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Aeroacoustic Simulations Using Compressible Lattice Boltzmann Method

Published online by Cambridge University Press:  08 July 2016

Kai Li*
Affiliation:
National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an 710072, China
Chengwen Zhong*
Affiliation:
National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an 710072, China
*
*Corresponding author. Email:[email protected] (K. Li), [email protected] (C.W. Zhong)
*Corresponding author. Email:[email protected] (K. Li), [email protected] (C.W. Zhong)
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Abstract

This paper presents a lattice Boltzmann (LB) method based study aimed at numerical simulation of aeroacoustic phenomenon in flows around a symmetric obstacle. To simulate the compressible flow accurately, a potential energy double-distribution-function (DDF) lattice Boltzmann method is used over the entire computational domain from the near to far fields. The buffer zone and absorbing boundary condition is employed to eliminate the non-physical reflecting. Through the direct numerical simulation, the flow around a circular cylinder at Re=150, M=0.2 and the flow around a NACA0012 airfoil at Re=10000, M=0.8, α=0° are investigated. The generation and propagation of the sound produced by the vortex shedding are reappeared clearly. The obtained results increase our understanding of the characteristic features of the aeroacoustic sound.

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Type
Research Article
Copyright
Copyright © Global-Science Press 2016 

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References

[1]Li, X., Leung, R. K. and So, R. C., One-step aeroacoustics simulation using lattice Boltzmann method, AIAA J., 44 (2006), pp. 7889.Google Scholar
[2]Viggen, E. M., Viscously damped acoustic waves with the lattice Boltzmann method, Philos. T. Roy. Soc. A, 369 (2011), pp. 22462254.CrossRefGoogle ScholarPubMed
[3]Tajiri, S., Tsutahara, M. and Tanaka, H., Direct simulation of sound and underwater sound generated by a water drop hitting a water surface using the finite difference lattice Boltzmann method, Comput. Math. Appl., 59 (2010), pp. 24112420.Google Scholar
[4]Ikeda, T., Atobe, T. and Takagi, S., Direct simulations of trailing-edge noise generation from two-dimensional airfoils at low Reynolds numbers, J. Sound Vibration, 331 (2012), pp. 556574.CrossRefGoogle Scholar
[5]Kusano, K., Yamada, K. and Furukawa, M., Toward direct numerical simulation of aeroacoustic field around airfoil using multi-scale lattice Boltzmann method, ASME 2013 Fluids Engineering Division Summer Meeting, American Society of Mechanical Engineers, Nevada, USA, 2013, V01AT09A005.CrossRefGoogle Scholar
[6]Xu, A., Zhang, G., Li, Y. and Li, H., Modeling and simulation of nonequilibrium and multiphase complex systems: lattice Boltzmann kinetic theory and application, Progress Phys., 34 (2014), pp. 136167, in Chinese.Google Scholar
[7]Xu, A., Lin, C., Zhang, G. and Li, Y., Multiple-relaxation-time lattice Boltzmann kinetic model for combustion, Phys. Rev. E, 91 (2015), 043306.CrossRefGoogle ScholarPubMed
[8]Bhatnagar, P. L., Gross, E. P. and Krook, M., A model for collision processes in gases i. small amplitude processes in charged and neutral one-component systems, Phys. Rev., 94 (1954), pp. 511525.Google Scholar
[9]Succi, S., The Lattice Boltzmann Equation: for Fluid Dynamics and Beyond, Oxford University Press, 2001.Google Scholar
