Abstracts - KTH Mechanics

Stability and sensitivity analysis of separation bubbles.
L.Marino ∗ , P.Luchini †
In the present contribution the linear stability of an incompressible flow in the
presence of a recirculating bubble is considered.
The problem is relevant to aeronautical applications; in fact separation bubbles
can arise near the leading edge of airfoils, under particular flight conditions, and can
dramatically change their performance (lift and drag).
The stability properties of separation bubbles on flat plates have been studied by
past authors through an approach based on parallel and weakly non-parallel approximations
1 , or by direct numerical simulation 2 . In both cases the separation bubble
has been induced by giving a predefined adverse pressure gradients to boundary-layer
velocity profiles.
Here the analysis is carried out both in a flat geometry with a prescribed external
pressure gradient and in the case of flow over a curved surface.
The properties of the ensuing global instability are obtained without any parallelflow
approximation; we remind that the term ”global” is here referred to instabilities
not amenable to the quasi-parallel approximation 3 . Consequently, the problem is
studied by solving the complete Navier-Stokes equations.
The critical Reynolds number and the structure of the possible instability of the
flow are the main topics of the present investigation. Moreover the sensitivity characteristics
are determined, by an adjoint analysis of the relevant eigenvalue problem.
In particular the effects of inflow disturbances and of structural perturbations (which
comprise base flow and boundary conditions changes) are analysed and discussed.
A general three-dimensional perturbation is assumed, with a sinusoidal dependence
on the spanwise coordinate. Such a formulation leads to a large-scale eigenvalue
problem which is then solved by an inverse-iteration algorithm.
A particular attention was given to the boundary conditions necessary in order
to achieve an asymptotic behaviour of both base flow and perturbation at the upper
computational boundary. The influence of different choices of such conditions will
also be discussed.
∗Dipartimento di Meccanica e Aeronautica, Universitá degli studi di Roma “La Sapienza”, Via
Eudossiana 18, Roma, I-00184.
† Dipartimento di Ingegneria Meccanica, Universitá di Salerno, Fisciano (SA), I-84084.
1D.A. Hammond, L.G. Redenkopp, Local and global properties of separation bubbles, Eur. J.
Mech. B/Fluids, 17,1998.
2U. Rist, U. Maucher, Investigations of time-growing instabilities in laminar separation bubbles,
Eur. J. Mech. B/Fluids, 21,2002.
3J. -M. Chomaz, Global instabilities in spatially developing flows: Non-normality and nonlinearity,
Ann. Rev. Fluid Mech., 37,2005.
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