Modeling, numerical methods, and simulation for particle-fluid two-phase flow problems

In this paper, we study the issues of modeling, numerical methods, and simulation with comparison to experimental data for the particle-fluid two-phase flow problem involving a solid-liquid mixed medium. The physical situation being considered is a pulsed liquid fluidized bed. The mathematical model is based on the assumption of one-dimensional flows, incompressible in both particle and fluid phases, equal particle diameters, and the wall friction force on both phases being ignored. The model consists of a set of coupled differential equations describing the conservation of mass and momentum in both phases with coupling and interaction between the two phases. We demonstrate conditions under which the system is either mathematically well posed or ill posed. We consider the general model with additional physical viscosities and/or additional virtual mass forces, both of which stabilize the system. Two numerical methods, one of them is first-order accurate and the other fifth-order accurate, are used to solve the models. A change of variable technique effectively handles the changing domain and boundary conditions. The numerical methods are demonstrated to be stable and convergent through careful numerical experiments. Simulation results for realistic pulsed liquid fluidized bed are provided and compared with experimental data. (C) 2004 Elsevier Ltd. All rights reserved.

Novel experimental phenomena of fine-particle fluidized beds

The dynamic response of bed height and concentration waves in liquid-solid fluidized beds to a step change in the fluidization velocity is considered. We experimentally study the liquid-solid fluidized beds, spherical beadings, with sizes ranging from 230 to 270 mesh and the inner diameter of columns made from glass is 2.4 mm. Experimental results find that under certain conditions, fine particles with large Richardson-Zaki exponent n display different dynamic behavior from usual particles with smaller n during expansion and collapse of the fluidized state. (c) 2007 Elsevier Inc. All rights reserved.

Ocean currents-induced pipeline lateral stability on sandy seabed

Unlike previous mechanical actuator loading methods, in this study, a hydrodynamic loading method was employed in a flow flume for simulating ocean currents induced submarine pipeline stability on a sandy seabed. It has been observed that, in the process of pipeline losing lateral stability in currents, there usually exist three characteristic times: (1) onset of sand scour; (2) slight lateral displacement of pipeline; and (3) breakout of pipeline. An empirical linear relationship is established between the dimensionless submerged weight of pipeline and Froude number for describing pipeline lateral stability in currents, in which the current-pipe-soil coupling effects are reflected. Scale effects are examined with the method of "modeling of models," and the sand particle size effects on pipeline stability are also discussed. Moreover, the pipeline stability in currents is compared with that in waves, which indicates that the pipeline laid directly upon the sandy seabed is more laterally stable in currents than in waves.

Drag on an ellipsoid particle in free-molecular plasma flow

Based on the analysis of molecular gas dynamics, the drag and moment acting on an ellipsoid particle of revolution X-2/a(2) + Y-2/a(2) + Z(2)/c(2) = 1, as an example of nonspherical particles, are studied under the condition of free-molecular plasma flow with thin plasma sheaths. A nonzero moment which causes nonspherical particle self-oscillation and self-rotation around its own axis in the plasma flow-similar to the pitching moment in aerodynamics-is discovered for the first time. When the ratio of axis length c/a is unity, the moment is zero and the drag formula are reduced to the well-known results of spherical particles. The effects of the particle-plasma relative velocity, the plasma temperature, and the particle materials on the drag and moment are also investigated.

Kinetic theory for particle concentration distribution in two phase flow

The results of experiments in open channels and closed pipelines show two kinds of patterns for the vertical distribution of particle concentration (i.e., pattern I and pattern II). The former shows a pattern of maximum concentration at some location above the bottom and the downward decay of the concentration below the location. The latter always shows an increase of the particle concentration downward over the whole vertical, with the maximum value at the bottom. Many investigations were made on the pattern II, but few were made on pattern I. In this paper, a particle velocity distribution function is first obtained in the equilibrium state or in dilute steady state for the particle in two-phase flows, then a theoretical model for the particle concentration distribution is derived from the kinetic theory. More attention is paid to the predictions of the concentration distribution of pattern I and comparisons of the present model are made with the data measured by means of laser doppler anemometry (LDA). Very good agreements are obtained between the measured and calculated results.

