Cluster Structure-dependent Drag Research Articles

Passive method-based clusters regulation of two-stage fluidized bed riser using dynamic cluster structure-dependent drag model

The passive method-based regulation and control of particle clusters is studied using two-fluid model (TFM) with kinetic theory of granular flow (KTGF) in two-stage fluidized bed risers which include an expanding two-stage riser and contracting two-stage riser. The occurrence of heterogeneous flow with clusters was discriminated using computational threshold in terms of the minimization of energy dissipation rate. The drag coefficient of heterogeneous flow with clusters was simulated using dynamic cluster structure-dependent (DCSD) drag model in a constant-diameter riser and diameter-transformed risers. Comparing to hydrodynamics of gas and particles in a constant-diameter riser, a transition regime exists from the first chamber to the second chamber in the diameter-transformed riser. The solid volume fraction and diameter of clusters decrease in the second chamber. The cluster velocity increased in the contracting-diameter two-stage risers, and decreased in the expanding-diameter two-stage risers. The cluster existence time fractions were reduced in diameter-transformed two-stage risers. Hydrodynamics of clusters are regulated by altering the diameter ratio of the diameter-transformed risers.

A dynamic cluster structure-dependent drag coefficient model applied to the riser in high density circulating fluidized bed

A dynamic cluster structure dependent (DCSD) drag model based on energy dissipation minimization using the two-fluid model (TFM) and the kinetic theory of granular flow (KTGF) is applied to the riser in high density circulating fluidized bed (HDCFB). The characteristics of gas and solid are predicted by means of the DCSD drag model with the convective and local accelerations. The law of granular collision energy dissipation and drag energy dissipation are compared and the influence of granular collision energy dissipation to agglomerate structure is researched. The study shows that granular collision energy dissipation has great influence on heterogeneous structure of riser. Simulated solid volume fraction, axial pressure drop and solid mass flux are compared to experimental measurements, numerical analysis suggests that the temporal-spatial heterogeneous structure characteristics and particle collision affect the flow of the riser in the literature.

Pulsation active method-based particle cluster regulation using dynamic cluster structure-dependent drag model in a fluidized bed riser

The knowledge of pulsation active method is essential for reliable regulation of particle clusters in pulsating fluidized bed risers. This study presents a comparison of the computed occurrence of particle clusters using a computational criterion in an inlet gas pulsation-assisted riser. The occurrence of clusters is identified according to the minimum rate of energy dissipations using dynamic cluster structure-dependent drag model. The influences of inlet gas velocity, frequency and amplitude on cluster characteristics are analyzed along lateral and axial directions. The cluster diameters and existence time fractions as well as the gas volume fractions of the dense phase vary with changing inlet gas velocity frequencies and amplitudes when compared to a constant inlet gas velocity. The particle cluster number is reduced from a large fraction at a constant inlet gas velocity to a low fraction in an inlet gas pulsation-assisted fluidized bed risers.

Comparative analysis of heterogeneous gas-solid flow using dynamic cluster structure-dependent drag model in risers

An energy dissipation minimization-based dynamic cluster structure-dependent (DCSD) drag model is proposed using Euler-Euler two-fluid model (TFM) and kinetic theory of granular flow (KTGF). The DCSD drag model consists of a set of transient nonlinear equations which includes eight balance equations and one extreme value equation of the minimization of energy dissipation rate. The criterion of cluster existence is proposed to identify the heterogeneous flow and homogenous flow of gas-particles suspension. The intermittency factor is defined to describe the occurrence time of clusters. Three clustering mechanisms named collision-dominant (CD), collision-hydrodynamic-dominant (CHD) and hydrodynamic-dominant (HD) are identified as a result of the compromise in competition of energy dissipation rate components of hydrodynamic interactions and interactions of collision of particles. The CHD for particle clustering is the central mechanism, and CD is next in importance to HD. The predicted cluster diameter and solids volume fraction of clusters are compared to calculations using empirical correlations in literature.

