Experimental Investigation of Unsteady Aerodynamics and Aeroacoustics of a Thin Airfoil

Abstract

An experimental investigation of the unsteady problem for a thin, symmetric airfoil exposed to periodic gusting was performed in a free-jet anechoic wind-tunnel facility. The gusting events were created upstream such that there was a small longitudinal, i.e., spanwise, wave number and the gust could be approximated as two dimensional. Measurements of the unsteady velocity eld, the unsteady pressure at the airfoil surface, and the acoustic eld were made for two values of axial and normal reduced frequency. The unsteady pressure distributionalong the airfoil was computed using the Sears method and unsteady velocity data. In addition, the pressure distribution was computed using acoustic data as input to a numerical inversion technique. The results of each technique were compared with the experimentally obtained unsteady pressure distribution. The inversion technique showed good agreement with the Sears method. However, comparison with experimental results illustrated that the theoretical estimates, although exhibitingtrends similar to the experimental data, consistently underestimated the experimental unsteady pressure distribution at the lower reduced frequency, indicating the presence of viscous effects. Better agreement between experimental and theoretical results was obtained at the higher reduced frequency where viscous effects were less prominent. Nomenclature a = gust velocity vector C p 0 = unsteady pressure coef cient, p 0 =½a 2 U 1 c = airfoil chord f k = single discrete value within the frequency range of spectral analysis f RPF = primary rod passage frequency H .2/ v = vth-order Hankel function of the second kind K = Helmholtz operator k = wave number vector M 1 = freestream Mach number m = harmonic (mode) number P. y/ = acoustic pressure measured at observation location S.k 1 / = Sears function U .t / = axial velocity component U.x; t / = total velocity eld U D = velocity de cit in stationary frame U G = gust velocity vector U m = velocity de cit in wake behind the rod U R = rotational velocity of rod U 0 = relative velocity seen by rotating rod U 1 = freestream velocity vector u.x; t / = unsteady portion of velocity eld u a .x; t / = acoustic portion of unsteady velocity u 1 .x; t / = rotational portion of unsteady velocity V .t / = normal velocity component x = source position vector y = acoustic eld observation position vector 1p 0 .x ¤ 1 ; k ¤ 1 / = unsteady pressure jump on airfoil ½ = density of air ! = gust frequency

Leading Edge Surface Pressures from Airfoils in a Turbulent Flow

“…This makes it likely that at high frequencies where the foil thickness reduces the magnitude of the dipole force, the incident pressures will dominate the near field components of the diffracted pressures. Minniti and Mueller (1998) In the current paper, cross specfral measurements of the surface pressures near the leading edges of the foils are used to distinguish between confributions to the measured total surface pressure field from the incident surface pressures and the surface pressures due to the near field component of the diffracted pressures. Since the normalized wave number spectrum of the up-wash velocity, ^(fe), does not couple directly to the diffracted pressures, it is anticipated that the cross spectrum of these pressures from measurements on opposite sides of the foil would not be a ftinction of the correlation coefficient of the up-wash velocity, 72(r2), in the thickness direction, r2, where -00…”