Density effects on postshock turbulence structure and dynamics
Abstract
Turbulence structure resulting from multifluid or multispecies, variabledensity isotropic turbulence interaction with a Mach 2 shock is studied using turbulenceresolving shockcapturing simulations and Eulerian (grid) and Lagrangian (particle) methods. The complex roles that density plays in the modification of turbulence by the shock wave are identified. Statistical analyses of the velocity gradient tensor (VGT) show that density variations significantly change the turbulence structure and flow topology. Specifically, a stronger symmetrization of the joint probability density function (PDF) of second and third invariants of the anisotropic VGT, PDF$$(Q^{\ast },R^{\ast })$$, as well as the PDF of the vortex stretching contribution to the enstrophy equation, are observed in the multispecies case. Furthermore, subsequent to the interaction with the shock, turbulent statistics also acquire a differential distribution in regions having different densities. This results in a nearly symmetric PDF$$(Q^{\ast },R^{\ast })$$ in heavyfluid regions, while the lightfluid regions retain the characteristic teardrop shape. To understand this behaviour and the return to ‘standard’ turbulence structure as the flow evolves away from the shock, Lagrangian dynamics of the VGT and its invariants is studied by considering particle residence times and conditional particle variables in different flow regions. The pressure Hessian contributions to the VGT invariants transport equations are shown to be not only affected by the shock wave, but also by the density in the multifluid case, making them critically important to the flow dynamics and turbulence structure.
 Authors:

 Michigan State Univ., East Lansing, MI (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1573337
 Report Number(s):
 LAUR1831241
Journal ID: ISSN 00221120
 Grant/Contract Number:
 89233218CNA000001
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Fluid Mechanics
 Additional Journal Information:
 Journal Volume: 880; Journal ID: ISSN 00221120
 Publisher:
 Cambridge University Press
 Country of Publication:
 United States
 Language:
 English
 Subject:
 42 ENGINEERING; compressible turbulence; shock waves; turbulence simulation
Citation Formats
Tian, Yifeng, Jaberi, Farhad A., and Livescu, Daniel. Density effects on postshock turbulence structure and dynamics. United States: N. p., 2019.
Web. doi:10.1017/jfm.2019.707.
Tian, Yifeng, Jaberi, Farhad A., & Livescu, Daniel. Density effects on postshock turbulence structure and dynamics. United States. doi:10.1017/jfm.2019.707.
Tian, Yifeng, Jaberi, Farhad A., and Livescu, Daniel. Fri .
"Density effects on postshock turbulence structure and dynamics". United States. doi:10.1017/jfm.2019.707. https://www.osti.gov/servlets/purl/1573337.
@article{osti_1573337,
title = {Density effects on postshock turbulence structure and dynamics},
author = {Tian, Yifeng and Jaberi, Farhad A. and Livescu, Daniel},
abstractNote = {Turbulence structure resulting from multifluid or multispecies, variabledensity isotropic turbulence interaction with a Mach 2 shock is studied using turbulenceresolving shockcapturing simulations and Eulerian (grid) and Lagrangian (particle) methods. The complex roles that density plays in the modification of turbulence by the shock wave are identified. Statistical analyses of the velocity gradient tensor (VGT) show that density variations significantly change the turbulence structure and flow topology. Specifically, a stronger symmetrization of the joint probability density function (PDF) of second and third invariants of the anisotropic VGT, PDF$(Q^{\ast },R^{\ast })$, as well as the PDF of the vortex stretching contribution to the enstrophy equation, are observed in the multispecies case. Furthermore, subsequent to the interaction with the shock, turbulent statistics also acquire a differential distribution in regions having different densities. This results in a nearly symmetric PDF$(Q^{\ast },R^{\ast })$ in heavyfluid regions, while the lightfluid regions retain the characteristic teardrop shape. To understand this behaviour and the return to ‘standard’ turbulence structure as the flow evolves away from the shock, Lagrangian dynamics of the VGT and its invariants is studied by considering particle residence times and conditional particle variables in different flow regions. The pressure Hessian contributions to the VGT invariants transport equations are shown to be not only affected by the shock wave, but also by the density in the multifluid case, making them critically important to the flow dynamics and turbulence structure.},
doi = {10.1017/jfm.2019.707},
journal = {Journal of Fluid Mechanics},
number = ,
volume = 880,
place = {United States},
year = {2019},
month = {10}
}
Web of Science
Works referenced in this record:
Simulations of Cellular Detonation Interaction with Turbulent Flows
journal, February 2016
 Jin, Tai; Luo, Kun; Dai, Qi
 AIAA Journal, Vol. 54, Issue 2
Turbulence structures of wallbounded shear flows found using DNS data
journal, February 1998
 Chong, M. S.; Soria, J.; Perry, A. E.
 Journal of Fluid Mechanics, Vol. 357
Flow topology in compressible turbulent boundary layer
journal, June 2012
 Wang, Li; Lu, XiYun
 Journal of Fluid Mechanics, Vol. 703
The influence of entropy fluctuations on the interaction of turbulence with a shock wave
journal, March 1997
 Mahesh, Krishnan; Lele, Sanjiva K.; Moin, Parviz
 Journal of Fluid Mechanics, Vol. 334
Compact finite difference schemes with spectrallike resolution
journal, November 1992
 Lele, Sanjiva K.
 Journal of Computational Physics, Vol. 103, Issue 1
Direct numerical simulations of isotropic compressible turbulence: Influence of compressibility on dynamics and structures
journal, December 2004
 Pirozzoli, S.; Grasso, F.
