Numerical Simulation Of Two-phase Flow Research Articles

Numerical and experimental investigations on injection effects of orifice injector plate in hybrid rocket motors

Orifice injector plates are widely used in hybrid rocket motors (HRM), but little work has been done on the influences of their design parameters on combustion performances of HRM. The effects of orifice diameter, injection pressure drop and orifices distribution of the orifice injector plate on combustion efficiency of HRM are investigated by experimental and numerical methods in this paper. The hydrogen peroxide (H2O2) and hydroxyl terminated polybutadiene (HTPB) with tube grain are selected as propellant. Firstly, 5 kinds of orifice injector plates with different orifice diameter and orifices distribution are designed, and 7 fire experiments are carried out. The experimental results show that the combustion efficiency of HRM increases with the decrease of orifice diameter and injection pressure drop. Moreover, the combustion efficiency of motor with plat using single-ring distribution is the highest, while the one using three-ring distribution is the lowest. Secondly, 36 orifice injector plates with different design parameters are calculated by three-dimensional numerical simulation of two-phase flow. The liquid oxidizer evaporation, solid-gas interaction, gaseous phase combustion, and turbulence are considered in the simulation model. The conclusions draw from simulation results agree with the experimental data, which illustrates the validity of numerical simulation model. The conclusions based on experimental and numerical results can provide guidance for designing high-performance orifice injector plate in HRMs.

Numerical simulation of two-phase flow of immiscible fluids by the finite element, discontinuous Galerkin and level-set methods

The subject of the paper is the numerical simulation of two-phase flow of immiscible fluids. Their motion is described by the incompressible Navier-Stokes equations with different constant density and viscosity for different fluids. The interface between the fluids is defined with the aid of the level-set method using a transport first-order hyperbolic equation. The Navier-Stokes system is equipped with initial and boundary conditions and transmission conditions on the interface between the two fluids. This system is discretized by the Taylor-Hood P2/P1 conforming finite elements in space and the second-order BDF method in time. The transport level-set problem is solved with the aid of the space-time discontinuous Galerkin method. Numerical experiments demonstrate that the developed method is accurate and robust.

A conservative pressure based solver with collocated variables on unstructured grids for two-fluid flows with phase change

Numerical simulation of two-phase flows based on the two-fluid six-equation model is the focus of this work. This approach is widely used in thermo-hydraulics for many industrial applications, particularly nuclear power plant safety analysis. A semi-implicit numerical method that has been successfully adopted in several industrial thermo-hydraulic codes, because of its efficiency and robustness, has been extended. In this paper, the governing equations are solved on unstructured grids with collocated variables to accommodate complicated geometries, and a deferred-correction method is used to deal with the non-orthogonality of unstructured grids. In addition, the numerical method is conservative, meaning that it is capable of capturing a shock wave exactly in single-phase flows, and ensuring the conservation of physically conservative quantities of a two-phase flow mixture. Numerical benchmarks and industrial test cases are performed in order to validate the numerical method and to evaluate its behavior with respect to different physical configurations.

Numerical simulation of two-phase flow in screw-conveyor sedimentation centrifuge

The paper simulates the aerodynamics of a two-phase flow in the cylindrical part of the screw auger precipitation centrifuge in order to estimate the centrifugal forces in the central region of the centrifuge, due to problems of sedimentation of the solid fraction from the suspension. According to the obtained velocity field, the time and the trajectory of the deposition of solid particles of different diameters of a two-phase flow of different diameters are calculated. This is necessary to estimate the speed of rotation and the pitch of the screw for outputting solid sediment to the discharge windows. The resulting model will optimize the existing apparatus for centrifuging two-phase flows, as well as help in the design of new plants.

