
0.00000
0.00000
0.00000
0.335110.00000
0.00000
0.00004
0.00000
0.391180.00000
0.00000
0.000030.00075* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MASS FRACTIONSWERE 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

3
2

4
4

3
2
3

5
5

2

1337.947
1340.166
1212.262
1210.1751121. 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 EQUILIBRIUMCOMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pinj
CASE

1000.0 PSIA
12
REACTANTENERGY
KJ/KG-MOL
54200.000-17549.000

CH6N2 (L)N204(L)WT FRACTION(SEE NOTE)
1.0000000
1.0000000

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

R,EQ.RATIO= 0.998555

FUEL
OXIDANT

TEMP
K

298.150
298.150

PHI,EQ.RATIO= 0.998555

161

pinf/P
P, BAR

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

(l/n)

(dLV/dLP)t(dLV/dLT)pCp, KJ/ (KG) (K)
GAMIvtAs

SON VEL,M/SEC
MACH NUMBER

EXIT
CHAMBERTHROAT
1.00001.7318 1322.19
68.94739.813 0.05215
3386.57 3207.55 1340.17
5.8414 a 3.6029 a 1.2063-2
199.89 -427.33 -5395.00-980.43 -1532.34 -5827.27-36876.0 -35543.4 -20067.0
10.9479 10.9479 10.9479

EXIT
2238.430.03080
1210.177.8911-3-5611.41-6001.74-18860.3
10.9479

EXIT
3253.04
0.021191123.66
5.8480-3-5752.06-6114.49-18053.8
10.9479

25.77823.85625.77824.13525.778-1.02415 -1.02080 -1.00001 -1.00000 -1.00000
1.00001.46081. 0004
1.0001
1. 4206
1.60995.1203
1. 6891
1. 6415
4.96901. 24461.2506
1.13781.1352
1.2362673.21158.91120.0
731.0
697.0
5.125
0.000
4.891
1.000
4.576

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

1. 0000
1708.60.65552106.61120.0100.001708.6
1.95783474.33345.1150.001708.6
1. 99533523.73409.2200.001708.62.01933555.23450.2

MASS FRACTIONS
*CO
*C02
*H
HNO
HN02
H02
*H2
H20
H202
*N
*NO
N02
*N2
N20
*0
*OH
*02

0.06751
0.166860.000340.00001
0.00000
0.00009
0.002680.293780.00001
0.00000
0.017740.00003
0.382890.00001
0.00387
0.02709
0.03708

0.00001
0.27291
0.00000
0.00000
0.00000
0.00000
0.00000
0.335150.00000
0.00000
0.000020.00000
0.391180.00000
0.00000
0.00001
0.00072

0.00000
0.272920.00000
0.00000
0.00000
0.00000
0.00000
0.335160.00000
0.00000
0.00001
0.00000
0.391190.00000
0.00000
0.00000
0.000710.00000
0.272920.00000
0.00000
0.00000
0.00000
0.00000
0.335160.00000
0.00000
0.00000
0.00000
0.391190.00000
0.00000
0.00000
0.00072

0.076960.15200
0.000440.000020.00001
0.000140.003140.28566
0.000020.00001
0.022140.00005
0.380820.00001
0.005150.032880.04055* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MASS FRACTIONSWERE 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

FUEL
OXIDANT

1000.0 PSIA
12
REACTANTWT FRACTION(SEE NOTE)
1.0000000
1.0000000

CH6N2 (L)N204 (L)ENERGY
KJ/KG-MOL
54200.000-l7549.000

TEMPK
298.150
298.150

REACTANT DENSITY= 1210.57 KG/CU M
O/F=

2.50000

pinf/P
P, BAR
T, K
RHO, KG/CU M
H, KJ/KG

U, KJ/KG
G, KJ/KG
S, KJI (KG) (K)M, (lin)Cp, KJ/ (KG) (K)GAMMAsSON VEL,M/SEC
MACH NUMBER%"FUEL= 28.571429

PHI,EQ.RATIO= 0.998555

R,EQ.RATIO= 0.998555

EXIT
CHAMBERTHROAT
EXIT
EXIT
EXIT
EXIT
EXIT
768.78 1327.00
1. 0000
1.731868.04633.32387.244302.3968.94739.8132.0691 0.79028 0.22801 0.08968 0.05196
1. 0132
3386.57 3207~55 1630.44 1871.65 1552.50 1204.85
985.62872 .375.8414 0 3.6029 0 1.8039-1 3.2089-1 1.4776-1 5.4932-2 2.6413-2 1.7288-2
199.89 -427.33 -3393.03 -2962.89 -3529.26 -4117.22 -4468.39 -4642.93-980.43 -1532.34 -3954.71 -3607.68 -4064.10 -4532.30 -4807.94 -4943.46-36876.0 -35543.4 -21243.0 -23453.6 -20525.9 -17307.9 -15258.9 -14193.6
10.9479 10.9479 10.9479 10.9479 10.9479 10.9479 10.9479 10.9479
23.8565.1203
1.13781158.90.000

24.1354.96901.13521120.01. 00024.135
1. 75121.2439835.9
3.207

1. 0000
1708.60.65552106.61120.08.34491708.6
1. 56892890.22680.624.13524.135

1. 8076
1. 2355

1. 7386
1. 2471

816.7
3.344

24.135
1. 6393
1. 2661
724.9
4.053

24.1351.5626
1. 2828
660.0
4.630

892.5
2.818

5.00001708.61.47202771. 42515.110.0001708.6
1. 59842926.82731.025.0001708.6
1.71983079.72938.450.0001708.6
1. 7884
3166.73055.624.135
1. 51941.2932
623.4
4.992

