Energy law preserving C finite element schemes for phase field models in two-phase flow computations

We use the idea in [33] to develop the energy law preserving method and compute the diffusive interface (phase-field) models of Allen–Cahn and Cahn–Hilliard type, respectively, governing the motion of two-phase incompressible flows. We discretize these two models using a C⁰ finite element in space and a modified midpoint scheme in time. To increase the stability in the pressure variable we treat the divergence free condition by a penalty formulation, under which the discrete energy law can still be derived for these diffusive interface models. Through an example we demonstrate that the energy law preserving method is beneficial for computing these multi-phase flow models. We also demonstrate that when applying the energy law preserving method to the model of Cahn–Hilliard type, un-physical interfacial oscillations may occur. We examine the source of such oscillations and a remedy is presented to eliminate the oscillations. A few two-phase incompressible flow examples are computed to show the good performance of our method.     

Spreading of viscous fluid drops on a solid substrate assisted by thermal fluctuations

We study the spreading of viscous drops on a solid substrate, taking into account the effects of thermal fluctuations in the fluid momentum. A nonlinear stochastic lubrication equation is derived and studied using numerical simulations and scaling analysis. We show that asymptotically spreading drops admit self-similar shapes, whose average radii can increase at rates much faster than these predicted by Tanner's law. We discuss the physical realizability of our results for thin molecular and complex fluid films, and predict that such phenomenon can in principal be observed in various flow geometries.     

多孔介质内受迫对流凝结时两相共存区的非达西模型

本文提出多孔介质内受迫对流凝结时两相共存区的二维非达西流模型。分析了蒸气在多孔介质内沿水平平板和填充国管内受迫对流凝结时两相共存区的厚度。假定局部平衡和暂先假设蒸气为理想气体，化简了能量方程。     

Surface Tension of Multi-phase Flow with Multiple Junctions Governed by the Variational Principle

We explore a computational model of an incompressible fluid with a multi-phase field in three-dimensional Euclidean space. By investigating an incompressible fluid with a two-phase field geometrically, we reformulate the expression of the surface tension for the two-phase field found by Lafaurie et al. (J Comput Phys 113:134–147, 1994) as a variational problem related to an infinite dimensional Lie group, the volume-preserving diffeomorphism. The variational principle to the action integral with the surface energy reproduces their Euler equation of the two-phase field with the surface tension. Since the surface energy of multiple interfaces even with singularities is not difficult to be evaluated in general and the variational formulation works for every action integral, the new formulation enables us to extend their expression to that of a multi-phase (N-phase, N\geqslant2N\geqslant2) flow and to obtain a novel Euler equation with the surface tension of the multi-phase field. The obtained Euler equation governs the equation for motion of the multi-phase field with different surface tension coefficients without any difficulties for the singularities at multiple junctions. In other words, we unify the theory of multi-phase fields which express low dimensional interface geometry and the theory of the incompressible fluid dynamics on the infinite dimensional geometry as a variational problem. We apply the equation to the contact angle problems at triple junctions. We computed the fluid dynamics for a two-phase field with a wall numerically and show the numerical computational results that for given surface tension coefficients, the contact angles are generated by the surface tension as results of balances of the kinematic energy and the surface energy.     

A lattice Boltzmann method for immiscible multiphase flow simulations using the level set method

We consider the lattice Boltzmann method for immiscible multiphase flow simulations. Classical lattice Boltzmann methods for this problem, e.g. the colour gradient method or the free energy approach, can only be applied when density and viscosity ratios are small. Moreover, they use additional fields defined on the whole domain to describe the different phases and model phase separation by special interactions at each node. In contrast, our approach simulates the flow using a single field and separates the fluid phases by a free moving interface. The scheme is based on the lattice Boltzmann method and uses the level set method to compute the evolution of the interface. To couple the fluid phases, we develop new boundary conditions which realise the macroscopic jump conditions at the interface and incorporate surface tension in the lattice Boltzmann framework. Various simulations are presented to validate the numerical scheme, e.g. two-phase channel flows, the Young–Laplace law for a bubble and viscous fingering in a Hele-Shaw cell. The results show that the method is feasible over a wide range of density and viscosity differences.     

