Stability Analysis of Laminar Separation Bubbles on Airfoils

Abstract

Laminar-to-turbulent transition prediction is of practical interest in aircraft design since aerodynamic quantities such as the drag are affected by the extent of the laminar, transitional and turbulent region. Local stability theory (LST) and parabolized stability equations (PSE), in conjunction with the $e^N$-method, have proven to be effective tools for predicting the transition location of attached boundary-layers. From a physical point of view, the application of these stability analysis tools should be restricted to the laminar region of the flow. The aim of this work is to apply these tools to flows exhibiting laminar separation bubbles with turbulent reattachment, i.e., transition occurs inside the bubble, and to compare the corresponding N-factor results with transition onset data from Large Eddy Simulations (LES). Two test cases are studied, the SD7003 airfoil at $Re_\infty=6.0 \times 10^4$ and the NACA 0015 airfoil at $Re_\infty=1.8 \times 10^5$. The results confirm the effectiveness of the PSE methodology in analyzing convective instabilities within laminar separation bubbles, with N-factor predictions showing consistent correlation with the turbulent kinetic energy fields in the LES. However, future work is required to identify specific mechanisms driving the laminar-turbulent transition within the LES computations.