Towards the development of RANS models for conjugate heat transfer

Abstract

The study is concerned with exploring the ability of eddy-viscosity-based Reynolds Averaged Navier Stokes models to compute conjugate heat transfer problems, and to capture the decay of turbulent temperature fluctuations across the wall region. This is done by extending the application of the modelled transport equations for temperature variance and its dissipation rate across the solid wall region. Comparisons are drawn with the existing direct numerical simulations data of plane channel flow, heated through a wall of non-zero thickness. Cases are simulated covering a range of solid/fluid thermal conductivity/diffusivity ratios. It is found that, in order to predict the correct decay of temperature variance across the wall, an accurate representation of it, and its dissipation rate, in the near-wall fluid flow region is required. This, in turn, requires an accurate representation of the near-wall dynamic field turbulence. A number of modifications are proposed to an existing four-equation k-ϵ--ϵ_θ model in order to provide good near-wall predictions under the two limiting thermal boundary treatments of isothermal and isoflux wall conditions. The resulting scheme is also shown to perform well in the fully conjugate heat transfer problems.

Keywords:

• conjugate heat transfer
• turbulence models
• eddy-viscosity model
• turbulent heat transfer