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Register a new userSettling of cohesive sediment: particle-resolved simulations
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We develop a physical and computational model for performing fully coupled, particle-resolved Direct Numerical Simulations of cohesive sediment, based on the Immersed Boundary Method. The model distributes the cohesive forces over a thin shell surrounding each particle, thereby allowing for the spatial and temporal resolution of the cohesive forces during particle-particle interactions. The influence of the cohesive forces is captured by a single dimensionless parameter in the form of a cohesion number, which represents the ratio of cohesive and gravitational forces acting on a particle. We test and validate the cohesive force model for binary particle interactions in the Drafting-Kissing-Tumbling (DKT) configuration. The DKT simulations demonstrate that cohesive particle pairs settle in a preferred orientation, with particles of very different sizes preferentially aligning themselves in the vertical direction, so that the smaller particle is drafted in the wake of the larger one. To test this mechanism in a system of higher complexity, we perform large simulations of 1,261 polydisperse settling particles starting from rest. These simulations reproduce several earlier experimental observations by other authors, such as the accelerated settling of sand and silt particles due to particle bonding. The simulations demonstrate that cohesive forces accelerate the overall settling process primarily because smaller grains attach to larger ones and settle in their wakes. For the present cohesion number values, we observe that settling can be accelerated by up to 29%. We propose physically based parametrization of classical hindered settling functions proposed by earlier authors, in order to account for cohesive forces. An investigation of the energy budget shows that the work of the collision forces can substantially modify the relevant energy conversion processes.
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We analyze the consolidation of freshly deposited cohesive and non-cohesive sediment by means of particle-resolved direct Navier-Stokes simulations based on the Immersed Boundary Method. The computational model is parameterized by material properties and does not involve any arbitrary calibrations. We obtain the stress balance of the fluid-particle mixture from first principles and link it to the classical effective stress concept. The detailed datasets obtained from our simulations allow us to evaluate all terms of the derived stress balance. We compare the settling of cohesive sediment to its non-cohesive counterpart, which corresponds to the settling of the individual primary particles. The simulation results yield a complete parameterization of the Gibson equation, which has been the method of choice to analyze self-weight consolidation.
A hybrid parallel approach for fully resolved simulations of particle-laden flows in sediment transport is proposed. To overcome the challenges of load imbalance in the traditional domain decomposition method when encountering highly uneven distributions of particles in space, we develop a hybrid parallel approach adopting the domain decomposition method for the carrier phase and a mirror domain technique for the disperse phase. We modify the mirror domain technique originally developed for point particles to fully resolved particle simulations, which are more challenging since a finite-sized particle may be split into different subdomains; thus, more complex treatments of particle-fluid interactions are needed. By utilizing the mirror domain technique, in which each processor handles nearly the same number of particles regardless of the particle spatial distribution, excellent load balance is achieved. The present hybrid parallel approach also shows strong scalability and high parallel efficiency in a test of a fully resolved simulation case of sediment transport. Furthermore, a novel memory optimization method is proposed for spherical particles of equal size, which can substantially reduce the memory cost and enable the simulation of millions of fully resolved particles on a common highly parallel computing platform. Our code is validated by several benchmark cases, and the results show good agreement with experimental and computational data in the literature.
We propose a one-way coupled model that tracks individual primary particles in a conceptually simple cellular flow setup to predict flocculation in turbulence. This computationally efficient model accounts for Stokes drag, lubrication, cohesive and direct contact forces on the primary spherical particles and allows for a systematic simulation campaign that yields the transient mean floc size as a function of the governing dimensionless parameters. The simulations reproduce the growth of the cohesive flocs with time, and the emergence of a log-normal equilibrium distribution governed by the balance of aggregation and breakage. Flocculation proceeds most rapidly when the Stokes number of the primary particles is textit{O}(1). Results from this simple computational model are consistent with experimental observations, thus allowing us to propose a new analytical flocculation model that yields improved agreement with experimental data, especially during the transient stages.
We perform $3$D numerical simulations to investigate the sedimentation of a single sphere in the absence and presence of a simple cross shear flow in a yield stress fluid with weak inertia. In our simulations, the settling flow is considered to be the primary flow, whereas the linear cross shear flow is a secondary flow with amplitude $10%$ of the primary flow. To study the effects of elasticity and plasticity of the carrying fluid on the sphere drag as well as the flow dynamics, the fluid is modeled using the elastovisco-plastic (EVP) constitutive laws proposed by cite{saramito2009new}. The extra non-Newtonian stress tensor is fully coupled with the flow equation and the solid particle is represented by an immersed boundary (IB) method. Our results show that the fore-aft asymmetry in the velocity is less pronounced and the negative wake disappears when a linear cross shear flow is applied. We find that the drag on a sphere settling in a sheared yield stress fluid is reduced significantly as compared to an otherwise quiescent fluid. More importantly, the sphere drag in the presence of a secondary cross shear flow cannot be derived from the pure sedimentation drag law owing to the non-linear coupling between the simple shear flow and the uniform flow. Finally, we show that the drag on the sphere settling in a sheared yield-stress fluid is reduced at higher material elasticity mainly due to the form and viscous drag reduction.
We explore the role of gravitational settling on inertial particle concentrations in a wall-bounded turbulent flow. While it may be thought that settling can be ignored when the settling parameter $Svequiv v_s/u_tau$ is small ($v_s$ - Stokes settling velocity, $u_tau$ - fluid friction velocity), we show that even in this regime the settling may make a leading order contribution to the concentration profiles. This is because the importance of settling is determined, not by the size of $v_s$ compared with $u_tau$ or any other fluid velocity scale, but by the size of $v_s$ relative to the other mechanisms that control the vertical particle velocity and concentration profile. We explain this in the context of the particle mean-momentum equation, and show that in general, there always exists a region in the boundary layer where settling cannot be neglected, no matter how small $Sv$ is (provided it is finite). Direct numerical simulations confirm the arguments, and show that the near-wall concentration is highly dependent on $Sv$ even when $Svll 1$, and can reduce by an order of magnitude when $Sv$ is increased from $O(10^{-4})$ and $O(10^{-2})$. The results also show that the preferential sampling of ejection events in the boundary layer by inertial particles when $Sv=0$ is profoundly altered as $Sv$ is increased, and is replaced by a preferential sampling of sweep events due to the onset of the preferential sweeping mechanism.
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