A composite mean temperature transformation for compressible turbulent boundary layers

In the present study, we introduce a new temperature transformation for compressible turbulent boundary layers with adiabatic and isothermal walls. Unlike existing transformations that rely on a single invariant function for the non-dimensional temperature gradient across the entire inner layer, a composite transformation strategy is proposed by leveraging two newly proposed Mach-number and wall-temperature invariant functions for the mean temperature field. This approach not only deploys appropriate Mach-number invariant functions in the viscous sublayer and the logarithmic region, but also introduces an improved solution to the long-standing singularity challenge inherent in single invariant function models. The performance of this composite transformation is verified by extensive direct numerical simulation (DNS) datasets (26 cases) of compressible turbulent boundary-layer flows. The results demonstrate that the proposed transformation maps the mean temperature profiles to the incompressible reference without case-specific parameter tuning, exhibiting significantly reduced scatter when compared with the existing temperature transformations.