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

75.0001708.6
1.82153208.73112.2

MASS FRACTIONS

*CO
RNO
H2O
N02
*0

0.067510.00001
0.293780.00003
0.00387

*C02
H02
H202
*N2
*OH

0.166860.00009
0.00001
0.382890.02709

0.00034
0.00268
0.017740.00001
0.03708

*H
*H2
*NO
N20
*02

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MASS FRACTIONSWERE 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
REACTANTWT FRACTION(SEE NOTE)
1.0000000
1.0000000

CH6N2 (L)N204(L)ENERGY
KJ/KG-MOL
54200.000-17549.000

TEMPK

298.150
298.150

REACTANT DENSITY= 1210.57 KG/CV M
O/F=

2.50000

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

PHI,EQ.RATIO= 0.998555%FUEL= 28.571429

R,EQ.RATIO= 0.998555

CHAMBERTHROAT
1. 0000
1.731839.81368.9473386.57 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
EXIT
EXIT
1955.79 3382.76 4995.07
0.03525 0.02038 0.01380
798.24639.53702.081.2819-2 8.4269-3 6.2651-3-4754.49 -4895.92 -4985.94-5029.48 -5137.79 -5206.26-13493.5 -12582.3 -11987.4
10.9479 10.9479 10.9479

24.1354.96901.13521120.01. 00024.1351.49021.3007598.1
5.263

24.1351.4516
1. 3112
563.1
5.669

24.1351.4264
1. 3184
539.0
5.975

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

1.00001708.60.65552106.61120.0100.001708.6
1.84233235.23147.8150.001708.6
1.86853268.23192.4:200.00
1708.6
1. 8849
3288.93220.5MASS FRACTIONS
*CO
RNO
H2O
N02
*0

*C02
H02
H202
*N2
*OH

M, (l/n)Cp, KJ/ (KG) (K)GAMMAsSON VEL,M/SEC
MACH NUMBER

23.8565.1203
1.13781158.90.000

0.067510.00001
0.293780.00003
0.00387

0.166860.00009
0.00001
0.382890.02709*H*H2

0.00034
0.00268
0.017740.00001
0.03708

*NO
N20
*02

* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MASS FRACTIONSWERE LESS THAN S.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

1EXAMPLE 13:
(a)
(b)

(c)
(d)

(e)
(f)
(g)

(h)
(i)

Rocket problem with an infinite-area combustor (rocket). This
problem was selected to show some unusual derivatives.
Tripropellant.
Fuels are N2H4(L) and Be(L) and oxidant is H202(L),all at 298.15 K.
Reactant mixture is given as 67% fuel by weight (%fuel=67.).
Chamber pressure is 3000 psia (p,psia=3000).
Calculations are to be for equilibrium conditions only (equilibrium).
Four exit pressure ratios are assigned (pi/p=3,10,30,300).
BeO(L) is included as possible combustion product for the firstpoint (insert).
Mole fractions> 1.e-10 are to be in e-format (trace=1.e-10).
Units in final tables to be non-SI (calories).

wt%= 80
t=298.15
wt%= 20
t=298.15
wt%=100
t=298.15
p,psia=3000, pi/P=3,lO,30,300,equilibrium

reac fuelN2H4{L)
fuel
Be{a)
oxid
H202(L)prob rocket case=13

%fuel

67.

outp trace= 1.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- 1.00E-10

S/R= O.OOOOOOE+OO

Pe,BAR

206.841913

Pe/P -

3.000010.0000

H/R= O.OOOOOOE+OO

30.0000

INCD=FTRNSPT=F

U/R= O.OOOOOOE+OO

300.0000

SUBSONIC AREA RATIOSSUPERSONIC AREA RATIOS
NFZ=

1Mdot/Ac= O.OOOOOOE+OO

Ac/At= O.OOOOOOE+OO

REACTANTWT.FRAC(ENERGY/R) , K
EXPLODED FORMULA
F: N2H4(L)0.800000
0.605929E+04
N 2.00000 H 4.00000
F: Be(a)0.200000 -0.130953E-05
BE 1. 00000
0: H202(L)
1.000000 -0.225846E+05
H 2.00000 0 2.00000

TEMP,KDENSITY

298.150.8740298.151.4310298.150.0000165

SPECIES BEING CONSIDERED IN THIS SYSTEM(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES)

1 7/88
1 5/90
1 7/88
1 4/901 1/90
1 5/90srd 93coda89J12/75
BeO (L)*Be
BeN
Be02H2
Be303
Be606
HN02
*H2
*N
NH3
N02
N2H2
N20
N205
*0
03
Be(b)
BeO(a)
Be02H2(b)INSERTED

OfF =0.492537

1 6/94
j 6/63
j12/75
j 9/63
j 9/63
tpis89tpis78
1 6/88

tpis89ENTHALPY(KG-MOL) (K) /KG
KG-FORM.WT./KG
*N
*H
*Be
*0
POINT ITN
T
133015.4 77
1
Pinf/Pt = 1.743807
2802.2032
4ADD BeO(b)242851.000
Pinf/pt = 1.630416
422851.000
Pinf/Pt :: 1.626685
222851.000352604.969
PHASE CHANGE, REPLACE
3
42922.003
ADD BeO(L)342851.000452204.200
PHASE CHANGE, REPLACE
42451.195
4
PHASE CHANGE, REPLACE
422451.58652061.574
5
PHASE CHANGE, REPLACE
522067.1186
51396.587

