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The near-field pressure radiated by planar high-speed free-shear-flow turbulence

Published online by Cambridge University Press:  26 October 2017

David A. Buchta Open the ORCID record for David A. Buchta [Opens in a new window]  and
Jonathan B. Freund Open the ORCID record for Jonathan B. Freund [Opens in a new window]
David A. Buchta
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801, USA
Jonathan B. Freund*
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801, USA Department of Aerospace Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801, USA
*
†Email address for correspondence: jbfreund@illinois.edu
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Abstract

Jets with Mach numbers $M\gtrsim 1.5$ are well known to emit an intense, fricative, so-called crackle sound, having steep compressions interspersed with weaker expansions that together yield a positive pressure skewness $S_{k}>0$. Its shock-like features are obvious hallmarks of nonlinearity, although a full explanation of the skewness is lacking, and wave steepening alone is understood to be insufficient to describe its genesis. Direct numerical simulations of high-speed free-shear flows for Mach numbers $M=0.9$, $1.5$, $2.5$ and $3.5$ in the Reynolds number range $60\leqslant Re_{\unicode[STIX]{x1D6FF}_{m}}\leqslant 4200$ are used to examine the mechanisms leading to such pressure signals, especially the pressure skewness. For $M=2.5$ and $3.5$, the pressure immediately adjacent the turbulence already has the large $S_{k}\gtrsim 0.4$ associated with jet crackle. It also has a surprisingly complex three-dimensional structure, with locally high pressures at compression-wave intersections. This structure is transient, and it simplifies as radiating waves subsequently merge through nonlinear mechanisms to form the relatively distinct and approximately two-dimensional Mach-like waves deduced from laboratory visualizations. A transport equation for $S_{k}$ is analysed to quantify factors affecting its development. The viscous dissipation that decreases $S_{k}$ is balanced by a particular nonlinear flux, which is (of course) absent in linear acoustic propagation and confirmed to be independent of the simulated Reynolds numbers. Together these effects maintain an approximately constant $S_{k}$ in the near acoustic field.

JFM classification

Acoustics: Aeroacoustics Acoustics: Jet noise Turbulent Flows: Shear layer turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 832 , 10 December 2017 , pp. 383 - 408
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Copyright
© 2017 Cambridge University Press 

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