基于混合RANS/LES方法与FW-H方程的气动声学计算研究
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摘要
在气动噪声的数值计算过程中,非定常流动的求解精度对声学计算结果有着重要的影响。以机体噪声计算的标准算例双圆柱绕流气动噪声问题为研究对象,采用基于非线性k-ε湍流模型的限制数值尺度(LNS)方法对双圆柱绕流进行了数值模拟,将计算得到的气动特性和流动特征与相应的试验结果进行了对比分析。为了求解远场观测点处的气动噪声,在精确求解双圆柱绕流流动的基础上结合基于FW-H(Ffowcs Williams-Hawkings)方程的声类比方法进行数值计算,并通过圆柱体的展向相关性对计算结果进行了修正,将得到的最终结果与相应的声学试验结果进行了对比,两者吻合良好,表明该数值方法是准确、可靠的。
The computational aeroacoustic result of aerodynamic noise problems is highly dependent on the capturing accuracy of an unsteady flow in the numerical prediction of aerodynamic noise.As a benchmark for airframe noise computation,the noise prediction for tandem cylinders is performed in this paper.The flow around the cylinders is simulated using the limited numerical scale(LNS) method based on a nonlinear k-ε model.The aerodynamic results and flow features obtained from the simulation are analyzed and compared with the experimental results.The flow parameters on the sound source surface are also recorded as the preparation data and then are combined with the acoustic analogy based on the FW-H(Ffowcs Williams-Hawkings) equation to predict the aerodynamic noise at the far-field receiver points.Since the spans in the simulation are relatively short,the predicted results have to be corrected for the span length.The final acoustic results are in good agreement with the experimental data,which indicates that the present numerical method is valid for this kind of aerodynamic noise problems.
The computational aeroacoustic result of aerodynamic noise problems is highly dependent on the capturing accuracy of an unsteady flow in the numerical prediction of aerodynamic noise.As a benchmark for airframe noise computation,the noise prediction for tandem cylinders is performed in this paper.The flow around the cylinders is simulated using the limited numerical scale(LNS) method based on a nonlinear k-ε model.The aerodynamic results and flow features obtained from the simulation are analyzed and compared with the experimental results.The flow parameters on the sound source surface are also recorded as the preparation data and then are combined with the acoustic analogy based on the FW-H(Ffowcs Williams-Hawkings) equation to predict the aerodynamic noise at the far-field receiver points.Since the spans in the simulation are relatively short,the predicted results have to be corrected for the span length.The final acoustic results are in good agreement with the experimental data,which indicates that the present numerical method is valid for this kind of aerodynamic noise problems.
引文
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[11]Fei B L,Zheng T H,Yang J L.Numerical simulation offlow over two tandem cylinders.Journal of SouthwestUniversity for Nationalities.Natural Science Edition,2007,33(2):376-380.(in Chinese)费宝玲,郑庭辉,杨骏六.数值分析串列双圆柱绕流.西南民族大学学报.自然科学版,2007,33(2):376-380.
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[13]Lin D K,Li X D,Hu F Q.Perfectly matched layerboundary conditions using in DNS of flow around cylinder.Journal of Engineering Thermophysics,2010,31(5):757-760.(in Chinese)林大楷,李晓东,胡方强.完全耦合层边界条件在圆柱绕流DNS中的应用.工程热物理学报,2010,31(5):757-760.
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[20]Han Z H,Song W P,Qiao Z D.Aeroacoustic calculationfor helicopter rotor in hover and in forward flight based onFW-H equation.Acta Aeronautica et Astronautica Sinica,2003,24(5):400-404.(in Chinese)韩忠华,宋文萍,乔志德.基于FW-H方程的旋翼气动声学计算研究.航空学报,2003,24(5):400-404.
[21]Speziale C G.Computing non-equilibrium turbulent flowswith time-dependent RANS and VLES.Lecture Notes inPhysics,1997,490:123-129.
[22]Wagner C A,Hüttl T,Sagaut P.Large-eddy simulationfor acoustics.London:Cambridge University Press,2007:441.
[23]Ffowcs Williams J E,Hawkings D L.Sound generation byturbulence and surfaces in arbitrary motion.PhilosophicalTransactions of the Royal Society of London.Series A,Mathematical and Physical Sciences,1969,264(1151):321-342.
[24]Yu L,Song W P,Yan L.An effective method for predic-ting aerodynamic noise for wind turbine flatback airfoils.Journal of Northwestern Polytechnical University,2012,30(4):513-517.(in Chinese)余雷,宋文萍,闫利.平底后缘风力机翼型气动噪声计算研究.西北工业大学学报,2012,30(4):513-517.
[25]Kato C,Iida A,Takano Y,et al.Numerical prediction ofaerodynamic noise radiated from low Mach number turbu-lent wake.AIAA-1993-145,1993.
[26]Bres G A,Wessels M,Noelting S.Tandem cylinder noisepredictions using lattice Boltzmann and Ffowcs Williams-Hawkings methods.AIAA-2010-3791,2010.
[2]Lockard D P,Khorrami M R,Choudhari M M,et al.Tandem cylinder noise predictions.AIAA-2007-3450,2007.
[3]Jenkins L N,Khorrami M R,Choudhari M M,et al.Characterization of unsteady flow structures around tan-dem cylinders for component interaction studies in airframenoise.AIAA-2005-2812,2005.
[4]Jenkins L N,Neuhart D H,Mcginley C B,et al.Meas-urements of unsteady wake interference between tandemcylinders.AIAA-2006-3202,2006.