A dynamic cluster structure-dependent drag coefficient model applied to gas-solid risers

A dynamic cluster structure-dependent (CSD) drag coefficient model is proposed to be consistent with the temporal-spatial characteristics of dynamic clusters through the convective accelerations and temporal accelerations of the dense phase and the dilute phase. The CSD drag coefficient is determined by a nonlinear micro-meso-grid scales equation set which consists of three momentum conservation equations, two mass balance equations, one equation for volume fraction balance, and an extreme value of a function in combination with the bivariate extreme value (BEV) theory. Flow behavior of gas and particles is predicted by means of gas-solid two-fluid model coupled with CSD drag model and kinetic theory of granular flow. The distributions of independent variables of dense phase and dilute phase are predicted in the riser. Numerical analysis suggests that the inertial difference between the dense phase and the dilute phase affects flow behavior of dynamically temporal-spatial clusters in risers. The simulated solids volume fraction, cluster existence time fraction and frequency of cluster occurrence are compared to experimental measurements in the literature.

Extension of cluster-structure dependent drag model to simulation of riser with Geldart B particles

To describe the impact of clusters as the meso-scale structure, a cluster-structure-dependent (CSD) drag model is proposed based on stability criterion of the minimum energy dissipation consumed by drag, where the heterogeneous flow structure is characterized by the gas-rich dilute phase and the particle-rich dense phase. Under the framework of the two-fluid model, the CSD drag model is employed for the investigation of the hydrodynamics in risers with Geldart B particles. By comparisons with experimental results, the CSD drag model shows reasonable predictions. Local structural parameters including dense phase fraction, local velocities in dense and dilute phases are obtained. Meanwhile, the profiles of energy consumption by drag with local gas volume fraction are analyzed, which reveals that the direction of particles will significantly alter the distribution of energy consumption by the heterogeneous drag.

Cluster structure-dependent drag model for liquid–solid circulating fluidized bed

The formation of clusters in liquid–solid circulating fluidized beds effects on momentum transfer between phases. In this article, a cluster structure-dependent drag model is proposed to take the effect of clusters on momentum transfer between dispersed phase and clusters into account by means of an Eulerian–Eulerian two-fluid model. The momentum and energy balances that characterize the clusters in the dense phase as well as dispersed particles in the dilute phase are described by the multi-scale resolution approach. The proposed model of cluster structure-dependent (CSD) drag coefficient is on the basis of the minimization of energy dissipation by heterogeneous drag (MEDHD) as a function of Reynolds number. The CSD drag coefficient model is incorporated into the two-fluid model to simulate flow behavior of liquid and particles in a liquid–solid riser. Predicted volume fraction and particle velocity distributions are in good agreement with experimental data published in the literature.

Hydrodynamics of gas–solid risers using cluster structure-dependent drag model

A modified cluster structure-dependent (CSD) drag model is proposed to improve drag predictions for heterogeneous gas–solid flows in risers. A micro-meso-grid scales (M2GS) equation set consists of six hydrodynamic equations and one stability criteria with bivariate extreme value (BEV) theory as a function of eight independent variables and four dependent parameters on the basis of grid parameters. The modified CSD drag model is further verified by CFD simulations by coupling with the two-fluid model for low and high solid fluxes in risers. The simulated results in 2D domain of the riser are compared with those using the Huilin–Gidaspow drag model and experimental data. The modified CSD drag model is verified by CFD simulations by coupling with a kinetic theory of granular flow based two-fluid model for low and high solid fluxes in risers. The comparison shows that the modified CSD drag model is able to capture the axial heterogeneity with the dense bottom and dilute top sections. The radial profiles using modified CSD drag models show only qualitative agreement with the experimental data. The results using the modified CSD drag model and Huilin–Gidaspow drag model show a reasonable agreement at the center. Thus, further improvements combining with wall friction effect are required to achieve quantitative agreement with experimental data.

CFD studies of dual circulating fluidized bed reactors for chemical looping combustion processes

Chemical looping combustion (CLC) processes in a dual circulating fluidized bed (DCFB) reactor are investigated by means of computational fluid dynamic (CFD) method. A two-fluid model with consideration of heterogeneous chemical reactions is adopted. The kinetic theory of granular flow is employed for closure. A cluster structure-dependent (CSD) drag coefficient model is applied to account for the effect of meso-scale heterogeneous structure involving clusters or strands. The simulations are performed to predict gas–solid flow behaviors and reactive characteristics in dual circulating fluidized bed reactors during the CLC process. By a comparison of the outlet gas concentrations with the measured data, the CSD drag model can obtain a more reasonable prediction than the Ergun/Wen–Yu drag model. The influence of reaction temperature and air/fuel ratio on the performance of the DCFB reactor is also evaluated.

