可压缩湍流的多尺度分析

Multi-scale analyses of compressible turbulence

作者的研究团队近几年在可压缩湍流的多尺度性质方面开展了系统的研究工作。通过多过程分解,研究了可压缩湍流中的速度和热力学量的剪切部分、胀压部分、伪声模态、声模态、熵模态的多尺度性质,并总结了各类可压缩条件下的速度和热力学量的谱的标度律。通过滤波方法,研究了动能和热力学量的多尺度传输现象,并重点分析了可压缩性对动能胀压部分的多尺度传输的影响。在可压缩均匀剪切湍流中,可压缩效应更加明显,可压缩湍动能和耗散率等物理量的马赫数标度率与各向同性湍流类似,但胀压分量所占比重更大,并且变形速度张量特征值的概率密度函数和流动拓扑结构的比例分布等统计量随马赫数的变化也更加明显。对于振动非平衡可压缩各向同性湍流,平动-转动内能模式和振动内能模式间的弛豫效应导致密度梯度与振动温度梯度方向的偏离,从而弱化了流场中压缩和膨胀运动对振动弛豫率的影响。化学反应放热会显著增加流场的压缩与膨胀运动,导致速度胀压分量和热力学量的能谱在所有尺度均增大,湍动能和耗散率的标度律表现出马赫数无关性。

Some recent studies on multi-scale properties of compressible turbulence conducted by the authors’group are reviewed.By multi-process decomposition methods,multi-scale properties of the solenoidal component,the dilatational component,the pseudo-sound mode,the acoustic mode,and the entropy modes of velocity and thermodynamic variables in compressible turbulence are studied.In addition,the scaling behaviors of spectra of velocity and thermodynamic variables in various situations of different compressibility are summarized.Interscale transfers of kinetic energy and thermodynamic variables are studied by filtering method,with the emphasis on the effects of compressibility on the inter-scale transfer of the dilatational component of kinetic energy.The compressible effects are stronger in compressible homogeneous shear turbulence.Mach number scaling behaviors of compressible kinetic energy and compressible dissipation rate are similar but have larger magnitudes as compared to those in compressible homogeneous isotropic turbulence.Distributions of eigenvalues of the strain rate tensor and the local flow topologies are more sensitive to the change of turbulent Mach number.For compressible isotropic turbulence in vibrational nonequilibrium,the vibrational relaxation between the translational-rotational and vibrational modes of internal energy results in the deviation between gradients of density and vibrational temperature,which further weakens the effect of compressibility on vibrational rate.Heat release through chemical reactions can greatly enhance compression and expansion motions and result in the increase of spectra of dilatational velocity components and thermodynamic variables at all length scales.The kinetic energy and its dissipation appear to be independent of the turbulent Mach number.