Development of filtered Euler–Euler two-phase model for circulating fluidised bed: High resolution simulation, formulation and a priori analyses

Euler–Euler two-phase model simulations are usually performed with mesh sizes larger than the smallscale structure size of gas–solid flows in industrial fluidised beds because of computational resource limitation. Thus, these simulations do not fully account for the particle segregation effect at the small scale and this causes poor prediction of bed hydrodynamics. An appropriate modelling approach accounting for the influence of unresolved structures needs to be proposed for practical simulations. For this purpose, computational grids are refined to a cell size of a few particle diameters to obtain mesh-independent results requiring up to 17 million cells in a 3D periodic circulating fluidised bed. These mesh-independent results are filtered by volume averaging and used to perform a priori analyses on the filtered phase balance equations. Results show that filtered momentum equations can be used for practical simulations but must take account of a drift velocity due to the sub-grid correlation between the local fluid velocity and the local particle volume fraction, and particle sub-grid stresses due to the filtering of the non-linear convection term. This paper proposes models for sub-grid drift velocity and particle sub-grid stresses and assesses these models by a priori tests

A posteriori study of filtered Euler-Euler two-phase model using a high resolution simulation of a 3D periodic circulating fluidized bed

Gas-particle flows in vertical risers are involved in many industrial scale fluidized bed applications such as catalytic cracking, fossil or biomass combustion. Risers flows are often simulated by two-fluid model equations coupled with closures developed in the frame the kinetic theory of granular media. However, two-fluid model discretized over coarse mesh with respect to particle clustering size are performed for large units because of limited computational resources. Now, it is well established that meso-scales cancelled out by coarse mesh simulations have dramatic effect on overall behaviour of flows. This study proposed a sub-grid modeling approach for effective drag force and particle stresses which accounts for the effects of unresolved structures on the resolved flows

Direct Simulation Monte-Carlo predictions of coarse elastic particle statistics in fully developed turbulent channel flows: Comparison with deterministic discrete particle simulation results and moment closure assumptions

The paper presents numerical simulations of particle-laden fully developed turbulent channel flows per- formed in a stochastic Lagrangian framework. The particle inertia is large in order to neglect the effect of the turbulent gas motion on the particle dispersion. In contrast the inter-particle collisions are impor- tant and accounted for by using Direct Simulation Monte-Carlo (DSMC) method. The comparison of the Monte-Carlo results with those obtained by Discrete Particle Simulation (DPS) shows that the stochastic collisions algorithm is able to predict accurately the particle statistics (number density, mean velocity, second- and third-order velocity moments) in the core flow. More, the paper analyses the number sec- tions needed for accurate predictions. In the very near-wall region, the Monte-Carlo simulation fails to account for the wall shelter effect due to the wall-normal unbalanced inter-particle collisions influence induced by the presence of the wall. Then, the paper shows that DSMC permits to assess the closure approximations required in moment approach. In particular, the DSMC results are compared with the corresponding moment closure assumptions for the third-order correlations of particle velocity, the cor- relations between the drag force and the velocity and the inter-particle collision terms. It is shown that at the opposite of the standard DSMC, the moment approach can predict the wall shelter effect. Finally, a model for the mean transverse force is proposed for taking into account wall shelter effect in DSMC

Numerical study of substrate assimilation by a microorganism exposed to fluctuating concentration

In most modelling works on bioreactors, the substrate assimilation is computed from the volume average concentration. The possible occurrence of a competition between the transport of substrate towards the cell and the assimilation at the cell level is generally overlooked. In order to examine the consequences of such a competition, a diffusion equation for the substrate is coupled with a specific boundary condition defining the up take rate at the cell liquid interface. Two assimilation laws are investigated, whereas the concentration far from the cell is varied in order to mimic concentration fluctuations. Both steady and unsteady conditions are investigated. The actual uptake rate computed from the interfacial concentration is compared to the time-averaged uptake rate based on the mean far-field concentration. Whatever the assimilation law, it is found that the uptake rate can be correlated to the mean far-field concentration, but the actual values of the parameters are affected in case of transport limitation. Moreover, the structure of the far-field signal influences the substrate assimilation by the microorganism, and the mean interfacial uptake rate depends on the ratio between the characteristic time of the signal and the diffusional time scale, as well as on the amplitude of the fluctuations around the mean far-field concentration in substrate. The present work enlightens some experimental results and helps in understanding the differences between the concentration measured and that present in the microenvironment of the cells

A spatial particle correlation-function analysis in non-isothermal dilute particle-laden turbulent flows

In dilute gas-solid turbulent flows, as that encountered, for example, in pulverized coal combustion processes, the correct prediction of the non-isothermal/reactive particle-laden turbulent mixture relies on the accuracy of the modeling of the local and unsteady particle behavior, which affects the hydro-thermodynamic coupling and the heat transfer and transport in and between the phases and at wall. In very dilute mixtures composed of highly inertial solid particles, such a local and unsteady behavior is the result of the particle interactions with very distant and independent turbulent eddies, namely with different dynamic and thermal turbulent scales. Such interactions strongly modify the local particle velocity and temperature distributions, changing the local evolution of the properties of the dispersed phase. Their knowledge is thus crucial when modeling unsteady particle-laden turbulent flows. In this work, the focus is on the particle temperature distribution. Its characterization is provided by means of an analysis of the two-particle correlation functions in the frame of the direct numerical simulation of non-isothermal homogeneous isotropic, statistically stationary, turbulent flows

