Modular Method for Estimation of Velocity and Temperature Profiles in High-Speed Boundary Layers

Abstract

The fluid property variation caused by viscous heating affects the mean velocity and Reynolds stresses in compressible turbulent boundary layers, and as a result also affects the resulting skin friction and wall heat transfer. We present a method based on the work of Huang et al. (AIAA Journal, Vol. 31, No. 9, 1993, pp. 1600–1604) that estimates the mean velocity and temperature profiles, and therefore also the friction and heat transfer coefficients, for a given Mach number, Reynolds number, and wall thermal condition. The method is modular in the sense that it works with multiple variable-property scaling formulas (or “transformations”), velocity–temperature relationships, viscosity–temperature relationships, and equations-of-state. The method is validated against multiple Direct Numerical Simulation (DNS) cases and was found to predict the skin friction and wall heat flux to within 8 and 11% compared to the current state-of-the-art (the Van Driest II method), which is within 16 and 13% for the same data.