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Fluid dynamics of airfoils with moving surface boundary-layer control Mokhtarian, Farzad


The concept of moving surface boundary-layer control, as applied to the Joukowsky and NACA airfoils, is investigated through a planned experimental program complemented by theoretical and flow visualization studies. The moving surface was provided by one or two rotating cylinders located at the leading edge, the trailing edge, or the top surface of the airfoil. Three carefully designed two-dimensional models, which provided a wide range of single and twin cylinder configurations, were tested at a subcritical Reynolds number (Re = 4.62 x 10⁴ or Re — 2.31 x 10⁵) in a laminar-flow tunnel over a range of angles of attack and cylinder rotational speeds. The test results suggest that the concept is indeed quite promising and can provide a substantial increase in lift and a delay in stall. The leading-edge rotating cylinder effectively extends the lift curve without substantially affecting its slope. When used in conjunction with a second cylinder on the upper surface, further improvements in the maximum lift and stall angle are possible. The maximum coefficient of lift realized was around 2.22, approximately 2.6 times that of the base airfoil. The maximum delay in stall was to around 45°. In general, the performance improves with an increase in the ratio of cylinder surface speed (Uc) to the free stream speed (U). However, the additional benefit derived progressively diminishes with an increase in Uc/U and becomes virtually negligible for Uc/U > 5. There appears to be an optimum location for the leading-edge-cylinder. Tests with the cylinder at the upper side of the leading edge gave quite promising results. Although the CLmax obtained was a little lower than the two-cylinder configuration (1.95 against 2.22), it offers a major advantage in terms of mechanical simplicity. Performance of the leading-edge-cylinder also depends on its geometry. A scooped configuration appears to improve performance at lower values of Uc/U (Uc/U ≤ 1). However, at higher rates of rotation the free stream is insensitive to the cylinder geometry and there is no particular advantage in using the scooped geometry. A rotating trailing-edge-cylinder affects the airfoil characteristics in a fundamentally different manner. In contrast to the leading-edge-cylinder, it acts as a flap by shifting the CL vs. α plots to the left thus increasing the lift coefficient at smaller angles of attack before stall. For example, at α = 4°, it changed the lift coefficient from 0.35 to 1.5, an increase of 330%. Thus in conjunction with the leading-edge- cylinder, it can provide significant improvements in lift over the entire range of small to moderately high angles of incidence (α ≤ 18°). On the theoretical side, to start with, the simple conformal transformation approach is used to obtain a closed form potential-flow solution for the leading-edge-cylinder configuration. Though highly approximate, the solution does predict correct trends and can be used at a relatively small angle of attack. This is followed by an extensive numerical study of the problem using: • the surface singularity approach including wall confinement and separated flow effects; • a finite-difference boundary-layer scheme to account for viscous corrections; and • an iteration procedure to construct an equivalent airfoil, in accordance with the local displacement thickness of the boundary layer, and to arrive at an estimate for the pressure distribution. Effect of the cylinder is considered either through the concept of slip velocity or a pair of counter-rotating vortices located below the leading edge. This significantly improves the correlation. However, discrepancies between experimental and numerical results do remain. Although the numerical model generally predicts CLmax with a reasonable accuracy, the stall estimate is often off because of an error in the slope of the lift curve. This is partly attributed to the spanwise flow at the model during the wind tunnel tests due to gaps in the tunnel floor and ceiling required for the connections to the externally located model support and cylinder drive motor. However, the main reason is the complex character of the unsteady flow with separation and reattachment, resulting in a bubble, which the present numerical procedure does not model adequately. It is expected that better modelling of the cylinder rotation with the slip velocity depending on a dissipation function, rotation, and angle of attack should considerably improve the situation. Finally, a flow visualization study substantiates, rather spectacularly, effectiveness of the moving surface boundary-layer control and qualitatively confirms complex character of the flow as predicted by the experimental data.

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