Effect of bulges on the stability of boundary layers

The instability of flows around hump and dip imperfections is investigated. The mean flow is calculated using interacting boundary layers, thereby accounting for viscous/inviscid interaction and separation bubbles. Then, the two‐dimensional linear stability of this flow is analyzed, and the amplification factors are computed. Results are obtained for several height/width ratios and locations. The theoretical results have been used to correlate the experimental results of Walker and Greening (British Aeronautical Research Council 5950, 1942). The observed transition locations are found to correspond to amplification factors varying between 7.4 and 10.0, consistent with previous results for flat plates. The method accounts for both viscous and shear‐layer instabilities. Separation is found to increase significantly the amplification factor.

[1]  E. C. Hastings,et al.  Natural laminar flow flight experiments on a turbine engine nacelle fairing , 1986 .

[2]  Tuncer Cebeci,et al.  Numerical and Physical Aspects of Aerodynamic Flows , 1986 .

[3]  J. E. Carter,et al.  Analysis of transitional separation bubbles on infinite swept wings , 1985 .

[4]  Frank T. Smith,et al.  On the non-parallel flow stability of the Blasius boundary layer , 1979, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[5]  P S Klebanoff,et al.  MECHANISM BY WHICH A TWO-DIMENSIONAL ROUGHNESS ELEMENT INDUCES BOUNDARY-LAYER TRANSITION: ROUGHNESS INDUCED TRANSITION , 1972 .

[6]  M. E. Goldstein,et al.  Scattering of acoustic waves into Tollmien-Schlichting waves by small streamwise variations in surface geometry , 1985, Journal of Fluid Mechanics.

[7]  R. Davis,et al.  Progress on interacting boundary-layer computations at high Reynolds number , 1982 .

[8]  J. E. Carter,et al.  Analysis of airfoil leading-edge separation bubbles , 1983 .

[9]  Arthur Veldman,et al.  A new, quasi-simultaneous method to calculate interacting boundary layers , 1980 .

[10]  H. A. Watts,et al.  Computational Solution of Linear Two-Point Boundary Value Problems via Orthonormalization , 1977 .

[11]  Counterrotating streamline pattern in a transitional separation bubble , 1986 .

[12]  A. Nayfeh.  Introduction To Perturbation Techniques , 1981 .

[13]  Vimal Singh,et al.  Perturbation methods , 1991 .

[14]  Ali H. Nayfeh,et al.  Effect of a bulge on the secondary instability of boundary layers , 1987 .

[15]  Frank T. Smith,et al.  Laminar flow over a small hump on a flat plate , 1973, Journal of Fluid Mechanics.