Numerical Study of the Influence of Gaps on Laminar-Turbulent Transition on Flat Plates and Airfoils

Abstract

The aviation industry is constrained to meet challenging greenhouse gas reduction targets to comply with climate mitigation programs. Reducing the viscous drag by maintaining laminar flow on the wing surface can significantly contribute to lower greenhouse gas emissions. Surface irregularities can reduce the benefit of laminar flow technologies by amplifying boundary-layer instabilities, which can lead to laminar-turbulent transition. This thesis studies the impact of surface irregularities in the form of shallow gaps on the spatial evolution of boundary-layer instabilities using a combined approach of Parabolized Stability Equations and Adaptive Harmonized Linearized Navier-Stokes Equations. The focus is to investigate how shallow gaps affect the 2D Tollmien-Schlichting (TS) instabilities on a flat plate without pressure gradients at subsonic conditions. Moreover, the effect of shallow gaps is studied for 3D boundary-layer instabilities on a realistic infinite swept transonic laminar airfoil with leading edge suction. This study addresses the question of whether conclusions from the flat plate study are transferable to more complex flows. In the flat plate study, the geometry of the gaps is systematically varied by combining three lengths with three depths. The effect of depth, length, and gap aspect ratio is quantified for each configuration in terms of N-factors and the expected transition location obtained by the eN method. An increased depth promotes instability and leads to an upstream movement of the transition location. Based on the investigations, careful consideration of the gap length is crucial when determining its dimensions. For reduced gap lengths, the negative impact on the laminarity resulting from increased depths can be minimized, if the mean flow pattern shifts within the gap from closed to open cavity flow. To study the effect of shallow gaps on the airfoil, three cases are computed, varying in depth and length. The instability analysis directly compares the spatial evolution of individual instability modes for different gap configurations. Results show that conclusions from the flat plate study cannot be transferred straight to the airfoil study. This is mainly due to the occurrence of 3D cross-flow instabilities, which show a different reaction on shallow gaps than TS instabilities.i