Synthetic Turbulence Methods for Leading Edge Noise Predictions

Abstract

An advanced digital filter method to generate synthetic turbulence is presented for efficient two-and three-dimensional leading edge noise predictions. The technique, which is based on the Random Particle-Mesh method, produces a turbulent inflow that matches a target isotropic energy spectrum. The discretized equations for the synthetic eddies, and the input parameters needed to recover the desired turbulence statistics, are presented. Moreover, a simple and fast implementation strategy, which does not require an additional boundary condition, is presented under the frozen turbulence assumption. The method is used in a linearized Euler solver to predict turbulence-airfoil interaction noise from a number of configurations, including variations in airfoil thickness, angle of attack and Mach number. For the first time, noise predictions from a digital filter method are directly compared to those provided by synthetic turbulence based on a summation of Fourier modes. The comparison indicates that the advanced digital filter method gives enhanced performance in terms of computational cost and simulation accuracy. In addition, initial tests show that this method is capable of reproducing experimental noise measurements within 3 dB accuracy.

Evaluation and Development of Non-Reflective Boundary Conditions for Aeroacoustic Simulations

“…Above f = 1000 Hz the numerical predictions deviate from the analytical prediction due to the thickness of the NACA 0012 airfoil. This effect is discussed in Gea-Aguilera et al 34 The noise predictions from the various domain sizes are in agreement to within 2 dB at all frequencies. This suggests that the noise predictions are unaffected by the changes in domain size, and that a domain which extends to 3 airfoil chords in all directions is sufficient if the zonal TCBC non-reflective boundary condition is used.…”

“…The methodology of this case is now outlined. However, additional detail is given in Gea-Aguilera et al, 34 which uses the same methodology. The purpose of Gea-Aguilera et al 34 is to study turbulence interaction noise, whereas the current work is using this case only to demonstrate the performance of the proposed non-reflective boundary condition.…”

“…The turbulence synthesis method has been developed by Gea-Aguilera et al, 34 and is described in the companion paper. This turbulence synthesis method allows the injection of isotropic turbulence in a localised region, as shown in Figure 15.…”

Analytical reconstruction of isotropic turbulence spectra based on the Gaussian transform

“…The main idea of the weighting function is to realise an arbitrary spectrum E(k) of length scale Λ with the superposition of a limited number of Gaussian spectra E G of length scales l m with 0 ≤ m ≤ M. For this we discretise the integral in Eq. (6) to…”

“…Others have adopted this method for other kinds of spectra, e.g. just recently Gea-Aguilera et al [6] and Kim et al [7] published their findings. Note that the here presented method has already been presented by the authors on conferences, but not derived in detail [8,9].…”