Numerical Study On The Sedimentation Of Different Shape Particles With The Direct Forcing Immersed Boundary Method

The free sedimentation of particles is universal in both nature and industrial production.In this study,the direct forcing immersed boundary method is adopted to conduct a series of direct numerical simulations for the sedimentation of three different shape particles under different conditions.First,the accuracy of the method is verified by the free sedimentation model of single spherical particle.Then the simulations are carried out to investigate sedimentation characteristics of individual sphere,ellipsoid and cube,and the influence of the rigid body assumption(RBA)on the accuracy of the results is discussed.After that,the sedimentation characteristics of the linear arranged two-particles and three-particles of different shapes are simulated.The main findings of this study are summarized below:(1)When the Reynolds number is less than 300,the settling of single sphere particle exhibits wake instability.A single ellipsoid starts rotating when the Reynolds number reaches 200.The Reynolds number corresponding to unstable wake flow for a cubic particle is higher than that for a spherical or ellipsoidal particle.(2)In the two-particle model,the distance between particles in the early stage of drafting will increase slightly,and in fluids with lower viscosity,the increase will be significant.The drafting,kissing and tumbling behaviors in the sedimentation of two particles of different shapes are different from each other.The linearly arranged two-particles system shows drafting,kissing and tumbling only when their initial separation is within a certain range.(3)The particle 1 and 2 in the linear three-particle model of different shapes,which are numbered 1,2,and 3 from bottom to top,behave the drafting kissing and tumbling.The introduction of No.3 particle accelerates the drafting,kissing,and tumbling movements of No.1 and No.2 particles.The sedimentation of linearly arranged three-particles is more complicated than that of two-particles,and the sedimentations of the three-particles of different shape are affected differently by the viscosity.When the relative initial distance is within a certain range,the sedimentation behaviors of the three-particles with different shapes are basically same.First,the particle 1 and 2 perform the drafting,kissing and tumbling,and then the two particles are as a new whole to perform the drafting,kissing,tumbling with the particle 3.The numerical investigation of the sedimentation of three different particles provides clues for solving relevant industrial problems.The numerical method adopted here can be extended straightforwardly to the simulation of particles of various shapes.