[5]Hutcheson F V,Brooks T F.Noise radiation from singleand multiple rod configurations.AIAA-2006-2629,2006.
[6]Farassat F,Casper J H.Towards an airframe noise pre-diction methodology:survey of current approaches.AIAA-2006-210,2006.
[7]Liu M,Liu F,Hu Y T,et al.Aerodynamics andaeroacoustics numerical simulation of flow past two circu-lar cylinders in tandem arrangements.Journal of Engi-neering Thermophysics,2008,29(3):403-406.(in Chi-nese)刘敏,刘飞,胡亚涛,等.三维串列双圆柱绕流气动流场及声场模拟.工程热物理学报,2008,29(3):403-406.
[8]Liu M,Wu K Q.The aero-acoustics simulation of flowaround a cylinder using unstructured CE/SE scheme.Journal of Engineering Thermophysics,2009,30(2):227-229.(in Chinese)刘敏,吴克启.基于非结构网格CE/SE算法圆柱绕流气动声场模拟.工程热物理学报,2009,30(2):227-229.
[9]Zhao L J,Yang N Q,Wu D,et al.Aeroacoustics numeri-cal simulation of flow past tow-dimensional two circularcylinders in tandem arrangements.Journal of ChongqingUniversity,2009,32(8):943-949.(in Chinese)赵良举,杨南奇,吴朵,等.横掠二维串列双圆柱绕流气动噪声的数值模拟.重庆大学学报,2009,32(8):943-949.
[10]Tang K F,Franke J.Numerical simulation of noise in-duced by flow around cylinder using the hybrid methodwith the solutions of NS equation and FW-H integration.Chinese Journal of Hydrodynamics,2009,24(2):190-199.(in Chinese)唐科范,Franke J.用解NS方程和FW-H积分的混合方法计算圆柱绕流噪声.水动力学研究与进展A辑,2009,24(2):190-199.
[11]Fei B L,Zheng T H,Yang J L.Numerical simulation offlow over two tandem cylinders.Journal of SouthwestUniversity for Nationalities.Natural Science Edition,2007,33(2):376-380.(in Chinese)费宝玲,郑庭辉,杨骏六.数值分析串列双圆柱绕流.西南民族大学学报.自然科学版,2007,33(2):376-380.
[12]Yu L,Song W P.Application of hybrid method for aero-dynamic noise prediction.The Sixth Intermational Confer-ence on Fluid Mechanics,2011:375-378.
[13]Lin D K,Li X D,Hu F Q.Perfectly matched layerboundary conditions using in DNS of flow around cylinder.Journal of Engineering Thermophysics,2010,31(5):757-760.(in Chinese)林大楷,李晓东,胡方强.完全耦合层边界条件在圆柱绕流DNS中的应用.工程热物理学报,2010,31(5):757-760.
[14]Zhang Z S,Cui G X,Xu C X.Theory and application oflarge eddy numerical simulation for turbulence.Beijing:Tsinghua University Press,2008:263.(in Chinese)张兆顺,崔桂香,许春晓.湍流大涡数值模拟的理论和应用.北京:清华大学出版社,2008:263.
[15]QuéméréP,Sagaut P.Zonal multi-domain RANS/LESsimulations of turbulent flows.International Journal forNumerical Methods in Fluids,2002,40(7):903-925.
[16]Labourasse E,Sagaut P.Reconstruction of turbulent fluc-tuations using a hybrid RANS/LES approach.Journal ofComputational Physics,2002,182(1):301-336.
[17]Batten P,Goldberg U,Chakravarthy S.Sub-grid turbu-lence modeling for unsteady flow with acoustic resonance.AIAA-2000-473,2000.
[18]Batten P,Goldberg U,Chakravarthy S.Reconstructedsub-grid methods for acoustics predictions at all Reynoldsnumbers.AIAA-2002-2511,2002.
[19]Batten P,Ribaldone E,Casella M,et al.Towards a gen-eralized non-linear acoustics solver.AIAA-2004-3001,2004.
[20]Han Z H,Song W P,Qiao Z D.Aeroacoustic calculationfor helicopter rotor in hover and in forward flight based onFW-H equation.Acta Aeronautica et Astronautica Sinica,2003,24(5):400-404.(in Chinese)韩忠华,宋文萍,乔志德.基于FW-H方程的旋翼气动声学计算研究.航空学报,2003,24(5):400-404.
[21]Speziale C G.Computing non-equilibrium turbulent flowswith time-dependent RANS and VLES.Lecture Notes inPhysics,1997,490:123-129.
[22]Wagner C A,Hüttl T,Sagaut P.Large-eddy simulationfor acoustics.London:Cambridge University Press,2007:441.
[23]Ffowcs Williams J E,Hawkings D L.Sound generation byturbulence and surfaces in arbitrary motion.PhilosophicalTransactions of the Royal Society of London.Series A,Mathematical and Physical Sciences,1969,264(1151):321-342.
[24]Yu L,Song W P,Yan L.An effective method for predic-ting aerodynamic noise for wind turbine flatback airfoils.Journal of Northwestern Polytechnical University,2012,30(4):513-517.(in Chinese)余雷,宋文萍,闫利.平底后缘风力机翼型气动噪声计算研究.西北工业大学学报,2012,30(4):513-517.
[25]Kato C,Iida A,Takano Y,et al.Numerical prediction ofaerodynamic noise radiated from low Mach number turbu-lent wake.AIAA-1993-145,1993.
[26]Bres G A,Wessels M,Noelting S.Tandem cylinder noisepredictions using lattice Boltzmann and Ffowcs Williams-Hawkings methods.AIAA-2010-3791,2010.