Inertial effects in three-dimensional spinodal decomposition of a symmetric binary fluid mixture: a lattice Boltzmann study
Inertial effects in three-dimensional spinodal decomposition of a symmetric binary fluid mixture: a lattice Boltzmann study
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DOI：
10.1017/s0022112001004682
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发表时间：
2001-08-10
影响因子：
3.7
通讯作者：
Bladon, P
中科院分区：
文献类型：
--
作者：
Kendon, VM;Cates, ME;Bladon, P
使用热力学一致的格子玻尔兹曼方法，对三维对称二元流体混合物旋节线分解后的后期分层进行了数值研究。我们将模拟结果与不同的数值参数相结合，以简化的物理单位表示时，获得前所未有的长度和时间尺度范围。 （这些是从流体密度、粘度和界面张力导出的长度和时间单位。）使用八个大型 (256(3)) 运行，所得的减小的域尺寸 I 与减小的时间 t 的复合图涵盖 1 小于或类似 l 小于或类似 10(5)、10(5)、10 小于或类似 t 小于或类似 10(8)。我们的数据与动态标度假设一致，即 1(t) 是通用标度曲线。在此类模拟中，我们首次对流体运动进行了详细的统计分析，而不仅仅是域演化，并引入了从流体速度和速度梯度场导出的几个量的比例图。使用该问题的雷诺数的传统定义，Re-phi = l dl/dt，我们获得接近 350 的值。在 Re-phi 大于或等于 100（这需要 t 大于或等于 10(6)）时，我们发现了古河惯性标度的明确证据（l 类似于 t(2/3)），尽管与粘性状态（l 类似于 t）的交叉既广泛又晚(10(2)小于或近似于t小于或近似于10(6))。尽管不能排除这种可能性，但我们没有发现任何迹象表明 Reo 在后期具有自限性（l 小于或类似于 t(1/2)），正如 Grant & Elder 最近提出的那样。对速度场的详细研究证实，对于大多数惯性运行，纳维-斯托克斯方程 R-2 中非线性项与粘性项的 RMS 比为 10 阶，流体混合物显示出初期湍流特征。然而，我们无法深入到惯性体系中来获得域大小、泰勒微尺度和柯尔莫哥洛夫尺度的清晰长度分离，而这是测试 Kendon 最近的“扩展”尺度理论（其中 R2 是自限制的，但 Re-phi 不是）所需要的。获得我们的结果需要仔细控制几个数控参数，以保持足够的算法稳定性、效率和各向同性，同时消除不需要的残余扩散。 （我们认为后者影响了文献中的一些研究，这些研究报告 l 与 t(2/3) 相似，而 t 小于或类似于 10(4)。）我们分析了各种误差源，发现它们在大多数数据集中都在可接受的水平内（每个误差几个百分点）。为了使这些受到更好的控制，或者进一步进入惯性状态，将需要更大的计算资源和/或算法设计方面的突破。
The late-stage demixing following spinodal decomposition of a three-dimensional symmetric binary fluid mixture is studied numerically, using a thermodynamically consistent lattice Boltzmann method. We combine results from simulations with different numerical parameters to obtain an unprecedented range of length and time scales when expressed in reduced physical units. (These are the length and time units derived from fluid density, viscosity, and interfacial tension.) Using eight large (256(3)) runs, the resulting composite graph of reduced domain size I against reduced time t covers 1 less than or similar to l less than or similar to 10(5), 10(5), 10 less than or similar to t less than or similar to 10(8). Our data are consistent with the dynamical scaling hypothesis that 1(t) is a universal scaling curve. We give the first detailed statistical analysis of fluid motion, rather than just domain evolution, in simulations of this kind, and introduce scaling plots for several quantities derived from the fluid velocity and velocity gradient fields. Using the conventional definition of Reynolds number for this problem, Re-phi = l dl/dt, we attain values approaching 350. At Re-phi greater than or equal to 100 (which requires t greater than or equal to 10(6)) we find clear evidence of Furukawa's inertial scaling (l similar to t(2/3)), although the crossover from the viscous regime (l similar to t) is both broad and late (10(2) less than or similar to t less than or similar to 10(6)). Though it cannot be ruled out, we find no indication that Reo is self-limiting (l less than or similar to t(1/2)) at late times, as recently proposed by Grant & Elder. Detailed study of the velocity fields confirms that, for our most inertial runs, the RMS ratio of nonlinear to viscous terms in the Navier-Stokes equation, R-2, is of order 10, with the fluid mixture showing incipient turbulent characteristics. However, we cannot go far enough into the inertial regime to obtain a clear length separation of domain size, Taylor microscale, and Kolmogorov scale, as would be needed to test a recent 'extended' scaling theory of Kendon (in which R2 is self-limiting but Re-phi not). Obtaining our results has required careful steering of several numerical control parameters so as to maintain adequate algorithmic stability, efficiency and isotropy, while eliminating unwanted residual diffusion. (We argue that the latter affects some studies in the literature which report l similar to t(2/3) for t less than or similar to 10(4).) We analyse the various sources of error and find them just within acceptable levels (a few percent each) in most of our datasets. To bring these under significantly better control, or to go much further into the inertial regime, would require much larger computational resources and/or a breakthrough in algorithm design.