Numerical simulation of two-phase flow in an energy recovery micro-hydraulic turbine based on Francis hydraulic model

In industrial processing, a centrifugal pump is mostly used reversely as the micro-hydraulic turbine for its lower cost. In some application situation, the working fluid will contain a part of gas which will reduce the efficiency, stability, and the power output of the machine. Due to the lower efficiency and stability of the pump as turbine (PAT) working with liquid flow, the working characteristic will deteriorate furtherly when the working fluid contains gas. Therefore, a micro-hydraulic turbine based on Francis turbine model is designed and proposed to except to obtain good performance under two-phase flow working condition. In this study, the three-dimensional transient two-phase flow model which adapts the k-ω model as turbulence model and Eulerian-Eulerian model as two-phase flow model with the commercial code ANSYS-CFX was established and solved to study the two-phase flow characteristics of the micro-hydraulic turbine with fixed guide vane openings under different gas volume fraction (GVF). The numerical simulation results show that the power, efficiency and torque of the turbine decrease with GVF. Due to the expansion of the gas in working fluid, the velocity of fluid increases with the gas, which leads to the bigger lower pressure area near the exit of the impeller. The vortex at the back of the blade is also intensified when the gas fraction increase. When the GVF is larger than 10%, the gas distribution is inhomogeneous, and most of them gather at the back side of the blade near the exit of the impeller where the GVF can reach 90%. The efficiency of the micro-hydraulic turbine is about 60% when the GVF is 20%, which needs to be improved in the future.

Numerical simulation of two-phase flow in porous media based on mimetic Green element method

Based on mimetic Green element method (GEM), which synthesizes some typical advantages of boundary element method (BEM), finite element method (FEM) and mimetic finite difference method (mimetic FDM), This paper study the application of mimetic GEM in the system of partial differential equations (PDEs) of oil-water two-phase flow in porous media. It is the first time to apply GEM to solve numerically the system of PDEs, which is one of novelties in this paper. For numerical simulation of oil-water two-phase flow in porous media, this paper provides a novel numerical method based on mimetic GEM, which is the other novelty of this work.

Numerical Simulation of Coalescence of Two-Phase Media in Packed-Bed Static Mixers

The paper describes the process of coupled numerical simulation of two-phase flow using the Dense Discrete Phase Model (DDPM), the Eulerian Wall Film model, and the k –ω turbulence model in static mixers filled with coalescing “Inzhekhim” packing elements. Device efficiency is mainly determined by the packed bed column height and the Reynolds number.

Parallel partitioning algorithm for numerical simulation of gas-liquid two-phase flow during the mold filling process

The two-phase simulation of casting filling, which has high accuracy for the velocity field, pressure field, and the gas-liquid interface behavior, has been widely applied to the many fields of materials processing, especially in the prediction of casting filling process. However, a disadvantage of two-phase simulation is the high demand for computation resource, which makes the calculation time-consuming for practical application. In the study, based on the SOLA Level-Set method for gas-liquid two-phase flow during the mold filling process, a new parallel partitioning algorithm standard is proposed by using MPI (Message Passing Interface) parallel programming technique. A region-based algorithm based on dynamic programming is designed and a parallel partition model is established. A parallel program for gas-liquid two-phase flow numerical simulation is developed. A mapping array method is proposed to reduce the communication overhead between sub-domains. The communication steps between sub-domains in the process of solving the complex flow field are designed. Tests on actual castings show that the parallel algorithm has a good performance. The speedup ratio with 4 to 8 processing cores is above 2, and the maximum can reach 4.6.

Effects of grain size and shape distribution on pore-scale numerical simulation of two-phase flow in a heterogeneous porous medium

Series of numerical simulations were done to quantify the effects of pore structure approximations on micro-scale displacement mechanisms. Coupled Cahn–Hilliard phase field and Navier–Stokes equations were solved using finite element method to simulate two-phase flow in a heterogeneous model -having a real pore network- as the base case, compared to two other approximated models; in one of those, the complex grain geometries were simplified to circular shapes; while in the other one, only the sizes of the real-shaped grains were gently (less than ±10%) modified. In both approximated models, the medium porosity and absolute permeability were kept unchanged, compared to the base case. The simplification of the grain shapes changed the morphologies of the formed fingers and the trapped oil volumes. The general trends of the oil recovery factor and macro-scale capillary pressure variations were similar during displacement at different medium wettabilities for the base and the simplified models. However, the simplified model showed higher displacement efficiency at water-wet conditions and lower capillary pressures at oil-wet conditions; due to less complexity of its pore network geometry. Different micro-scale events were captured similarly in both models, including reverse displacement, interface coalescence, water bursting and stick-slip motion. But the oil trapping mechanisms were totally different. Slight modification of the grain sizes resulted in different displacement profiles, especially at neutral and oil-wetting conditions and low capillary numbers (log Ca < −3.69), due to modification of capillarity in the medium, hence variation of the preferred paths of the displacing phase finger(s).

