Stability of spatially developing boundary layers in pressure gradients

Govindarajan, Rama and Narasimha, R (1994) Stability of spatially developing boundary layers in pressure gradients. Technical Report. National Aerospace Laboratories, Bangalore, India.

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    Abstract

    A new formulation of the stability of boundary-layer flows in pressure gradients is presented. Taking into account the spatial development of the flow. The formulation assumes that disturbance wavelength and eigenfunction vary downstream no more rapidly than the boundary-layer thickness, and includes all terms of order R-1 in the boundary-layer Reynolds number R. In Blasius flow, the present approach is consistent with that of Bertolotti et al. (1992) to 0 (R-1 ), and may best be seen as providing a parametric differential equation which can be solved without having to march in space. The computed neutral boundaries depend strongly on distance from the surface, but the one corresponding to the inner maximum of the streamwise velocity perturbation happens to be close13; to the Orr-Sommerfeld boundary. For this quantity,solutions for the Falkner-Skan flows show the,effects of spatial growth to be striking only in the presence of strong adverse pressure gradients. As a rational analysis to 0 (R -1 ) demands inclusion of higher-order corrections on the mean flow, an illustrative calculation of one such correction, due to the displacement effect of the boundary layer, is made, and shown to have a significant destabilising influence on the stability boundary in strong adverse pressure gradients. The effect of non-parallelism on the growth of relatively high frequencies can be significant at low Reynolds numbers, but is marginal in other cases. As an extension of the present approach, a method of dealing with non-similar flows is also presented and illustrated. It is finally argued that the lowest order stability boundary for a prescribed boundary layer can be adequately computed from a reduced Orr-Sommerfeld equation.

    Item Type: Proj.Doc/Technical Report (Technical Report)
    Uncontrolled Keywords: Stability;Boundary layers
    Subjects: ENGINEERING > Fluid Mechanics and Thermodynamics
    Division/Department: Computational and Theoretical Fluid Dynamics Division, Other
    Depositing User: Mr. N A
    Date Deposited: 14 Aug 2006
    Last Modified: 24 May 2010 09:42
    URI: http://nal-ir.nal.res.in/id/eprint/1499

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