Flow-induced noise from a sharp-edged flat plate using a quasi-periodic CFD-BEM technique

The flow-induced noise from a sharp-edged flat plate submerged in low Mach number flow is predicted using a quasi-periodic computational fluid dynamics (CFD)-boundary element method (BEM) technique. A high-order reconstruction scheme is used to extract acoustic sources based on Lighthill’s analogy from the flow field data. Acoustic waves generated by these flow noise sources propagate to and are scattered by the trailing edge of the plate. The fluctuating flow field is obtained using an incompressible CFD solver. A BEM model of the sharp-edged flat plate is used to predict the scattered sound pressure field. A quasi-periodic technique is implemented in the BEM model so that the sound generated by the entire span of the plate can be predicted by modelling only a small spanwise segment. The computed aerodynamic and acoustic results are compared with experimental data obtained using the anechoic wind tunnel at the University of Adelaide. Introduction Hybrid large eddy simulation (LES) acoustic analogy techniques have been developed that provide a high fidelity approach to predict the interaction of flow induced noise with a body submerged in the flow. The LES simulations are able to capture the flow noise sources with great detail over a wide range of frequencies and this leads to accurate acoustic predictions. Wang and Moin [13] performed an incompressible large eddy simulation of turbulent flow over a flat strut, with the predicted hydrodynamics comparing well with the experiments conducted by Blake [1]. Wang et al. [14] conducted a similar hybrid LES acoustic analogy simulation on the cambered airfoil of an industrial fan blade. Seo and Moon [12] developed a modified version of the perturbed compressible equations known as the linearised perturbed compressible equation (LPCE). They showed that the LPCE method can accurately predict the sound pressure field radiated from turbulent flow past a cylinder. Wolf and Lele [15] developed a hybrid technique based on compressible LES simulation of the flow field, coupled with the FWH acoustic analogy to predict the radiated field. Their approach uses both the fluctuating surface pressures and volume quadrupole sources calculated during the LES simulation to drive the subsequent acoustic propagation analysis. They make no assumptions about the compactness of the acoustic source region, nor on the shape of the scattering surface. Moreau et al. [9, 10] conducted a number of aeroacoustic experiments on sharp-edged flat plates in an anechoic wind tunnel at lowto-moderate Reynolds number. They examined a variety of semi-empirical methods for predicting trailing edge noise which were shown to underestimate noise at lower frequencies [9]. Lee and Cheong [5] developed an efficient methodology for frequency-domain prediction of broadband trailing edge noise from a blunt flat plate. They used a semi-analytical model to specify the incident pressure spectrum. They then applied a point pressure spectrum within the boundary layer as the input for prediction of the broadband trailing edge noise. Khalighi et al. [4] developed a boundary integral equation from Lighthill’s wave equation which was solved using BEM. The method was applied to predict the sound pressure field radiated by turbulent flow past a cylinder and an automotive side mirror, as well as the trailing edge noise from an airfoil [3]. In this work, the self-generated noise from a sharp-edged flat plate submerged in low Mach number flow is predicted using a quasi-periodic CFD-BEM technique. The unsteady incompressible flow field past a flat plate with a sharp trailing edge is simulated using an LES method. The acoustic field is then computed using Lighthill’s analogy by extracting sources from the unsteady flow data. Finally, the incident acoustic field is applied to a quasi-periodic BEM model based on the Burton-Miller formulation to predict the scattered sound pressure. The quasiperiodic technique predicts the sound generated by the entire span of the plate by modelling only a small spanwise segment. Acoustic Formulation Boundary Element Method The non-homogeneous Helmholtz equation is given by ∆p(x)+ k2 p(x) =−F (1) where p(x) is the acoustic pressure at field point x, F is the source, ∆ is the Laplacian operator, k = ω/c is the acoustic wave number, ω is the angular frequency and c is the speed of sound. The non-homogenous Helmholtz equation can be written in a weak formulation after integrating by parts twice as follows [8]