##
###
Validating the Ffowcs Williams and Hawkings acoustic analogy implementation in Antares

Danilo Di Stefano, Aldo Rona, Edward Hall, Christopher L. Morfey, Guillaume Puigt

2016
*
22nd AIAA/CEAS Aeroacoustics Conference
*
unpublished

Progress is presented in the development of a Ffowcs Williams and Hawkings (FW-H) acoustic analogy post-processor for time-resolved Computational Fluid Dynamics (CFD) simulations. The tool is coded in Python and embedded in Antares, a post-treatment package (developed by Cerfacs, France) of wide access and usability for the scientific community. Tests on monopoles, dipoles, and quadrupoles show good predictions of pressure fluctuation and directivity against reference analytical results,
## more »

... cal results, validating the software for applications to stationary elementary sources. The proximity of these sources to a corner of the FW-H integration surface is shown to adversely affect the predictions and good agreement with the benchmark sound field is restored by an appropriate sizing and placement of the FW-H surface. Guidelines for obtaining predictions that are substantially independent of the size and placement of the FW-H surface are provided in terms of the spatial resolution of the discretised FW-H surface. * Marie Curie Fellow. to the acoustic pressure fluctuation. The different contributions are finally summed up by synchronising their advanced time 1 to obtain the acoustic pressure history. The formulation of the FW-H acoustic analogy described by Casalino 1 is used to obtain the results of Sections A-D. The analogy with an acoustic medium at rest described by Lighthill 2 is revisited by Casalino 1 and an integral solution of the FW-H equation 3 in the advanced time formulation 4 is obtained. 1 The FW-H equation is a generalization of the Lighthill acoustic analogy that takes into account the presence of bodies in arbitrary motion. 3 As sketched in figure 1(a), in this generalization a closed surface (FW-H integration surface) determines three different regions in which the fluid is assumed to have different properties. 3 Brentner and Farassat discussed the integration surface requirements and propose a permeable/porous formulation in which the closed surface does not coincide with a physical body 5, 6 The flow outside this surface is modelled by the Navier-Stokes equations. Inside the closed surface, the conservation laws are assumed not to apply and the flow state is specified arbitrarily. In order to maintain the discontinuity generated in such a way across the surface, mass and momentum sources are distributed over the closed integration surface. 3 A distribution of quadrupole-like sources in the volume outside the integration surface completes the noise radiation model by taking into account of non-linear effects. 2, 3 This process is carried out from the time-resolved estimates of pressure, density and velocity on the FW-H integration surface, obtained independently, for instance, by CFD. The equations of conservation of mass and momentum are taken as valid everywhere in an exterior flow domain free from solid boundaries. The theory of generalized functions is used to combine these equations in the form of an inhomogeneous wave equation. Therefore the FW-H surface needs to enclose all the solid bodies interacting with the flow. This embedding procedure is detailed by Farassat 7 and only a brief outline is given herein for conciseness. Let g (x, t) = 0 be the equation describing the moving control surface of figure 1(a) , whose points move at velocity v (x, t). 1 g is defined to satisfy the property ∇g =n on the surface, wheren is the outward pointing unit normal vector. Following this procedure, the flow is partitioned into three regions according to the value of g, as shown in figure 1(a) . A point enclosed by the integration surface satisfies g < 0 and this flow field portion can be replaced by a quiescent fluid. A point outside the integration surface satisfies g > 0 and lies in an acoustically perturbed fluid. The fluid motion is therefore discontinuous across g = 0. Mass and momentum sources are hence distributed on the surface g (x, t) = 0, which allows the conservation laws across g (x, t) = 0 to be satisfied. In implementing this formulation, an object oriented language is used (Python 2.7.9) and the tool is embedded in Antares 1.4.0. 8 This represents an innovative approach in flow simulations, where a high-level programming language, such as Fortran, is usually preferred. The Antares software package presents many advantages to support the development of the FW-H post-processor. The package contains numerical tools which enable steady and unsteady flow analyses in real time and/or a posteriori and flow visualization. Antares also supports popular structured and unstructured CFD geometries and solutions, which provides a significant usability advantage in the aero-acoustic field. Besides this, Antares is an unrestricted, royalty-free software, freely obtainable subject to a license agreement for copyright purposes. The new FW-H post-processor is expected to be further developed and used in collaboration with Cerfacs, France, which coordinates the development of Antares. This aims to keep the software up-to-date and continuously improved, including, for instance, new features and adapting the implementation to the new requirements of researchers in the field, so that the benefit of the overall aero-acoustic community can be pursued. A reliable validation process of the software is necessary and this has been undertaken by the authors. The first stage of this process, with sample results, was presented by Di Stefano et al. 9 The predictive ability of the code was shown by applying the FW-H acoustic analogy implementation to three test cases: a monopole source, a dipole source and a subsonic jet flow modelled by Bogey and Bailly. 10 Pressure fluctuations predicted by the tool were compared against reference solutions for each of the three test cases. These comparisons showed a satisfactory quantitative match in each test and built up confidence in the reliability of the code for estimating near-field and far-field noise radiation from both simple sources and more complex flows. This paper presents the second stage of the validation process, aimed at demonstrating the ability of the code to model the radiation characteristics of compact sources located off-centre inside the FW-H integration surface that can have a more directive, multi-lobar radiation pattern than the previous test cases. Three

doi:10.2514/6.2016-3059
fatcat:jqiey5tevjcn7n77p2fn45q6hu