Uncertainty quantification of transition delay properties of miniature vortex generators

Abstract

Friction drag reduction by delaying the laminar-turbulent transition has a huge potential in aerospace applications. Miniature vortex generators (MVGs) are a promising passive control method to attenuate the growth of Tollmien-Schlichting (TS) waves, the dominant instability mechanism that triggers transition in the presence of low sweep. MVGs dampen the TS wave growth by introducing streamwise-elongated spanwise-periodic slow-fast regions (streaks), which are generated by counter-rotating streamwise vortices through the lift-up mechanism. In the development of MVGs, it is important to assess the performance of the flow control method in the presence of changes in the nominal parameters, such as off-design conditions and uncertainties. Therefore, statistical uncertainty analysis of the MVGs is performed using the direction-adaptive sparse grid stochastic collocation method. Two uncertain parameters are considered: change in the free-stream velocity magnitude and change in the sweep angle. Two configurations are investigated in this study: one from previous wind-tunnel experiments (Sattarzadeh & Fransson, Exp. Fluids 56, 58 (2015)), and one based on a numerical study (Szabó et al. Comp. & Fluids, 269, 106123 (2024)), whose methodology was utilized in this work. The quantities of interest are the streak amplitude and the transition Reynolds number. It is shown that the presence of uncertainties can severely impact the MVG performance. Changes in the sweep angle are much more influential than changes in the velocity magnitude, and overall, a deteriorated MVG performance is expected. Moreover, the importance of appropriately choosing the input probability density distribution is also highlighted.