California Institute of Technology

Explosion Dynamics Laboratory

Thermodynamic Data

Thermodynamic data for individual species are necessary for performing equilibrium chemistry and finite-rate chemical kinetics calculations. These data typically provide the thermodynamic properties (enthalpy, entropy, and specific heat) of a species as a function of temperature.

Sources of Data

Primary sources of thermodynamic data are the NIST and NASA on-line databases:
  • NIST-JANAF Tables. Provides pdf files for species in the 4th Edition (1998) print-on-paper version of the JANAF tables. The periodic table interface enables downloading tables in printable or tab-delimited text files.
  • NIST Chemistry Webbook Searchable database for thermodynamic and molecular data. Data available as text tables, plots and coefficients of Shomate polynomials.
  • CEA website for NASA Thermodynamic Database and Chemical Equilibrium Computation. The thermobuild tool accessed from the periodic table interface enables creating data tables and downloading 7 and 9-term polynomial coefficients.

  • Other useful on-line sources include:

  • DLR website Extended Third Millennium Ideal Gas and Condensed Phase Thermochemical Database for Combustion with Updates from Active Thermochemical Tables of Elke Goos, Alexander Burcat and Branko Ruscic. This is an extensive file of 7-term polynomial coefficients available for download.
  • ANL website The Active Thermochemical Tables at ANL provides values of heats of formation for many species.

NASA Glenn Documentation

Computing and fitting thermodynamic properties is a research activity in its own right. The group at NASA Glenn did the foundational work in this area to support the development of the NASA CEA chemical equilibrium software. The computational methodology, molecular data and coefficients are described in the following reports:
  • (PDF) S. Gordon and B. J. McBride. Thermodynamic data to 20 000 k for monatomic gases. Technical Paper 1999-208523, NASA, 2001.
  • (PDF) B. J. McBride and S. Gordon. Computer program for calculating and fitting thermodynamic functions. Reference Publication 1271, NASA, 1992.
  • (PDF) B. J. McBride, M.J. Zehe, and S. Gordon. NASA Glenn coefficients for calculating thermodynamic properties of individual species. Technical Paper 2002-211556, NASA, 2002.
  • (PDF) M.J. Zehe, S. Gordon, and B. J. McBride. CAP: A computer code for generating tabular thermodynamic functions from NASA lewis coefficients. Technical Paper 2001-210959, NASA, 2001.

  • The NASA CEA software based on the older file format (7-coefficient polynomial fits) is described in:

  • (PDF) S. Gordon and B.J. McBride, "Computer Program for Calculation of Complex Chemical Equilibrium Composition, Rocket Performance, Incident and Reflected Shocks and Chapman-Jouguet Detonations", NASA Report SP-273, 1971.
  • (PDF) B.J. McBride, S. Gordon, and M.A. Reno, "Coefficients for Calculating Thermodynamic and Transport Properties of Individual Species", NASA Report TM-4513, October 1993.
  • The NASA CEA software based on the new file format (mix of 7 and 9-coefficient polynomial fits) is described in:

  • (PDF) S. Gordon and B.J. McBride, "Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications: I. Analysis", NASA Reference Publication 1311, October 1994.
  • (PDF) B.J. McBride and S. Gordon, "Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications: II. Users Manual and Program Description", NASA Reference Publication 1311, June 1996.

Element Potential Methods

The element potential method of computing equilibrium was used in the STANJAN program developed by Prof. William Reynolds at Stanford University. Reynolds's documentation and the thesis of Wrobel provide useful background on the theory and implementation of this method.
  • (PDF) Reynolds, W. C. 1981. “STANJAN Interactive Computer Programs for Chemical Equilibrium Analysis.” Stanford University. This document is for an early version of STANJAN and contains examples of hand calculations to illustrate the method.
  • (PDF) Reynolds, W. C. 1986. “The Element Potential Method for Chemical Equilibrium Analysis: Implementation in the Interactive Program STANJAN, Version 3.” Stanford, CA: Mechanical Engineering, Stanford University. This is more complete explanation of the method including important details about the preconditioning steps for the initial guess and the dual method used for solving the constrained optimization problem to obtain the equilibrium state.
  • (PDF) Wrobel, J. R. 1963. “Application of the Element Potential Method to Gaseous Chemical Equilibrium.” Engineer Thesis, Pasadena, CA (USA): California Institute of Technology.

Data files with NASA polynomial coefficients for selected species:

Data files are available for download is several file formats.
    NASA formats:

  • nasa7.dat (360 kB) 7-term polynomial coefficients in 1971 format.
  • nasa9.dat (1.07 MB) 9-term coefficients in 1996 format.
  • nasa7mod.dat (410 kb) of the 7-term NASA database that is compatible with the old CHEMKIN II standard (contains all three temperatures on the first line of each set) and is useful for generating Cantera .cti files by converting Chemkin-style input files. The upper bound is 6000 K for most of these species which is useful for shock and detonation computations.

  • Cantera format:

  • CTI files available on this website use either the 7 or 9-coefficents in the Cantera format.

File Formats

There are several prominent thermodynamic database file formats, and variations of some of them. For instance, there are two NASA formats, and the format used by the Chemkin library is a variation of one of those. Stanjan can use two different file formats - one is formatted-text, based on the JANAF data tables, and the other is unformatted-binary. A summary of these file formats is given below:

Programs - Checking and Updating Data

  • ( This python script scans a Cantera .cti mechanism file to determine the size of jumps in thermodynamic properties and derivatives. Identifies species with largest Cp/R jump. Provides routines for finding all jumps and plotting thermodynamic properties of individual species. Only works for NASA-7 polynomials with the current version of Cantera 2.3.
  • (thermo_refit.m) This Matlab script refits thermo data to eliminate jumps in properties at midpoint temperature. Works with a list of species created by or individual species specified by user. Creates a new NASA-7 fit and data structure for polynomial coefficients, writes output files in three formats (cti, NASA-7 and NASA-9).
  • (thermo_replace.m) This Matlab script reads new thermodynamic data fits generated by thermo_refit.m and batch processes replaces the data in the NASA format data file using the list generated by Currently only works for NASA-7 polynomials.
  • (thermo_fit.m) Program to fit tabular thermodynamic data to generate NASA-7 polynomial fits and writes files in three formats. Example input file given for (twobutenal.m) 2-butenal.
  • poly_cp.m) Function to generate NASA-7 polynomial fits from specific heat data and reference thermodynamic state. Included in thermo_fit.m and thermo_refit.m.

Programs - Statistical thermodynamics

  • (partition_rotvib.m) Matlab script to compute partition functions and thermodynamic properties (including coefficients for polynomial fits in Cantera cti and NASA formats) from spectroscopic data for heteronuclear diatomic molecules.
  • Spectroscopic data for three diatomic molecules. Nitric oxide (NO); Hydroxyl (OH); Methylidyne (CH).
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