A GHOST FLUID BASED FRONT TRACKING METHOD FOR MULTIMEDIUM COMPRESSIBLE FLOWS

Recent years the modify ghost fluid method （MGFM） and the real ghost fluid method （RGFM） based on Riemann problem have been developed for multimedium compressible flows. According to authors, these methods have only been used with the level set technique to track the interface. In this paper, we combine the MCFM and the RGFM respectively with front tracking method, for which the fluid interfaces are explicitly tracked by connected points. The method is tested with some one-dimensional problems, and its applicability is also studied. Furthermore, in order to capture the interface more accurately, especially for strong shock impacting on interface, a shock monitor is proposed to determine the initial states of the Riemann problem. The present method is applied to various one- dimensional problems involving strong shock-interface interaction. An extension of the present method to two dimension is also introduced and preliminary results are given.

NUMERICAL STUDY OF TWO INTERFACE METHODS FOR COMPRESSIBLE MULTI-FLUID FLOWS

Two interface capturing methods are studied for multi fluid flows, governed by the stiffened gas equation of state. The mixture type interface capturing algorithm uses a simple volume fraction model Euler equations written in a quasi conservative form, which is solved by a standard high resolution piecewise parabolic method (PPM) with multi fluid Riemann solver. The level set interface capturing method uses a narrow band ghost fluid method (GFM) with no numerical smearing. Several examples are presented and compared for one and two dimensions, which show the feasibility of the two methods applied to various multi fluid problems.

UNIFIED COMPUTATION OF FLOW WITH COMPRESSIBLE AND INCOMPRESSIBLE FLUID BASED ON ROE'S SCHEME

A unified numerical scheme for the solutions of the compressible and incompressible Navier-Stokes equations is investigated based on a time-derivative preconditioning algorithm. The primitive variables are pressure, velocities and temperature. The time integration scheme is used in conjunction with a finite volume discretization. The preconditioning is coupled with a high order implicit upwind scheme based on the definition of a Roe＇s type matrix. Computational capabilities are demonstrated through computations of high Mach number, middle Mach number, very low Mach number, and incompressible flow. It has also been demonstrated that the discontinuous surface in flow field can be captured for the implementation Roe＇s scheme.

Implementation of Non-Newtonian Fluid Properties for Compressible Multiphase Flows in OpenFOAM

The paper presents the implementation of non-Newtonian fluid properties for compressible multiphase solver in the open source framework OpenFOAM. The transport models for Power Law, Cross Power Law, Casson, Bird-Carreau and Herschel-Bulkley fluids were included in the thermophysical model library. Appropriate non-Newtonian liquids have been chosen from literature, and pressure driven test simulations are carried out. Therefore, the solver compressibleInterFoam is used to compute air-liquid mixture flows over a backward facing step. A validation of the novel models has been performed by means of a sample-based comparison of the strain rate viscosity relation. The theoretical rheological properties of the selected liquids agree well with the results of the simulated data.

Gas flow characteristics of argon inductively coupled plasma and advections of plasma species under incompressible and compressible flows

In this work, incompressible and compressible flows of background gas are characterized in argon inductively coupled plasma by using a fluid model, and the respective influence of the two flows on the plasma properties is specified. In the incompressible flow, only the velocity variable is calculated, while in the compressible flow, both the velocity and density variables are calculated. The compressible flow is more realistic; nevertheless, a comparison of the two types of flow is convenient for people to investigate the respective role of velocity and density variables. The peripheral symmetric profile of metastable density near the chamber sidewall is broken in the incompressible flow. At the compressible flow, the electron density increases and the electron temperature decreases. Meanwhile, the metastable density peak shifts to the dielectric window from the discharge center, besides for the peripheral density profile distortion, similar to the incompressible flow.The velocity profile at incompressible flow is not altered when changing the inlet velocity, whereas clear peak shift of velocity profile from the inlet to the outlet at compressible flow is observed as increasing the gas flow rate. The shift of velocity peak is more obvious at low pressures for it is easy to compress the rarefied gas. The velocity profile variations at compressible flow show people the concrete residing processes of background molecule and plasma species in the chamber at different flow rates. Of more significance is it implied that in the usual linear method that people use to calculate the residence time, one important parameter in the gas flow dynamics, needs to be rectified. The spatial profile of pressure simulated exhibits obvious spatial gradient. This is helpful for experimentalists to understand their gas pressure measurements that are always taken at the chamber outlet. At the end, the work specification and limitations are listed.

