Advertisement

Advances in Particle Representation Modeling of Homogeneous Turbulence. From the Linear PRM Version to the Interacting Viscoelastic IPRM

Chapter
Part of the ERCOFTAC Series book series (ERCO, volume 18)

Abstract

In simple flows with mild mean deformation rates the Reynolds stresses are determined by the strain rate. On the other hand, when the mean deformation is very rapid, the turbulent structure takes some time to respond and the Reynolds stresses are determined by the amount of total strain. A good turbulence model should exhibit this viscoelastic character of turbulence, matching the two limiting behaviors and providing a reasonable blend in between. We show that in order to achieve this goal one needs to include structure information in the tensorial base used in the model, because non-equilibrium turbulence is inadequately characterized by the turbulent stresses themselves. We also argue that the greater challenge in achieving visco-elasticity in a turbulence model is posed by matching Rapid Distortion Theory (RDT). In this direction, we present the linear Particle Representation Model (PRM), and its extension in order to account for non-linear interactions. The key idea in the linear PRM version, is to evaluate the one-point statistics of an evolving turbulence field by following an ensemble of hypothetical “particles” with properties governed by equations chosen so that the statistical results for an ensemble of particles are exactly the same as in linear RDT. The non-linear extension of the PRM, the Interacting Particle Representation model (IPRM), incorporates a relatively simple model for the non-linear turbulence-turbulence interactions, and is able to handle quite successfully a wide range of different flows.

Keywords

Turbulent Kinetic Energy Reynolds Stress Structure Tensor Homogeneous Turbulence Reynolds Stress Tensor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This work was partly supported by a Center of Excellence grant from the Norwegian Research Council to Center for Biomedical Computing.

References

  1. 1.
    Akylas, E., Kassinos, S.C., Langer, C.: Analytical solution for a special case of rapidly distorted turbulent flow in a rotating frame. Phys. Fluids 18, 085104 (2006) MathSciNetCrossRefGoogle Scholar
  2. 2.
    Arnold, L.: Stochastic Differential Equations. Wiley, New York (1974) zbMATHGoogle Scholar
  3. 3.
    Cambon, C., Scott, J.F.: Linear and nonlinear models of anisotropic turbulence. Annu. Rev. Fluid Mech. 31, 1–53 (1999) MathSciNetCrossRefGoogle Scholar
  4. 4.
    Durbin, P.A., Speziale, C.G.: Realizability of second moment closures via stochastic analysis. J. Fluid Mech. 280, 395–407 (1994) zbMATHCrossRefGoogle Scholar
  5. 5.
    Hunt, J.: A review of the theory of rapidly distorted turbulent flow and its applications. Fluid Dyn. Trans. 9, 121–152 (1978) Google Scholar
  6. 6.
    Hunt, J., Carruthers, D.J.: Rapid distortion theory and the “problems” of turbulence. J. Fluid Mech. 212, 497–532 (1990) MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Kassinos, S.C., Reynolds, W.C.: A structure-based model for the rapid distortion of homogeneous turbulence. Report TF-61, Thermosciences Division, Department of Mechanical Engineering. Stanford University (1994) Google Scholar
  8. 8.
    Kassinos, S.C., Reynolds, W.C.: A particle representation model for the deformation of homogeneous turbulence. In: Annual Research Briefs 1996, pp. 31–50. Stanford University and NASA Ames Research Center: Center for Turbulence Research (1996) Google Scholar
  9. 9.
    Kassinos, S.C., Reynolds, W.C., Rogers, M.M.: One-point turbulence structure tensors. J. Fluid Mech. 428, 213–248 (2001) MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Lee, M.J., Reynolds, W.C.: Numerical experiments on the structure of homogeneous turbulence. Report TF-24, Thermosciences Division, Department of Mechanical Engineering, Stanford University (1985) Google Scholar
  11. 11.
    Mahoney, J.F.: Tensor and isotropic tensor identities. Matrix Tensor Q. 34(5), 85–91 (1985) Google Scholar
  12. 12.
    Pope, S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2000), p. 421 zbMATHGoogle Scholar
  13. 13.
    Reynolds, W.C.: Effects of rotation on homogeneous turbulence. In: Proc. 10th Australasian Fluid Mechanics Conference. University of Melbourne, Melbourne (1989) Google Scholar
  14. 14.
    Rogallo, R.S.: Numerical experiments in homogeneous turbulence. NASA Tech. Memo. 81315 (1981) Google Scholar
  15. 15.
    Rogers, M.M., Moin, P.: The structure of the vorticity field in homogeneous turbulent flows. J. Fluid Mech. 176, 33–66 (1985) CrossRefGoogle Scholar
  16. 16.
    Savill, A.M.: Recent developments in rapid distortion theory. Annu. Rev. Fluid Mech. 19, 531–575 (1987) CrossRefGoogle Scholar
  17. 17.
    Townsend, A.A.: The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press, Cambridge (1976) zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.University of CyprusNicosiaCyprus

Personalised recommendations