166

tpis81
j 12/74
j 9/63
j 9/63
1 6/94
1 4/90
1 8/89111/89
tpiS89j12/64
tpis89
1 4/90tpis89tpis78srd 93srd 93coda89
1 8/89

BeH
*BEO
Be20
Be404
*H
lIN03
H2O
*NH
NH20H
N03
NH2N02
N203
N3
*OH
Be(a)
Be(L)
BeO(b)
H20(s)EFFECTIVE FUELh(2)/R
0.15126831E+03bi(2)0.49929412E-01
O.99858825E-01
0.22192184E-01
O.OOOOOOOOE+OO

j 12/60
j12/75
j 9/63
j 9/63
112/89
1 5/89
1 2/93
112/89tpis89tpis78
1 5/90tpis891 7/88
tpis89srd 93coda89coda89
1 8/89EFFECTIVE OXIDANTh(l)/R-0.66396668E+03
bi(1}O.OOOOOOOOE+OO
O.58798142E-01
O.OOOOOOOOE+OO
O.58798142E-01

BeH2
BeOH
Be202
Be50S

RNa
H02
H202
NH2
*NO
*N2
N2H4
N204
N3H
*02
Be(a)
BeO(a)BeO(L)
H20 (L)MIXTURE
hO/R-0.11775924E+03
hOi
0.33452706E-01
0.86308799E-01
0.14868763E-Ol
O.19403387E-01

N-12.175

H-7.991BE-13.104-20.398-12.317-8.137-13.670-21.009-12.349-8.168-13.530-20.860-12.315-8.135-13.530-20.860-12.314-12.455
BeO (L)-12.667-8.133-13.530-14.318-8.281
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)-15.487-8.779WITH BeO(b}-15.484-8.779-18.232-9.042
WITH BeO(a)-18.191-9.046-27.072-9.603-20.859-23.4640-20.656-22.276-22.274-24.282-24.247-30.583

THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUMCOMPOSITION DURING EXPANSION FROM INFINITE AREA COMBUSTOR
Pinj

CASE

3000.0 PSIA
13

REACTANTWT FRACTION(SEE NOTE)

ENERGY
CAL/MOL

FUEL
FUEL

N2H4(L)OXIDANT

H202 (L)0.8000000
0.2000000
1.0000000

12041.109
0.000-44880.497

O/F=

Be(a)

0.49254%FUEL: 67.000000

P, ATM
T, K

RHO, G/ec
H, CAL/G
U, CAL/G
G, CAL/G
S, CAL/(G) (K)
M,

(l/n)

MW, MOL WT(dLV/dLP) t{dLV/dLT)p
Cp, CAL/ (G) (K)GAMMAsSON VEL,M/SEC
MACH NUMBER

THROAT

EXIT

EXIT

K

298.150
298.150
298.150

PHI,EQ.RATIO= 4.980725
EXIT

EXIT

1. 0000
1.62673.000010.00030.000125.49204.1468.04620.4146.80463015.48 2851. 00 2851. 00 2451. 59 2067.12
1.3715-2 8.9279-3 4.8341-3 1.6916-3 6.6969-4-234.01 -403.86 -612.35 -997.47 -1292.67-594.46 -744.26 -953.24 -1289.71 -1538.74-10112.8 -9743.85 -9952.34 -9028.96 -8064.63
3.27603.27603.27603.27603.2760300.000.680461396.599.9159-5-1762.88-1929.07-6338.16
3.2760CHAMBER
Pinf/PR,EQ.RATIO= 2.990363

TEMP

16.64416.62016.62516.67016.69416.70013.37613.36113.37213.37013.37613.378-1. 00283 -1.00209 -1. 00262 -1. 00098 -1.00023 -1. 00002
1.04650.00000.00001.02091.00531.00010.00000.00000.79840.95750.74480.66490.99790.9974
1.1546
1.18291.1923
1.21801319.61192.21192.71202.71108.0
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

1.00006375.80.6135243.4
121.6

1.23746375.80.9156263.2
181.4

2.48946375.8
1. 3006
307.1
257.7

5.33986375.8
1. 5316
338.8
303.5

30.0106375.8
1. 8405
384.6
364.7

167

MOLE FRACTIONS
*Be
BeH
BeH2
BeN
*BEO
BeOH
Be02H2
Be20
Be202
Be303
Be404
Be505
Be606

*H
RNO
RN02
H02
*H2
H20
H202

*N
*NH
NH2
NII3

NH20H

*NO
N02

*N2
N2H2
N20
N3H
*0
*OH
*02
BeO(a)
BeO(b)BeO(L)

