Kinetic shear-stress of particles in the particle-laden flow simulated using classic and second-order moment of kinetic theory of granular flow--颗粒学报PARTICUOLOGY

Kinetic viscosity of particles in the kinetic theory of granular flow (KTGF) was derived from the turbulence viscosity of the gas phase based on the kinetic theory of gas, with the effects of the dense phase of granular materials. KTGF is prominent in predicting the dense particle flow, being the primary numerical method for the gas-particle flow in fluidization, predominantly in the large-scale simulations as a Eulerian method. Recent studies presented that the second-order moment (SOM) of KTGF is superior to the classic KTGF in the particle-flow prediction. The difference between classic KTGF and SOM KTGF exists in the numerical model of the kinetic stresses of particles, which is calculated by the pseudo kinetic viscosity of particles in classic KTGF and by the SOM of the fluctuating velocity of particles by using the partial differential equations in SOM-KTGF. In this study, the gas-particle flow was simulated using SOM-KTGF and the stress tensors of particles predicted by the two methods were compared. It was demonstrated that the normal components of the kinetic stress tensor predicted by the two methods were close in value. However, the kinetic shear-stress was over-predicted by the classic KTGF in the dilute phase of particles in the gas-particle flow of fluidization, when the volume fraction of particles was less than 0.01. Therefore, SOM-KTGF is superior to the classic KTGF, particularly when the particle flow is dominated by the interstitial gas phase, as the particle-laden flow occurs in the lower volume fraction of particles in the dense regime, and further in the dilute and median regimes, when the volume fraction of particles less than 0.01. This superiority is caused by the high-fidelity prediction of the kinetic shear stress in SOM-KTGF rather than the prediction by classic KTGF. In addition, SOM-KTGF extended the application of KTGF from dense flows of particles in fluidization to median-dilute flows of particles in pneumatic conveying, when the volume fraction is less than 0.001.

Graphical abstract

Keywords

Kinetic viscosity; Shear stress; Kinetic theory of granular flow; Second-order moment; Fluidization

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