Paál, György
(BME, Department of Hydrodynamic Systems)
On the sensitivity of jets and shear
layers
An interesting class of
flow configurations is that of self-sustained flow oscillations. All the boundary
conditions are steady (independent of time) and yet the flow is unsteady
(time-dependent), usually in the form of a more or less complex oscillation.
Two examples of the many are the edge tone (the basis of the organ pipe and the
flute) and the cavity tone (basis of the cavity-induced noise, like in
automobile door gaps). The above configurations will be exlpained
during the lecture. These configurations always include a jet or a shear layer,
and an obslacle. It is well-known that jets and shear
layers spontaneously develop instabilities which grow in the flow direction.
The oscillations caused by these instabilities meet the obstcle
and through some mechnanism the oscillating force on
the obstacle acts back to the origin of the shear layer or jet and initiates a
new instability wave, esentially forming a feedback
loop. It has been accepted for over 150 years that the "most sensitive
part" of a jet is the part immediately after leaving the nozzle. One topic
of our research was to find out why. The basic equations of fluid mechanics,
the Navier-Stokes eqations
are perturbed, linearised and simplified, leading to
the well-known Orr-Sommerfeld equation. This can be solved for various simple
flow configurations, such as jets or shear layers but also boundary layers. The
eqation is an ordinary linear fourth order
differential equation, differing only in the boundary conditions for various
flow configurations. Since it is a so-called stiff problem, a special solution
method, the Compound Matrix Method is applied and that will be also explained
in the lecture. The solutions provide an answer to the question of sensitivity.
Applying the same method to
a boundary layer in a creative way allows the development of new coatings
(inspired by the dolphin skinI for large ships. Under
favourable conditions these coatings can reduce
frictional losses to a significant extent and thus save a large amount of fuel.
The talk is held in English!
Az előadás nyelve angol!
Date: Oct 30, Tuesday 4:15pm
Place: BME, Building „Q”, Room QBF13