Numerical investigation of separation efficiency of the cyclone with supercritical fluid–solid flow

The utilization of hydrogen is gaining increasing attention due to its high heating value and environmentally friendly combustion product. The supercritical water circulating fluidized bed reactor is a promising and potentially clean technology that can generate hydrogen from coal gasification. Cyclone is a vital part of the reactor which can separate incomplete decomposition of pulverized coal particles from mixed working fluid. This paper aims to gain in-depth understanding of the cyclone separation mechanisms under supercritical fluid by computational fluid dynamics (CFD). Although the amount of supercritical carbon dioxide in mixed working fluid is minor, it obviously influences the flow fields and separation efficiency of a cyclone. The simulation results suggest that both the decreasing content of supercritical carbon dioxide and adding the extra dipleg cause the promoting performance of cyclones. Research findings could refine the design of supercritical fluid–solid cyclones.     

Transport modeling of sedimenting particles in a turbulent pipe flow using Euler–Lagrange large eddy simulation

A volume-filtered Euler–Lagrange large eddy simulation methodology is used to predict the physics of turbulent liquid–solid slurry flow through a horizontal periodic pipe. A dynamic Smagorinsky model based on Lagrangian averaging is employed to account for the sub-filter scale effects in the liquid phase. A fully conservative immersed boundary method is used to account for the pipe geometry on a uniform cartesian grid. The liquid and solid phases are coupled through volume fraction and momentum exchange terms. Particle–particle and particle–wall collisions are modeled using a soft-sphere approach. Three simulations are performed by varying the superficial liquid velocity to be consistent with the experimental data by Dahl et al. (2003). Depending on the liquid flow rate, a particle bed can form and develop different patterns, which are discussed in light of regime diagrams proposed in the literature. The fluctuation in the height of the liquid-bed interface is characterized to understand the space and time evolution of these patterns. Statistics of engineering interest such as mean velocity, mean concentration, and mean streamwise pressure gradient driving the flow are extracted from the numerical simulations and presented. Sand hold-up calculated from the simulation results suggest that this computational strategy is capable of predicting critical deposition velocity.     

Numerical simulation of counter-current flow field in the downcomer of a liquid–solid circulating fluidized bed

A comprehensive study on the hydrodynamics in the downcomer of a liquid–solid circulating fluidized bed (LSCFB) is crucial in the control and optimization of the extraction process using an ion exchange LSCFB. A computational fluid dynamics model is proposed in this study to simulate the counter-current two-phase flow in the downcomer of the LSCFB. The model is based on the Eulerian–Eulerian approach incorporating the kinetic theory of granular flow. The predicted results agree well with our earlier experimental data. Furthermore, it is shown that the bed expansion of the particles in the downcomer is directly affected by the superficial liquid velocity in downcomer and solids circulation rate. The model also predicts the residence time of solid particles in the downcomer using a pulse technique. It is demonstrated that the increase in the superficial liquid velocity decreases the solids dispersion in the downcomer of the LSCFB.     

Experimental study and numerical simulation of the characteristics of a percussive gas–solid separator

The presence of solid particles in the flow of hypersonic wind tunnels damages the appearance of the experiment models in the wind tunnel and influences the accuracy of experimental results. The design of a highly efficient gas–solid separator was therefore undertaken. Particle trajectory imaging methods were used to measure trajectories under different conditions. The flow field and particle movement characteristics for different head angles (HAs) and separation tooth angles (STAs), inlet velocities, and the exhaust gas outlet pressures in the separator, were calculated using simulations based on the discrete phase model. The particle separation efficiency, pressure loss, and flow loss resulting from different structural parameters were also studied. In line with experimental observations, the characteristic angle of particle movements in the separator and the separation efficiency of the separator were found to increase with decreasing HA and with increasing STA. Separation efficiency improves with increasing inlet velocity and with increasing negative pressure of the exhaust gas outlet; however, the corresponding pressure loss and the flow rate of the waste gas also increased.     

