A resolved Eulerian–Lagrangian numerical approach is used to study the heat transfer of 1204 heated spheres fluidized in a slit bed. This approach uses a direct numerical simulation combined with the immersed boundary method (DNS-IB). Pan et al. (2002, “Fluidization of 1204 Spheres: Simulation and Experiment,” J. Fluid Mech., 451, pp. 169–192) studied the fluidization of 1204 spheres by a uniform flow without heat transfer using a fictitious domain-based DNS. The focus of this study is placed on the heat transfer between the heated spheres and fluid and also the fluidization by a jet flow. In the DNS-IB method, fluid velocity and temperature fields are obtained by solving the modified momentum and heat transfer equations, which result from the presence of heated spheres in the fluid. Particles are tracked individually and their velocities and positions are solved based on the equations of linear and angular motions; particle temperature is assumed to be a constant. The momentum and heat exchange between a particle and the surrounding fluid at its surface are resolved using the IB method with the direct forcing scheme. By exploring the rich data generated from the DNS-IB simulations, we are able to obtain statistically averaged fluid and particle velocity as well as particle heat transfer rate in a fluidized bed. Our results on the pressure drop and bed height are compared to the results of Pan et al. (2002, “Fluidization of 1204 Spheres: Simulation and Experiment,” J. Fluid Mech., 451, pp. 169–192), which show good agreements. The case of the fluidization of 1204 spheres by a jet flow has also been studied and compared against the case of the fluidization by a uniform flow. The flow structures, drag, and heat transfer rate of two spheres placed along flow directions have been studied to understand the influence of a neighboring sphere. Results show that the trailing sphere has an insignificant effect on the leading sphere when it comes to the drag and heat transfer rate. On the contrary, the leading sphere can reduce the drag and heat transfer rate of the trailing sphere by more than 20% even when the two spheres are separated by six diameters. This demonstrates the need of a fully resolved DNS in accurately modeling dense particulate flows where a particle could be surrounded by multiple neighboring particles.
This study presents a numerical prediction of particle deposition on an impingement wall for nozzle-tosurface distance, L/D = 2. The continuous phase flow was solved using Reynolds-averaged Navier Stokes (RANS) along with Baseline Reynolds stress turbulence model (RSM-BSL). The particulate phase was simulated using a one-way coupling Lagrangian random-walk eddy-interaction model (EIM). The particle deposition density using turbulent tracking and mean flow tracking was predicted and the effect of the near-wall correction of the normal Reynolds stress component was evaluated. The effect of anisotropic flow using the minimum eddy lifetime is examined. To assess the accuracy of EIM in framework of RANS, large eddy simulation (LES) with Lagrangian particle tracking was used to predict the particle deposition in impinging jet flow. LES prediction was compared to RANS/EIM predictions and experimental data. Moreover, simulation findings demonstrate the superiority of LES compared to RANS/EIM in predicting the particle deposition. The results obtained using RANS/EIM showed that the deposition of the particles using the minimum eddy lifetime and near-wall correction yields close results to LES prediction and the experimental data. In addition, the deposition exhibits a ring-like pattern similar to experiments.
This study presents a numerical prediction of the particle size behaviour near the wall of an impinging jet with nozzle-to-surface distance, L/D = 2. The continuous phase flow was solved using Reynolds-averaged Navier Stokes (RANS) along with Shear Stress Transport turbulence model (SST). The particulate phase was simulated using a one-way coupling Lagrangian random-walk eddy-interaction model (EIM) implemented in an in-house FORTRAN code, where the equation of motion of particles was solved numerically using 4 th order Rung-Kutta method. The main forces working on the solid particles were the drag force and the gravity force. Three different particle sizes of 5, 10, 20 µm were used in the simulation. In EIMs [1], one particle is allowed to interact successively with various eddies. Each eddy has a characteristic lifetime, length, and velocity scales obtained from the single-phase flow calculation results. The end of the interaction between the particle and one eddy occurs when the lifetime of the eddy is over or when the particle crosses the eddy. At this instant, a new interaction with the particle and a new eddy is started. The particle will have another trajectory according to its equation of motion [2] and [3]. In order to obtain velocity or deposition statistics, hundreds of particles must be released into the flow. In the present study, for the time scale or the eddy life time is maintained constant during one eddy particle interaction. However, the eddy characteristic velocity scale (known as eddy velocity) is varying during the interaction. The eddy velocity is obtained by multiplying, the root-mean-square (RMS) fluid fluctuating velocity by a random number, N, generated from a Gaussian probability density function of zero mean and unity standard deviation. The fluid velocity components in the equation of motion of particles are instantaneous quantities composed of the mean part and the fluctuating part. The fluctuating part of the instantaneous fluid velocity is obtained through modelling. Therefore, three local fluctuating velocities are computed for each eddy at the start of one eddy-particle interaction. In this study, airflow at 25 C o incompressible and steady state fluid flow was assumed in the solution. Inlet conditions consisted of a top hat profile (u = 10.5 m/s), a turbulence intensity of 5% of the mean velocity and a turbulence length scale of 10 % of the inlet diameter (15 mm). The Reynolds number based on the inlet diameter is Re = ρuD/μ = 10000, where the air density is ρ =1.18 kg/m 3 and μ is the viscosity of the fluid (μ= 1.824x10-5 kg/m.s). A constant zero gage pressure was applied at the outlet opening of the computational domain. In addition, no slip condition was applied on the impingement and side walls. The results showed that the smallest particles (5 µm) behave closely as the streamline of the fluid phase due to its small inertia effect. However, for the largest particles (20 µm), they deposit on the wall immediately as it enters the stagnation region, due to their large size, in...
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