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.
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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)
Arnold, L.: Stochastic Differential Equations. Wiley, New York (1974)
Cambon, C., Scott, J.F.: Linear and nonlinear models of anisotropic turbulence. Annu. Rev. Fluid Mech. 31, 1–53 (1999)
Durbin, P.A., Speziale, C.G.: Realizability of second moment closures via stochastic analysis. J. Fluid Mech. 280, 395–407 (1994)
Hunt, J.: A review of the theory of rapidly distorted turbulent flow and its applications. Fluid Dyn. Trans. 9, 121–152 (1978)
Hunt, J., Carruthers, D.J.: Rapid distortion theory and the “problems” of turbulence. J. Fluid Mech. 212, 497–532 (1990)
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)
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)
Kassinos, S.C., Reynolds, W.C., Rogers, M.M.: One-point turbulence structure tensors. J. Fluid Mech. 428, 213–248 (2001)
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)
Mahoney, J.F.: Tensor and isotropic tensor identities. Matrix Tensor Q. 34(5), 85–91 (1985)
Pope, S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2000), p. 421
Reynolds, W.C.: Effects of rotation on homogeneous turbulence. In: Proc. 10th Australasian Fluid Mechanics Conference. University of Melbourne, Melbourne (1989)
Rogallo, R.S.: Numerical experiments in homogeneous turbulence. NASA Tech. Memo. 81315 (1981)
Rogers, M.M., Moin, P.: The structure of the vorticity field in homogeneous turbulent flows. J. Fluid Mech. 176, 33–66 (1985)
Savill, A.M.: Recent developments in rapid distortion theory. Annu. Rev. Fluid Mech. 19, 531–575 (1987)
Townsend, A.A.: The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press, Cambridge (1976)
Acknowledgements
This work was partly supported by a Center of Excellence grant from the Norwegian Research Council to Center for Biomedical Computing.
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Kassinos, S.C., Akylas, E. (2012). Advances in Particle Representation Modeling of Homogeneous Turbulence. From the Linear PRM Version to the Interacting Viscoelastic IPRM. In: Nicolleau, F., Cambon, C., Redondo, JM., Vassilicos, J., Reeks, M., Nowakowski, A. (eds) New Approaches in Modeling Multiphase Flows and Dispersion in Turbulence, Fractal Methods and Synthetic Turbulence. ERCOFTAC Series, vol 18. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2506-5_6
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DOI: https://doi.org/10.1007/978-94-007-2506-5_6
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