Advances in global linear instability analysis of nonparallel and three-dimensional flows

A focus has been put on the stability characteristics of different flow types existing on air vehicles. Flow passing over wings and different junctions on an aircraft face numerous local features, ...

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Stability and transition of three-dimensional boundary layers

Laminar-turbulent transition on aerodynamic surfaces occurs between often widely apart limits, namely the upper limit relevant in extremely low-disturbance environments and the lower limit given by the "bypass transition." The eN method only provides the upper bound on the transition location, while experimental information or direct NavierStokes simulations are required to determine the lower bound. Computational tools (receptivity theory/linear Navier-Stokes, nonlinear parabolized stability equations, etc.) are now available to estimate the departure from the upper bound due to factors such as surface roughness and acoustic disturbances but await validation against experiments. In this paper, progress made in boundary-laye r stability and transition is reviewed and description is given for the computational tools developed to ease the determination of the upper limit via N-factor calculations. This includes a suction optimization code for the efficient design of laminar flow control wings. A brief discussion of some of the physical issues associated with boundary-layer transition is given and some key results, including those pertaining to the question of absolute instability, are presented.

Boundary-Layer Transition Prediction Toolkit

The incompressible boundary layer in the corner formed by two intersecting perpendicular semi-infinite planes is investigated; the freestream flow, aligned with the corner, is of the form xn,x repr...

The effects of freestream pressure gradient on a corner boundary layer

Linear stability of the incompressible flow along a stream wise corner is studied by solving the two-dimensional eigenvalue problem governed by partial differential equations. It is found that this fully three-dimensional flow is subject to inviscid instability due to the inflectional nature of the stream wise velocity profile. The higher growth rates for the inviscid instability mode, which is symmetric about the corner bisector, as compared to the viscous Tollmien-Schlichting instability operative away from the corner is consistent with the experimental findings that the corner flow transitions to turbulence earlier than the two-dimensional Blasius flow away from the corner.

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Inviscid instability of streamwise corner flow

The study of laminar viscous flow along the line of intersection of two solid surfaces at right angles is examined in its present state, and outstanding differences between various experimental and theoretical results are analysed. New experimental results are presented in which the stability of the corner boundary layer is examined in terms of the degree of streamwise similarity of its velocity profiles. Conclusive evidence is found that the layer does not exist in stable laminar form when the streamwise pressure gradient is zero and the Reynolds number much above about 10$^4$. The new results also help to explain the differences between various experimental results, and between theory and experiment, which have characterized the corner boundary layer problem for several years. By extrapolation, an approximate prediction is obtained of what the velocity profile of the corner boundary layer would be in the limiting case of zero pressure gradient, if the layer were stable in that state. The predicted profile is compared with the results of current theories.

M. Zamir

Papers

Similarity and stability of the laminar boundary layer in a streamwise corner