A volume integral implementation of the Goldstein generalised acoustic analogy for unsteady flow simulations

Abstract

A new volume integral method based on the Goldstein generalised acoustic analogy is developed and directly applied with large-eddy simulation (LES). In comparison with the existing Goldstein generalised acoustic analogy implementations, the current method does not require the computation and recording of the expensive fluctuating stress autocovariance function in the seven-dimensional space–time. Until now, the multidimensional complexity of the generalised acoustic analogy source term has been the main barrier to using it in routine engineering calculations. The new method only requires local pointwise stresses as an input that can be routinely computed during the flow simulation. On the other hand, the new method is mathematically equivalent to the original Goldstein acoustic analogy formulation, and, thus, allows for a direct correspondence between different effective noise sources in the jet and the far-field noise spectra. The implementation is performed for conditions of a high-speed subsonic isothermal jet corresponding to the Rolls-Royce SILOET experiment and uses the LES solution based on the CABARET solver. The flow and noise solutions are validated by comparison with experiment. The accuracy and robustness of the integral volume implementation of the generalised acoustic analogy are compared with those based on the standard Ffowcs Williams–Hawkings surface integral method and the conventional Lighthill acoustic analogy. As a demonstration of its capabilities to investigate jet noise mechanisms, the new integral volume method is applied to analyse the relative importance of various noise generation and propagation components within the Goldstein generalised acoustic analogy model.

Modelling of jet noise: a perspective from large-eddy simulations

“…We will restrict ourselves to a brief summary here. Karabasov et al [107] and the follow-on studies (see [108,109] and references therein) adopted Goldstein's generalized acoustic analogy (GAA) [90], i.e. the Reynolds stress fluctuation covariances, enthalpy flux fluctuation covariances and the crosscovariances with the former, for modelling jet noise sources.…”

Eddy viscosity for resolvent-based jet noise models

“…Returning to equation 3, only a very limited set of Green's functions have been found numerically (see, for example [11][12][13][14][15] ). Considering that a full characterization of the Green's function implies solving the full linearized equations of motion for a point source in any variable at any location within the jet, it is doubtful that this approach can fully succeed without further simplifications.…”

Simulations of co-axial jet flows on graphics processing units: the flow and noise analysis

“…For converting the computed time signal to the far-field pressure power spectral density based on the common definition of 1 Hz for the reference frequency and 20 µPa for the reference pressure, the standard statistical post-processing is applied based on the Welch method to deal with the Fourier transform of short time series. Details of the LES signal post-processing method can be found in [26].…”

“…It can be noted that in comparison with more advanced far-field propagation methods such as based on solving acoustic perturbation equations (APEs) [27] or the hyperbolic part of the generalized acoustic analogy equations [26], the standard FW-H method is simpler. However, it requires an appropriate calibration of the acoustic integration surface including the closing discs which should be adjusted a posteriori by comparison with the far-field noise data.…”