A numerical study is presented for unsteady laminar flow past a NACA 0015 airfoil that is pitched, at a nominally constant rate, from zero incidence to a very high angle of attack. The flowfield simulation is obtained by solving the full two-dimensional compressible Navier-Stokes equations on a moving grid employing an implicit approximate-factorization algorithm. An evaluation of the accuracy of the computed solutions is presented, and the numerical results are shown to be of sufficient quality to merit physical interpretation. The highly unsteady flowfield structure is described and is found to be in qualitative agreement with available experimental observations. A discussion is provided for the effects of pitch rate and pitch axis location on the induced vortical structures and on the airfoil aerodynamic forces.

Investigation of the flow structure around a rapidly pitching airfoil

Experimental studies of the flow topology, leading-edge vortex dynamics and unsteady force produced by pitching and plunging flat-plate aerofoils in forward flight at Reynolds numbers in the range 5000–20 000 are described. We consider the effects of varying frequency and plunge amplitude for the same effective angle-of-attack time history. The effective angle-of-attack history is a sinusoidal oscillation in the range to with mean of and amplitude of . The reduced frequency is varied in the range 0.314–1.0 and the Strouhal number range is 0.10–0.48. Results show that for constant effective angle of attack, the flow evolution is independent of Strouhal number, and as the reduced frequency is increased the leading-edge vortex (LEV) separates later in phase during the downstroke. The LEV trajectory, circulation and area are reported. It is shown that the effective angle of attack and reduced frequency determine the flow evolution, and the Strouhal number is the main parameter determining the aerodynamic force acting on the aerofoil. At low Strouhal numbers, the lift coefficient is proportional to the effective angle of attack, indicating the validity of the quasi-steady approximation. Large values of force coefficients () are measured at high Strouhal number. The measurement results are compared with linear potential flow theory and found to be in reasonable agreement. During the downstroke, when the LEV is present, better agreement is found when the wake effect is ignored for both the lift and drag coefficients.

Unsteady force generation and vortex dynamics of pitching and plunging aerofoils

Nomenclature AR = aspect ratio; amplitude ratio B = probability density function of velocity c = root chord length f = frequency k = reduced frequency; axial wave number n =w ave number in angular direction P = probability p = pressure fluctuation Re =R eynolds number based on chord length S = spectral density s = local semispan T = period t = time U∞ = freestream velocity u = axial velocity v = swirl velocity x = streamwise distance xbd = breakdown location y = spanwise distance z =v ertical distance above wing surface α = angle of attack � = circulation δ = flap angle � = sweep angle ν = kinematic viscosity τ = time constant � =fi nangle ω =v orticity; radial frequency

Review of Unsteady Vortex Flows over Slender Delta Wings

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

Research into vortex breakdown control

FLOW visualization and near-surface hot-wire experiments were performed in the U.S.A.F Academy Aeronautics Laboratory subsonic wind tunnel on an airfoil undergoing large-amplitude pitching motions about its quarter chord. The experiments were conducted using a NACA 0015 airfoil at an airfoil Reynolds number of 45,000. Two cases are presented in which the angular pitching rate a is maintained constant during the motion. These two cases represent two different nondimensional pitching rates a+, where ot+ is equal to 6; nondimensionalized by the chord c and the freestream velocity U^ (a + ^ac/U^). Data for the two cases where values of a+ are equal to 0.2 and 0.6 show the dramatic effect of pitch rate on flow structure. Largescale vortical structures are seen in both cases at high angles of attack but appear much later and are of a different form for the case with the larger a+ value. These structures are very energetic, producing reverse flow velocities near the airfoil surface of 1.0-2.1 times the freestream velocity.

An Experimental Investigation of an Airfoil Undergoing Large-Amplitude Pitching Motions

This paper examines the effects of trailing-edge jet entrainment on the streamwise vortices over a delta wing. Although studies have examined the effects of leading-edge suction and blowing on the burst location of delta wing vortices, very little research has focused on the effects of trailing-edge jet exhaust on the burst location. Using a 60-deg delta wing model in a water tunnel with dye to mark the vortex core, it was possible to visualize how the location of the vortex breakdown changes with trailing-edge jet velocity. This research has determined that at moderate angles of attack it is possible to delay the burst location up to 18% of the chord by increasing the flow velocity from the exhaust ports. In addition, at higher angles of attack, the trailing-edge jets stabilized the asymmetric separated vortices by reattaching the flow and moving the burst location aft on the wing.

H. E. Helin

Papers

An Experimental Investigation of an Airfoil Undergoing Large-Amplitude Pitching Motions

Effects of trailing-edge jet entrainment on delta wing vortices

An experimental investigation of an airfoil undergoing large amplitude pitching motions