  The objective of this study is to understand the dynamics of freely evolving
particle suspensions over a wide range of particle-to-fluid density ratios. The
dynamics of particle suspensions are characterized by the average momentum
equation, where the dominant contribution to the average momentum transfer
between particles and fluid is the average drag force. In this study, the
average drag force is quantified using particle-resolved direct numerical
simulation in a canonical problem: a statistically homogeneous suspension where
an imposed mean pressure gradient establishes a steady mean slip velocity
between the phases. The effects of particle velocity fluctuations, particle
clustering, and mobility of particles are studied separately. It is shown that
the competing effects of these factors could decrease, increase, or keep
constant the drag of freely evolving suspensions in comparison to fixed beds at
different flow conditions. It is also shown that the effects of particle
clustering and particle velocity fluctuations are not independent. Finally, a
correlation for interphase drag force in terms of volume fraction, Reynolds
number, and density ratio is proposed. Two different approaches (symbolic
regression and predefined functional forms) are used to develop the drag
correlation. Since this drag correlation has been inferred from simulations of
particle suspensions, it includes the effect of the motion of the particles.
This drag correlation can be used in computational fluid dynamics simulations
of particle-laden flows that solve the average two-fluid equations where the
accuracy of the drag law affects the prediction of overall flow behavior.
