Stabilizing effect of longitudinal wall oscillation on two dimensional channel flow is analytically investigated. Model flow considered here is constituted of a superposition of the plane Poiseuille flow and the Stokes layer. The two walls are periodically oscillated in phase. Since the present system has a periodicity, the Floquet method is employed for the stability analysis. For this, a partial difference equation with a periodic function is derived from the time dependent version of the Orr-Sommerfeld equation using the Chebyshev spectral collocation method. The parameters governing the present system are the Reynolds number Re, the period Ω and amplitude Uw of the wall oscillation. Depending on the parameters, it is found that the 2D Tollmein-Shlichtin (TS) modes can be stabilized by the wall oscillation. Furthermore there are some case that 2D TS modes are more stabilized than the oblique TS mode. These results suggest that the oblique TS mode can appear earlier than the TS mode contrary to the Squire’s Theorem.
Stabilizing effects on 2D channel flow due to longitudinal wall oscillation
ICNPAA 2016 WORLD CONGRESS: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences ; 2016 ; La Rochelle, France
AIP Conference Proceedings ; 1798 , 1
2017-01-27
6 pages
Conference paper
Electronic Resource
English
STABILIZING EFFECT OF LONGITUDINAL-WALL OSCILLATION ON 2D CHANNEL FLOW
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