A calculation method for turbulent boundary layers and wall jets has been developed in which the effects of large longitudinal surface curvature and the associated normal pressure gradients are included for the first time. This is achieved by using finite difference techniques to represent the equations of mean motion in a system of curvilinear orthogonal coordinates. The Reynolds stress terms in the equations of motion are approximated using an eddy viscosity approach based on the concept of intermittency. Application of the method to wall jet boundary layers is achieved through extension of the basic eddy viscosity model. Comparisons between theory and experiment for boundary layers and wall jets developing over flat or curved surfaces for a wide variety of pressure distributions show encouraging agreement.
NomenclatureA + = function in van Driest's damping factor, Eq. (4) C = eddy Reynolds number, Eq. (8) c f = local skin-friction coefficient H = shape factor, ratio of displacement to momentum thickness (&*/0) K = von Karman's mixing length coefficient K! = constant of proportionality / = mixing length / -Ky, in. M L = local Mach number M x = freestream Mach number P = static pressure, psi absolute r = longitudinal radius of curvature, in. R = local radius of curvature R 0 = momentum thickness Reynolds number U6/v U = local freestream velocity, fps U^ = freestream velocity, fps u, v = components of velocity in x and y directions, fps U T = friction velocity, (i ( Jp) 1/2 , fps x,y = components of length, in. (5* = displacement thickness, in. 6 = local boundary-layer thickness 6 -momentum thickness, in. ~1 p = density, slugs/ft 3 K = curvature, l/r, in. i = shear stress, psi absolute i ( , ) = local surface shear stress, psi absolute v = kinematic viscosity, ft 2 /sec v t -eddy viscosity, ft 2 /sec y = intermittency function c = standard deviation of intermittency function, in. Subscripts d = value at point of departure from law of wall i = inviscid / = local conditions t = turbulent Superscripts ( ) = mean value ( )' = fluctuating component
