Elliptical Cylinder in Shear Flow: A Second Transition From Steady to Periodic State
Abstract
The effect of inertia on the dynamics of an elliptical cylinder suspended in shear flow has been studied by solving the lattice-Boltzmann equation. It is shown that increasing the Reynolds number, the period of rotation increases, and eventually becomes infinitely large at a critical Reynolds number, Re_c. At Reynolds number above Re_c, the particle becomes stationary in a steady state flow. The transition from periodic rotation to steady state is through a saddle-node bifurcation, and, consequently, the period of rotation near the critical Reynolds number is proportional to \vert p-p_c\vert -1/2, where p is any parameter which leads to the transition. In the present study it is shown that there is another critical Reynolds number, Res (larger than Re_c), above which the particle may rotate in shear flow. At this state, the period of rotation decreases as Reynolds number increases. The transition from periodic rotation to steady state, occurring at the second critical Reynolds number, is also through a saddle-node bifurcation. The scaling relation, found near the transition, will be presented.
- Publication:
-
APS Division of Fluid Dynamics Meeting Abstracts
- Pub Date:
- November 2002
- Bibcode:
- 2002APS..DFD.DD003D