Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

Transport, growth and stability of disturbances in weakly rarefied channel flows

Francesco Fedele, Darren L. Hitt*
Department of Mechanical Engineering, University of Vermont, Burlington, VT 05405, USA

  Full Text
We examine the linear stability to axisymmetric disturbances in weakly rarefied flows ('slip regime') on the micro- and nano-scale. A semi-analytical solution of the Orr-Sommerfeld equation shows that pulsatile flow is linearly stable in the slip regime although a sudden change in the stability properties of the flow occurs at a critical value of the Knudsen number Kncr = (2 - σ)/8σ, where σ is the accommodation coefficient. Flow structures corresponding to the largest energy growth are toroidal vortex tubes that are transported diffusively and convectively by the mean flow. Transient energy growth is found to decrease at larger Knudsen numbers indicating that the Orr-Sommerfeld operator for slip flow is less non-normal compared to continuum-based no-slip flows.

Keywords:  Slip flow; Stability; Pulsatile pipe flow; Orr-Sommerfeld operator; Galerkin projection; Non-normality; Vortex tubes; Energy growth

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