Parallel processing of numerical simulation of two-phase flow in fractured reservoirs considering the effect of natural flow barriers using the streamline simulation method

Because of the large size of reservoirs and complexity of the fluid behavior, especially in fractured porous media, simulation of hydrocarbon reservoirs is costly to compute using common simulators based on an Eulerian grid. For this reason, the streamlines method, which offers high computational speed and low computational hardware requirements with suitable accuracy can replace common simulators. The current study investigated parallel processing of numerical simulation for two-phase flow in two-dimensional fractured porous media using the streamlines method in OpenMp programming model. For validation, the results of water flooding simulation were compared with the IMPES method and the effect of natural flow barriers for the injection wells has been modeled. The dual porosity model is used to model the fractured reservoirs and transport equations are solved independently on 1D streamlines. It was found that the ability and performance of the streamlines method is better for parallel processing than for other methods based on the Eulerian grid.

Numerical simulations of two-phase flow in a proton-exchange membrane fuel cell based on the generalized design method

ABSTRACTThe water management of proton-exchange membrane fuel cell (PEMFC) has a major impact on the performance of the cell system. In order to investigate the influence of air velocity and wettability on the whole process during penetration of liquid water, a generalized two-dimensional model in conjunction with the volume of fluid (VOF) method was used to simulate the whole processes from gas diffusion layer (GDL) to gas channel (GC). The results show that the wettability of the medium plays a significant role than flow rate for the penetration of liquid water in the GDL. It is shown that favorable hydrophobicity and high air velocity in GC is helpful to remove liquid droplets on the GDL surface. By contrast, the stable droplets spacing on GDL surface is more concentrated and the percentage of liquid area is more extensive under the hydrophilic and low-velocity case, which would aggravate the liquid water and hard to remove from the GDL surface.

Numerical simulation of non-isothermal two-phase flow in pipelines using a two-fluid model

The analysis of two-phase flows through numerical simulations is a very useful tool to design and operate long pipelines. It is also important for monitoring the flow during adverse situations, such as the formation of hydrates and wax deposition that may occur due to temperature variations in the fluids along the pipe. The present work aims to validate a model along with a numerical technique for analyzing non-isothermal stratified-pattern two-phase flows that occur in typical gas-gathering offshore pipelines. The mathematical model is one-dimensional and based on a two-fluid model that comprises two mass and two momentum conservation equations, one for each phase, along with one energy conservation equation for the mixture. The system of equations is discretized in a conservative form within a finite-difference framework and is solved by the flux-corrected transport (FCT) numerical method. Because an ill-posed mathematical problem is obtained if the system of equations is not hyperbolic, a hyperbolicity analysis is performed for all cases simulated in this work, which also indicates how to impose the boundary conditions adequately and avoids the production of non-physical output. The results obtained for the distribution of pressure, fluid velocities, holdup and temperature along the pipeline demonstrated that even relatively small temperature differences between the fluids and the external environment at the pipe inlet cause significant thermal effects on the entire flow. The simulations also predicted results in good agreement with those of a commercial software used for comparison, for steady-state regime, and significantly different results from those produced by an isothermal-flow model, which emphasizes the importance of considering the heat transfer in the problem. In summary, the results showed that the mathematical model and the numerical method form together a reliable tool of second-order accuracy in space that perform accurate numerical simulations of two-phase flows in long pipelines that are subject to non-isothermal conditions.

Diffuse interface models for two-phase flows in artificial compressibility approach

We present an approach to numerical simulation of two-phase flows in the so-called one-fluid formulation, combining the Entropically Damped Artificial Compressibility (EDAC) method for flow solution and a chosen variant of the Phase Field Method (PFM) that belongs to a wider family of the Diffuse Interface (DI) methods of interface capturing. The resulting governing equations express a set of conservation laws and are of the advection–diffusion type, convenient in numerical handling. These equations, rewritten in the semi-discrete form, can be efficiently solved on parallel devices using the method of lines. We applied the conservative finite difference method for the spatial discretisation and a variant of the Runge–Kutta method to advance the solution in time. The results presented in this work contain the analysis of spurious currents in the case of stationary droplet together with the pressure jump across its surface, as well as the deformation of a droplet subjected to the laminar Couette flow. The presented EDAC–DI approach, offering very high computational efficiency, gives results comparable to other well-established methods for the simulations of the interfacial flows.

