Compressible Temperature Transformation Toward Law of the Wall in Turbulent Channel Flows

For compressible wall-bounded turbulence, the logarithmic law for velocity profiles has been extensively investigated through various successful velocity transformations, yet a robust counterpart for the mean temperature remains absent. To bridge this gap, the present study introduces a novel temperature transformation tailored for compressible turbulent channel flows, based on the integrated momentum and energy balances. This approach explicitly incorporates the effects of the external driving force and its work on the fluid while employing the total-heat-flux-based temperature scale that aligns with the well-established Mach-number-invariant function in the velocity field. Extensive direct numerical simulation (DNS) validations (26 cases) involving a wide range of bulk Mach numbers (ranging from 0.7 to 4.0) and Reynolds numbers (ranging from 3000 to 34,000) demonstrate that the proposed transformation effectively maps the mean temperature profiles to the incompressible reference without case-specific tuning, exhibiting superior performance compared to existing temperature transformations.