8.681 -6 3.857 -6 7.111 -6 2.586 -7 1.859 -9 1.351-16
1.104 -6 3.684 -7 4.994 -7 8.737 -9 3.040-11 4.032-19
1.171 -5 5.070 -6 5.054 -6 2.194 -7 3.305 -9 7.002-15
4.457 -8 1.236 -8 1.677 -8 1.685-10 2.807-13 3.873-22
3.551 -7 1.342 -7 2.476 -7 5.763 -9 2.341-11 3.240-19
1.240 -4 6.727 -5 9.125 -5 6.858 -6 1.620 -7 7.729-13
2.9966-3 2.5056-3 2.5000-3 7.9244-4 1.6333-4 1.1620-6
7.060 -7 2.511 -7 4.630 -7 4.580 -9 5.497-12 1.278-21
3.894 -7 1.728 -7 3.188 -7 6.143 -9 1.750-11 5.868-20
7.665 -7 4.787 -7 8.831 -7 2.536 -8 1.184-10 1.538-18
2.173 -7 1.434 -7 2.646 -7 4.831 -9 1.201-11 2.030-20
6.079 -9 4.184 -9 7.718 -9 8.580-11 1.070-13 1.914-23
3.717-10 2.827-10 5.216-10 4.205-12 3.317-15 1.280-25
7.4008-3 5.5693-3 7.5542-3 2.8642-3 6.2153-4 3.5990-6
9.938 -8 4.355 -8 4.349 -8 3.791 -9 1.498-10 8.418-15
2.406-10 9.046-11 9.038-11 4.939-12 1.004-13 7.126-19
2.553 -9 1.015 -9 1.379 -9 7.839-11 1.296-12 2.695-18
5.1230-1 5.1354-1 5.1214-1 5.1486-1 5.1624-1 5.1664-1
5.7363-2 5.7964-2 5.7835-2 5.9767-2 6.0485-2 6.0664-2
5.504 -9 2.426 -9 2.422 -9 2.117-10 7.944-12 3.489-16
4.529 -7 1.904 -7 2.585 -7 1.721 -8 3.711-10 1.810-15
2.470 -6 1.086 -6 1.084 -6 9.309 -8 3.580 -9 1.671-13
1.921 -5 9.841 -6 7.222 -6 1.113 -6 1.197 -7 2.226-10
3.0252-4 2.1058-4 1.1363-4 4.9681-5 2.7432-5 1.3148-5
2.905 -9 1.107 -9 5.975-10 4.397-11 2.287-12 9.065-16
1.860 -5 1.087 -5 1.476 -5 2.620 -6 2.002 -7 4.479-11
1.236-10 4.605-11 6.258-11 2.930-12 3.760-14 3.713-20
2.2349-1 2.2362-1 2.2342-1 2.2360-1 2.2372-1 2.2376-1
7.477 -9 2.733 -9 1.476 -9 9.647-11 4.461-12 1.288-15
9.032 -9 4.103 -9 4.101 -9 3.946-10 1.757-11 1.410-15
1.480-10 4.527-11 2.447-11 9.231-13 2.001-14 5.124-19
2.448 -6 1.245 -6 2.297 -6 2.389 -7 7.057 -9 5.241-14
2.7768-4 1.8428-4 2.5007-4 6.4898-5 8.1758-6 8.2744-9
1.083 -7 5.610 -8 1.036 -7 1.142 -8 3.535-10 2.936-15
0.0000 0 0.0000 0 0.0000 0 0.0000 0 1.9873-1 1.9892-1
0.0000 0 1.3853-2 1.5511-1 1.9799-1 0.0000 0 0.0000 0
1.9567-1 1.8245-1 4.0950-2 0.0000 0 0.0000 0 0.0000 0* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONSWERE LESS THAN l.OOOOOOE-I0 FOR ALL ASSIGNED CONDITIONS
RN03
N204
Be(b)

N03
N205
Be(L)

NH2N02N3
Be02H2(b)N2H403
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 ofcondensed species on volume and molecular weight (see sec.2.2,part I)(b)
Assigned-temperature-and-pressureproblem (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 themup. Reactant enthalpies are not needed for assigned temperatureproblems.
(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=100
name 02{L} moles=60

reac

H 2

o 2

prob

tp p,atm=.05 case=14
t,k = 1000,500,350,305,304.3,304.2,304,300,

outputsiunits

debug = 5

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

1000.0000

TRACE=:·O.OOE~OO

P,BAR =

500.0000

350.0000

S/R= O.OOOOOOE+OO

305.0000

304.3000

H/R= O.OOOOOOE+OO

INCD=FTRNSPT=F

304.2000

304.0000

30

U/R= O.OOOOOOE+OO

0.050663

REACTANTMOLESEXPLODED FORMULA
N: H2 (L)100.000000
H
2.00000
60.000000
N: 02(L}0 2.00000(ENERGY/R) , K

TEMP,KDENSITY

O.OOOOOOE+OO

0.00

0.8740-0.156101E+04

90.17

1. 4310SPECIES BEING CONSIDERED IN THIS SYSTEM(CONDENSED PHASE MAY HAVE NAME LISTED SEVERAL TIMES)
1 6/94
1 8/89tpis78
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
*0
03

169

OfF

0.000000ENTHALPY(KG-MOL) (K)/KG
KG-FORM.WT./KG*H*0
POINT ITN
10
1
2
3
3
1
4
1

EFFECTIVE FUELh(2)/R-0.44147845E+02

EFFECTIVE OXIDANTh(l)/RO.OOOOOOOOE+OO

MIXTURE
hO/R-0.44147845E+02bi(2)O.94272209E-01
0.5656332?E-Olbi(l)O.OOOOOOOOE+OO
O.OOOOOOOOE+OO

bOi
0.94272209E-Ol
0.56563325E-Ol

T
1000.000
500.000
350.000
305.000

H-20.527-34.596-46.944-53.061ITERATION 1
MATRIX
0.188544E+00
0.942722E-Ol
O.942722E-Ol
0.6S990SE-Ol
0.942722E-Ol
0.S65633E-Ol

