Computational Aeroacoustics: Progress on Nonlinear Problems of Soundgeneration Tim Coloniusa,Ã, Sanjiva K
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ARTICLE IN PRESS Progress in Aerospace Sciences 40 (2004) 345–416 Computational aeroacoustics: progress on nonlinear problems of soundgeneration Tim Coloniusa,Ã, Sanjiva K. Leleb aDepartment of Mechanical Engineering, California Institute of Technology, Mail Code 104-44 Pasadena, CA 91125, USA bDepartment of Aeronautics and Astronautics and Department of Mechanical Engineering, Stanford University, Stanford, CA 94305-4035, USA Abstract Computational approaches are being developed to study a range of problems in aeroacoustics. These aeroacoustic problems may be classifiedbasedon the physical processes responsible for the soundradiation,andrange from linear problems of radiation, refraction, and scattering in known base flows or by solid bodies, to sound generation by turbulence. In this article, we focus mainly on the challenges andsuccesses associatedwith numerically simulating soundgeneration by turbulent flows. We discuss a hierarchy of computational approaches that range from semi-empirical schemes that estimate the noise sources using mean-flow and turbulence statistics, to high-fidelity unsteady flow simulations that resolve the sound generation process by direct application of the fundamental conservation principles. We stress that high-fidelity methods such as Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) have their merits in helping to unravel the flow physics and the mechanisms of sound generation. They also provide rich databases for modeling activities that will ultimately be needed to improve existing predictive capabilities. Spatial and temporal discretization schemes that are well-suited for aeroacoustic calculations are analyzed, including the effects of artificial dispersion and dissipation on uniform and nonuniform grids. We stress the importance of the resolving power of the discretization as well as computational efficiency of the overall scheme. Boundary conditions to treat the flow of disturbances in and out of the computational domain, as well as methods to mimic anechoic domain extension are discussed. Test cases on some benchmark problems are included to provide a realistic assessment of several boundary condition treatments. Finally, highlights of recent progress are given using selected model problems. These include subsonic cavity noise and jet noise. In the end, the current challenges in aeroacoustic modeling and in simulation algorithms are revisited with a look towardthe future developments. r 2004 Elsevier Ltd. All rights reserved. ÃCorresponding author. Tel.: +1 626 395 4021; fax: +1 626 568 2719. E-mail address: [email protected] (T. Colonius). 0376-0421/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.paerosci.2004.09.001 ARTICLE IN PRESS 346 T. Colonius, S.K. Lele / Progress in Aerospace Sciences 40 (2004) 345–416 Nomenclature Roman characters t eddy turnover time tij viscous stress tensor A amplitude function y momentum thickness a finite-difference coefficients, Section 4.1 y phase function, Section 4.1 a speedof sound C airfoil chord Subscripts c wave speed cg group velocity 1 free-stream or far-fieldvalue cp phase speed c centerline Cp; Cs; CT LES model coefficients j jet value at nozzle lip D (jet) diameter p peak E three-dimensional energy spectrum t turbulent El total energy density f frequency Superscripts and constructs h gridspacing K modified wavenumber hð Þi ensemble or time averaged k wavenumber ðÞ LES filtered L turbulence integral scale ðÞb LES test-filteredor Fourier transformed M Mach number ðÞ~ windowed 0 mi subgridmass flux vector fluctuating quantity or derivative n order of accuracy p pressure Abbreviations qi heat flux vector rij subgridmomentum flux tensor BC boundary condition Re Reynolds number CAA computational aeroacoustics Sij symmetric strain rate tensor CFD computational fluiddynamics St Strouhal number CFL Courant–Friedrichs–Levy T temperature DNS direct numerical simulation T ij Lighthill stress tensor DRP dispersion-relation-preserving U velocity (usually reference value) ENO essentially non-oscillatory u velocity FCT flux-correctedtransport Uc convective velocity FD finite difference w window function Ff–H Ffowcs Williams–Hawkings q vector of dependent variables IC initial condition qsi subgridenergy flux vector LDD low dissipation and dispersion LEE LinearizedEuler equations Greek characters LES large eddy simulation LM linear multi-step a finite-difference coefficients, Section 4.1 NPSE nonlinear ParabolizedStability equations a shear layer spreading rate OASPL overall soundpressure level aj apparent