Prediction of Hovering Rotor Noise Based on Reynolds-Averaged Navier-Stokes Simulation

Abstract

O VER the past decade, the hybrid method [coupling computational fluid dynamics (CFD) techniques with advanced analytic methods based on acoustic analogy, such as the Ffowcs Williams–Hawkings equation with penetrable data surface (FW–Hpds) method] has been successfully applied to predict the complicated acoustic field of helicopter rotors. The Ffowcs Williams–Hawkings (FW–H) equation [1], a rearrangement of Navier–Stokes equations by using generalfunction theory, provides an accurate theoretical model for describing the propagation of noise from a moving surface to the far field. The Farassat 1Amethod for solving the linear part of the FW–H equation was developed by Farassat and Succi [2]. It has been successfully applied in linear noise prediction [2,3] for more than 20 years. The Farassat 1A method predicts discrete frequency noise quite well, but it would run into complication when predicting nonlinear quadrupole noise of helicopter rotors, because the data surface is the blade itself and nonlinear effects are not included in the surface integral. To calculate the nonlinear noise [e.g., high-speed impulsive (HSI) noise], Farassat and Myers [4] derived the general form of the Kirchhoff equation and its solution (known as the Kirchhoff formulation) to describe the noise radiation from amoving surface. The data surface of the Kirchhoff formulation is fictitious and penetrable. The main benefit of the Kirchhoff method is that the nonlinear effect is accounted for by performing the integral on the data surface covering the nonlinear flow region. The Kirchhoff method coupled with the near-field CFD solution (called the CFD/ Kirchhoff method) has proven to be accurate and efficient when predicting impulsive noise. More recently, a new form of FW–H equation with a penetrable surface (called the FW–Hpds equation) was proposed by Crighton et al. [5] to improve the efficiency of solving the quadrupole noise. The method using a penetrable data surface for solving the FW–H equation with the Euler solution as input data was first implemented by di Francescantonio [6] for prediction of far-field noise from transonic helicopter rotors in hover. Brentner and Farassat [7] conducted an analytical comparison of the FW–Hpds method with the Kirchhoff method and concluded that the FW–Hpds method is more accurate and robust than the Kirchhoff method when the data surface is located in the nonlinear flow region. The FW–Hpds method rapidly showed promise in the studywork of a few researchers [7–10] when it was used for predicting the noise generated by helicopter rotors in hover and forward flight. More recently, Farassat and Casper [11] emphasized the role of analytical methods in computational aeroacoustics and recommended FW–Hpds as a very promising method for noise prediction of a complicated flowfield. To predict nonlinear noise generated by transonic rotors in hover, three-dimensional Euler equations were commonly used to consider the nonlinear effect related to shockwaves. To consider the influence of viscous effect in the near field and get more accurate information about noise sources, this paper uses Reynolds-Averaged Navier– Stokes (RANS) equations to model the nonlinear viscous flowfield near the rotor blades. The far-field noise is calculated by a retardedtime integral formula solving the FW–Hpds equation, with the solution of the RANS equations taken as input data.