A Higher-Resolution Flow-Oriented Scheme With an Adaptive Correction Strategy for Distorted Meshes Coupled With a Robust MPFA-D Method for the Numerical Simulation of Two-Phase Flow in Heterogeneous and Anisotropic Petroleum Reservoirs

Summary In this paper, we propose a full-cell-centered finite-volume approach to simulate two-phase flow in heterogeneous and anisotropic petroleum reservoirs. We adopt a segregated formulation where the pressure equation is discretized by a multipoint flux approximation with a diamond-type support (MPFA-D). To solve the saturation equation, we propose a higher-order modified flow-oriented scheme (M-FOS). In this scheme, adaptive weights tune the formulation multidimensionality according to the grid distortion. Also, we adopt a multidimensional limiting process (MLP) and an efficient entropy fix to produce convergent solutions. We evaluate the performance of our numerical schemes by solving some relevant benchmark problems.

Numerical simulations of two-phase flow in open-cell metal foams with application to aero-engine separators

Oil/air separation is a critical process in aero engines since a two-phase flow is created in bearing chambers with closed-loop oil systems. This work describes an application of a two-phase pore-scale modeling method to open-cell metal foams, which are used in secondary oil separation in aero-engine separators. The dispersed oil-phase flow through open-cell foams was studied using a Lagrangian approach: discrete phase model (DPM) and investigated on foam structures of pore densities 10–50 ppi and porosities 75, 85 and 95%. The simulations were performed over flow velocities ranging from 5 m/s to 50 m/s, and for separate uniform droplets of diameters ranging from 0.5 to 15 μm, with the commercial CFD analysis package Ansys Fluent. Results indicated that the fraction of non-captured droplets decreased when the flow velocity rose, and the higher the foam porosity, the higher the number of non-captured oil droplets. The flow velocity had a significant impact on the oil capture for intermediate droplet diameters of 1–3 μm. The fraction of non-captured oil droplets increased as the pore density of the open-cell foam increased at the normalized position of x/dp = 5. Foams with a larger pore size and smaller specific surface area showed an increased oil capture when compared with foams with smaller pore sizes and larger specific surface area. For Stokes numbers below 0.1, the oil capture efficiency was small and remained rather constant independent of the Stokes number. However, for 0.1 < Stokes numbers < 1.0, the oil capture efficiency increased substantially with increasing Stokes numbers. Stokes number values above 1.0 were associated with a high capture efficiency, which remained stable with increasing Stokes numbers.

Moving mesh method for direct numerical simulation of two-phase flow with phase change

A moving mesh approach is employed to simulate two-phase flow with phase change. The mathematical model is based on the Arbitrary Lagrangian–Eulerian (ALE) description of the axisymmetric Navier–Stokes equations and energy conservation. These equations are discretized by the Finite Element Method (FEM) on a triangular unstructured mesh in which the phase boundary is represented by a set of interconnected nodes and segments that are part of the computational mesh. Here, phase change and surface tension are implemented as source terms, using the one fluid approach. The method is shown to provide an accurate description of the interfacial forces, heat and mass transfer between phases. Several different verifications are presented where the results are compared to analytical and semi-analytical solutions.