velocity, Section 4.1 PML perfectly matchedlayer D LES filter width, or difference PSE ParabolizedStability equations d shock thickness RANS Reynolds-averaged Navier–Stokes d% displacement thickness RK Runge–Kutta do vorticity thickness SAT simultaneous approximation term turbulence dissipation SBP summation-by-parts Z Kolmogorov scale SGS sub-gridstress g ratio of specific heats SPL soundpressure level l1 Taylor microscale TKE turbulent kinetic energy m viscosity TVD total variation diminishing r density URANS unsteady Reynolds-averaged Navier–Stokes s damping coefficient WENO weightedessentially non-oscillatory ARTICLE IN PRESS T. Colonius, S.K. Lele / Progress in Aerospace Sciences 40 (2004) 345–416 347 Contents 1. Introduction . 348 2. Classification of aeroacoustic problems . 349 2.1. Linear problems of propagation andgeneralizedscattering . 349 2.2. Nonlinear problems of flow acoustics or aeroacoustics . 349 2.3. Illustrative examples . 350 2.3.1. Airfoil/hydrofoil trailing-edge noise at low speed . 350 2.3.2. High speedjet noise . 352 3. A hierarchy of CAA simulations . 353 3.1. Direct computation of sound. 353 3.1.1. DNS or LES with compressible Navier–Stokes . 354 3.1.2. Extension of DNS or LES near-fields. 355 3.2. Hybrid methods for noise prediction . 355 3.2.1. DNS/LES with acoustic analogy . 355 3.2.2. Vortex methods with acoustic analogy . 357 3.2.3. Incompressible/acoustic split . 357 3.2.4. LinearizedEuler with source terms . 357 3.3. Large eddy simulation . 358 3.3.1. LES equations andsubgridmodeling. 358 3.3.2. Numerical issues particular to LES . 359 3.3.3. Refinedsubgridmodels. 360 3.3.4. Acoustic implications of SGS models. 360 4. Computational issues . 362 4.1. Spatial discretization . 362 4.1.1. Wave propagation characteristics of finite-difference schemes. 364 4.1.2. Dispersion anddissipation . 366 4.1.3. Spurious waves, artificial viscosity, andfiltering . 367 4.1.4. Boundary closures . 369 4.1.5. Computational efficiency . 369 4.1.6. Viscous and second-derivative terms . 371 4.1.7. Gridstretching andgeneralizedcurvilinear coordinates. 372 4.2. Temporal discretization . 375 4.3. Boundary conditions . 377 4.3.1. LinearizedBC . 378 4.3.2. Nonlinear BC: Thompson’s approach . 382 4.3.3. Nonlinear BC: Buffer zone techniques . 384 4.3.4. Solid wall boundary conditions . 388 4.4. Shocks . 388 5. Recent progress in nonlinear CAA . 389 5.1. CAA studies related to vortex dynamics and interaction of vortices with shock waves . 389 5.2. CAA studies related to jet noise . 392 5.2.1. Representation of jet turbulence andjet mixing noise . 392 5.2.2. Jet screech andshock-associatednoise . 393 5.2.3. Computation of jet noise using DNS andLES . 394 5.2.4. Model problems related to jet noise . 395 5.3. Model problems of cavity noise . 401 5.3.1. Computational efforts . 402 5.3.2. Summary. 404 6. Closure . 404 ARTICLE IN PRESS 348 T. Colonius, S.K. Lele / Progress in Aerospace Sciences 40 (2004) 345–416 Acknowledgements . 406 References . 406 1. Introduction to make some pragmatic simplification. The first step is a classification of the problem according to the The aerodynamic noise of airplanes at take-off and in dominant mechanism of sound generation. Such a the landing configuration continues to be a critical classification is presentedin Section 2. The next step is factor in the future development of aviation. Commu- a careful synthesis of a computational problem nity noise concerns at busy airports constrain the design that incorporates the requireddetailsof the sound of new airplanes, subsonic or supersonic, andof generation process. In a general flow it is not possible rotorcraft. The current operational fleet is also subject to unambiguously separate the ‘flow’ from the ‘sound’. to new increasingly stringent noise regulations. Aviation However, when the flow Mach number is small it is technology with dramatically lower community noise advantageous to separate the task of predicting footprint, for example one that limits the noise footprint the unsteady vortical motion, i.e. flow prediction, to the airport perimeter, is envisionedin NASA’s from that of noise prediction. To help gain a pers- ambitious long term plan for the next 20 years. Such pective on this issue two specific model problems long term targets andspecific near-term noise reduction of trailing-edge noise and jet-noise are presented in goals are driving active research in aeroacoustics. As Section 2.3. an example, jet noise has traditionally been reduced Predicting the noise radiation associated with un- by increasing the bypass ratio of turbofan engines. steady flows is the central theme of aeroacoustics. A However, this trendcannot be continuedindefinitely variety of.