Numerical simulation of sound generation in a mixing layer by the finite difference lattice Boltzmann method

We simulated aerodynamic sound in a two-dimensional mixing layer using the finite difference lattice Boltzmann method (FDLBM). We introduced a finite difference scheme, called the dispersion relation preserving (DRP) scheme, into the FDLBM to carry out an accurate simulation of aerodynamic problems. The scheme is designed such that the dispersion relation of the finite difference scheme is the same as that of the original partial differential equations and is useful for acoustic simulations. A turbulent flow field was simulated by large-eddy simulation (LES), using the Smagorinsky model, and the results were compared with those from a direct simulation based on the Navier–Stokes equations to confirm the usefulness of this method. The combination of the FDLBM and the DRP scheme was shown to be very effective for direct simulations of aerodynamic sound.     

Numerical prediction of sound generated from flows with a low Mach number

Numerical computations of sound generated from flows with a low Mach number are presented based on Lighthill’s acoustic analogy with an assumption that sound does not alter the flow field from which it is generated. The source fluctuations of the flow field are computed by a large-eddy simulation (LES) with Dynamic Smagorinsky Model (DSM) and they are fed to the following acoustical computation as input data. An explicit/implicit finite element method with second order accuracy both in time and space is used for flow field discretization. The method is applied to the prediction of sound in three different classes of problems: far-field sound generated from flow around a bluff body, sound resulting from blade-stator interaction of turbomachinery and sound due to a turbulent boundary layer on an aerofoil. The computed frequency spectra of the sound show a fairly good agreement with the measured spectra for all the cases.     

多物理场耦合软件GTEA开发及应用

围绕多物理场耦合问题,基于连续介质假设,采用非结构化网格和有限体积方法开发多物理场耦合并行计算软件GTEA。该软件包括计算流体力学、结构应力波传播、流 声耦合和声 固耦合等4个功能模块。介绍GTEA前处理网格读取、网格格式转换、求解器开发等关键技术。通过柴油机缸内工作过程模拟、船舶水动力计算、自然对流与辐射传热耦合作用、流场动力噪声计算和结构 声耦合计算等5个典型应用展示该软件的应用能力和适用范围。     

Coupling of a nonlinear finite element structural method with a Navier-Stokes solver

A new three-dimensional viscous aeroelastic solver is developed in the present work. A well validated full Navier-Stokes code is coupled with a nonlinear finite element plate model. Implicit coupling between the computational fluid dynamics and structural solvers is achieved using a subiteration approach. Computations of several benchmark static and dynamic plate problems are used to validate the finite element portion of the code. This coupled aeroelastic scheme is then applied to the problem of three-dimensional panel flutter. Inviscid and viscous supersonic results match previous computations using the same aerodynamic method coupled with a finite difference structural solver. For the case of subsonic flow, multiple solutions consisting of static, upward and downward deflections of the panel are discussed. The particular solution obtained is shown to be sensitive to the cavity pressure specified underneath the panel.     

Multi-solver algorithms for the partitioned simulation of fluid–structure interaction

In partitioned fluid–structure interaction simulations, the flow equations and the structural equations are solved separately. As a result, a coupling algorithm is needed to enforce the equilibrium on the fluid–structure interface in cases with strong interaction. This coupling algorithm performs coupling iterations between the solver of the flow equations and the solver of the structural equations. Current coupling algorithms couple one flow solver with one structural solver. Here, a new class of multi-solver quasi-Newton coupling algorithms for unsteady fluid–structure interaction simulations is presented. More than one flow solver and more than one structural solver are used for a single simulation. The numerical experiments demonstrate that the duration of a simulation decreases as the number of solvers is increased.     

A block LU-SGS implicit unsteady incompressible flow solver on hybrid dynamic grids for 2D external bio-fluid simulations

