Fluid flows subject to time-dependent external forces or boundary conditions are ubiquitous in aeronautical applications. Whether one considers pitching wings, dynamic stall or the gust response of wind turbines, the flow is unsteady or non-autonomous. We investigate the influence of unsteadiness on the non-linear flow evolution, as well as on the linear response to small disturbances that determines their stability and the subsequent transition to turbulence.
The simulations are performed with a high-order spectral-element method (SEM) with the domain discretized by up to several billion grid points. The capabilities of our SEM solvers are presented and two flow cases are studied in more detail. First, a small amplitude pitching wing where the laminar-turbulent interface drastically changes its cordwise location, and subsequently the dynamic stall of an airfoil undergoing a large pitchup motion.
We assess the potential of the optimally time-dependent (OTD) framework for transient linear stability analysis of flows with arbitrary time-dependence using a localized linear/non-linear implementation. This framework is used to track the linear stability of the laminar separation bubbles on the unsteady wings. For the pitching wise case the global mode corresponding to an absolute local instability is identified at the rear of the separation bubble, causing its breakdown to turbulence. In the case of an airfoil undergoing dynamic stall, the OTD modes reveal the main instability on the shear layer of the bubble as well as growth bursts correlated with vortex shedding.
The influence of low-amplitude free-stream disturbances on the onset of dynamic stall is also investigated and the onset of intermittent vortex shedding during the bubble bursting is documented. Here the Proper Orthogonal Decomposition framework is extended to include time dependence. This allows for the objective extraction of transient structures from data. Large structures shedding the bubble are identified as precursors of the detachment of the dynamic stall vortex.
Dan Henningson is Professor of Fluid Mechanics at KTH Royal Institute of Technology, where he also obtained his Ph.D. He previously held positions as Assistant Professor of Applied Mathematics at MIT and as Senior Researcher at the Aeronautical Research Institute of Sweden.
Professor Henningson has made contributions to the areas of large-scale numerical simulation of laminar-turbulent transition and its control, in particular so-called bypass transition in boundary layers under free stream turbulence, and more recently in the area of unsteady aerodynamics flows. His early theoretical work is summarized in the Springer monograph, Stability and Transition in Shear Flows, where the work on transient growth and non-normal effects in the transition process was highlighted.
Professor Henningson has been instrumental in creating a number of excellent research environments, in particular as the founding Director of both the Linné FLOW Center and the Swedish e-Science Research Center. He is the recipient of the prestigious Humbolt Prize and a European Research Council Advanced Grant. He is also an American Physical Society and EUROMECH Fellow as well as a member of the Royal Swedish Academy of Engineering Sciences.