Modeling merging and breakup in the moving mesh interface tracking method for multiphase flow simulations

The three-dimensional, moving mesh interface tracking (MMIT) method coupled with local mesh adaptations by Quan and Schmidt [S.P. Quan, D.P. Schmidt, A moving mesh interface tracking method for 3D incompressible two-phase flows, J. Comput. Phys. 221 (2007) 761–780] demonstrated the capability to accurately simulate multiphase flows, to handle large deformation, and also to perform interface pinch-off for some specific cases. However, another challenge, i.e. how to handle interface merging (such as droplet coalescence) has not been addressed. In this paper, we present a mesh combination scheme for interface connection and a more general mesh separation algorithm for interface breakup. These two schemes are based on the conversion of liquid cells in one phase to another fluid by changing the fluid properties of the cells in the combination or separation region. After the conversion, the newly created interface is usually ragged, and a local projection method is employed to smooth the interface. Extra mesh adaptation criteria are introduced to handle colliding interfaces with almost zero curvatures as the distance between the interfaces diminishes. Simulations of droplet pair collisions including both head-on and off-center coalescences show that the mesh adaptations are capable of resolving very small length scales, and the mesh combination and mesh separation schemes can handle the topological transitions in multiphase flows. The potential of our method to perform detailed investigations of droplet coalescence and breakup is also displayed.     

Numerical simulations of gas-liquid two-phase flows in a micro porous structure

The lattice Boltzmann method for two-phase fluid flows is applied to the simulations of gas-liquid two-phase flows in a micro porous structure for various capillary numbers at low Reynolds numbers. The behaviors of the gas-liquid interface and the velocities of the two-phase fluid in the structure are simulated, and the permeability of gas and liquid through the structure are estimated from the calculated results. By changing the void fraction, the contact angle of the interface on walls, and the surface tension, the effect of these properties on the behaviors and the permeability of the two-phase flows in the micro porous structure is investigated. It is found that the permeability of liquid flows depends on the contact angle and it increases for hydrophobic walls. It is also seen that liquid flows are choked in pores for large void fractions and low capillary numbers.     

A two-phase diffuse-interface model for Hele-Shaw flows with large property contrasts

A novel two-phase diffuse-interface model is used to simulate flows inside a Hele-Shaw cell. The model assumes that the two phases coexist inside the diffuse interface, with different velocities and properties. A separate equation is used to calculate the slip velocity between the two phases inside the diffuse interface. It is shown that for one-dimensional flows parallel to the diffuse interface, the results are independent of the diffuse-interface width, regardless of the magnitude of the density and viscosity contrasts between the phases. This two-phase approach is coupled with a phase-field equation for calculating the interface motion. The model is applied to a buoyancy-driven two-phase flow involving a Rayleigh-Taylor instability and validated through a comparison with available sharp-interface results. The flows and interface topology changes are investigated for large density and viscosity contrasts between the phases. The convergence of the results with respect to the interface width is examined in detail. It is shown that the two-phase model converges better than a standard diffuse-interface model that assumes the presence of a single velocity inside the diffuse interface. Remaining interface width dependencies can be attributed to the capillary stress term in the momentum equation.     