A discrete unified gas-kinetic scheme for immiscible two-phase flows

In this work, a discrete unified gas-kinetic scheme (DUGKS) is proposed for two-phase flows. In the framework of DUGKS, two kinetic equations are used to solve the quasi-incompressible phase-field governing equations (Yang and Guo, 2016), one of the kinetic models is developed for the Chan-Hilliard (CH) equation and the other is for the Navier-Stokes equations. The DUGKS can correctly recover the quasi-incompressible phase-field governing equations through the Chapman-Enskog analysis. Unlike previous phase-field-based lattice Boltzmann equation (LBE) models, the Courant-Friedricks-Lewy (CFL) condition in DUGKS is adjustable which can increase numerical stability. Furthermore, with the finite-volume formulation the model can be easily implemented on non-uniform meshes which can improve numerical precision. The proposed model is validated by simulating several benchmark problems, including a stationary drop, the layered Poiseuille flow, a rising bubble in the liquid and the Rayleigh-Taylor instability and some comparisons with the quasi-incompressible LBE model are presented. Numerical results show that the present model is capable of dealing with a wider range of viscosity and density ratios than the quasi-incompressible LBE model. In particular, the numerical accuracy can be improved by using non-uniform meshes. Overall, the present model is a promising tool for numerical simulation of two-phase flows.

A coupled level set and volume of fluid method on unstructured grids for the direct numerical simulations of two-phase flows including phase change

In the present study, a coupled level set and volume of fluid (CLSVOF) method is developed for two-dimensional unstructured grids to perform direct numerical simulations of two-phase flows including phase change. The volume fraction is advected using a multi-directional advection algorithm, where the flux polygons are constructed using vertex velocities and a scaling factor based on cell face velocities is used to correct the advected volume fraction. The level set field is advected using a total variational diminishing (TVD) scheme and geometrically reinitialized at the end of each time step. The performance of the proposed CLSVOF method is evaluated in detail on unstructured grids, both qualitatively and quantitatively, prior to simulation of phase change problems. A number of advection test cases and two-phase flow problems are considered for this purpose. Results obtained for film boiling over a horizontal flat plate using an unstructured grid show excellent agreement with results available in the literature. The numerical study of natural convection film boiling over a horizontal cylinder at different wall superheats shows a better agreement with semi-empirical correlations compared to other available numerical results.

Influence of capillary end effects on steady-state relative permeability estimates from direct pore-scale simulations

We investigate and characterize the influence of capillary end effects on steady-state relative permeabilities obtained in pore-scale numerical simulations of two-phase flows. Our study is motivated by the observation that capillary end effects documented in two-phase laboratory-scale experiments can significantly influence permeability estimates. While numerical simulations of two-phase flows in reconstructed pore-spaces are increasingly employed to characterize relative permeabilities, a phenomenon which is akin to capillary end effects can also arise in such analyses due to the constraints applied at the boundaries of the computational domain. We profile the relative strength of these capillary end effects on the calculation of steady-state relative permeabilities obtained within randomly generated porous micro-structures using a finite volume-based two-phase flow solver. We suggest a procedure to estimate the extent of the regions influenced by these capillary end effects, which in turn allows for the alleviation of bias in the estimation of relative permeabilities.

Numerical simulation of two-phase flow in porous media using a wavelet based phase-field method

An understanding of the transport and dynamics of two fluids in porous media, as well as the bubbly flow regime, is important for many engineering applications, such as enhanced oil recovery (EOR) method, drilling technology, multiphase production system, etc. In this respect, the dependence of capillary stresses on the excess free-energy of a thin interfacial layer formed by two immiscible fluids is not fully clear, particularly in porous media. Of particular interests are the closure models for interphase forces which often hinder the reliable prediction of the homogeneous flow regime. This article presents a multiphase Computational Fluid Dynamics (CFD) study of bubbles in homogeneous porous media to model the flow of oil and gas, and investigates a closure model that is based on the Allen-Cahn phase-field method, where the capillary stress is derived from the excess free-energy. The governing dynamics is simulated with the volume averaged Navier-Stokes equations extended for multiphase flow in porous media. The equations have been discretized by a wavelet transform method to accurately capture the topological change of the fluid-fluid interface. To validate the closure model for interphase forces, the results of the present phase-field method have been compared with that from experiments, as well as from reference numerical models. An excellent agreement among the results from present phase-field simulations, experiments, and some reference numerical simulations has been observed. The terminal velocity of the rising gas bubble in a liquid saturated porous medium, as well as in a pure liquid has been investigated. The bubble rising velocity in both cases have been compared with respect to the theoretical and experimental results. The study illustrates how the bubble dynamics in porous media depend on the excess free energy of a thin interfacial layer formed by two immiscible fluids.