Simplified Method for Natural Laminar Flow Prediction on Supersonic Highly Swept Wings

Incorporating natural laminar flow (NLF) into aircraft preliminary design contributes to enhancing the performance of the next-generation supersonic transports. However, conducting shape design optimizations to analyze the achievable NLF extent and assess the drag reduction potential on supersonic wings is too time-consuming for preliminary designs. This paper proposes a simplified method to predict the achievable NLF extent on supersonic wings. First, linear stability analyses are conducted to calculate transition Reynolds numbers under an ideal pressure distribution. Second, the precalculated transition Reynolds numbers are used to establish a simplified model via symbolic regression. Next, the effects of Mach number, flight altitude, and sweep angle on the achievable NLF regions of supersonic wings are investigated based on the established model. Results show that a higher flight altitude and a freestream Mach number around 1.7 are favorable for enlarging the laminar extent. A decrease of wing leading-edge sweep angle leads to a higher transition Reynolds number but not necessarily to an expanded NLF region. Accordingly, an alternative parameter, the laminar flow length, is proposed to characterize the laminar extent on a wing instead of the transition Reynolds number, and the laminar extents for conventional NLF designs and novel crossflow-attenuated NLF designs are presented.