Development of Computational Aeroacoustics Tools for Airframe Noise Calculations

This paper discusses the development of computational aeroacoustics (CAA) tools for airframe noise analysis and prediction. We review recent progress in this topic, but emphasize our vision for the future development of such tools. Our intention is for this vision to drive future CAA research in directions that will accelerate widespread use of CAA for airframe noise applications. We discuss the needs for accuracy, efficiency, and easy interface with other design tools and illustrate how CAA tools may help future aircraft design. We explain what appears to be achievable in a 20-year time frame, and what goals will probably take longer.

Important barrier issues include the effects of numerical dispersion and dissipation, the treatment of highly curved, irregular boundary surfaces, and grid generation. Beyond these largely numerical issues, we discuss the role of physics-based modeling, including turbulence modeling in unsteady flow computations and the importance of developing sophisticated techniques for analyzing results of computations. Numerical simulations combined with the acoustic analogy methodology to predict noise are also reviewed. Finally, we discuss how to use recent advances in measurement techniques for CAA tool validation, which is an integral part of future development.     

Contributions of Computational Aeroacoustics to Jet Noise Research and Prediction

A brief review of recent progress in the field of computational aeroacoustics (CAA) is proposed. This paper is complementary to the previous reviews of Tam [(1995a) “Computational aeroacoustics: issues and methods”, AIAA J. 33(10), 1788–1796], Lele [(1997) “Computational Aeroacoustics: a review”, AIAA Paper 97–0018, 35th Aerospace Sciences Meeting and Exhibit, Reno, Nevada] and Glegg [(1999) “Recent advances aeroacoustics: the influence of computational fluid dynamics”, 6th International Congress on Sound and Vibration, Copenhagen, Danemark, 5–8 July, 43–58] on advances in CAA. After a short introduction concerning the current motivations of jet noise studies, connections between computational fluid dynamics (CFD) and CAA using hybrid approaches are discussed in the first part. The most spectacular advances are probably provided by the direct computation of jet noise, and some recent results are shown in the second part.     

关于气动声学数值计算的方法与进展

气动声学数值计算是近年才出现的研究领域。本文介绍了气动声学数值计算的方法和有关的问题、边界条件的处理以及计算非线性声波的数值方法和进展。讨论了计算气动声学(CAA)的特性及其与计算流体力学(CFD)的差异，指出气动声学数值方法的关键是建立能保持色散关系的差分方程和正确处理无反射边界条件。对于非线性声波传播的问题，为了得到正确的解，应注意提高差分格式对短波的分辨能力，同时发展能抑制“伪”振荡(短波)而对长波基本不起作用的数值方法。     

Recent advances of computational aeroacoustics

Computational aeroacoustics (CAA) is an interdiscipline of aeroacoustics and computational fluid dynamics (CFD) for the investigation of sound generation and propagation from various aeroacoustics problems. In this review, the foundation and research scope of CAA are introduced firstly. A review of the early advances and applications of CAA is then briefly surveyed, focusing on two key issues, namely, high order finite difference scheme and non-reflecting boundary condition. Furthermore, the advances of CAA during the past five years are highlighted. Finally, the future prospective of CAA is briefly discussed.     

Optimized sixth‐order monotonicity‐preserving scheme by nonlinear spectral analysis

In this paper, sixth‐order monotonicity‐preserving optimized scheme (OMP6) for the numerical solution of conservation laws is developed on the basis of the dispersion and dissipation optimization and monotonicity‐preserving technique. The nonlinear spectral analysis method is developed and is used for the purpose of minimizing the dispersion errors and controlling the dissipation errors. The new scheme (OMP6) is simple in expression and is easy for use in CFD codes. The suitability and accuracy of this new scheme have been tested through a set of one‐dimensional, two‐dimensional, and three‐dimensional tests, including the one‐dimensional Shu–Osher problem, the two‐dimensional double Mach reflection, and the Rayleigh–Taylor instability problem, and the three‐dimensional direct numerical simulation of decaying compressible isotropic turbulence. All numerical tests show that the new scheme has robust shock capturing capability and high resolution for the small‐scale waves due to fewer numerical dispersion and dissipation errors. Moreover, the new scheme has higher computational efficiency than the well‐used WENO schemes. Copyright © 2013 John Wiley & Sons, Ltd.     

