THE GLOBAL WELL-POSEDNESS OF SOLUTIONS TO COMPRESSIBLE ISENTROPIC TWO-FLUID MAGNETOHYDRODYNAMICS IN A STRIP DOMAIN

In this paper,we consider a model of compressible isentropic two-fluid magneto-hydrodynamics without resistivity in a strip domain in three dimensional space.By exploiting the two-tier energy method developed in[Anal PDE,2013,6:1429–1533],we prove the global well-posedness of the governing model around a uniform magnetic field which is non-parallel to the horizontal boundary.Moreover,we show that the solution converges to the steady state at an almost exponential rate as time goes to infinity.Compared to the work of Tan and Wang[SIAM J Math Anal,2018,50:1432–1470],we need to overcome the difficulties caused by particles.

High-order targeted essentially non-oscillatory scheme for two-fluid plasma model

The weakly ionized plasma flows in aerospace are commonly simulated by the single-fluid model,which cannot describe certain nonequilibrium phenomena by finite collisions of particles,decreasing the fidelity of the solution.Based on an alternative formulation of the targeted essentially non-oscillatory(TENO)scheme,a novel high-order numerical scheme is proposed to simulate the two-fluid plasmas problems.The numerical flux is constructed by the TENO interpolation of the solution and its derivatives,instead of being reconstructed from the physical flux.The present scheme is used to solve the two sets of Euler equations coupled with Maxwell's equations.The numerical methods are verified by several classical plasma problems.The results show that compared with the original TENO scheme,the present scheme can suppress the non-physical oscillations and reduce the numerical dissipation.

Screening effect of plasma flow on the resonant magnetic perturbation penetration in tokamaks based on two-fluid model

Numerical simulation on the resonant magnetic perturbation penetration is carried out by the newly-updated initial value code MDC(MHD@Dalian Code).Based on a set of two-fluid fourfield equations,the bootstrap current,parallel,and perpendicular transport effects are included appropriately.Taking into account the bootstrap current,a mode penetration-like phenomenon is found,which is essentially different from the classical tearing mode model.To reveal the influence of the plasma flow on the mode penetration process,E×B drift flow and diamagnetic drift flow are separately applied to compare their effects.Numerical results show that a sufficiently large diamagnetic drift flow can drive a strong stabilizing effect on the neoclassical tearing mode.Furthermore,an oscillation phenomenon of island width is discovered.By analyzing it in depth,it is found that this oscillation phenomenon is due to the negative feedback regulation of pressure on the magnetic island.This physical mechanism is verified again by key parameter scanning.

Effects of diamagnetic drift on nonlinear interaction between multi-helicity neoclassical tearing modes

A numerical study of the diamagnetic drift effect on the nonlinear interaction between multi-helicity neoclassical tearing modes(NTMs) is carried out using a set of four-field equations including two-fluid effects.The results show that,in contrast to the single-fluid case,5/3 NTM cannot be completely suppressed by 3/2 NTM with diamagnetic drift flow.Both modes exhibit oscillation and coexist in the saturated phase.To better understand the effect of the diamagnetic drift flow on multiple-helicity NTMs,the influence of typical relevant parameters is investigated.It is found that the average saturated magnetic island width increases with increasing bootstrap current fraction f_(b) but decreases with the ion skin depth δ.In addition,as the ratio of parallel to perpendicular transport coefficients χ_(‖)/χ_(⊥) increases,the average saturated magnetic island widths of the 3/2 and 5/3 NTMs increase.The underlying mechanisms behind these observations are discussed in detail.

Temperature and current sensitivity extraction of optical superconducting transition-edge sensors based on a two-fluid model

Optical superconducting transition-edge sensor(TES)has been widely used in quantum information,biological imaging,and fluorescence microscopy owing to its high quantum efficiency,low dark count,and photon number resolving capability.The temperature sensitivity(α_(I))and current sensitivity(β_(I))are important parameters for optical TESs,which are generally extracted from the complex impedance.Here we present a method to extractα_(I)andβ_(I)based on a two-fluid model and compare the calculated current-voltage curves,pulse response,and theoretical energy resolution with the measured ones.This method shows qualitative agreement that is suitable for further optimization of optical TESs.

