Fundamentals of turbulent gas-solid flows applied to circulating fluidized bed combustion

Numerical simulation and validation of dilute turbulent gas–particle flow with inelastic collisions and turbulence modulation

“…The pressure velocitydivergence correlation describes the transfer of energy between the turbulence and the inner energy of the fluid. Such energy exchange is nearly always negligible for gas-solid flows of interest [9]. The term P l accounts for the rate of production of turbulence kinetic energy from the mean flow…”

“…The effect of gravity is included into the external force term, B i l , in (9). Thus, the momentum equation for the gas-phase mean motion becomes…”

“…Expressions for these terms are derived from the kinetic theory of dry granular flow in [4] and modifications to incorporate the interstitial gas effect on the constitutive relations are described in [9]. The latter constitutive equations are employed here to provide the closures for the dispersed phase.…”

“…As the particle diameter can be somewhere in between the Kolmogorov length scale and the integral length scale of the gas turbulence, the presence of particles may also modulate the turbulence structure in the gas phase [8]. As pointed out by Peirano and Leckner [9], the vortex shedding and work done by eddies are thought to be the dominant mechanisms for turbulence modulation in gas-solid flows. An alternative derivation of the two-fluid model equations including fluid-solid interaction was developed by Simonin [6] based also on particle PDF transport equations.…”

“…Further investigation on how the interstitial turbulent gas modifies the constitutive relations of the solid phase was carried out by Reeks [5], Simonin [6], Zhang and Reese [7] and Lun and Savage [8]. Peirano and Leckner [9] derived suitable relations for the solid-phase stress tensor and fluctuating energy flux under the Eulerian framework, which incorporate the effect of gas turbulence on the random motion of particles.…”