Quadratic stochastic estimation of far-field acoustic pressure with coherent structure events in a 2D compressible plane mixing layer. (English) Zbl 1423.76400
Summary: Mathematical tools based on cross correlations between aerodynamic quantities of interest inside the shear flow region and the radiated sound pressure are used to investigate noise generation mechanisms in a plane compressible mixing layer. An original methodology relying on an efficient coupling between proper orthogonal decomposition (POD) and stochastic estimation procedures is developed to analyze the main aerodynamic mechanisms that govern noise production. POD is used to split the instantaneous flow fluctuations as the sum of three components: the large- and small-scale coherent structures (LCS and SCS) and the background quasi-Gaussian fluctuations. Based on this flow partitioning, quadratic stochastic estimation is implemented to estimate the far-field acoustic pressure associated with each flow component. The far field acoustic pressure associated with both LCS and SCS is then investigated. By analyzing the RMS and temporal spectra of the far-field acoustic pressure, it is observed that the SCSs, as defined thanks to the POD basis, are responsible for the main part of the noise emission.
MSC:
| 76Q05 | Hydro- and aero-acoustics |
| 76G25 | General aerodynamics and subsonic flows |
| 76M35 | Stochastic analysis applied to problems in fluid mechanics |
Keywords:
aeroacoustic; plane mixing layer; coherent structures; proper orthogonal decomposition; quadratic stochastic estimation; pressure/velocity correlationsReferences:
| [1] | Lighthill, On sound generated aerodynamically: I general theory, Proceedings of the Royal Society of London 211 pp 564– (1952) · Zbl 0049.25905 |
| [2] | Tam, Computational aeroacoustic examples showing the failure of the acoustic analogy theory to identify the correct noise sources, Journal of Computational Acoustics 10 (4) pp 387– (2002) · Zbl 1360.76302 |
| [3] | Peake, A note on ’computational aeroacoustic examples showing the failure of the acoustic analogy theory to identify the correct noise sources’ by CKW Tam, Journal of Computational Acoustics 12 (4) pp 631– (2004) |
| [4] | Spalart, Application of full and simplified acoustic analogies to an elementary problem, Journal of Fluid Mechanics 578 pp 113– (2007) · Zbl 1112.76070 |
| [5] | Colonius, Sound generation in a mixing layer, Journal of Fluid Mechanics 330 pp 375– (1997) · Zbl 0901.76075 |
| [6] | Avital, Mach wave radiation by mixing layers. Part I: analysis of the sound field, Theoretical and Computational Fluid Dynamics 12 (2) pp 73– (1998) · Zbl 0928.76100 |
| [7] | Bogey, Numerical simulation of sound generated by vortex pairing in a mixing layer, AIAA Journal 40 (2) pp 235– (2000) |
| [8] | Fortuné, Noise radiated by a non-isothermal, temporal mixing layer. Part I: direct computation and prediction using compressible DNS, Theoretical and Computational Fluid Dynamics 18 (1) pp 61– (2004) · Zbl 1148.76355 |
| [9] | Panda, Investigation of noise sources in high-speed jets via correlation measurements, Journal of Fluid Mechanics 537 pp 349– (2005) · Zbl 1138.76304 |
| [10] | Tinney, On spectral linear stochastic estimation, Experiments in Fluids 41 (5) pp 763– (2007) |
| [11] | Bogey, An analysis of the correlations between the turbulent flow and the sound pressure fields of subsonic jets, Journal of Fluid Mechanics 583 pp 71– (2007) · Zbl 1116.76073 |
| [12] | Jordan, Subsonic jet aeroacoustics: associating experiment, modelling and simulation, Experiments in Fluids 44 (1) pp 1– (2008) |
| [13] | Babucke, DNS of a plane mixing layer for the investigation of sound generation mechanisms, Computers and Fluids 37 (4) pp 360– (2008) · Zbl 1237.76163 |
| [14] | Freund, Noise sources in a low-Reynolds-number turbulent jet at Mach 0.9, Journal of Fluid Mechanics 438 pp 277– (2001) · Zbl 1013.76075 |
| [15] | Ffwocs Williams, The noise from the large-scale structure of a jet, Journal of Fluid Mechanics 84 pp 673– (1978) |
| [16] | Jung, Downstream evolution of the most energetic modes in a turbulent axisymmetric jet at high Reynolds number. Part 1. The near-field region, Journal of Fluid Mechanics 514 pp 173– (2004) · Zbl 1067.76507 |
