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

Abstract

[1] 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 − " 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.

Laboratory measurements and multi-block numerical simulations of the mean flow and turbulence in the non-aerated skimming flow region of steep stepped spillways

“…We are currently at the development stage of those more sophisticated models which, naturally, fall outside of the scope of this paper. Jha and Bombardelli [52] have very recently addressed the non-dilute sediment-laden flow in open channels with success and, thus, such work is a good starting point for our developments. We believe that the incorporation of more formal two-phase flow theories to the current model may yield the desired answers.…”

On the Values for the Turbulent Schmidt Number in Environmental Flows

“…In that regard, Greimann et al [87] developed a similar analysis to Rouse's, but incorporated notions of the two-phase flow theory and approximate turbulence closure to produce a modified Rouse formula. Bombardelli and Jha [40], Jha and Bombardelli [43][44][45] developed a hierarchy of models based on the two-phase flow theory, which has its roots on early developments by Bombardelli [88], Bombardelli et al [89] and Buscaglia et al [90]. This theory not only solves for the mass and momentum equations of both the carrier (water) and disperse phases (sediment), but it also includes a full turbulence closure and additional closures for the different combinations of the equations.…”

“…A number of studies about the turbulent Schmidt number have dealt with the simulation of flow and tracer transport in open channels [22][23][24][25], while others have addressed those issues in contact or water tanks [26][27][28][29][30][31][32][33][34][35][36], inclined negatively-buoyant discharges [37], sediment-laden open channel flows [38][39][40][41][42][43][44][45][46][47][48], density stratified turbulence [49,50] and T-junction mixing experiments [51] ( Table 2). The terms "Exp" and "Num" mean the application of experimental and numerical methods, respectively, in each study.…”

SedFoam-2.0: a 3-D two-phase flow numerical model for sediment transport

“…This term is equivalent to the turbulent suspension flux of the Rouse profile in the two-phase flow formalism (see Chauchat, 2017, Appendix 1 for a detailed demonstration). Other forces such as the lift force or the added mass force could play a role in sediment transport: according to Jha and Bombardelli (2010), the lift force in dilute suspended sediment transport only represents 4 % of the drag force and the added mass force can be on the order of 10 % in the near-bed region. The influence of the added mass force would require further investigation that is beyond the scope of the present paper.…”

“…The other turbulence model that has been used is the k − ε model (e.g., Hsu et al, 2003;Longo, 2005;Bakhtyar et al, 2009). The k − ω model has been tested by Jha and Bombardelli (2009) and Amoudry (2014), and the Reynolds stress model has been tested by Jha and Bombardelli (2010). Concerning the granular stress models, the first model that has been tested by Hanes and Bowen (1985) is the empirical rheology of Bagnold (1954).…”