A zonal detached eddy simulation (DES) method is presented that predicts the buffet phenomenon on a supercritical airfoil at conditions very near shock buffet onset. Some issues concerning grid generation, as well as the use of DES for thin-layer separation, are discussed. The periodic motion of the shock is well reproduced by averaged Navier–Stokes equations (URANS) and zonal DES, but the URANS calculation has needed to increase the angle of attack compared to the experimental value and the standard DES failed to reproduce the self-sustained motion in the present calculation. The main features, including spectral analysis, compare favorably with experimental measurements (Jacquin, L., Molton, P., Deck, S., Maury, B., and Soulevant, D., “An Experimental Study of Shock Oscillation over a Transonic Supercritical Profile,” AIAA Paper 2005-4902, June 2005). A very simple model based on propagation velocities yields the main frequency of the motion. As suggested by Lee (Lee, B. H. K., “Transonic Buffet on a Supercritical Airfoil,” Aeronautical Journal, May 1990, pp. 143–152), this calculation highlights that upstream propagating waves are generated by the impingment of large-scale structures on the upper surface of the airfoil in the vicinity of the trailing edge. These upstream propagating waves can regenerate an instability leading to a feedback mechanism.

Numerical Simulation of Transonic Buffet over a Supercritical Airfoil

This review article addresses the dynamics and control of low-frequency unsteadiness, as observed in some aerodynamic applications. It presents a coherent and rigorous linearized approach, which enables both to describe the dynamics of commonly encountered open-flows and to design open-loop and closed-loop control strategies, in view of suppressing or delaying instabilities. The approach is global in the sense that both cross-stream and streamwise directions are discretized in the evolution operator. New light will therefore be shed on the streamwise properties of open-flows. In the case of oscillator flows, the unsteadiness is due to the existence of unstable global modes, i.e., unstable eigenfunctions of the linearized Navier-Stokes operator. The influence of nonlinearities on the dynamics is studied by deriving nonlinear amplitude equations, which accurately describe the dynamics of the flow in the vicinity of the bifurcation threshold. These equations also enable us to analyze the mean flow induced by the nonlinearities as well as the stability properties of this flow. The open-loop control of unsteadiness is then studied by a sensitivity analysis of the eigenvalues with respect to base-flow modifications. With this approach, we manage to a priori identify regions of the flow where a small control cylinder suppresses unsteadiness. Then, a closed-loop control approach was implemented for the case of an unstable open-cavity flow. We have combined model reduction techniques and optimal control theory to stabilize the unstable eigenvalues. Various reduced-order-models based on global modes, proper orthogonal decomposition modes, and balanced modes were tested and evaluated according to their ability to reproduce the input-output behavior between the actuator and the sensor. Finally, we consider the case of noise-amplifiers, such as boundary-layer flows and jets, which are stable when viewed in a global framework. The importance of the singular value decomposition of the global resolvent will be highlighted in order to understand the frequency selection process in such flows. © 2010 by ASME.

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Dynamics and Control of Global Instabilities in Open-Flows: A Linearized Approach

Predicting the onset of flow unsteadiness based on global instability

Buffeting flow on transonic aerofoils serves as a model problem for the more complex three-dimensional flows responsible for aeroplane buffet. The origins of transonic aerofoil buffet are linked to a global instability, which leads to shock oscillations and dramatic lift fluctuations. The problem is analysed using the Reynoldsaveraged Navier–Stokes equations, which for the foreseeable future are a necessary approximation to cover the high Reynolds numbers at which transonic buffet occurs. These equations have been shown to reproduce the key physics of transonic aerofoil flows. Results from global-stability analysis are shown to be in good agreement with experiments and numerical simulations. The stability boundary, as a function of the Mach number and angle of attack, consists of an upper and a lower branch – the lower branch shows features consistent with a supercritical bifurcation. The unstable modes provide insight into the basic character of buffeting flow at nearcritical conditions and are consistent with fully nonlinear simulations. The results provide further evidence linking the transonic buffet onset to a global instability.

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Origin of transonic buffet on airfoils.

A review of recent developments in the understanding of transonic shock buffet

Shock wave/turbulent boundary-layer interaction and flow separation may induce self-sustained large-scale oscillations on a profile at transonic Mach number. This phenomenon, known as transonic buffet, is at the origin of intense pressure fluctuations which can have detrimental effects, both in external and internal aerodynamics. The present paper describes a new experiment executed in the ONERA S3Ch transonic wind tunnel on shock oscillations over the OAT15A supercritical profile. These experiments have allowed the precise definition of the conditions for buffet onset and the characterization of the properties of the periodic motion from unsteady surface pressure measurements. The flowfield behavior has been described in great detail thanks to high-speed schlieren cinematography and surveys with a two-component laser Doppler velocimetry along with a conditional sampling technique. The first aim of this study was to provide the computational fluid dynamics community with well-documented test cases to validate advanced computing methods. Concerning the physics of the phenomenon, it is suggested that it is mediated by acoustic waves which are produced at the trailing edge and which travel on the two sides of the airfoil. Also, the experimental results strongly suggest that the phenomenon is essentially two-dimensional, even if three-dimensional effects are also detected.

Didier Soulevant

Papers

Experimental Study of Shock Oscillation over a Transonic Supercritical Profile

An Experimental Study of Shock Oscillation over a Transonic Supercritical Profile