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

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

An insight into the dynamic stall lift characteristics

: A straight wing having an NACA 0015 cross section and rectangular planform was attached to a circular splitter plate. This configuration was pitched at a constant rate to angles exceeding the static stall angel. The unsteady, vortex-dominated flow that developed over the wing and splitter plate was characterized in detail using surface pressure measurements and flow visualization. Both types of data showed that the leading-edge vortex underwent profound three-dimensional alterations to cross section and convection over the entire wing span. These changes in leading-edge vortex structure and kinematics were correlated with prominent spanwise variations in force coefficients. When appropriately dissected, visualization results and pressure data suggested physical mechanisms to account for these three-dimensional variations in unsteady forces and surface pressures.

Unsteady vortex dynamics and surface pressure topologies on a finite pitching wing

On the formation and control of the dynamic stall vortex on a pitching airfoil

: Surface pressure measurements were taken in an experimental investigation of energetic dynamic stall vortices. The associated unsteady flowfield was generated by a 6-in. NACA 0015 airfoil pitching at high rates to large angles of attack. The airfoil pitch rates varied from 230 deg/sec to 1380 deg/sec and angles of attack varied from zero degrees to 60 degrees. Pitching occurred about its quarter-chord axis. Pitch rate, Reynolds number, and the non- dimensional pitch rate, alpha plus, were varied to determine the effects on pressure and lift coefficients. It was found that increases in pitch rate and Reynolds number has inverse effects on the flowfield in the immediate vicinity of the airfoil. Maintenance of a constant non-dimensional pitch rate produced very similar flowfields and pressure coefficients.

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J. Walker

Papers

Unsteady Surface Pressure Measurements on a Pitching Airfoil