Control of transonic buffet through deployable flaps

Transonic buffet is a well known phenomenon of quasi-periodic shock oscillation with associated unsteady flow separation occurring on the suction side of airfoils in the transonic regime, and as such it has important impact in external aero dynamics and in turbomachinery. Transonic buffet is responsible for severe, low-frequency excitation of structural components, with incurred strong vibrations which in worst case may threaten the integrity of aircraft. The buffet mechanism has been the subject of several experimental and numerical studies, many of which are summarized in the review paper of [4]. However, to date there is no consensus on what its causes may be. The most commonly accepted scenario involves an acoustic feedback loop, whereby the shock motion produces the unsteady shedding of eddies towards the trailing edge, where they scatter acoustic waves. Those waves travel upstream through the outer potential flow, thus reaching the shock foot and closing the loop. An alternative explanation [8] suggests that buffet is primarily associated with the intrinsic dynamics of the separation bubble, which periodically grows and bursts as it reaches the airfoil trailing edge. In this scenario, the shock would play an essentially passive role. A recent thorough scrutiny of the possible mechanisms underlying transonic buffet was carried out by the present research group [5]. Numerical simulations including LES, DES and RANS were used to reach the following conclusions: i) buffet dynamics is inherently limited to the suction side, and pressure waves propagating upstream on the pressure side have no dynamical effect; ii) the acoustic mechanism, while being possible is in significant disagreement with the numerical data, and not supported by available evidence. Another important finding was that RANS is capable of predicting transonic buffet with good accuracy, hence it is unlikely that the scattering of acoustic waves from eddies at the trailing edge (which is not resolved in RANS) may be advocated as a convincing explanation. Hence, we are personally more prone to believe that buffet arises as a result of the breathing motion of the separation bubble. Whatever its causes may be, the control of transonic buffet has been the subject of several past investigations, which had variable degree of success. Two main types of actuation have mainly been considered: i) periodic deflection of the trailing edge to counteract shock excursion [2]; ii) airfoil-mounted vortex generators and bumps to mitigate the strength of the shock/boundary layer interaction [6, 3]. In the present research we propose a novel technique for buffet control based on the use of deployable tabs. We show that these are capable of fully suppressing buffet, with minimal loss of aerodynamic efficiency. Numerical simulations of the Navier-Stokes equations relying on the Spalart-Allmaras turbulence model are hereafter presented to show the feasibility of a new type of controlscheme for buffet suppression. The finite-volume solver relies on a baseline second-order discretization which guarantees discrete preservation of the total flow kinetic energy from convection in the inviscid limit [9]. The scheme is made to switch to third-order weighted essentially-non-oscillatory (WENO) near discontinuities, as controlled by a shock sensor. The gradients normal to the cell faces needed for the viscous fluxes, are evaluated through second-order central-difference approximations, obtaining compact stencils and avoiding numerical odd-even decoupling phenomena. Of special importance in the study of external flows is the correct enforcement of the far-field numerical boundary conditions. Here, we rely on characteristic decomposition to identify waves entering and leaving the domain and estimate the contribution of outgoing waves at the boundary through extrapolation of interior information. Time advancement of the semi-discretized system of ODEs resulting from the spatial discretization is carried out by means of an semi-implicit low-storage third-order Runge-Kutta algorithm [7], whereby the convective and the viscous terms in the wall-normal direction are handled implicitly through Beam-Warming linearization. As a representative geometry we have considered the V2C airfoil, a supercritical laminar profile designed by Dassault Aviation within the TFAST European research project (http://tfast.eu/). A structured C-type mesh including 1024x512 cells was used for all simulations, in which the external boundary is placed 50 chords away from the airfoil surface, and which has the first point off the wall at a distance Dy/c = 0.000065, corresponding to about 0.6 wall units. For the purpose of controlling the flow and suppressing buffet, we herein propose to use a deployable flap, which is placed in the aft part of the airfoil suction side. The main rationale is to mimic the behavior of shock holders, which are frequently used in experiments to stabilize normal shock waves [1]. Another plausible reason is that a wall-parallel flap would create a ‘channeling’ effect with the airfoil surface, which mitigates the adverse pressure gradient, thus reducing the separated flow extent. Probably, the two effects are related to each other. For preliminary simulations, the flap has been shaped as a bi-convex airfoil. Two sample configurations have been considered, namely a HIGH configuration, with flap chord cf/c = 0.2, relative thickness of 6%, and distance of about 0.15c from the airfoil, and a LOW configuration, with flap chord cf=0.1c, relative thickness of 12%, and distance of about 0.075c from the airfoil. The flap is mounted at approximately the local flow direction in the absence of it, to try to avoid flow separation. The selected flow conditions correspond to at M0=0.7, Rec=300000, alpha=7°, at which the airfoil under investigation is known to undergo substantial buffet. Further, it has been shown that frequency and amplitude of buffeting is correctly predicted by RANS, which well matches LES predictions [5]. The computed time-averaged Mach number contours and the time history of the overall aerodynamic efficiency (also incorporating the forces acting on the flap) are shown in figure 1 and 2, respectively. The main result is that both the HIGH and the LOW configuration are capable of effectively suppressing buffet, after an initial transient. Both types of control have the main effect of pushing the main shock upstream (x/c=0.35) than its time-average uncontrolled location (x/c=0.4). However, whereas LOW actuation has the effect of slightly extending the region of flow reversal past the airfoil trailing edge, HIGH actuation is effective in reducing its size. Accompanied with HIGH actuation also comes some small flow separation past the flap, whereas in the LOW case the flap is embedded in a low-speed region, and flow does not separate. The practical implications of control are visible in the time history of the aerodynamic efficiency. While the efficiency levels off in both cases, LOW actuation retains the (time-average) efficiency of the uncontrolled case, whereas HIGH actuation is responsible for additional losses. Additional simulations (not shown) have shown that buffet suppression comes under a variety of different flap geometrical configurations, and in a wide range of flow parameters, hence it is a robust phenomenon. Further confirmation of the viability of the proposed control method should come from DNS, currently in progress.