Abstract
Our concern in this paper is in the fine-tuning of the arbitrary parameters within the upstream turbulence structure for the acoustic spectrum of a rapid-distortion theory (RDT)-based model of trailing-edge noise. RDT models are based on an appropriate asymptotic limit of the Linearized Euler Equations and apply when the interaction time of the turbulence with the surface edge discontinuity is small compared to the eddy turnover time. When an arbitrary transversely sheared jet mean flow convects a finite region of nonhomogeneous turbulence, the acoustic spectrum of the pressure field scattered by the trailing-edge depends on (among other things) the upstream turbulence via the Fourier transform of the correlation function, R22 (where subscript 2 refers to a co-ordinate surface normal to the plate). We show that the length and time scale parameters that govern the spatial and temporal de-correlation of R22 can be found using formal optimization methods to avoid any uncertainty in their selection by hand-tuning. We assess various optimization methods that are broadly categorized into an ‘evolutionary’ and ‘non-evolutionary’ paradigm. That is, we optimize the acoustic spectrum using the Multi-Start algorithm, Particle Swarm Optimization and the Multi-Population Adaptive Inflationary Differential Evolution Algorithm. The optimization is based upon different objective functions for the acoustic spectrum and/or turbulence structure. We show that this approach, while resulting in the total modest increase in computation time (on average 2 h), gives excellent prediction over most frequencies (within 2–4 dB) where the trailing-edge noise associated amplification in sound exists.
Highlights
The advent of the jet engine in the mid-twentieth century [1] brought with it the intrusion caused by aircraft noise to the communities living near airports
The trailing-edge component is a dangerous noise source owing to the large increase in low frequency sound when the observation point is above or below the plate surface and vertical location (h) of the trailing-edge is of the order of jet diameter, h ∼ D
An extension of the differential evolution algorithm, which we use in this paper, is the Multi-Population Adaptive Inflationary Differential Evolution Algorithm (MP-AIDEA) [35]. This uses multiple populations and combines basic differential evolution with monotonic basin hopping (MBH) to reduce the risk of converging to a minimum which is not global, it adapts the optimization parameters autonomously. It is a further advancement on the inflationary differential evolution algorithm (IDEA) which only uses a single population and requires the parameters to be chosen by the programmer [41]
Summary
The advent of the jet engine in the mid-twentieth century [1] brought with it the intrusion caused by aircraft noise to the communities living near airports. Goldstein et al [10,11,12] used the method of matched asymptotic expansions at the low frequency limit to construct the gust-induced boundary condition and the homogeneous solutions to the Rayleigh equation that enter in the solution to the Wiener-Hopf problem for the acoustic field scattered by the edge This solution (Equations (6.26) and (6.27) in [12]) was analytically continued to high frequencies, and (Equations (6.28)–(6.30)) show that the mean square scattered pressure depends on the upstream structure of the two-point time-delayed turbulence correlation R22 where the subscript 2 denotes the co-ordinate plane normal the plate surface. 20 μPa). noise is largest [36] to illustrate the benefit of optimization
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