Resistant effect of non-equilibrium inter-particle collisions on dense solids transport

There exist big gaps between measurements and modeling predictions on solids holdup and pressure drop in dense solids transport, such as those occuring in the bottom sections of gas-solids risers. The inability of closing this gap by common modeling approaches indicates certain missing and/or misrepresentation of some controlling mechanisms in modeling the transport. Previous research efforts show that the gap can not be effectively narrowed by simply modifying the drag force formulations without inclusion of the collision effect. This paper explores the origin of some controlling mechanisms that might have been overlooked in previous modeling approaches, and recommends how to make the model dense solids transport better. Our analysis shows the presence of a resistant force arising from inter-particle collision when the solids are accelerated in dense-phase transport. This may be caused by non-equilibrium collision during solids acceleration, which differs from local-equilibrium assumptions on which the current kinetic theory modeling of granular particles is based. A complete modeling of this collision-induced resistance calls for a total revision of the kinetic theory, with the inclusion of non-equilibrium collisions and offcenter collisions in dense solids transport.     

气固两相流中颗粒碰撞的Monte-Carlo数值模拟

利用颗粒碰撞动力学模型和颗粒几何碰撞率模型,采用Monte—Carlo算法来模拟颗粒之间碰撞,把该算法与求解雷诺应力-概率密度函数模型的有限差分-Monte Carlo算法耦合起来,对轴对称突扩通道内的两相旋流场进行了数值模拟,模拟结果表明,由于颗粒碰撞使颗粒的动能和湍动能在三个坐标方向上进行了再分配,从而导致颗粒的动能和湍动能在三个坐标方向上趋于各向同性;另外,由于颗粒碰撞破坏了颗粒-颗粒、颗粒-流体微团之间的速度关联,从而造成颗粒湍动能及两相速度脉动关联的降低。     

The effect of two-way coupling and inter-particle collisions on turbulence modulation in a vertical channel flow

Turbulence modulation due to its interaction with dispersed solid particles in a downward fully developed channel flow was studied. The Eulerian framework was used for the gas-phase, whereas the Lagrangian approach was used for the particle-phase. The steady-state equations of conservation of mass and momentum were used for the gas-phase, and the effect of turbulence on the flow-field was included via the standard k–ε model. The particle equation of motion included the drag, the Saffman lift and the gravity forces. Turbulence dispersion effect on the particles was simulated as a continuous Gaussian random field. The effects of particles on the flow were modeled by appropriate source terms in the momentum, k and ε equations. Particle–particle collisions and particle–wall collisions were accounted for in these simulations. Gas-phase velocities and turbulence kinetic energy in the presence of 2–100% mass loadings of two particle classes (50 μm glass and 70 μm copper) were evaluated, and the results were compared with the available experimental data and earlier numerical results. The simulation results showed that when the inter-particle collisions were important and was included in the computational model, the fluid turbulence was attenuated. The level of turbulence attenuation increased with particle mass loading, particle Stokes number, and the distance from the wall. When the inter-particle collisions were negligible and/or was neglected in the model, the fluid turbulence was augmented for the range of particle sizes considered.     

考虑颗粒间碰撞的气固两相流拉格朗日模拟

在均匀,稳定的各向同性气固两相紊流场颗粒弥散的拉格朗日模拟计算方法基础上,进一步考虑了流场中颗粒之间的碰撞对于模拟计算结果的影响。与Lavieville用大涡模拟所做的计算结果进行了对比,以对本方法进行验证,并考察了颗粒间的碰撞分别对流体相和颗粒相的影响。     

Gas-solid flow in a diffuser:Effect of inter-particle and particle-wall collisions

This article investigates the role of the specularity coefficient(φ,the extent of the energy dissipation due to particle-wall collisions),inter-particle restitu...     