Application of the Hierarchical Functions Expansion Method for the Solution of the Two Dimensional Navier-Stokes Equations for Compressible Fluids in High Velocity

This work presents a new application for the Hierarchical Function Expansion Method for the solution of the Navier-Stokes equations for compressible fluids in two dimensions and in high velocity. This method is based on the finite elements method using the Petrov-Galerkin formulation, know as SUPG (Streamline Upwind Petrov-Galerkin), applied with the expansion of the variables into hierarchical functions. To test and validate the numerical method proposed as well as the computational program developed simulations are performed for some cases whose theoretical solutions are known. These cases are the following: continuity test, stability and convergence test, temperature step problem, and several oblique shocks. The objective of the last cases is basically to verify the capture of the shock wave by the method developed. The results obtained in the simulations with the proposed method were good both qualitatively and quantitatively when compared with the theoretical solutions. This allows concluding that the objectives of this work are reached.

Thermal Radiation Effect on the MHD Turbulent Compressible Boundary Layer Flow with Adverse Pressure Gradient, Heat Transfer and Local Suction

The combined effect of magnetic field, thermal radiation and local suction on the steady turbulent compressible boundary layer flow with adverse pressure gradient is numerically studied. The magnetic field is constant and applied transversely to the direction of the flow. The fluid is subjected to a localized suction and is considered as a radiative optically thin gray fluid. The Reynolds Averaged Boundary Layer (RABL) equations with appropriate boundary conditions are transformed using the compressible Falkner Skan transformation. The nonlinear and coupled system of partial differential equations (PDEs) is solved using the Keller box method. For the eddy-kinematic viscosity the Baldwin Lomax turbulent model and for the turbulent Prandtl number the extended Kays Crawford model are used. The numerical results show that the flow field can be controlled by the combined effect of the applied magnetic field, thermal radiation, and localized suction, moving the separation point, xs , downstream towards the plate’s end, and increasing total drag, D . The combined effect of thermal radiation and magnetic field has a cooling effect on the fluid at the wall vicinity. The combined effect has a greater influence in the case of high free-stream temperature.

COMPUTATIONALINTELLECTUAL ANALYTICAL THEORYOF COMPUTATIONAL ANALYTICAL APPROACH TOROTATING FLOW OF NON_NEWTONIAN FLUID

A combination of the computational symbolic calculation, mathematical approach and physico-mechanical model lends to a computational intellectual analytical approach developed by the author. There is a principal difference between the computer proof and the computer derivation completed by the computer, also difference between the numerical and symbolic calculations. In this investigation the computational analytical approach is extended, and an unsteady flow of non-Newtonian fluid in the gap between two rotating coaxial cylinders is studied. The Oldroyd fluid B model is used by which the Weissenberg effects are explained in a good comparison with the experiments. The governing equations are reduced to a partial differential equation of 3 rd order for the dimensionless velocity. Using the computer software Macsyma and an improved variational approach the problem with the initial and boundary conditions is then reduced to a problem of an ordinary differential equation for different approximations. The analytical solutions are given for the 1 st, 2 nd and 3 rd approximations. The present investigation shows the ability of the computational symbolic manipulation in solving the problems of non-Newtonian fluid flows. There is a possibility of that to solve the problems in mathematics and mechanics. An important conclusion can be drawn from the results that the transition from a steady state to another steady state is non-unique.

Hot Compressive Flow Stress of TA5 Alloy

The compressive true stress-true strain curves of TA5 alloy in α phase region have been measured and mathematically analyzed at Ε=10-1&middots-1 and 800-900°C. It is concluded that the curves are characteristic of dynamic recovery. A mathematical model of flow stress has been proposed on the basis of mathematical analysis.

