Predicting mean profiles in compressible turbulent channel and pipe flows

A modified iterative method is proposed to predict the mean profiles in compressible channel and pipe turbulence by solving a nonlinear system, which is constituted by the perfect gas assumption, the Sutherland's viscosity law, the variable-property scaling models for compressible wall turbulence, the incompressible velocity law of the wall and the relationship between the mean temperature and velocity. Systematic parametric studies display that the proposed iterative method is robust and does not depend on the initial guess of the undetermined parameters. The results also indicate that the present method works very well in both channel and pipe flows at various Reynolds and Mach numbers, and the relative errors of mean temperature profiles and velocity profiles, as compared with the available direct numerical simulation databases, in most cases are within 2% and 5%, respectively.