טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentManela Avshalom
SubjectStability of Rarefied Gas Flows
DepartmentDepartment of Aerospace Engineering
Supervisor Professor Itzchak Frankel


Abstract

We study the hydrodynamic stability of rarefied gas flows. While the problems under consideration are already well known in the context of incompressible fluids there is evident interest in clarifying the effects of  rarefaction on instability phenomena, especially in the limit of small Knudsen numbers (`continuum limit').


Stability analyses of rarefied gas flows have appeared in the literature during the recent years. They are essentially based on numerical simulations. However, the statistical `noise' and time demands of these simulations at low Knudsen numbers make it difficult to clearly identify and characterize the final states

obtained, especially in the vicinity of transition to instability. Consequently, only two-dimensional investigations are available in limited number of parameter combinations.


We focus on linear temporal stability analysis of rarefied gas flows. Making use of the `slip-flow' model, we consider the classical  Rayleigh-Benard and Taylor-Couette problems. The results obtained enable exact delineation of the instability boundaries and characterization of the transition states in each problem. Good agreement is found with simulation results appearing in the literature and carried out during the research.


In all cases considered we find that instability phenomena are limited to small Knudsen numbers. We show that this results from the combined effects of viscous and compressible mechanisms in the fluid. In the Rayleigh-Benard problem the convection domain is confined to small Knudsen numbers due to the combination of a minimal Rayleigh number criterion and a mechanism of adiabatic expansion. In the Taylor-Couette problem the instability domain is bounded by a minimal (incompressible) value of the Reynolds number based on the mean thermodynamic properties of the fluid. Additionally, we show that the traditional Boussinesq approximation used in the Rayleigh-B\'{e}nard problem becomes singular when compressibility effects are dominant and analyse this case asymptotically.