Dilute Gas-particle Suspensions Research Articles

Dynamics of particle-laden turbulent Couette flow: Turbulence modulation by inertial particles

In particle-laden turbulent flows, it is established that the turbulence in the carrier fluid phase gets affected by the dispersed particle phase for volume fractions above 10−4. Hence, reverse coupling or two-way coupling becomes relevant in that volume fraction regime. Due to their greater inertia, larger particles change either the mean flow or the intensity of fluid-phase fluctuations. In a recent study [Muramulla et al., “Disruption of turbulence due to particle loading in a dilute gas–particle suspension,” J. Fluid Mech. 889, A28 (2020)], a discontinuous decrease of turbulence intensity is observed in a vertical particle-laden turbulent channel flow for a critical volume fraction O(10−3) for particles with varying Stokes numbers (St) in the range of 1−420 based on the fluid-integral time scales. The collapse of turbulent intensity is found out to be the result of a “catastrophic reduction of turbulent energy production rate.” Mechanistically, a turbulent Couette flow differs from a pressure-driven channel flow in many ways, such as fluid-phase mean-velocity profile and turbulent coherent structures. In the particle-laden Couette flow, particles are treated as neutrally buoyant. Therefore, it is worth investigating the mechanism of turbulence modulation by inertial particles in the particle-laden turbulent Couette flow. In this article, the turbulence modulation in the fluid phase in the presence of inertial particles is investigated using two-way coupled direct numerical simulations of a particle-laden sheared turbulent suspension. The particle volume fraction (ϕ) is varied from 1.75×10−4 to 1.05×10−3 and the Reynolds number based on the half-channel width (δ) and the wall velocity (U) (Reδ) is 750. The particles are of high inertia with St∼367 based on a fluid integral timescale represented by δ/U. A discontinuous decrease in turbulence intensity and Reynolds stress is observed beyond a critical volume fraction ϕcr∼7.875×10−4. The drastic reduction of shear production of turbulence leads to the collapse of fluid-phase turbulence. The stepwise particle injection and stepwise removal study confirm the role of critical volume loading in the discontinuous transition. Additionally, the effect of the nature of particle–particle and particle–wall collisions has been investigated. It is observed that the inelastic collisions increase the ϕcr marginally although the nature of turbulence modulation remains similar. The explicit role of the inter-particle collisions has also been investigated by switching off the particle–particle collisions. In this case, ϕcr increases more than in the case of an inelastic collision. The turbulence modulation carries the signatures of transition from sheared turbulence to particle-driven fluid fluctuation at higher volume loading.

Acoustic probing of the particle concentration in turbulent granular suspensions in air

Dilute gas–particle suspensions in which the particles are carried by the fluid are found in various industrial and geophysical contexts. One fundamental issue that limits our understanding of such systems is the difficulty to obtain information on the particle concentration inside these often optically opaque suspensions. To overcome this difficulty, we develop ultrasonic spectroscopy to monitor the local particle concentration phi of glass particles (with diameters dsim 77 upmum or 155 upmum) suspended in air. First, we determine the minimal air velocity, U^*, necessary to suspend the particles from the maximum decrease in the transmitted wave amplitude and velocity of ultrasound propagating through the suspension. Next, setting the air velocity at U^*, we increase the mass of particles and monitor acoustically the local solid volume fraction, phi, by measuring the ultrasound wave attenuation coefficient and phase velocity as a function of frequency on the basis of classical scattering and hydrodynamic models. For the frequency ranges and suspensions considered here, the viscous dissipation dominates over scattering and thermal conduction losses. We show that, for a characteristic air velocity U^*, the locally measured phi reaches a critical value, in agreement with a recent study on turbulent gas–particle mixtures. Moreover, we find that this critical phi increases with the size of the particles. Finally, analysis of the temporal fluctuations of the locally measured solid volume fraction, suggests that high density regions (clusters) are present even in suspensions with concentrations below the critical concentration. This differs from the current hypothesis according to which the critical concentration coincides with the onset of cluster formation.

