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Near-wall variable-Prandtl-number turbulence model for compressible flows. (English) Zbl 0809.76043

A near-wall variable Prandtl number \((\text{Pr}_ t)\) turbulence model has been developed for the calculations of compressible flat plate turbulent boundary layers with constant heat flux and constant temperature wall boundary conditions. The model consists of solving four additional equations describing the transport of turbulent kinetic energy \((k)\), solenoidal dissipation rate \((\varepsilon)\) of \(k\), square of Favre fluctuating temperature \((\theta^ 2)\) and the dissipation rate of temperature variance \((\varepsilon_ \theta)\). The calculated values of \(k\), \(\varepsilon\), \(\theta^ 2\), \(\varepsilon_ \theta\), are used to define the turbulent diffusivities for momentum and heat, thus allowing the assumption of dynamic similarity between momentum and heat transport to be relaxed. The Favre-averaged equations of motions are solved together with four transport equations mentioned earlier.
Calculations are compared with direct numerical simulation data, with experimental measurements, and with the predictions of other models where the assumption of a constant turbulent Prandtl number is invoked. Incompressible channel/pipe flows and compressible boundary layer-layer flows with adiabatic as well as constant temperature wall boundary conditions are considered. Computations for the cases where the free stream Mach number as high as 10 and where the wall temperature ratio as low as 0.3 have been done.
The analysis shows that the variable \(\text{Pr}_ t\) model yields an asymptotically correct prediction of the temperature variance and the normal heat flux for incompressible flows. In the case of compressible boundary layer flows, the numerical results are in good agreement with measured mean flow and skin friction for flows with an adiabatic wall, which leads to substantial improvements in the predictions of mean flow properties compared to the constant \(\text{Pr}_ t\) results for cooled wall cases.

MSC:

76F10 Shear flows and turbulence
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76N20 Boundary-layer theory for compressible fluids and gas dynamics
80A20 Heat and mass transfer, heat flow (MSC2010)
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