An Interacting Two-Fluid Scenario for Quintom Dark Energy

The Quintom dark energy is a proposal that explains the recent observations that mildly favor the equation of state of dark energy ω crossing -1 near the past. The Quintom model is often constructed by two scalar fields, where one is the quintessence feld and another is the phantom field. The cosmological implication of the coupling of the two fields of the dark energy is out of question worth investigating. However, the consideration of the coupling in the field scenario is somewhat complex thus we propose an interacting two-fluid Quintom scenario for simplicity. The interaction between the two components is parametrized by a constant 71 in this scenario. The cosmological implications of this parametrization are investigated in detail in this paper. Also, a diagnostic for this model is performed by using the statefinder pairs {s, r} and {q, r}.

A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters： the nonlinearity ratio ε, represented by the ratio of amplitude to depth, and the dispersion ratio μ, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin et al in the study of the surface waves when considering the order up to O（μ^2）. As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin et al for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.

Two-fluid oscillatory flow in a channel

The validity of Navier’s partial slip condition is investigated by studying the oscillatory flow in a coated channel.The two-fluid model is used to solve the unsteady viscous equations exactly.Partial slip is experienced by the core fluid.It is found that Naviers condition does not hold for an unsteady core fluid.

Anisotropic Plane Symmetric Two-Fluid Cosmological Model with Time-Varying G and A

We investigate a two-fluid anisotropic plane symmetric cosmological model with variable gravitational constant G（t） and cosmological term A（t）. In the two-fluid model, one fluid is chosen to be that of the radiation field modeling the cosmic microwave background and the other one a perfect fluid modeling the material content of the universe. Exact solutions of the field equations are obtained by using a special form for the average scale factor which corresponds to a specific time-varying deceleration parameter. The model obtained presents a cosmological scenario which describes an early acceleration and late-time deceleration. The gravitation constant increases with the cosmic time whereas the cosmological term decreases and asymptotically tends to zero. The physical and kinematical behaviors of the associated fluid parameters are discussed.

Numerical Simulation of Countercurrent Flow in a PWR Hot Leg by Using Two-Fluid Model

In order to evaluate CCFL （countercurrent flow limitation） characteristics in a PWR （pressurized water reactor） hot leg under reflux condensation, numerical simulations have been conducted using a 2F （two-fluid） model and a VOF （volume of fluid） method implemented in the CFD （computational fluid dynamics） software, FLUENT6.3.26. The 2F model gave good agreement with CCFL data in low pressure conditions but did not give good results for high pressure steam-water conditions. In the previous study, the computational grid and schemes were improved in the VOF method to improve calculations in circular tubes, and the calculated CCFL characteristics agreed well with the UPTF （Upper Plenum Test Facility） data at 1.5 MPa. In this study, therefore, using the 2F model and the computational grid previously improved for the VOF calculations, numerical simulations were conducted for steam-water flows at 1.5 MPa under PWR full-scale conditions. In the range of medium gas volumetric fluxes, the calculated CCFL characteristics agreed well with the values calculated by the VOF method and the UPTF data at 1.5 MPa. This indicated that the reference set of the interfacial drag correlations employed in this study could be applied not only to low pressures but also to high pressures.

Prediction of pressure gradient and hold-up in horizontal liquid-liquid pipe flow

