A Three-Dimensional Hybrid LES-Acoustic Analogy Method for Predicting Open-Cavity Noise

A three-dimensional (3D) hybrid LES-acoustic analogy method for computational aeroacoustics (CAA) is presented for the prediction of open-cavity noise. The method uses large-eddy simulation (LES) to compute the acoustic source while the Ffowcs Williams-Hawkings (FW-H) acoustic analogy is employed for the prediction of the far-field sound. As a comparison, a two-dimensional (2D) FW-H analogy is also included. The hybrid method has been assessed in an open-cavity flow at a Mach number of 0.85 and a Reynolds number of Re=1.36×10⁶, where some experimental data are available for comparison. The study has identified some important technical issues in the application of the FW-H acoustic analogy to cavity noise prediction and CAA in general, including the proper selection of the integration period and the modes of sound sources in the frequency domain. The different nature of 2D and 3D wave propagation is also highlighted, which calls for a matching acoustic solver for each problem. The developed hybrid method has shown promise to be a feasible, accurate and computationally affordable approach for CAA.     

Direct noise computation of adaptive control applied to a cavity flowSimulation directe de l'atténuation par contrôle adaptatif du rayonnement d'une cavité affleurée par un écoulement

The Large Eddy Simulation of closed-loop active flow control applied to a 3D cavity excited by a compressible airflow with a Mach number of 0.6 is presented. The control actuator is an idealized synthetic jet located at the upstream cavity edge, and the control function is supplied by a feedback LMS-type algorithm whose input is a pressure signal measured inside the cavity. The radiated sound, provided directly by the LES simulation, was shown to decrease substantially when active control was applied. A simultaneous reduction of the vertical velocity fluctuations in the shear layer was observed. The intensity of vortical structures inside the cavity was also reduced, although the general aspect of the recirculation zone was not modified. The direct noise computation technique, which supplies the pressure field by solving the fluid mechanics equations, is shown to constitute a powerful tool for studying active aeroacoustic noise control. To cite this article: O. Marsden et al., C. R. Mecanique 331 (2003).     

A novel optimization technique for explicit finite‐difference schemes with application to AeroAcoustics

The present paper addresses the optimization of finite‐difference schemes when these are to be used for numerically approximating spatial derivatives in aeroacoustics evolution problems. With that view in mind, finite‐difference operators are firstly detailed from a theoretical point of view. Secondly, time, the way such operators can be optimized in a spectral‐like sense is recalled, before the main limitations of such an optimization are highlighted. This leads us to propose an alternative optimization approach of innovative character. Such a novel optimization technique consists of enhancing the scheme's formal accuracy through a minimization of its leading‐order truncation error. This so‐called intrinsic optimization procedure is first detailed, before it is thoroughly analyzed, from both a theoretical and a practical point of view. The second part of the paper focuses on two particular intrinsically optimized schemes, which are carefully assessed via a direct comparison against their standard and/or spectral‐like optimized counterparts, such a comparative exercise being conducted utilizing several academic test cases of increasing complexity. There, it is shown how intrinsically optimized schemes indeed constitute an advantageous alternative to either the standard or the spectral‐like optimized ones, being allotted with both (i) the better scalability of the former scheme with respect to grid convergence effects when the grid density increases and (ii) the higher accuracy of the latter scheme when the discretization level becomes marginal. Thanks to that, such intrinsically optimized schemes offer very good trade‐offs in terms of (i) accuracy; (ii) robustness; and (iii) numerical efficiency (CPU cost). Copyright © 2015 John Wiley & Sons, Ltd.     

Multi‐size‐mesh multi‐time‐step algorithm for noise computation on curvilinear meshes

Aeroacoustic problems are often multi‐scale and a zonal refinement technique is thus desirable to reduce computational effort while preserving low dissipation and low dispersion errors from the numerical scheme. For that purpose, the multi‐size‐mesh multi‐time‐step algorithm of Tam and Kurbatskii [AIAA Journal, 2000, 38 (8), p. 1331–1339] allows changes by a factor of two between adjacent blocks, accompanied by a doubling in the time step. This local time stepping avoids wasting calculation time, which would result from imposing a unique time step dictated by the smallest grid size for explicit time marching. In the present study, the multi‐size‐mesh multi‐time‐step method is extended to general curvilinear grids by using a suitable coordinate transformation and by performing the necessary interpolations directly in the physical space due to multidimensional interpolations combining order constraints and optimization in the wave number space. A particular attention is paid to the properties of the Adams–Bashforth schemes used for time marching. The optimization of the coefficients by minimizing an error in the wave number space rather than satisfying a formal order is shown to be inefficient for Adams–Bashforth schemes. The accuracy of the extended multi‐size‐mesh multi‐time‐step algorithm is first demonstrated for acoustic propagation on a sinusoidal grid and for a computation of laminar trailing edge noise. In the latter test‐case, the mesh doubling is close to the airfoil and the vortical structures are crossing the doubling interface without affecting the quality of the radiated field. The applicability of the algorithm in three dimensions is eventually demonstrated by computing tonal noise from a moderate Reynolds number flow over an airfoil. Copyright © 2013 John Wiley & Sons, Ltd.     

