| The transport of micro-particles in viscous flows is a common fundamental problem encontoured widely in the fields of energy,environment,biology,chemical engineering and microelectronics,where the particle scale effects become significant and must be carefully considered.Such two-phase flow systems are expected to reveal additional non-trivial hydrodynamic features when compared to conventional single phase flows.Therefore,it is necessary to investigate the underlying dynamics of particle-fluid and particle-particle interactions.This need motivated the development of the particle-resolved direct numerical simulation in the recent decades,because this approach can provide accurate prediction for the microscopic details and macroscopic properties of these two-phase flows.This disssertation is based on the above background,and intended to investigate the pertinent issues,such as drag force correlation,sedimentation and inertial migration of micro particles using an improved LBM model.The main contents of the dissertation are summarized as follows:First,a kinetic scheme is proposed for the treatment of curved boundary conditions in the slip regime.The method is derived from the conventional diffusive bounce back(DBB)scheme to retain the advantage of local computation.We find that to obtain a desired slip velocity and preserve the geometric integrity of particle shape,the values of the combination parameter r and the relazation time ?q should be specified properly.The accuracy and adaptability of the scheme are validated in several micro flow problems.Second,we perform a comprehensive comparison of the seven momentum exchange(ME)methods and five refilling(RF)schemes in the simulations of particulate flows.It is found that the three corrected-ME methods can yield reasonable results and produce relatively weak spurious oscillation.The equilibrium plus non-equilibrium RF method has the best performance.However,once coupled with a local iteration algorithm,the performances of the five RF schemes are improved up to the same level.Third,the drag forces of a micro particle at finite Reynolds number and in packed beds are studied.The effective-relaxation-time model is first improved in order to treat the micro sphere.It is found that the expression by a simple combination of finite Reynolds number Re and Knudsen number Kn effects generally overestimates the drag coefficient Cd,while the widely-used Cunningham formulation has a relative error of 4.2%?27.1%in the range of 0.1<Kn<1.0.Therefore,the Re effect should be considered for micro particles,especially when Kn is small.Three ordered arrays of particles are considered:the simple cubic(SC),body-centered cubic(BCC)and face-centered cubic(FCC).The results reveal that Cd increases with increasing solid volume fraction ? and decreases as Kn is increased,and these relationships are generally non-linear.The values of Cd are comparable for the three array configurations.Furthermore,the reduction of Cd is more pronounced for the dense packing case.Cd of spheres in SC array is found to be larger than that of circular cylinder in square array at the same Kn.Finally,the micro particulate suspension flows are studied.Two flow configurations are considered:(1)The sedimentation of slippery particles in a container.The results show that the slippery particle falls faster than that of no-slip one.The blockage effect of channel walls is attenuated at larger Kn,and the slip effect is more pronounced for the narrow channel.For the two-sphere case,while only the lower sphere is slippery,the drafting,kissing and trailing(DKT)phenomenon hardly emerges.If reversing the order,the falling process will reach the kissing stage faster.Therefore,there exists a critical gap distance and Kn for the occurrence of DKT.When the spheres are both slippery,the drafting process is similar to that of the no-slip case,except that the settling velocities of spheres are larger and the duration of kissing stage is shorter.For the multiple particles case,it is found that the initial particle configuration has significant effect on the sedimentation dynamics.In general,putting the slippery ones into the particle cluster will increase the fluctuation velocity and position of the cluster in the early stage and expedite the attenuation of those quantities in the later stage.(2)The inertial-induced migration of particles in a tube.The influences of Re,particle size(D/a),particle concentration(?)and Kn are investigated.The results indicate that,the inertial focusing is strengthened with the increase of Re and D/a,while the equilibrium position migrates to the tube wall and the center line of tube,respectively.With larger ?,the degree of focusing is first weakened and then enhanced.We interpret this to be a result of the competition between the mechanisms of shear-induced focusing and particle-collision-induced diffusion.Furthermore,the particle velocity decreases and the degree of focusing is strengthened at larger Kn. |
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