Anti-diffusion method for interface steepening in two-phase incompressible flow

In this paper, we present a method for obtaining sharp interfaces in two-phase incompressible flows by an anti-diffusion correction, that is applicable in a straight-forward fashion for the improvement of two-phase flow solution schemes typically employed in practical applications. The underlying discretization is based on the volume-of-fluid (VOF) interface-capturing method on unstructured meshes. The key idea is to steepen the interface, independently of the underlying volume-fraction transport equation, by solving a diffusion equation with reverse time, i.e. an anti-diffusion equation, after each advection time step of the volume fraction. As the solution of the anti-diffusion equation requires regularization, a limiter based on the directional derivative is developed for calculating the gradient of the volume fraction. This limiter ensures the boundedness of the volume fraction. In order to control the amount of anti-diffusion introduced by the correction algorithm we propose a suitable stopping criterion for interface steepening. The formulation of the limiter and the algorithm for solving the anti-diffusion equation are applicable to 3-dimensional unstructured meshes. Validation computations are performed for passive advection of an interface, for 2-dimensional and 3-dimensional rising-bubbles, and for a rising drop in a periodically constricted channel. The results demonstrate that sharp interfaces can be recovered reliably. They show that the accuracy is similar to or even better than that of level-set methods using comparable discretizations for the flow and the level-set evolution. Also, we observe a good agreement with experimental results for the rising drop where proper interface evolution requires accurate mass conservation.     

Efficient kinetic schemes for steady and unsteady flow simulations on unstructured meshes

This paper presents efficient second-order kinetic schemes on unstructured meshes for both compressible unsteady and incompressible steady flows. For compressible unsteady flows, a time-dependent gas distribution function with a discontinuous particle velocity space at a cell interface is constructed and used for the evaluations of both numerical fluxes and conservative flow variables. As a result, a compact scheme on the unstructured meshes is developed. For incompressible steady flows, a continuous second-order gas-kinetic BGK type scheme is presented, for which the time-dependent gas distribution function with a continuous particle velocity is used on unstructured meshes. The efficiency of the schemes lies in the fact that the slopes of the flow variables inside each cell can be constructed using values of the flow variables within that cell only without involving neighboring cells. Therefore, even with the stencil of a first-order scheme, a high resolution method is constructed. Numerical examples are presented which are compared with the benchmark solutions and the experimental measurements.     

改进粒子水平集法及其应用

针对传统粒子水平集方法的缺陷提出一种虚拟粒子对距离函数的修正方法.改进算法针对虚拟粒子与待修正网格点的各种相对位置进行误差修正,可以避免虚拟粒子在非界面法线方向移动而产生的误差.数值求解涡旋流场问题显示:改进算法的界面捕捉性能得到显著提高.在此基础上,结合投影法求解Navier-Stokes方程组,数值模拟存在高密度比(10³量级)及粘性比(10²量级)的不可压缩两相流问题(气泡上升及自由面不稳定性问题).计算结果与已有结果吻合良好,详细分析主要控制参数对瑞利-泰勒不稳定性现象的影响.     

Modeling Three-Dimensional Multiphase Flow Using a Level Contour Reconstruction Method for Front Tracking without Connectivity

Three-dimensional multiphase flow and flow with phase change are simulated using a simplified method of tracking and reconstructing the phase interface. The new level contour reconstruction technique presented here enables front tracking methods to naturally, automatically, and robustly model the merging and breakup of interfaces in three-dimensional flows. The method is designed so that the phase surface is treated as a collection of physically linked but not logically connected surface elements. Eliminating the need to bookkeep logical connections between neighboring surface elements greatly simplifies the Lagrangian tracking of interfaces, particularly for 3D flows exhibiting topology change. The motivation for this new method is the modeling of complex three-dimensional boiling flows where repeated merging and breakup are inherent features of the interface dynamics. Results of 3D film boiling simulations with multiple interacting bubbles are presented. The capabilities of the new interface reconstruction method are also tested in a variety of two-phase flows without phase change. Three-dimensional simulations of bubble merging and droplet collision, coalescence, and breakup demonstrate the new method's ability to easily handle topology change by film rupture or filamentary breakup. Validation tests are conducted for drop oscillation and bubble rise. The susceptibility of the numerical method to parasitic currents is also thoroughly assessed.     

