Abstract
This work presents an experimental validation study of Isaacs’ incompressible unsteady-airfoil theory at Reynolds numbers above $10^{6}$ , and explores the validity of the classical Kutta condition applied to surging flows. Harmonic variation of the free-stream velocity was produced by rotating choke vanes in an unsteady transonic wind tunnel, with time-resolved lift coefficients determined from surface pressure measurements on a NACA 0018 airfoil. Unsteady lift results demonstrate the same trends with reduced frequency and velocity amplitude ratio that are predicted by Isaacs’ theory. However, significant deviations of the lift magnitude and phase angle are observed. In order to understand the cause of these deviations, the background-oriented schlieren technique was used to visualize density gradients in the immediate vicinity of the airfoil trailing edge. The time-resolved background-oriented schlieren displacement field indicates oscillatory behaviour of the trailing-edge stagnation streakline, which violates the classical Kutta condition for this unsteady surging flow.
Highlights
Introduction and backgroundFluctuating forces and moments on an airfoil immersed in a surging flow are commonly encountered on helicopters in forward flight and on horizontal-axis wind turbines rotating through a vertical velocity gradient
This work was performed in the Ohio State University (OSU) Unsteady Transonic Wind Tunnel, which is a blowdown-type facility capable of oscillating the airfoil pitch α and modulating the free-stream Mach number M∞, either independently or synchronously
The present findings show that the violation of the classical Kutta condition produces a non-negligible impact on Cl(t), where movement of the trailing-edge stagnation point dominates Isaacs’ effect of induced upwash or downwash from shed vorticity
Summary
Fluctuating forces and moments on an airfoil immersed in a surging flow are commonly encountered on helicopters in forward flight and on horizontal-axis wind turbines rotating through a vertical velocity gradient. An airfoil section at a given spanwise location (r) on a helicopter rotor blade will encounter fluctuations of the local velocity. In the blade frame of reference, the airfoil experiences a steady component of velocity due to the rotational speed of the blade (Ω) along with a sinusoidal component due to the forward flight speed of the helicopter (U∞), expressed as U(r, t) = Ωr + U∞ sin(Ωt). In order to develop effective design 893 R2-1. W. Gregory tools, reduced-order models of sufficient accuracy are required for modelling the time-varying forces and moments acting on the airfoil
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