Improved Dynamic-Stall-Onset Criterion at Low Mach Numbers

cN = normal force coefficient, N=qc cp = pressure coefficient, p=q D = drag f = dimensionless separation point in terms of chord length, x=c L = lift of airfoil section M = Mach number m = pitching moment about the axis of the quarter-chord N = normal force q = dynamic pressure, 0:5 V r = reduced pitch rate, _ c=2V (for oscillatory motion of an airfoil, 0 cos!t) r0 = reduced pitch rate that delimits the dynamic stall and quasi-steady stall (normally, 0:01) s = nondimensional time, 2Vt=c T = time-delay constant for angle of attack t = time V = freestream velocity = angle of attack or incidence 0 = lagged angle of attack cr = critical onset angle (dependent on reduced pitch rate) ds = angle of dynamic-stall onset ds0 = constant critical onset angle ss = static stall angle = a step change in a sampled system 0 = amplitude of airfoil oscillation k = reduced frequency, !c=2V = linear fit coefficient for stall-onset incidences ! = frequency of oscillatory motion of airfoils Introduction