Three-Fluid Model with Kinetic Theory of Granular Flow Closure

4 Three-Fluid Model with Kinetic Theory of Granular Flow Closure 

Chao [21] and Chao et al. [20, 22, 23] made a three-fluid model for a binary particle system with an interstitial gas to simulate particle segregation due to size and weight differences between the two particle types. The first part of the work considered a cold flow study of a binary particle mixture. Later, Chao [21] and Chao et al. [24] made a three-fluid model for a reactive binary particle system with a multi-component interstitial gas. The process investigated was sorption-enhanced steam methane reforming (SE-SMR) which is steam methane reforming (SMR) and a gas-solid adsorption reaction CO2 capture process. 

In all these KTGF closure models, there are many integral terms related to Cij. From the kinetic theory, we know that the random particle velocity c is defined as the sum of the peculiar velocity Q and fluid dynamic velocity v , i.e., c = C - - v , hence the correct definition for c j should be = C, -f Vy. In all previous models, 

Cij is approximated by the peculiar particle-particle velocity differences Qj only, thus the fluid dynamic particle-particle velocity differences Vy are neglected. This simplification may lead to an under-prediction of the particle-particle momentum coupling. Moreover, the main momentum coupling between the binary particle fluids are through the particle-particle drag. Therefore, when deriving the particle-particle 

Ci j and V j respectively. In accordance with the theoretical basis of the kinetic theory of dilute gases, these properties are transported by short-term collisional contacts. For this reason, the KTGF models including the total particle-particle drag model, Fij = Ffj + f(J represent the solid flow dynamics for dilute binary fluidized beds. However, for dense beds, additional frictional effects need to be considered. An extra frictional particle-particle drag term, f(P must be taken into account. The 

---