Numerical simulations of gas–liquid–solid flows in a hydrocyclone separator

The flow behavior in hydrocyclones is quite complex. In this study, the computational fluid dynamics (CFD) method was used to simulate the flow fields inside a hydrocyclone in order to investigate its separation efficiency. In the computational fluid dynamics study of hydrocyclones, the air-core dimension is a key to predicting the mass split between the underflow and overflow. In turn, the mass split influences the prediction of the size classification curve. Three models, the model, the Reynolds stress model (RSM) without considering the air-core, and the Reynolds stress turbulence model with the volume of fluid (VOF) multiphase model for simulating the air-core, were compared in terms of their predictions of velocity, axial and tangential velocity distributions, and separation proportion. The RSM with air-core simulation model, since it reproduces some detailed features of the turbulence and multiphase, clearly predicted the experimental data more closely than did the other two models.     

Numerical simulation of gas–solid flow with two fluid model in a spouted-fluid bed

The flow characteristics in a spouted-fluid bed differ from those in spouted or fluidized beds because of the injection of the spouting gas and the introduction of a fluidizing gas. The flow behavior of gas–solid phases was predicted using the Eulerian–Eulerian two-fluid model (TFM) approach with kinetic theory for granular flow to obtain the flow patterns in spouted-fluid beds. The gas flux and gas incident angle have a significant influence on the porosity and particle concentration in gas–solid spouted-fluid beds. The fluidizing gas flux affects the flow behavior of particles in the fountain. In the spouted-fluid bed, the solids volume fraction is low in the spout and high in the annulus. However, the solids volume fraction is reduced near the wall.     

Euler–Lagrange simulation of high pressure shock waves

This paper presents the numerical simulation of overdriven detonation (or O.D.D.) that occurs when a high velocity object impacts an explosive. The pressure and the velocity at this state are higher than those of the Chapman–Jouguet (C–J) state. First, before the simulation of this event, a study of PBX air blast by using multi-material Eulerian method is presented. Pressure peaks are computed for several distances from the explosive. Second, the O.D.D. phenomenon is modeled by the Euler–Lagrange penalty coupling, which permits to couple a Lagrangian mesh of the flyer plate to multi-material Eulerian mesh of explosives and air. This coupling gives us the high detonation velocities in the acceptor explosive and demonstrates that it is able to handle shock–structure interaction problems.     

Estimation of solid concentration in solid–liquid two-phase flow in horizontal pipeline using inverse-problem approach

In this study, an inverse-problem method was applied to estimate the solid concentration in a solid–liquid two-phase flow. An algebraic slip mixture model was introduced to solve the forward problem of solid–liquid convective heat transfer. The time-average conservation equations of mass, momentum, energy, as well as the volume fraction equation were computed in a computational fluid dynamics (CFD) simulation. The solid concentration in the CFD model was controlled using an external program that included the inversion iteration, and an optimal estimation was performed via experimental measurements. Experiments using a fly-ash–water mixture and sand–water mixture with different solid concentrations in a horizontal pipeline were conducted to verify the accuracy of the inverse-problem method. The estimated results were rectified using a method based on the relationship between the estimated results and estimation error; consequently, the accuracy of the corrected inversion results improved significantly. After a verification through experiments, the inverse-problem method was concluded to be feasible for predicting the solid concentration, as the estimation error of the corrected results was within 7% for all experimental samples for a solid concentration of less than 50%. The inverse-problem method is expected to provide accurate predictions of the solid concentration in solid–liquid two-phase flow systems.     

