Multi-Time-Scale Algorithm For Particle Resolved Simulation And Its Application In Particle-Laden Flow Over Erodible Sediment Bed

Particle-resolved simulation method is regarded as of the highest resolution for particle-laden flow simulation by simultaneously resolving turbulent and particle scale flows.In particleladen flows,particle-particle/particle-wall collisions are ubiquitous and greatly affect particle motion,particle spatial distribution,and particle-turbulence modulation.In the particle-laden wall turbulence(e.g.aeolian and fluvial transport,etc.),since the time scale required for resolving a collision process is more than one order of magnitude smaller than that for fluid flow,the computational cost in the traditional soft-sphere model is quite high.It brings great challenges to the numerical simulation of particle-laden flows.The stretching collision time algorithm is widely used in the existing particle-resolved simulations,in which the collision time is stretched several times the flow solver time step.However,the stretched collision time is not physical,and the simulation results were reported to be definitely affected by the stretched collision time.To overcome these problems,a multi-time-scale integration algorithm(MTSA)is presented in this paper.The MTSA employs three different time scales to compute fluid flow,fluid-particle interactions,and particle collisions,respectively.It can resolve the issue of time scale difference between particle collision and fluid flow with physical particle stiffness.By analyzing the influence of different time steps on particle collision restitution coefficient and rebound trajectory,the optimal parameters of the MTSA are determined as Rf≥ 0.5,Ri=4,Rm=40,where Rf,Ri,and Rm represent the number of fluid,fluid-particle interaction and particle motion time steps within a single collision time Tc,respectively.The MTSA can not only ensure the accuracy of the traditional soft-sphere model,but also improve the computational efficiency by one order of magnitude.Particle-resolved simulation of sediment transport with physical particle stiffness is implemented using the MTSA.The influence of particle stiffness on the turbulence statistics is analyzed.The results show that reducing the particle stiffness will weaken particle entrainment,which in turn affects the turbulence and particle statistics near the sediment bed.And the error increases as the particle stiffness decreases.The computation scale of particle-resolved simulation is at least ten million Eulerian grids and ten thousand particles.The coputation load is extremely high that it needs to use highperformance supercomputer for large-scale parallel computation.In sediment transport,particles are usually concentrated near the bottom of the bed due to gravity.The particle distribution is highly uneven in the vertical direction.Moreover,when the fluid erodes the sediment bed,the particles on the bed surface will aggregate and increase the heterogeneity in the spanwise direction.These two particle distribution characteristics will lead to load difference among computation cores,significantly affecting the parallel efficiency and bringing great challenges to the parallel simulation.However,the existing parallel approaches of particleresolved simulation did not pay much attention to the load imbalance caused by uneven distribution of particles.Therefore,a hybrid parallel approach is developed in this paper.The carrier phase is parallelized by the common domain decomposition method,while the disperse phase is parallelized by the mirror domain technique.It overcomes the issue of load imbalance when encountering a highly uneven distribution of particles.It is demonstrated that the hybrid parallel approach has excellent parallel performance for sediment transport simulation.The parallel efficiency of the hybrid parallel approach can still maintain more than 90%in the sediment transport simulation with more than a million spherical particles.In analyzeing sediment transport,it is useful to extract collision events between particles and mobile bed surface.A novel extraction method is presented in this paper.It can accurately locate particle-bed collision events and distinguish the impact,rebound,and entrained particles.Based on the current sediment transport simulation data,the statistical feature of particle-bed collision is analyzed,and the splashing function is established for the first time considering the combined effects of turbulence and mobile bed surface.It is found that there is a negative exponential relationship between the rebound probability and impact velocity,and the particle cannot rebound when the impact velocity is less than a critical value.The probability density distribution of the rebound velocity for a given impact velocity follows normal distribution,and there is a linear relationship between the location and scale parameters and the dimensionless impact velocity.The probability density distribution of the rebound angle follows lognormal distribution for a given impact angle,and there is a linear relationship between the location parameter and the impact angle,and the scale parameter is a constant.The probability density distribution of rebound spanwise angular velocity follows normal distribution for a given spanwise angular velocity of impact.There is a linear relationship between the location parameter and the dimensionless spanwise angular velocity of impact,and the scale parameter is a constant.The present development of the MTSA,the hybrid parallel approach,and the particle-bed collision extraction method lay a foundation for the particle-resolved simulation of particleladen flow over erodible sediment bed.The particle-resolved simulation of sediment transport provides high-quality data for revealing the interaction mechanism between turbulence and particle and establishing high-precision splashing model.