Development of a two-equation heat transfer model based on direct simulations of turbulent flows with different Prandtl numbers

Low-Reynolds-number type k-epsilon and k(t)-epsilon(t) models have been constructed with the aid of direct numerical simulation (DNS) databases. The proposed models incorporate new velocity and time scales to represent various sizes of eddies in velocity and thermal fields with different Prandtl numbers. The validity of the present k-epsilon model was tested by application to basic and complex flows such as flows with injection and suction, flows with strong adverse and favorable pressure gradients, and flows with separation and reattachment, while comparing the relevant DNS and reliable experimental data. Fundamental properties of the proposed k(t)-epsilon(t) model were first verified in basic hows under arbitrary wall thermal boundary conditions and next in backward-facing step flows at various Prandtl numbers through a comparison of the predictions with the DNS and measurements. These comparisons have proven that the proposed models for both velocity and thermal fields have wide applicability to science and engineering and have sufficient capability to perform highly stable computations at any Prandtl numbers, irrespective of flow configurations. (C) 1996 American Institute of Physics.