Numerical issues in the application of an amiet model for spanwise-varying incoming turbulence

The present paper investigates the possible application of Amiet’s theory in spanwise varying conditions. This study encompasses two different aspects. Firstly, all the parameters of the turbulent flow upstream of the airfoil have to be known to rescale the theoretical turbulence spectrum used in the turbulence interaction theory. In that framework, a methodology to compute the turbulence length scale upstream of the airfoil has been developed through the use of Fourier transforms of the upwash velocity of the incoming flow. Secondly, Amiet’s theory has been developed for airfoil noise radiation in uniform flow. In case of spanwise varying conditions, a Segmentation Method is proposed to predict the radiated noise. This method consists in cutting the airfoil in segments having each its own upstream flow conditions and to sum up the resulting individual emitted noise to obtain the total radiated noise in the far-field. This direct method reveals that spurious effect due to radiation angle and finite size of segments can appear. A rescaling based on listener position and a new Inverse Segmentation Method using a combination of large span airfoils are proposed to solve both problems. This method has been tested for several flow parameters and has shown its potential to reproduce correctly the radiated noise. The methods proposed in this paper have been combined and used on the jet-airfoil interaction case, for which acoustic prediction using Amiet’s theory has shown a satisfactory agreement compared to experimental noise measurements. Noise pollution is encountered in various industrial applications : noise emitted by landing gear in transport industry; noise from wings and high-lift devices in aeronautics; noise due to windshield wipers, rear-view mirrors, engine cooling systems and mufflers in car industry. It also exists in other domains of applications, as wind turbines or fans. In most of the cases, the noise produced is spread among all the frequency spectrum leading sometimes to a significant participation of high frequencies to the overall sound produced. The definition itself of the limit between low and high frequencies is not straightforward but a common rule is to consider the non-compactness limit of the problem. In such situations of non-compactness, the influence of the higher frequencies is an important factor to take into account in the noise predictions and specific methods for these frequencies have to be developed. Among the methods available and widely used to predict the low frequency components are the hybrid methods (indirect methods) in which the computation of the flow is decoupled from the computation of the sound. The computational cost to obtain the acoustic field is highly reduced compared to direct methods, computing the flow and its sound field together, when high Reynolds number and low Mach number are considered, as in most of industrial applications of interest. These hybrid methods consist in two steps : a) firstly, near the noise source, the flow field is obtained from an unsteady computation ; b) secondly, the acoustic source radiation is computed in the far-field by the use of an analogy. 1–3 This methodology is based on the substitution of the real flow by equivalent sources, computed as a post-processing of the flow data.