A new droplet collision and coalescence model was presented a quick-sort method for locating collision partners was also devised and based on theoretical and experimental results, further advancement was made to the droplet collision outcome. The advantages of the two implementations of smoothed particle hydrodynamics (SPH) method were used to limit the collision of droplets to a given number of nearest droplets and define the probability of coalescence, numerical simulations were carried out for model validation. Results show that the model presented is mesh-independent and less time consuming, it can not only maintains the system momentum conservation perfectly, but not susceptible to initial droplet size distribution as well.

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To predict the characteristics of dense liquid-solid two-phase flow, K-e-Tmodel is established, in which the turbulent flow of fluid phase is described with fluid turbulent kinetic energy Kf and its dissipation rate ef , and the particles random motion is described with particle turbulent energy K v and its dissipation rate e p and pseudothermal temperature

A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concept of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision. The proposed model is used to simulate gas-particle downer reactor flows. The computational results of both particle volume fraction and mean velocity are in agreement with the experimental results. After analyzing effects of empirical coefficient on prediction results, we can come to a conclusion that, inside the limit range of empirical coefficient, the predictions do not reveal a large sensitivity to the empirical coefficient in the downer reactor, but a relatively great change of the constants has important effect on the prediction. Nomenclatureαp-particle volume fraction β-drag coefficient U -mean velocity(m/s) u,v -fluctuating velocity (m/s) uu, vv-Reynolds stress or fluctuation velocity correlation(m 2 /s 2 ) e-restitution coefficient d -particle diameter(m) k -kinetic energy(m 2 /s 2 ) ε-kinetic energy dissipation rate(m 2 /s 3 ) Subscripts: 1-large-scale fluctuation 2-small-scale fluctuation p-particle f-gas