Influence of suspended particles and particle cover over the density interface

The effect of the particle cover over the density interface between two layers of fluids and of the suspended solid particles in the upper turbulcnt layer on the turbulent entrainment has been studied experimentally. The entrainment distance D is a function of the time of power: D=kt, where =0.200-0.130p. For suspended particles in the upper layer and pure 2-layer fluid is equal to 0.200, but the value of k for the suspended particles is smaller than that for the pure 2-layer fluid. The non-dimensional entrainment velocity is E=KRiln, where n=1.50+0.93 p. It is shown that the particle cover over the interface changes the power of Ril in the entrainment and hinders the turbulent entrainment. The variation rule of E for the suspended particles is the same as that for the pure 2-layer fluid, but the K value of the former is smaller than that of the latter. The turbulent mixing mechanism has been discussed.

Stratification by solid particle suspensions

Turbulence was generated by an oscillating grid above a bed of sediment of spherical glass beads. As expected, part of the sediment was lifted up by the grid action and a suspension layer of depth D formed above the grid. This depth was found remaining independent of grid action but varying with the sediment layer depth when the grid action was kept constant. Volume concentration measurements show the existence of only weak concentration gradients over the layer depth with a rapid fall off in concentration at the outer edge. The theoretical analysis based on a concentration flux model is in good qualitative agreement with observations.

Interface cracking and particulate size effect in particle-reinforced metal-matrix composites

The mechanical behaviors of the ceramic particle-reinforced metal matrix composites are modeled based on the conventional theory of mechanism-based strain gradient plasticity presented by Huang et al. Two cases of interface features with and without the effects of interface cracking will be analyzed, respectively. Through comparing the result based on the interface cracking model with experimental result, the effectiveness of the present model can be evaluated. Simultaneously, the length parameters included in the strain gradient plasticity theory can be obtained.

Prediction of particle distribution in isotropic turbulence by large-eddy simulation

The recent application of large-eddy simulation (LES) to particle-laden turbulence requires that the LES with a subgrid scale (SGS) model could accurately predict particle distributions. Usually, a SGS particle model is used to recover the small-scale structures of velocity fields. In this study, we propose a rescaling technique to recover the effects of small-scale motions on the preferential concentration of inertial particles. The technique is used to simulate particle distribution in isotropic turbulence by LES and produce consistent results with direct numerical simulation (DNS). Key words: particle distribution, particle-laden turbulence, large-eddy simulation, subgrid scale model.

An algorithm for coarse particle sedimentation simulation by Stokesian dynamics

Coarse Particle sedimentation is studied by using an algorithm with no adjustable parameters based on stokesian dynamics. Only inter-particle interactions of hydrodynamic force and gravity are considered. The sedimentation of a simple cubic array of spheres is used to verify the computational results. The scaling and parallelism with OpenMP of the method are presented. Random suspension sedimentation is investigated with Mont Carlo simulation. The computational results are shown in good agreement with experimental fitting at the lower computational cost of O(N In N).

Effects of geometric shape on the hydrodynamics of a self-propelled flapping foil

The hydrodynamics of a free flapping foil is studied numerically. The foil undergoes a forced vertical oscillation and is free to move horizontally. The effect of chord-thickness ratio is investigated by varying this parameter while fixing other ones such as the Reynolds number, the density ratio, and the flapping amplitude. Three different flow regimes have been identified when we increase the chord-thickness ratio, i.e., left-right symmetry, back-and-forth chaotic motion, and unidirectional motion with staggered vortex street. It is observed that the chord-thickness ratio can affect the symmetry-breaking bifurcation, the arrangement of vortices in the wake, and the terminal velocity of the foil. The similarity in the symmetry-breaking bifurcation of the present problem to that of a flapping body under constraint is discussed. A comparison between the dynamic behaviors of an elliptic foil and a rectangular foil at various chord-thickness ratios is also presented.

Turbulent collision of inertial particles: point-particle based, hybrid simulations and beyond

Point-particle based direct numerical simulation (PPDNS) has been a productive research tool for studying both single-particle and particle-pair statistics of inertial particles suspended in a turbulent carrier flow. Here we focus on its use in addressing particle-pair statistics relevant to the quantification of turbulent collision rate of inertial particles. PPDNS is particularly useful as the interaction of particles with small-scale (dissipative) turbulent motion of the carrier flow is mostly relevant. Furthermore, since the particle size may be much smaller than the Kolmogorov length of the background fluid turbulence, a large number of particles are needed to accumulate meaningful pair statistics. Starting from the relative simple Lagrangian tracking of so-called ghost particles, PPDNS has significantly advanced our theoretical understanding of the kinematic formulation of the turbulent geometric collision kernel by providing essential data on dynamic collision kernel, radial relative velocity, and radial distribution function. A recent extension of PPDNS is a hybrid direct numerical simulation (HDNS) approach in which the effect of local hydrodynamic interactions of particles is considered, allowing quantitative assessment of the enhancement of collision efficiency by fluid turbulence. Limitations and open issues in PPDNS and HDNS are discussed. Finally, on-going studies of turbulent collision of inertial particles using large-eddy simulations and particle- resolved simulations are briefly discussed.

