On the Receptivity and Non-Parallel Stability of Travelling Disturbances in Rotating Disk Flow
INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA
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The generation and evolution of small amplitude long wavelength travelling disturbances in rotating disk flow is the subject of this paper. The steady rotational speed of the disk is perturbed so as to introduce high frequency oscillations in the flow field. Secondly, we introduce surface imperfections on the disk such as roughness elements. The interaction of these two disturbances will generate the instability waves whose evolution is governed by parabolic partial differential equations which are solved numerically. It is found that, for the class of disturbances considered here wavelength on the order of Reynolds number, eigensolutions exist which decay or grow algebraically in the radial direction. However, these solutions grow only for frequencies larger than 4.58 times the steady rotational speed of the disk. The computed receptivity coefficient shows that there is an optimum size of roughness for which these modes are excited the most. The width of these roughness elements in the radial direction is about .1r sub 0 where r 0 is the radial location of the roughness. It is also found that the receptivity coefficient is larger for a negative spanwise wavenumber than for a positive one. Typical wave angles for these disturbances are about -26 deg.
- Fluid Mechanics