可压缩两气体流动的简化神经网络模型

实用的虚拟流体方法(practical ghost fluid method, PGFM)利用Riemann问题速度解对可压缩多介质流场界面条件进行建模。基于构造的嵌入物理约束的神经网络模型预测Riemann问题速度解的方式,给出一种两气体流动的神经网络模型简化方法。首先提出完全气体状态方程下神经网络模型输入特征采样范围从无界域到有界域的转换方法,改善模型预测不同初始条件下Riemann解的泛化性能。根据该转化方法,进一步提出一种结构更加简单的神经网络优化方法,将输入维度从5个减少到3个,有效提高神经网络的训练效果。将该神经网络代理模型应用于PGFM程序框架,通过典型的一维与二维两气体流动问题进行数值验证与对比分析。结果表明,简化的网络模型与已有研究的神经网络模型相比,能取得精度相近的计算结果。而在神经网络训练效率上,简化神经网络具有明显优势。同时因为简化神经网络采样维度少,方便尝试加密采样提高拟合精度,更具备发展潜力。

基于可压缩两相流模型的注射成型填充模拟

基于现有的超算平台及有限体积法计算程序,开发了一种用于注射成型的三维数值模拟计算模型。该模型数值方法基于可压缩两相流,考虑了熔体和气体的密度变化,即将熔体和空气这两种不同性质的流体,采用同一套控制方程进行计算。采用有限体积法进行离散,通过压力隐式算子分割算法(PISO)求解压力-速度耦合方程组,结合流体体积(VOF)法进行界面追踪。首先模拟了带圆柱嵌件的平板型腔填充过程,采用六面体为主导的方法划分了三种不同网格系统,定量比较三种网格下的速度基本一致,从而验证了网格的收敛性。考虑到计算效率,选取M2(网格数为106876个)网格系统,模拟了温度、剪切速率和压力在不同截面上的分布。结果表明,在填充时间(t)为0.6,0.8,1.4 s时刻下熔体流体前沿的界面追踪模拟与实验吻合;在更复杂的不均匀厚度凹槽平板熔体填充模拟过程中,塑料熔体注入型腔时,会先在薄壁凹槽内流动,随后流进厚壁区域。在t为0.125,0.25,0.375 s时刻下的流动前沿会产生形状像喷泉的流锋,这种流动现象可以通过三维模型预测,与商业软件仿真结果呈现基本一致。随着填充速率的增大,注射压力数值与Moldflow结果更接近。

A Conservative Lagrangian Scheme for Solving Compressible Fluid Flows with Multiple Internal Energy Equations

Lagrangianmethods arewidely used inmany fields formulti-material compressible flow simulations such as in astrophysics and inertial confinement fusion(ICF),due to their distinguished advantage in capturing material interfaces automatically.In some of these applications,multiple internal energy equations such as those for electron,ion and radiation are involved.In the past decades,several staggeredgrid based Lagrangian schemes have been developed which are designed to solve the internal energy equation directly.These schemes can be easily extended to solve problems with multiple internal energy equations.However such schemes are typically not conservative for the total energy.Recently,significant progress has been made in developing cell-centered Lagrangian schemes which have several good properties such as conservation for all the conserved variables and easiness for remapping.However,these schemes are commonly designed to solve the Euler equations in the form of the total energy,therefore they cannot be directly applied to the solution of either the single internal energy equation or the multiple internal energy equations without significant modifications.Such modifications,if not designed carefully,may lead to the loss of some of the nice properties of the original schemes such as conservation of the total energy.In this paper,we establish an equivalency relationship between the cell-centered discretizations of the Euler equations in the forms of the total energy and of the internal energy.By a carefully designed modification in the implementation,the cell-centered Lagrangian scheme can be used to solve the compressible fluid flow with one or multiple internal energy equations and meanwhile it does not lose its total energy conservation property.An advantage of this approach is that it can be easily applied to many existing large application codes which are based on the framework of solving multiple internal energy equations.Several two dimensional numerical examples for both Euler equations and three-temperature hydrodynamic equations in cylindrical coordinates are presented to demonstrate the performance of the scheme in terms of symmetry preserving,accuracy and non-oscillatory performance.

