Prediction of Porous Trailing Edge Noise Reduction via Acoustic Perturbation Equations and Volume Averaging

Abstract

Edge noise is generated if turbulence interacts with solid edges. Reduction of trailing edge noise of airfoils can be achieved by replacing the solid material at the trailing edge by inlays of porous permeable material. The acoustic benefit of approximately 6 dB of such treatment is known from experiments. Enroute to numerically optimized porous properties, this paper presents a first principle based Computational Aeroacoustics (CAA) method for predicting the acoustic effect of a porous NACA0012 trailing edge. In a hybrid two-step CFD/CAA procedure the turbulence statistics from a solution of the Volume Averaged Navier-Stokes (VANS) equations is used as a basis for the prediction of turbulent-boundarylayer trailing-edge noise (TBL-TEN). For the acoustic part of the calculation, the Acoustic Perturbation Equations (APE) are solved in the flow field. Inside the porous regions, a different set of governing equations, referred to as Linear Perturbation Equations (LPE) will be solved. The LPE represent a modified form of the Linearized Euler Equations (LEE) with the APE vorticity source term shifted to the right-hand side. The new set of equations is derived by volume averaging the Navier-Stokes equations and decomposing the flow variables into a time-averaged mean part and a fluctuating part and isolating the vorticity source term to the right-hand side of the momentum equation. The LPE are verified by an analytical solution. The simulation results of a NACA0012 airfoil geometry with and without porous trailing edge treatment are compared to wind tunnel measurements. The noise reduction effect of such a trailing edge treatment is successfully demonstrated.

Self Noise Reduction and Aerodynamics of Airfoils with Porous Trailing Edges

“…There are also approaches to combine the successful concept of serrated trailing edges with a porous modification [11]. In addition, there are a variety of analytical [12] and numerical studies [13][14][15][16] on porous trailing edges for noise reduction available.…”

Numerical investigation of porous materials for trailing edge noise reduction

“…With increasing flow speed turbulent drag becomes relevant, which is accounted for by extending the Darcy law with a term formulated by Forchheimer (equation (2)) 36 that takes the Forchheimer constant c F as an additional parameter. With these material parameters, a volume-averaged formulation of the Linearized Euler Equations (LEE) in perturbation form can be found (equations (3) to (5)), 32,37 with ρ as the fluid density, γ the isentropic expansion factor, e i the unity vectors of the coordinate system and δ ij the Kronecker delta. In the present perturbation form, ρ0, [ui]0, p0 denote quantities of the constant mean flow field, while ρ′, [ui]′, p′ denote the perturbation variables.…”

Hybrid Aeroacoustic Computations: State of Art and New Achievements

“…[176][177][178] Recently, there have been developments towards the application of APE to porous trailing edge models of airfoils via volume averaging. 179,180…”