Shuyan Wang, Xu Wang, Ruichen Wang, Juntian Zhao, Shuren Yang, Yang Liu, Qun Dong, Simulations of flow behavior of particles in a liquid-solid fluidized bed using a second-order moments model, Powder Technology, Volume 302, November 2016, Pages 21-32, ISSN 0032-5910, http://dx.doi.org/10.1016/j.powtec.2016.08.019.
Abstract: Flow behavior of liquid and particles is simulated using an Eulerian-Eulerian two-fluid model based on the theory of granular flow in a liquid-solid fluidized bed. The kinetic interaction of particle collisions is modeled using a second-order moments method. Comparing to simulated results from the kinetic theory of granular flow, the simulated results from the second-order moments method are in agreement with the experimental data of Razzak et al.  in a riser. Simulated results indicate that the component of second-order moments in the axial direction is higher than that in the radial direction. The distribution of velocity and volume fraction is predicted at the different inlet liquid velocities. Simulations indicate that axial velocities of particles increase with increasing inlet liquid velocity. The granular temperature is computed from simulations as a function of solid volume fraction. Roughly, the granular temperature increases, reach a maximum, and then decreases with the increase of solid volume fraction. To verify the numerical model further, the liquid-solid flow in the downcomer is simulated, and the simulated results are agreement with the experimental results from Lan et al. . As well as, the liquid-solid circulation fluidized bed loop is investigated, and comparisons with Roy et al. simulations  are conducted.
Keywords: Second-order moments method; Kinetic theory of granular flow; Liquid-solid fluidized bed; Numerical simulation