Mixed velocity–passive scalar statistics in high-Reynolds-number turbulence
Mixed velocity–passive scalar statistics in high-Reynolds-number turbulence
复制标题
高雷诺数湍流中的混合速度-被动标量统计
DOI：
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发表时间：
2003
影响因子：
3.7
通讯作者：
L. Mydlarski
中科院分区：
文献类型：
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作者：
L. Mydlarski
研究了具有平均温度梯度的准各向同性衰减网格湍流中，混合速度被动标量场的统计特性及其与雷诺数的关系。湍流雷诺数(使用泰勒微尺度作为长度尺度)Rλ在85[LES]Rλ[LES]582.正在考虑的被动标量是空气中的温度。湍流是通过活动网格产生的，而温度起伏是湍流对平均温度梯度的作用造成的。后者是通过对风洞真空室入口处的元件进行差动加热而产生的。速度被动混合标量场随着雷诺数的增加而缓慢演化。横向速度和温度共谱的惯性标度指数EVθ(K1)和它的真实空间模拟‘热流结构函数’<Δv(R)Δθ(R)>分别向−7/3和4/3的理论预测缓慢演化。六阶纵向混合结构函数<(Δu(R))2(Δθ(R))4>表现出1.36-1.52的惯性范围结构函数指数。然而，对于用于估计标度指数的各种方法、标量间歇指数μθ的值以及大尺度现象(即<θ2>的剪切、衰变和湍流产生)对<(Δu(R))2(Δθ(R))4>的影响，仍然存在分歧。在局部各向同性流动中，所有测量的细尺度统计量都必须为零，或者在大雷诺数的极限下趋向于零。Δv(R)Δθ(R)的概率密度函数(PDF)在大间隔时呈现近似指数尾，在小间隔时呈现超指数尾，从而显示出内部间歇性的影响。随着雷诺数的增加，PDF在最小尺度上变得对称--符合局部各向同性。以标量脉动为条件的横向速度脉动的期望值对于所有雷诺数都是线性的，斜率等于v与θ之间的相关系数。当以横向速度涨落为条件时，标量拉普拉斯量的期望(替代)表现出雷诺数的依赖关系(但当以标量涨落为条件时则不表现出这种依赖关系)。这种以前的雷诺数依赖性与泰勒的扩散独立性假设是一致的。最后，对于测量的统计量，没有观察到局部各向同性的破坏。
Statistics of the mixed velocity–passive scalar field and its Reynolds number dependence are studied in quasi-isotropic decaying grid turbulence with an imposed mean temperature gradient. The turbulent Reynolds number (using the Taylor microscale as the length scale), Rλ, is varied over the range 85 [les ] Rλ [les ] 582. The passive scalar under consideration is temperature in air. The turbulence is generated by means of an active grid and the temperature fluctuations result from the action of the turbulence on the mean temperature gradient. The latter is created by differentially heating elements at the entrance to the wind tunnel plenum chamber. The mixed velocity–passive scalar field evolves slowly with Reynolds number. Inertial-range scaling exponents of the co-spectra of transverse velocity and temperature, Evθ(k1), and its real-space analogue, the ‘heat flux structure function,’ 〈Δv(r)Δθ(r)〉, show a slow evolution towards their theoretical predictions of −7/3 and 4/3, respectively. The sixth-order longitudinal mixed structure functions, 〈(Δu(r))2(Δθ(r))4〉, exhibit inertial-range structure function exponents of 1.36–1.52. However, discrepancies still exist with respect to the various methods used to estimate the scaling exponents, the value of the scalar intermittency exponent, μθ, and the effects of large-scale phenomena (namely shear, decay and turbulent production of 〈θ2〉) on 〈(Δu(r))2(Δθ(r))4〉. All the measured fine-scale statistics required to be zero in a locally isotropic flow are, or tend towards, zero in the limit of large Reynolds numbers. The probability density functions (PDFs) of Δv(r)Δθ(r) exhibit roughly exponential tails for large separations and super-exponential tails for small separations, thus displaying the effects of internal intermittency. As the Reynolds number increases, the PDFs become symmetric at the smallest scales – in accordance with local isotropy. The expectation of the transverse velocity fluctuation conditioned on the scalar fluctuation is linear for all Reynolds numbers, with slope equal to the correlation coefficient between v and θ. The expectation of (a surrogate of) the Laplacian of the scalar reveals a Reynolds number dependence when conditioned on the transverse velocity fluctuation (but displays no such dependence when conditioned on the scalar fluctuation). This former Reynolds number dependence is consistent with Taylor’s diffusivity independence hypothesis. Lastly, for the statistics measured, no violations of local isotropy were observed.