Abstract
An airfoil undergoing transonic buffet exhibits a complex combination of unsteady shock-wave and boundary-layer phenomena, for which prediction models are deficient. Recent approaches applying computational fluid mechanics methods using turbulence models seem promising, but are still unable to answer some fundamental questions on the detailed buffet mechanism. The present contribution is based on direct numerical simulations of a laminar flow airfoil undergoing transonic buffet at Mach number M = 0.7 and a moderate Reynolds number Re = 500, 000. At an angle of attack α = 4∘, a significant change of the boundary layer stability depending on the aerodynamic load of the airfoil is observed. Besides Kelvin Helmholtz instabilities, a global mode, showing the coupled acoustic and flow-separation dynamics, can be identified, in agreement with literature. These modes are also present in a dynamic mode decomposition (DMD) of the unsteady direct numerical solution. Furthermore, DMD picks up the buffet mode at a Strouhal number of St = 0.12 that agrees with experiments. The reconstruction of the flow fluctuations was found to be more complete and robust with the DMD analysis, compared to the global stability analysis of the mean flow. Raising the angle of attack from α = 3∘ to α = 4∘ leads to an increase in strength of DMD modes corresponding to type C shock motion. An important observation is that, in the present example, transonic buffet is not directly coupled with the shock motion.
Highlights
Transonic buffeting is usually characterised in the literature [1,2,3] as a structural response to an aerodynamic instability, which causes significant low-frequency fluctuations in theFlow, Turbulence and Combustion (2020) 104:509–532 aerodynamic lift forces
direct numerical simulations (DNS) data has firstly been analysed in terms of local and global linear stability in order to investigate the transonic buffet mechanism of a narrow wing section at α = 4◦ and Mach and Reynolds numbers of M = 0.7 and Re = 500,000, respectively
Local linear stability theory associates KH roll-ups seen in the DNS with convective linear instabilities, as has been previously observed for a high-pressure turbine vane at similar freestream conditions [30]
Summary
Turbulence and Combustion (2020) 104:509–532 aerodynamic lift forces. This aerodynamic instability has been observed in experimental [4, 5] and numerical [6] studies of rigid airfoils as well and is known as “transonic buffet”. While traditional explanations (e.g. acoustic feedback and wave propagation models) have difficulties to directly couple the shock motion with the low-frequency fluctuations in the lift [7], more recent studies describe transonic buffet as a global instability [8]. It is not quite clear whether the shock motion plays a fundamental active role or is rather a symptom of the periodically accelerating and decelerating flow over the airfoil suction side.
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