Effects of specularity and particle-particle restitution coefficients on the hydrodynamic behavior of dispersed gas-particle flows through horizontal channels

Specularity coefficient ($?$) and particle–particle restitution coefficient (e) are two important parameters governing the flow physics of dispersed gas-particle flows. In this work, a detailed numerical analysis is carried out to get an insight into the effects of these two parameters in the flow hydrodynamics of dispersed gas-particle flows through horizontal channels. Investigations have also been carried out to find the $?$-e pair for which the phase velocities become an extremum. It has been found that at a particular value of e, both gas and particle velocities at the centerline of the channel increase with increase in the value of $?$, whereas near the wall, they tend to decrease. At a fixed non-zero value of $?$, both gas and particle velocities tend to increase with increase in the value of e. For $?$ equal to zero, which corresponds to free-slip boundary condition for particle velocity, there is no significant variations in gas and particle velocities with changes in e. Out of all combinations of values of $?$ and e investigated herein, it is found that both gas and particle velocities attain a maximum value when both the values of $?$ and e are maximum.     

Numerical investigation of gas-particle hydrodynamics in a vortex chamber fluidized bed

Gas-particle hydrodynamic behaviour inside a vortex chamber fluidized bed is studied numerically with respect to different design and operating conditions. A three-dimensional computational fluid dynamics (CFD) model of a cylindrical vortex chamber is developed. Simulations are carried out with particles and without particles. In order to understand the gas-particle flow behavior velocity distribution, particle volume fraction distribution, radial pressure distribution and axial pressure distribution inside the vortex chamber are analyzed in detail. Particles of different diameters are used and its effect on the gas-particle flow behaviour is studied. Design parameters like the number of gas inlet slots and slot width are varied and their impact on the hydrodynamics of the vortex chamber is investigated. The numerical model is validated by comparing the numerical results with experimental results reported in literature.     

Effects of specularity and particle-particle restitution coefficients on the recirculation characteristics of dispersed gas-particle flows through a sudden expansion

We numerically investigate the effects of restitution and specularity coefficients on the characteristics of dispersed gas-particle flows through a sudden expansion. The studies are carried out using an indigenous finite volume flow solver in a collocated framework with two-fluid model. Parametric studies are performed to gain insights into the differences in recirculation patterns that arise due to variations in restitution and specularity coefficients. The simulations show that particle-particle interactions, quantified by restitution coefficient (e) have a greater impact on recirculation characteristics than particle-wall interactions, which are quantified by specularity coefficient ($?$). Studies reveal that the recirculation lengths tend to decrease as particle collisions become more elastic (as e tends to unity) while they increase, as the value of $?$ increases. However, the changes in recirculation length are very gradual and less pronounced when only particle-wall interactions are considered as compared to particle-particle interactions. From the range of parametric variations studied in this work, the maximum recirculation length has been found when the value of $?$ is maximum and that of e is minimum.     

Direct numerical simulation of two-dimensional channel flows of electro-rheological fluids

Direct numerical simulation (DNS) of electro-rheological (ER) fluid flows in two-dimensional (2D) electrode channel has been performed by adopting a combined finite element method (FEM). Hydrodynamic interactions between the particles and the fluid are described by the Navier-Stokes equations for the fluid in combination with the equations of motion for the particles, while the multi-body electrostatic interaction is represented by the point-dipole model.ER effects on the plane channel flow for a given pressure gradient have been studied by varying the Mason number and volume fraction of the particles, and interrogating the motion of the particles in views of the formation of ER chain structures, the fluid velocity profile in the channel, and the shear stress versus the shear rate. As the Mason number decreases and volume fraction increases, the tendency that particles align to form chain structures becomes stronger. The yield stress of the ER fluid increases with the electric field intensity and the particle concentration. The quadratic correlation between the yield stress and the electric field intensity has been extracted from the present direct numerical simulation. Lastly, it has been shown that the yield stress linearly increases with the volume fraction in the intermediate range.     

Magnetohydrodynamic (MHD) flows of viscoelastic fluids in converging/diverging channels

The present work is a theoretical investigation of the applicability of magnetic fields for controlling hydrodynamic separation in Jeffrey-Hamel flows of viscoelastic fluids. To achieve this goal, a local similarity solution was found for laminar, two-dimensional flow of a viscoelastic fluid obeying second-order/second-grade model as its constitutive equation with the assumption being made that the flow is symmetric and purely radial. These assumptions enabled a third-order nonlinear ODE to be obtained as the single equation governing the MHD flow of this particular fluid in flow through converging/diverging channels. With three physical boundary conditions available, Chebyshev collocation-point method was used to solve this ODE numerically. Results are presented in terms of parameters such as Reynolds number, Weissenberg number, channel half-angle, and the magnetic number. It was found that these parameters all have a profound effect on the velocity profiles in Jeffrey-Hamel flows. The effect of magnetic field was found to be more striking in that it is predicted to force fluid elements near the wall to exceed centerline velocity in converging channels and to suppress separation in diverging channels. Interestingly, the effect of the magnetic field in delaying flow separation is predicted to become more pronounced the higher the fluid’s elasticity.     