Some applications of the concept of minimized integrated exponential error for low dispersion and low dissipation

Several techniques to optimize parameters that regulate dispersion and dissipation effects in finite difference schemes have been devised in our previous works. They all use the notion that dissipation neutralizes dispersion. These techniques are the minimized integrated square difference error (MISDE) and the minimized integrated exponential error for low dispersion and low dissipation (MIEELDLD). It is shown in this work based on several numerical schemes tested that the technique of MIEELDLD is more accurate than MISDE to optimize the parameters that regulate dispersion and dissipation effects with the aim of improving the shock‐capturing properties of numerical methods. First, we consider the family of third‐order schemes proposed by Takacs. We use the techniques MISDE and MIEELDLD to optimize two parameters, namely, the cfl number and another variable which also controls dispersion and dissipation. Second, these two techniques are used to optimize a numerical scheme proposed by Gadd. Moreover, we compute the optimal cfl for some multi‐level schemes in 1D. Numerical tests for some of these numerical schemes mentioned above are performed at different cfl numbers and it is shown that the results obtained are dependent on the cfl number chosen. The errors from the numerical results have been quantified into dispersion and dissipation using a technique devised by Takacs. Finally, we make use of a composite scheme made of corrected Lax–Friedrichs and the two‐step Lax–Friedrichs schemes like the CFLF4 scheme at its optimal cfl number, to solve some problems in 2D, namely: solid body rotation test, acoustics and the circular Riemann problem. Copyright © 2011 John Wiley & Sons, Ltd.     

Review of Computational Aeroacoustics Algorithms

This paper presents a review of recent advancements in computational methodology for aeroacoustics problems. High-order finite difference methods for computation of linear and nonlinear acoustic waves are the primary focus of the review. Schemes for numerical simulation of linear waves include explicit optimized and DRP finite-difference operators, compact schemes, wavenumber extended upwind schemes and leapfrog-like algorithms. Both spatial approximations and time-integration techniques, which include low-dissipation low-dispersion Adams-Bashforth and Runge-Kutta (RK) methods, are examined. Wave propagation properties are analysed in the wavenumber and frequency space. Different approaches to eliminate short-wave spurious numerical waves are also reviewed. Methods for simulating nonlinear acoustic phenomena include essentially non-oscillatory (ENO) schemes, numerical adaptive filtering for high-order explicit and compact finite-difference operators, MacCormack and adaptive compact nonlinear algorithms. A literature survey of other CAA methods is provided in the introductory part.     

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.     

Stable,high-order computation of traveling water waves in three dimensions

The Euler equations of free-surface ocean dynamics constitute a model of central importance in fluid mechanics due to the wide range of physical phenomena they are intended to represent, from shoaling and breaking of waves in nearshore regions to energy and momentum transport in the open ocean. From a mathematical perspective, these equations present rather unique challenges for analysis and simulation as they couple the subtleties of nonlinear wave equations (balancing nonlinearity with dispersion in the absence of dissipation) to the difficulties of free-boundary problems. In this paper a new, stable high-order boundary perturbation algorithm for the numerical simulation of traveling water waves is described. Its performance is compared to that of classical surface deformation algorithms and it is shown that the new scheme displays significantly enhanced conditioning properties and a lower computational cost, which enable very accurate predictions of physical observables such as velocity, energy, height/steepness, and shape.     

High-order schemes for predicting computational aeroacoustic propagation with adaptive mesh refinement

High-order schemes based on block-structured adaptive mesh refinement method are prepared to solve computational aeroacoustic (CAA) problems with an aim at improving computational efficiency. A number of numerical issues associated with high-order schemes on an adaptively refined mesh, such as stability and accuracy are addressed. Several CAA benchmark problems are used to demonstrate the feasibility and efficiency of the approach.     