Numerical simulation of flow over an airfoil in heavy rain via a two-way coupled Eulerian–Lagrangian approach

Airfoil performance degradation in heavy rain has attracted many aeronautical researchers’ eyes. In this work, a two-way momentum coupled Eulerian–Lagrangian approach is developed to study the aerodynamic performance of a NACA 0012 airfoil in heavy rain environment. Scaling laws are implemented for raindrop particles. A random walk dispersion approach is adopted to simulate raindrop dispersion due to turbulence in the airflow. Raindrop impacts, splashback and formed water film are modeled with the use of a thin liquid film model. The steady-state incompressible air flow field and the raindrop trajectory are calculated alternately through a curvilinear body-fitted grid surrounding the airfoil by incorporating an interphase momentum coupling term. Our simulation results of aerodynamic force coefficients agree well with the experimental results and show significant aerodynamic penalties at low angles of attack for the airfoil in heavy rain. An about 3° rain-induced increase in stall angle of attack is predicted. The loss of boundary momentum by raindrop splashback and the effective roughening of the airfoil surface due to an uneven water film are testified to account for the degradation of airfoil aerodynamic efficiency in heavy rain environment.     

Direct simulation of liquid–gas–solid flow with a free surface lattice Boltzmann method

Direct numerical simulation of liquid–gas–solid flows is uncommon due to the considerable computational cost. As the grid spacing is determined by the smallest involved length scale, large grid sizes become necessary – in particular, if the bubble–particle aspect ratio is on the order of 10 or larger. Hence, it arises the question of both feasibility and reasonability. In this paper, we present a fully parallel, scalable method for direct numerical simulation of bubble–particle interaction at a size ratio of 1–2 orders of magnitude that makes simulations feasible on currently available super-computing resources. With the presented approach, simulations of bubbles in suspension columns consisting of more than 100,000 fully resolved particles become possible. Furthermore, we demonstrate the significance of particle-resolved simulations by comparison to previous unresolved solutions. The results indicate that fully resolved direct numerical simulation is indeed necessary to predict the flow structure of bubble–particle interaction problems correctly.     

Fuel injection model for Euler–Euler and Euler–Lagrange large-eddy simulations of an evaporating spray inside an aeronautical combustor

Large-Eddy Simulations (LES) of an evaporating two-phase flow in an experimental burner are investigated. Two different numerical approaches for the simulation of the dispersed phase are coupled to the same gaseous solver: a mesoscopic Eulerian method and a Lagrangian particle tracking technique. The spray is represented by a single droplet size owing to the locally monodisperse formulation of the employed mesoscopic Eulerian approach. Both approaches use the same drag and evaporation models. They do not take into account the atomization process and a simplified injection model is applied instead. The presented methodology, referred as FIM-UR (Fuel Injection Method by Upstream Reconstruction) defines injection profiles for the monodisperse spray produced by a pressure-swirl atomizer. It is designed so as to ensure similar spray characteristics for both approaches and allows for a direct comparison between them. After a validation of the purely gaseous flow in the burner, liquid-phase dynamics and droplet dispersion are qualitatively and quantitatively evaluated for the Eulerian and Lagrangian simulations. Results obtained for both approaches are in very good agreement and compare reasonably with experiments, indicating that simplified injection methods are appropriate for the simulation of realistic combustor geometries.     

Numerical study of gas–solid two-phase flow and erosion in a cavity with a slope

Gate valve is mainly used to turn on or turn off the pipeline in pneumatic conveying. When the gate valve is fully open, the particles are easy to collide with the cavity rear wall and enter into the cavity, resulting in particles’ accumulation in the cavity. The particles in cavity will accumulate between the cavity bottom and the flashboard bottom wall and prevent the gate from turning off normally. Meanwhile, the particles’ collision with cavity rear wall will cause serious erosion. Both the particles’ accumulation and erosion will cause the poor sealing of the gate valve, further resulting in the leakage of the pipeline system. To reduce the particles’ accumulation in cavity and erosion on cavity when the gate valve is fully open, we simplify the gate valve into a cavity structure and study it. We find that adding a slope upstream the cavity can effectively reduce the particles’ accumulation in the cavity and the erosion on the cavity rear wall. In this work, Eulerian–Lagrangian method in commercial code (FLUENT) was used to study the gas–solid two-phase flow and erosion characteristics of a cavity with a slope. The particle distribution shows that the particles with Stokes number St = 1.3 and St = 13 cannot enter the cavity due to the slope, but the particles with St = 0.13 enter the cavity following the gas. For St = 13, the particles collide with the wall many times in the ideal cavity. Erosion results show that the slope can transfer the erosion on cavity rear wall to the slope and reduce the maximum erosion rate of the wall near the cavity to some degrees.     

