BIFURCATION STUDIES OF FLOWS OF A GAS BETWEEN ROTATING COAXIAL CIRCULAR CYLINDERS WITH EVAPORATION AND CONDENSATION BY THE BOLTZMANN SYSTEM

ABSTRACT

Bifurcation of flows of a gas between rotating coaxial circular cylinders made of the condensed phase of the gas, where evaporation or condensation takes place, is studied on the basis of the Boltzmann equation. First, the studies for the case where the flow field is axially symmetric and uniform are reviewed. Then, the stability and bifurcation of the solution when the restriction of axial uniformity is removed are studied numerically by the direct simulation Monte-Carlo method. Three types of solution: two axially uniform solutions and a roll-type solution are found to exist stably in some parameter range. Finally, the difficulty of this method in studying stability and bifurcation problems is discussed, and a false solution of oscillatory behavior is presented.

Keywords:

• Bifurcation
• Boltzmann equation
• Stability
• Taylor-Couette flow
• Evaporation and condensation
• Kinetic theory

ACKNOWLEDGMENTS

The paper was read at the Workshop “Asymptotic and Numerical Methods for Kinetic Equations” held at Oberwolfach 15–21 April 2001. Y. Sone expresses his hearty thanks to the organizers Professors P. Degond, A. Klar, and R. Illner for the invitation to the workshop.