0-15.973-15.230-15.049-15.028

0.942722E-01
0.565633E-01
O.OOOOOOE+OO-O.114417E+02-0.'600419E+Ol-O.586253E+Ol

SOLUTION VECTORo

H-0.531707E+02-0.lS0274E+02

O.OOOOOOE+OO

T= 0.30430000E+03 ENN= 0.51B49715E-01 ENNL=-0.29594058E+Ol PP= O.50662500E-Ol
LN P/N=-O.23163446E-Ol AMBDA= O.10000000E+Ol
LN Nj
DEL LN Nj
HOj/RT
SOj/R
GOj/RT
Gj/RT
0.862123E+02
O.OOOOOOE+OO -O.125204E+03 -0.307497E+OO
0.138484E+02
O.723640E+02 -O.528633E+02
O.OOOOOOE+OO -0.604867E+02 -0.121044E+OO
0.504603E+Ol
0.276408E+02 -0.225947E+02 -O.831046E+02
O.OOOOOOE+OO -0.903810E+02 -O.219421E+00
O.701441E-Ol
O.157881E+02 -O.157179E+02 -0.106122E+03
O.471361E-Ol -O.305472E+01
0.177636E-14 -0.954977E+02
0.227933E+02 -O.118291E+03 -0.121369E+03
O.OOOOOOE+OO -O.541943E+02 -0.956804E-01 -0.537719E+02
0.283113E+02 -0.820832E+02 -O.136301E+03
O.OOOOOOE+OO -0.938907E+02 -0.226071E+OO
O.985373E+02
0.791125E+02 -O.148014E+02
O.194248E+02
O.OOOOOOE+OO -0.614818E+02 -0.145407E+OO
0.156242E+02
0.221720E+02 -0.654785E+Ol -O.680S28E+02
0.471361E-02 -O.535730E+01 -O.639488E-13
0.714483E-Ol
O.247458E+02 -0.246744E+02 -0.300549E+02
O.OOOOOOE+OO -O.722284E+02 -O.128601E+OO
O.561412E+02
O.272979E+02 -O.449537E+02
O.288433E+02
O.OOOOOOE+OO
O.OOOOOOE+OO
O.OOOOOOE+OO -0.115317E+03
O.550772E+Ol -0.120825E+03 -O.172966E+03
O.OOOOOOE+OO
O.OOOOOOE+OO
O.OOOOOOE+OO -O.112509E+03
O.861762E+Ol -O.121126E+03 -O.230622E+03
304.300-15.027-53.171
Nj

*H
H02
*H2
H2O
H202
*0
*OH
*02
03
H20(s)
H20(L)
5170

1

200.000

H20(s)

273.150

O.OOOOOOOE+OO

H20(L)
273.150
600.000[GOj-SUM(Aij*Pli)]/Mj = -0.9021700E-03
ADD H20(L)

ITERATION

00.188544E+00
0.942722E-Ol
O.200000E+01
O.942722E-01

MATRIX
0.942722E-Ol
0.659905E-Ol
0.100000E+Ol
0.565633E-Ol

O.OOOOOOOE+OO
MAX NEG DELTA G

0.200000E+Ol
O.lOOOOOE+Ol
O.OOOOOOE+OO
O.OOOOOOE+OO

O.942722E-Ol
O.565633E-Ol
O.OOOOOOE+OO
0.770217E-15

O.842705E-02-O.162528E+OO-0.9021700E-03-O.114417E+02-O.600419E+Ol-O.121385E+03-O.586253E+Ol

SOLUTION VECTOR
H-0.532195E+02

o-O.149462E+02

T= O.30430000E+03" ENN= 0.51849715E-Ol ENNL=-O.29594058E+Ol PP= O.50662500E-Ol
LN P/N=-O.23163446E-Ol AMBDA= O.lOOOOOOOE+Ol
Nj*H

O.OOOOOOE+OO

H02

O.OOOOOOE+OO*H2

O.OOOOOOE+OO

H2O

O.471361E-Ol

H202

O.OOOOOOE+OO*0O.OOOOOOE+OO*OHO.OOOOOOE+OO*02

O.471361E-02

03

O.OOOOOOE+OO

H20(s)O.OOOOOOE+OO

H20(L)O.OOOOOOE+OO

ITERATION

1

O.157678E+OO
O.788388E-Ol
O.200000E+Ol
0.788388E-Ol

MATRIX
O.788388B-Ol
0.582738E-Ol
O.lOOOOOE+Ol
0.488466E-Ol

LN Nj

DEL LN Nj
HOj/RT
SOj/R
GOj/RT
Gj/RT-O.125512E+03 -O.211287E+OO
0.862123E+02
0.138484E+02
0.723640E+02 -0.531707E+02-O.606077E+02 -0.487585E-Ol
O.504603E+Ol
0.276408E+02 -0.225947E+02 -0.832256E+02-O.906004E+02 -0.260046E+00
0.701441E-Ol
O.157881E+02 -O.157179E+02 -O.lQ6341E+03-O.305472E+Ol -0.178781E+00 -O.954977E+02
O.227933E+02 -O.118291E+03 -O.121369E+03-O.542900E+02 -O.975171E-Ol -O.537719E+02
O.283113E+02 -O.820832E+02 -O.136396E+03-0.941168E+02 -O.812642E-Ol
0.985373E+02
O.194248E+02
O.791125E+02 -O.150274E+02-O.616272E+02 -O.130023E+OO
O.156242E+02
O.221720E+02 -O.654785E+Ol -O.681982E+02-O.535730E+Ol
O.124345E-12
O.714483E-Ol
0.247458E+02 -O.246744E+02 -O.300549E+02-O.723570E+02
O.812642E-01
O.561412E+02
O.288433E+02
O.272979E+02 -O.450823E+02
O.OOOOOOE+OO
O.OOOOOOE+OO -O.115594E+03
O.549580E+Ol -O.121090E+03 -O.172966E+03
O.OOOOOOE+OO
O.842705E-02 -O.112788E+03
O.859679E+Ol -O.121385E+03 -O.121385E+03

