The Reynolds analogy is known to give inadequate results for strongly anisotropic turbulence. The use of an anisotropic diffusivity, through the Generalized Gradient Diffusion Hypothesis (GGDH), can partially overcome these deficiencies.
The quality of the heat transfer prediction then relies on the accuracy of the Reynolds stresses estimation, which requires a second order closure. The article presents applications of an Algebraic Stress Model (ASM) coupled with a GGDH to the computations of various internal flows. The computations were done using the NS3D MATHILDA code, developed at ONERA, and largely used in the French aerospace industry.
The study compares the ASM+GGDH results with experimental measurements for heated configurations such as a pipe, a rotor/stator cavity and a channel with ribs, ie covering a wide spectrum of turbine gas internal flows.
The ASM+GGDH model leads to major improvements for the latter case, where the wall fluxes were largely underestimated in a standard k-ε calculation. The difference is due to an overestimation of the turbulent Prandtl number, closer to 0.5 for a mixing layer. The ASM+GGDH model also gives a correct hierarchy of the turbulent heat fluxes for pipe flows, contrary to a standard isotropic model. Concerning the rotor/stator cavity the results are in good agreement with the measurements provided by Owen et al .