On the computation of space-time correlations by large-eddy simulation

The effect of subgrid-scale (SGS) modeling on velocity (space-) time correlations is investigated in decaying isotropic turbulence. The performance of several SGS models is evaluated, which shows superiority of the dynamic Smagorinsky model used in conjunction with the multiscale large-eddy simulation (LES) procedure. Compared to the results of direct numerical simulation, LES is shown to underpredict the (un-normalized) correlation magnitude and slightly overpredict the decorrelation time scales. This can lead to inaccurate solutions in applications such as aeroacoustics. The underprediction of correlation functions is particularly severe for higher wavenumber modes which are swept by the most energetic modes. The classic sweeping hypothesis for stationary turbulence is generalized for decaying turbulence and used to analyze the observed discrepancies. Based on this analysis, the time correlations are determined by the wavenumber energy spectra and the sweeping velocity, which is the square root of the total energy. Hence, an accurate prediction of the instantaneous energy spectra is most critical to the accurate computation of time correlations. (C) 2004 American Institute of Physics.

可压缩流气动声场的数值模拟

气动声学是一门流动力学和声学之间的交叉学科，主要研究流动及其与物体相互作用产生噪声的机理。动用计算技术研究气动声学问题的手段称为计算气动声学。本文的目的是，基于高精度数值算法的研究，分别运用Lighthill比拟理论、Kirchhoff积分和直接数值模拟等方法，针对翼型绕流、激波-涡干扰和轴对称射流，研究了物面非定常脉动压力、涡脱落、激波-涡干扰以及涡对并等产生噪声的机理。首先针对声场与主流场在能级和特征尺度等方面的差异，从空间离散角度分析了几种差分格式，表明迎风紧致格式/对称紧致格式有较小的数值色散、耗散和各向异性误差，因而适用于气动噪声的计算。以Runge-Kutta格式为例，对时间离散带来的误差进行了分析。指出对声波计算来说，仅考虑格式稳定性是不够的，时间步长还受到允许色散误差和耗散误差的限制。基于保色戎关系的思想，构造了优化Runge-Kutta格式。处例显示优化Runge-Kutta格式相对于经典格式有更高的计算效率。采用3阶迎风紧致格式和3阶Runge-Kutta格式数值模拟了NACA0012翼型的可压缩非定常绕流流场，并将此流场作为近场声源，运用声学比拟理论对偶极子声和四极子声进行研究。结果指出，主流速度对远场声压有决定性影响，在来流马赫数较大时，四极子噪声和偶极子噪声具有相同量级，不能被忽略，表明了可压缩效应对声场的影响。采用5阶迎风紧致格式和4阶Runge-Kutta格式求解非定常可压缩Navier-Stokes方程，对激波-单涡/双涡干扰导致的声场进行了直接数值模拟。详细研究了激波-涡干扰产生噪声的机理，指出噪声的产生及其性质和激波变形密切相关。研究了近场噪声衰减和传播距离r的关系，发现噪声衰减大致和r~(4/5)而不是r~(1/2)成反比关系，提出这种差异是由流场的非线性效应引起的。构造了Kirchhoff积分和非定常流动计算相结合的算法。采用5阶迎风紧致格式和3阶Runge-Kutta格式对亚声速轴对称射流进行直接数值模拟。将射流流场作为近场声源，结合Kirchhoff方法求解远场 气动噪声。数值结果表明远场噪声具有方向性，噪声声压在离开对称轴20°处达到最大值。随着传播距离增大，噪声方向性逐渐减弱。