Research Papers: Flows in Complex Systems

Modeling of Reynolds Stress Models for Diffusion Fluxes Inside Shock Waves

[+] Author and Article Information
D. Souffland

F-91297 Arpajon, France
e-mail: denis.souffland@cea.fr

O. Soulard

F-91297 Arpajon, France
e-mail: olivier.soulard@cea.fr

J. Griffond

F-91297 Arpajon, France
e-mail: jerome.griffond@cea.fr

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 22, 2013; final manuscript received April 7, 2014; published online July 9, 2014. Assoc. Editor: Stuart Dalziel.

J. Fluids Eng 136(9), 091102 (Jul 09, 2014) (4 pages) Paper No: FE-13-1036; doi: 10.1115/1.4027381 History: Received January 22, 2013; Revised April 07, 2014

In Reynolds stress models (RSM), the use of first gradient closures to model diffusion fluxes may lead to a nonconvergence with mesh refinement, especially if the flow experiences episodes of dominant compressibility effects like during interactions with shock waves. In our turbulence mixing model, we have implemented two methods to prevent the divergence of these fluxes inside shocks. They are based on the use of Schwarz inequalities and on the detection of zones where compressibility effects are the dominant source of turbulence. The necessity of a specific adjustment and the efficiency of the method are demonstrated in the case of shock interaction with homogeneous turbulence. The sensitivity of the results in the more practical case of mixing zones generated in shock tubes is illustrated.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Andronov, V., Bakhrakh, S., Meshkov, E., Nikiforov, V., Pevnitskii, A., and Tolshmyakov, A., 1982, “An Experimental Investigation and Numerical Modeling of Turbulent Mixing in One-Dimensional Flows,” Dock. Akad. Nauk SSSR, 264, pp. 76–82.
Besnard, D. C., Haas, J. F., and Rauenzahn, 1989, “Statistical Modeling of Shock-Interface Interaction,” Physica D, 37, pp. 227–247. [CrossRef]
Banerjee, A., Gore, R., and Andrews, M., 2010, “Development and Validation of a Turbulent-Mix Model for Variable-Density and Compressible Flows,” Phys. Rev. E, 82, p. 046309. [CrossRef]
Grégoire, O., Souffland, D., and Gauthier, S., 2005, “A Second-Order Turbulence Model for Gaseous Mixtures Induced by Richtmyer–Meshkov Instability,” J. Turb., 6(29), pp. 1–20. [CrossRef]
Griffond, J., Soulard, O., and Souffland, D., 2010, “A Turbulent Mixing Reynolds Stress Model Fitted to Match Linear Interaction Analysis Predictions,” Phys. Scr., T142, p. 014059. [CrossRef]
Pope, S. B., 2000, Turbulent Flows, Cambridge University Press, Cambridge, UK.
Pope, S. B., 1994, “On the Relationship Between Stochastic Lagrangian Models of Turbulence and Second-Moment Closures,” Phys. Fluids, 6(2), pp. 973–985. [CrossRef]
Soulard, O., Griffond, J., and Souffland, D., 2012, “Pseudocompressible Approximation and Statistical Turbulence Modeling: Application to Shock Tube Flows,” Phys. Rev. E, 85, p. 026307. [CrossRef]
Poggi, F., Thorembey, M.-H., and Rodriguez, G., 1998, “Velocity Measurements in Turbulent Gaseous Mixtures Induced by Richtmyer–Meshkov Instability,” Phys. Fluids, 10(11), pp. 2698–2700. [CrossRef]


Grahic Jump Location
Fig. 1

Turbulent diffusivity k˜2/ɛ˜ with respect to abscissa (origin at the shock front) for the interaction of a Mach 3 shock front with HIT. Mesh refinement without (a) FLM and with (b) FLM.

Grahic Jump Location
Fig. 2

Turbulent mixing zone (TMZ) width with respect to time for the shock tube experiment of Poggi et al. [9]. Mesh refinement (a) without FLM and (b) with FLM.




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In