Computational Modeling of Roughness-Based Laminar Flow Control on a Subsonic Swept Wing

Abstract

A combination of parabolized stability equations and secondary instability theory has been applied to a low-speed swept airfoil model with a chord Reynolds number of 7.15 million, with the goal of evaluating this methodology in the context of transition prediction for a known configuration for which roughness-based crossflow transition control has been demonstrated under flight conditions. Nonlinear parabolized stability equations computations indicate that progressive reduction in the growth of the linearly most amplified stationary crossflow mode can be achieved via increasingly stronger control input corresponding to the first harmonic of the target mode. The reduction in the target mode amplitude is accompanied by reduced linear growth rates of the high-frequency secondary instabilities that lead to rapid breakdown of the laminar flow. The secondary instability predictions based on secondary instability theory are shown to agree well with those based on the parabolized stability equations. The possibility of overcontrol is also assessed, and it is found that premature transition due to excessive control can be avoided by keeping the control amplitude below a certain threshold. The nonlinear development of the most unstable Z-mode secondary instability is traced using the parabolized stability equation method, so as to yield physics-based prediction of crossflow-dominated transition.