Numerical Study of Nonlinear Dynamics of Particles and Chaotic Mixing in Two Dimensional Periodic Driven Cavity Flows
Abstract
This dissertation employs numerical methods to study the chaotic mixing processes and the nonlinear behavior of both point and finite particles in two dimensional periodic cavity flows. The steady flow field is obtained by solving the governing equations of the flow in terms of stream function and vorticity using finite difference methods. It has been found from this steady flow field that the flow in a cavity is essentially in the Stokes regime when the flow Reynolds number is under 10. Therefore, the periodic flows can be simulated by applications of the steady flow data. The motion of finite particles is described by the equation of motion derived by Maxey and Riley (30). The positions of particles are then found by numerical integration of the equation of motion using 4th order RungeKutta method. In the course of particle tracking, flow data is interpolated using a 4th order scheme. Several parameters are involved in the problem. The most important one is the period of the wall motion. Parameters for finite particle motion include nondimensional numbers for gravity force and Stokes drag force, and the ratio of particle density to the surrounding fluid density. Numerical results show that both regular and chaotic particle trajectories exist in the flow, depending on initial particle positions and parameter ranges of the system. The nonlinear motions of particles are visualized by Poincare sections and are quantified by the calculated Liapunov exponents. The chaotic stretching field of the flow is also studied using statistical methods. The simulated topologic structures of the stretched and folded fluid blobs agree very well with laboratory experiments (26). In the cases of chaotic mixing, a global intrinsic structure is found to exist that is deterministic and periodic. The probability distributions of stretching and short time Liapunov exponents are found to have a temporal selfsimilarity and scaling behavior. When the system is in global chaos, these distributions are found to be Gaussian. Several scaling forms are studied for stretching and short time Liapunov exponents. For finite particles, strange attractors are found on Poincare sections of physical space.
 Publication:

Ph.D. Thesis
 Pub Date:
 1992
 Bibcode:
 1992PhDT.......280L
 Keywords:

 NONLINEAR PARTICLE DYNAMICS;
 Physics: Fluid and Plasma; Engineering: Mechanical; Engineering: Chemical