A hybrid dynamic grid generation technique for two-dimensional (2D) morphing bodies and a block lower-upper symmetric Gauss-Seidel (BLU-SGS) implicit dual-time-stepping method for unsteady incompressible flows are presented for external bio-fluid simulations. To discretize the complicated computational domain around 2D morphing configurations such as fishes and insect/bird wings, the initial grids are generated by a hybrid grid strategy firstly. Body-fitted quadrilateral (quad) grids are generated first near solid bodies. An adaptive Cartesian mesh is then generated to cover the entire computational domain. Cartesian cells which overlap the quad grids are removed from the computational domain, and a gap is produced between the quad grids and the adaptive Cartesian grid. Finally triangular grids are used to fill this gap. During the unsteady movement of morphing bodies, the dynamic grids are generated by a coupling strategy of the interpolation method based on ‘Delaunay graph’ and local remeshing technique. With the motion of moving/morphing bodies, the grids are deformed according to the motion of morphing body boundaries firstly with the interpolation strategy based on ‘Delaunay graph’ proposed by Liu and Qin. Then the quality of deformed grids is checked. If the grids become too skewed, or even intersect each other, the grids are regenerated locally. After the local remeshing, the flow solution is interpolated from the old to the new grid. Based on the hybrid dynamic grid technique, an efficient implicit finite volume solver is set up also to solve the unsteady incompressible flows for external bio-fluid dynamics. The fully implicit equation is solved using a dual-time-stepping approach, coupling with the artificial compressibility method (ACM) for incompressible flows. In order to accelerate the convergence history in each sub-iteration, a block lower-upper symmetric Gauss-Seidel implicit method is introduced also into the solver. The hybrid dynamic grid generator is tested by a group of cases of morphing bodies, while the implicit unsteady solver is validated by typical unsteady incompressible flow case, and the results demonstrate the accuracy and efficiency of present solver. Finally, some applications for fish swimming and insect wing flapping are carried out to demonstrate the ability for 2D external bio-fluid simulations.     

Evaluation of multigrid acceleration for preconditioned time-accurate Navier-Stokes algorithms

The development of a two-dimensional time-accurate dual time step Navier-Stokes flow solver with time-derivative preconditioning and multigrid acceleration is described. The governing equations are integrated in time with both an explicit Runge-Kutta scheme and an implicit lower-upper symmetric-Gauss-Seidel scheme in a finite volume framework, yielding second-order accuracy in space and time. Issues concerning the implementation of multigrid for preconditioned, dual time step algorithms are discussed. Steady and unsteady computations were made of lid driven cavity flow, thermally driven cavity flow and pulsatile channel flow for a variety of conditions to validate the schemes and evaluate the effectiveness of multigrid for time-accurate simulations. Significant speedups were observed for steady and unsteady simulations. The speedups for unsteady simulations were problem dependent, a function of how rapidly the flow varied in time and the size of the allowable time step.     

Flow field eigenmode decompositions in aeroacoustics

In this paper an efficient method to study sound generation processes in low Mach number flows is presented. We apply the methodology on a two-dimensional flow over a cavity with smoothed corners. Instead of the full flow field obtained from, for example a Direct Numerical Simulation (DNS), we use a reduced model based on global modes to obtain the aeroacoustic sources. Global modes are eigenmodes to the Navier-Stokes equations, linearized about a steady base flow. In a reduced model the perturbations from a steady state are approximated by a linear combination of the eigenmodes. The time dependence is determined by the corresponding eigenvalues. Curle’s equation is used to calculate the acoustic field, and by studying the source terms in Curle’s equation, mechanisms for sources of sound are identified. Results of acoustic pressure in the far-field and source strengths for different superpositions of eigenmodes are presented.     

基于结构网格的高超声速流动大规模并行数值模拟研究

本文采用MPI消息传递模式自主开发出适用于高超声速流动数值模拟的并行计算软件,该软件以三维Navier-Stokes方程为基本控制方程来求解层流问题,应用基于结构网格的有限体积法对计算域进行离散,采用AUSMPW+格式求解对流通量,利用MUSCL插值方法获得高阶精度,时间格式上采用LU-SGS方法进行时间迭代以加快求解定常流动的收敛过程。在高性能计算机上针对不同高超声速流动进行大规模并行计算的结果表明,所开发的CFD并行计算软件具有较高的并行计算效率,为高超声速飞行器气动力/热的准确预测提供了高效工具。     

Time domain computation of flow induced sound

We present a recently developed numerical scheme for computational aeroacoustics (CAA). Therewith, we solve the flow field by a large eddy simulation (LES) and the generation as well as propagation of acoustic noise by Lighthill’s analogy applying the finite element method. The developed scheme allows a direct coupling in time domain as well as a sequential coupling in frequency domain and provides the acoustic sound field not only in the far field but also in the region of the flow. Furthermore, we can directly investigate the acoustic source terms in the flow region. The scheme is well suited for interior aeroacoustic problems with complex geometries as well as for fluid-structure interaction problems. Implementation is validated and a two-dimensional simple application example is used to investigate the acoustic sources and to evaluate the acoustic pressure field from both transient and harmonic analyses.     

