Experimental Validation of a Cascade Response Function For Fan Broadband Noise Predictions

B = number of vanes c = vane chord length Ci = cascade i, i 1 (B 49) or i 2 (B 98) c0 = speed of sound Em; = duct eigenfunction of the mode m; exd = unit vector in the axial direction of the duct f = frequency H i m x = Hankel function of kind i of order m Kd = vector of wave numbers in the duct reference frame Kx = streamwise aerodynamic wave number, !=Uxd kxd0 ; kzd0 = axial and radial wave numbers of the excitation in the duct reference frame, Kd0 Kd kzc0 = spanwise wave number in the cascade reference frame, Q Kd0j3 k0 = acoustic wave number, !=c0 k x;m ;d = axial wave number of the duct mode m; k x;m ;cd r = axial wave number of the duct mode m; in the cascade frame before the rotation of sweep angle Li = measured acoustic power with a turbulence grid installed (i mes) and with no grid (i 0) lr ! = spanwise correlation length Mxd = axial Mach number, Uxd=c0 m; = azimuthal and radial orders of a duct mode mg = azimuthal order of an incident turbulent component nc = unit vector normal to the blade Q = transformation matrix from duct to cascade reference frame, Qij Rc = reference frame attached to the rectilinear cascade at the radius r after rotation of stagger, lean, and sweep angle Rcd = reference frame attached to the rectilinear cascade at the radius r after rotation of stagger and lean angle Rd = stationary duct reference frame RH = hub radius Rm = mean radius at midspan, RT RH =2 RT = tip radius r = current radius St = Strouhal number, fRT=Uxd Ti = turbulence grid i, i 1 (Tu 3%) or i 2 (Tu 5:5%) Tu r = local turbulent intensity at radius r, urms r =Ux r t = time Ux r = measured axial mean flow velocity at radius r Uxd = nominal value of the axial mean flow velocity at midspan u = fluctuating velocity vector in the duct stationary reference frame u = streamwise velocity fluctuation urms = root-mean-square value of the streamwise velocity fluctuation, u p