The diffusive sheet method for scalar mixing
The diffusive sheet method for scalar mixing
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标量混合的扩散片法
DOI：
10.1017/jfm.2017.862
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发表时间：
2018
影响因子：
3.7
通讯作者：
E. Villermaux
中科院分区：
文献类型：
--
作者：
D. Martínez-Ruiz;P. Meunier;B. Favier;L. Duchemin;E. Villermaux
扩散条法(DSM)是一种用于混合计算的近似精确的数值方法，最初是在二维发展起来的(Meunier&Villermaux，J.《流体力学》，第662卷，2010，第134-172页)。该方法包括沿拉伸的物质线后验地计算所得到的标量场，这里将其推广到三维流动。我们描述了这一过程及其三维特性，它依赖于三角化曲面的拉格朗日平流，从中提取伸缩率来推断标量场。该方法首先在中等Péclet数下与求解Batchelor涡的对流扩散方程的经典拟谱方法进行了比较，然后将该方法应用于一种简单的Taylor-Couette实验构型，该构型在顶端圆盘、底端圆盘和外圆柱处具有非旋转边界条件。这一运动产生了一种精细但可控的稳定三维流动，依赖于内筒旋转产生的埃克曼泵。在层流条件下，循环的两室结构被水平中面分开，并由呈嵌套环状的流管形成。流动中的标量斑点经历拉格朗日振荡动力学，经历拉伸和压缩，驱动混合过程。DSM可以通过沿平流斑点表面的单变量计算来计算斑点伸长和标量浓度分布，捕捉到在实验中观察到的丰富的演化。有趣的是，在这种轴对称和稳定的三维流动中的混合过程导致了表面在时间上的线性增长，类似于在二维剪切中得到的结果。最后讨论了该方法在更一般流动中的潜力、局限性和推广。
The diffusive strip method (DSM) is a near-exact numerical method for mixing computations initially developed in two dimensions (Meunier & Villermaux, J. Fluid Mech., vol. 662, 2010, pp. 134–172). The method, which consists of following stretched material lines to compute the resulting scalar field a posteriori, is extended here to three-dimensional flows. We describe the procedure and its three-dimensional peculiarity, which relies on the Lagrangian advection of a triangulated surface from which the stretching rate is extracted to infer the scalar field. The method is first validated at moderate Péclet number against a classical pseudospectral method solving the advection–diffusion equation for a Batchelor vortex, and then applied to a simple Taylor–Couette experimental configuration with non-rotating boundary conditions at the top-end disk, bottom-end disk and outer cylinder. This motion, producing an elaborate although controlled steady three-dimensional flow, relies on Ekman pumping arising from the rotation of the inner cylinder. A recurrent two-cell structure is separated by the horizontal mid-plane and formed by stream tubes shaped as nested tori under laminar flow conditions. A scalar blob in the flow experiences a Lagrangian oscillating dynamics undergoing stretchings and compressions, driving the mixing process. The DSM enables the calculation of the blob elongation and scalar concentration distributions through a single variable computation along the advected blob surface, capturing the rich evolution observed in the experiments. Interestingly, the mixing process in this axisymmetric and steady three-dimensional flow leads to a linear growth of surfaces in time similar to the one obtained in a two-dimensional shear. The potentialities, limits and extension of the method to more general flows are finally discussed.
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拉伸模型在层流和湍流中的混合、扩散和反应中的应用
DOI：
--
发表时间：
1979
期刊：
影响因子：
--
作者：
W. Ranz
通讯作者：
W. Ranz
影响因子：
3.7
作者：
P. Meunier;E. Villermaux
通讯作者：
E. Villermaux
影响因子：
4.6
作者：
P. Yeung;D. Donzis;K. Sreenivasan
通讯作者：
P. Yeung;D. Donzis;K. Sreenivasan
影响因子：
2.7
作者：
de Rivas, A.;Villermaux, E.
通讯作者：
Villermaux, E.
各向同性湍流中材料表面的拉伸率
DOI：
--
发表时间：
2002
期刊：
Proc.9th.Euro.Turb.Conf.
影响因子：
--
作者：
S.Goto;S.Kida
通讯作者：
S.Kida