A high order Discontinuous Galerkin Finite Element solver for the incompressible Navier–Stokes equations

The paper presents an unsteady high order Discontinuous Galerkin (DG) solver that has been developed, verified and validated for the solution of the two-dimensional incompressible Navier–Stokes equations. A second order stiffly stable method is used to discretise the equations in time. Spatial discretisation is accomplished using a modal DG approach, in which the inter-element fluxes are approximated using the Symmetric Interior Penalty Galerkin formulation. The non-linear terms in the Navier–Stokes equations are expressed in the convective form and approximated through the Lesaint–Raviart fluxes modified for DG methods.Verification of the solver is performed for a series of test problems; purely elliptic, unsteady Stokes and full Navier–Stokes. The resulting method leads to a stable scheme for the unsteady Stokes and Navier–Stokes equations when equal order approximation is used for velocity and pressure. For the validation of the full Navier–Stokes solver, we consider unsteady laminar flow past a square cylinder at a Reynolds number of 100 (unsteady wake). The DG solver shows favourably comparisons to experimental data and a continuous Spectral code.     

Two-step simulation of slat noise

The flow field and the acoustic field of a high-lift configuration consisting of a slat and a main wing are numerically investigated by a hybrid method. In a first step, the unsteady flow field is computed via a large-eddy simulation (LES) and in a second step, the acoustic field is determined by solving the acoustic perturbation equations (APE). The mean flow field is compared to experimental findings followed by an investigation of the turbulent structures which are visualized by λ₂ contours. The analysis of the acoustic field shows that at the main wing trailing edge acoustic pressure fluctuations of approximately 5 kHz are generated. Correlations between the noise sources and the acoustic pressure identify the slat-gap region to be responsible for the mixture of broadband and tonal noise between 1 and 3 kHz. The decay of the pressure spectrum is found to be approximately f⁻² which is in agreement with the literature.     

结构变形对整流罩分离轨迹的影响

为研究弹性体在稠密大气中的分离问题,基于非结构网格,采用运动网格与局部网格重构相结合的方法求解大位移相对运动的流场,并耦合6自由度刚体运动方程得到整流罩的运动.非定常流动方程使用格心有限体积法进行空间离散,并运用LU-SGS进行求解.应用标准算例验证该方法的准确性,并用于某整流罩飞行轨迹的计算.结果表明结构变形可能会使...     

Parallel-multigrid computation of unsteady incompressible viscous flows using a matrix-free implicit method and high-resolution characteristics-based scheme

A three-dimensional parallel unstructured non-nested multigrid solver for solutions of unsteady incompressible viscous flow is developed and validated. The finite-volume Navier–Stokes solver is based on the artificial compressibility approach with a high-resolution method of characteristics-based scheme for handling convection terms. The unsteady flow is calculated with a matrix-free implicit dual time stepping scheme. The parallelization of the multigrid solver is achieved by multigrid domain decomposition approach (MG-DD), using single program multiple data (SPMD) and multiple instruction multiple data (MIMD) programming paradigm. There are two parallelization strategies proposed in this work, first strategy is a one-level parallelization strategy using geometric domain decomposition technique alone, second strategy is a two-level parallelization strategy that consists of a hybrid of both geometric domain decomposition and data decomposition techniques. Message-passing interface (MPI) and OpenMP standard are used to communicate data between processors and decompose loop iterations arrays, respectively. The parallel-multigrid code is used to simulate both steady and unsteady incompressible viscous flows over a circular cylinder and a lid-driven cavity flow. A maximum speedup of 22.5 could be achieved on 32 processors, for instance, the lid-driven cavity flow of Re = 1000. The results obtained agree well with numerical solutions obtained by other researchers as well as experimental measurements. A detailed study of the time step size and number of pseudo-sub-iterations per time step required for simulating unsteady flow are presented in this paper.     