Disruption of turbulence due to particle loading in a dilute gas–particle suspension

The modification of fluid turbulence due to suspended particles is analysed using direct numerical simulations for the fluid turbulence and discrete particle simulations where the point-particle approximation is used for the particle force on the fluid. Two values of the Reynolds number based on the channel width $h$ and the average gas velocity $\bar{u}$ , $(\unicode[STIX]{x1D70C}_{f}\bar{u}h/\unicode[STIX]{x1D702}_{f})=3300$ and 5600 are considered, where $\unicode[STIX]{x1D70C}_{f}$ and $\unicode[STIX]{x1D702}_{f}$ are the gas density and viscosity. The particle Reynolds number based on the root mean square of the difference in the particle and fluid velocities is in the range 4–15. The particle volume fraction is small, in the range $0{-}3.5\times 10^{-3}$ , the mass loading is varied in the range 0–13.5 and the particle Stokes number (ratio of particle relaxation time and fluid integral time) is varied in the range 1–420. Multiple models for the force on the particles are examined, the Stokes drag law, the Schiller–Naumann correlation, a correction to determine the ‘undisturbed’ fluid velocity at the particle centre, the lift force and wall corrections. In all cases, as the particle volume fraction is systematically increased, there is a discontinuous decrease in the turbulence intensities at a critical volume fraction. The mean square velocities and the rate of production of turbulent energy decrease by 1–2 orders of magnitude when the volume fraction is increased by $10^{-4}$ at the critical volume fraction. There is no compensatory increase in the particle fluctuating velocities or the energy dissipation rate due to the drag force on the particles, and there is a significant decrease in the total fluid energy dissipation rate at the critical volume fraction. This shows that the turbulence collapse is due to a catastrophic reduction in the turbulent energy production rate. This is contrary to the current understanding that turbulence attenuation is caused by the enhanced dissipation due to particle drag.

Pressure recovery characteristics for a dilute gas–particle suspension flowing vertically downward in a pipe with a sudden expansion: A two-fluid modeling approach

This work applies the Eulerian‒Eulerian model in conjunction with the kinetic theory of granular flow and inter-particle collisions to study the characteristics of pressure recovery for a dilute gas–particle suspension flowing through a pipe with a sudden expansion at a relatively higher solid loading. To do so, the numerical procedure was validated against experimental results for relatively small dilute phase flows in a pipe with a sudden expansion; a satisfactory agreement was obtained. Initially, the effect of the two significant numerical parameters namely, the speculairty coefficient and the coefficient of restitution for particle–particle collisions were investigated and then, for fixed combinations of these parameters the effect of particle-phase volume fraction, particle density, particle size, and inlet slip ratio were studied. It was concluded that pressure recovery diminishes as the speculairty coefficient increases and the particle–particle coefficient of restitution decreases. Pressure recovery was found to increase with increasing solid volume fraction for coarse particles whereas, for fine particles, a critical volume fraction is obtained above which pressure recovery reduces. An increase in slip ratio is found to diminish pressure recovery. Similarly, at relatively higher solid volume fractions, a critical diameter was found, above and below which pressure recovery decreases.

Dilute gas-particle flow through thin and thick orifice: a computational study through two fluid model

The present work deals with the three-dimensional computational study of dilute gas-particle suspension through thin and thick orifice. The objective of the study is to predict the two phase pressure drop across an orifice for relatively higher solid loading but within the limit of dilute phase flow situation. The study involves the investigation of effect of five pertinent parameters namely area ratio, thickness of orifice, particle phase volume fraction, particle size, and particle phase density on the two phase pressure drop across orifice. The Eulerian–Eulerian model (Two fluid model) has been used for this purpose. The numerical procedure adopted in the present work has been validated with the experimental data for gas-particle flow through a horizontal sudden expansion pipe and good agreement has been revealed. The study reveals that the two phase pressure drop across orifice increases with increases in solid volume fraction and particle density, whereas it decreases with increase in particle diameter and area ratio of the pipe. Moreover, slight increase in pressure drop across orifice is observed with increase in thickness of orifice. Thus, higher pressure drop is observed for thick orifice as compared to thin orifice.

HEAT TRANSFER IN MULTIPLE-TURBULENT-SLOT IMPINGING JETS OF GAS–PARTICLE SUSPENSIONS

ABSTRACT The heat transfer in a dilute gas–particle suspension flow through multiple-slot impinging jets has been numerically investigated employing a new Eulerian-Lagrangian model. The two-phase turbulent flow is simulated using the standard k–ϵ model and Lagrangian particle tracking, which includes coupling terms to simulate the fluid–particle interactions. The numerical results are compared with the available experimental data. Good agreement between the experiment and simulation is obtained only if the conduction heat transfer due to particle–wall collisions is considered in the model. Effects of particle loading ratio, wall reflection coefficient, and wall materials properties on the heat transfer rate are discussed.