A fast integral approach for drag force calculation due to oscillatory slip stokes flows

In this paper, we describe an efficient numerical method for modelling oscillatory incompressible slip Stokes flows in three dimensions. The efficiency is achieved by employing an integral approach combined with an accelerated boundary‐element‐method (BEM) solver. First the integral representations for slip flows with two different slip models are formulated. The resulting integral equations are then solved using the BEM combined with the precorrected‐FFT accelerated technique. 3D numerical codes have been developed based on the method described above. These codes are then used to calculate the drag forces on oscillating objects immersed in an unbounded slip flow. Three objects are considered, namely a sphere, a pair of plates and a comb structure. The simulated drag forces on these objects obtained from the two slip models are compared. In the sphere case, the simulated results are also compared with the analytical solutions for both the steady‐state case and the no‐slip oscillatory case and are found to be in good agreement. In addition, qualitative comparison of the simulation results with the experimental results in the plate problem is also presented in this paper. Copyright © 2004 John Wiley & Sons, Ltd.     

Simulations of pressure-driven flows through channels and pipes with unified flow solver

The aim of this paper is to demonstrate the benefits of direct methods of solving kinetic equations and adaptive kinetic-fluid solvers for vacuum science and technology. We consider pressure-driven flows through short channels for a wide range of gas rarefaction degrees. Our Unified Flow Solver combines Adaptive Mesh Refinement (AMR) with automatic selection of kinetic and fluid solvers in different parts of computational domain. The discrete velocity method is used for direct numerical solution of Boltzmann and model kinetic equations. The advantages of adaptive hybrid method are demonstrated for compressible flows at large pressure gradients. For small pressure drops, direct solutions of the Boltzmann equation provide accurate solutions of rarefied flows not achievable by the traditional direct simulation Monte Carlo methods.     

A coupled BEM and arbitrary Lagrangian–Eulerian FEM model for the solution of two‐dimensional laminar flows in external flow fields

This paper describes a new computational model developed to solve two‐dimensional incompressible viscous flow problems in external flow fields. The model based on the Navier–Stokes equations in primitive variables is able to solve the infinite boundary value problems by extracting the boundary effects on a specified finite computational domain, using the pressure projection method. The external flow field is simulated using the boundary element method by solving a pressure Poisson equation that assumes the pressure as zero at the infinite boundary. The momentum equation of the flow motion is solved using the three‐step finite element method. The arbitrary Lagrangian–Eulerian method is incorporated into the model, to solve the moving boundary problems. The present model is applied to simulate various external flow problems like flow across circular cylinder, acceleration and deceleration of the circular cylinder moving in a still fluid and vibration of the circular cylinder induced by the vortex shedding. The simulation results are found to be very reasonable and satisfactory. Copyright © 2001 John Wiley & Sons, Ltd.     

Simulated pulsed flow of gas and particles in a horizontal oppose-pulsed gas jets of bubbling fluidized bed

Flow behavior of gas and particles with a horizontal oppose-pulsed gas jets are simulated by means of a three dimensional Computational Fluid Dynamics (CFD) model with the kinetic theory of granular flow in a gas-particles bubbling fluidized bed. The effects of amplitudes and frequencies on the hydrodynamics of gas and particles are analyzed. The simulation results are presented in terms of phase velocity vector plot, volume fraction of phases, granular temperature, power spectrum and Reynolds stresses in the bed. Results show that the impingement caused by the oppose-pulsed gas jets oscillates with the variation of pulsed gas velocity. The impingement zone with the high solid volume fraction reciprocates from the left side to the right side through the bed center with the variation of pulsed jet gas velocities. The lateral velocity and gas turbulent kinetic energy, granular temperature and Reynolds stresses of gas and particles are larger near the pulsed gas jets than that at the center of the bed. The large dispersion coefficients of particles using the horizontal oppose-pulsed gas jets enhance the mixing of particles in gas-solid fluidized bed.     

