The properties of a gas mixture in thermochemical equilibrium can be computed using the CEA program (https://www.grc.nasa.gov/WWW/CEAWeb/). By pre-computing the properties for a range of densities and internal energies, a look-up table can be created. The use of a look-up table is much more efficient to use than calling out to the CEA program during simulation execution.

This manual describes the use of the build-uniform-lut program for constructing your own look-up-table gas model.

1. Getting started

The build-unform-lut program is built upon the core gas models and the Python library that is wrapped around that gas-model library. This is part of a larger gas-dynamics toolkit and general getting started notes can be found at http://cfcfd.mechmining.uq.edu.au/docs/getting-started There, you will see how to get a copy of the source code, and a list of what other software you will need to build and install the tool kit, and a collection of environment variables that need to be set.

To install the build-uniform-lut program, move to the gas source directory and use the make utility.

cd dgd/src/gas
make install

This will also install files associated with the gas models.

We also expect that you have arranged to get a copy of the CEA2 program. It is not our’s to give away, so don’t ask. Once you have a copy of the CEA2 program executable, place it in the directory ${DGD}/bin/ as cea2. Also, place the database input files thermo.inp and trans.inp into the directory ${DGD}/share/cea-cases/. Our CEAGas model code expects to find those files in place.

# makefile for cea2, in the context of the Eilmer4 project.
#
# Author: PJ
# Version: 15-May-2013
#          14-Jan-2020 Revise install commands for Eilmer4

INSTALL_DIR ?= $(HOME)/dgdinst

build_new: cea2
	@echo "cea2 program should be up to date."

install: cea2
	- mkdir -p $(INSTALL_DIR)
	- cp cea2 $(INSTALL_DIR)/bin/
	- mkdir -p $(INSTALL_DIR)/share/cea-cases
	- cp thermo.inp trans.inp $(INSTALL_DIR)/share/cea-cases/

clean:
	- rm cea2

# The -m32 option sometimes gives grief
# (on 64-bit linux systems with dodgy compatability libraries)
# but it seems to be needed to make a well behaved executable.
# If the -m32 gives grief, try removing it and building again.
cea2 : cea2.f cea.inc
	gfortran -m32 -std=legacy -o cea2 cea2.f

2. Defining a CEAGas model

To build a look-up table model, you are going to need a CEAGas model file in your working directory. Let’s just copy one from the samples in the source code repository.

cp ${DGD_REPO}/src/gas/sample-data/cea-air13species-gas-model.lua .

The contents of this file are:

model = "CEAGas"

CEAGas = {
  mixtureName = 'air13species',
  speciesList = {"N2","O2","Ar","N","O","NO","Ar+","NO+","N+","O+","N2+","O2+","e-"},
  reactants = {N2=0.7811, O2=0.2095, Ar=0.0093},
  inputUnits = "moles",
  withIons = true,
  trace = 1.0e-6
}

Note that the file contains valid Lua code. The assignment to the variable called model is used to identify, to our gas package, the flavour of the gas model that this file defines. The CEAGas variable is then assigned a table of key=value entries that specify the parameters to be passed through to the CEA2 program in order to get it to compute our gas properties. The items are:

mixtureName

a string name to assign as the pseudo-species name. Out gas model code does not know about the internal species of the the equilibrium mixture.

speciesList

an array of strings specifying the internal mixture species, as known by the CEA2 program.

reactants

an initial mixture, specified by fractions in a table where the keys are the names of the species. Lua has a nice feature that simple names may appear without quote characters, however, names with special characters such as the plus sign will need to specified in quotes. In the table above, N2=0.7811 is equivalent to ["N2"]=0.7811 and a nonzero fraction for N2+ would need to have its key specified as ["N2+"].

inputUnits

for the reactant fractions. Options are "moles" or "massf".

withIons

a boolean indicating to CEA2 if ionization is permitted.

trace

the fraction value below which CEA2 is permitted to ignore a chemical species.

3. Building a look-up table model

To see what specific inputs are required, start the program as:

build-uniform-lut --help

With the output:

Begin build-uniform-lut.py...
Usage: build-uniform-lut [options]

Options:
  -h, --help            show this help message and exit
  -g GASMODELFILE, --gas-model=GASMODELFILE
                        file name of the input gas-model
  -n TABLENAME, --table-name=TABLENAME
                        file name for the generated look-up table
  -b BOUNDS, --bounds=BOUNDS
                        bounds of the table in form
                        "T_min,T_max,log_rho_min,log_rho_max"
  -T T_FOR_OFFSET, --T-for-offset=T_FOR_OFFSET
                        Temperature (degree K) at which to evaluate the
                        internal energy offset.
GASMODELFILE

The input gas model is usually a CEAGas model file, as described above, however, any gas model for our gas package may be used.

TABLENAME

The tabluated data is written to a file, as a valid Lua script. It can then be used as a gas-model file in out gas package.

BOUNDS

Sometimes CEA2 has problems and the table will fail to build. The best approach to fixing the problem seems to be to raise the lower temperatures, as shown in examples 2, 3 and 4 (below).

T_FOR_OFFSET

The program does its best to make the tabulated model appear as an ideal gas at low temperatures. The internal energy offset is evaluated to try to make the internal energy zero at T=0 K. It is sometimes convenient to have the reference temperature of 0 degrees K for internal energy and enthalpy, so that u = C_v * T, approximately. This is quite different to the reference temperature of 298 degrees K used by CEA. Mostly, any low temperature will suffice, however, some gas mixtures need moderately high values. For example, CO2 needs T=600.

3.1. Examples

build-uniform-lut --gas-model=cea-air5species-gas-model.lua --table-name=air5species
build-uniform-lut --gas-model=cea-air13species-gas-model.lua --table-name=air13species \
                  --T-for-offset=600.0 --bounds="600,20000,-6.0,2.0"
build-uniform-lut --gas-model=cea-co2-gas-model.lua --table-name=co2 \
                  --T-for-offset=650.0 --bounds="1000.0,20000,-6.0,2.0"
build-uniform-lut --gas-model=cea-co2-ions-gas-model.lua --table-name=co2-ions \
                  --T-for-offset=1000.0 --bounds="1000.0,20000,-6.0,2.0"