Particle-particle drag force in inertial bidisperse gas-particle suspensions

Particle-resolved direct numericalsimulations are employed to investigate theparticle-particle drag force in the bidisperse gas-particle suspensions where the particlesare smooth and the single-particle velocity distribution function is Maxwellian. Theparticle Reynolds number ranges from 6.7 to 123.8, and in this range the particle inertia ishigh enough that the lubrication force is not essential. It is found that the relation derivedby the kinetic theory of granular flow (KTGF) highly overestimates the particle-particledrag force. This is because the pre-collision velocities of colliding particles are notcompletely uncorrelated with each other. From the time sequence of collision events, itis observed that the particle pair that has just collided will probably collide again aftera short time due to the restriction of the particle motion in dense suspensions. Sincethe post-collision velocities of the first collision cannot relax entirely in such a shorttime, the relative velocity before the subsequent collision is statistically smaller thanthe domain-averaged relative velocity. Consequently, the particle-particle drag force isover-predicted when the domain-averaged relative velocity is used. For this reason, thiswork assumes that the particle-particle drag force is determined by the relative velocitywithin a local region near large particles. When the local region is set to be the sphericalshellscentred on the centres of large particles and with an outer radius of a mean free pathof small particles, the KTGF-based relation can reasonably predict the particle-particledrag force.