Numerical investigation on permeability evolution behavior of rock by an improved flow-coupling algorithm in particle flow code

岩石渗透性的意义重大,构造应力和人类工程活动会对渗透性产生巨大影响。岩石内部孔压与流速分布情况的全面监测对阐明渗透性的演化机制至关重要,其在试验中难以实施,但在数值模拟中可容易实现。因此,本文采用一种离散元方法—颗粒流程序(Particle Flow Code,简称PFC)开展岩石材料渗透性行为的模拟研究。针对PFC中原流–固耦合算法的不足,对其进行改进,使改进后的算法更能体现流体在岩石裂隙中的流动优势。分别采用原算法与改进算法对三轴压缩过程中的渗透性演化进行数值模拟,对比结果表明改进算法能更好地反映试验现象。本文利用改进流–固耦合算法,进一步分析了渗流过程中的孔压和流速分布的演化情况。结果表明,孔压和流速都优先通过裂隙传递而非岩石基质。根据运移流体的能力将裂隙划分为三类:Ⅰ)贯穿进口端和出口端的裂隙;Ⅱ)仅与进口端连接的裂隙;Ⅲ)仅与出口端连接的裂隙。Ⅰ)类裂隙始终是最主要的流速和孔压的传递通道。Ⅱ)类裂隙中孔压首先增大并逐渐趋于稳定,而流速首先增大,当流体运移到裂隙终端后流速减小甚至降低为零。在Ⅲ)类裂隙中,无明显的流体运移或孔压集中。

Computational fluid dynamics simulation of Hyperloop pod predicting laminar–turbulent transition

Three-dimensional compressible flow simulationswere conducted to develop a Hyperloop pod. Thenovelty is the usage of Gamma transition model, in whichthe transition from laminar to turbulent flow can be predicted.First, a mesh dependency study was undertaken,showing second-order convergence with respect to themesh refinement. Second, an aerodynamic analysis for twodesigns, short and optimized, was conducted with thetraveling speed 125 m/s at the system pressure 0.15 bar.The concept of the short model was to delay the transitionto decrease the frictional drag;meanwhile that of theoptimized design was to minimize the pressure drag bydecreasing the frontal area and introduce the transitionmore toward the front of the pod. The computed resultsshow that the transition of the short model occurred moreon the rear side due to the pod shape, which resulted in 8%smaller frictional drag coefficient than that for the optimizedmodel. The pressure drag for the optimized designwas 24% smaller than that for the short design, half ofwhich is due to the decrease in the frontal area, and theother half is due to the smoothed rear-end shape. The totaldrag for the optimized model was 14% smaller than that forthe short model. Finally, the influence of the systempressure was investigated. As the system pressure and theReynolds number increase, the frictional drag coefficientincreases, and the transition point moves toward the front,which are the typical phenomena observed in the transitionregime.

REVIEW ON MATHEMATICAL ANALYSIS OF SOME TWO-PHASE FLOW MODELS

The two-phase flow models are commonly used in industrial applications, such as nuclear, power, chemical-process, oil-and-gas, cryogenics, bio-medical, micro-technology and so on. This is a survey paper on the study of compressible nonconservative two-fluid model, drift-flux model and viscous liquid-gas two-phase flow model. We give the research developments of these three two-phase flow models, respectively. In the last part, we give some open problems about the above models.

SPECTRAL-DIFFERENCE METHOD FOR TWO-DIMENSIONAL COMPRESSIBLE FLUID FLOW

We develop a combined Fourier spectral-finite difference method for solving 2-dimensional, semi-periodic compressible fluid how problem. The error estimation, as well as the convergence rate, is presented.

