Aerodynamic Loads on Airfoil with Trailing-Edge Flap Pitching with Different Frequencies

Abstract

Unsteady aerodynamic loads on NACA 0012 airfoil with a trailing-edge flap were measured in wind tunnel and calculated from a simple theoretical model. The airfoil model of 0.18 m chord length used in wind-tunnel test was oscillating in pitch about an axis located at 35% chord length from the airfoil leading edge. The length of trailingedge flap was 22.6% of airfoil chord. The flap was also deflecting harmonically, but with frequency different from airfoil pitching motion. The influence of phase delay between airfoil angle of incidence and flap deflection at the beginning of the motion was considered. The theoretical method used for calculation of unsteady airfoil loads is based on two-dimensional, inviscid, incompressible flow model at subsonic Mach numbers. The expressions for unsteady aerodynamic loads calculations on the airfoil and on the flap were obtained in a closed form using distribution of flow velocity potential along the airfoil chord and along the flap length. Lift and aerodynamic moment measured in the wind tunnel were compared with results of calculations. The correlation between experimental and theoretical results is adequate. Nomenclature a ( )n , b ( )n = polynomials coefficients in approximation of the lift deficiency function ab = distance of the airfoil aerodynamic centre from the midchordposition of flap hinge relative to the midchord f = frequency of airfoil oscillations f δ = frequency of flap oscillations H (s) = polynomial N th order in the numerator of lift deficiency function approximation h(t) = plunge translation of airfoil K (s) = polynomial N th order in the denominator of lift deficiency function approximation k = reduced frequency, =(ωb)/U = (π f c)/U L ( ) = airfoil lift M = Mach number M h = flap hinge moment M ( ) = airfoil pitching moment N = order of approximation of lift deficiency function p = pressure Q(s) = forcing function in flow state equation for circulatory lift . Associate Fellow AIAA. R = radius of helicopter rotor Re = Reynolds number r = distance of the blade section from the rotor axis s = complex variable, = jω T ( ) = period of oscillations t = time U (t) = freestream velocity W (t, x) = velocity of airfoil in the x coordinate w(t, x) = flow velocity perpendicular to the airfoil surface w ( )i = Fourier series coefficients of velocity distribution along the chord; i = 0, 1, 2, 3 x = distance along the chord from the leading edge y ( ) (s) = state variable in differential equation for circulation part of the flow α(t) = airfoil angle of attack α 0 = mean airfoil angle of attack for harmonic motion γ ( )w = circulation in the wakē γ ( )w = complex amplitude of assumed periodic wake p = pressure difference between upper and lower airfoil surface t = time of angle phase lag α = amplitude of the airfoil angle of attack harmonic oscillations δ = amplitude of the flap angle of deflection harmonic oscillations = difference of velocity potential at the upper and the lower airfoil surfaces δ(t) = angle of flap deflection δ 0 = mean angle of flap deflection ξ = coordin...

Physically-based reduced order model for unsteady aerodynamic loads of a L-shaped Gurney flap

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