Computational investigation of contraction behavior in a liquid-solid fluidized bed

Contraction behavior of a liquid-solid fluidized bed has been investigated numerically. Based on a simple hydrodynamic model proposed by Brandani and Zhang （2006）, a case study for solid particles with a density of 3,000 kg/m^3 and a diameter of 2.5× 10^-3 m is simulated in a two-dimensional fluidized bed （0.50 m height and 0.10 m width）. Due to the continuity of numerical computation, there is a transition region between two zones of different solid holdups when the liquid velocity is suddenly changed. The top, middle and bottom interfaces are explored to obtain a reasonable interface height. The simulated results show that the steady time of the middle interface is more close to Gibilaro＇s theory and suitable for describing the contraction process of a phase interface. Furthermore, the effect of liquid velocity and particle diameter is simulated in the other two-dimensional fluidized bed （0.10 m height and 0.02 m width） where the solid particles are glass beads whose properties are similar to those of the catalyst particles used in the alkylation process. The results also show good agreement with Gibilaro＇s theory, and that larger particles lead to a more obvious bed contraction.

Real-time solution of nonlinear potential flow equations for lifting rotors

Analysis of rotorcraft dynamics requires solution of the rotor induced flow field.Often,the appropriate model to be used for induced flow is nonlinear potential flow theory（which is the basis of vortex-lattice methods）.These nonlinear potential flow equations sometimes must be solved in real time––such as for real-time flight simulation,when observers are needed for controllers,or in preliminary design computations.In this paper,the major effects of nonlinearities on induced flow are studied for lifting rotors in low-speed flight and hover.The approach is to use a nonlinear statespace model of the induced flow based on a Galerkin treatment of the potential flow equations.

Optimal contract wall for desired orientation of fibers and its effect on flow behavior

The orientation of suspended fibers in the turbulent contraction is strongly related to the contraction ratio,which in some cases may be detrimental to the actual production.Here for a certain contraction ratio,the contraction geometry shape is optimized to obtain the desired fiber orientation.In view of the nonlinearity and the complexity of the turbulent flow equations,the parameterized shape curve,the dynamic mesh and a quasi-static assumption are used to model the contraction with the variable boundary and to search the optimal solution.Furthermore the Reynolds stress model and the fiber orientation distribution function are solved for various wall shapes.The fiber orientation alignment at the outlet is taken as the optimization objective.Finally the effect of the wall shape on the flow mechanism is discussed in detail.