THE SLOP FLUX METHOD FOR NUMERICAL BALANCE IN USING ROE'S APPROXIMATE RIEMANN SOLVER

Imbalance arises when the Roe＇s method is directly applied in the shallow water simulation.The reasons are different for the continuity equation and the momentum equations.Based on the Roe＇s method,a partial surface method is proposed for a perfect balance for the continuity equation.In order to generate a mathematically hyperbolic formulation,the momentum equations are split,which causes incompatibility in the calculation of the momentum equations.In this article a numerical approach named the Slop Flux Method（SFM）is proposed to balance the source terms and the flux gradient based on the finite volume method.The method is first applied to shallow water equations.The model is verified by analytical results of classical test cases with good agreement.Finally the method is applied to a steady flow simulation over a practical complicated topography and the result shows good balance and conservation.

3D full-loop simulation and experimental verification of gas-solid flow hydrodynamics in a dense circulating fluidized bed

Because of their advantages of high efficiency and low cost, numerical research methods for large-scale circulating fluidized bed （CFB） apparatus are gaining ever more importance. This article presents a numer- ical study of gas-solid flow dynamics using the Eulerian granular multiphase model with a drag coefficient correction based on the energy-minimization multi-scale （EMMS） model. A three-dimensional, full-loop, time-dependent simulation of the hydrodynamics of a dense CFB apparatus is performed. The process parameters （e.g., operating and initial conditions） are provided in accordance with the real experiment to enhance the accuracy of the simulation. The axial profiles of the averaged solid volume fractions and the solids flux at the outlet of the cyclone are in reasonable agreement with experimental data, thereby verifying the applicability of the mathematical and physical models. As a result, the streamline in the riser and standpipe as well as the solids distribution contours at the cross sections is analyzed. Computational fluid dynamics （CFD） serves as a basis for CFB modeling to help resolve certain issues long in dispute but difficult to address experimentally. The results of this study provide the basis of a general approach to describing dynamic simulations of gas-solid flows.

Investigation of particle-wall interaction in a pseudo-2D fluidized bed using CFD-DEM simulations

We report on discrete element method simulations of a pseudo-two-dimensional （pseudo-2D） fluidized bed to investigate particle-wall interactions. Detailed information on macroscopic flow field variables, including solids pressure, granular temperature, and normal and tangential wall stresses are analyzed. The normal wall stress differs from the solids pressure because of the strong anisotropic flow behavior in the pseudo-2D system. A simple linear relationship exists between normal wall stress and solids pressure. In addition, an effective friction coefficient can be derived to characterize particle-wall flow interaction after evaluating the normal and tangential wall stresses. The effects of inter-particle and particle-wall friction coefficients are evaluated. Strong anisotropic flow behavior in the pseudo-2D system needs to be considered to validate the two-fluid model where the boundary condition is usually developed based on an isotropic assumption. The conclusion has been confirmed by simulation with different particle stiffnesses. Assumptions in the newly developed model for 2D simulation are further examined against the discrete element method simulation.

Application of CFD-DEM to the study of solid exchange in a dual-leg fluidized bed

The CFD-DEM model was developed to simulate solid exchange behavior between two half beds in a bench-scale two-dimensional dual-leg fluidized bed （DL-FB）. Power spectrum density （PSD） analysis was applied to obtain the dominant frequency （F） of the simulated differential particle number （APLR） between the two half beds. Effects of fluidization velocity （u） and bed material inventory （H） on the solid exchange behavior were studied using the CFD-DEM model. Not only snapshots of the simulated particle flow patterns using the OpenGL code but also the dominant frequency of APLR was similar to the experimental results. The simulation results show that higher fluidization velocity assists the exchange of more particles between the two half beds, but the dispersion of clusters on the bed surface into single particles decreases the cluster exchange frequency. A greater bed material inventory results in more intense cluster exchange. The cluster exchange frequency decreases with an increase of the bed material inventory.