On the mathematical foundations of the k-epsilon turbulent model
Abstract
The derivation of the k-epsilon turbulence model from the Euler problem with random initial data is investigated analytically, applying homogenization theory (Bensoussan et al., 1978) and the asymptotic expansions proposed by Perrier and Pironneau (1981) and Papanicolaou and Pironneau (1981). The k-epsilon model is shown to be similar to a first-order approximation of the general model for two-dimensional mean flows, but with a modified formulation of the Reynolds stress tensor and replacement of the dissipated-energy rate with the helicity (or a length scale based on it). Typical numerical results are presented graphically.
- Publication:
-
IN: Vistas in applied mathematics: Numerical analysis
- Pub Date:
- 1986
- Bibcode:
- 1986vamn.rept...44C
- Keywords:
-
- Asymptotic Series;
- Computational Fluid Dynamics;
- Heuristic Methods;
- High Reynolds Number;
- K-Epsilon Turbulence Model;
- Turbulent Flow;
- Isotropic Turbulence;
- Kinetic Energy;
- Two Dimensional Flow;
- Vorticity;
- Fluid Mechanics and Heat Transfer