基于相场方法的孔隙尺度油水两相流体流动模拟

基于真实岩心颗粒粒径分布,利用过程法构建疏松砂岩油藏的三维孔隙结构模型,利用相场方法建立两相流体流动数学模型并利用有限元方法进行求解,研究驱替速度、流体性质、润湿性对剩余油分布以及采出程度的影响.结果表明：驱替速度的增大和油水粘度比的减小会导致较大的毛管数,进而有利于采出程度的提高;就润湿性而言,水湿条件下毛管力是水驱油的动力,而在油湿条件下是阻力,因此水湿岩心采出程度更高.同时,从孔隙尺度对油水渗流机理及剩余油分布机理进行揭示,结果表明：由于多孔介质的复杂孔隙结构,流体在流经不同孔隙时呈现不同的流动特征,进而对油水两相流整体的压力分布、流速分布造成重要影响.     

Shear Stress in a Couette Flow of Liquid-Particle Suspensions

The mechanisms of momentum transfer and shear stress of liquid-particle suspensions in two-dimensional Couette flow are studied using direct numerical simulation by lattice-Boltzmann techniques. The results obtained display complex flow phenomena that arise from the two-phase nature of the fluid including a nonlinear velocity profile, layering of particles, and apparent slip near the solid walls. The general rheological behaviour of the suspension is dilatant. A detailed study of the various momentum transfer mechanisms that contribute to the total shear stress indicates that the observed shear thickening is related to enhanced relative solid phase stress for increasing shear rates.     

A Riemann solver for single-phase and two-phase shallow flow models based on relaxation. Relations with Roe and VFRoe solvers

We present a Riemann solver derived by a relaxation technique for classical single-phase shallow flow equations and for a two-phase shallow flow model describing a mixture of solid granular material and fluid. Our primary interest is the numerical approximation of this two-phase solid/fluid model, whose complexity poses numerical difficulties that cannot be efficiently addressed by existing solvers. In particular, we are concerned with ensuring a robust treatment of dry bed states. The relaxation system used by the proposed solver is formulated by introducing auxiliary variables that replace the momenta in the spatial gradients of the original model systems. The resulting relaxation solver is related to Roe solver in that its Riemann solution for the flow height and relaxation variables is formally computed as Roe’s Riemann solution. The relaxation solver has the advantage of a certain degree of freedom in the specification of the wave structure through the choice of the relaxation parameters. This flexibility can be exploited to handle robustly vacuum states, which is a well known difficulty of standard Roe’s method, while maintaining Roe’s low diffusivity. For the single-phase model positivity of flow height is rigorously preserved. For the two-phase model positivity of volume fractions in general is not ensured, and a suitable restriction on the CFL number might be needed. Nonetheless, numerical experiments suggest that the proposed two-phase flow solver efficiently models wet/dry fronts and vacuum formation for a large range of flow conditions.As a corollary of our study, we show that for single-phase shallow flow equations the relaxation solver is formally equivalent to the VFRoe solver with conservative variables of Gallouët and Masella [T. Gallouët, J.-M. Masella, Un schéma de Godunov approché C.R. Acad. Sci. Paris, Série I, 323 (1996) 77–84]. The relaxation interpretation allows establishing positivity conditions for this VFRoe method.     

Etude expérimentale du fonctionnement au sol d'une boucle diphasique à ammoniac en vue d'une régulation thermique en milieu spatial

Experimental terrestrial study of an ammonia two-phase loop for thermal control in spatial environment. This paper presents the terrestrial test results of a mechanically pumped two-phase fluid loop, using ammonia as the working fluid. The 600 W experimental set-up (main components, instrumentation) is described. The two-phase flow patterns observed are compared with several flow regime maps. The experimental results are in good agreement with the predictions of Taitel and Dukler. The condensation lengths and the mean heat transfer coefficients of the condenser are given. The friction pressure gradients of adiabatic two-phase flow increases with mass flow rate and quality. The wall temperatures and heat transfer coefficients of the evaporator show the influence of the liquid distribution on the heat transfer : it is better at the top than at the bottom of the tube and at the ends than in the center part of the evaporator. The best evaporation coefficients are obtained with high mass flow rates and low qualities. The results obtained show the good operation of the system.     

