BAIL 2006 Book of Abstracts - Institut für Numerische und ...

S.A. GAPONOV, G.V. PETROV, B.V. SMORODSKY: Boundary layer intercation with
external disturbances
✬
✫
BOUNDARY LAYER INTERACTION WITH EXTERNAL DISTURBANCES
S.A.Gaponov, G.V.Petrov, B.V.Smorodsky
Institute of Theoretical and Applied Mechanics SB RAS, Novosibirsk 630090,
Russia; E-mail: gaponov@itam.nsc.ru, Fax:+7(3832)342268
Generation of initial unstable eigen disturbances inside the boundary layer (BL) by external
perturbations is an actual problem nowadays in the investigation of laminar-turbulent transition.
Morkovin [1] was the first who has formulated so called BL receptivity problem. Up to now a lot of
experimental and theoretical works studying subsonic BL has been performed. The detailed review of
these efforts can be found in [2,3]. The knowledge about the supersonic BL is much shorter at the
present moment. The existing papers are devoted mainly to the investigation of external acoustic field
interaction with a supersonic BL on a smooth flat plate [4-6]. However an oncoming supersonic flow
always comprises not only acoustic but also vortical and thermal (entropy) perturbations [7]. This
paper presents results concerning irrotational external disturbances with zero damping in the direction
of the main flow. Present paper is devoted to the investigation of disturbance excitation in sub- and
supersonic BL by external vortical and thermal waves. Interaction of the acoustic waves with the BL
on the non-smooth surface has also been investigated and is reported here.Studies were conducted
both in an approaching of parallel basic flow and taken in consideration dependence of the main flow
in boundary layer on longitudinal coordinate. In the second case were used of an equation of stability
offered in [8].
For the acoustic field we distinguish two different kinds of interaction with the BL. In the first case
the incidence angle of the acoustic wave onto the BL is finite. In the second case the incidence angle is
zero. If the incidence angle is equal to zero, then in the result of the interaction the normal to the-wall
disturbance velocity at the BL outer edge is non-zero and it is an additional source of the streamwise
acoustic field. Such interaction leads to a very fast amplification of initial wave. For nonzero incidence
angles we have performed computations of the reflection coefficient. It is important to note here that
in some cases such reflectance is greater than unity. The amplitude of mass flux perturbation inside the
BL excited by an external acoustic wave is practically always an order of magnitude larger than the
initial wave amplitude in the free stream. Comparison of theoretical results with the experiment [6]
leads authors to necessary to consider the problem of diffraction of acoustic waves on a plate leading
edge. Using Fourier transformation and the equations of gas dynamics, one can show, that mass flux
fluctuations along the plate could be completely determined by means of the jump of normal-to-thewall
disturbance velocity at the plate leading edge. The normal velocity disturbance upstream of the
plate leading edge ( x < 0 ) is determined by the distribution of the mass flux. The obtained formulas
give the relations of the mass flux in the region x > 0 with its distribution at x < 0 . It was shown that
intensity of the mass flux fluctuation is reduced with distance from the leading edge and is dependent
of the orientation of the incident wave.
Tollmien-Schlichting (TS) wave excitation in the supersonic BL by a pair of acoustic waves has
been also investigated theoretically. The receptivity coefficient and the range of wave parameters
where TS-wave generation takes place have been computed. It was obtained, that at enough large
values of a Reynold's number, in narrow range of the acoustic wave numbers, the excited disturbances
practically do not differ from an own increasing disturbance. Outside of this range the TS wave is not
excited. The parameters of excited disturbances hardly differ from TS wave parameters near a neutral
point, the coincidence is observed only at essential move away from neutral area downstream
Beside in the paper investigation of the sound interaction with BL on the flat plate with roughness
is consider also. The problem of the disturbance generation by small amplitude spatially periodic wall
roughness has been formulated and solved in the linear approximation. The parameters of sound
irradiated by the model with roughness in the supersonic flow have been computed. The peculiarities
of the disturbances in the case when the angle between the wave fronts and the mean flow is close to
the Mach angle have been investigated specially. It has been shown that the amplitude of the
disturbance streamline inside the BL is greatly reduced in the near-wall sub-layer. At M = 1 mass
flux perturbations in the main part of the BL are close to zero also. Considerable reduction of the
Speaker: GAPONOV, S.A. 85 BAIL 2006
✩
✪