A Numerical Method on Eulerian Grids for Two-Phase Compressible Flow

We develop a numerical method to simulate a two-phase compressible flow with sharp phase interface on Eulerian grids. The scheme makes use of a level set to depict the phase interface numerically. The overall scheme is basically a finite volume scheme. By approximately solving a two-phase Riemann problem on the phase interface, the normal phase interface velocity and the pressure are obtained, which is used to update the phase interface and calculate the numerical flux between the flows of two different phases. We adopt an aggregation algorithm to build cell patches around the phase interface to remove the numerical instability due to the breakdown of the CFL constraint by the cell fragments given by the phase interface depicted using the level set function. The proposed scheme can handle problems with tangential sliping on the phase interface, topological change of the phase interface and extreme contrast in material parameters in a natural way. Though the perfect conservation of the mass, momentum and energy in global is not achieved, it can be quantitatively identified in what extent the global conservation is spoiled. Some numerical examples are presented to validate the numerical method developed.     

Sharp interface immersed-boundary/level-set method for wave–body interactions

A sharp interface Cartesian grid method for the large-eddy simulation of two-phase turbulent flows interacting with moving bodies is presented. The overall approach uses a sharp interface immersed boundary formulation and a level-set/ghost–fluid method for solid–fluid and fluid–fluid interface treatments, respectively. A four-step fractional-step method is used for velocity–pressure coupling, and a Lagrangian dynamic Smagorinsky subgrid-scale model is adopted for large-eddy simulations. A simple contact angle boundary condition treatment that conforms to the immersed boundary formulation is developed. A variety of test cases of different scales ranging from bubble dynamics, water entry and exit, landslide-generated waves, to ship hydrodynamics are performed for validation. Extensions for high Reynolds number ship flows using wall-layer models are also considered.     

两相方腔流的格子Boltzmann模拟

利用基于Shan-Chen多相模型的格子Boltzmann方法对方腔内上板拖动的两相流动问题开展较为系统的数值模拟,详细研究雷诺数(Re),毛细数(Ca)和壁面润湿性对流动以及混合特性的影响.结果表明:Re数、Ca数越大,方腔内两相流体的混合界面长度越大,混合效果越好.另外,壁面憎水程度越高,混合界面长度增加越快,然而对于强亲水壁面,混合界面长度最终趋于一常数.     

FIVER: A finite volume method based on exact two-phase Riemann problems and sparse grids for multi-material flows with large density jumps

A robust finite volume method for the solution of high-speed compressible flows in multi-material domains involving arbitrary equations of state and large density jumps is presented. The global domain of interest can include a moving or deformable subdomain that furthermore may undergo topological changes due to, for example, crack propagation. The key components of the proposed method include: (a) the definition of a discrete surrogate material interface, (b) the computation of a reliable approximation of the fluid state vector on each side of a discrete material interface via the construction and solution of a local, exact, two-phase Riemann problem, (c) the algebraic solution of this auxiliary problem when the equation of state allows it, and (d) the solution of this two-phase Riemann problem using sparse grid tabulations otherwise. The proposed computational method is illustrated with the three-dimensional simulation of the dynamics of an underwater explosion bubble.     

Numerical simulation of continuum models for fluid-fluid interface dynamics

This paper is concerned with numerical methods for two-phase incompressible flows assuming a sharp interface model for interfacial stresses. Standard continuum models for the fluid dynamics in the bulk phases, for mass transport of a solute between the phases and for surfactant transport on the interface are given. We review some recently developed finite element methods for the appropriate discretization of such models, e.?g., a pressure extended finite element (XFE) space which is suitable to represent the pressure jump, a space-time extended finite element discretization for the mass transport equation of a solute and a surface finite element method (SurFEM) for surfactant transport. Numerical experiments based on level set interface capturing and adaptive multilevel finite element discretization are presented for rising droplets with a clean interface model and a spherical droplet in a Poisseuille flow with a Boussinesq-Scriven interface model.     

