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-   -   K-Epsilon model? (http://www.cfd-online.com/Forums/main/2280-k-epsilon-model.html)

 Brindaban Ghosh June 24, 2000 02:47

K-Epsilon model?

What is the physical interpretation of "Destruction" term in Epsilon equation ?

 John C. Chien June 24, 2000 03:33

Re: K-Epsilon model?

(1). In general, an equation can have second-order terms, which we call diffusion terms. It can be related to second-order terms in a diffusion equation, such as a Laplace equation. (2). Then there will be first order terms, which we call convection terms. It can be related to first-order terms in an inviscid equation, such as Euler equation. (3). Other than the diffusion and convection terms, there will be zeroth-order terms, which are called source terms. It can be related to the heat source terms of an energy equation. (4). Within the source terms, they sometimes can be separated into two parts, one is the production term which will have the effect of the positive heat source term. The other is the sink term or the dissipation term, which has the effect of sink effect. (cooling effect instead of the heating effect) (5). So, the terms in the equation are typically classified or identified by this method. This does not mean that the terms identified will have the same physical meaning at all. (6). This is because, in the mathematical operations, sucha as the coordinate transformation, a second-order term will be expanded into several second-order terms and several first-order terms. (7). The first -order terms will still be grouped into the first-order terms, but these are derived from the transformation rather than the physical process. Still, these first order terms will have the effect of convection in the mathematical sense. (8). So, the production term in the equation will have the effect of increasing the value of the variable in the solution. On the other hand, the dissipation term will have the effect of lowering the value of the variable in the solution. (9). Sometimes, especially for the case of the epsilon equation, the absolute contribution from the diffusion and the convection terms are relatively small. Therefore, the equation will be dominated by the production and the dissipation terms. It is like two persons in front of a blackboard, one the writing, the other is erasing. (10) the epsilon function can be used to derive the length scale, thus the equation for epsilon is like the equation for the length scale. (the dissipation term will in a way has the effect of reducing the length scale value in the solution. But this is not directly related because it also involves the turbulence kinetic energy. The length scale l is equal to Cd*k^1.5(power)divided by epsilon. So, epsilon is sort of the inverse of the length scale. So, you can figure out the exact effect on the length scale by the dissipation term of the epsilon equation.) (11). You must really know also the zero-equation model, one-equation model as well as the two -equation model in order to understand the meaning of the length scale.

 andy June 24, 2000 04:22

Re: K-Epsilon model?

Despite its label, do not be tempted to consider it the viscous dissipation of the isotropic dissipation rate of the turbulent kinetic energy since this scales as Re^0.5 unlike the term in the epsilon equation. One needs to look at the difference between the modelled "production" and "destruction" terms to get something that scales correctly. Even then, the modelled difference is not really amenable to mapping onto related terms in the transport equation for the isotropic dissipation rate except, possibly, in equilibrium regions or by the wildly optimistic.

In other words, the "production" and "dissipation" terms taken together produce something that behaves in a defendable manner but they are not closely related to terms in the transport equation for the isotropic dissipation of turbulent kinetic energy.

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