O.200000E+Ol
O.lOOOOOE+Ol
O.OOOOOOE+OO
O.OOOOOOE+OO

O.788388E-Ol
0.488466E-Ol
O.OOOOOOE+OO
O.611676E-04-0.122861E-02

O.131474E-Ol-O.957128E+Ol-O.506744E+Ol-0.121385E+03-O.492589E+Ol

SOLUTION VECTOR
H-0.532162E+02

o-O.149527E+02

171

T= 0.30430000E+03 ENN= 0.44071839E-01 ENNL=-0.31219343E+01 PP= 0.50662500E-01
LN P/N= 0.13936499E+00 AMBDA= 0.10000000E+01
Nj*H

O.OOOOOOE+OO

H02

O.OOOOOOE+OO*H2

O.OOOOOOE+OO

H2O

0.394194E-01

H202

O.OOOOOOE+OO*0O.OOOOOOE+OO*OHO.OOOOOOE+OO*02

0.471361E-02

03

O.OOOOOOE+OO

H20 (s)O.OOOOOOE+OO

H20(L)

0.84270SE-02

ITERATION 2
MATRIX
0.159764E+00
0.798822E-01
0.587955E-01
0.798822E-01
0.200000E+01
0.100000E+01
0.798822E-01
0.493683E-01

LN Nj
DEL LN Nj
HOj/RT
SOj/R
GOj/RT
Gj/RT-0.125723E+03
0.164343E-01
0.862123E+02
0.138484E+02
0.723640E+02 -0.532195E+02-0.606565E+02
0.328686E-02
0.504603E+01
0.276408E+02 -0.225947E+02 -0.831118E+02-0.908604E+02
0.197211E-01
0.701441E-01
0.157881&+02 -0.157179&+02 -0.106439E+03-0.323350&+01
0.131474E-01 -0.954977E+02
0.227933E+02 -0.118291E+03 -0.121385E+03-0.543875E+02
0.657371E-02-0.537719E+02
0.283113&+02 -0.820832E+02 -0.136331E+03-0.941980E+02
0.657371E-02
0.985373E+02
0.194248E+02
0.791125E+02 -0.149462E+02-0.617572E+02
0.986057E-02
0.156242&+02
0.221720E+02 -0.654785E+01 -0.681657E+02-0.535730E+01 -0.127898E-120.714483E-01
0.247458E+02 -0.246744E+02 -0.298923E+02-0.722758&+02 -0.657371E-02
0.561412E+02
0.288433&+02
0.272979&+02 -0.448385E+02
O.OOOOOOE+OO
O.OOOOOOE+OO -0.115594E+03
0.549580E+01 -0.121090E+03 -0.172966E+03
0.000000&+00 -0.122861&-02 -0.112788E+03
0.859679&+01 -0.121385E+03 -0.121385E+03

0.200000E+01
0.100000E+01
O.OOOOOOE+OO
0.000000&+00

0.798822&-01
0.493683E-01
O.OOOOOOE+OO-0.403867E-06

0.126035E-13-0.856736E-04

SOLUTION VECTOR
H-0.532162E+02172

o-0.149527E+02-0.969652E+01-0~513018E+01-0.121385E+03-0.498922E+01

T= 0.30430000E+03 ENN= 0.44655096E-01 ENNL=-0.31087869E+01 PP= 0.50662500E-01
LN p/N= 0.12621757E+00 AMBDA= 0.10000000E+01
Nj

LN Nj

SOj/R
*H

O.OOOOOOE+OO

H020.0000008+00*H2

O.OOOOOOE+OO

H2O

0.399411E-01

H202

O.OOOOOOE+OO*0O.OOOOOOE+OO*OHO.OOOOOOE+OO*02

0.471361E-02

03

O.OOOOOOE+OO

H20(s)O.OOOOOOE+OO

H20 (L)0.719845E-02

ITERATION 3
MATRIX
0.7987538-01
0.159751E+00
0.587921E-01
0.798753E-01
0.100000E+01
0.200000E+01
0.493649E-01
0.798753E-01

DEL LN Nj

GOj/RT

HOj/RT

Gj/RT-0.125706E+03 -0.107092E-03
0.862123E+02
0.138484E+02
0.723640E+02 -0.532162E+02-0.606532E+02 -0.214184E-04
0.504603E+01
0;276408E+02 -0.225947E+02 -0.831217E+02-0.908407E+02 -0.128510E-03
0.701441E-01
0.157881E+02 -0.157179E+02 -0.106432E+03-0.322035E+01 -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
0.194248E+02
0.791125E+02 -0.149527E+02-0.617473E+02-0.642552E-04
0.156242E+02
0.221720E+02 -0.654785E+01 -0.681690E+02-0.535730E+01 -0.284217E-13
0.714483E-01
0.247458E+02 -0.246744E+02 -0.299055E+02-0.722823E+02
0.428368E-04
0.561412E+02
0.288433E+02
0.272979E+02 -0.448582E+02
0.0000008+00
O.OOOOOOE+OO -0.115594E+03
0.549580E+01 -0.121090E+03 -0.172966E+03
O.OOOOOOE+OO
0.126035E-13 -0.112788E+03
0.859679E+01 -0.121385E+03 -0.121385E+03

