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Characteristic Scales in Shock–Turbulence Interaction

Lacombe, Francis and Roy, Subhajit and Sinha, Krishnendu and Karl, Sebastian and Hickey, Jean-Pierre (2020) Characteristic Scales in Shock–Turbulence Interaction. AIAA Journal, pp. 1-7. American Institute of Aeronautics and Astronautics (AIAA). doi: 10.2514/1.J059499. ISSN 0001-1452.

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Official URL: https://doi.org/10.2514/1.J059499


A semi-empirical estimate of the time-averaged thickness of a planar shock embedded in a turbulent mean flow is presented in an effort to quantify the characteristic time and length scales for turbulence modeling. Simplified Favre-averaged Navier–Stokes equations are reformulated and combined with the Rankine–Hugoniot relations to obtain an equation that relates the shock structure and its characteristic thickness to the upstream turbulent and mean flow quantities. The only mean flow and turbulence quantities needed to compute the shock thickness or velocity profile through the shock are upstream Mach number Mu, turbulent Mach number Mt, and the Taylor-based Reynolds number Reλ. The accuracy of method for the shock structure is validated against direct numerical simulations of shock–turbulence interaction and shows a very good agreement over a wide range of Mach, Reynolds, and turbulent Mach numbers. Finally, the obtained ratio of characteristic shock time scale to the upstream turbulence time scale is shown to be proportional to the turbulent kinetic energy amplification through the shock and supported through direct numerical simulations.

Item URL in elib:https://elib.dlr.de/137116/
Document Type:Article
Title:Characteristic Scales in Shock–Turbulence Interaction
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Lacombe, FrancisEcole Polytechnique de Montreal, Department of Mechanical Engineering, Montreal, CanadaUNSPECIFIEDUNSPECIFIED
Roy, SubhajitIndian Institute of Technology BombayUNSPECIFIEDUNSPECIFIED
Sinha, KrishnenduIndian Institute of Technology BombayUNSPECIFIEDUNSPECIFIED
Karl, SebastianUNSPECIFIEDhttps://orcid.org/0000-0002-5558-6673UNSPECIFIED
Hickey, Jean-PierreUniversity of WaterlooUNSPECIFIEDUNSPECIFIED
Date:28 October 2020
Journal or Publication Title:AIAA Journal
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In ISI Web of Science:Yes
Page Range:pp. 1-7
EditorsEmailEditor's ORCID iDORCID Put Code
Publisher:American Institute of Aeronautics and Astronautics (AIAA)
Series Name:Article in advance (online)
Keywords:Turbulence, Shock thickness
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space Transportation
DLR - Research area:Raumfahrt
DLR - Program:R RP - Space Transportation
DLR - Research theme (Project):R - Wiederverwendbare Raumfahrtsysteme (old)
Location: Göttingen
Institutes and Institutions:Institute for Aerodynamics and Flow Technology > Spacecraft, GO
Deposited By: Karl, Dr. Sebastian
Deposited On:11 Nov 2020 12:37
Last Modified:11 Nov 2020 12:37

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