Most of my current research activity is concentrated on studying
the transition to turbulence of some two- and three-dimensional
boundary layer flows. Such flows arise naturally in many
important practical situations, for example in the flow past
high speed flight vehicles. An understanding of the instability
of these flows can aid in the development of an improved design
as well as in the prediction and control of important
flow features. The
techniques we have adopted for this work are a combination of
asymptotic and numerical methods, and these are used to
obtain self-consistent descriptions of the underlying flow
properties. One advantage of such methods is that they can
be readily used to derive more efficient numerical schemes
for the full Navier-Stokes equations and which have the
ability to capture the relevant scales in the limit of
high Reynolds numbers.
Current research projects include:
1) The stability of compressible boundary layer flows.
work is concerned with studying the effects of compressibility on the
linear and nonlinear stability of compressible boundary layers.
With the renewed interest in high speed flight vehicles an
understanding of some of these effects may be important,
especially as very little is known about the the nonlinear stability
of such flows. Much of the work is based on using matched asymptotic
expansions, and exploiting the asymptotic solution properties in the
limit of large Reynolds numbers. A lot of the work also utilises the
important scaling ideas of unsteady non-linear critical layer theory.
Some results from this work may be found in publications 13, 17,18,23, 28.
2) Cross-flow instability in incompressible and compressible
Cross-flow instability plays an important role
in the transition of a fully three-dimensional boundary layer,
as for example in the flow past a swept wing,
and as such it is important to understand the underlying
mechanisms as well as possible interactions with other
stabilities. Our effort in this area has been directed at trying
to understand firstly, the linear stability properties from an analytical
as well as numerical viewpoint, and secondly to study the nonlinear
development of such instabilities. In the latter context, the research
has led to studying the properties of some complicated
novel partial-integro-differential equations which govern the nonlinear
evolution of some of the modes, see publications 10,20,23,25,26,27,28.
We are also investigating the absolute instabilities
of three-dimensional boundary layer flows. One of my students Jeff Cole, was
one of the first to demonstrate absolute instability in compressible
rotating disk flow, ( 1995, Ph.D. thesis Univ. of Exeter). With another
student Mustapha Turkyilmazoglu,
we are currently studying other aspects of this including
the importance of algebraic growth.
3) Full numerical of the Navier-Stokes equations for both
steady and unsteady flows.
This work complements that of (1) and
(2) above in trying to explore the flow properties when the
analytical methods can no longer be used because of strong
nonlinearities present in the problem. With the trends towards
increased parallelism in computer architectures, we have concentrated
on developing techniques making use of parallel algorithms. In this context
some parallel multigrid techniques were successfully developed to
study the flow in 2D and 3D lid-driven cavities. This is described in the
M.Sc and Ph.D. dissertations of Turkyilmazoglu and Jackson. The work is being
written up for submission to a journal.
4) The stability of flow over compliant surfaces.
drag reducing properties of compliant surfaces has motivated much of
this work. The underlying theme is again to develop suitable
techniques for analysing the nonlinear properties either numerically
or using asymptotic methods. Of several ongoing projects one is concerned with
the full numerical solution of the triple-deck model. Another is aimed at
understanding modal interactions using unsteady nonlinear critical theory.
We have also extended some of the ideas to internal flows, as described
in publication 24. Recently through 2 EPSRC grants we are looking at
the stability of flow in compliant channels, pipes and boundary layers, to
investigate the effects of heat transfer on the flow stability.
5) Absolute instabilities in boundary layer flows.
Recently we have spent
considerable effort in devising techniques for studying absolute instabilities
in two- and three-dimensional boundary layer flows, see for example publications 30-34,36. A number of significant results have emerged from these studies
in particular for the wedge shaped and cusp shaped
trailing edge configurations, where we have for the first time been able
to look at the effects of separation and compressibility
on the flow stability. One of our tentative suggestions is that
for thicker aerofoils the flow upstream of the trailing-edge is
absolutely unstable and if correct, this has enormous
implications for laminar flow control on such aerofoils. Our current efforts
are being directed at trying to compute much larger regions of separated flow
over real aerofoil shapes and investigate their stability.
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