| [17] | Bonnet, Stochastic estimation and proper orthogonal decomposition: complementary techniques for identifying structure, Experiments in Fluids 17 pp 307– (1994) |
| [18] | Taylor, Towards practical flow sensing and control via POD and LSE based low-dimensional tools, Journal of Fluids Engineering 126 (3) pp 337– (2004) |
| [19] | Murray, Modified quadratic stochastic estimation of resonating subsonic cavity flow, Journal of Turbulence 8 (53) pp 1– (2007) |
| [20] | Hudy, Stochastic estimation of a separated-flow field using wall-pressure-array measurements, Physics of Fluids 19 (2007) · Zbl 1146.76419 |
| [21] | Picard, Pressure velocity coupling in a subsonic round jet, International Journal of Heat and Fluid Flow 21 (3) pp 359– (2000) |
| [22] | Lu, Pseudo-characteristic formulation and dynamic boundary conditions for computational aeroacoustics, International Journal for Numerical Methods in Fluids 53 (2) pp 201– (2007) · Zbl 1113.76056 |
| [23] | Sesterhenn, A characteristic-type formulation of the Navier-Stokes equations for high order upwind schemes, Computers and Fluids 30 pp 37– (2001) · Zbl 0991.76056 |
| [24] | Shu, Efficient implementation of essentially non-oscillatory shock capturing schemes, Journal of Computational Physics 83 pp 32– (1989) · Zbl 0674.65061 |
| [25] | Monkewitz, The influence of the velocity ratio on the spatial instability of mixing layers, Physics of Fluids 25 pp 1137– (1982) |
| [26] | Lumley JL. The structure of inhomogeneous turbulent flows. In Atmospheric Turbulence and Radio Wave Propagation, Yaglom AM, Tatarsky VI (eds). 1967; 166-178. |
| [27] | Holmes P, Lumley JL, Berkooz G. Turbulence, coherent structures, dynamical systems and symmetry. Cambridge Monograph on Mechanics, 1996. · Zbl 0890.76001 |
| [28] | Sirovich, Turbulence and the dynamics of coherent structures. Part I: coherent structures, Quaterly of Applied Mathematics XLV pp 561– (1987) · Zbl 0676.76047 |
| [29] | Druault, Proper orthogonal decomposition of the mixing layer flow into coherent structures and turbulent Gaussian fluctuations, Comptes Rendus Mécanique 333 pp 824– (2005) · Zbl 1177.76149 |
| [30] | Roudnitzky, Proper orthogonal decomposition of in-cylinder engine flow into mean component, coherent structures and random Gaussian fluctuations, Journal of Turbulence 7 (70) pp 1– (2006) |
| [31] | Farge, Non-Gaussianity and coherent vortex simulation for two-dimensional turbulence using an adaptative orthogonal wavelet basis, Physics of Fluids 11 (8) pp 2187– (1999) · Zbl 1147.76386 |
| [32] | Farge, Coherent vortex extraction in three dimensional homogeneous turbulence: comparison between CVS-wavelet and POD-Fourier decompositions, Physics of Fluids 15 pp 2886– (2003) · Zbl 1186.76165 |
| [33] | Adrian, The 4th Biennial Symposium on Turbulence in Liquids pp 322– (1977) |
| [34] | Adrian, Approximation of turbulent conditional averages by stochastic estimation, Physics of Fluids 1 (6) pp 992– (1989) |
| [35] | Brereton, Stochastic estimation as a statistical tool for approximating turbulent conditional averages, Physics of Fluids 4 (9) pp 2046– (1992) |
| [36] | Druault, Experimental 3D analysis of the large scale behaviour of a plane turbulent mixing layer, Flow Turbulence and Combustion 74 (2) pp 207– (2005) |
| [37] | Murray, Estimation of the flow field from surface pressure measurements in an open cavity, AIAA Journal 41 (5) pp 969– (2003) |
| [38] | Naguib, Stochastic estimation and flow sources associated with surface pressure events in a turbulent boundary layer, Physics of Fluids 13 (9) pp 2611– (2001) · Zbl 1184.76386 |
| [39] | Tung, Higher order estimates of conditional eddies in isotropic turbulence, Physics of Fluids 23 (7) pp 1469– (1980) |
| [40] | Papoulis, Probability Random Variables, and Stochastic Processes (1965) |
| [41] | Laufer, Noise generation by a low-Mach-number jet, Journal of Fluid Mechanics 134 pp 1– (1983) |
| [42] | Boree, Extended proper orthogonal decomposition: a tool to analyse correlated events in turbulent flows, Experiments in Fluids 35 pp 188– (2003) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
