Calculation methods for three-dimensional turbulent boundary layers

A solution method for the three-dimensional compressible turbulent boundary-layer equations

“…Local values of density and viscosity are evaluated using the equation of state and Sutherland's law respectively. (7) where m = 1, 2, 3 correspond to the A'-momentum, Ymomentum and energy equations respectively. A m and B m are functions of (X, Y); b m and R m are functions of (X, Y, Z) and all are defined in the Appendix.…”

“…A major distinguishing feature of the various existing finite-difference calculation methods* 6 ' 7) is their treatment of the spanwise convection terms in the mean-flow equations. The present method adopts a general discretisation procedure for these terms, so allowing the sensitivity of the calculation to a particular numerical scheme to be investigated.…”

“…appearing in the above equations are evaluated numerically using finite-difference formulae.The mean-flow equations are written in the general form given in equation(7), wherem = 1 (X-momentum equation) ax=U /cicote, B , = k\ 2 , b (^ + M-t) R e r.in, n cosec 2 6 dP cote cosece dP Ri = -V z A:2Cosec6; i, 62 = -focotO, bi =(M-The integral thicknesses are defined in a coordinate system comprising the external flow streamlines and their orthogonal projections. U s and U c are the local mean-velocity components within the boundary layer in these two directions.…”