Prof. Norbert Peters
RWTH Aachen
Building Scalar Mixing and Dissipation from Small Dissipation Elements
Abstract: Existing theories of turbulence and turbulent mixing are based on the cascade process whereby large eddies break up into small ones which eventually are dissipated by molecular processes. The general idea for scalar mixing is that stirring of the scalar field by turbulent motion is rate controlling, whereas molecular diffusion just completes the sequence. As a consequence the scalar dissipation rate is modelled by considering the transfer rate from the large scales and not by an analysis of the small scale processes where it actually occurs. In this work we will formulate a theory of mixing based on small scale structures called dissipation elements. These elements extend between minimum and maximum points as well as saddle points of the scalar field. They are space filling and bounded by surfaces on which the normal scalar gradients vanish. Within the dissipation elements molecular diffusion competes with strain. These two processes essentially determine the rate at which the maximum and minimum value of the scalar move towards each other. This rate is identified as the small scale mixing rate. The elements are characterized by a number of paramaters, namely the difference between maximum and minimum of the scalar, the strain rate and the mixing rate as well as geometric dimensions. A "Boltzmann" equation for the joint pdf of these parameters is derived using the rates at which these paraters change by internal processes. Interaction between dissipation elements is ignored except for the case where an element disappears and the surrounding elements combine. This process bears similarities with the collision process in molecular gas dynamics. The theory is compared to DNS results for scalar mixing. Moments of the joint pdf allow to reconstruct the scalar pdf as well as the conditional scalar dissipation rate. This formulation therefore has the the potential to replace existing models of scalar dissipation based on the transfer from the large scales by building it up from the small scales.
| Zeit: | Freitag, 23. Januar 2004, 16.00 (Kaffee/Tee um 15.30 p.m.) |
| Ort: | FU Berlin, Arnimalle e 2-6, Raum 032 im EG |