Nomenclature C h C (t , C m = lift, drag, and moment coefficients C M = blowing coefficient, rhjVj/q^c c = chord M = Mach number rhj = mass flow rate of jet, pjSVj sin > q x = dynamic pressure, \pJJL Re ( = chord Reynolds number, U^clvŝ = slot width t + = nondimensional time, tUJc U^ = freestream velocity Vj = velocity of jet jc, y = coordinates of moving reference frame attached to airfoil a = angle of attack a h = onset angle of attack (blowing or suction) v = dynamic viscosity f, j] = transformed coordinates p = density 4> = jet blowing angle, 10 deg H + = nondimensional pitch rate, a>c/UÎ ntroduction A TTEMPTS have been made by numerous researchers toharness the large aerodynamic forces temporarily generated on a streamlined body rapidly pitched beyond its steady stall angle of attack. Dynamically pitched airfoils exhibit maximum lift coefficients two or three times the static maximum lift. 1 Uncontrolled, the ensuing unsteady motion results in dynamic stall. The dynamic stall phenomenon arises in several applications: wind turbine blades, helicopter rotor blades, jet engine compressor blades, and rapidly pitched airfoils. The current study compares and contrasts two approaches to dynamic stall suppression: 1) suction and 2) nearly tangential blowing, applied in the vicinity of the leading edge of a NACA 0015 airfoil.Dynamic stall suppression via leading-edge suction and leading-edge tangential blowing focuses on the removal of low momentum fluid that accumulates along the airfoil upper surface as it is pitched upward. Specifically, as the airfoil is pitched up, the adverse pressure gradient along the upper surface promotes the forward propagation of reverse-flowing fluid into the leading-edge region. The thickening of this low momentum fluid region near the leading edge ultimately forces an upward displacement and "kinking" of the feeding shear layer. The kinking of this shear layer marks the initial formation of the dynamic stall vortex. Suction experiments by Karim and Acharya 2 demonstrated that the key to dynamicstall-vortex-formation suppression is to remove fluid from underneath the leading-edge-originating shear layer at the same rate as the reverse-flowing-fluid-pooling accumulation rate. Results by Towne 3 verify their findings numerically and demonstrate that tangential blowing applied upstream and/or in this pooling region is also effective in eliminating the low momentum region, and hence, in delaying dynamic stall vortex (DSV) formation.The flow regime of interest is one of low speed and low Reynolds number. A compressible Navier-Stokes code developed by Visbal to numerically investigate dynamic stall 4 -5 is used. The nominal flow and pitch-rate conditions are M= 0.2, Re c = 2.4 x 10 4 , and H+ -0.2.
Numerical MethodologyThe strong conservation law form of the two-dimensional compressible Navier-Stokes equations are cast in an inertial frame of reference using a general time-dependent coordinate transformation to account for the motion of the body. Closure of the system is provided by the per...