 Physics of Fluids, Vol. 16, Issue 12
Thermodynamic fluctuations in canonical shock–turbulence interaction: effect of shock strength
journal, June 2018
 Sethuraman, Yogesh Prasaad M.; Sinha, Krishnendu; Larsson, Johan
 Theoretical and Computational Fluid Dynamics, Vol. 32, Issue 5
Effect of compressibility on the smallscale structures in isotropic turbulence
journal, October 2012
 Wang, Jianchun; Shi, Yipeng; Wang, LianPing
 Journal of Fluid Mechanics, Vol. 713
Reynolds and Machnumber effects in canonical shock–turbulence interaction
journal, February 2013
 Larsson, Johan; BermejoMoreno, Ivan; Lele, Sanjiva K.
 Journal of Fluid Mechanics, Vol. 717
A general classification of three‐dimensional flow fields
journal, May 1990
 Chong, M. S.; Perry, A. E.; Cantwell, B. J.
 Physics of Fluids A: Fluid Dynamics, Vol. 2, Issue 5
Topological evolution in compressible turbulent boundary layers
journal, September 2013
 Chu, YouBiao; Lu, XiYun
 Journal of Fluid Mechanics, Vol. 733
Direct numerical simulation of isotropic turbulence interacting with a weak shock wave
journal, June 1993
 Lee, Sangsan; Lele, Sanjiva K.; Moin, Parviz
 Journal of Fluid Mechanics, Vol. 251
Interaction of isotropic turbulence with shock waves: effect of shock strength
journal, June 1997
 Lee, Sangsan; Lele, Sanjiva K.; Moin, Parviz
 Journal of Fluid Mechanics, Vol. 340
Analysis of smallscale scalar mixing processes in highly underexpanded jets
journal, September 2015
 Buttay, R.; Lehnasch, G.; Mura, A.
 Shock Waves, Vol. 26, Issue 2
Simulation of spatially evolving turbulence and the applicability of Taylor’s hypothesis in compressible flow
journal, July 1992
 Lee, Sangsan; Lele, Sanjiva K.; Moin, Parviz
 Physics of Fluids A: Fluid Dynamics, Vol. 4, Issue 7
Turbulent energy flux generated by shock/homogeneousturbulence interaction
journal, April 2016
 Quadros, Russell; Sinha, Krishnendu; Larsson, Johan
 Journal of Fluid Mechanics, Vol. 796
A Description of Eddying Motions and Flow Patterns Using CriticalPoint Concepts
journal, January 1987
 Perry, A. E.; Chong, M. S.
 Annual Review of Fluid Mechanics, Vol. 19, Issue 1
The interaction of an isotropic field of acoustic waves with a shock wave
journal, October 1995
 Mahesh, Krishnan; Lee, Sangsan; Lele, Sanjiva K.
 Journal of Fluid Mechanics, Vol. 300
Evolution of the velocity gradient tensor invariant dynamics in a turbulent boundary layer
journal, February 2017
 Bechlars, P.; Sandberg, R. D.
 Journal of Fluid Mechanics, Vol. 815
Direct numerical simulation of canonical shock/turbulence interaction
journal, December 2009
 Larsson, Johan; Lele, Sanjiva K.
 Physics of Fluids, Vol. 21, Issue 12
A study of the evolution and characteristics of the invariants of the velocitygradient tensor in isotropic turbulence
journal, February 1999
 Ooi, Andrew; Martin, Jesus; Soria, Julio
 Journal of Fluid Mechanics, Vol. 381
Numerical study of variable density turbulence interaction with a normal shock wave
journal, September 2017
 Tian, Yifeng; Jaberi, Farhad A.; Li, Zhaorui
 Journal of Fluid Mechanics, Vol. 829
An algorithm for tracking fluid particles in numerical simulations of homogeneous turbulence
journal, December 1988
 Yeung, P. K.; Pope, S. B.
 Journal of Computational Physics, Vol. 79, Issue 2
Local flow topology and velocity gradient invariants in compressible turbulent mixing layer
journal, June 2015
 Vaghefi, Navid S.; Madnia, Cyrus K.
 Journal of Fluid Mechanics, Vol. 774
L AGRANGIAN I NVESTIGATIONS OF T URBULENCE
journal, January 2002
 Yeung, P. K.
 Annual Review of Fluid Mechanics, Vol. 34, Issue 1
Evolution of scalar and velocity dynamics in planar shockturbulence interaction
journal, January 2018
 Boukharfane, R.; Bouali, Z.; Mura, A.
 Shock Waves, Vol. 28, Issue 6
Characteristics of chemically reacting compressible homogeneous turbulence
journal, May 2000
 Jaberi, F. A.; Livescu, D.; Madnia, C. K.
 Physics of Fluids, Vol. 12, Issue 5
Lagrangian Dynamics and Models of the Velocity Gradient Tensor in Turbulent Flows
journal, January 2011
 Meneveau, Charles
 Annual Review of Fluid Mechanics, Vol. 43, Issue 1
A highorder finite difference method for numerical simulations of supersonic turbulent flows
journal, January 2011
 Li, Zhaorui; Jaberi, Farhad A.
 International Journal for Numerical Methods in Fluids, Vol. 68, Issue 6
Turbulence structure behind the shock in canonical shock–vortical turbulence interaction
journal, September 2014
 Ryu, Jaiyoung; Livescu, Daniel
 Journal of Fluid Mechanics, Vol. 756
Vorticity dynamics after the shock–turbulence interaction
journal, July 2015
 Livescu, D.; Ryu, J.
 Shock Waves, Vol. 26, Issue 3
Velocity gradient invariants and local flowfield topology in compressible turbulence
journal, January 2010
 Suman, Sawan; Girimaji, Sharath S.
 Journal of Turbulence, Vol. 11
Direct Numerical Simulation of a Mach 2 shock interacting with isotropic turbulence
journal, April 1995
 Hannappel, R.; Friedrich, R.
 Applied Scientific Research, Vol. 54, Issue 3