Modelling of two-phase,transient airflow and particles distribution in the indoor environment by Large Eddy Simulation

Prediction of particles distribution in the smaller-scale atmospheric environment, such as the indoor atmosphere, is of major importance for the comfort and the well-being of its occupants. The objective of this study is to investigate the airflow and particles transport, as well as the particles concentration evolution indoors, using Computational Fluid Dynamics (CFD) techniques. A three-dimensional, Euler–Euler two-phase flow model for the investigation of the indoor aerosol is developed, within a CFD general-purpose computer program (PHOENICS), and is validated against experimental measurements from the literature, for an ordinary case of indoor dilute aerosol. Turbulent flow is simulated by Large Eddy Simulation (LES) and the results are compared with those obtained applying the Reynolds-averaged Navier–Stokes (RANS) equations together with the ReNormalisation Group (RNG) k–? model. Τwo-way coupling between the two phases is modelled by means of appropriate interphase interactions. This study focused on particles of one size group (mean aerodynamic diameter of 10 μm) but the numerical method described can equally well be applied for a broader size range. It is concluded that for the very dilute aerosols considered here, simpler models (such as single-phase and drift flux) do as well in predicting the important parameters of the flow, as the more complex ones.     

气粒两相流传热问题的光滑离散颗粒流体动力学方法数值模拟

在气粒两相流动问题中,颗粒间以及气体与颗粒间的传热问题不可忽略.光滑离散颗粒流体动力学(SDPH)模型作为一种新的求解气粒两相流动问题的方法,已经成功应用于模拟风沙运动等问题.在此基础上,提出了SDPH方法的热传导模型,模拟了气粒两相流动问题中的热传导过程以及颗粒蒸发过程.首先引入各相的能量方程,利用有限差分与光滑粒子流体动力学一阶导数相结合的方法,处理各相内部热传导项中的二阶导数问题,基于气粒两相间温度差及对流换热系数计算颗粒与气体间的热传导量,推导得到了含热传导模型的气粒两相流SDPH计算方程组,模拟计算了圆盘形颗粒团算例及鼓泡流化床内部热传导算例,并与双流体模型计算结果进行对比,结果基本符合;其次利用离散液滴模型中的颗粒蒸发传质传热定律计算颗粒的蒸发过程,数值模拟了颗粒射流蒸发过程,并与离散颗粒模型结果进行对比,两者符合得较好,验证了该方法的准确性及实用性.     

Complex network analysis in inclined oil--water two-phase flow

Complex networks have established themselves in recent years as being particularly suitable and flexible for representing and modelling many complex natural and artificial systems. Oil--water two-phase flow is one of the most complex systems. In this paper, we use complex networks to study the inclined oil--water two-phase flow. Two different complex network construction methods are proposed to build two types of networks, i.e. the flow pattern complex network (FPCN) and fluid dynamic complex network (FDCN). Through detecting the community structure of FPCN by the community-detection algorithm based on K-means clustering, useful and interesting results are found which can be used for identifying three inclined oil--water flow patterns. To investigate the dynamic characteristics of the inclined oil--water two-phase flow, we construct 48 FDCNs under different flow conditions, and find that the power-law exponent and the network information entropy, which are sensitive to the flow pattern transition, can both characterize the nonlinear dynamics of the inclined oil--water two-phase flow. In this paper, from a new perspective, we not only introduce a complex network theory into the study of the oil--water two-phase flow but also indicate that the complex network may be a powerful tool for exploring nonlinear time series in practice.     

稠密可压缩气粒两相流动中的等熵声速计算建模及物理规律

气体相与颗粒相混合流场的声速研究, 由于具有重要的基础理论价值与广泛的工程应用背景, 逐渐受到人们重视. 针对稠密可压缩气粒两相流动, 综合考虑颗粒相所占空间体积以及颗粒间相互作用, 推导给出了新的等熵声速计算公式; 新公式包含了已有的纯气体、稀疏气粒两相流情形的计算公式作为其特例, 一方面验证了公式推导的正确性, 另一方面说明新公式更具有通用性; 分析了不同颗粒质量分数条件下的声速变化规律, 相应结果与普朗特的理论分析符合, 特别对于稠密气粒两相流动工况得到了一些新的物理认识; 开展了颗粒间相互作用建模参数的物理分析, 揭示了其对气粒两相流动声速的影响机理. 本文取得的成果为稠密可压缩气粒两相流动研究以及相关工程应用提供理论支撑.     

