This keyword can be used to activate the variable turbulent Prandtl number capability for structured grids. The available models include constant zonal values, algebraic models, and two-equation differential models based on the transport of a thermal scalar variance. The differential models require use of a two-equation turbulence model, while the other Prandtl models generally work with any turbulence model.

Keyword Options

This keyword option selects the turbulent Prandtl number model to be used. The table below summarizes the available Prandtl models and recommended turbulence models to be used with them.

The default setting is to use the constant FREESTREAM turbulent Prandtl number, as specified by the PRANDTL keyword.

The CONSTANT model allows a different value to be specified for each zone. The KC and WC models are simple algebraic functions that are designed to mimic the increase in Prandtl number in the near-wall region. Of the two, the KC model is a somewhat more general formulation. Since these models are only dependent upon the ratio of turbulent to laminar viscosity (μ_t/μ_l), they should work with any turbulence model. The BUSH model uses an SST-like f1 blending function to switch between prescribed wall and freestream values. It requires the use of a two-equation turbulence model and has primarily been calibrated using the SST model.

The remaining models are two-equation transport models for the variance of a thermal quantity and a corresponding dissipation rate. The BASED ON {H|H0|EI} option allows the user to choose which type of flow variance to compute: static enthalpy, total enthalpy, or internal energy, respectively. If not specified, it will default to the variance type (generally H) in the original formulation of the selected model. These two-equation models require the use of a two-equation turbulence model such as BSL, SST, or one of the many k-ε turbulence models. The recommended turbulence models listed in the table are those used by the original Prandtl model developers.

For more details on the turbulent Prandtl number models, see:

• [Kays, W. M. and Crawford, E. M. (1973) Convective Heat and Mass Transfer, McGraw-Hill, New York, 3rd ed.]
• [Wassel, A. T. and Catton, I. (1973) "Calculation of Turbulent Boundary Layers Over Flat Plates with Different Phenomenological Theories of Turbulence and Variable Turbulent Prandtl Number," International Journal of Heat and Mass Transfer, Vol. 16, No. 8, pp. 1547-1563.]
• [Brinckman, K. W., Calhoon, W. H. J., and Dash, S. M. (2007) "Scalar Fluctuation Modeling for High-Speed Aeropropulsive Flows," AIAA Journal, Vol. 45, No. 5, pp. 1036-1046.
• [Abe, K., Kondoh, T., and Nagano, Y. (1995) "A New Turbulence Model for Predicting Fluid Flow and Heat Transfer in Separating and Reattaching Flows-II. Thermal Field Calculations," International Journal of Heat and Mass Transfer, Vol. 38, No. 8, pp. 1467-1481.]
• [Deng, B., Wu, W., and Xi, S. (2000) "A Near-Wall Two-Equation Heat Transfer Model for Wall Turbulent Flows," International Journal of Heat and Mass Transfer, Vol. 44, No. 4, pp. 691-698.]
• [Nagano, Y., Tagawa, M., and Tsuji, T. (1991) "An Improved Two-Equation Heat Transfer Model for Wall Turbulent Shear Flows," ASME/JSME Thermal Engineering Proceedings, Vol. 3, pp. 233-240.]
• [Sommer, T., So, R., and Zhang, H. (1993) "Near-Wall Variable-Prandlt-Number Turbulence Model for Compressible Flow," AIAA Journal, Vol. 31, No. 1, pp. 27-35.]

The MINIMUM and MAXIMUM values are limiters applied to all models. The turbulent Prandtl number is not allowed to exceed these limits. The default range is 0.10≤Pr_t≤2.00.

The LIMITER MODE applies to the two-equation transport models and controls which variables are adjusted when the Prandtl number is limited.

For some models, particularly the AKN model, it is difficult to invert the thermal diffusivity relation to extract adjusted values for the scalar transport terms. This can lead to even greater numerical instability.

The default setting is therefore LIMITER MODE 1 which will adjust the thermal diffusivity but not the transport variables for the scalar variance or its dissipation. However, adjusting the diffusivity will affect the production term in both of the scalar transport equations and hopefully drive the solution to a more consistent state.

Note that LIMITER MODE is a global setting, not a zonal setting.

The WALL and MAX_WALL_DISTANCE parameters are primarily used by the BUSH model to prescribe the turbulent Prandtl number at viscous wall points and the distance from the wall over which the Prandtl number will be blended to the freestream value. The default value for Prt_wall is 0.90 and the default value for dist is 1.0E+08 grid units. The F2FIX option uses the same wall distance as the SST F2FIX setting specified in the TURBULENCE keyword.

The transport equations to be solved are organized into logical "groups" that are solved together. It also allows multiple iterations of a specific group (i.e., sub-iterations) for each "iteration per cycle". If NAVIER-STOKES ITERATIONS is defaulted, this corresponds to iter iterations of the turbulent Prandtl model equations for each iteration of the mean flow equations.

The default value for iter is one, indicating that each iteration per cycle corresponds to one iteration of the turbulent Prandtl model equations.

Usage Suggestions

The algebraic and two-equation Prandtl number models will initialize themselves from the existing turbulent Prandtl number and turbulent viscosity fields. Insufficient turbulence values can result in difficulties during startup or initial transients. Users should ensure that the starting solution is at least partially converged and that turbulent shear layers are present.

In addition, the turbulent Prandtl number can vary significantly in the near-wall region. Simulation of turbulent heat transfer may require a finer grid than needed to resolve the velocity field. For examples using the turbulent Prandtl number models in the Wind-US code, see:

• [Yoder, D. A. (2016) "Comparison of Turbulent Thermal Diffusivity and Scalar Variance Models," AIAA Paper 2016-1561.]

For the two-equation models, the turbulent Prandtl number is a function of the ratio of the turbulent velocity and thermal time scales. In regions of relatively uniform flow, the predicted Prandtl number may be particularly low or high depending upon the values of these time scales. The MINIMUM and MAXIMUM keywords may be used to limit the Prandtl values to an acceptable range. The exact value of the Prandtl number is of little consequence if there is no corresponding thermal gradient to produce a heat flux.

The WRITE keyword may be used to output the Prandtl number to the solution file.

See Also: PRANDTL, TURBULENCE, WRITE