图  1  剪切力驱动的弱可压缩湍流中，速度的胀压部分的谱

Figure  1.  Spectrum of dilatational velocity in weakly compressible turbulence driven by solenoidal force

图  2  剪切力驱动的强可压缩湍流中，速度的胀压部分的谱

Figure  2.  Spectrum of dilatational velocity in highly compressible turbulence driven by solenoidal force

图  3  剪切力和胀压力同时驱动的可压缩湍流中，速度的胀压部分的谱

Figure  3.  Spectrum of dilatational velocity in compressible turbulence driven by both solenoidal and dilatational forces

图  4  剪切力驱动、有热源的可压缩湍流中，速度的胀压部分的谱

Figure  4.  Spectrum of dilatational velocity in compressible turbulence driven by solenoidal force and heat source

图  5  (a) 动能传输项之和(实线)、亚格子动能流量(虚线)和黏性耗散(点划线)；(b)压力做功

Figure  5.  (a) Sum of kinetic energy transfer terms (solid line), SGS kinetic energy flux (dashed line), and viscous dissipation (dash-dotted line); (b) Pressure work

图  6  胀压部分动能的传输项

Figure  6.  Dilatational kinetic energy transfer terms

图  7  温度脉动的亚格子流量、胀压项、热扩散和黏性耗散项以及各项之和

Figure  7.  Transfer terms of temperature fluctuations

图  8  熵的脉动的亚格子流量、胀压项、热扩散和黏性耗散项以及各项之和

Figure  8.  Transfer terms of entropy fluctuations

图  9  无量纲的可压缩湍动能K^d/K^S和可压缩耗散率ε^d/ε^S随湍流马赫数的变化^[51]

Figure  9.  Normalized compressible kinetic energy K^d/K^S and compressible dissipation rate ε^d/ε^S as a function of M_t^[51]

图  10  无量纲的压力、密度和温度的均方根值随湍流马赫数的变化^[51]

Figure  10.  Normalized r.m.s. values of pressure, density, and temperature at different turbulent Mach numbers and Taylor Reynolds numbers^[51]

图  11  变形速度张量S_ij三个特征值β_k(k=1, 2, 3) 的概率分布和条件概率密度分布^[52]

Figure  11.  The PDFs and conditional PDFs of β_k(k=1, 2, 3) of the strain rate tensor S_ij at M_t≈0.6^[52]

图  12  变形速度张量度第二、第三不变量的联合概率密度分布函数对数lgPDF(R^*, Q^*)的等值线.红线表示各向同性湍流的结果，黑线表示均匀剪切湍流的结果

Figure  12.  Iso-contours lines of lgPDF(R^*, Q^*) in strong compression regions. Black and red lines represent for homogeneous shear turbulence and red line for homogeneous isotropic turbulence, respectively

图  13  振动能级被激发的双原子分子气体内能模式与热非平衡态概念示意图。振动能级被激发情况下，根据振动弛豫时间与特征流动时间尺度的比值，可划分为振动平衡态和振动非平衡态, 在振动非平衡态下，比热比是温度的函数(≠ 1.4)。

Figure  13.  A schematic overview of the internal energy modes for a diatomic molecule with and without vibrational excitation, as well as thermal nonequilibrium. With vibrational excitation, the ratio of specific heat is a function of temperature.

图  14  瞬时的等值面图

Figure  14.  Instantaneous iso-surfaces

图  15  振动温度和密度梯度间夹角cosine函数值的概率分布函数

Figure  15.  PDFs of the cosine functions of angle between gradients of the vibrational temperature and density

图  16  归一化振动弛豫率的条件平均振动弛豫时间的影响、振动特征温度的影响

Figure  16.  Conditioned average of normalized vibrational rate: Relaxation time effect; Characteristic temperature effect

图  17  等温反应与放热反应中流场瞬时速度散度云图，Re_λ≈160，M_t=0.2

Figure  17.  Instantaneous contour of velocity divergence for isother-mal and exothermal reactions at Re_λ≈160 and M_t=0.2

图  18  密度归一化能谱在放热反应中(Da=200, Ze=8, Ce=3.168)随无量纲化学反应时间t/τ的变化，Re_λ≈100

Figure  18.  The temporal variation of compensated spectrum of density for exothermal reaction (Da=200, Ze=8, Ce=3.168)at Re_λ≈100

图  19  速度胀压分量归一化能谱在放热反应中(Da=200, Ze=8, Ce=3.168)随无量纲化学反应时间t/τ的变化，Re_λ≈100

Figure  19.  The temporal variation of compensated spectrum of dilatational velocity component for exothermal reaction (Da=200, Ze=8, Ce=3.168) at Re_λ≈100

图  20  等温反应和放热反应中，动能胀压部分与剪切部分比值以及动能耗散胀压部分与剪切部分比值随湍流马赫数的变化

Figure  20.  The ratio of dilatational to solenoidal kinetic energy and the ratio of dilatational component to solenoidal component of kinetic energy dissipation for isothermal and exothermal reactions