Numerical study on heavy rigid particle motion in a plane wake flow by spectral element method

Experimental particle dispersion patterns in a plane wake flow at a high Reynolds number have been predicted numerically by discrete vortex method (Phys. Fluids A 1992; 4:2244-2251; Int. J. Multiphase Flow 2000; 26:1583-1607). To address the particle motion at a moderate Reynolds number, spectral element method is employed to provide an instantaneous wake flow field for particle dynamics equations, which are solved to make a detail classification of the patterns in relation to the Stokes and Froude numbers. It is found that particle motion features only depend on the Stokes number at a high Froude number and depend on both numbers at a low Froude number. A ratio of the Stokes number to squared Froude number is introduced and threshold values of this parameter are evaluated that delineate the different regions of particle behavior. The parameter describes approximately the gravitational settling velocity divided by the characteristic velocity of wake flow. In order to present effects of particle density but preserve rigid sphere, hollow sphere particle dynamics in the plane wake flow is investigated. The evolution of hollow particle motion patterns for the increase of equivalent particle density corresponds to that of solid particle motion patterns for the decrease of particle size. Although the thresholds change a little, the parameter can still make a good qualitative classification of particle motion patterns as the inner diameter changes.

Subgrid scale fluid velocity timescales seen by inertial particles in large-eddy simulation of particle-laden turbulence

Large-eddy simulation (LES) has emerged as a promising tool for simulating turbulent flows in general and, in recent years,has also been applied to the particle-laden turbulence with some success (Kassinos et al., 2007). The motion of inertial particles is much more complicated than fluid elements, and therefore, LES of turbulent flow laden with inertial particles encounters new challenges. In the conventional LES, only large-scale eddies are explicitly resolved and the effects of unresolved, small or subgrid scale (SGS) eddies on the large-scale eddies are modeled. The SGS turbulent flow field is not available. The effects of SGS turbulent velocity field on particle motion have been studied by Wang and Squires (1996), Armenio et al. (1999), Yamamoto et al. (2001), Shotorban and Mashayek (2006a,b), Fede and Simonin (2006), Berrouk et al. (2007), Bini and Jones (2008), and Pozorski and Apte (2009), amongst others. One contemporary method to include the effects of SGS eddies on inertial particle motions is to introduce a stochastic differential equation (SDE), that is, a Langevin stochastic equation to model the SGS fluid velocity seen by inertial particles (Fede et al., 2006; Shotorban and Mashayek, 2006a; Shotorban and Mashayek, 2006b; Berrouk et al., 2007; Bini and Jones, 2008; Pozorski and Apte, 2009).However, the accuracy of such a Langevin equation model depends primarily on the prescription of the SGS fluid velocity autocorrelation time seen by an inertial particle or the inertial particle–SGS eddy interaction timescale (denoted by $\delt T_{Lp}$ and a second model constant in the diffusion term which controls the intensity of the random force received by an inertial particle (denoted by C_0, see Eq. (7)). From the theoretical point of view, dTLp differs significantly from the Lagrangian fluid velocity correlation time (Reeks, 1977; Wang and Stock, 1993), and this carries the essential nonlinearity in the statistical modeling of particle motion. dTLp and C0 may depend on the filter width and particle Stokes number even for a given turbulent flow. In previous studies, dTLp is modeled either by the fluid SGS Lagrangian timescale (Fede et al., 2006; Shotorban and Mashayek, 2006b; Pozorski and Apte, 2009; Bini and Jones, 2008) or by a simple extension of the timescale obtained from the full flow field (Berrouk et al., 2007). In this work, we shall study the subtle and on-monotonic dependence of $\delt T_{Lp}$ on the filter width and particle Stokes number using a flow field obtained from Direct Numerical Simulation (DNS). We then propose an empirical closure model for $\delta T_{Lp}$. Finally, the model is validated against LES of particle-laden turbulence in predicting single-particle statistics such as particle kinetic energy. As a first step, we consider the particle motion under the one-way coupling assumption in isotropic turbulent flow and neglect the gravitational settling effect. The one-way coupling assumption is only valid for low particle mass loading.