Prediction of sound generated by a rod-airfoil configuration using EASM DES and the generalised Lighthill/FW-H analogy

Sound generated by an airfoil in the wake of a rod is predicted numerically by using a Detached-Eddy Simulation (DES) unsteady flow field and a Ffowcs Williams and Hawkings acoustic analogy formulation for the far field computation. Volume sources from the rod wake are found to play a non-negligible role at high frequencies and surface contributions might be flawed if the surfaces cross highly turbulent flow regions even if surrounding volume terms are accounted for. The DES approach is based on a novel cubic explicit algebraic stress turbulence model which is built on a two-equation k-ε model from Lien and Lechziner. This DES has been recently implemented at the Berlin University of Technology in the compressible Navier-Stokes flow solver ELAN. The aerodynamic results are compared to experimental data obtained at the ECL by Jacob et al., as well as to previous Large Eddy Simulations results from the Proust/Turbflow code by Boudet et al. and DES simulations from Greschner et al. based on standard turbulence models. The acoustic analogy is applied both with and without volume terms to rigid and permeable control surfaces surrounding the rod-airfoil system. Aeroacoustic results are compared to experimental data from the literature, showing that the inclusion of volume terms improves the aeroacoustic prediction in the broadband high frequency range.     

Computation of unsteady viscous flow and aeroacoustic noise of cross flow fans

Time-accurate viscous flow solutions are sought for the prediction of unsteady flow characteristics and associated aeroacoustic blade tonal noise of a cross flow fan. The two-dimensional incompressible Navier-Stokes equations in a moving coordinate are time-accurately solved by an unstructured finite-volume method on triangular meshes, and a sliding mesh technique is utilized at the interface between the domain rotating with blades and the stationary one for allowing the unsteady interactions. An accuracy assessment of the present method is made by comparing the fan performances with experimental data for a rotational speed at 1000 rpm and the Reynolds number 5300 based on blade tip speed and chord length. With the computed unsteady viscous flow solutions, sound pressure is predicted using Curle’s equation and narrow-band noise characteristics of three impellers with a uniform and two random pitch (type-A and -B) blades are compared by their sound pressure level spectra. Also, the frequency modulations of the blade passing frequency noise by random pitch fans are discussed.     

A hybrid algorithm for far-field noise minimization

A general unsteady adjoint formulation is applied to a hybrid acoustic prediction algorithm to provide an efficient far-field noise minimization algorithm. Two-dimensional unsteady Navier-Stokes (NS) computations for calculating the properties of acoustic sources are combined with the Ffowcs Williams and Hawkings (FW-H) wave propagation formulation to calculate the resulting far-field noise. Two different time-marching methods, namely an implicit multi-stage and an implicit multi-step method, are used for time discretization. The hybrid NS/FW-H solver is verified by comparison to an analytical solution and a Navier-Stokes solution. A discrete-adjoint Newton-Krylov algorithm is used to enable gradient-based shape optimization to minimize far-field noise computed using the hybrid solver. Objective functions considered include remote inverse shape designs for verification as well as the far-field pressure fluctuations for a blunt trailing edge airfoil in an unsteady turbulent flow environment. The examples presented demonstrate that the combination of a discrete-adjoint Newton-Krylov algorithm with a hybrid NS/FW-H far-field noise prediction method can be an efficient design tool for reducing aerodynamically generated noise.     

Investigation of flow structures involved in sound generation by two- and three-dimensional cavity flows

Proper Orthogonal Decomposition and Stochastic Estimation are combined to shed some light on the link between organized flow structures and noise generation by turbulent flows. Proper Orthogonal Decomposition (POD) is firstly used to extract selected flow events. Based on the knowledge of these structures, the Quadratic Stochastic Estimation of the acoustic pressure field is secondly performed. Both procedures are successively applied to two- and three-dimensional numerical databases of a flow over a cavity. It is demonstrated that POD can extract selected aerodynamic events which can be associated with selected frequencies in the acoustic spectra. Reconstructed acoustic fields also indicate the aerodynamic events which are responsible of the main energy of the noise emission. Such mathematical tools offer new perspectives in analysing flow structures involved in sound generation by turbulent flows and in the experimental design of a flow control strategy.     

串列双圆柱绕流的气动噪声特性分析

在OpenFOAM求解器中采用改进型延迟分离涡模拟(improved delayed detached eddy simulation,IDDES)方法对串列双圆柱的绕流流场进行数值模拟,使用K FWH方程分析其气动噪声特性,比较不同来流速度、圆柱间距比和圆柱直径的双圆柱绕流的气动噪声特性。分析结果表明：来流速度、圆柱间距比和圆柱直径对串列双圆柱的气动噪声特性都有显著影响,在特定情况下还会出现冲击纯音噪声、高分贝噪声等声品质恶化现象。