Effect of a hump on the stability of subsonic boundary layers over an airfoil

Abstract

The effect of a hump on the stability of subsonic boundary layers over an airfoil is investigated. The mean flow is calculated using an interacting boundary-layer solver which accounts or strong viscous-inviscid interaction and separation bubbles. The two-dimensional stability of the calculated two-dimensional mean flows is determined. The growth rates are integrated along a prescribed path to yield the amplification factor (i.e. N-factor), which is used to predict transition from laminar to turbulent flow. The analysis is performed for different heights and locations of the hump and for different Mach numbers. The results show that increasing the Mach number enhances separation, which partially offsets the stabilizing influence of compressibility. The most dangerous frequency decreases as the Mach number increases for a fixed hump location or the hump is moved downstream for a fixed Mach number. Moreover, the amplification factor increases as the hump height increases and the peak amplification factor increases and moves further downstream as the hump is moved downstream. The influence of suction and heat-transfer strips on controlling the destabilizing influence of the hump is investigated. The results show that cooling and suction strips stabilize the flow and therefore delay transition from laminar to turbulent flow, whereas, a heating strip destabilizes the flow. Applying suction through multiple strips can be as effective as suction through a single strip. Also the total flow rate required using multiple strips may be less than that required using a single strip. Moreover, cooling through multiple strips is as effective as cooling through a single strip. We investigate optimal locations of suction and cooling strips for a certain hump location.