Stability analysis of boundary layers controlled by miniature vortex generators

It is currently known that Tollmien–Schlichting (TS) waves can be attenuated by the introduction of spanwise mean velocity gradients in an otherwise two-dimensional boundary layer (BL). The stabilizing effect, associated with an extra turbulence production term, is strong enough to obtain a delay in transition to turbulence induced by TS waves, with the implication of reducing skin-friction drag. Miniature vortex generators (MVGs), mounted in an array, have successfully been used to obtain velocity modulations by the generation of alternating high- and low-speed streaks in the spanwise direction to control the BL. Experimentally, an initial amplification of the TS waves has been reported, which takes place in the near-wake region of the MVG array. The higher the streak amplitude, the stronger the downstream stabilizing effect becomes, but with the drawback of experiencing an even stronger initial amplification. This can lead to a sub-critical transitional Reynolds number, which would not only mean that the control has failed but, even worse, also lead to an advancement of the transition location. Here, direct numerical simulations and a local spatial stability analysis have been performed in order to reach a deeper understanding of this behaviour. The results agree well with experiments and we propose an explanation of the described behavior in terms of stability properties of the controlled BL. This important knowledge can be used in future designs of BL modulators, which can lead to improved stability of the control and to an extended region of laminar flow.