Computational analysis of exit conditions on the sound field of turbulent hot jets

A hybrid computational fluid dynamics (CFD) and computational aeroacoustics (CAA) method is used to compute the acoustic field of turbulent hot jets at a Reynolds number $Re=316,000$ and a Mach number $M=0.12$. The flow field computations are performed by highly resolved large-eddy simulations (LES), from which sound source terms are extracted to compute the acoustic field by solving the acoustic perturbation equations (APE). Two jets are considered to analyze the impact of exit conditions on the resulting jet sound field. First, a jet emanating from a fully resolved non-generic nozzle is simulated by solving the discrete conservation equations. This computation of the jet flow is denoted free-exit-flow (FEF) formulation. For the second computation, the nozzle geometry is not included in the computational domain. Time averaged exit conditions, i.e. velocity and density profiles of the first formulation, plus a jet forcing in form of vortex rings are imposed at the inlet of the second jet configuration. This formulation is denoted imposed-exit-flow (IEF) formulation. The free-exit-flow case shows up to 50% higher turbulent kinetic energy than the imposed-exit-flow case in the jet near field, which drastically impacts noise generation. The FEF and IEF configurations reveal quite a different qualitative behavior of the sound spectra, especially in the sideline direction where the entropy source term dominates sound generation. This difference occurs since the noise sources generated by density and pressure fluctuations are not perfectly modeled by the vortex ring forcing method in the IEF solution. However, the total overall sound pressure level shows the same qualitative behavior for the FEF and IEF formulations. Towards the downstream direction, the sound spectra of the FEF and IEF solutions converge.     

基于DCS5格式的LDDRK算法

基于五阶线性耗散紧致格式(DCS5)和七级龙格原库塔时间积分算法,根据数值增长因子对精确增长因子的最佳逼近原则,提出与DCS5格式耗散性相适应的优化方法,并得到相应的七级五阶低耗散低色散龙格原库塔(LDDRK)算法.求解标量线性对流方程和线化Euler方程得到的一维波传播问题的数值结果显示,七级五阶LDDRK算法的精度优于七级七阶精度的标准龙格原库塔算法.     

Shear layer instability and acoustic interaction in solid propellant rocket motors

Segmentation of solid propellant rocket motors has been demonstrated to be a source of unpredicted and undesirable pressure and thrust oscillations. Surface discontinuities are the primary cause of these vortex-shedding-driven oscillations, which result from a strong coupling between the shear layer instability and the acoustic motion in the chamber. The analysis of an axisymmetric geometry corresponding to a {1\over 15} subscale P230 motor of the Ariane 5 rocket is numerically computed. With a suitable mesh for the viscosity value studied, the aeroacoustics in the chamber is fully described. A coupling between the hydrodynamic instability and the organ-pipe acoustic mode is clearly demonstrated. The mechanism for frequency selection is discussed. © 1997 John Wiley & Sons, Ltd.     

空腔的非定常可压缩过流及相关气动声学问题

使用大涡模拟-声学比拟相结合的方法,研究三维开式空腔的非定常可压缩过流及其相关的气动声学问题.近场的声源流场部分使用大涡模拟,声音向远场的辐射使用Ffowcs Williams-Hawkings(FW-H)声学比拟,建立了适合于开式空腔的全三维计算气动声学预测方法.文中突出了声源采样时间和积分模数的选择问题.     

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.     

Development of optimized weighted‐ENO schemes for multiscale compressible flows

The present paper deals with the development of optimized weighted–ENO schemes to improve the resolution of a class of compressible flows characterized by a wide disparity of scales, typical of compressible turbulence and/or aeroacoustic phenomena, and shock waves. The approach relies on a least square minimization of both the dispersion and dissipation error components together with the use of symmetric stencil support. Extensive numerical simulations of sound propagation, shock–sound interaction and isotropic compressible turbulence have been carried out, and the results confirm that the optimized schemes yield a resolution in wave number space greater than the non‐optimized ones. Copyright © 2003 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.     

High-accuracy large-step explicit Runge–Kutta (HALE-RK) schemes for computational aeroacoustics

In many realistic calculations, the computational grid spacing required to resolve the mean flow gradients is much smaller than the grid spacing required to resolve the unsteady propagating waves of interest. Because of this, the high temporal resolution provided by existing optimized time marching schemes can be excessive due to the small time step required for stability in regions of clustered grid. In this work, explicit fourth-order accurate Runge–Kutta time marching schemes are optimized to increase the inviscid stability limit rather than the accuracy at large time steps. Single and multiple-step optimized schemes are developed and analyzed. The resulting schemes are validated on several realistic benchmark problems.     

Numerical Simulation of Acoustic Waves Interacting with a Shock Wave in a Quasi-ID Convergent-Divergent Nozzle Using an Unstructured Finite Volume Algorithm

Numerical simulations of a very small amplitude acoustic wave interacting with a shock wave in a quasi-ID convergent-divergent nozzle is performed using an unstructured finite volume algorithm with piece-wise linear, least square reconstruction, Roe flux difference splitting, and second-order MacCormack time marching. First, the spatial accuracy of the algorithm is evaluated for steady flows with and without the normal shock by running the simulation with a sequence of successively finer meshes. Then the accuracy of the Roe flux difference splitting near the sonic transition point is examined for different reconstruction schemes. Finally, the unsteady numerical solutions with the acoustic perturbation are presented and compared with linear theory results.     

High‐order numerical simulations of flow‐induced noise

In this paper, the flow/acoustics splitting method for predicting flow‐generated noise is further developed by introducing high‐order finite difference schemes. The splitting method consists of dividing the acoustic problem into a viscous incompressible flow part and an inviscid acoustic part. The incompressible flow equations are solved by a second‐order finite volume code EllipSys2D/3D. The acoustic field is obtained by solving a set of acoustic perturbation equations forced by flow quantities. The incompressible pressure and velocity form the input to the acoustic equations. The present work is an extension of our acoustics solver, with the introduction of high‐order schemes for spatial discretization and a Runge–Kutta scheme for time integration. To achieve low dissipation and dispersion errors, either Dispersion‐Relation‐Preserving (DRP) schemes or optimized compact finite difference schemes are used for the spatial discretizations. Applications and validations of the new acoustics solver are presented for benchmark aeroacoustic problems and for flow over an NACA 0012 airfoil. Copyright © 2010 John Wiley & Sons, Ltd.