Stochastic computational model of 3D acoustic noise predictions for nacelle liners

Abstract

This paper is devoted to the uncertainty quantification for 3D acoustic performance model of nacelle liners (acoustic treatments). Uncertainties are taken into account in order to increase the robustness of the predictions. A full computational acoustic propagation model based on the convected Helmholtz equation in presence of a non-homogeneous flow velocity field computed by solving the Linearized Euler Equations (LEE) is used. A reduced-order computational model is deduced in order to implement the probabilistic model of uncertainties. The model uncertainties induced by modeling errors have been taken into account for the acoustic propagation model and the liner model, using the nonparametric probabilistic approach. In addition, the uncertainties on the acoustic excitation induced by the fan have been introduced using the parametric probabilistic approach. The developed methodology is applied to a 3D nacelle intake and allows for computing the confidence regions of the random far-field radiated pressure in terms of random SPL (Sound Pressure Level), which are compared to experiments for several flight conditions and frequencies. Nomenclature r(x, y, z), t, ω = Space three-dimensional vector, time scalar variable, and angular frequencỹ X, X 0 , X = Total, static, and fluctuating thermodynamic variable, function of space and time M ∞ , M = Uniform and local Mach number c α , ϕ α (x, y), k z α , k xy α = Amplitude, eigenfunction, axial, and transversal wave numbers of a duct mode α S duct = Cross section of the duct domain Ω duct ρ, ρ 0 , ρ ∞ , ρ = Total, steady-flow, uniform, and fluctuating fluid mass densitỹ v, v 0 , v ∞ , v = Total, steady-flow, uniform, and fluctuating fluid velocitỹ p, p 0 , p = Total, steady-flow, and fluctuating pressure fields Ω i , Ω o , Ω duct = Inner, outer, and duct domains of the intake acoustic problem ∂Ω i , ∂Ω o , ∂Ω duct = Inner, outer, duct domain boundaries Γ io , Γ h , Γ, Γ f , Γ ho , Γ duct , = Interface between inner and outer domains, hardwall, liner, fan, outer hardwall, and duct surfaces n io , n h , n, n f , n ho , n duct = Outward unit normal of surfaces Γ io , Γ