Trailing-edge noise is a significant component of the noise generated by low-Mach-number wall-bounded turbulent flow. It is therefore important to develop an efficient method for computing this noise in practical applications. Instead of using computationally expensive methods or an empirical model to predict the true time history of surface pressure, a model of trailing-edge noise for a hydrofoil combining widely used computational-fluid-dynamics Reynoldsaveraged Navier-Stokes solutions with the edge source acoustic Green's function of arbitrary chord is presented. The model takes the nature of the anisotropic turbulence in boundary-layer flow derived from Reynolds-averaged Navier-Stokes solution into consideration. The model has been applied to the trailing-edge noise of a NACA 0012 foil at a chord-based Reynolds number equal to 2.36 × 10 6 and to a strut with hemicylindrical leading edge and tapered trailing edge at Reynolds number equal to 5.12 × 10 5 . It has been compared with existing empirical models, and a significant improvement has been obtained. The predicted results are in good agreement with existing experimental data.
Nomenclaturein the model spectrum density c 0 = speed of sound in the far field, m∕s E 0 ψ , E N ψ = normalized model cross-spectrum density of velocity E N 22 = normalized cross-spectrum density of u 0 2 G = Green's function K = κ 2 1 κ 2 3 p , 1∕m K ν = νth-order Bessel function k = turbulence kinetic energy, m 2 ∕s 2 L s = spanwise length of foil, m l i = pressure fluctuation correlate length scale in i direction, m p = hydrodynamic pressure, Pa p = mean pressure, Pa p 0 = pressure fluctuation, Pa p a = acoustic pressure, Pa p aI = incident acoustic pressure, Pa U c = convection velocity in streamwise direction, m∕s u = velocity vector, m∕s u i = mean velocity in i direction, m∕s u 0 i = velocity fluctuation in i direction, m∕s u = wall shear velocity, m∕s x, x 0 = coordinate vector, with i equal to 1 (streamwise), 2 (vertical), or 3 (spanwise), m y y i = observation coordinates, m δ = boundary-layer thickness, m δ = boundary-layer displacement thickness, m κ i = wave number in i direction, 1∕m κ 0 = acoustic wave number, 1∕m Λ = streamwise turbulence integral length scale, m μ = dynamic viscosity of fluid, kg∕m · s ρ = density of fluid kg∕m 3= radiated trailing-edge noise spectrum for a semiinfinite foil, Pa 2 ∕Hz ϕ pp = point surface pressure spectrum, Pa 2 ∕Hz ψ = angle between the observer direction and the trailing edge of a foil, deg ω = angular frequency, rad∕s