
AN EFFICIENT AND ROBUST METHOD FOR PREDICTING
HELICOPTER ROTOR HIGHSPEED IMPULSIVE NOISE
Kenneth S. Brentner?
NASA Langley Research Center
Hampton, Virginia
Abstract
A new formulation for the Ffowcs Williams{ Hawkings quadrupole source, which is valid for a farfield inplane observer, is presented. The farfield approximation is new and unique in that no further approximation of the quadrupole source strength is made and integrands with r?2 and r?3 dependence are retained. This paper focuses on the development of a retardedtime formulation in which time derivatives are analytically taken inside the integrals to avoid unnecessary computational work when the observer moves with the rotor. The new quadrupole formulation is similar to Farassat's thickness and loading formulation 1A. Quadrupole noise prediction is carried out in two parts: a preprocessing stage in which the previously computed flow field is integrated in the direction normal to the rotor disk, and a noise computation stage in which quadrupole surface integrals are evaluated for a particular observer position. Preliminary predictions for hover and forward flight agree well with experimental data. The method is robust and requires computer resources comparable to thickness and loading noise prediction.
Notation
2 wave operator
c sound speed in undisturbed medium
d? element of the collapsingsphere surface
dS element of the rotorblade surface
f = function that describes the rotorblade
surface
f+ = surface described by union of rotorblade
surface and rotor disk
?Research Engineer, Aerodynamic and Acoustics Methods Branch, Fluid Mechanics and Acoustics Division, Senior Member AIAA.
Copyright c 1996 by the American Institute of Aeronautics and Astronautics, Inc. No copyright is asserted in the United States under Title 17, U.S. Code. The U.S. Government has a royaltyfree license to exercise all rights under the copyright claimed herein for government purposes. All other rights are reserved by the copyright owner.
g = surface that describes the collapsing sphere,
g = o ? t + r=c
H(f) Heaviside function
li local force that acts on body
~M local velocity vector of source normalized by
c, with components Mi
_Mi @Mi=@o
Mr Mach number of source in radiation
direction, Mi^ri
_Mr _Mi ^ri
?Mr ?Mi ^ri
MAT advancing tip Mach number
MH hover tip Mach number
^n unit outward normal vector to surface, with
components ^ni
p0 acoustic pressure, p ? po
Qij quadrupole surface source tensor, symmetric
QMM QijMiMj
QMr QijMi^rj
Q _M r Qij _Mi^rj
Qrr Qij^ri^rj
_QMr _Qij Mi^rj
_Qrr _Qij ^ri^rj
?Qrr ?Qij ^ri^rj
r distance between observer and source,
r = j~x ? ~yj
^r unit vector in the radiation direction, with
components ^ri
R rotor radii
t observer time
Tij Lighthill stress tensor, aeuiuj + (p0 ? c2oae0)ffiij
(inviscid form)
vn local normal velocity of source surface
~x observer position vector, with components xi
~y source position vector, with components yi
Greek symbols:
? intersection of collapsing sphere g = 0, and
source surface f = ffi (f) Dirac delta function
? angle between ^n and ^r
aeo density of undisturbed medium