Modeling of dynamics, heat transfer, and combustion in two-phase turbulent flows: 1. Isothermal flows

Kinetic modeling of dilute solid-liquid two-phase flows with inelastic collisions

“…The kinetic equation can be either the classic Boltzmann equation [1,2,6] or an equation derived from the Lagrangian equation of single particle movement [16,19,20] . The latter equation is advantageous in accounting for the effects of fluid turbulence on particle motion and is adopted in this work for the modeling of dilute solid-liquid two-phase flows with inelastic collisions.…”

“…Interparticle collisions are usually represented by the Boltzmann collisional operator [17,19] . In fact, it only applies for nearly elastic collisions.…”

“…Boelle et al [17] extended Jenkins and Richman's [2] kinetic model to gas-solid flows by incorporating the drag force; Balzer [18] showed the applicability of this modeling approach in dense gas-solid flows. Zaichik et al [19] described the interactions of particles with gas turbulence with a Fokker-Planck diffusion operator and quantified interparticle collisions with the Boltzmann operator. With the Chapman-Enskog perturbation method, solutions for the PDF and accordingly constitutive relations for the particle phase were constructed.…”

“…With the Chapman-Enskog perturbation method, solutions for the PDF and accordingly constitutive relations for the particle phase were constructed. Differing from Zaichik et al [19] , Fu and Wang [20] admitted more possibilities in specifying the diffusion operator and modeled interparticle collisions with the Shakov revised BGK operator for dilute flows; this model was applied to characterizing sediment diffusion and transport in open-channel flows [21,22] . Wang et al [23] generalized this model to moderately concentrated flows with additional modifications to the BGK operator.…”

“…Wang et al [23] generalized this model to moderately concentrated flows with additional modifications to the BGK operator. In terms of the way dealing with interparticle collisions, the Boltzmann operator [17,19] only applies for description of nearly elastic collisions, the revised Enskog theory (RET) becomes a unique alternative to describe collisions in considerably dissipative flow systems [24] , and the BGK operators preserve the essential properties of the Boltzmann and RET collisional operators. In contrast to difficulties in finding solutions to the Boltzmann equation and the RET theory equation, the BGK operators are simple in form facilitating analytical studies for practical applications.…”