0.200000E+01
0.100000E+01
O.OOOOOOE+OO
O.OOOOOOE+OO

0.798753E-01
0.493649E-01
O.OOOOOOE+OO-0.172989E-10-0.757420E-14-0.367002E-08-0.969568E+01-0.512976E+01-0.121385E+03-0.498880E+01

SOLUTION VECTOR
H-0.532162E+02

o-0.149527E+02

T= 0.30430000E+03 ENN= 0.44651270E-01 ENNL=-0.3108872SE+01 pp= 0.50662500E-01
LN P/N= 0.12630324E+00 AMBDA= 0.100000008+01

173

LN Nj
DEL LN Nj
HOj/RT
SOj/R
GOj/RT
Gj/RT
O.862123E+02
O.OOOOOOE+OO -O.125707E+03 -O.458755E-08
O.138484E+02
O.723640E+02 -O.532162E+02
O.504603E+Ol
O.OOOOOOE+OO -O.606532E+02 -O.917481E-09
O.276408E+02 -O.225947E+02 -0.831216E+02
O.701441E-Ol
O.OOOOOOE+OO -O.908408E+02 -O.550507E-08
O.157881E+02 -O.157179E+02 -O.106432E+03
O.399377E-Ol -O.322044E+Ol -0.367004E-08 -O.954977E+02
O.227933E+02 -O.118291E+03 -O.121385E+03
O.OOOOOOE+OO -O.543810E+02 -O.183496E-08 -O.537719E+02
O.283113E+02 -O.820832E+02 -O.136338E+03
O.985373E+02
O.OOOOOOE+OO -O.941915E+02 -O.183497E-08
O.194248E+02
O.791125E+02 -O.149527E+02
O.156242E+02
O.OOOOOOE+OO -O.617474E+02 -O.275250E-08
O.221720E+02 -O.654785E+01 -O.681689E+02
0.746070E-13
O.714483E-Ol
0.471361E-02 ~0.535730E+01
O.247458E+02 -O.246744E+02 -O.299054E+02
0.183512E-08
0.561412E+02
O.OOOOOOE+OO -O.722823E+02
0.288433E+02
0.272979E+02 -0.448581E+02
O.OOOOOOE+OO
O.OOOOOOE+OO
O.OOOOOOE+OO -0.115594E+03
0.549580E+Ol -0.121090E+03 -O.172966E+03
O.OOOOOOE+OO -O.757420E-14 -0.112788E+03
O.719845E-02
0.859679E+Ol -0.121385E+03 -0.121385E+03-14.953304.300-53.216

Nj

*H
H02
*H2
H2O
H202
*0
*OH
*02
03
H20 (8)
H20(L)
53

H20(s)

200.000

273.150

O.OOOOOOOE+OO

H20(L)

273.150

600.000

O.7198445E-02

T DERIV MATRIX
O.159751E+OO
O.798753E-Ol
O.200000E+Ol
O.798753E-Ol

O.798753E-Ol
O.587921E-Ol
0.100000E+01
O.493649E-Ol

O.200000E+01
O.100000E+Ol
O.OOOOOOE+OO
O.OOOOOOE+OO

O.798753E-Ol
O.493649E-Ol
O.OOOOOOE+OO
O.OOOOOOE+OO

SOLUTION VECTOR
H-O.930373E+02

0O.732862E+02

O.654145E+01-O.146501E+03

P DERIV MATRIX
O.159751E+OO
O.798753E-01
O.200000E+Ol
O.798753E-01

O.798753E-01
0.587921E-Ol
O.100000E+Ol
O.493649E-Ol

O.200000E+Ol
O.100000E+Ol
O.OOOOOOE+OO
O.OOOOOOE+OO

O.798753E-Ol
0.493649E-Ol
O.OOOOOOE+OO
O.OOOOOOE+OO

0.378323E+OO-O.847284E+Ol

SOLUTION VECTOR
H-O.236821E+Ol

0

O.473642E+Ol

POINT= 5
P= O.506625E-Ol
T= O.304300E+03
H/R=-O.140755E+04
S/R= 0.123707E+Ol
M= 0.223958E+02
CP/R= O.113349E+03
DLVPT=-O.947284E+01
DLVTP= 0.147501E+03
GAMMA(S)= O.110818E+01
V= O.222990E+07

174-0.762791E+Ol-O.381328E+Ol-0.112788E+03-O.381362E+Ol

0.798753E-Ol
O.493649E-Ol
O.OOOOOOE+OO
O.446513E-Ol678

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 ASSIGNEDTEMPERATURE AND PRESSURE
CASE

14REACTANTMOLES

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/CU M
O/F=

0.00000~FUEL=

0.000000

R,EQ.RATIO= 0.833333

0.05066
500.002.3504-2-11.043.6-11259.2-17139.8
1.2.1924

0.05066
350.003.3577-2-11309.1-11460.0-15355.8
11. 5619

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,

(lin)

MW, MOL WT(dLVjdLP)t(dLV/dLT)pCp, KJ/ (KG) (K)GAMMAsSON VE~,M/SEC

0.05066
1000.00
1.1752-2-10066.0-10497.1-23601.6
13.5356

0.05066305.003.8530-2-1.1.386.9-11518.4-14840.7
11.32390.05066304.304.4845-2-11703.1-11816.0-14833.0
10.2856

