Bifurcation studies of flows of a gas between rotating coaxial circular cylinders with evaporation and condensation by the Boltzmann system. (English) Zbl 1127.76353
Summary: 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.
MSC:
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 76P05 | Rarefied gas flows, Boltzmann equation in fluid mechanics |
| 82C40 | Kinetic theory of gases in time-dependent statistical mechanics |
Keywords:
Bifurcation; Boltzmann equation; Stability; Taylor-Couette flow; Evaporation and condensation; Kinetic theoryReferences:
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