Optimised composite numerical schemes in 2‐D for hyperbolic conservation laws

One of the techniques available for optimising parameters that regulate dispersion and dissipation effects in finite difference schemes is the concept of minimised integrated exponential error for low dispersion and low dissipation. In this paper, we work essentially with the two‐dimensional (2D) Corrected Lax–Friedrichs and Lax–Friedrichs schemes applied to the 2D scalar advection equation. We examine the shock‐capturing properties of these two numerical schemes, and observe that these methods are quite effective from the point of being able to control computational noise and having a large range of stability. To improve the shock‐capturing efficiency of these two methods, we derive composite methods using the idea of predictor/corrector or a linear combination of the two schemes. The optimal cfl number for some of these composite schemes are computed. Some numerical experiments are carried out in two dimensions such as cylindrical explosion, shock‐focusing, dam‐break and Riemann gas dynamics tests. The modified equations of some of the composite schemes when applied to the 2D scalar advection equation are obtained. We also perform some convergence tests to obtain the order of accuracy and show that better results in terms of shock‐capturing property are obtained when the optimal cfl obtained using minimised integrated exponential error for low dispersion and low dissipation is used. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Computational fluid dynamics applied to internal gas-turbine blade cooling: a review

This paper reviews current capabilities for predicting flow in the cooling passages and cavities of jet engines. Partly because of the need to enhance heat transfer coefficients, these flow domains entail complicated passage shapes where the flow is turbulent, strongly three-dimensional (3-D) and where flow separation and impingement, complicated by strong effects of rotation, pose severe challenges for the modeler. This flow complexity means that more elaborate models of turbulent transport are needed than in other areas of turbine flow analysis. The paper attempts to show that progress is being made, particularly in respect to the flow in serpentine blade-cooling passages. The first essential in modeling such flows is to adopt a low Reynolds number model for the sublayer region. The usual industrial practice of using wall functions cannot give a better than qualitative account of effects of rotation and curvature. It is shown that Rayleigh number effects can modify heat transfer coefficients in the cooling passages by at least 50%. The use of second-moment closure in the modeling is shown to be bringing marked improvements in the quality of predictions. Areas where, at present, more computational fluid dynamics (CFD) applications are encouraged are impingement cooling and pin-fin studies.     

Radiation and Wall Boundary Conditions for Computational Aeroacoustics: A Review

A review of unsteady computational boundary conditions for computational aeroacoustics (CAA) problems is presented. This review is meant to serve as a general overview of previous work on solid wall, radiation and outflow boundary conditions that have been proposed and used in CAA calculations. Both the physical nature of the boundary condition problem as well as the numerical considerations affecting their implementation are discussed.     

Synthesis of highly convergent 2D and 3D finite elements for short acoustic wave simulation

New higher-order finite elements of enhanced convergence properties for acoustic wave simulation are presented in the paper. The element matrices are obtained by combining modal synthesis and optimization techniques in order to achieve minimum errors of higher modes of the computational domain. As a result, simulation models of propagating wave pulses require a smaller number of finite element divisions per wavelength compared to the conventional element model thus significantly reducing computational costs. Though finite element matrices are obtained in optimization, the resulting patterns of the matrices are versatile and further can be used in any wave propagation model. The mass matrices of the elements are diagonal, so explicit time integration schemes are applicable. The usage of new elements is especially efficient in situations where wavelengths of the simulated signal are much shorter than the dimensions of the computational domain. This is referred to as short wave propagation analysis. The results of wave propagation simulation for ultrasonic measurements are presented as application examples. The B-scans and computed dispersion curves are provided for visual interpretation of the results.     

