THE GLOBAL EXISTENCE AND UNIQUENESS OF SMOOTH SOLUTIONS TO A FLUID-PARTICLE INTERACTION MODEL IN THE FLOWING REGIME

This paper is concerned with the Cauchy problem for a 3D fluid-particle interaction model in the so-called flowing regime inℝ3.Under the smallness assumption on both the external potential and the initial perturbation of the stationary solution in some Sobolev spaces,the existence and uniqueness of global smooth solutions in H3 of the system are established by using the careful energy method.

BLOWUP CRITERION FOR THE COMPRESSIBLE FLUID-PARTICLE INTERACTION MODEL IN 3D WITH VACUUM

In this article, we consider the blowup criterion for the local strong solution to the compressible fluid-particle interaction model in dimension three with vacuum. We establish a BKM type criterion for possible breakdown of such solutions at critical time in terms of both the L^∞ （0, T; L^6）-norm of the density of particles and the ^L1（0, T; L^∞）-norm of the deformation tensor of velocity gradient.

CLASSICAL SOLUTIONS OF THE 3D COMPRESSIBLE FLUID-PARTICLE SYSTEM WITH A MAGNETIC FIELD

This paper addresses the 3-D Cauchy problem of a fluid-particle system with a magnetic field.First,the local classical solutions of the linearized model on the sphere Br are obtained by some a priori estimates that do not depend on the radius r.Second,the classical solutions of the linearized model in R^(3) are obtained by combining the continuation and compactness methods.Finally,the classical solutions of the original system are proved by use of the picard iteration argument and the energy method.

Numerical modeling of fluid-particle interaction in granular media

Fluid-particle interaction underpins important behavior of granular media. Particle-scale simulation may help to provide key microscopic information governing the interaction and offer better understanding of granular media as a whole. This paper presents a coupled computational fluid dynamics and discrete element method （CFD-DEM） approach for this purpose. The granular particle system is modeled by DEM, while the fluid flow is simulated by solving the locally averaged Navier-Stokes equation with CFD. The coupling is considered by exchanging such interaction forces as drag force and buoyancy force between the DEM and CFD. The approach is benchmarked by two classic geomechanics problems for which analytical solutions are available, and is further applied to the prediction of sand heap formation in water through hopper flow. It is demonstrated that the key characteristic of granular materials interacting with pore water can be successfully captured by the proposed method.

Interpretable machine learning analysis and automated modeling to simulate fluid-particle flows

The present study extracts human-understandable insights from machine learning(ML)-based mesoscale closure in fluid-particle flows via several novel data-driven analysis approaches,i.e.,maximal information coefficient(MIC),interpretable ML,and automated ML.It is previously shown that the solidvolume fraction has the greatest effect on the drag force.The present study aims to quantitativelyinvestigate the influence of flow properties on mesoscale drag correction(H_(d)).The MIC results showstrong correlations between the features(i.e.,slip velocity(u^(*)_(sy))and particle volume fraction(εs))and thelabel H_(d).The interpretable ML analysis confirms this conclusion,and quantifies the contribution of u^(*)_(sy),εs and gas pressure gradient to the model as 71.9%,27.2%and 0.9%,respectively.Automated ML without theneed to select the model structure and hyperparameters is used for modeling,improving the predictionaccuracy over our previous model(Zhu et al.,2020;Ouyang,Zhu,Su,&Luo,2021).

A FLUID-PARTICLE MODEL WITH ELECTRIC FIELDS NEAR A LOCAL MAXWELLIAN WITH RAREFACTION WAVE

The paper is concerned with time-asymptotic behavior of solution near a local Maxwellian with rarefaction wave to a fluid-particle model described by the Vlasov-Fokker-Planck equation coupled with the compressible and inviscid fluid by Euler-Poisson equations through the relaxation drag frictions,Vlasov forces between the macroscopic and microscopic momentums and the electrostatic potential forces.Precisely,based on a new micro-macro decomposition around the local Maxwellian to the kinetic part of the fluid-particle coupled system,which was first developed in[16],we show the time-asymptotically nonlinear stability of rarefaction wave to the one-dimensional compressible inviscid Euler equations coupled with both the Vlasov-Fokker-Planck equation and Poisson equation.

Modeling of Motion of Particle Clouds Formed by Dumping Dredged Material

The motion of particle clouds formed by dumping dredged material into quiescent waters is experimentally and numerically studied. In the numerical model, the particle phase is modeled by the dispersion model, and turbulence is calculated by the large eddy simulation. The governing equations, including the filtered Navier-Stokes equations and mass transport equation, are solved based on the operator-splitting algorithm and an implicit cubic spline interpolation scheme. The eddy viscosity is evaluated by the modified Smagorinsky model including the buoyancy term. Comparisons of main flow characteristics, including shape, size, average density excess, moving speed and the amount of particles deposited on the bed, between experimental and computational results show that the numerical model well predicts the motion of the cloud from the falling to spreading stage. The effects of silt-fence on the motion of the particle cloud are also investigated.