An interaction potential based lattice Boltzmann method with adaptive mesh refinement (AMR) for two-phase flow simulation

The lattice Boltzmann method (LBM) for two-phase flow simulation is often hindered by insufficient resolution at the interface. As a result, the LBM simulation of bubbles in bubbling flows is commonly limited to spherical or slightly deformed bubble shapes. In this study, the adaptive mesh refinement method for the LBM is developed to overcome such a problem. The approach for this new method is based on the improved interaction potential model, which is able to maintain grid-independent fluid properties in the two-fluid phases and at the interface. The LBM–AMR algorithm is described, especially concerning the LBM operation on a non-uniform mesh and the improved interaction potential model. Numerical simulations have been performed to validate the method in both single phase and multiphase flows. The 2D and 3D simulations of the buoyant rise of bubbles are conducted under various conditions. The agreement between the simulated bubble shape and velocity with experiments illustrates the capability of the LBM–AMR approach in predicting bubble dynamics even under the large bubble deformation conditions. Further, the LBM–AMR technique is capable of simulating a complex topology change of the interface. Integration of LBM with AMR can significantly improve the accuracy and reduce computation cost. The method developed in this study may appreciably enhance the capability of LBM in the simulation of complex multiphase flows under realistic conditions.     

Numerical method of the Riemann problem for two-dimensional multi-fluid flows with general equation of state

Based on the classical Roe method, we develop an interface capture method according to the general equation of state, and extend the single-fluid Roe method to the two-dimensional (2D) multi-fluid flows, as well as construct the continuous Roe matrix for the whole flow field. The interface capture equations and fluid dynamic conservative equations are coupled together and solved by using any high-resolution schemes that usually suit for the single-fluid flows. Some numerical examples are given to illustrate the solution of 1D and 2D multi-fluid Riemann problems.     

耦合界面力的两相流相场格子Boltzmann模型

提出了一种改进的基于相场理论的两相流格子Boltzmann模型.通过引入一种新的更加简化的外力项分布函数,使得此模型克服了前人工作中界面力尺度与理论分析不一致的问题,并且通过Chapman-Enskog多尺度分析表明,所提出的模型能够准确恢复到追踪界面的Cahn-Hilliard方程和不可压的Navier-Stokes方程,并且宏观速度的计算更为简化.利用所提模型对几个经典两相流问题,包括静态液滴测试、液滴合并问题、亚稳态分解以及瑞利-泰勒不稳定性进行了数值模拟,发现本模型可以获得量级为10^-9极小的虚假速度,并且这些算例获取的数值解与解析解或已有的文献结果相吻合,从而验证了模型的准确性和可行性.最后,利用所发展的两相流格子Boltzmann模型研究了随机扰动的瑞利-泰勒不稳定性问题,并着重分析了雷诺数对流体相界面的影响.发现对于高雷诺数情形,在演化前期,流体界面出现一排“蘑菇”形状,而在演化后期,流体界面呈现十分复杂的混沌拓扑结构.不同于高雷诺数情形,低雷诺数时流体界面变得相对光滑,在演化后期未观察到混沌拓扑结构.     

Surface/interface effects on the formation of misfit dislocation in a core–shell nanowire

The misfit strain within the core of a two-phase free-standing core–shell nanowire resulting in the generation of an edge misfit dislocation or an edge misfit dislocation dipole at the core–shell interface is considered theoretically within both the classical and surface/interface elasticity approaches. The critical conditions for the misfit dislocation generation are studied and discussed in detail with special attention to the non-classical surface/interface effect. It is shown that this effect is significant for fine cores of radius smaller than roughly 20 interatomic distances. The positive and negative surface/interface Lamé constants mostly make the generation of the misfit dislocation easier and harder, respectively. Moreover, the positive (negative) residual surface/interface tensions mostly make the generation of the misfit dislocation harder (easier). The formation of individual misfit dislocation is energetically more preferential in finer two-phase nanowires, while the formation of misfit dislocation dipole is more expectable in the coarser ones.     

