The Motion Of The Particles In Simple Flows Using The Lattice Boltzmann Method

The behaviours of an ellipsoidal particle in three kinds of simple flows are studied by a multi-relaxation-time lattice Boltzmann method. The present study consists of three parts, the rotation behaviours of an ellipsoid in a Couette flow, the sedimentation modes inside tubes and the motion of an ellipsoid in a Poiseuille flow. The results and conclusions are briefly given as follows:(1) Several new periodic and steady rotation modes for ellipsoidal particles are ob-tained in the Couette flow. For 305< Re< 345 we find that the prolate spheroid reaches a periodic mode characterized by precession and nutation around an in-clined axis which is located close to the middle plane where the velocity is zero. For 345< Re< 385, the prolate spheroid precesses around the vorticity direc-tion with a nutation. The rotational behaviour of the spheroid appears to be not only sensitive to the Reynolds number but also to its initial orientation. We discuss the effects of initial orientation in detail. The initial-orientation effects are studied by simulations of 57 evenly distributed initial orientations for each Re investigated. Only one mode is found for the prolate spheroid for Re< 120 and 385< Re< 445. In other Re regimes, more than one mode is possible and the final mode is sensitive to the initial orientation. However, the oblate spheroid dynamics are insensitive to its initial orientation.(2) Two kinds of tubes and two kinds of ellipsoidal particles are considered in the present study. Several sedimentation modes are obtained, including the tumbling mode, the inclined mode, the horizontal mode, the spiral mode, the anomalous mode and the oscillatory mode. The final sedimentation is independent of the initial position and orientation of the particle, but dependent of the confinement ratio and Re. The diagonal effect is observed in the square tubes. The phase diagram of the modes as a function of Ga and the confinement ratio is obtained. Through comparisons between the anomalous and oscillatory modes, it is found that the confinement ratio plays a critical role for the anomalous mode. Near a transitional regime, in terms of average settling velocity, it is found that a lighter ellipsoid may settle faster than a heavier one. This might shed some light on why the particle adopts a specific mode under a certain circumstance.(3) The motion and rotation of an ellipsoidal particle inside circular, square and rect-angular tubes are studied. The Reynolds numbers (Re) up to 50 are considered. Several typical rotational modes which depend on the confinement ratio R/a are identified. The diagonal effect appears in moderate wide square tubes obvious-ly while it dose not occur in the rectangular tubes because the particle tends to rotates on the plane where the shear rate is biggest. The geometric effect of the tube (R/a) plays a critical role in the mode selection and the rotational plane transformation. It is observed that the log-rolling mode is unstable for the prolate particle while it is stable for the oblate ellipsoid inside the square tubes. But in the rectangular tubes, the log-rolling mode becomes stable for the prolate particle with specific parameters. It is also found that the kinetic energy of the particle decreases with the mode transformation or the rotational plane transformation.