Zhukovaky Central Aerodynamics Institute

Abstract:

Large-scale structures play an important role in the dynamics of turbulent shear layer. they originate as the instability modes of the "fictious" time-averaged mean flow. The object of the present work is to study the effect of small particles on the shear-layer instability. The particle effect on the instability wave may be significant because of the unsteady momentum transfer between phases.

Linear stability of 2D flow of a dusty gas in a laminar boundary layer was investigated recently by Asmolov & Manuilovich (1998). It was shown that even small amounts of the dust can suppress Tollmien-Schlichting wave significantly. Solution based on the approach of local parallel flow predicted the discontinuity of eigenvalue in the space of parameters Reynolds number-wavenumber. The cause of the phenomenon is the resonant acceleration of the particles in the critical layer.

Solution for the instability wave in the shear layer is constructed using the method of multiple scales (Tam & Morris 1980). It accounts for effects of slightly divergent basic flow and slow variation of the wavenumber with streamwise coordinate. The particles experience not only the Stokes Drag but also the lift which due to the combination of slip velocity and fluid shear. As a result the discontinuity can arise for either damped or unstable waves. In the small regions near the resonant points the continuous asymptotic solution is obtained which predicts large particle velocity and large modification of the wave.

References

Asmolov, E.S. & Manuilovich, S.V. 1998 J. Fluid Mech. v.365 pp. 137-170.

Tam, C.K.W. & Morris, P.J. 1980 J. Fluid Mech. v. 98, pp. 349-381.