[10]Xu, A. G., Zhang, G. C., Gan, Y. B., Chen, F. and Yu, X. J., Lattice Boltzmann modeling and simulation of compressible flows, Frontiers Phys., 7 (2012), pp. 582600.Google Scholar
[11]Alexander, F. J., Chen, S. and Sterling, J. D., Lattice Boltzmann thermohydrodynamics, Phys. Rev. E, 47 (1993), pp. R2249–R2252.CrossRefGoogle ScholarPubMed
[12]Qian, Y., Simulating thermohydrodynamics with lattice BGK models, J. Sci. Comput., 8 (1993), pp. 231242.Google Scholar
[13]Yan, G., Chen, Y. and Hu, S., Simple lattice Boltzmann model for simulating flows with shock wave, Phys. Rev. E, 59 (1999), pp. 454459.Google Scholar
[14]Yan, G., Zhang, J., Liu, Y. and Dong, Y., A multi-energy-level lattice Boltzmann model for the compressible Navier-Stokes equations, Int. J. Numer. Methods Fluids, 55 (2007), pp. 4156.Google Scholar
[15]Sun, C., Lattice-Boltzmann models for high speed flows, Phys. Rev. E, 58 (1998), pp. 72837287.Google Scholar
[16]Sun, C., Adaptive lattice Boltzmann model for compressible flows: viscous and conductive properties, Phys. Rev. E, 61 (2000), pp. 26452653.CrossRefGoogle Scholar
[17]Shi, W., Shyy, W. and Mei, R., Finite-difference-based lattice Boltzmann method for inviscid compressible flows, Numer. Heat Transfer B Fundamentals, 40 (2001), pp. 121.Google Scholar
[18]Kataoka, T. and Tsutahara, M., Lattice Boltzmann model for the compressible Euler equations, Phys. Rev. E, 69 (2004), 056702.Google Scholar
[19]Kataoka, T. and Tsutahara, M., Lattice Boltzmann model for the compressible Navier-Stokes equations with flexible specific-heat ratio, Phys. Rev. E, 69 (2004), 035701.Google Scholar
[20]Watari, M., Finite difference lattice Boltzmann method with arbitrary specific heat ratio applicable to supersonic flow simulations, Phys. A Stat. Mech. Appl., 382 (2007), pp. 502522.CrossRefGoogle Scholar
[21]He, X., Chen, S. and Doolen, G. D., A novel thermal model for the lattice Boltzmann method in incompressible limit, J. Comput. Phys., 146 (1998), pp. 282300.Google Scholar
[22]Guo, Z., Zheng, C., Shi, B. and Zhao, T. S., Thermal lattice Boltzmann equation for low Mach number flows: decoupling model, Phys. Rev. E, 75 (2007), 036704.Google Scholar
[23]Li, K. and Zhong, C., A lattice Boltzmann model for simulation of compressible flows, Int. J. Numer. Methods Fluids, 77 (2015), pp. 334357.Google Scholar
[24]Buick, J., Greated, C. and Campbell, D., Lattice BGK simulation of sound waves, Europhys. Lett., 43 (1998), pp. 235240.CrossRefGoogle Scholar
[25]Buick, J., Buckley, C., Greated, C. and Gilbert, J., Lattice Boltzmann BGK simulation of nonlinear sound waves: the development of a shock front, J. Phys. A Math. General, 33 (2000), pp. 39173928.Google Scholar
[26]Haydock, D. and Yeomans, J., Lattice Boltzmann simulations of acoustic streaming, J. Phys. A Math. General, 34 (2001), pp. 52015213.Google Scholar
[27]Marié, S., Ricot, D. and Sagaut, P., Accuracy of lattice Boltzmann method for aeroacoustics simulations, AIAA Paper, 3515 (2007).Google Scholar
[28]Marié, S., Ricot, D. and Sagaut, P., Comparison between lattice Boltzmann method and Navier-Stokes high order schemes for computational aeroacoustics, J. Comput. Phys., 228 (2009), pp. 10561070.Google Scholar
[29]Xu, H. and Sagaut, P., Optimal low-dispersion low-dissipation LBM schemes for computational aeroacoustics, J. Comput. Phys., 230 (2011), pp. 53535382.Google Scholar
[30]Kang, H. K., Ro, K. D., Tsutahara, M. and Lee, Y. H., Numerical prediction of acoustic sounds occurring by the flow around a circular cylinder, KSME Int. J., 17 (2003), pp. 12191225.CrossRefGoogle Scholar
