On the application of time dependent scaling to the modelling of turbulence undergoing compression
Abstract
In this paper we study the implications of a time dependent scaling which makes the Navier-Stokes equations invariant under an external isotropic compression. In addition to the use of rapid distortion theory (RDT), a rescaling of the elapsed time allows the nonlinear turbulence mechanisms to be accounted for in a straightforward way. The approach provides analytical laws for the evolution of the kinetic energy, its dissipation rate and the typical length scales, under isotropic compression. Several k-epsilon models are compared for different compression laws, including applications to reciprocating engines. Finally, an extension towards axisymmetrical compression is proposed using both specific RDT calculations and the 'isotropic' time-rescaling. Promising comparisons are made with 'best' (in accordance with the above comparisons) k-epsilon models and with direct numerical simulations.
- Publication:
-
European Journal of Mechanics, B/Fluids
- Pub Date:
- 1992
- Bibcode:
- 1992EuJMB..11..683C
- Keywords:
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- Compressible Flow;
- Flow Theory;
- K-Epsilon Turbulence Model;
- Turbulent Flow;
- Boussinesq Approximation;
- Formalism;
- Scaling Laws;
- Time Dependence;
- Fluid Mechanics and Heat Transfer