Stability analysis of a streaky boundary layer generated by miniature vortex generators

Abstract

Delaying laminar-turbulent transition is an attractive method to reduce friction drag on streamlined bodies. In the case of natural transition, in which turbulence is triggered by the growth of two-dimensional Tollmien Schlichting (TS) instabilities, this growth of TS instabilities can be attenuated by introducing steady streamwise streaks into the boundary layer. These streamwise streaks are generated by streamwise vortices, which rearrange the flow via the lift-up mechanism. Such streamwise vortices can be induced by so-called miniature vortex generators (MVGs). Although recently considerable attention has been devoted to the investigation of MVGs, and multiple studies investigated MVGs with different parameters, the previously investigated MV configurations are likely suboptimal. This study aims at (partially) filling this knowledge gap by complementing previous studies by conducting a parametric study of rectangular MVGs and assessing them with local linear stability analysis. Three parameters are varied simultaneously: the height, the spanwise distance of the MVGs pairs, and the distance between MVGs in each pair. First, the modelling approach is presented, which consist of an efficient base flow computation, and BiGlobal stability analysis. The base flow calculation is validated by comparing our results with the experiments of Shattarzadeh and Fransson (2015). Then, the streak amplitude, the growth factors of the TS-waves and the secondary shear-layer instabilities are analysed in a parametric study. It is shown that with the variation of the spanwise distances, the maximum amplitude and the streamwise extent of the streaks in the boundary layer can be controlled, reminiscent of the behaviour of the optimal vortices. The findings and the test of the methodology provide valuable insight, which may be useful for the optimisation of MVGs.