M.: Prediction of rod-airfoil interaction noise using the Ffowcs–Williams and Hawkings analogy

Soundgenerated at lowMachnumberby an airfoil in the wakeof a rod is investigatednumerically.TheGaussian spanwise loss of coherence of the vortex shedding is shown to have a signi cant in uence on the broadbandnoise. Spanwise effects are successfully introduced into a time-domain formulation of the Ffowcs-Williams–Hawkings analogy,which is applied to aerodynamicdata computed on various contours around the source region. It is shown that a careful choice of these contours is required. The ow eld is obtained from a two-dimensional Reynolds averaged Navier–Stokes calculation. Computed far- eld spectra compare very well to measurements obtained in an accompanying experiment. Nomenclature C p = pressure coef cient c = airfoil chord d = rod diameter f = frequency g = integration surface, 0 k = turbulent kinetic energy L g = Gaussian correlation length l = span length Mi = Mach number of gD 0 Moi = observerMach number vector Mref = referenceMach number M1 = in ow Mach number Oni = unit outward normal vector to gD 0 p, p1 = pressure and in ow pressure pd = reference dynamic pressure p0 = acoustic pressure qi = dimensionless relative ow momentum R = dimensionless observation distance r = observation distance Sr = Strouhal number u i = ow velocity; also.u; v/ Qu i = ow velocity relative to gD 0 Vi = dimensionless velocity of gD 0 V1 = in ow velocity X = dimensionless observer position Y = dimensionless source position w = Gaussian variance ´ = spanwise dimensionless co-ordinate µ = observation angle and dimensionless time ¸i, Âi = loading noise source terms = correlation coef cient 1 = in ow density Á = angular rod coordinate Q ’ = vortex shedding phas