Multiphase Laminar Flow with More Than Two Phases
Multiphase Laminar Flow with More Than Two Phases
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两相以上的多相层流
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发表时间：
2015
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通讯作者：
W. Vetterling
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作者：
W. Vetterling
COMSOL Multiphysics®软件及其CFD模块具有一个物理界面，可使用Level Set方法求解层流两相流问题（1）。本文讨论了如何使用的工具时，流动是层流两个以上的阶段。然后介绍了解决这类问题的第二种方法。COMSOL Multiphysics的使用COMSOL软件中的层流两相流水平集界面使用平滑辅助函数0≤ λ（r，t）≤1，λ = 0. 5水平集将模型几何体划分为包含两种流体相的区域。求解器被提供有原始流体配置，用于构造初始函数f（r，t0）。然后，使用Navier-Stokes方程计算流体速度u，并将微分方程应用于ε（r，t），使得其ε =0.5水平集正确地跟踪流体边界。一个无初始化的方案（2，3）已被用于改善稳定性和质量守恒。该方法可以推广到三种或三种以上的流体，通过使用多个实例的两流体界面。每个实例对应于N ≥ 3个流体中的一个，尽管其中一个流体（表示为j=0）不需要一个。因此，N-1个界面代表N种流体。每个界面模拟两种流体。第一个是对应于界面的流体j，并由Δ j（r，t）跟踪。另一种是所有剩余流体的混合物。复合流体的密度ρ和粘度ν是使用来自其他界面的辅助函数计算的，使得流体中的每个点具有正确的性质。所有接口共享相同的压力和速度，并通过辅助功能耦合。另一种追踪流体的方法是将稀释物质的浓度cj（初始设定为某个方便的值，如cj=1[M/m^3 ]）纳入N-1个流体中。这些N-1种物质由COMSOL软件中的单个稀释物质传输界面提供。在这种情况下，使用单个纳维尔-斯托克斯层流模型，并且存在单个复合流体。该流体的密度和粘度是根据稀释物质浓度的阈值计算的，其揭示了在每个位置处存在哪种流体。结果通过一个受COMSOL应用程序库模型启发的油滴在水中上升的问题说明了该方法。在修改后的模型中，有两个液滴，ρ1=0.6[g/（cm^3）]和ρ2=0.8[g/（cm^3）]（见图1）。下面的液滴上升得更快，在到达表面之前超过上面的液滴。表面张力不包括在内。图2和图3显示了0.3秒后两次模拟的结果。图2是使用两个层流两相流、水平集界面获得的，并且该图显示了表示两个液滴的水平集函数的Δ（r，t）=0.5的轮廓。图3是使用两种稀释物质浓度cj得到的，显示了cj=0.5[M/m^3 ]的等值线。结论我们已经证明了两种方法来解决层流多相流体动力学问题的两种流体。两者都提供了类似的结果，但目前只有水平设置版本实现了表面张力。参考文献1. Sethian，J. A.，水平集方法和快速推进方法：计算几何、计算机视觉和材料科学中的界面演化，剑桥应用和计算数学专著，剑桥大学出版社，纽约，纽约（1999年）。2. Chunming Li等人，水平集进化无重映射：一种新的变分公式，2005年IEEE计算机协会计算机视觉和模式识别会议论文集，第1卷，第110页。430-436（2005）。3. Chunming Li等人，Distance Regularized Level Set Evolution and its Application to Image Segmentation，IEEE Trans. On Image Processing，2009，No. 12，pp. 3243-3254（2010年）。图1：两个不同的液滴悬浮在第三种流体中的测试问题。图2：t=0.3秒时测试问题的水平集解决方案。尺寸单位为cm。图3：t=0.3秒时试验问题的稀释物质溶液。尺寸单位为cm。
Introduction The COMSOL Multiphysics® software and its CFD Module have a physics interface for solving Laminar Two-Phase Flow problems using the Level Set method (1). This paper discusses how the tool may be used with more than two phases when the flow is laminar. It then introduces a second method for solving such problems. Use of COMSOL Multiphysics The Laminar Two-Phase Flow, Level Set interface in the COMSOL software uses a smooth auxiliary function 0≤ξ(r,t)≤1 with a ξ=0.5 level-set dividing the model geometry into regions containing each of two fluid phases. The solver is provided with an original fluid configuration for use in constructing the initial function ξ(r,t0). The Navier-Stokes equation is then used to compute fluid velocity u and a differential equation is applied to ξ(r,t) so that its ξ=0.5 level-set properly tracks the fluid boundaries. An initialization-free scheme (2, 3) has been used for improved stability and mass conservation. This method can be extended to three or more fluids by using of multiple instances of the twofluid interface. Each instance corresponds to one of the N ≥ 3 fluids, though one of the fluids (denoted j=0) does not require one. Therefore, N-1 interfaces represent N fluids. Each interface models two fluids. The first is the fluid j corresponding to the interface, and tracked by ξj (r,t). The other is a composite of all remaining fluids. The density ρ and viscosity ν of the composite fluid are computed using the auxiliary functions from the other interfaces, so that each point in the fluid has the correct properties. The interfaces all share the same pressure and velocity and are coupled by the auxiliary functions. An alternative method of tracking fluids is to incorporate a concentration cj of dilute species (initially set at some convenient value such as cj=1[M/m^3 ]) into N-1 of the fluids. These N-1 species are provided by a single Transport of Diluted Species interface in the COMSOL software. In this case, one uses a single Navier-Stokes laminar flow model and there is a single composite fluid. This density and viscosity of this fluid is computed from thresholded values of the dilute species concentrations, which reveal which of the fluids is present at each location. Results The methods are illustrated by a problem inspired by a COMSOL Application Library model of an oil drop rising in water. In the modified model there are two droplets with ρ1=0.6[g/(cm^3 )] and ρ2=0.8[g/(cm^3 )] (see Fig 1). The lower droplet rises faster and overtakes the upper droplet before reaching the surface. Surface tension is not included. Figures 2 and 3 show the results of two simulations after 0.3 seconds. Figure 2 was obtained using two Laminar Two-Phase Flow, Level-Set interfaces, and the graph shows the ξ(r,t)=0.5 contours of the level-set functions representing the two droplets. Figure 3 was obtained using two dilute species concentrations cj and shows the cj=0.5[M/m^3 ] contours. Conclusions We have demonstrated two methods of solving laminar multiphase fluid-dynamic problems with more than two fluids. Both provide similar results, but only the level-set version currently implements surface tension. Reference 1. Sethian, J. A., Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Computer Vision and Materials Science, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, New York, NY (1999). 2. Chunming Li et al., Level Set Evolution without Re-Initialization: A New Variational Formulation, Proc. Of the 2005 IEEE Computer Society Conf. on Computer Vision and Pattern Recognition, Vol. 1, pp. 430-436 (2005). 3. Chunming Li et al., Distance Regularized Level Set Evolution and its Application to Image Segmentation, IEEE Trans. On Image Processing, Vol 19, No. 12, pp. 3243-3254 (2010). Figures used in the abstract Figure 1: Test problem with two dissimilar droplets suspended in a third fluid. Figure 2: Level Set solution of the test problem at t=0.3 sec. Dimensions are in cm. Figure 3: Dilute species solution of the test problem at t=0.3 sec. Dimensions are in cm.