Appendix: Transport Properties

Transport properties are required for viscous flow simulations. These include both the laminar transport properties due purely to molecular motion as well as the turbulent transport properties due to the turbulent motions of a flow.

The run control file variables for specifying transport properties are the transport_model and the diffusion_model variables.

A high-level summary of the available options for the transport_model variable is given below:

Transport Model Options
Option	Description
`none` or `module`	no transport model applied.
`sutherland`	Sutherland’s law (with default properties for air).
`powerLaw`	A Power law dependence on temperature.
`const_viscosity`	Constant viscosity and thermal conductivity.
`chemkin`	Use a CHEMKIN formatted transport file (`.tran`) for multi-component flow viscosity and thermal conductivity properties.
`transportDB`	Use a set of data files that have curve fits of viscosity, thermal conductivity, and diffusion coefficients (`_con.dat`, `_vis.dat`, `*_.dif.dat`)
`database`	Species p,T database using Wilke’s mixture rule.
`tabularEoS`	Use a database of files that contain a tabular fit of transport data from the `tabularEoS` module.

A high-level summary of the available options for the diffusion_model variable is given below:

Diffusion Model Options
Option	Description
`const_diffusivity`	Constant diffusivity.
`chemkin`	Use a CHEMKIN formatted transport file (`.tran`) for multi-component flow diffusion coefficient properties.
`laminarSchmidt`	Diffusivity based on viscosity and a specified Schmidt number.
`unityLewisNumber`	Use the unity Lewis number assumption for computing the diffusion coefficient.
`transportDB`	Use a database of files that contain a tabular fit of transport data from the `tabularEoS` module.
`default`	Selects the diffusion model based on the transport model: `chemkin` when Chemkin is selected for `transport_model`, or `laminarSchmidt` otherwise.

The following sections go into more detail on the available options for the different specification types of transport properties.

Laminar Transport Properties

Laminar transport properties include the laminar viscosity, the thermal conductivity, and the mass diffusivity for each of the species for multi-species simulations. The run control file variable transport_model is used to specify the form of transport properties desired. One must always include transport_model in the run control file because there is no default value. Based on the value of this variable, other auxiliary variables may also be used. Several methods of specification are possible, as detailed in the following sub-sections.

Inviscid Flow

Inviscid flow is activated by setting the value of transport_model to none.

transport_model: none

No other transport property variables are required with this specification.

Constant Properties

Constant transport properties for viscous flow simulations can be specified in the run control file.

Constant transport property specification

transport_model: none
mu: 1.0e-04
kcond: 0.1

The variable mu is used to set the laminar dynamic viscosity value (units \(\frac{N \cdot s}{m^{2}}\)). This variable has no default value and must be included in the run control file. The variable kcond is required only for compressible flows and is used to set the thermal conductivity value (units \(\frac{W}{m \cdot K}\)). This is also a required variable as there is no default value. For multi-species simulations with constant laminar viscosity and thermal conductivity, one should specify the laminar mass diffusivity using the laminar Schmidt number as follows:

laminarSchmidtNumber: 0.9

This variable need not be present in the run control file if the default value of 1.0 is desired.

Power Law Model

An option for specifying the viscosity and thermal conductivity variation with a power law dependence on temperature is available. The power law model is a simple model that is defined by the following relation.

\[\mu = \mu_{ref} \left( \frac{T}{T_{ref}} \right)^{n}\]

The required run control file variables for the power law model are as follows:

Power Law Options
Variable	Description
`T_ref`	Reference temperature
`power`	The exponent in the power law model
`mu_ref`	Reference viscosity

Power law transport properties for viscous flow simulations can be specified in the run control file as follows.

Power law transport property specification

powerLawParam: <mu_ref=1.8e-5, T_ref=300, power=0.7>

Turbulent Transport Properties

The turbulent dynamic viscosity is computed directly from the turbulence models. Turbulent thermal conductivity and mass diffusivity are computed using turbulent Prandtl and Schmidt numbers, respectively. The default values are shown below along with the way to specify the variables in the run control file.

Default turbulent transport property values

turbulentPrandtlNumber: 0.7
turbulentSchmidtNumber: 0.95

These variables need not be present in the run control file if the default values are desired.

Multi-Species CHEMKIN Transport Properties

For multi-species simulations, a more detailed specification of the transport properties is required. A thermodynamic model file (.mdl) file is required and a dataset containing transport properties is required. The methods for generation of the thermodynamic model file as well as some of the transport properties databases is outlined here.

CHEMKIN Transport Properties

Specifying the chemkin option for the transport_model or diffusion_model run control file variables will result in transport property data being obtained from a CHEMKIN formatted transport file (called *.tran). The method for generating the CHEMKIN transport .tran file is outlined here.

Curve Fit Transport Properties

Specifying the transportDB option for the transport_model or diffusion_model run control file variables will result in transport property data being obtained from a set of data files that have curve fits of viscosity, thermal conductivity, and diffusion coefficients (*_con.dat, *_vis.dat, *_.dif.dat). These files are expected to be in the same directory as the run control file, and located in a folder named transport. The method for generating the curve fit transport data files is outlined here , specifically the section regarding the --transport_tables flag passed to the chemkin-converter.py utility.