A fast Eulerian method for disperse two-phase flow
A fast Eulerian method for disperse two-phase flow
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DOI：
10.1016/s0301-9322(00)00069-0
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发表时间：
2001-07-01
影响因子：
3.8
通讯作者：
Balachandar, S
中科院分区：
文献类型：
--
作者：
Ferry, J;Balachandar, S
我们提出了一个变种的欧拉方法的两相流是有效的小颗粒的响应时间τ。对于小的τ，粒子速度保持v（x，t）接近唯一的平衡场，与初始条件无关。一个精确的不等式推导出指定如何小，我必须为这种情况发生。当它这样做时，v（x，t）仅取决于局部流体量（速度及其空间和时间导数），并且可以表示为τ的展开。我们得到一个扩展，概括了以前的研究人员。这种展开的一阶截断可以有效地计算，因此通过使用它来近似v，该方法避免了求解额外的偏微分方程的需要，因此比标准欧拉方法快得多。槽道湍流的直接数值模拟结果表明，这种一阶近似的v是足够准确的。在一个时刻进行的静态测试表明，在拉格朗日方式演变的粒子的实际速度估计以及通过评估的一阶近似的v在粒子的位置。特别是，浊度电泳被准确地表示。动态测试检查使用v的一阶近似来演化粒子的效果。以这种方式演化的粒子的分布与使用标准拉格朗日方法演化的粒子的分布几乎没有区别，这表明静态误差不会随着时间的推移而积累。特别是，近似的方法准确地捕捉优先集中在高应变和低涡度的区域。类似的结果也适用于气泡。因此，对于任何密度的足够小的粒子，对v的一阶近似是准确的，因此所提出的欧拉方法的变体既准确又快速。(C)2001爱思唯尔科技有限公司版权所有。
We propose a variant of the Eulerian method for two-phase flow that is valid for small particle response time tau. For small tau, the particle velocity held v(x, t) approaches a unique, equilibrium field, independent of initial conditions. A precise inequality is derived specifying how small I must be for this to occur. When it does, v(x, t) depends only on local fluid quantities (velocity and its spatial and temporal derivatives), and may be expressed as an expansion in tau. We derive an expansion which generalizes those of previous researchers. The first-order truncation of this expansion may be computed efficiently, so by using it to approximate v, the method avoids the need to solve additional partial differential equations, and therefore is much faster than the standard Eulerian method. Results from a direct numerical simulation of turbulent channel flow indicate that this first-order approximation of v is sufficiently accurate. Static tests performed at one time-instance show the actual velocities of particles evolved in a Lagrangian fashion are estimated well by evaluating the first-order approximation of v at the particles' positions. In particular, turbophoresis is represented accurately. Dynamic tests examine the effect of using the first-order approximation of v to evolve particles. The distribution of particles evolved in this way differs little from that of particles evolved using the standard Lagrangian method, indicating that static errors do not accumulate over time. In particular, the approximate method accurately captures preferential concentration in regions of high strain and low vorticity. Analogous results hold for bubbles. Therefore, for sufficiently small particles of any density, the first-order approximation to v is accurate, so the proposed variant of the Eulerian method is both accurate and fast. (C) 2001 Elsevier Science Ltd. All rights reserved.