Lagrangian model of bed-load transport in turbulent junction flows

Abstract

Motivated by the need to gain fundamental insights into the mechanisms of bed-load sediment transport in turbulent junction flows, we carry out a computational study of Lagrangian dynamics of inertial particles initially placed on the bed upstream of a surface-mounted circular cylinder in a rectangular open channel (Dargahi, J. Hydraul. Engng, vol. 116, 1990, pp. 1197–1214). The flow field at Re = 39000 is simulated using the detached eddy simulation (DES) approach (Spalart et al., In Advances in DNS/LES, ed. C. Liu & Z. Liu, 1997, Greyden), which has already been shown to accurately resolve most of the turbulent stresses produced by the low-frequency, bimodal fluctuations of the turbulent horseshoe vortex (Paik et al., J. Hydraul. Engng, vol. 131, 1990, pp. 441–456; Escauriaza & Sotiropoulos, Flow Turbul. Combust., 2010, in press). The trajectory and momentum equations for the sediment particles are integrated numerically simultaneously with the flow governing equations assuming one-way coupling and neglecting particle-to-particle interactions (dilute flow) but taking into account bed–particle interactions and the effects of the instantaneous hydrodynamic forces induced by the resolved fluctuations of the coherent vortical structures. The computed results show that, in accordance with the simulated clear-water scour condition (i.e. the magnitude of the particle stresses is near the threshold of motion), the transport of sediment grains is highly intermittent and exhibits essentially all the characteristics of bed-load sediment transport observed in laboratory and field experiments. Groups of sediment grains are dislodged from the bed simultaneously in seemingly random bursting events and begin to move, saltating or sliding along the bed. Furthermore, particles that are not entrained into the bed-load layer are found to form streaks aligned with near-wall vortices around the cylinder. The global transport of particles is studied by performing a statistical analysis of the bed-load flux to reveal scale-invariance of the process and multifractality of particle transport as the overall effect of the coherent structures of the flow. A major finding of this work is that a relatively simple Lagrangian model coupled with a coherent-structure resolving simulation of the turbulent flow is able to reproduce the sediment dynamics observed in multiple experiments performed under similar conditions, and provide fundamental information on the initiation of motion and the multifractal nature of bed-load transport processes. The results also motivate the development of new Eulerian bed-load transport models that consider unsteady conditions and incorporate the intermittency of the unresolved scales of sediment motion.

Numerical simulation of sand waves in a turbulent open channel flow

“…Their model included only bedload sediment transport by solving the Exner equation coupled with the flow to simulate the evolution of the bed and naturally could not account for stratification effects. Escauriaza & Sotiropoulos (2011b), however, proposed and employed in their model a new transport equation for calculating the distribution of the instantaneous velocity field of computational sediment particles within the bedload layer derived from Lagrangian considerations and incorporating most of the relevant forces imparted on the sediment grains by the fluctuating turbulent flow in the vicinity of the bed. They showed that in their simulation small-scale ripples appear spontaneously at approximately the same time as observed in laboratory experiments (Dargahi 1990), grow and merge to form larger slowly travelling sand waves that migrate continuously with speeds also similar to the experimental observations (Dargahi 1989(Dargahi , 1990.…”

Simulating Collisions for Hydrokinetic Turbines

“…In another study related to Lagrangian particle tracking supported by eddy-resolving flow simulations (Escauriaza and Sotiropoulos 2011), spheres showed intermittent, sudden, rapid motion rather than smooth displacements. The latter study is particularly of interest because it describes environmental flows altered by the presence of engineered systems, which makes it relevant to our case.…”

Synthetic velocity gradient tensors and the identification of statistically significant aspects of the structure of turbulence

“…The associated Q-R diagram has played an important role in our understanding of the nature of HIT and other types of turbulent flow [1,23,25], and correctly resolving the Q-R diagram has been used recently as a means of checking the effective resolution of numerical simulations [26]. In addition, positive values of Q are used in more applied studies as a local approach to identify vortical structures in the flow field [16,17,27,28]. Consequently, a suite of analyses for turbulence may be undertaken given a database of velocity gradient tensor fields, obtained numerically [29] or experimentally [30].…”