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Stochastic Lagrangian Modeling for Large Eddy Simulation of Dispersed Turbulent Two-Phase Flows
Concepts an Your name. Close Send. Remember me Forgot password? In Chapter 8, we regarded RANS as a method to grasp roughly how many people are crossing the crosswalk. In LES, we can compass every tiny movement of each person, moment by moment, as long as we prepare mesh with the right size.
Large-Eddy Simulation for Acoustics
Let us learn about Smagorinsky model, which is a leading example of SGS model. Smagorinsky model uses a similar model to RANS, namely a model that considers hypothetical stress proportional to velocity gradient. That is, the stress is expressed as:. In RANS model, eddy viscosity is given by turbulence energy and turbulence dissipation rate, which are obtained by solving the separate equations from the equation for velocity.
In Smagorinsky model, on the other hand, eddy viscosity is given not by solving any equation but by the following formula, assuming that it is proportional to mesh size and the magnitude of velocity gradient:. As described in the above formula, eddy viscosity of Smagorinsky model contains a model constant CS. It is known that CS takes some value between 0. To resolve this inconvenience, a calculation method which adjusts CS automatically was proposed.
Smagorinsky model is a convenient model and it is still one of the leading models, but it has one big shortcoming: It cannot represent adverse energy flow from small eddies to large eddies.
Industrial and Environmental Applications of Direct and Large-Eddy Simulation | SpringerLink
In a turbulent flow, larger eddies generate smaller eddies; however, in some cases, smaller eddies unite with each other to form a large eddy, which leads to adverse flow of energy so-called inverse cascade. In other words, the energy carried by smaller eddies becomes the energy of a large eddy, which is opposite of the usual direction of energy transfer. Smagorinsky model, however, is a model that only increases a hypothetical viscosity that is eddy viscosity; it only has the effect of taking energy away from larger eddies.
In the scale similarity model, modeling is carried out by assuming the similarity between eddies that are slightly larger than mesh size and eddies that are slightly smaller than mesh size Figure Since this model does not use velocity gradient or eddy viscosity like Smagorinsky model does, it can represent the inverse cascade.
I suppose this model is rarely employed by commercial software, but I wanted to introduce it as one of the SGS models. In the next column, we will discuss a calculation example of LES.