Domain Decomposition Preconditioners for Discontinuous Galerkin Discretizations of Compressible Fluid Flows

In this article we consider the application of Schwarz-type domain decomposition preconditioners to the discontinuous Galerkin finite element approximation of the compressible Navier-Stokes equations.To discretize this system of conservation laws,we exploit the(adjoint consistent)symmetric version of the interior penalty discontinuous Galerkin finite element method.To define the necessary coarse-level solver required for the definition of the proposed preconditioner,we exploit ideas from composite finite element methods,which allow for the definition of finite element schemes on general meshes consisting of polygonal(agglomerated)elements.The practical performance of the proposed preconditioner is demonstrated for a series of viscous test cases in both two-and three-dimensions.

气相压缩性对气液混输泵设计工况点性能的影响

为研究气相压缩性对气液混输泵性能的影响规律,以螺旋轴流式气液混输泵为研究对象,采用欧拉-欧拉双流体模型,在20%~80%进口含气率范围内对混输泵设计工况点进行数值计算,分析气相压缩性对混输泵外特性曲线和内流场的影响。研究表明,在高含气率下气相可压缩性对混输泵的外特性预测结果影响明显增大;考虑气相压缩性后,混输泵叶轮单个流道内最先出现气堵问题,并且气相压缩性明显影响叶轮叶片上压力载荷分布以及叶轮内的气液两相的相间速度差分布。

A Front TrackingMethod for the Simulation of Compressible Multimedium Flows

A front trackingmethod combinedwith the real ghost fluidmethod(RGFM)is proposed for simulations of fluid interfaces in two-dimensional compressible flows.In this paper the Riemann problem is constructed along the normal direction of interface and the corresponding Riemann solutions are used to track fluid interfaces.The interface boundary conditions are defined by the RGFM,and the fluid interfaces are explicitly tracked by several connected marker points.The Riemann solutions are also used directly to update the flow states on both sides of the interface in the RGFM.In order to validate the accuracy and capacity of the new method,extensive numerical tests including the bubble advection,the Sod tube,the shock-bubble interaction,the Richtmyer-Meshkov instability and the gas-water interface,are simulated by using the Euler equations.The computational results are also compared with earlier computational studies and it shows good agreements including the compressible gas-water system with large density differences.

A High Order Sharp-Interface Method with Local Time Stepping for Compressible Multiphase Flows

In this paper,a new sharp-interface approach to simulate compressible multiphase flows is proposed.The new scheme consists of a high order WENO finite volume scheme for solving the Euler equations coupled with a high order pathconservative discontinuous Galerkin finite element scheme to evolve an indicator function that tracks the material interface.At the interface our method applies ghost cells to compute the numerical flux,as the ghost fluid method.However,unlike the original ghost fluid scheme of Fedkiw et al.[15],the state of the ghost fluid is derived from an approximate-state Riemann solver,similar to the approach proposed in[25],but based on a much simpler formulation.Our formulation leads only to one single scalar nonlinear algebraic equation that has to be solved at the interface,instead of the system used in[25].Away from the interface,we use the new general Osher-type flux recently proposed by Dumbser and Toro[13],which is a simple but complete Riemann solver,applicable to general hyperbolic conservation laws.The time integration is performed using a fully-discrete one-step scheme,based on the approaches recently proposed in[5,7].This allows us to evolve the system also with time-accurate local time stepping.Due to the sub-cell resolution and the subsequent more restrictive time-step constraint of the DG scheme,a local evolution for the indicator function is applied,which is matched with the finite volume scheme for the solution of the Euler equations that runs with a larger time step.The use of a locally optimal time step avoids the introduction of excessive numerical diffusion in the finite volume scheme.Two different fluids have been used,namely an ideal gas and a weakly compressible fluid modeled by the Tait equation.Several tests have been computed to assess the accuracy and the performance of the new high order scheme.A verification of our algorithm has been carefully carried out using exact solutions as well as a comparison with other numerical reference solutions.The material interface is resolved sharply and accurately without spurious oscillations in the pressure field.