Migration of a solid particle in the vicinity of a plane fluid–fluid interface

The slow migration of a small and solid particle in the vicinity of a gas–liquid, fluid–fluid or solid–fluid plane boundary when subject to a gravity or an external flow field is addressed. By contrast with previous works, the advocated approach holds for arbitrarily shaped particles and arbitrary external Stokes flow fields complying with the conditions on the boundary. It appeals to a few theoretically established and numerically solved boundary-integral equations on the particle’s surface. This integral formulation of the problem allows us to provide asymptotic approximations for a distant boundary and also, implementing a boundary element technique, accurate numerical results for arbitrary locations of the boundary. The results obtained for spheroids, both settling or immersed in external pure shear and straining flows, reveal that the rigid-body motion experienced by a particle deeply depends upon its shape and also upon the boundary location and properties.     

Numerical simulation of a compressible vortex–wall interaction

The wall interaction of isolated compressible vortices generated from a short driver section shock tube has been simulated numerically by solving the Navier–Stokes equations in axisymmetric form. The dynamics of shock-free (incident shock Mach number \(M = 1.36\)) and shock-embedded \((M = 1.57)\) compressible vortices near the wall has been studied in detail. The AUSM+ scheme with a fifth-order upwind interpolation formula is used for the convective fluxes. Time integration is performed using a low dissipative and dispersive fourth-order six-stage Runge–Kutta scheme. The evolution of primary and wall vortices has been shown using the velocity field, vorticity field, and numerical schlierens. The vortex impingement, shocklets, wall vortices, and their lift-off are clearly identified from the wall pressure time history. It has been observed that the maximum vorticity of the wall vortices reaches close to 30 % of the primary vortex for \(M = 1.36\) and it reaches up to 60 % for \(M = 1.57\). The net pressure force on the wall due to incident shock impingement is dominant compared to the compressible vortex impingement and their evolution.     

Numerical investigations on gas–solid flow in circulating fluidized bed risers using a new cluster-based drag model

A cluster-based drag model is proposed for the gas–solid circulating fluidized bed (CFB) riser by including the cluster information collected from image processing and wavelet analysis into the calculation of system drag. The performance of the proposed drag model is compared with some commonly used drag models. A good agreement with the experimental data is achieved by the proposed cluster-based drag model. Error analysis of the proposed cluster-based drag model based on the local distributions of solids holdup and particle velocity is conducted. The clustering phenomenon in the low-density and high-density CFB risers and the effect of the cluster size on the simulation accuracy are also numerically studied by the proposed drag model.     

Viscoelastic flow past confined objects using a micro–macro approach

This paper is concerned with the numerical prediction of viscoelastic flow past a cylinder in a channel and a sphere in a cylinder using molecular-based models. The basis of the numerical method employed is a micro–macro model in which the polymer dynamics is described by the evolution of an ensemble of Brownian configuration fields. The spectral element method is used to discretize the equations in space. Comparisons are made between the macroscopic simulations based on the Oldroyd B constitutive model and microscopic simulations based on Hookean dumbbells, and excellent agreement is found. The micro–macro approach can be used to simulate models, such as the finitely extensible nonlinear elastic (FENE) dumbbell model, which do not possess a closed-form constitutive equation. Numerical simulations are performed for the FENE model. The influence of the model parameters on the flow is described and, in particular, the dependence of the drag as a function of the Weissenberg number.