CFD STUDY OF THE HEAT TRANSFER BETWEEN A DILUTE GAS PARTICLE SUSPENSION FLOW AND AN OBSTRUCTION

The heat transfer process between a dilute gas-particle suspension flow and an obstruction has been numerically investigated employing our novel Eulerian formulation for dilute gas particle suspension flows [1], which allows interaction of the key mechanisms to be quantified for the first time. As the particle reflection occurs around the obstruction, the heat transfer process has been modeled taking into account the incident and reflected particles explicitly. In the energy equations these particle families are treated separately. Only the effect on the gas convective heat transfer is expected to be of primary significance and investigated. The numerical computation is performed using the commercial computational fluid dynamics code, FLUENT, with our User Defined Subroutines. We study the heat transfer process between a dilute gas particle flow and an obstruction with simple geometries such as a 45 ramp and a cylindrical tube. The theoretical results for the latter case are compared with the available experimental data. Our numerical simulation shows that both the particle size and the particle concentration (in the thermal boundary layer) affect the heat transfer process. Since both the particle incidence and reflection depend on the particle size and strongly influence the particle concentration distribution, they have to be physically correctly treated in the modeling of the heat transfer, as is demonstrated in our novel formulation. There is an optimum particle size for a maximum enhancement of the heat transfer. The particle concentration increases the efficiency of the heat transfer process expressed in terms of the local Nusselt numbers.

98/01493 Heat transfer in dilute gas-particle suspensions: Wang, X. S. et al. Chemical Eng. Sci., 1997, 52, (20), 3617–3621

98/01493 Heat transfer in dilute gas-particle suspensions: Wang, X. S. et al. Chemical Eng. Sci., 1997, 52, (20), 3617–3621

Heat transfer in dilute gas-particle suspensions

In this study a model is proposed for the process of heat transfer in circulating fluidized bed risers under dilute conditions, and its predictions are compared with experimental results.

Shock-induced two-phase flows in an aligned baffle system filled with suspended particles

This paper describes the shock propagation through a dilute gas-particle suspension in an aligned baffle system. Numerical solution to two-phase flows induced by a planar shock wave is given based on the two-continuum model with interphase coupling. The governing equations are numerically solved by using high-resolution schemes. The computational results show the shock reflection and diffraction patterns, and the shock-induced flow fields in the 4-baffle system filled with the dusty gas.

Shock-induced two-phase flows in an aligned baffle system filled with suspended particles

This paper describes the shock propagation through a dilute gas-particle suspension in an aligned baffle system. Numerical solution to two-phase flows induced by a planar shock wave is given based on the two-continuum model with interphase coupling. The governing equations are numerically solved by using high-resolution schemes. The computational results show the shock reflection and diffraction patterns, and the shock-induced flow fields in the 4-baffle system filled with the dusty gas.

The flow structure of dilute gas-particle suspensions behind a shock wave moving along a flat surface

The asymptotic and numerical investigations of shock-induced boundary layers in gas-particle mixtures are presented. The Saffman lift force acting on a particle in a shear flow is taken into account. It is shown that particle migration across the boundary layer leads to intersections of particle trajectories. The corresponding modification of dusty gas model is proposed in this paper. The equations of two-phase sidewall boundary layer behind a shock wave moving at a constant speed are obtained by using the method of matched asymptotic expansions. The method of the calculation of particle phase parameters in Lagrangian coordinates is described in detail. Some numerical results for the case of small particle concentration are given.

Effects of inertia on the diffusional deposition of small particles to spheres and cylinders at low Reynolds numbers

A formalism that accounts for inertial and diffusive effects in the dynamics of a dilute gas-particle suspension is introduced. The treatment is purely deterministic away from a very thin Brownian diffusion sublayer, while, within the sublayer, inertial effects are small, permitting a near-equilibrium expansion in powers of the Stokes number (particle relaxation time divided by flow characteristic residence time). This expansion provides phenomenological expressions for the particle velocity including two terms : the standard Brownian diffusion, and an additional inertial drift velocity which is closely related to the pressure diffusion term of the Chapman-Enskog expansion. As an example, the general formalism is applied in detail to the case of Stokes flow about a sphere, and sketched for the similar case of a cylinder. Two competing mechanisms are seen to affect the total rate of particle capture by the sphere : (if the stagnation-point region is considerably enriched in particles owing to the high compressibility of the particle phase, which leads to locally enhanced deposition; (ii) centrifugal forces tend to deplete the Brownian diffusion sublayer of particles, reducing diffusion rates away from the stagnation point to the surface. The first effect is seen to dominate over the second except in a very narrow zone of small Stokes numbers. Our method bridges the gap between Levich's solution for the ‘pure-diffusion’ limit and Michael's treatment in the ‘pure-inertia’ limit.