Numerical simulation of a supersonic gas–solid flow over a blunt body: The role of inter-particle collisions and two-way coupling effects

A supersonic dusty gas flow over a blunt body is considered. The mathematical model of the two-phase gas–particle flow takes into account the inter-particle collisions and the two-way coupling effects. The carrier gas is treated as a continuum, the averaged flow field of which is described by the complete Navier–Stokes equations with additional source terms modeling the reverse action of the dispersed phase. The dispersed phase is treated as a discrete set of solid particles, and its behavior is described by a kinetic Boltzmann-type equation. Particles impinging on the body surface are assumed to bounce from it. Numerical analysis is carried out for the cross-wise flow over a cylinder. The method of computational simulation represents a combination of a CFD-method for the carrier gas and a Monte Carlo method for the “gas” of particles. The dependence of the fine flow structure of the continuous and dispersed phases upon the free stream particle volume fraction α_p∞ and the particle radius r_p is investigated, particularly in the shock layer and in the boundary layer at the body surface. The particle volume fraction α_p∞ is varied from a negligibly low value to the value α_p∞ = 3 × 10⁵ at which inter-particle collisions and two-way coupling effects are simultaneously essential. Particular attention has been given to the particles of radii close to the critical value r_p1, because in this range of particle size the behavior of the particles and their effect on the carrier gas flow are not yet completely understood. An estimate of the turbulent kinetic energy produced by the particles in the shock layer is obtained.     

Direct numerical simulation of particle dispersion in a turbulent jet considering inter-particle collisions

To investigate the behaviour of inter-particle collision and its effects on particle dispersion, direct numerical simulation of a three-dimensional two-phase turbulent jet was conducted. The finite volume method and the fractional-step projection algorithm were used to solve the governing equations of the gas phase fluid and the Lagrangian method was applied to trace the particles. The deterministic hard-sphere model was used to describe the inter-particle collision. In order to allow an analysis of inter-particle collisions independent of the effect of particles on the flow, two-way coupling was neglected. The inter-particle collision occurs frequently in the local regions with higher particle concentration of the flow field. Under the influence of the local accumulation and the turbulent transport effects, the variation of the average inter-particle collision number with the Stokes number takes on a complex non-linear relationship. The particle distribution is more uniform as a result of inter-particle collisions, and the lateral and the spanwise dispersion of the particles considering inter-particle collision also increase. Furthermore, for the case of particles with the Rosin–Rammler distribution (the medial particle size is set d₅₀ = 36.7 μm), the collision number is significantly larger than that of the particles at the Stokes number of 10, and their effects on calculated results are also more significant.     

Role of inter-particle collision on solids acceleration in riser

Collision among particles plays a significant role in governing the structure of gas-solids flow in a riser,especially in the dense and acceleration region.The inter-particle collision is the major cause not only for the kinetic energy dissipation(in terms of additional pressure drop beyond the solids hold-up) but also for the control of solids acceleration(in terms of a balancing force to prevent a free acceleration of solids).A neglect of the balancing force of inter-particle collision against the hydrody...     

Numerical study of elbow erosion due to sand particles under annular flow considering liquid entrainment

Sand particle erosion is always a challenge in natural gas production. In particular, the erosion in gas–liquid–solid annular flow is more complicated. In this study, a three-phase flow numerical model that couples the volume of fluid multiphase flow model and the discrete phase model was developed for prediction of erosion in annular flow. The ability of the numerical model to simulate the gas–liquid annular flow is validated through comparison with the experimental data. On the basis of the above numerical model, the phase distribution in the pipe was analyzed. The liquid entrainment behavior was reasonably simulated through the numerical model, which guaranteed the accuracy of predicting the particle erosion. Additionally, four erosion prediction models were used for the erosion calculation, among them, the Zhang et al. erosion model predicted the realistic results. Through the analysis of the particle trajectory and the particle impact behavior on the elbow, the cushion effect of the liquid film on the particles and the erosion morphology generation at the elbow were revealed.     

Design optimization of guide vane for mitigating elbow erosion using computational fluid dynamics and response surface methodology

A 90° elbow equipped with guide vanes was developed with the intent of reducing elbow erosion.Numer-ical models were formed to predict the maximum erosion rate ...     