THE APPLICATION OF A FINITE DIFFERENCE/FINITE VOLUME ALGORITHM TO SOLVE MAXWELL'S EQUATIONS IN THE TIME DOMAIN

Abstract

A finite volume/finite difference method based on Ni's multigrid formulation is introduced for the solution of Maxwell's equations. The scheme is presented for the cases of transverse magnetic scattering from two-dimensional circular and square cylinders, as well as from NACA 0012 airfoil. The codes are validated against the traditional Method of Moments, which is analogous to a panel method in CFD. The circular cylinder scattering is compared to the analytical series solution for better understanding how the roles of numerical dispersion and dissipation errors affect the solution. The reflecting boundary conditions are modeled by the idea of inducing fields inside the conductor and a method of modeling the singularities that arise at a sharp corner is presented. Absorbing boundary conditions are modeled by integrating along the characteristic compatibility equations in the direction of the outgoing wave.     

The concept of minimized integrated exponential error for low dispersion and low dissipation schemes

We devise two novel techniques to optimize parameters which regulate dispersion and dissipation effects in numerical methods using the notion that dissipation neutralizes dispersion. These techniques are baptized as the minimized integrated error for low dispersion and low dissipation (MIELDLD) and the minimized integrated exponential error for low dispersion and low dissipation (MIEELDLD) . These two techniques of optimization have an advantage over the concept of minimized integrated square difference error (MISDE) , especially in the case when more than one optimal cfl is obtained, out of which only one of these values satisfy the shift condition. For instance, when MISDE is applied to the 1‐D Fromm's scheme, we have obtained two optimal cfl numbers: 0.28 and 1.0. However, it is known that Fromm's scheme satisfies shift condition only at r=1.0. Using MIELDLD and MIEELDLD , the optimal cfl of Fromm's scheme is computed as 1.0. We show that like the MISDE concept, both the techniques MIELDLD and MIEELDLD are effective to control dissipation and dispersion. The condition ν²>4µ is satisfied for all these three techniques of optimization, where ν and µ are parameters present in the Korteweg‐de‐Vries‐Burgers equation. The optimal cfl number for some numerical schemes namely Lax–Wendroff, Beam–Warming, Crowley and Upwind Leap‐Frog when discretized by the 1‐D linear advection equation is computed. The optimal cfl number obtained is in agreement with the shift condition. Some numerical experiments in 1‐D have been performed which consist of discontinuities and shocks. The dissipation and dispersion errors at some different cfl numbers for these experiments are quantified. Copyright © 2010 John Wiley & Sons, Ltd.     

数据驱动计算力学研究进展

以数字孪生、人工智能为核心的大数据理念正深刻影响着第四次工业革4 命,数据驱动计算力学在此背景下应运而生并展现勃勃生机。与此同时,航5 空航天等尖端工业领域对高性能材料与结构的先进制造与安全评估提出了更6 严峻的挑战,经典计算力学已很难实现成倍缩短产品研发周期、实时跟踪产7 品信息并提供解决方案的目标。因此,发展面向高性能材料与结构的数据驱8 动计算力学正当其时且刻不容缓。本文拟通过梳理数据驱动计算力学的部分9 研究现状,探讨并浅析数据驱动计算力学的发展趋势.     

An effective limiting algorithm for particle-based numerical simulations of compressible flows

Eulerian computational fluid dynamics (CFD) and Lagrangian computational structural dynamics (CSD) are used extensively in the aerospace industry. Combined mesh-based Eulerian and particle-based Lagrangian algorithms arevery effective for modelling and simulation due to the increased efficiency of combining the two numerical simulations. However, when compressible flows are simulated using a particle-based algorithm, calculations of strong discontinuity, such as a shock wave, may become unstable. In the present study, a numerical limiter is integrated with a particle-based CFD code to remedy this instability. The limiting algorithm incorporates an ‘averaging’ technique which calculates average values using the properties of neighbouring particles (also known as material points), including mass, momentum and energy. These averaged values are then input to a min-mode limiter to eliminate numerical noise and incur dissipation in the flow in areas with steep property gradients. The results of this algorithm show very stable solutions with minimal oscillations when applied to the one-dimensional shock tube problem and an increased accuracy with reduced oscillations for a two-dimensional cylinder cross-flow problem.