[Back]


Habilitation Theses:

S. Braun:
"Leading edge separation from an asymptotic point of view";
Technische Universität Wien, Fakultät für Maschinenwesen und Betriebswissenschaften, 2003.



English abstract:
The present work is mainly based on the concept of Prandtl's boundary layer
theory which was developed 1904 and related
asymptotic techniques referred to as matched asymptotic expansions and singular
perturbation methods. Although Prandtl's seminal contribution to the
understanding of viscous flows at high Reynolds numbers dates back nearly
100 years quite a number of open problems in the context of boundary layer
separation
and laminar-turbulent boundary layer transition remain still unsolved.
The clarification of these open questions is desirable of course not only from
a theoretical point of view but is also essential for practical purposes such
as accurate numerical computations with a minimum amount of model assumptions.

Milestones in the development of boundary layer theory are, among others, the
clarification of the singular behaviour (breakdown) of the boundary layer
equations near a point of vanishing skin friction by Goldstein 1948 and the
concept of viscous-inviscid interaction by Neiland,
Stewartson, Williams and Messiter 1969/70. Although the application of triple
deck theory turned out to be very successful in a number of unsolved problems
it could not resolve Goldstein's square root singularity associated with
(strong) boundary layer separation, Stewartson 1970. In this time computer power
increased in such a way that it became possible to calculate boundary layer
flows around airfoils with high resolution. These calculations showed that the
strength of
Goldstein's singularity can be reduced by varying e.g.the angle of
attack of the airfoil until the wall shear vanishes just in one point, but
recovers downstream.
As demonstrated by Ruban 1981 and Stewartson, Smith and Kaups 1982 it is
possible to treat this limiting case of socalled marginal separation with the
interactive approach successfully to enable the description of small reverse
flow regions.
In the following years considerable extensions of these fundamental findings
including complex three-dimensional and unsteady effects have been accomplished.
While steady problems of this type seemed to be analyzed adequately, another
breakdown of the solutions in the form of finite time blow-up appeared in
the numerical investigations of the fundamental integro-differential equation
of marginal separation if transient effects are taken into account.

A point to which attention has not been payed in a satisfactory manner is
the occurrence of non-unique solutions of the corresponding equations. It is
well known that there exist at least two solutions in the range below the
critical (maximal) angle of attack, beyond which the interaction mechanism
is not applicable. Our aim was to investigate the behaviour of these different
solutions in the vicinity of this limit. Numerical calculations showed an
unexpected and surprising result which points to a bifurcation problem.
A combination of analytical and numerical techniques was used to analyze this
problem in detail and we could show, as a main result, that the primary
integral equation is reduced to a nonlinear partial differential evolution
equation.
As a further result, it is possible to incorporate local three-dimensional
unsteady effects such as vibrating surface mounted obstacles into this approach
which can act as effective means to affect the flow properties (flow
control, `smart structures'). Recent investigations of this evolution equation
support the hope once to clarify the (fast) transition process to turbulent
boundary layer flow within the framework of asymptotic analysis.

Created from the Publication Database of the Vienna University of Technology.