Rarefied gas flow through channels of finite length at various pressure ratios

A rarefied gas flow through channels (i.e. flow through parallel plates) of finite length has been modeled based on the direct simulation Monte Carlo method. The reduced flow rate and the flow field have been calculated as function of the gas rarefaction, the length-to-height ratio and the pressure ratio upstream and downstream of the channel. The whole range of the gas rarefaction including the free-molecular, transitional and hydrodynamic regimes and a wide range of the length-to-height ratio representing both short and long channels have been considered. Several values of the pressure ratio between 0 and 0.5 have been used in the calculations. It is shown that the rarefaction parameter has the most significant effect on the flow field characteristics and patterns, followed by the pressure ratio, while the length-to-height ratio has a rather modest impact. The Mach belt phenomenon is discussed in detail.     

Volume fraction and velocity fields of nearly uniform granular flows in a narrow channel geometry with smooth bed

The combined knowledge of the velocity and volume fraction fields is crucial for investigating the dynamics of granular flows, especially in the dense-collisional regime where both frictional and collisional dissipation mechanisms are significant. A laboratory investigation on steady dry granular flows in a straight channel is reported, where slip conditions are allowed at the basal surface and side walls. The stochastic-optical method (SOM), proposed by Sarno et al. (2016) for estimating the volume fraction in granular mixtures, is applied for the first time to granular flows. The velocity at the free surface and at the flume sidewall is measured by using a multi-pass particle image velocimetry (PIV) approach. The measurements of the velocity and volume fraction reveal a superimposition of different dynamic structures, which can be distinguished by means of a volume fraction threshold. Additionally, the profiles of measured volume fraction are exploited to estimate the pressure distribution, so as to numerically describe the velocity profiles by using the μ(I) rheology. It is found that the employment of the experimental volume fraction is superior in describing the flow dynamics, especially near the free surface.     

Parametric analysis and optimization of gas-particle flow through axial cyclone separator: A numerical study

The separation of particles through an axial swirl tube cyclone separator is numerically investigated using Eulerian-Lagrangian approach by solving Reynolds Averaged Navier-Stokes equations with RNG K-epsilon model as turbulence closure and Discrete phase modeling (DPM) of particles. The four significant geometric parameters in an axial swirl tube cyclone separator for improving the performance are identified to be blade angle, blade length, blade-tube distance and number of blades. The impact of these parameters on the output parameters of a cyclone separator, is studied through numerical analysis with the open source CFD solver OpenFOAM. A one factor analysis is performed to understand the individual contributions of the parameters and a multiobjective optimisation is done using the Design of Experiments (DoE) approach. The blade length was found to be the most sensitive parameter whereas the blade tube distance had the least effect. Using statistical methods such as Analysis of Variance (ANOVA) and Multi Objective Genetic algorithm (MOGA), a set of Pareto optimum solutions are generated, with an effective trade off between the pressure drop and filtration efficiency. The configurations obtained after optimisation are validated with CFD simulations and found to be having a better overall performance as compared to the conventional configuration.     

Visualization and analysis of longitudinal vortices at curved walls of 2D laminar and turbulent channel flows

The three-dimensional structure of longitudinal vortices at the curved walls of both laminar and turbulent channel flows is visualized by the hydrogen bubble technique. Together with the conditional sampling of the turbulent characteristics at the wall processed by thevita method the dynamics of the near-wall structure is discussed.     

A new application of the reciprocity relations to the study of fluid flows through fixed beds

Creeping flow through an array of spheres with small volume fraction is studied theoretically. It is observed that it can be described macroscopically by Brinkman's equation. A generalized version of the reciprocity relations is used to determine the viscous term up to O(²) for the case of random configuration and up to O(³) for the case of periodic, cubic configurations of the fixed bed.     

A numerical study of the similarity of fully developed laminar flows in orthogonally rotating rectangular ducts and stationary curved rectangular ducts of arbitrary aspect ratio

 The present study showed that a quantitative analogy of fully developed laminar flow in orthogonally rotating rectangular ducts and stationary curved rectangular ducts of arbitrary aspect ratio could be established. In order to clarify the similarity of the two flows, the dimensionless parameters K _LR=Re/(Ro)^1/2 and the Rossby number, Ro=w _m /Ωd _h , in a rotating straight duct were used as a set corresponding to the Dean number, K _LC=Re/λ^1/2, and curvature ratio, λ=R/d _h , in a stationary curved duct. Under the condition that the value of the Rossby number and the curvature ratio was large enough, the flow field satisfied the `asymptotic invariance property'; there were strong quantitative similarities between the two flows such as in the friction factors, flow patterns, and maximum axial velocity magnitudes for the same values of K _LR and K _LC. Based on these similarities, it is possible to predict the flow characteristics in rotating ducts by considering the flow in stationary curved ducts, and vice versa. Received: 10 September 2001 / Accepted: 13 May 2002     

A numerical study of laminar and turbulent flows in a two-dimensional bend with or without a guide vane

A numerical study of the flow in a two-dimensional 90° circular-arc bend is presented. The study is based on the solution of the governing equations using a finite volume technique. Both laminar and turbulent flows are considered. Particular attention is given to the occurrence and size of the separation regions and, in this respect, the effects of Reynolds number and bend radius to height ratio are discussed. The study includes the effect of a guide vane, placed in the bend, on the flow characteristics. It is shown that the emerging velocity distribution is more uniform than that associated with flow in a bend without a guide vane. The presence of a guide vane is shown to suppress the formation of regions of flow separation. Comparisons are made between the effects on the flow of two different designs of guide vane.     

