Nomenclature c = chord CD =drag coefficient, D/qA CL =lift coefficient, L/qa CP = pressure coefficient, P-PW /q CM = pitching-moment coefficient, M/qA D =drag, Ib k = reduced frequency, wc/2U L =lift, Ib M =Mach number; pitching moment, ft-lb P = pressure, lb/in q = dynamic pressure, 1 /2p U R, Re, Re, Rn = Reynolds number t time U,V = freestream velocity, ft/s x = distance a = angle of attack, deg f =nondimensional chord length, x/c $tr transition location co = rotational frequency, rad/s p = density, lb/ft A = sweep angle, deg

Progress in analysis and prediction of dynamic stall

Mathematical modeling of unsteady aerodynamic forces and moments plays an important role in aircraft dynamics investigation and stability analysis at high angles of attack. In this article the state-space representation of aerodynamic forces and moments for unsteady aircraft motion is proposed. Consideration of separated flow about an airfoil and flow with vortex breakdown about a slender delta wing gives the base for mathematical modeling using internal variables describing the flow state. Coordinates of separation points or vortex breakdown can be taken, e.g., as internal state-space variables. These variables are governed by some differential equations. Within the framework of the proposed mathematical model it is possible to achieve good agreement with different experimental data obtained in water and wind tunnels. These high angle-of-attack experimental results demonstrate considerable dependence of aerodynamic loads on motion time history.

State-Space Representation of Aerodynamic Characteristics of an Aircraft at High Angles of Attack

The general features of dynamic stall on oscillating airfoils are explained in terms of the vortex shedding phenomenon, and the important differences between static stall, light dynamic stall, and deep stall are described. An overview of experimentation and prediction techniques is given.

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The phenomenon of dynamic stall

Computational prediction of airfoil dynamic stall

: The dynamic stall characteristics of eight airfoils have been investigated in sinusoidal pitch oscillations over a wide range of two-dimensional unsteady flow conditions. The results provide a unique comparison of the effects of section geometry in a simulated rotor environment. Important differences between the various airfoils were observed, particularly when the stall regimes were penetrated only slightly. Under these circumstances, the profiles that stall gradually from the trailing edge appear to offer an advantage. However, all of the airfoils tended increasingly toward leading-edge stall when both the severity of dynamic stall and the free-stream Mach number increased. In all cases, the parameters of the unsteady motion appear to be more important than airfoil geometry for configurations that are appropriate for helicopter rotors. (Author)

Dynamic Stall on Advanced Airfoil Sections

Unsteady airfoil stall in incompressible flow, including pitch rate induced accelerated flow effect on leading edge and trailing edge stall

Unsteady Airfoil Stall, Review and Extension

Terminal shock-boundary layer interaction on slender cone-cylinder payloads at supersonic speeds and resulting flow separation

Aeroelastic instability caused by slender payloads.

An earlier developed engineering analysis of dynamic stall is reviewed in light of recent numerical and experimental results. It is found that the concept of equivalence between boundary-layer improvement due to piich-rate-induced effects and increasing Reynolds number is supported by the available numerical and experimental results. The existence of the postulated plunging-induced improvement of the boundary layer and associated delay of stall, the controversial "leading-edge jet'* effect, is indicated by oscillatory stall data for different oscillation centers and by the measured negative aerodynamic damping for plunging oscillations in the stall region. More work is needed before the dynamic stall characteristics can be predicted for high frequencies. Until then, the present technique offers a reliable means for prediction of low-frequency (d)<0.5) dynamic stall characteristics from static experimental data.

Dynamic Stall Analysis in Light of Recent Numerical and Experimental Results

A previously developed quasisteady analytic method has been shown to give predictions that are in good agreement with experimental stall results as long as the oscillation amplitude and frequency are of moderate magnitudes. In the present paper, this quasisteady method is extended to include the transient effect of the "spilled" leading-edge vortex, thereby providing simple analytic means for prediction of dynamic stall characteristics at high frequency and large amplitudes. The veracity of the method is demonstrated by critical comparisons with the extensive experiments performed by Carr et al. c Ka / m

Dynamic Stall at High Frequency and Large Amplitude

The effect of boundary-laye r transition on vehicle dynamics is a well known, but poorly understood, phenomenon. Severe loss of dynamic stability has been observed to result on ablating vehicles when boundary-layer transition moves up over the base onto the aft body. This effect is caused by the increased (turbulent) aft body heating, and is equivalent to changing to a coating with higher ablation rate on the aft body. Another more subtle effect of boundary-layer transition results from the transition sensitivity to body attitude. Dynamic tests of nonablating slender cones have shown that increased damping and decreased static stability results when boundary-layer transition occurs on the aft body. An analysis using previously developed unsteady concepts for separated flow correctly predicts the relation between dynamic and static effects of boundary-layer transition. The dynamic amplification of static effects is twice as large for sharp as for blunted cones because of oscillatory flow acceleration effects on the sharp cone boundary-layer transition. It is found that the boundary-layer transition sensitivity to body attitude has beneficial effects on the vehicle dynamics up to high supersonic speeds. However, at hypersonic speeds nose-bluntness-induced entropy swallowing may cancel and even reverse this trend, greatly aggravating the undamping effect of turbulent aft body (heating and) ablation.

Lars E. Ericsson

Papers

Unsteady Airfoil Stall, Review and Extension

Aeroelastic instability caused by slender payloads.

Dynamic Stall Analysis in Light of Recent Numerical and Experimental Results

Dynamic Stall at High Frequency and Large Amplitude

Effect of boundary-layer transition on vehicle dynamics