Numerous experiments were conducted on an oscillating airfoil in a subsonic wind tunnel. The experiments involved measuring the surface pressure distribution when the model oscillated in two types of motion, pitch and plunge, at three different Reynolds numbers, 0.42, 0.63 and 0.84 million, and over a range of reduced frequencies, k = 0.03–0.09. The unsteady aerodynamic loads were calculated from the surface pressure measurements, 64 ports, along the chord for both upper and lower surfaces of the model. Particular emphasis was placed on the effects of different types of motion on the unsteady pressure distribution of the airfoil at pre‐stall, near‐stall and post‐stall conditions. It was found that variations of the pressure distribution and aerodynamic loads with angle of attack were strongly sensitive to the displacement, oscillation frequency and mean angle of attack. The width of the hysteresis loop, position of the ‘figure‐8 shape’ and slope of the pressure coefficient curve are influenced by both types of motion, pitch and plunge. The main difference between plunging and pitching motions is due to the presence of the pitch rate for the pitching motion case, which was absent in the plunging case. Pitch rate had the strongest influence on pressure data in the near‐stall and post‐stall conditions. The trend of increasing the width of the hysteresis loops of lift coefficients with changing reduced frequency was different in two motions in the pre‐stall and post‐stall regions. The aerodynamic damping was greater for the pitching case than for the plunging one at higher reduced frequencies due to the existence of the pitch rate in the pitching oscillation, which was reversed at lower reduced frequencies. In the near‐stall region, at higher reduced frequency, the dynamic stall angle for the pitching oscillation increased while for the plunging one the effect was minimal. Increasing the oscillation amplitude was more effective for the plunging motion than for the pitching one. The effects of surface grit roughness on the pressure signature for both types of motion were also investigated. Applying the surface roughness near the leading edge affected the performance of the airfoil significantly. Copyright © 2008 John Wiley & Sons, Ltd.
In many engineering applications (e.g. helicopters, turbines, compressors), lifting surfaces experience unsteady motion or are perturbed by unsteady incoming flows. Horizontal axis wind turbine rotors experience large time dependent variations in angle-of-attack as a result of control input angles, blade flapping, structural response and wake inflow. In addition, the blade sections encounter substantial periodic variations in local velocity and sweep angle. Thus, the unsteady aerodynamic behaviour of the blade sections must be properly understood to enable accurate predictions of the air loads and aero elastic response of the rotor system.
A series of experiments were carried out to investigate unsteady behavior of the flow field as well as the boundary layer of an airfoil oscillating in plunging‐type motion in a subsonic wind tunnel. The measurements involved surface‐mounted hot films complimented with surface pressure. In addition, wind tunnel wall pressure distribution was acquired to furnish a baseline for the wall interference corrections. The airfoil is the section of a 660‐kW wind turbine blade. The experiments were conducted at a Reynolds number of 0.42 million, and over two reduced frequencies of k = 0.06 and 0.085, at prestall, nearstall, and poststall regions. The unsteady aerodynamic loads were calculated from the surface pressure measurements, 64 ports, along the chord for both upper and lower surfaces of the model. The plunging displacements were transformed into the equivalent angle of attack. The surface hot‐film measurements provided information about the boundary‐layer events. The boundary‐layer transition occurred via a laminar separation bubble. Variations of the surface pressure coefficients and aerodynamic loads with the equivalent angle of attack showed strong sensitivity to the reduced frequency and the mean angles of attack. The wall pressure distribution was affected by the model oscillation especially the region underneath the model.
This is an experimental study on the boundary layer over an airfoil under steady and unsteady conditions. It specifically deals with the effect of plunging oscillation on the laminar/turbulent characteristics of the boundary layer. The wind tunnel measurements involved surfacemounted hot-film sensors and boundary-layer rake. The experiments were conducted at Reynolds numbers of 0.42×10 6 to 0.84 × 10 6 and the reduced frequency was varied from 0.01 to 0.11. The results of the quasi-wall-shear stress as well as the boundary layer velocity profiles provided important information about the state of the boundary layer over the suction surface of the airfoil in both static and dynamic cases. For the static tests, boundary layer transition occurred through a laminar separation bubble. By increasing the angle of attack, disturbances and the transition location moved toward the leading edge. For the dynamic tests, earlier transition occurred with increasing rather than decreasing effective angle of attack. The mean angle of attack and the oscillating parameters significantly affected the state of the boundary layer. By increasing the reduced frequency, the boundary layer transition was promoted to the upstroke portion of the equivalent angle of attack, but the quasi skin friction coefficient was decreased. NomenclatureA Amplitude of the plunging motion (cm) C f Skin friction coefficient E Hot-film output voltage (V)
In this study, we applied the homotopy perturbation (HP) method for solving linear and nonlinear fourth-order boundary value problems. The analytical results of the boundary value problems have been obtained in terms of a convergent series with easily computable components. Comparisons between the results of the HP method and the analytical solution showed that this method gives very precise results with a few terms. In the implied HP method, some unknown parameters in the initial guess are introduced, which are identified after applying boundary conditions. This improvement results in higher accuracy.
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