MHD convective heat transfer of nanofluids through a flexible tube with buoyancy: A study of nano-particle shape effects

This paper presents an analytical study of magnetohydrodynamics and convective heat transfer of nanofluids synthesized by three different shaped (brick, platelet and cylinder) silver (Ag) nanoparticles in water. A two-phase nanoscale formulation is adopted which is more appropriate for biophysical systems. The flow is induced by metachronal beating of cilia and the flow geometry is considered as a cylindrical tube. The analysis is carried out under the low Reynolds number and long wavelength approximations and the fluid and cilia dynamics is of the creeping type. A Lorentzian magnetic body force model is employed and magnetic induction effects are neglected. Solutions to the transformed boundary value problem are obtained via numerical integration. The influence of cilia length parameter, Hartmann (magnetic) number, heat absorption parameter, Grashof number (free convection), solid nanoparticle volume fraction, and cilia eccentricity parameter on the flow and heat transfer characteristics (including effective thermal conductivity of the nanofluid) are examined in detail. Furthermore a comparative study for different nanoparticle geometries (i.e. bricks, platelets and cylinders) is conducted. The computations show that pressure increases with enhancing the heat absorption, buoyancy force (i.e. Grashof number) and nanoparticle fraction however it reduces with increasing the magnetic field. The computations also reveal that pressure enhancement is a maximum for the platelet nano-particle case compared with the brick and cylinder nanoparticle cases. Furthermore the quantity of trapped streamlines for cylinder type nanoparticles exceeds substantially that computed for brick and platelet nanoparticles, whereas the bolus magnitude (trapped zone) for brick nanoparticles is demonstrably greater than that obtained for cylinder and platelet nanoparticles. The present model is applicable in biological and biomimetic transport phenomena exploiting magnetic nanofluids and ciliated inner tube surfaces.     

考虑扣件温频变的车轨桥垂向耦合系统振动能量研究

通过对扣件进行定频变温试验,结合温频等效原理与高阶分数导数FVMP模型建立扣件的温频变动态力学模型,并在车-轨-桥耦合系统中采用新建模型模拟扣件,基于功率流法系统地分析与评价扣件温频变动态力学性能对车轨桥耦合系统振动能量分布与传递的影响.结果 表明:考虑扣件动参数频变会使中高频段内的轨道结构振动能量增大,对低频段的轨道...     

Network numerical analysis of magneto-micropolar convection through a vertical circular non-Darcian porous medium conduit

The fully developed, mixed convection heat transfer of a magneto-micropolar fluid in a Darcy–Forchheimer porous medium containing heat sources contained in a vertical circular conduit is investigated in this article. The conservation equations for mass, linear momentum, micro-inertia, angular momentum (micro-rotation) and energy are presented in a cylindrical coordinate system (r, θ, z) with appropriate boundary conditions. A Darcy–Forchheimer drag force model is employed to simulate the effects of bulk linear porous impedance and second order porous resistance. The governing partial differential equations are non-dimensionalized into a set of ordinary differential equations in a single independent variable (η) and solved using the Network Simulation Method. Benchmark solutions are compared with earlier computations using the finite element method, showing excellent agreement. The influence of Darcy number, Forchheimer number, Grashof number, Hartmann number, geometric scale ratio (conduit radius to length ratio), Eringen parameter (ratio of vortex viscosity to Newtonian viscosity) and heat source/sink parameter on the linear velocity, angular velocity (micro-rotation) and temperature functions are studied in detail. Flow i.e. linear (translational) velocity, f, is seen to be inhibited with increasing magnetic field (Hartmann number), Forchheimer number and Eringen parameter, but accelerated with increasing Darcy number. Micro-rotation (g) is decreased with increasing Forchheimer number and Hartmann number, but increased with a rise in Grashof number, Darcy number, geometric scale ratio and Eringen parameter. Both velocity (f) and micro-rotation (g) are increased in the presence of a heat source but decreased with a heat sink. Several special cases of the flow regime are also documented. Applications of the problem include the cooling of porous combustion chambers, geophysical transport in electrically-conducting zones, exhaust nozzles of porous walled flow reactors, hydromagnetic control processes in nuclear engineering and magnetic materials processing (ceramic foams).