Phenomenology
If we observe turbulence in flows, we distinguish large scale structures that can well be resolved by overlying the picture with computational grid that is economically feasible and small scale eddies smaller than the used grid size that can not be resolved. The large eddies are directly born from what is subjectively called mean flow. Their size is in a way limited by the geometry of the flow boundaries and in a way how they are generated. They are responsible for effective turbulent transport of mass and energy. Due to their interactions with the mean flow and with the other eddies they collide and coalesce to larger eddies or split to smaller eddies: an endless game that fascinate children and make scientist desperate to describe them mathematically because of the enormous complexity of the process. For the same reason a chain of the smaller eddies with all possible sizes is generated. Those eddies which size is smaller than what is called Kolmogoroff small scales dissipate their rotation- and fluctuation energy into heat. While the large eddies hardly have the same structure in all directions, the small scale eddies tend to similarity independent on the flow direction – a property named isotropy. Exactly this observation lead Smagorinski in 1963 to the idea to look for such conservation equations that describe physics that can really be resolved on the used computational grid and separate the remaining physics that have to be resolved by additional modeling. The non resolved part or the so-called filtered part is modeled in such a way that the energy for the unresolved eddies is taken from the resolved mechanical energy. This approach is called Large Scale Simulation and is getting since that time very popular in the single phase fluid mechanics.
Applying this method to multiphase flow dynamics is very new branch of the science and up to now limited to bubbly and droplet flows only. Nevertheless, because it is very promising, we will describe briefly the main ideas behind this modeling technique.
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Kolev, N.I. (2011). Large eddy simulation. In: Multiphase Flow Dynamics 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20749-5_10
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