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

An experiment has been performed to study the aerodynamics of dynamic stall penetration at constant pitch rate and high Reynolds number, in an attempt to model more accurately conditions during aircraft poststall maneuvers and during helicopter high-speed forward flight. An airfoil was oscillated at pitch rates, A = ac/2U between 0.001 and 0.020, Mach numbers between 0.2 and 0.4, and Reynolds numbers between 2-4 x 10. Surface pressures were measured using 72 miniature transducers, and the locations of transition and separation were determined using 8 surface hot-film gages. The results demonstrate the influence of the leading-edge vorticity on the unsteady aerodynamic response during and after stall. The vortex is strengthened by increasing the pitch rate and is weakened by increasing the Mach number and by starting the motion close to the steady-state stall angle. A periodic pressure oscillation occurred after stall at high pitch angle and moderate Reynolds number; the oscillation frequency was close to that predicted for a von Karman vortex street. A small supersonic zone near the leading edge at M = 0.4 was found to reduce significantly the peak suction pressures and the unsteady increments to the airloads. These results provide the first known data base of constant-pitch-rate aerodynamic information at realistic combinations of Reynolds and Mach numbers.

Airfoil dynamic stall at constant pitch rate and high Reynolds number

A computational study is presented for the dynamic stall of an airfoil that is pitched at a constant rate from zero incidence to a high angle of attack. The unsteady flow is simulated employing the mass-averaged NavierStokes equations and an algebraic turbulent eddy viscosity model. The approach is first validated by comparison of computed and experimental results for a pitching airfoil at low freestream Mach numbers. The computed dynamic stall events, as well as the computed effects of pitch rate and axis location, are found in qualitative agreement with experimental observations. The effect of compressibility on dynamic stall is investigated. As the freestream Mach number increases, the appearance of a supersonic region provides—through the shock/boundarylayer interaction—an additional mechanism in the dynamic stall process. The main effects of compressibility are found to be 1) a change from trailing-edge stall to leading-edge stall and 2) a reduction in the stall delay and in the attained maximum lift.

Dynamic stall of a constant-rate pitching airfoil

The onset of unsteady separation and dynamic stall vortex formation over a constant-rate pitching airfoil is analyzed by means of high-fidelity large-eddy simulations. The flowfields are computed b...

G. M. Graham

Papers

Force coefficients for a NACA-0015 airfoil undergoing constant pitchrate motions