CFD simulation of gas–solid flow with a cluster structure-dependent drag coefficient model in circulating fluidized beds

To model the effect of clusters on hydrodynamics of gas and particles phases in risers, the interfacial drag coefficient is taken into account in computational fluid dynamic simulations by means of a two-fluid model. The momentum and energy balances that characterize the clusters in the dense phase and dispersed particles in the dilute phase are described by the multi-scale resolution approach. The model of cluster structure-dependent (CSD) drag coefficient is proposed on the basis of the minimization of energy dissipation by heterogeneous drag (MEDHD) in the full range of Reynolds number. The model of CSD drag coefficient is then incorporated into the two-fluid model to simulate flow behavior of gas and particles in a riser. The distributions of volume fraction and velocity of particles are predicted. Simulated results are in agreement with experimental data published in the literature.

Simulation of flow behavior of particles by cluster structure-dependent drag coefficient model for chemical looping combustion process: Air reactor modeling

A computational fluid dynamic (CFD) model for the air reactor of chemical looping combustion (CLC) technology has been developed, with special focus on flow of clusters. To model effects of clusters on flow behavior of gas and particles in a riser of air reactor, the model of cluster structure-dependent (CSD) drag coefficient is proposed on the basis of the minimization of energy dissipation by heterogeneous drag (MEDHD). The momentum balances that characterize the clusters in the dense phase and dispersed particles in the dilute phase are proposed. The CSD drag coefficient model is incorporated into the two-fluid model. The distributions of concentration and velocity of particles are predicted in a riser of air reactor. The Ergun/Wen and Yu drag model underestimates the distribution of concentration of particles in the riser. Dynamic evolution of clusters is reproduced and the profile of concentration and solid fluxes is analyzed. Predictions using the CSD drag coefficient model are in agreement with experimental data published in the literature. The distributions of O2 concentration and temperatures of gas phase and particles are predicted with CuO as oxygen carrier in the AR.

A cluster structure-dependent drag coefficient model applied to risers

Cluster structures affect macroscopic hydrodynamic behavior in gas–solid risers. The moment and energy balances for the dense phase and dilute phase are presented by the multi-scale resolution approach to investigate the dependence of drag coefficient on structure parameters. The modified model of cluster structure-dependent (CSD) drag coefficient is proposed on the basis of the minimization of energy dissipation by heterogeneous drag (MEDHD). Unlike previous works on CSD drag coefficient model, the modified CSD drag model takes wall friction into account. The closure for the drag coefficient depends not only on flow behavior of gas and particles but also on the wall friction. The structure-dependent drag coefficients calculated from the approach of the minimization of energy dissipation by drag force are then incorporated into the two-fluid model to simulate the behavior of gas–solid flow in a riser. The distributions of concentration and velocity of particles are predicted. Simulated results are in agreement with experimental data published in the literature. The effect of the wall friction on flow behavior of particles is analyzed.

Modeling of cluster structure-dependent drag with Eulerian approach for circulating fluidized beds

Flow behavior of gas and solids is simulated in combination the gas–solid two-fluid model with a cluster structure-dependent (CSD) drag coefficient model. The dispersed phase is modeled by a Eulerian approach based upon the kinetic theory of granular flow (KTGF) including models for describing the dispersed phase interactions with the continuous phase. The drag forces of gas–solid phases are predicted from the local structure parameters of the dense and dilute phases based on the minimization of the energy consumed by heterogeneous drag. The cluster structure-dependent (CSD) drag coefficients are incorporated into the two-fluid model to simulate flow behavior of gas and particles in a riser. Simulation results indicate that the dynamic formation and dissolution of clusters can be captured with the cluster structure-dependent drag coefficient model. Simulated solid velocity and concentration of particles profiles are in reasonable agreement with experimental results.