[31]Tsutahara, M., Kondo, T. and Mochizuki, K., Direct simulations of acoustic waves by finite volume lattice Boltzmann method, AIAA Paper, 2570 (2006).Google Scholar
[32]Laffite, A. and Pérot, F., Investigation of the noise generated by cylinder flows using a direct lattice-Boltzmann approach, AIAA Paper, 3268 (2009).Google Scholar
[33]Tamura, A., Tsutahara, M., Kataoka, T., Aoyama, T. and Yang, C., Numerical simulation of two-dimensional blade-vortex interactions using the finite difference lattice Boltzmann method, AIAA J., 46 (2008), pp. 22352247.Google Scholar
[34]Satti, R., Lew, P. T., Li, Y., Shock, R. and Noelting, S., Unsteady flow computations and noise predictions on a rod-airfoil using lattice Boltzmann method, AIAA Paper, 497 (2009).Google Scholar
[35]Jones, L. E., Numerical Studies of the Flow Around an Airfoil at Low Reynolds Number, PhD thesis, University of Southampton, 2008.Google Scholar
[36]Qu, K., Development of Lattice Boltzmann Method for Compressible Flows, PhD thesis, National University of Singapore, 2009.Google Scholar
[37]Li, Q., He, Y. L., Wang, Y. and Tao, W. Q., Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations, Phys. Rev. E, 76 (2007), 056705.Google ScholarPubMed
[38]Tsutahara, M., The finite-difference lattice Boltzmann method and its application in computational aero-acoustics, Fluid Dyn. Research, 44 (2012), 045507.CrossRefGoogle Scholar
[39]Van Leer, B., Towards the ultimate conservative difference scheme. v. a second-order sequel to godunov's method, J. Comput. Phys., 32 (1979), pp. 101136.CrossRefGoogle Scholar
[40]Kermani, M., Gerber, A. and Stockie, J., Thermodynamically based moisture prediction using Roe's scheme, 4th Conference of Iranian Aerospace Society, Amir Kabir University of Technology, Tehran, Iran, 2003, pp. 2729.Google Scholar
[41]Pareschi, L. and Russo, G., Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation, J. Sci. Comput., 25 (2005), pp. 129155.Google Scholar
[42]Patil, D., Chapman-Enskog analysis for finite-volume formulation of lattice Boltzmann equation, Phys. A Stat. Mech. Appl., 392 (2013), pp. 27012712.Google Scholar
[43]Van Albada, G., Van Leer, B. and Roberts, W. Jr, A comparative study of computational methods in cosmic gas dynamics, Astronomy Astrophys., 108 (1982), pp. 7684.Google Scholar
[44]Guo, Z., Zheng, C. and Shi, B., Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method, Chinese Phys., 11 (2002), pp. 366374.Google Scholar
[45]Da Silva, A. R., Numerical Studies of Aeroacoustic Aspects of Wind Instruments, PhD thesis, McGill University, 2008.Google Scholar
[46]Inoue, O. and Hatakeyama, N., Sound generation by a two-dimensional circular cylinder in a uniform flow, J. Fluid Mech., 471 (2002), pp. 285314.Google Scholar
[47]Tsutahara, M., Kataoka, T., Shikata, K. and Takada, N., New model and scheme for compressible fluids of the finite difference lattice Boltzmann method and direct simulations of aerodynamic sound, Comput. Fluids, 37 (2008), pp. 7989.Google Scholar
[48]Mavriplis, D. J. and Jameson, A., Multigrid solution of the Navier-Stokes equations on triangular meshes, AIAA J., 28 (1990), pp. 14151425.Google Scholar
[49]Bassi, F. and Rebay, S., A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations, J. Comput. Phys., 131 (1997), pp. 267279.Google Scholar
[50]Bouhadji, A. and Braza, M., Organised modes and shock-vortex interaction in unsteady viscous transonic flows around an aerofoil: part i: Mach number effect, Comput. Fluids, 32 (2003), pp. 12331260.CrossRefGoogle Scholar