Modeling turbulent dissipation at low and moderate Reynolds numbers

Abstract

The dissipation of kinetic energy is one of the key features of turbulent flows that must be modeled accurately in order to obtain useful engineering predictions. At high Reynolds numbers the assumption of scale separation can be invoked in the modeling of the dissipation process. This paper focuses on the more difficult issue of modeling the dissipation process at moderate and low Reynolds numbers. The low and moderate Reynolds number range is very important for tuning turbulence models and for many practical engineering problems. To approach this problem, an alternative formulation to the classic dissipation scale equation is proposed. The interesting feature of this formulation, an inverse lengthscale equation, is that it captures both the high Reynolds number and low Reynolds number decay limits. A careful assessment of existing data then allows us to clearly identify the region of transition between high and low Re and propose a very simple equation system which can accurately model dissipation at any Reynolds number. The equivalent K/ϵ model is derived and the proposed model is compared with a number of other low Re dissipation modifications for the K/ϵ equation system. To complete the discussion, the issue of near-wall dissipation modeling is carefully examined and shown to be fundamentally different from the low Reynolds number limit. This is shown to be an important distinction of practical modeling importance.

Keywords:

• Dissipation
• Low Reynolds mumber
• Isotropic decay
• Turbulence modeling

Acknowledgments

We gratefully acknowledge the financial support of this work by the Office of Naval Research (grant number N00014-01-1-0267), and partial support by the Air Force Office of Scientific Research (grant number FA9550-04-1-0023), and the National Science Foundation (grant number CTS-0522089). High performance computing (HPC) resources were provided by the Arctic Region Supercomputing Center.