计算流体成像技术重构方法及其应用

建立系统的计算流体成像(CFI)技术,并论证其为流动数值模拟与风洞实验相互佐证的重要手段。采用纯数值模拟技术重构得到流场计算阴影、纹影以及干涉图,主要技术包括复杂湍流模拟技术、三线性插值技术和流动图像重构技术等。同时将CFI技术应用于激波管内绕障碍物三维复杂流动计算图像重构,并与双向全息实验结果进行了比较分析。研究证明该CFI技术可以用于复杂几何边界、分区域、非定常流动图像重构,不仅能够为流场结构特征分析提供重要参考依据,而且能够用于数值模拟与风洞实验结果的比较印证。     

基于POD模态分解的液环泵瞬态气液两相流分析

针对液环泵内气液两相流动的复杂时空规律,采用本征正交分解(POD)方法对其瞬态气液两相流场进行特征分解,分析其相态场、速度场的空间基模态特征及模态系数的时域特征,建立非定常流场降阶模型,并对流场进行预测分析.结果表明POD方法可实现对液环泵内复杂流场的时空解耦分析,相态场及速度场的各阶模态系数在时域内的变化能够反映各阶...     

场协同理论在椭圆型流动中的数值验证

本文用数值模拟的方法，通过四个椭圆型流动传热的例子验证了场协同理论的正确性．结果表明，场协同理论不仅适合于抛物型流动，亦适合于复杂的有回流的椭圆型流动．     

A high-order cell-centered Lagrangian scheme for compressible fluid flows in two-dimensional cylindrical geometry

The goal of this paper is to present high-order cell-centered schemes for solving the equations of Lagrangian gas dynamics written in cylindrical geometry. A node-based discretization of the numerical fluxes is obtained through the computation of the time rate of change of the cell volume. It allows to derive finite volume numerical schemes that are compatible with the geometric conservation law (GCL). Two discretizations of the momentum equations are proposed depending on the form of the discrete gradient operator. The first one corresponds to the control volume scheme while the second one corresponds to the so-called area-weighted scheme. Both formulations share the same discretization for the total energy equation. In both schemes, fluxes are computed using the same nodal solver which can be viewed as a two-dimensional extension of an approximate Riemann solver. The control volume scheme is conservative for momentum, total energy and satisfies a local entropy inequality in its first-order semi-discrete form. However, it does not preserve spherical symmetry. On the other hand, the area-weighted scheme is conservative for total energy and preserves spherical symmetry for one-dimensional spherical flow on equi-angular polar grid. The two-dimensional high-order extensions of these two schemes are constructed employing the generalized Riemann problem (GRP) in the acoustic approximation. Many numerical tests are presented in order to assess these new schemes. The results obtained for various representative configurations of one and two-dimensional compressible fluid flows show the robustness and the accuracy of our new schemes.     

Modeling slender bodies with the method of regularized Stokeslets

The motion and flow generated by immersed structures in a fluid in the Stokes regime can be modeled with a variety of different numerical methods. The mathematical structure of the Stokes equations allows one to describe the flow around a three-dimensional object using only information regarding its geometry. This leads to computational techniques such as boundary integral methods or the method of regularized Stokeslets that discretize the surface of the immersed object in the flow. However, when the body in question is slender, a more computationally efficient alternative is to represent the flow by a one-dimensional discretization along the centerline of the object rather than a discretization of the boundary. Using an exact and an asymptotic solution describing the nontrivial three-dimensional fluid flow generated by a slender precessing spheroid, we present a careful analysis of the approximation of the flow using the method of regularized Stokeslets, where the regularized Stokeslets are placed along the centerline of the spheroid. Guidance is presented on how best to choose the numerical parameters within the method of regularized Stokeslets to minimize the error for a given application.