Critical shear stress for incipient motion of a particle on a rough bed

Abstract

[1] The main objectives of the present study are to obtain improved models of hydrodynamic forces and torque on a particle sitting on a bed and to use these models for the investigation of incipient motion and resuspension of particles. The improved models for force and torque are obtained from numerical simulations of a particle sitting on a bed with a turbulent flow of logarithmic mean velocity profile approaching the particle. Since the mean turbulent velocity profile can depart from the logarithmic profile in case of macroscale rough beds or flow down steep slopes, we have also considered forces and torque on a particle due to both linear and uniform mean flow profiles. The computed drag and lift coefficients and the predicted critical shear stress for incipient particle motion and resuspension are compared against available experimental results. The improved force and torque models are also used to evaluate the effect of turbulent velocity fluctuations on the critical shear stress for incipient motion and resuspension. The present results are of direct relevance to cases where the particle is mostly exposed to the ambient flow. In cases where the particle protrusion is small and is submerged mostly within a pocket of other particles, the above formulation can be used with a redefined area of exposure and flow velocity seen by the particle. However, the drag, lift, and torque coefficients and the resisting forces will be influenced by the partial exposure and the details of pocket geometry, which require further investigation.

Onset of erosion of a granular bed in a channel driven by fluid flow

“…Further, we have analyzed our data in terms of torque balance condition for threshold of motion, which has been noted 16 to give a lower threshold for motion compared with force balance condition as captured by the critical Shields number. By analyzing the torque condition for stability, we find evidence that the estimated torque acting to dislodge grains at the bed surface is significantly lower than that acting on a sphere fully exposed to a linear shear flow.…”

“…16 An analytical form for the force and torque acting on a sphere in an exponentially decaying flow field is not available. However, we can use the stability condition in Eq.…”

“…Numerical simulations by Derksen and Larsen 14 have shown that the drag and lift forces are further significantly affected by the surface coverage of the spheres in the top layer of the bed. More recently, Lee and Balachandar 16 have noted that the torque balance about a pivot point given by the angle of repose is the appropriate condition to consider the stability of a grain for the onset of erosion at the bed surface, which leads to a different condition than that using force balance especially at low Reynolds numbers.…”

“…[13][14][15][16] A mathematical expression for the critical shear stress was derived by Wiberg and Smith 13 using force balance as the condition for stability at the granular surface and compared to the Shields curve. Numerical simulations by Derksen and Larsen 14 have shown that the drag and lift forces are further significantly affected by the surface coverage of the spheres in the top layer of the bed.…”

Modeling particle transport and discoloration risk in drinking water distribution networks

“…The hydrodynamic forces and torque on a particle sitting on a bed with a destabilizing turbulent flow were developed in a model by Lee and Balachandar (2012). Entrainment occurs when the lift force on a particle exceeds the gravitational force and their model demonstrates that -similar to the threshold for incipient motion -the decrease in θ rs is nearly inversely proportional to Re * , but values of θ rs are approximately an order of magnitude larger than θ c for Re * < 1.…”