Rotor noise due to atmospheric turbulence ingestion. I - Fluid mechanics

Abstract

An analysis has been developed to predict helicopter rotor noise due to ingestion of turbulence. The method incorporates an upstream isotropic turbulence model and a (rapid distortion) turbulence contraction description to determine the statistics of the anisotropic turbulence at the rotor plane. Ah important feature of the contraction process is the differential drift of fluid particles on adjacent streamlines, which leads to tipping and stretching of the vortex filaments associated with the turbulence. The analysis is applied to a main rotor operating in atmospheric turbulence. For mean-flow contraction ratios representative of hover and low-speed forward flight and vertical ascent, computations are carried out to show that accurate prediction of the vorticity components and hence nonisotropic turbulence at the rotor face requires accounting for this differential drift. A companion paper, 1 presented as Part II, describes the rotor acoustic model and the resulting atmospheric turbulence ingestion noise prediction based on the method. Although the predictions in both papers are limited to atmospheric turbulence, the method is applicable to isotropic upstream turbulence fields undergoing generalized distortions. NomenclatureC T = rotor thrust coefficient = T/picR 2 (QR ) 2 e -unit vector along one of the three upstream or downstream axes E(k) = wave-number energy spectrum g = gravitational acceleration k -wave number k = wave vector of turbulence L £ = integral length scale n = direction of the principle normal to the streamline q,Q = velocity field and magnitude of a Fourier component of turbulence R = rotor radius T = thrust u -turbulence fluctuation U = local time mean velocity C/oo = mean horizontal freestream velocity FOO = mean vertical freestream velocity .___ VQ = rotor-induced velocity = C T QR /2V\ 2 + /x 2 v___ = vertical turbulence fluctuations Vt^/C/oo = rms turbulence intensity x t = upstream Cartesian coordinate system, / = 1,2,3 X = vector location Z = height above ground a = rotor tip path plane angle of attack eyk = alternating tensor X = wavelength of Fourier component of turbulence, or rotor inflow ratio = (£/« sina-= rotor advance ratio = U^ cosa/(tiR) = downstream Cartesian coordinate system = density = wake skew angle = tan" 1 x [-I/. cosa/(£/oo sine*-V Q )\ = rotation rate = vorticity field and magnitude of a Fourier component of turbulence [see Eq. (6)] ij f k = specify either a vector (such as one of the vectors £1, ^2, £3) or a 1 , 2, 3 component of a vector (such as the first Cartesian component of the vector e 2 ) Superscripts U,D = upstream or downstream location, respectively

Rapid distortion theory of turbulent flow around a porous cylinder

“…Simonich et al. (1990) evaluated the vorticity deformation caused by the mean flow in the case of a helicopter rotor in order to investigate the noise radiated due to inflow turbulence. Similarly, Majumdar & Peake (1998) developed an analytical model for the prediction of the unsteady distortion noise generated by the interaction of turbulence with a multi-bladed fan rotor.…”

Noise generation by turbulence–propeller interaction in asymmetric flow

“…In a pair of papers Simonich et al 1990), a full UDN prediction method was set out in the context of a helicopter rotor. This involved the solution of a series of model problems, to calculate:…”

Noise generation by the interaction between ingested turbulence and a rotating fan

“…Ganz represented the turbulent field by a statistical distribution of distortion elements and, using two-dimensional blade loading theory for single airfoils, the forces on the fan and scattered sound were calculated. The most comprehensive analytical study involving unsteady distortion theory was performed by Simonich et al (1986Simonich et al ( , 1990 who applied rapid distortion theory to evaluate the noise generated by a helicopter rotor. Using an isotropic turbulence model in the free stream, Simonich et al analysed the evolution of the turbulence as it travels along the contracting flow towards the rotor, under several typical helicopter operating conditions.…”