Prediction of Very High Reynolds Number Compressible Skin Friction

Flat plate skin friction calculations over a range of Mach numbers from 0.4 to 3.5 at Reynolds numbers from 16 million to 492 million using a Navier Stokes method with advanced turbulence modeling are compared with incompressible skin friction coefficient correlations. The semi-empirical correlation theories of van Driest; Cope; Winkler and Cha; and Sommer and Short T’ are used to transform the predicted skin friction coefficients of solutions using two algebraic Reynolds stress turbulence models in the Navier-Stokes method PAB3D. In general, the predicted skin friction coefficients scaled well with each reference temperature theory though, overall the theory by Sommer and Short appeared to best collapse the predicted coefficients. At the lower Reynolds number 3 to 30 million, both the Girimaji and Shih, Zhu and Lumley turbulence models predicted skin-friction coefficients within 2% of the semi-empirical correlation skin friction coefficients. At the higher Reynolds numbers of 100 to 500 million, the turbulence models by Shih, Zhu and Lumley and Girimaji predicted coefficients that were 6% less and 10% greater, respectively, than the semi-empirical coefficients. NOMENCLATURE = surface area, A,B = temperature ratio constants for Van Driest equation = incremental surface area = speed of sound = average skin friction coefficient = transformed average skin friction coefficient = constants for K-e equations _______________ *Senior Scientist, Aeroand Gas-Dynamics Division. Copyright 1998 by the American Institute of Aeronautics and Astronautics, Inc. No copyright is asserted in the United States under Title 17, U.S. Code, the U.S. Government has a royalty-free license to exercise all rights under the copyright claimed herein for Governmental purposes. All other rights reserved by the copyright owner. = local skin friction coefficient, = skin friction drag = shape function = near-wall damping function for = total enthalpy = freestream turbulence intensity = turbulent kinetic energy = mixing-length constant = length of flat plate, 5-m = mixing length = Mach number = number of grid points = distance normal to wall = production term for turbulent kinetic energy = static pressure, Pa = dynamic pressure, Pa = Reynolds number, = transformed Reynolds number = turbulent Reynolds number, = strain tensor = Sutherland’s constant, 110.33 K = temperature = intermediate reference temperature = time = velocity = magnitude of velocity, = Cartesian velocity components = friction velocity, = law-of-the-wall coordinate, = vorticity tensor = streamwise distance = Cartesian displacement components = law-of-the-wall coordinate, = law-of-the-wall height of first cell = vertical distance = free parameter for K turbulent tripping profile = boundary layer thickness = turbulent dissipation = ratio of specific heats, 1.4 = boundary layer momentum thickness = von Karman constant = laminar viscosity A Ai ∑