This paper aims to propose correlations to predict pressure gradient,friction factor and fluid phase hold-up in liquid-liquid horizontal pipe flow.To develop the correlations,experiments are conducted using high viscous oils(202 and 630 mPa⋅s)in a steel pipe of length 11.25 m and length-to-diameter ratio of 708.In addition,the experimental data from the literature comprising wide range of flow and fluid properties is analyzed.For the analysis,the liquid-liquid pipe flow data is categorized into two as:stratified and dispersed.The existing friction factor correlations are modified to incorporate the effects of viscosity of the oil phase,interfacial curvature(contact/wetting angle-in lieu of material of the pipe)and fluid phase fraction.In the two-fluid model of stratified flow,the wall stress and interfacial stress correlations are substituted with superficial velocities of fluids and superficial Reynolds numbers of fluid phases replacing fluid phase velocities and fluid Reynolds numbers.Similarly,for dispersed flow,an effective Reynolds number is described as the sum of superficial Reynolds number of oil and water phases.Substituting the generally employed mean or mixture Reynolds number with the effective Reynolds number into the existing single-phase turbulent flow friction factor correlation,an effective friction factor for oil-water flow is proposed.Employing the proposed correlations,the pressure gradient across the oil-water flow and hold-up volume fraction are predicted with significant reduction in error compared with that of conventionally employed correlations.The average error and standard deviation values of−7.06%,20.72%and 0.31%,18.79%are found for stratified flow and dispersed flow respectively.

Numerical Study of Solid-Liquid Two-Phase Flow in StirredTanks with Rushton Impeller(Ⅱ) Prediction of Critical Impeller Speed

Three-dimensional solid-liquid flow is mathematically formulated by means of the 'two-fluid' approach and the two-phase k-ε-AP turbulence model. The turbulent fluctuation correlations appearing in the Reynolds time averaged governing equations are fully incorporated. The solid-liquid flow field and solid concentration distribution in baffled stirred tanks with a standard Rushton impeller are numerically simulated using an improved 'inner-outer'iterative procedure. The flow pattern is identified via the velocity vector plots and a recirculation loop with higher solid concentration is observed in the central vicinity beneath the impeller. Comparison of the simulation with experimental data on the mean velocities and the turbulence quantities of the solid phase is made and quite reasonable agreement is obtained except for the impeller swept volume. The counterpart of liquid phase is presented as well.The predicted solid concentration distribution for three experimental cases with the average solid concentration up to 20% is also found to agree reasonably with the experimental results published in the literature.

Flow Behaviors of Gas-Solid Injector by 3D Simulation with Kinetic Theory of Granular Flow

A computational study on the flow behavior of a gas-solid injector by Eulerian approach was carried out. The gas phase was modeled with k-ε turbulent model and the particle phase was modeled with kinetic theory of granular flow. The simulations by Eulerian two-fluid model （TFM） were compared with the corresponding results by discrete element method （DEM） and experiments. It was showed that TFM simulated results were in reasonable agreement with the experimental and DEM simulated results. Based on TFM simulations, gas-solid flow pattern, gas velocity, particle velocity and the static pressure under different driving jet velocity, backpressure and convergent section angle were obtained. The results showed that the time average axial gas velocity sharply decreased and then slightly increased to a constant value in the horizontal conveying pipe. The time average axial particle velocity increased initially and then decreased, but in the outlet region of the convergent section the particle velocity remarkably increased once more to the maximal value. As a whole, the static pressure distribution change trends were found to be independent on driving gas velocity, backpressure and convergent section angle. However, the static pressure increased with increase of convergent section angle and gas jet velocities. The difference of static pressure to backpressure increased with increasing backpressure.

Analysis of Flow Structure and Calculation of Drag Coefficient for Concurrent-up Gas-Solid Flow

This study investigates the heterogeneous structure and its influence on drag coefficient for concurrent-up gas-solid flow. The energy-minimization multi-scale (EMMS) model is modified to simulate the variation of structure parameters with solids concentration, showing the tendency for particles to aggregate to form clusters and for fluid to pass around clusters. The global drag coefficient is resolved into that for the dense phase, for the dilute phase and for the so-called inter-phase, all of which can be obtained from their respective phase-specific structure parameters. The computational results show that the drag coefficients of the different phases are quite different, and the global drag coefficient calculated from the EMMS approach is much lower than that from the correlation of Wen and Yu. The simulation results demonstrate that the EMMS approach can well describe the heterogeneous flow structure, and is very promising for incorporation into the two-fluid model or the discrete particle model as the closure law for drag coefficient.

