The diffuselet concept for scalar mixing
The diffuselet concept for scalar mixing
复制标题
标量混合的扩散概念
DOI：
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发表时间：
2022
影响因子：
3.7
通讯作者：
E. Villermaux
中科院分区：
文献类型：
--
作者：
P. Meunier;E. Villermaux
摘要：本文利用Ranz变换解析求解了标量小曲面元在三维（或二维）中的平流扩散问题（Ranz, AIChE J., vol. 25, issue 1, 1979, pp. 41-47）。作为任何复杂混合物的量子或基本块，我们称这种元素为扩散波。它的演化是由沿轨迹的速度梯度的积分来计算的，就像经典的李雅普诺夫指数一样。扩散波的浓度分布是由扩散波的初始方向与无量纲张量的乘积得到的。对所有初始方向进行平均可以得到标量均值方差和标量概率分布函数（p.d.f）的简单公式。然后将该技术应用于二维和三维正弦流，与直接数值模拟非常吻合。对于这些简单的流动，通过解析得到时间积分，得到标量方差和p.d.f的简单积分，并计算了拉伸率的统计数据。Lyapunov指数接近于短时相关流动的值(Kraichnan， J.流体力学。， vol. 64, issue 4, 1974, pp. 737-762)在每一步小位移的情况下；它接近于大位移情况下的简单剪切值。拉伸因子的p.d.f.为对数正态，对于小位移，平均值与方差之比等于空间维数的一半（与Kraichnan， J.流体力学一致）。，第64卷，第4期，1974年，第737-762页)，但增加强烈的大位移。
Abstract The advection–diffusion of a small surface element of scalar in three dimensions (or of a small line element in two dimensions) is solved analytically thanks to the Ranz transform (Ranz, AIChE J., vol. 25, issue 1, 1979, pp. 41–47). As the quantum or elementary brick of any complex mixture, we call this element a diffuselet. Its evolution is computed numerically from the integration of the velocity gradient along the trajectory, as classically done for the Lyapunov exponents. The concentration profile across the diffuselet is obtained from the product of its initial orientation with a dimensionless tensor. Averaging over all initial orientations yields simple formulae for the mean scalar variance and the scalar probability distribution function (p.d.f.). This technique is then applied to two-dimensional and three-dimensional sine flows, in excellent agreement with direct numerical simulations. For these simple flows, the temporal integration is obtained analytically leading to simple integrals for the scalar variance and p.d.f. Statistics of stretching rates are calculated as well. The Lyapunov exponent is close to the value for short-time correlated flows (Kraichnan, J. Fluid Mech., vol. 64, issue 4, 1974, pp. 737–762) in the case of a small displacement during each step; it is close to the value for a simple shear in the case of a large displacement. The p.d.f. of stretching factors are log normal with a ratio between the mean and the variance equal to half the dimension of space for small displacements (in agreement with Kraichnan, J. Fluid Mech., vol. 64, issue 4, 1974, pp. 737–762), but increases strongly for large displacements.
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影响因子：
3.7
作者：
D. Martínez-Ruiz;P. Meunier;B. Favier;L. Duchemin;E. Villermaux
通讯作者：
E. Villermaux
影响因子：
2.7
作者：
de Rivas, A.;Villermaux, E.
通讯作者：
Villermaux, E.
多孔介质中的标量混合物
DOI：
10.1103/physrevfluids.2.104502
发表时间：
2017
期刊：
影响因子：
--
作者：
M. Kree;E. Villermaux
通讯作者：
E. Villermaux
关于形状和形式：波纹搅拌锋的群体平衡动力学
影响因子：
1.4
作者：
E. Villermaux
通讯作者：
E. Villermaux