Mathematical concepts and their physical foundation in the nonstandard analysis theory of turbulence

Main mathematical concepts and their physical foundation in the nonstandard analysis theory of turbulence are presented and discussed. The underlying fact is that there does not exist the absolute zero fluid-volume. Therefore, the physical object corresponding to the absolute point is just the uniform fluid-particle. The fluid-particle, in general, corresponds to the monad. The uniform fluid-particle corresponds to the uniform monad, while the nonuniform fluid-particle to the nonuniform monad. There are two kinds of the differentiations, one is based on the absolute point, and the other based on the monad. The former is adopted in the Navier-Stokes equations, and the latter in the fundamental equations presented in this paper for the nonstandard analysis theory of turbulence. The continuity of fluid is elucidated by virtue of the concepts of the fluid-particle and fluid-particle at a lower level. Furthermore, the characters of the continuity in two cases, i.e. in the standard and nonstandard analyses, are presented in this paper. And the difference in discretization between the Navier-Stokes equations and the fundamental equations given herein is also pointed out.

Boundary Layer Flow of an Unsteady Dusty Fluid and Heat Transfer Over a Stretching Sheet with Non-Uniform Heat Source/Sink

An analysis has been carried out to study the effect of hydrodynamic laminar boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface in the presence of non-uniform heat source/sink. Heat transfer characteristics are examined for two different kinds of boundary conditions, namely 1) variable wall temperature and 2) variable heat flux. The governing partial differential equations are transformed to system of ordinary differential equations. These equations are solved numerically by applying RKF-45 method. The effects of various physical parameters such as magnetic parameter, dust interaction parameter, number density, Prandtl number, Eckert number, heat source/sink parameter and unsteadiness parameter on velocity and temperature profiles are studied.

Boundary Layer Flow and Heat Transfer of a Dusty Fluid over a Stretching Vertical Surface

This paper presents the study of convective heat transfer characteristics of an incompressible dusty fluid past a vertical stretching sheet. The governing partial differential equations are reduced to nonlinear ordinary differential equations by using similarity transformation. The transformed equations are solved numerically by applying Runge Kutta Fehlberg fourth-fifth order method (RKF45 Method). Here obtained non-dimensional velocity and temperature profiles has been carried out to study the effect of different physical parameters such as fluid-particle interaction parameter, Grashof number, Prandtl number, Eckert number. Comparison of the obtained numerical results is made with previously published results.

Global Weak Solutions for Compressible Navier-Stokes-Vlasov-Fokker-Planck System

The one-dimensional compressible Navier-Stokes-Vlasov-Fokker-Planck system with density-dependent viscosity and drag force coefficients is investigated in the present paper.The existence,uniqueness,and regularity of global weak solution to the initial value problem for general initial data are established in spatial periodic domain.Moreover,the iong time behavior of the weak solution is analyzed.It is shown that as the time grows,the distri-bution function of the particles converges to the global Maxwellian,and both the fluid velocity and the macroscopic velocity of the particles converge to the same speed.

Modeling micro-particle deposition in human upper respiratory tract under steady inhalation

A representative human upper respiratory tract （URT） with idealized oral region and asymmetric tracheo- bronchial （TB） airway has been modeled, and laminar-to-turbulent airflow for typical inhalation modes as well as micro-particle transport and deposition has been simulated using CFX10.0 software from Ansys Inc. on a personal computer. The asymmetric TB airway could not be replaced by an extended straight tube as outlet of the oral region while investigating the tracheal airflow field and particle deposition. Compared to an idealized oral airway with an extended straight tube, several differences could be noted： （i） The laryngeal jet extends further down the trachea and inclines towards the anterior wall; （ii） the turbulence level in trachea is less and decays more quickly; （iii） three recirculation zones are visible with intense adverse current after the glottis; （iv） deposition of small particles in trachea is reduced due to lower turbulence. Refined unstructured mesh with densified boundary layer mesh could be a proper substitute for the structured mesh in the human URT model with asymmetric TB airway. Based on the refined unstructured mesh, the physiological structure of uvula in the soft palate is properly simulated in the present human URT model.

DIRECT NUMERICAL SIMULATIONS OF THE DYNAMICS OF PARTICLES WITH ARBITRARY SHAPES IN SHEAR FLOWS

A fluid-structure interaction method based on the arbitrary Lagrangian-Eulerian method and a dynamic mesh method was developed to simulate the dynamics of a rigid particle in shear flows.In the method,the governing equations for the fluid flow and particle motion were sequentially solved in a two-way coupling fashion.The mesh system was deformed or re-meshed by the dynamic mesh method.The method was employed to simulate the dynamics of a single particle suspended in a flow channel and the dynamics of the particle were studied.The simulation results show that the angular velocity is not only a function of the inclination angle,is but also influenced by the aspect ratio yielding a hysteresis,while the angular velocity obtained from the Keller-Scalak model is a function only of the inclination angle and does not show a hysteresis.The present simulations clearly demonstrate that the Fluid-Structure Interaction（FSI） module is very stable,accurate and robust.

