P = nondimensional scaled disturbance pressure, //. (P PO)lAP060e"/) A new methodology0has been developed to predict the P0 = atmospheric pressure, N/M 2 impulsive noise generated by a transonic rotor blade. The r = dimensional distance along the rotor in the formulation uses a full-potential finite-difference method to spanwise direction, m obtain the pressure field close to the blade. A Kirchhoff R = radial distance to the rotor tip, m integral formulation is then used to extend these finite. R. = free stream subtraction term in Eqn. (5) difference results into the far-field. This Kirchhoff foumula, = nondimensional time in nontransformed coordiie written in a blade-fixed coordinate system, 4]6requires nate system initial data across a plane at the sonic radius. This data = dimensinal time,a is provided by the finite-difference soluti,ia. Acoustic pressure predictions show excellent agreement with hover experT = scaled azimuthal angle location, imental data for two hover cases of 0.88 and 0.90 tip Mach (1/0)(0 + 0 tan ' 3) number, The latter of which has delocalized transonic flow. U = contravariant velocity normal to the n/, C plane These results represent the first successful prediction techV = contravariant velocity normal to the f, C plane nique for peak pressure amplitudes using a computational V, = nondimensional scaled radial velocity compocode. nent, #,/wRe LIST OF SYMBOLS W = contravariant velocity normal to the e,v/ plane z, y, = nondimensional coordinate system aligned with ao = atmospheric speed of sound, m/a the blade C = rotor chord length, m ( = blade radial location, 1((1) 11/2 h = nondimensional time step = P2 I = identity matrix = inverse of the blade aspect ratio, e/R J = Jacobian of coordinate transform matrix "y = specific heat ratio M = hover tip Mach number r = jump in potential across the wake normalized * = local Mach number by (aoc) p = absolute pressure, N/m 2 w = blade angular speed, rad/a * = dimensional velocity potential, m /3 Presented at the AHS Specialists' Meeting on Aero= non-dimensional velocity potential, 0/cao dynamics and Aeroacoustics, Arlington, Texas, February P = fluid density normalized by free-stream values 25-27, 1987. This is a work of the U. S. Government and is therefore P = p/J in the public domain. P0 = atmospheric density, kg/m 3

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@inproceedings{RogerCfUPYN0, title={CfUPY N 0 PREDICTION OF HIGH - SPEED ROTOR NOISE WITH A KIRCHHOFF}, author={Roger and Strawn and Yung Hoon Yu and Aeroflightdynamics Directorate} }