Chaotic behavior of particles in 2-D cavity flow

Abstract

A mathematical model for study of cavity flows is constructed using a deformed Hill’s vortex flow together with superposition of the basic flow and its image. By changing direction of the flow and its image, corotating and counter-rotating modes can be obtained. Unsteady flow is simulated by periodic activation of the basic flow and/or its image. The objective of the study is examination of the details of chaotic behavior of particles in the flow. Poincaré sections are used and the primary parameter varied is T, the period of the moving walls. For very small T the particle trajectories are quasiperiodic and there is no chaotic region for either co- or counter-rotating flows, regardless of initial particle positions. Chaotic regions appear when T is large. By following a single particle, it was determined that its trajectory becomes chaotic only within a specific range of T which depends on the initial condition; this implies a relationship between T and the period of the particle motion. Within the test range of T (1.0 – 40.0), for a given T the chaotic regions are larger for the counter-rotating case. When the velocity field was perturbed with a small unsteady component added to the basic flow, it was found that the regular (nonchaotic) trajectories in the counter-rotating flow were more easily perturbed than those in the corotating flow. It is expected that mixing in counter-rotating flows is more efficient than in corotating flow. Both continuous and discontinuous wall motions were used. Symmetric regular regions in the Poincaré section are found in both space and time. By following particle paths, it was found that the regular and quasiperiodic trajectories are symmetric in space. The conclusions obtained thus far are consistent with laboratory experiments.1 In addition to T, we are examining the effects of geometric aspect ratio, position of fixed points, etc. Future plans include study of particles with inertia, and study of three-dimensional cavities.