NASA Technical Memorandum 4557 CET93 and CETPC: An Interim Updated Version of the NASA Lewis Computer Program for Calculating Complex Chemical Equilibria With Applications Bonnie J. McBride Lewis Research Center Cleveland, Ohio Martin A. Reno Heidelberg College Tiffin, Ohio and Sanford Gordon San ford Gordon and Associates Cleveland, Ohio N94-32948 (NASA-TM-4557) CET93 AND CETPC: AN National Aeronautics and Space Administration INTERIM UPDATED VERSION OF THE NASA LEWIS COMPUTER PROGRAM FOR Office of Management Unc 1 as CALCULATING COMPLEX CHEMICAL Scientific and Technical EQUILIBRIA WITH APPLICATIONS information Program (NASA. Lewis Research Center) 34 p 1994 Hl125 0O09988 Contents Introduction .................... • ........ .,,,, ........ , .......... H,, ....... .,, .......... , ................... °,.,.,,,,,.,.,, ...... , ........ ,*°,, ........ , ........ 1 Program Capabilities ....................................................................................................................................... 1 Thermodynamic and Thermal Transport Mixture Properties .............................................................. 1 Rocket, Shock, and Detonation Problems ........................................................................................... I Initial Estimates, Iteration, and Convergence ...................................................................................... 2 General Input Instructions ............................................................................................................................... 2 Thermodynamic and Thermal Transport Mixture Properties .............................................................. 2 Outline of Input Preparation ................................................................................................................ 3 Example Problems ........................................................................................................................................... 6 Output .............................................................................................................................................................. 6 CETPC Version of CET93 .............................................................................................................................. 6 Appendixes A--Thermodynamic Data Species List ................................................................................... 7 B--Example Problems .......................................................................................................... 23 References ..................................................................................................................................................... 31 i:_,;_ P_,Ir__.di_ NOT FIUIt_ iii Introduction Program Capabilities For more than 40 years the NASA Lewis Research Center Thermodynamic and Thermal Transport Mixture has been involved in developing methods and computer pro- Properties grams for calculating complex chemical equilibrium composi- tions and thermodynamic and transport properties of the Chemical equilibrium compositions are obtained by the equilibrium mixtures and for applying these properties to a method of free energy minimization. A thermodynamic state is number of problems. The latest version of these programs is characterized by two independent state variables, such as documented in Gordon et al. (1976, 1984, 1988). Prior to this temperature and pressure. If pressure is 'one of the state vari- report the source code has been known most recently as CET89. ables, Gibbs energy is minimized. This is the case for the Two new options have been added to CET89, and the thermo- following combination of variables permitted to be assigned by dynamic data for many species have been updated. The code the program: temperature and pressure (tp), enthalpy and containing these changes is now called CET93. The CET93 pressure (hp), and entropy and pressure (sp). If volume (or code, with smaller arrays, has been compiled for use on an IBM density) is one of the state variables, Helmholtz energy is or IBM-compatible personal computer and is called CETPC. minimized. This is the case for the following combination of The source code for CET93 and/or a CETPC diskette of the variables permitted by the program: temperature and volume compiled PC code may be obtained for a fee from COSMIC, (or density) (tv), internal energy and volume (or density) (uv), 382 E. Broad Street, University of Georgia, Athens, GA 30602 and entropy and volume (or density) (sv). (Tel: 706-542-3265). It is assumed that all gases are ideal and that interactions This report is intended to be primarily a users manual for among phases can be neglected. An ideal-gas equation of state CET93 and CETPC. It does not repeat the more complete is used to represent the mixture and is assumed to be correct documentation of the previously mentioned reports, which even when small amounts of condensed phases are present. cover details of capabilities, assumptions, options, and math- Equilibrium properties of plasmas (mixtures containing ion- ematical equations for obtaining chemical equilibrium compo- ized species) may also be calculated if the plasma is considered sitions, mixture properties, rocket performance, shock to be ideal, that is, if columbic interactions are not considered. parameters, and Chapman-Jouguet detonations. However, a Thermodynamic properties of mixtures include the contri- brief summary of some of these topics is given. bution of condensed as well as gaseous phases. However, The discussion in this report covers primarily input and thermal transport mixture properties include the contributions output files, the two new options (ONLY and comments), and of gas-phase species only. If condensed phases are present, implementation of CETPC. The ONLY option permits equilib- mole fractions for the gas-phase species are first normalized to rium composition calculations to be made that consider only gases only prior to calculating thermal transport mixture prop- those species which are specified in the input. The comments erties. The thermodynamic and thermal transport mixture prop- option permits the user to provide comments in the input and erties calculated by the program are discussed in the section output. The thermodynamic data file includes updated data for Output. many species, such as the reference elements (McBride et al., 1993a) and species in the carbon-hydrogen-oxygen-nitrogen (C-H-O-N) chemical system (McBride et al., 1993b). Input Rocket, Shock, and Detonation Problems files for 13 example problems are also included with CET93 and CETPC for testing and illustrating some features of the In addition to calculating equilibrium compositions and program. mixture properties for the assigned thermodynamic states previouslydiscussed,CETPCiscapableofcalculatingtheo- condition special methods are used to obtain excellent initial reticalrocketperformance,shockparameters,andChapman- estimates in order to minimize the number of iterations required Jouguetdetonationparameters.Someinputoptionsforthese for a solution. In addition, because of these excellent initial applicationproblemsaregivenin thesectionGeneralInput estimates, control factors are not needed to limit the size of the Instructions.Thefollowingisabriefsummaryofsomeaddi- iteration corrections. tionalaspectsofthesecalculations. Shock parameters.---The shock problem in CETPC is Rocket performance.--Options are provided for two limited to gaseous state reactants only. Special procedures are rocket models---one with an infinite-area combustor (IAC) and used to obtain excellent initial estimates of temperature and the other with a finite-area combustor (FAC) (Gordon et al., pressure for the incident shock conditions. A control factor is 1976, 1984). The IAC model permits both equilibrium and used to limit the size of the iteration corrections. The initial frozen performance. Equilibrium performance assumes that estimate for the reflected shock temperature is simply twice the the combustion gases attain instantaneous chemical equilib- incident shock temperature. The initial estimate for the re- rium as they flow through the nozzle. Frozen performance flected shock pressure is obtained from a special formula. assumes that the combustion products remain constant after Except for high Mach numbers, convergence is often obtained some specified station in the rocket, such as at the combustor, in three to five iterations. the throat, or some assigned exit point downstream of the Chapman-Jouguet detonations.--The detonation prob- throat. The FAC model permits equilibrium performance only. lem in CETPC is limited to gaseous state reactants only. Special Shockparameters.--Options are provided for calculating procedures are used to obtain initial estimates for temperature incident and reflected shocks in a constant-area duct, such as a and pressure. A recursion formula is used to improve these shock tube. Reactants are limited to gas phase only. Options are estimates in order to provide generally excellent initial esti- also provided for the assumption of equilibrium or frozen mates prior to the final iteration procedure. composition during the flow of the shocked gases. Chapman.Jouguet detonations.---Chapman-Jouguet deto- nations are characterized by the condition that the difference in General Input Instructions flow velocity of the shock and flame fronts is the velocity of sound in the burned gases. Reactants are limited to gas phase only. Input consists of two general