Parametric study of gas−liquid two-phase flow field in horizontal stirred tank

Based on Fluent software,the gas−liquid two-phase flow in the horizontal stirred tank was simulated with SST k−ωturbulence model,Eulerian−Eulerian two-fluid model,and multi-reference flame method.The mixing process in the tank was calculated by tracer method.The results show that increasing the rotating speed or gas flow is conducive to a more uniform distribution of the gas phase and accelerates the mixing of the liquid phase.When the rotating speed exceeds 93 r/min,the relative power demand remains basically constant.The change in the inclination angle of the upper impeller has minimal effect on the gas phase distribution.When the inclination angle is 50°,the relative power demand reaches the maximum.An appropriate increase in the impeller distance from the bottom improves the gas holdup and gas phase distribution but increases the liquid phase mixing time.

Influence of core box vents distribution on flow dynamics of core shooting process based on experiment and numerical simulation

Core shooting process plays a decisive role in the quality of sand cores, and core box vents distribution is one of the most important factor determining the effectiveness of core shooting process. In this paper, the influence of core box vents distribution on the flow dynamics of core shooting process was investigated based on in situ experimental observations with transparent core box, high-speed camera and pressure measuring system. Attention was focused on the variation of both the flow behavior of sand and pressure curves due to different vents distribution. Taking both kinetic and frictional stress into account, a kinetic-frictional constitutive model was established to describe the internal momentum transfer in the solid phase. Two-fluid model(TFM) simulation was then performed and good agreement was achieved between the experimental and simulated results on both the flow behavior of sand and the pressure curves. It was found that vents distribution has direct effect on the pressure difference of different locations in the core box, which determines the buoyancy force exerting on the sand particles and significantly influences the filling process of core sand.

Stability of Stratified Gas-Liquid Flow in Horizontal and Near Horizontal Pipes

A viscous Kelvin-Helmholtz criterion of the interfacial wave instability is proposed in this paper based on the linear stability analysis of a transient one-dimensional two-fluid model. In thismodel, the pressure is evaluated using the local momentum balance rather than the hydrostatic approximation. The criterion predicts well the stability limit of stratified flow in horizontal and nearly horizontal pipes. The experimental and theoretical investigation on the effect of pipe inclination on the interfacial instability are carded out. It is found that the critical liquid height at the onset of interfacial wave instability is insensitive to the pipe inclination. However, the pipe inclination significantly affects critical superficial liquid velocity and wave velocity especially lor low gas velocities.

Physically based modeling and animation of tornado

Realistic modeling and rendering of dynamic tornado scene is recognized as a challenging task for researchers of computer graphics. In this paper a new physically based method for simulating and animating tornado scene is presented. We first propose a Two-Fluid model based on the physical theory of tornado, then we simulate the flow of tornado and its interaction with surrounding objects such as debris, etc. Taking the scattering and absorption of light by the participating media into account, the illumination effects of the tornado scene can be generated realistically. With the support of graphics hardware, various kinds of dynamic tornado scenes can be rendered at interactive rates.

Numerical simulations of gas-particle flow behavior created by low-level rotary-winged aircraft flight over particle bed

The aerodynamics of gas-particle suspensions is simulated as an Euler-Euler two-fluid model in a revolving rotor over a particle bed. The interactions of collisions between the blade and particles and particle-particle interactions are modeled using the kinetic theory of granular flow(KTGF). The gas turbulence induced by the rotation of the rotor is modeled using the kg-εg model. The flow field of a revolving rotor is simulated using the multiple reference frame(MRF) method. The distributions of velocities, volume fractions, and gas pressure are predicted while the aircraft hovers at different altitudes.The gas pressure decreases from the hub to the tip of the blade, and it is higher at the pressure side than that at the suction side of the rotor. The turbulent kinetic energy of the gas increases toward the blade tip. The volume fraction of particles decreases as the hovering altitude increases. The simulated pressure coefficient is compared with that in experimental measurements.

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.