Evaluation of numerical strategies for large eddy simulation of particulate two-phase recirculating flows

Predicting particle dispersion in recirculating two-phase flows is a key issue for reacting flows and a potential application of large eddy simulation (LES) methods. In this study, Euler/Euler and Euler/Lagrange LES approaches are compared in the bluff body configuration from Borée et al. [J. Borée, T. Ishima, I. Flour, The effect of mass loading and inter-particle collisions on the development of the polydispersed two-phase flow downstream of a confined bluff body, J. Fluid Mech. 443 (2001) 129–165] where glass beads are injected into a complex recirculating flow. These tests are performed for non-reacting, non-evaporating sprays but are mandatory validations before computing realistic combustion chambers. Two different codes (one explicit and compressible and the other implicit and incompressible) are also tested on the same configuration. Results show that the gas flow is well predicted by both codes. The dispersed phase is also well predicted by both codes but the Lagrangian approach predicts root-mean-square values more accurately than the Eulerian approach. The effects of mesh, solvers and numerical schemes are discussed for each method.     

Monitoring of multiphase flows for superconducting accelerators and others applications

This paper is a review on implementation of measuring systems for two-phase helium, hydrogen, liquefied natural gas (LNG), and oil-formation/salty water flows. Two types of such systems are presented. The first type is based on two-phase flow-meters combining void fraction radio-frequency (RF) sensors and narrowing devices. They can be applied for superconducting accelerators cooled with two-phase helium, refueling hydrogen system for space ships and some applications in oil production industry. The second one is based on combination of a gamma-densitometer and a narrowing device. These systems can be used to monitor large two-phase LNG and oil-formation water flows. An electronics system based on a modular industrial computer is described as well. The metrological characteristics for different flow-meters are presented and the obtained results are discussed. It is also shown that the experience gained allows separationless flow-meter for three-phase oil-gas-formation water flows to be produced.     

Numerical simulation of instantaneous flow structure of swirling and non-swirling coaxial-jet particle-laden turbulence flows

A subgrid scale two-phase second-order-moment (SGS-SOM) model based on the two-fluid continuum approach is presented for the analysis of the instantaneous flow structures of swirling and non-swirling coaxial-jet particle-laden turbulence flows. Since the interaction between the two-phase subgrid scale stresses and the anisotropy of two-phase subgrid scale stresses is fully considered, it is superior to the conventional subgrid scale model on the basis of single gas phase or together with their similar forms for the particle phase for not taken these characters thoroughly into account. The swirling numbers s=0.47 and s=0 of coaxial-jet particle-laden turbulence flows (measured by M. Sommerfeld, H.H. Qiu, Detailed measurements in a swirling particulate two-phase flow by a phase Doppler anemometer, Int. J. Heat Fluid Flow 12 (1991) 20-28) are numerically simulated by large eddy simulation using this model, together with a Reynolds-averaged Navier-Stokes model using the unified second-order-moment two-phase turbulence model (RANS-USM). The instantaneous results show that the multiple recirculating gas flow structure is similar to that of single-phase swirling flows; but the particle flow structure contains less vortices. Both SGS-SOM and RANS-USM predicted that the two-phase time-averaged velocities and the root-mean-square fluctuation velocities are validated and are in good agreement with the experimental results. It is seen that for the two-phase time-averaged velocities both the models give almost the same results, hence the RANS-USM modeling is validated by large eddy simulation. For the two-phase root-mean-square fluctuation velocities the SGS-SOM results are obviously better than the RANS-USM results.     

考虑壁面接触效应的微流动数值模拟

使用level set和volume of fluid(VOF)方法对考虑壁面接触效应的不可压缩两相微流动进行数值模拟.对于level set方法,计算基于MAC网格,使用二阶投影算法求解二维Navier-Stokes(N-S)方程和level set函数方程;对于VOF方法,通过引入计算网格内的体积分数,将流场的参数转化为体积平均值,界面的形状由体积分数连续方程的解决定.给出一些计算实例,并和现有的实验结果进行比较.