Direct Numerical Simulations Of Particles Settling Over A Wide Range Of Density Ratios Based On Boundary-thickening Based Immersed Boundary Method

Pressurized gas-solid fluidization is a novel high-efficiency and low-carbon energy utilization technology,which is one of the most promising technologies to achieve the goals of "carbon peak" and "carbon neutralization" in China.Previous studies have shown that the change of density ratio caused by pressure is the essential reason for the difference of flow characteristics between pressurized and atmospheric pressure.However,the basic law of the effect of density ratio on particle two-phase flow dynamics is unclear.In this paper,a highly efficiency and accuracy large-scale parallel computing framwork is developed based on IBM-LBM-DEM.Direct numerical simulations of density ratio effect on the particle settling is carried out.The particle dynamics and structures over a wide range of density ratios are obtained and analyzed.The main research work and conclusions are as follows.Firstly,a boundary thickening based direct forcing immersed boundary method(BTDF-IBM)is proposed for improving the non-slip boundary conditions,which is not fully satisfied by the original direct force IBM.BTDF-IBM is a simple and efficient explicit method.Its accuracy and efficiency are analyzed by simulations of static and moving particles under Re=0.01?200.The results show that the accuracy of BTDF can be comparable with other improving methods but with a much higher efficiency,which is especially suitable for large-scale simulations.Furthermore,it is found that the boundary thickness in the three-dimensional frame is equivalent to that in the two-dimensional frame,which can also achieve good accuracy.The IBM calculation and the lubrication force correction between two approaching particles are also disscussed.Secondly,a highly efficient parallel computing framework PFlows based on IBM-LBM-DEM is developed by fully distributed MPI technique.A series of optimization method of serial and parallel computing,as well as Forth-Back metho for LBM streaming on a set grid are proposed.The serial computing efficiency is improved about 1.5 ? 4 times after optimization.The weak and strong scaling efficiency of parallel computing is about0.9 on up to 4800 CPU cores.The multi GPU accelerated computing is also developed by MPI-CUDA technique.After optimization,the bandwidth utilization of a single GPU reaches 93%.The parallel efficiency is about 0.5?0.8 on up to 64 GPUs by testing up to 4billion fluid grids and and 4 million particles.Three different of large-scale simulations of complex particle-laden flows are used to verify the robust and accuracy of the framework.Thirdly,the effects of density ratio(?*=2?1000)on the behaviour of particles settling at Re=1?100 and different volume fractions(?=0.0 ?0.5)are studied by DNS simulations.The results show that the increase of density ratio does not change the trend of average velocity with volume fraction,but changes the function between them.As the density ratio increases,the particle settling velocity,velocity variance,anisotropy of velocity variance and the diffusion coefficient first increase and then decrease.The transition point occurs at?*?100.The increase of density ratio can signifcantly reduce the anisotropy of particle distribution at low volume fraction,but not significant at high volume fraction,at which the volume fraction effect is dominant.As the density ratio increases,the value of rdf g(2.1a)increases first and then decreases,while the structure factor S(k?0)monotonically increases.The competition between them makes the changes of particle dynamics.Finally,the effect of density ratio when the transition of particle stability happened in multi-scale computational domain is studied by DNS simulation.A theoretical linear stability analysis is first performed to give a prediction of the domain scale that may occur instability under different density ratios.The multi-scale quasi one-dimensional and quasi two-dimensional simulations are exerted by DNS.It is found that the theoretical model can not predict the stability well at medium density ratio.The variations of particle volume fraction show a high frequency oscillation with small amplitude and a low frequency oscillation with large amplitude in the stable and unstable flows,respectively.The one-dimensional cluster reduces the particle settling velocity,while the two-dimensional cluster increases the particle settling velocity.The particle cluster formed at medium density ratio is smaller and denser than that at high density ratio,resulting in a stronger convective motion and larger velocity fluctuation in the flow field.The instability is also found in the large-scale three-dimensional DNS simulation at a medium density ratio.The DNS researches show that the density ratio has an important influence on the behaviour of particle-laden flows.The influence trend at low to medium density ratio and high to medium density ratio is opposite,and the transition occurs at the medium density ratio.The change of density ratio affects the particle dynamics by affecting the spatial structure of particles.The influence intensity is different under different volume fractions.Present work will lay a solid foundation for the follow-up research and the application of pressurized fluidized bed.