The physical processes that sustain discrete-frequency oscillations of cavities adjacent to compressible flow are modeled analytically, yielding a formula which predicts excitation frequencies as a function of Mach number and cavity geometry. These physical processes are similar to those used by Powell in describing the mechanism underlying the production of edge tones. The empirically determined constants appearing in Rossiter's formula for excitation frequencies are computed from the model. It appears that instability of the shear layer as well as interaction between the shear layer and the cavities' trailing edge is required to sustain discrete-frequency oscillation. It is suggested that the simultaneous excitation of two or more discrete frequencies (which are not harmonic), as have been observed in practice, correspond to the simultaneous participation of two or more vortex sheet displacement modes. The model analyzed yields qualitatively correct acoustic mode shapes in the cavity. Theoretical results include the calculation of possible excitation frequencies over the range 0.8 ^ M ^ 3 for rectangular cavities and show their dependence on cavity depth. Analytic results are in general agreement with experimental data. Nomenclature A = magnitude of harmonic force acting on vortex sheet at \x\ ^ e, y = 0 a = sound speed B = constant in mass-flux equation [Eq. (27)] C(u) = Fresnal integral D = cavity depth / = frequency H(u) = Hankel function i = (-l)" 2 K = complex wave number in x direction and Fourier transform variable L = cavity length M = u/ a , Mach number m = mass flux at cavity trailing edge n, m = summation indices in x, y direction, respectively P = perturbation pressure R = image-correction sum r = thermal recovery factor rj, 7 = source and observation point position vectors, respectively S = -i(tt-KU} 51 = fL/U+, exterior Strouhal number 5 2 = coL/a_, interior Strouhal number S(u) = Fresnal integral t = time U= convection velocity (note U = 0 inside the cavity) x, y = coordinate system (see Fig. 1) y = ratio of specific heats A = dispersion relation e = small physical length Y\ = shear-layer displacement K = fractional vortex convection speed A a = wavelength of acoustic wave A B = wavelength of shed vortices

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Subscale test data have shown that airfoils operating in a simulated heavy-rain environment can experience significant performance penalties. The physical mechanism resulting in this performance penalty has yet to be conclusively identified. Therefore, the extrapolation of subscale data to full-scale conditions must be undertaken with extreme caution since complete scaling laws are unknown. This paper discusses some of the technical issues that must be addressed and resolved prior to extrapolating the performance of full-scale airfoils from subscale test data. A set of scaling laws is suggested based on the neglect of thermodynamic interactions between the droplets and the air/water vapor phase.heat at constant volume D =drop diameter hj g = latent heat of vaporization of water £ = mean distance between droplets m = mass M =Mach number n(D) = raindrop size spectrum n 0 =8xl0 3 m-3 mm-1 =« 0/5 N = aerodynamic force ND = droplet number density p = pressure R = rainfall rate, mm/h, or gas constant T = temperature Uj = velocity vector U x = flight speed V = volume or droplet impact velocity V T = drop terminal velocity W L = liquid water content, g/m 3 We = Weber number x,y,z = Cartesian coordinate system a. = angle of attack 13 = impact angle 7 = ratio of specific heat 0 = contact angle A = reciprocal of rain spectrum scale JJL = absolute viscosity u = kinematic viscosity p = density o = surface tension r = shear stress $ = velocity potential Subscripts a fs ss s V w = air = full scale = subscale = solid = vapor = water Presented as Paper 85-0257 at

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