Boundary-layer receptivity

In the study of viscous, boundary-layer instability, Tollmien-Schlichting waves are typically considered. The term receptivity is used to define the mechanism through which a generic disturbance present in the external flow or at the wall enters in the boundary layer and produces a wave. The latter can be stable or unstable. When its amplitude exceeds a certain threshold, however, transition from laminar to turbulent motion is observed. On the wing of an aircraft, or on the blades of a turbine, it is convenient to delay this transition so as to reduce the aerodynamic drag and to save in terms of boarded fuel, or to obtain a larger turbine efficiency.

Methods used until today for transition prediction do not consider the effects of disturbances present in the free stream. On the contrary, receptivity calculations have proved that they can be important and should, therefore, be considered. The applications of the receptivity analysis to the aerodynamic design of airplane wings or turbine blades are hence of remarkable interest.

From the theoretical point of view, the problem is solved using perturbation methods such as Multiple Scales. Non parallel effects due to the boundary layer growth are therefore taken into account and the introduction of the non homogeneous version of the multiple scales allows their used for a receptivity approach. The technique, coupled with the solution of the adjoint equations, computed the sensitivity of the solution to the external, exciting disturbances.

Certain coupling behaviors are particularly interesting. Some of them are the interaction between an acoustic wave and the wall roughness, the interaction between a vorticity wave and the wall roughness, the interaction between wall vibration of the wall roughness, and the interaction between a vorticity wave and an acoustic wave, both present in the external flow.

From the result obtained up to now, it is observed that an external perturbation (acoustic or vorticity wave, vibration of the wall, etc.), can induce an unstable wave in the boundary layer only if coupled to a fast adaptation of the boundary layer. This can be achieved, for example, in the zone of the leading edge (as a consequence of the boundary layer growth)or in presence of wall roughness, blowing/suction at the wall, temperature gradient at the wall.

For more details, see the following related publications.

Zuccher, S. & Luchini, P. 2014 Boundary-layer receptivity to external disturbances using multiple scales. Meccanica, 49, 2, 441-467.

Zuccher, S. 2002 Receptivity and control of flow instabilities in a boundary layer, Ph.D thesis, Politecnico di Milano, Milano.