Toward two‐phase flow modeling of nondilute sediment transport in open channels

Abstract

In this paper, we generalize several models based upon the multiphase flow theory to address the nondilute transport of suspended sediment in open channels. These models naturally include the dilute condition as a special case. We assess the range of validity of models through simulations of the experimental tests by Vanoni (1946), Einstein and Chien (1955), Taggart et al. (1972), Coleman (1986), and Wang and Qian (1992). The K − ɛ model is used to represent the turbulence in the carrier phase, and the kinetic theory of gases is employed for the closure of stresses due to inter‐particle collisions. We test various closures for the eddy viscosity of the disperse phase; we show the effects of increasing sediment concentration on the interaction forces between the two phases and on the stresses developed due to inter‐particle collisions. We determine the values of the Schmidt number required to approximate the experimental profiles of the volumetric concentration of sediment, suggesting that while the Schmidt number is smaller than one for dilute mixtures, it is larger than one for nondilute flows. Results indicate that nondilute models of increasing complexity are indeed necessary for flows having high solid volume fractions. Our results also suggest a more tested range of values for the threshold of sediment concentration of nondilute flows; this threshold can be located between 2 and 5%. It is observed that the virtual mass force becomes important in the simulation of nondilute flows. The eddy viscosity of the carrier phase is found to decrease with the increasing volumetric concentration in the flow.