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

Dynamic stall is an incredibly rich fluid dynamics problem that manifests itself on an airfoil during rapid, transient motion in which the angle of incidence surpasses the static stall limit. It is an important element of many manmade and natural flyers, including helicopters and supermaneuverable aircraft, and low–Reynolds number flapping-wing birds and insects. The fluid dynamic attributes that accompany dynamic stall include an eruption of vorticity that organizes into a well-defined dynamic stall vortex and massive excursions in aerodynamic loads that can couple with the airfoil structural dynamics. The dynamic stall process is highly sensitive to surface roughness that can influence turbulent transition and to local compressibility effects that occur at free-stream Mach numbers that are otherwise incompressible. Under some conditions, dynamic stall can result in negative aerodynamic damping that leads to limit-cycle growth of structural vibrations and rapid mechanical failure. The mechanisms leading to negative damping have been a principal interest of recent experiments and analysis. Computational fluid dynamic simulations and low-order models have not been good predictors so far. Large-eddy simulation could be a viable approach although it remains computationally intensive. The topic is technologically important owing to the desire to develop next-generation rotorcraft that employ adaptive rotor dynamic stall control.

Dynamic Stall in Pitching Airfoils: Aerodynamic Damping and Compressibility Effects

The inspiring review oflaminar separation by Brown & Stewartson (1969) begins thus: "The phenomenon of separation is one of the most interesting features of the motion of an incompressible fluid past a bluff body at high Reynolds number. Here the main stream, which has hitherto been in close contact with the body, suddenly, and for no obvious reason, breaks away, and downstream a region of eddying flow, which is usually turbulent even if the flow elsewhere is laminar, is set up." These opening lines-which were followed by the above authors' brilliant and timely discourse emphasizing the difficulties associated with separation in classical boundary layers­ make an apt beginning for the present article on the current state of the art. The main feature, to which Brown & Stewarts on in fact alluded strongly, is that given the failure [due to singularities of the S. Goldstein (1948) type] in classical theory at separation, a fresh nonclassical start is necessary for high-Reynolds-number theory to encompass separating flow. This start was made by Stewartson & Williams (1969), Neiland (1969), and Messiter (1970). Our aim is to go from the significant advances made since 1969 to the recent developments and the possible areas of progress in the near future for the rational theory 'of steady and unsteady separation. The physical and theoretical understanding that can emerge from the study of flow structures at large characteristic Reynolds numbers Re is valuable for many reasons. Three major ones are the helpful comparisons with experiments and numerical results, the foundation such study gives to

Steady and Unsteady Boundary-Layer Separation

The breakdown and separation or reattachment of boundary layers adjoining a mainstream are studied in the three related situations (i)-(iii) of the title. For (i) the classical steady boundary laye...

Breakdown of boundary layers: (i) on moving surfaces; (ii) in semi-similar unsteady flow; (iii) in fully unsteady flow

Delta wings in steady flow can provide high lift at large angles of attack and are therefore used on many highperformance aircrafts. However, the unsteady aerodynamic properties of a delta wing are practically unknown, although vital for operating and designing airplanes for poststall and other maneuvering. In this study, the flowfields around two pitching delta wings with apex angles of 90 and 60 deg were visualized in a towing tank at chord Reynolds numbers up to 3.5 xlO. The reduced frequency was varied in the range 0.05-3. The leadingedge separation vortex went through a growth-decay cycle with hysteresis during a pitching period. A distinct change of the separated flow was observed at a reduced frequency around ir.

K. W. McAlister

Papers

Water Tunnel Visualizations of Dynamic Stall