Numerical simulation of a periodic circulating fluidized bed of binary mixture of particles: Budget analysis

Detailed sensitivity numerical studies have shown that the mesh cell-size may have a drastic effect on the modelling of circulating fluidized bed. Typically the cell-size must be of the order of few particle diameters to predict accurately the dynamical behaviour of a fluidized bed. Then the Euler-Euler numerical simulations of industrial processes are generally performed with grids too coarse to allow the prediction of the local segregation effects. A filtered approach is developed where the unknown terms, called sub-grid contributions,have to be modelled. Highly resolved simulations are used to develop the model. They consist of Euler-Euler simulations with grid refinement up to reach a mesh independent solution. Then spatial filters can be applied in order to measure each sub-grid contribution appearing in the theoretical filtered approach. Such kind of numerical simulation is very expensive and is restricted to very simple configurations. In the present study, highly resolved simulations are performed to investigate the sub-grid contributions in case of a binary particle mixture in a periodic circulating gas-solid fluidized bed. A budget analysis is carried out in order to understand and model the effect of sub-grid contribution on the hydrodynamic of polydisperse gas-solid circulating fluidized bed

Monte-Carlo simulation of colliding particles or coalescing droplets transported by a turbulent flow in the framework of a joint fluid–particle pdf approach

The aim of the paper is to introduce and validate a Monte-Carlo algorithm for the prediction of an ensemble of colliding solid particles, or coalescing liquid droplets, suspended in a turbulent gas flow predicted by Reynolds Averaged Navier Stokes approach (RANS). The new algorithm is based on the direct discretization of the collision/coalescence kernel derived in the framework of a joint fluid–particle pdf approach proposed by Simonin et al. (2002). This approach allows to take into account correlations between colliding inertial particle velocities induced by their interaction with the fluid turbulence. Validation is performed by comparing the Monte-Carlo predictions with deterministic simulations of discrete solid particles coupled with Direct Numerical Simulation (DPS/DNS), or Large Eddy Simulation (DPS/LES), where the collision/coalescence effects are treated in a deterministic way. Five cases are investigated: elastic monodisperse particles, non-elastic monodisperse particles, binary mixture of elastic particles and binary mixture of elastic settling particles in turbulent flow and finally coalescing droplets. The predictions using the new Monte-Carlo algorithm are in much better agreement with DPS/DNS results than the ones using the standard algorithm

Effect of unresolved structures on the Euler-Euler simulation of 3D periodic circulating fluidized of binary mixture

It is well established that small-scale structures have an important effect on the overall hydrodynamic behaviour of dense and circulating fluidized bed. Due to computational constraints, the numerical simulations of practical applications with Euler-Euler two-phase approach are usually performed with relatively coarse mesh with respect to the local segregation of solid. These simulations cancel out the small-scale solid structures. All previous studied attempted to take into account the effect of unresolved structures on the drag force in the case where the particulate phase is monodisperse. This paper is dedicated to analyse the unresolved structures effects on polydisperse gas-solid flow by multi-fluid Eulerian approach. In this study, the binary mixture is conducted by gas at an ambient condition in a 3D periodic circulating fluidized bed. The aim is first to obtain mesh independent results where further mesh refinement is not necessary. Then these results are used to investigate the unresolved structures effects on resolved field by following a priori methodology. In particular, the role of small-scale structures on the momentum transfer by inter-particle collisions is pointed out

3D numerical simulation of a lab-scale pressurized dense fluidized bed focussing on the effect of the particle-particle restitution coefficient and particle–wall boundary conditions

3D numerical simulations of dense pressurized fluidized bed are presented. The numerical prediction of the mean vertical solid velocity are compared with experimental data obtained from Positron Emission Particle Tracking. The results show that in the core of the reactor the numerical simulations are in accordance with the experimental data. The time-averaged particle velocity field exhibits a large-scale toroidal (donut shape) circulation loop. Two families of boundary conditions for the solid phase are used: rough wall boundary conditions (Johnson and Jackson, 1987 and No-slip) and smooth wall boundary conditions (Sakiz and Simonin, 1999 and Free-slip). Rough wall boundary conditions may lead to larger values of bed height with flat smooth wall boundary conditions and are in better agreement with the experimental data in the near-wall region. No-slip or Johnson and Jackson׳s wall boundary conditions, with sufficiently large value of the specularity coefficient (ϕ≥0.1)(ϕ≥0.1), lead to two counter rotating macroscopic toroidal loops whereas with smooth wall boundary conditions only one large macroscopic loop is observed. The effect of the particle-particle restitution coefficient on the dynamic behaviour of fluidized bed is analysed. Decreasing the restitution coefficient tends to increase the formation of bubbles and, consequently, to reduce the bed expansion

Numerical study of solid particle axial mixing in a fixed cylindrical drum with rotating paddles

Axial mixture characterization is a wide spread problem in granular particle blending processes such as in an horizontal drum mixer. The homogeneous mixture of particles is obtained by blending the particles via rotating paddles in a fixed cylindrical drum. This problem, common to many technological devices, is crucial in the manufacture of a broad variety of industrial products, such as polypropylene. The granular flow behavior in these systems is still poorly understood and the numerical study of such configurations receives increasing academic and industrial attention. In this paper, a study is conducted to investigate the effects of different aspects of the reactor design on the axial transport of monodisperse, uniform density and spherical polypropylene particles. Results show that principally the shape of the paddles is the important design consideration to enhance the axial transport of particles