Influence of a cavity on the dynamical behaviour of an airfoil

A new wing design has been the subject of study in the European project VortexCell2050. For several reasons (structural and fuel load) it is desirable to use relatively thick wings. However, thick wings promote flow separation and/or massive vortex shedding, reducing flight performance. The new design airfoil is equipped with a cavity ("vortex cell") in the wing in order to prevent massive flow separation. This thesis aims to obtain insight into the dynamical behaviour of such a wing with a cavity and to explore which numerical methods are suitable for estimating the unsteady forces. In this thesis experiments and computations are presented, using a geometry that was inspired by cavity shapes which are considered in the VortexCell2050 project. For an airfoil with a cavity, oscillations of the shear layer are expected at Strouhal numbers of order unity, based on the width of the cavity opening. For the size of the cavities considered this implies high values, O(10), of the reduced frequency, based on the chord length of the airfoil. In order to conduct experiments in this high reduced frequency range, a new experimental method has been developed. In this experimental setup the airfoil is fixed to the wind tunnel wall and the first acoustic transversal eigenmode of the wind tunnel test section is used to drive an oscillating flow. In the conventional method the airfoil is oscillating. The main fundamental difference between the two methods is the presence of a time dependent uniform pressure gradient, which drives the oscillating flow, in the new method. The results obtained with both methods are equivalent after correcting for an effective buoyancy force induced by this driving pressure gradient. The new method avoids the use of a complex mechanical system to drive the oscillation of the airfoil. The acoustical forcing amplitude is very easy to vary within two orders of magnitude. The method appears to be most suitable for the conduction of experiments at high values of the reduced frequency. The new measurement method is validated by means of experiments on a standard NACA0018 airfoil complemented with two-dimensional Euler simulations. Thereafter two airfoils with slightly different cavity geometries are investigated in the wind tunnel. These experiments consist of measurements of local surface pressures. For the case of an airfoil with a cavity the Euler equations are not suitable. Two-dimensional simulations using the frictionlass flow approximation approach a so-called Batchelor flow, with a uniform rotation in the cavity. This flow is not observed in experiments. For this reason two-dimensional incompressible Navier–Stokes simulations at a Reynolds number, based on the chord length of the airfoil, of 2 · 104 are performed and indicate shear layer oscillations. In order to validate these low Reynolds number numerical results and to gain more insight in the flow physics, flow visualisations are performed in a waterchannel at the same Reynolds numbers as the numerical simulations. The visualisations also show oscillations of the shear layer at the first and second hydrodynamic mode, this is confirmed by hot-wire measurements in the wind tunnel at low Reynolds numbers. The hot-wire measurements also demonstrate that the expected lock-in of the shear layer does occur in a limited range of Reynolds numbers, based on the chord, sufficiently low such that no turbulence is generated, but higher than a critical value. Experiments and two-dimensional Navier–Stokes simulations indicate that for values of the reduced frequency, in the range of 2–10, no significant deviations in the unsteady lift force occur between an airfoil with cavity and the same airfoil without cavity. The cavity does display shear layer oscillations around the expected Strouhal numbers, however, the associated fluctuations in the lift coefficient appear to be neglegible. For the geometries considered the pressure differences over the airfoil are dominated by the added mass of the airfoil.