Assessment of the Contribution of Surface Roughness to Airframe Noise

A = area of the rough wall Aj = jth equal subarea of the rough region, A=NA B = empirical constant for the mean velocity profile on a rough wall; Eq. (29) CA = A-weighting factor CF = overall skin friction coefficient, 1 L R L 0 cf dx1 c = speed of sound in free field cf = local skin friction coefficient, w= 1 2 0U 2 cf0 = local skin friction coefficient at a distance xle from the leading edge D = directivity function f = frequency G = Green function g = function of Strouhal number Sh ; Eq. (44) H = aircraft height to the ground I1–I3 = integrals with respect to the polar coordinates and of the wave number plane J1 = Bessel function of order unity ks = equivalent roughness height k0 = acoustic wave number, !=c L = length of the flat plate Lc = equivalent chord of an aircraft wing Ls = equivalent span of an aircraft wing M = freestream Mach number, U=c N = average number of roughness bosses per unit area NA = number of subareas in the rough region n = empirical coefficient in R; Eq. (35) ~ n = unit observer vector PR = acoustic frequency spectrum of far-field radiated roughness noise Ps = smooth-wall wave-number-frequency spectrum p = pressure fluctuation ps = hypothetical smooth-wall pressure fluctuation Q = turbulence Reynolds stress source R = roughness height ReL = Reynolds number based on the whole plate, UL= Rele = Reynolds number based on the distance between the rough region and leading edge, Uxle= Re = roughness Reynolds number, ksu = S = cross-spectral density of the turbulence Reynolds stress Sh = Strouhal number based on the displacement boundarylayer thickness, ! =U t = observer time U = freestream velocity Uc = eddy convection velocity u = streamwise mean velocity u = friction velocity v = x2 component of the perturbation velocity v = perturbation velocity w = wake function x = observer position xle = distance between the rough region and the leading edge x0 = hypothetical extension of the rough region Y = velocity potential of an ideal incompressible flow over the rough wall y = source position = polar angle of the wave number plane = empirical coefficient in R; Eq. (35) = k0 2 1 2