Aerofoil broadband and tonal noise modelling using stochastic sound sources and incorporated large scale fluctuations

Abstract

The present work discusses modifications to the stochastic Fast Random Particle Mesh (FRPM) method featuring both tonal and broadband noise sources. The technique relies on the combination of incorporated vortexshedding resolved flow available from Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulation with the fine-scale turbulence FRPM solution generated via the stochastic velocity fluctuations in the context of vortex sound theory. In contrast to the existing literature, our method encompasses a unified treatment for broadband and tonal acoustic noise sources at the source level, thus, accounting for linear source interference as well as possible non-linear source interaction effects. When sound sources are determined, for the sound propagation, Acoustic Perturbation Equations (APE-4) are solved in the timedomain. Results of the method's application for two aerofoil benchmark cases, with both sharp and blunt trailing edges are presented. In each case, the importance of individual linear and non-linear noise sources was investigated. Several new key features related to the unsteady implementation of the method were tested and brought into the equation. Encouraging results have been obtained for benchmark test cases using the new technique which is believed to be potentially applicable to other airframe noise problems where both tonal and broadband parts are important.

Analytical models of the wall-pressure spectrum under a turbulent boundary layer with adverse pressure gradient

“…However, DNS is still far from being considered a viable design tool. A compromise in terms of computational cost for the generation of broadband noise sources is the fast random particle mesh method, which superimposes a synthetic field of turbulent fluctuations to the mean flow calculated by a Reynolds-averaged Navier-Stokes (RANS) simulation (see Proskurov, Darbyshire & Karabasov 2017). However, this method depends on the assumed functional expression of the turbulence energy spectrum, as shown by Wohlbrandt et al (2016), similar to the family of methods that is presented in this paper.…”

Trailing-Edge Noise Prediction by Solving Helmholtz Equation with Stochastic Source Term

“…where is the fluctuating vorticity vector, and 0 is the mean vorticity vector. Following [20,37], the non-linear term ( × ) in Eq. ( 5) is neglected.…”

“…The value of must be chosen sufficiently high to compute velocity fluctuations that statistically follow the prescribed turbulence properties [18]. In the literature, the number of particles per RPM grid cell ppc usually varies between 2.5 and 10 [18,26,37,46]. The particles are convected by the mean flow velocity 0 preliminarily computed on the Cartesian grid.…”

“…Based on those works, Ewert et al [6,[18][19][20] introduced the Random Particle-Mesh (RPM) method, a divergence-free stochastic approach accounting for flow convection effects. Applied by several research groups for different applications including airfoil noise [21,22], jet noise [23], fan noise [24] or HVAC duct noise [25], the RPM technique permits relative assessments between different configurations at moderate computational costs. For trailing-edge noise problems, it can even provide absolute levels via some calibration of the sound levels using reference measurement or numerical data [26].…”

“…Concerning the propagation of the sound waves with sound sources generated stochastically, the literature mostly reports about time-based acoustic solvers, discretizing the Linearized Euler Equations (LEE) or the Acoustic Perturbation Equations (APE) [20,22,27]. While this fits the time-marching nature of the RPM source generation, the stability requirements imposed by the Courant-Friedrichs-Lewy (CFL) criterion for explicit time-discretization schemes [28] can severely limit the maximum admissible time step.…”