Prediction of Trailing-Edge Noise Based on Reynolds-Averaged Navier–Stokes Solution

Abstract

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

Prediction of small-scale UAS rotor noise

“…The LE noise is estimated by using the model of Amiet [1]. Trailing-edge noise was predicted by using the RANSbased TE noise model of Chen & M acGillivray [5]. The inputs for those models are the local aerodynamic conditions experienced by the rotor blades, which are obtained either from CFD simulations or simplified aerodynamic models.…”

Numerical prediction of turbulent boundary layer noise from a sharp‐edged flat plate

“…[22][23][24][25][26] Several hybrid RANS-acoustic analogy methods have been developed with specific application for trailing edge noise prediction in aeroacoustics by approximating the airfoil as an infinitely thin flat plate. 27,28 Maxit 29 modeled a vibrating panel excited by a TBL in which the wall pressure field from a TBL was simulated using realizations of uncorrelated wall plane waves (UWPWs). Using the UWPW technique, a good estimation of the panel response was obtained even when a relatively small number of realizations were considered.…”