A novel nonreflecting boundary condition for unsteady flow

A novel nonreflecting boundary condition, which converges to the specified time‐dependent boundary condition within any degree of accuracy, is introduced for the numerical simulation of hyperbolic systems and validated against the solution of two fundamental boundary value problems in fluids. First, transonic nozzle flow with backward acoustic disturbance is considered. Using high‐order aeroacoustic numerical schemes, the proposed nonreflecting boundary condition yields results that are in excellent agreement with those obtained using conventional nonreflecting boundary conditions based on the method of characteristics as well as with the results of the exact solution. The novel nonreflecting boundary condition, implemented into a semi‐analytical solution algorithm of unsteady bubbly cavitating nozzle flows, is also validated against results obtained using a Lagrangian finite volume scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

基于比拟理论的翼型扰流声场数值模拟

从二维模型方程的全离散形式出发,重点分析了差分格式的色散特性和各向异性效应,证实迎风紧致格式比对称格式有更好的色散和各向同性特性,故有利于声场的数值模拟,并采用三阶迎风紧致格式（ＵＣＤ３）和四阶对称紧致格式（ＳＣＤ４）计算了绕ＮＡＣＡ００１２翼型的可压缩非定常流场,并将此流场作为近场声源,运用声学比拟理论对气动声进行模拟。     

Optimal low-dispersion low-dissipation LBM schemes for computational aeroacoustics

Lattice Boltmzann Methods (LBM) have been proved to be very effective methods for computational aeroacoustics (CAA), which have been used to capture the dynamics of weak acoustic fluctuations. In this paper, we propose a strategy to reduce the dispersive and disspative errors of the two-dimensional (2D) multi-relaxation-time lattice Boltzmann method (MRT-LBM). By presenting an effective algorithm, we obtain a uniform form of the linearized Navier–Stokes equations corresponding to the MRT-LBM in wave-number space. Using the matrix perturbation theory and the equivalent modified equation approach for finite difference methods, we propose a class of minimization problems to optimize the free-parameters in the MRT-LBM. We obtain this way a dispersion-relation-preserving LBM (DRP-LBM) to circumvent the minimized dispersion error of the MRT-LBM. The dissipation relation precision is also improved. And the stability of the MRT-LBM with the small bulk viscosity is guaranteed. Von Neuman analysis of the linearized MRT-LBM is performed to validate the optimized dispersion/dissipation relations considering monochromatic wave solutions. Meanwhile, dispersion and dissipation errors of the optimized MRT-LBM are quantitatively compared with the original MRT-LBM. Finally, some numerical simulations are carried out to assess the new optimized MRT-LBM schemes.     

Iterative optimization based on an objective functional in frequency-space with application to jet-noise cancellation

In many technical applications, like supersonic jets, noise with a characteristic spectrum including certain dominant frequencies (e.g. jet-screech) is prevalent, and the elimination of sharp peaks in the acoustic spectrum is the aim of active or passive flow/noise control efforts. A mathematical framework for the optimization of control strategies is introduced that uses a cost objective in frequency-space coupled to constraints in form of partial differential equations in the time domain. An iterative optimization scheme based on direct and adjoint equations arises, which has been validated on two examples, the one-dimensional Burgers equation and the two-dimensional compressible Navier–Stokes equations. In both cases, the iterative scheme has proven effective and efficient in targeting and removing specified frequency bands in the acoustic spectrum. It is expected that this technique will find use in acoustic and other applications where the elimination or suppression of distinct frequency components is desirable.     

Rijke管自激热声振荡的数值模拟

为了对热声不稳定的发生及控制机理进行研究,对Rijke管内的自激热声振荡现象进行了数值模拟。采用具有低频散低耗散特点的计算气动声学方法,对带有非线性热源项的声波方程进行数值求解,并比较了不同的热源模型及边界条件对非线性效应的影响。结果表明,计算气动声学方法可以成功捕捉到Rijke管内压力的起振过程,而且在速度扰动达到平均流速度的1/3时,振荡会由线性增长转为非线性增长,最终达到有限幅值极限循环。相比热源项,考虑管口辐射耗散的非线性边界条件在振荡幅值和频谱方面对结果的影响都比较小。数值模拟得到的结果与实验符合较好,表明计算气动声学方法适合于热声振荡问题的研究。     

Toward accurate hybrid prediction techniques for cavity flow noise applications

A large variety of hybrid computational aeroacoustics (CAA) approaches exist differing from each other in the way the source region is modeled, in the way the equations are used to compute the propagation of acoustic waves in a non-quiescent medium, and in the way the coupling between source and acoustic propagation regions is made. This paper makes a comparison between some commonly used numerical methods for aeroacoustic applications. The aerodynamically generated tonal noise by a flow over a 2D rectangular cavity is investigated. Two different cavities are studied. In the first cavity (L/D=4, M=0.5), the sound field is dominated by the cavity wake mode and its higher harmonics, originating from a periodical vortex shedding at the cavity leading edge. In the second cavity (L/D=2, M=0.6), shear-layer modes, due to flow-acoustic interaction phenomena, generate the major components in the noise spectrum. Source domain modeling is carried out using a second-order finite-volume large eddy simulation. Propagation equations, taking into account convection and refraction effects, are solved using high-order finite-difference schemes for the linearized Euler equations and the acoustic perturbation equations. Both schemes are compared with each other for various coupling methods between source region and acoustic region. Conventional acoustic analogies and Kirchhoff methods are rewritten for the various propagation equations and used to obtain near-field acoustic results. The accuracy of the various coupling methods in identifying the noise-generating mechanisms is evaluated. In this way, this paper provides more insight into the practical use of various hybrid CAA techniques to predict the aerodynamically generated sound field by a flow over rectangular cavities. Copyright © 2009 John Wiley & Sons, Ltd.