0.05066304.204.7014-2-11792.8-11900.5-14831.99.99070.05066 0.05066
304.00300.005.1325-2 1.3024-1-11948.7 -12988.1-12047.4 -13027.0-14830.0 -14801.2
9.4781
6.04351.9.287
19.28719.28725.60764.1251.9.287
22.39623.47119.28719.28719.28719.28719.28719.28719.28719.287-1.00000 -1. 00000 -1. 00000 -1. 00000 -9.47284 -9.03875 -8.28504 -3.30842
1..0000
1.00001. 0000
1. 0000 147.5009 140.0542 127.1235
41. 6525
1.80692.1108
1. 7370
1.7233 942.4445 854.1858 711.2554 96.0625
1. 3133
1. 2567
1.33011.3336
1.1082
1.10611.1019
1. 0345532.1.
736.0
448.0
418.8
353.8
345.2
329.8
200.6

MOLE FRACTIONS
H20*02
H20(L)

0.909090.09091
0.00000

0.909090.09091
0.00000

0.909090.09091
0.00000

0.909090.09091
0.000000.77026
0.09091
0.138830.73080
0.090910.17830

0.662280.090910.246810.20986
0.090910.69923* THERMODYNAMIC PROPERTIES FITTED TO 20000.K
PRODUCTS WHICH WERE CONSIDERED BUT WHOSE MOLE FRACTIONSWERE LESS THAN 5.000000E-06 FOR ALL ASSIGNED CONDITIONS
*H
*OH

H02
03

*H2
H20(s)

H202

*0

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, lANAFThermochemical Tables, 3rd Ed., Pts. 1 & 2. (Also, Journal of Physical andChemical 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," National Bureau of Standards Journal ofResearch, 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 andA'ltronautics Journal, Vol. 9, No. I, pp. 179-182.
Gordon S. and McBride, B..1., 1976, Computer Program for Calculation of Complex Chemical Equilibrium
Compositions, Rocket Performance, Incident and Reflected Shocks, and Chapman-.!ouguet Detonations, NASA
SP-273, Interim Revision.
Gordon, S., 1982, "Thermodynamic and Transport Combustion Properties of Hydrocarbons With Air. I-Properties
in SI Units," NASA TP-1906.
Gordon, S. and McBride, RJ., 1988, "Finite Area Combustor Theoretical Rocket Performance," NASA TM100785.
Gordon S. and McBride, RI., 1994, Computer Program for Calculation of Complex Chemical Equilibrium
Compositions and Applications. I. Analysis, NASA RP~ 1311.
Gupta, RN., Yos, .I.M., Thompson RA., and Lee, KP., 1990, A Review of Reaction Rates and Thermodynamic
and Transport Properties for an ll-Species Air Model for Chemical and Thermal Nonequilibrium Calculations to
30000 K, NASARP~1232.

Lide, D.R, ed., 1992-1993, CRC Handbook of Chemistry and Physics, 73rd Ed., eRC Press, Inc., Boca Raton,
FL, pp. 6-12.
McBride, B.J. and Gordon, S., 1992, Computer Programfor Calculating and Fitting Thermodynamic Functions,
NASARP-1271.
McBride, B.1., Gordon, S., and Reno, M.A., 1993, "Coefficients for Calculating Thermodynamic and Transport
Properties ofIndividual Species," NASA TM-4513.
McBride, B.1., 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, B.J., 1973, "FORTRAN IV Computer Program for the Calculation of Thermodynamic
andTransIJort Properties of Complex Chemical Systems," NASATND-7056.
Svehla, RA., 1995, "Transport Coefficients for the NASA Lewis Chemical f':;quilibrium Program," NASA TM4647.
Svehla, R.A., 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 revlewlng Instructions. searching existing data sources,
gathering and maintaining the data needed, and col'Tl>leting and reviewing the collection of Information. Send comments regarding this burden estimate or any other aspect aI thiscollection of Information, Including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefterson
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, 2. REPORT DATE

1. AGENCY USE ONLY (Leave blank), 3. REPORT TYPE AND DATES COVEREDJune 1996

Reference Publication

4. TITLE AND SUBTITLE

5. FUNDING NUMBERS

Computer Program for Calculation of Complex Chemical Equlibrium
Compositions and Appl;cations

n. Users Manual and Frogl:UTI Description
WU-505-62-52

6. AUTHOR(S)

Bonnie J. McBride and Sanford Gordon

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)8. PERFORMING ORGANIZATIONREPORT NUMBER

National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135-3191

E-8017-1

10. SPONSORINGIMONITORINGAGENCY 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 NOTESBonnie 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

128. DISTRIBUTION!AVAILABILITY STATEMENT

Unclassified -Unlimited
Subject Categories 20 and 25
This publication is available from the NASA Center for AeroSpace Infonnation, (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) adescription of output tables for various types of problems; (3) the overall modular organization of the program withinformation on how to make modifications; (4) a description of the function of each subroutine; (5) error messages andtheir 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 andthermal 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
performance
17. SECURITY CLASSIFICATIONOF REPORT

18. SECURITY CLASSIFICATION
OF THIS PAGE

Unclassified

Unclassified

NSN 7540-01-280-5500

19. SECURITY CLASSIFICATION
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178
16. PRICE CODE

A09
20. LIMITATION OF ABSTRACT

Unclassified
Standard Form 298 (Rev. 2-89)
Prescrbed by ANSI Std. Z39-18
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