Skip to main content Accessibility help
×
Home

Toward approximating non-local dynamics in single-point pressure–strain correlation closures

  • Aashwin A. Mishra (a1) and Sharath S. Girimaji (a2)

Abstract

A key hurdle in turbulence modelling is the closure for the pressure–strain correlation. Herein, the challenge stems from the fact that the non-local dynamics due to pressure cannot be comprehensively incorporated in a single-point closure expression. In this article, we analyse different aspects of the dynamics due to pressure for their amenability with the single-point modelling framework. Based on this, an approach is proposed that incorporates a set of pragmatic compromises in the form and the scope of the model to augment the degree of non-local dynamics that may be approximated by a single-point pressure strain correlation model. Thence, this framework is utilized to formulate an illustrative model. The predictions of this model are compared to numerical and experimental data and contrasted against other established closures over a range of homogeneous flows, under diverse conditions. Finally, the regions of validity in anisotropy space for this illustrative model are delineated using the process realizability criteria for different flows.

Copyright

Corresponding author

Email address for correspondence: aashwin@neo.tamu.edu

References

Hide All
Bardina, J., Ferziger, H. & Reynolds, W. C.1983 Improved turbulence models based on large-eddy simulation of homogeneous, incompressible turbulent flows. Tech. Rep. TF-19. Stanford University.
Blaisdell, G. A. & Shariff, K. 1996 Simulation and modeling of the elliptic streamline flow. In Studying Turbulence Using Numerical Simulation Databases: Proceedings of the 1996 Summer Program, pp. 433446. Stanford University.
Cambon, C.1982 Étude spectrale d’un champ turbulent incompressible, soumis à des effets couplés de déformation et de rotation, imposés extérieurement. Thèse de Doctorat d’État, Université de Lyon, France.
Cambon, C., Benoit, J. P., Shao, L. & Jacquin, L. 1994 Stability analysis and large-eddy simulation of rotating turbulence with organized eddies. J. Fluid Mech. 278, 175200.
Cambon, C., Jacquin, L. & Lubrano, J. L. 1992 Toward a new Reynolds stress model for rotating turbulent flows. Phys. Fluids 4, 812824.
Cambon, C., Jeandel, D. & Mathieu, J. 1981 Spectral modelling of homogeneous non-isotropic turbulence. J. Fluid Mech. 104, 247262.
Cambon, C. & Rubinstein, R. 2006 Anisotropic developments for homogeneous shear flows. Phys. Fluids 18 (8), 085106.
Chou, P. Y. 1945 On velocity correlations and the solutions of the equations of turbulent fluctuation. Q. Appl. Maths 3 (1), 3854.
Durbin, P. A. 1993 A Reynolds stress model for near-wall turbulence. J. Fluid Mech. 249, 465498.
Johansson, A. V. & Hallback, M. 1994 Modeling the rapid pressure-strain in Reynolds stress closures. J. Fluid Mech. 269, 143168.
Kassinos, S. C. & Reynolds, W. C.1994 A structure-based model for the rapid distortion of homogeneous turbulence. Tech. Rep. TF-61. Stanford University.
Launder, B. E., Reece, G. J. & Rodi, W. 1975 Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech. 68 (03), 537566.
Lee, M. J. & Reynolds, W. C.1985 Numerical experiments on the structure of homogeneous turbulence. Tech. Rep. TF-24. Stanford University.
Lumley, J. L. 1978 Computational modeling of turbulent flows. Adv. Appl. Mech. 18, 123176.
Mishra, A. A.2010 A dynamical systems approach towards modeling the rapid pressure strain correlation. Master’s thesis, Texas A&M University.
Mishra, A. A.2014 The art and science in modeling the pressure-velocity interactions. PhD thesis, Texas A&M University.
Mishra, A. A. & Girimaji, S. S. 2010 Pressure-strain correlation modeling: towards achieving consistency with rapid distrotion theory. Flow Turbul. Combust. 85, 593619.
Mishra, A. A. & Girimaji, S. S. 2012 Manufactured turbulence with Langevin equations. ERCOFTAC Bulletin 92, 1116.
Mishra, A. A. & Girimaji, S. S. 2013 Intercomponent energy transfer in incompressible homogeneous turbulence: multi-point physics and amenability to one-point closures. J. Fluid Mech. 731, 639681.
Mishra, A. A. & Girimaji, S. S. 2014 On the realizability of pressure-strain closures. J. Fluid Mech. 755, 535560.
Mishra, A. A. & Girimaji, S. S. 2015 Hydrodynamic stability of three-dimensional homogeneous flow topologies. Phys. Rev. E 92 (5), 053001.
Mishra, A. A., Hasan, N., Sanghi, S. & Kumar, R. 2008 Two-dimensional buoyancy driven thermal mixing in a horizontally partitioned adiabatic enclosure. Phys. Fluids 20 (6), 063601.
Mishra, A. A., Iaccarino, G. & Duraisamy, K. 2015 Epistemic uncertainty in statistical Markovian turbulence models. In CTR Annu. Res. Briefs 2015, pp. 183195. Stanford University.
Mishra, A. A., Iaccarino, G. & Duraisamy, K. 2016 Sensitivity of flow evolution on turbulence structure. Phys. Rev. Fluids 1 (5), 052402.
Moffatt, H. K. 1967a The interaction of turbulence with a strong wind shear. In URSI-IUGG International Colloquim on Atmospheric Turbulence and Radio Wave Propagation, pp. 139156. Nauka.
Moffatt, H. K. 1967b On the supression of turbulence by a uniform magnetic field. J. Fluid Mech. 28, 571592.
Mons, V., Cambon, C. & Sagaut, P. 2016 A spectral model for homogeneous shear-driven anisotropic turbulence in terms of spherically averaged descriptors. J. Fluid Mech. 788, 147182.
Rotta, J. 1951 Statistische theorie nichthomogener turbulenz. Z. Phys. 129, 547572.
Sagaut, P. & Cambon, C. 2008 Homogeneous Turbulence Dynamics. Cambridge University Press.
Salhi, A., Cambon, C. & Speziale, C. G. 1997 Linear stability analysis of plane quadratic flows in a rotating frame with applications to modeling. Phys. Fluids 9 (8), 23002309.
Schumann, U. 1977 Realizability of Reynolds stress turbulence models. J. Fluid Mech. 20, 721725.
Speziale, C. G., Abid, R. & Durbin, P. A. 1994 On the realizability of Reynolds stress turbulence closures. J. Sci. Comput. 9, 369403.
Speziale, C. G. & Durbin, P. A. 1994 Realizability of second-moment closure via stochastic analysis. J. Fluid Mech. 280, 395407.
Speziale, C. G., Sarkar, S. & Gatski, T. B. 1991 Modelling the pressure strain correlation of turbulence: an invariant dynamical systems approach. J. Fluid Mech. 227, 245272.
du Vachat, R. 1977 Realizability inequalities in turbulent flows. Phys. Fluids 20 (4), 551556.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Toward approximating non-local dynamics in single-point pressure–strain correlation closures

  • Aashwin A. Mishra (a1) and Sharath S. Girimaji (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed