Contribution of viscous stress work to wall heat flux in compressible turbulent channel flows
Peng Zhang, Zhenhua Xia
Abstract
In this paper we derive an exact expression for the mean heat flux at the wall for the compressible turbulent channel flow. In the expression, the heat flux at the wall can be decomposed into four parts, including the contribution from the turbulent heat transfer, the contribution from the molecular heat transfer, the contribution from the pressure work, and the contribution from the work from viscous stress (VW). The decomposition is validated in compressible turbulent channel flows with isothermal walls at three different Reynolds and Mach numbers, and the results match very well with the direct estimations at the wall. The data also show that the VW term dominates the contributions (around 90%) in the decomposition while around 90% of VW is from the near-wall region (y/h<0.2), illustrating the importance of the viscous stress work in the near-wall region.