Uncertainty Quantification for the Trailing-Edge Noise of a Controlled-Diffusion Airfoil

Abstract

i n t r o d u c t i o nIn modern rotating machines, due to the significant effort put on reducing annoying discrete tones, the broadband noise is an important contribution to the overall noise level, as in fans, turboengines or wind turbines. A key source of broadband noise is the trailing-edge noise, caused by the scattering of boundary-layer pressure fluctuations into acoustic waves at the trailing-edge of any lifting surface. Numerical methods to evaluate this noise are more often using steady RANS computations for computational cost reasons, requiring modelling and introducing then uncertainties. The present study aims at assessing uncertainties associated with the prediction of trailing-edge noise, through an uncertainty quantification (UQ) framework, using RANS computations or conventional LES computations, in order to determine their respective robustness and accuracy. m e t h o d o l o g y f o r u qThe approach to uncertainty quantification (UQ) of airfoil trailing-edge noise is illustrated in Figure 1. The considered case is a Controlled-Diffusion airfoil of chord C placed in the large anechoic wind tunnel in Ecole Centrale de Lyon (LWT), and held by two horizontal side plates. The angle of attack (aoa) is 8o and the airfoil upstream velocity U0 is 16 m/s, which corresponds to a Reynolds number based on the airfoil chord ReC=1.6 x 105.As in previous studies (Moreau et al. 2006), a RANS computation of the complete experimental setup of the large anechoic wind tunnel in Ecole Centrale de Lyon (LWT), including the nozzle and part of the anechoic chamber has been done that captures the strong jet-airfoil interaction and its impact on airfoil loading. The boundary conditions are extracted (U and V profiles) for a smaller domain embedded in the je t potential core. This final result is obtained by two different procedures, both producing a wall frequency pressure spectrum @pp used in Amiet's theory (Amiet 1976) to predict the far-field sound spectrum Spp.In the first approach, an unsteady LES on the restricted domain with the above extracted velocity profiles, directly yields the trailing edge wall pressure spectrum. The second approach, less expensive but requiring more modeling, uses steady RANS computations on a two-dimensional slice of the restricted domain, with the same boundary condition profiles as for the LES. From this RANS computation, the primitive variables (Uj, U2, k and a> or s depending on the RANS turbulence model) are extracted through a boundary layer profile at the trailing-edge of the airfoil. Those The uncertainty is introduced at the inlet boundary of the restricted computational domain. The physical variations in the experimental flow measurements are taken into account by selecting a 2.5% error bound on the streamwise velocity U and a 10% error bound on the crosswise velocity V around the deterministic numerical solution. A set of 9 velocity inlet profiles are determined using a Clenshaw-Curtis quadrature and the corresponding RANS and LES computations are run. Both components U and V...

Modal analysis of the laminar boundary layer instability and tonal noise of an airfoil at Reynolds number 150,000

“…Such a flow regime has been extensively studied both experimentally [1][2][3][4][5] and numerically. [6][7][8][9][10] In addition to this broadband behavior, sharp tones that rise above the broadband noise spectrum have also been experimentally observed for the same airfoil for certain flow configurations. 1,5 Such a tonal noise has been observed within the context of several different applications, including UAVs and low-speed fans.…”

Computation of the self-noise of a controlled-diffusion airfoil based on the acoustic analogy

“…The present work is inscribed in that line and aims at contributing to the field by exploring in deeper detail the respective contributions of dipoles and quadrupoles to the noise emitted by the flow developing over a controlled-diffusion (CD) thin airfoil, which has already been studied in previous works, both experimentally and numerically. [23][24][25][26][27][28] The general framework is based on Lighthill/Curle acoustic analogies, addressing in particular the respective strengths and weaknesses of dipole-or quadrupole-based formulations when an incompressible flow model is used as an input and the chord is noncompact. Different implementations of these analogies are presented, for different choices of GFs.…”

Tonal noise of a controlled-diffusion airfoil at low angle of attack and Reynolds number

“…This profile reduces drag and has been used for turboengine compressor blades, automotive engine cooling fan systems, and heat and ventilation air-conditioning systems. The aerodynamic and acoustic characteristics of this profile have been investigated both numerically and experimentally [8][9][10][11][12] especially at moderate and high angles of attack. In the present study, noise generated by this profile at low angle of attack is experimentally studied.…”