Transport Property Override
For FlameMaster flamelets that have been generated using the LiquidBias option in the FlameMaster run control file, there exists a discrepancy for the transport properties of the liquid state. FlameMaster uses a high-pressure gaseous transport property model that does not provide accurate values of viscosity or thermal conductivity. This results in simulations that have liquid densities but gaseous viscosities and thermal conductivities. A remedy for this was added to the Flamelet Table Tool via the ability to provide values of the liquid viscosities and thermal conductivities for the fuel and oxidizer streams.
There are several caveats that will be discussed in this section regarding the use of this feature. When changing the viscosities of the flamelet table, this does have the effect of introducing an error in the tabulation, because FlameMaster did not solve the 1D diffusion flamelet solution using the viscosities that are newly written to a table. The flame shape & characteristics would be different. The degree of this error is not known.
To activate the transport property override, add the following sections to the control file for the Flamelet Table Tool as shown below in a sample portion of a Flamelet Table Tool control file.
Figure : Sample inputs for activating the transport property override in the Flamelet Table Tool.
The general behavior of the transport property override feature hinges on the user-provided values of fuel_cutoff_temperature and oxidizer_cutoff_temperature. These control the transition between user-defined viscosity and original viscosities of the flamelet solution, along with the thermal conductivities as well. The cutoff temperatures are best thought of as estimates for the saturation temperatures of the fuel and oxidizer streams. If the temperature within the table is less than a provided cutoff temperature, then the user-provided viscosity will be used for whichever cutoff the table temperature is below. Below is the linear combination used for a case when the table temperature is below both cutoff temperatures i.e. the viscosity is a linear combination of the user-defined viscosities based on the mixture fraction.
If the table temperature is higher than the oxidizer cutoff temperature, then the combination function that governs the table viscosity would be:
In this case the new viscosity is a combination of the user-defined fuel viscosity and the original table viscosity. This is a combination that introduces an error, because the original flamelet table viscosity contains the fuel viscosity in its gaseous form. Here we assume that the contribution of the gaseous fuel viscosity to the table viscosity is negligible compared to the liquid fuel viscosity that it is being averaged with.
If the table temperature is higher than both the user-defined cutoff
temperatures, then nothing is done, and the original table viscosities
are used. This feature is currently only supported for the thickened
flame closure with compressible flamelet tables as this time. To see the
profile of the viscosity in the flamelet table, be sure to include the
vtk keyword in the OUTPUTTYPE line to get a Paraview formatted output
of the table that can be visualized. The variable in the table is named
MU0.
Using Liquid Bias in FlameMaster
To generate the flamelet solutions using the liquid bias option in the
FlameMaster, the user should only need to include the keyword
LiquidBias in the control file for FlameMaster. An example is shown
below for how to activate the liquid bias option.
LiquidBias is TRUE
This keyword should be used in conjunction with the Peng-Robinson equation of state also activated in the FlameMaster control file. This keyword will pick the smallest density root for the Peng-Robinson equation of state during the inversion process at any time there is more than one root available. The choice of the liquid bias will be recorded in the flamelet solution files that are output by FlameMaster, and this information will be read in by the Flamelet Table Tool and used to consistently evaluate the Peng-Robinson equation of state that it used for table generation. The liquid bias option will also be passed through as an entry in the generated flamelet tables and this information will be read by Stream and used to evaluate the Peng-Robinson equation of state used in Stream in a manner that is consistent with how it was evaluated in FlameMaster and in the Flamelet Table Tool.