Design optimization of guide vane for mitigating elbow erosion using computational fluid dynamics and response surface methodology

A 90° elbow equipped with guide vanes was developed with the intent of reducing elbow erosion. Numerical models were formed to predict the maximum erosion rate of elbow and Face-1, and the response surface methodology was used to study the relationship between the erosion rate and structural parameters of guide vane. A second-order response surface model was established to determine the relationship between R₁ and variables, and a reduced cubic (RC) polynomial model was obtained to reveal the relationship between R₂ and the three factors. The numerical results show that the low-speed region is expended and the maximum discrete particle matter (DPM) concentration is reduced after installing the guide vane. This internal component provides a shelter for the elbow from the direct impact of high-speed solids.     

Role of particle stiffness and inter-particle sliding friction in milling of particles

Discrete element method （DEM） has been used to investigate the effects of particle elastic modulus and coefficient of inter-particle sliding friction on milling of mineral particles. An autogeneous mill of 600 mm diameter and 320 mm length with 14,500 particles has been selected for the simulation. Various mill performance parameters, for example, particle trajectories, collision frequency, collision energy and mill power have been evaluated to understand the effects of particle elastic modulus and inter-particle sliding friction during milling of particles. For the given model, it has been concluded that at high energy range, as the elastic modulus and particle sliding friction increase the energy dissipated among the particles increases. The collision frequency increases with the increase in elastic modulus, however, this trend is not clearly observed with increasing inter-particle sliding friction. The power draw of the mill increases with the increase in fraction of mill critical speed.     

Binary droplet collisions in a vacuum environment: an experimental investigation of the role of viscosity

An experimental investigation of viscous binary droplet collisions in a vacuum environment is conducted. The fundamental ramifications of conducting such experiments in a vacuum environment are twofold. The first, which is the motivating factor of this work, assures that the collision products are unimpeded by aerodynamic effects which tend to disrupt the collision process at a much earlier stage in the processes than if they were absent, and second, the phenomenon of encapsulation of the host medium between the colliding droplets is not present in this study; a fact that limits the scope of direct application of this study to a number of (but not all) applications. Droplets are generated from capillary stream breakup with the imposition of an amplitude-modulated disturbance which results in the generation of highly uniform pre-collision drops at separations far extending those which are possible from a standard (monochromatic) sinusoidal disturbance. Hence, the collision products are able to deform unimpeded by interactions with neighboring collision products. Measurements over a broad range of Weber number, We, indicate that the value of the critical Weber number, We_c, is more than 100 times greater for the 30-cSt fluid than the corresponding value for similarly sized water drops in a standard ambient environment. Measurements of the oblate and prolate half-cycle oscillation periods resulting from the binary collision reveal a distinct behavior that is observed and documented here for the first time. Additionally, measurements of the radial extent of the deformed mass at the instant of maximum deformation have been conducted and allow quantification of the energy dissipation. These measurements show that the energy dissipation increases with increasing fluid viscosity, which contradicts the results published by others.     

The study on three-dimensional mathematical model of river bed erosion for water-sediment two-phase flow

Based on the tensor analysis of water-sediment two-phase flow, the basic model equations for clear water flow and sediment-laden flow are deduced in the general curve coordinates for natural water variable-density turbulent flow. Furthermore, corresponding boundary conditions are also presented in connection with the composition and movement of non-uniform bed material. The theoretical results are applied to the calculation of the float open caisson in the construction period and good results are obtained.     

The erosion transition of tungsten-alloy long rods into aluminum targets

This work extends and refines the phenomenological understanding of ballistic penetration in the vicinity of the erosion-threshold velocity, for the case of hemispherical-nosed tungsten rods striking ductile targets. Analysis, supported by experimentation, indicates a period of noneroding penetration for these configurations, which results from lateral support exerted by the target crater upon the deforming, yet noneroding, penetrator. Experiments indicate that the magnitude of the lateral support, the direct result of an interference fit between rod and crater, must be on the order of the target’s ballistic-penetration resistance, and does not vary with the impact velocity over the range studied. Analysis suggests that the duration of the noneroding portion of the ballistic event is neither governed by a fixed time, nor by a fixed depth of penetration, but rather by a fixed, permissible level of deformation in the penetrator.