Gas–solid interaction force from direct numerical simulation (DNS) of binary systems with extreme diameter ratios

Fluid-particle systems as commonly encountered in chemical, metallurgical and petroleum industries are mostly polydisperse in nature. However, the relations used to describe fluid-particle interactions are originally derived from monodisperse systems, with ad hoc modifications to account for polydispersity. In previous work it was shown that for bidisperse systems with moderate diameter ratios of 1：2 to 1：4, this approach leads to discrepancies, and a correction factor is needed. In this work we demonstrate that this correction factor also holds for more extreme diameter ratios of 1：5, 1：7 and 1： 10, although the force on the large particles is slightly overestimated when using the correction factor. The main origin of the correction is that the void surrounding the large particles becomes less in case ofa bidisperse mixture, as compared to a monodisperse system with the same volume fraction. We further investigated this discrepancy by calculating the volume per particle by means of Voronoi tessellation.

Algorithms in a Robust Hybrid CFD-DEM Solver for Particle-Laden Flows

A robust and efficient solver coupling computational fluid dynamics(CFD)with discrete element method(DEM)is developed to simulate particle-laden flows in various physical settings.An interpolation algorithm suitable for unstructured meshes is proposed to translate between mesh-based Eulerian fields and particle-based Lagrangian quantities.The interpolation scheme reduces the mesh-dependence of the averaging and interpolation procedures.In addition,the fluid-particle interaction terms are treated semi-implicitly in this algorithm to improve stability and to maintain accuracy.Finally,it is demonstrated that sub-stepping is desirable for fluid-particle systems with small Stokes numbers.A momentum-conserving sub-stepping technique is introduced into the fluid-particle coupling procedure,so that problems with a wide range of time scales can be solved without resorting to excessively small time steps in the CFD solver.Several numerical examples are presented to demonstrate the capabilities of the solver and the merits of the algorithm.

Superquadric DEM-SPH coupling method for interaction between non-spherical granular materials and fluids

The research on the coupling method of non-spherical granular materials and fluids aims to predict the particle-fluid interaction in this study.A coupling method based on superquadric elements is developed to describe the interaction between non-spherical solid particles and fluids.The discrete element method(DEM)and the smoothed particle hydrodynamics(SPH)are adopted to simulate granular materials and fluids.The repulsive force model is adopted to calculate the coupling force and then a contact detection method is established for the interaction between the superquadric element and the fluid particle.The contact detection method captures the shape of superquadric element and calculates the distance from the fluid particle to the surface of superquadric element.Simulation cases focusing on the coupling force model,energy transfer,and large-scale calculations have been implemented to verify the validity of the proposed coupling method.The coupling force model accurately represents the water entry process of a spherical solid particle,and reasonably reflects the difference of solid particles with different shapes.In the water entry process of multiple solid particles,the total energy of the water entry process of multiple solid particles tends to be stable.The collapse process of the partially submerged granular column is simulated and analyzed under different parameters.Therefore,this coupling method is suitable to simulate fluid-particle systems containing solid particles with multiple shapes.

The impact of interphase forces on the modulation of turbulence in multiphase flows

The modulation of turbulence by particles has been rigorously investigated in the literature yielding either a reduction or an enhancement of the turbulent kinetic energy at different spatial length scales.However,a general description of the turbulence modulation in multiphase flows due to the presence of an interphase force has attracted less attention.In this paper,we investigate the turbulent modulation for interfacial and fluid-particle flows analytically and numerically,where surface tension and drag define the interphase coupling,respectively.It is shown that surface tension and drag appear as additional production/dissipation terms in the transport equations for the turbulent kinetic energies(TKE),which is of particular importance for the turbulence modelling of multiphase flows.Furthermore,we study the modulation of turbulence in decaying homogenous isotropic turbulence(HIT)for both types of multiphase flow.The results clearly unveil that in both cases the energy is reduced at large scales,while the small-scale energy is enhanced compared to single-phase flows.Particularly,at large scales surface tension works against the turbulent eddies and hinders the ejection of droplet from the corrugated interface.In contrast,at the small scales,the surface tension force and the velocity fluctuations are aligned leading to an enhancement of the energy.In the case of fluid-particle flows,particles retain their energy longer than the surrounding fluid increasing the energy at the small scales,while at the large scales the particles do not follow exactly the surrounding fluid reducing its energy.For the latter effect,a considerable dependence on the particle Stokes number is found.

Global Weak Solutions for Compressible Navier-Stokes-Vlasov-Fokker-Planck System

The one-dimensional compressible Navier-Stokes-Vlasov-Fokker-Planck system with density-dependent viscosity and drag force coefficients is investigated in the present paper.The existence,uniqueness,and regularity of global weak solution to the initial value problem for general initial data are established in spatial periodic domain.Moreover,the long time behavior of the weak solution is analyzed.It is shown that as the time grows,the distribution function of the particles converges to the global Maxwellian,and both the fluid velocity and the macroscopic velocity of the particles converge to the same speed.