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Valdemir G. Ferreira June 3, 2000 10:15

The effect of E term in the EPSILON equation
Hi Dear Friends,

I have seen an E term in the epsilon equation of the K-E model. I don't know what is its physical meaning. Please, can anyone explain?


John C. Chien June 3, 2000 11:37

Re: The effect of E term in the EPSILON equation
(1). Turbulence models are not based on the physics of the flow. It is more on the math model side. (2). So, the idea is to create a math model first, then add and substract terms, fine tune the parameters and parametric functions, so that when applied to the well documented cases, it will match the data. (3). E term is a source term in the epsilon equation, so, it will act as a source effect to the solution of epsilon. It appears in the so-called low Reynolds number model of k-epsilon equations. The low Reynolds number model is the one which can be used everywhere in the flow field, including the near wall sublayer region. ( In a way, it is related to Van Driest's near wall damping function concept in the mixing length theory of boundary layer) (4). By the way, you are free to add and substract terms to the model to improve the result. So, it is a model. (not the real thing.)

Jonas Bredberg June 6, 2000 02:45

Re: The effect of E term in the EPSILON equation

Turbulence modellers would prefer to relate this term to physics although the correctness of what John says. I would presume that people like B.E. Launder wouldn't be particularly pleased with the above explanation. Anyhow here is what I read the other day: "In separated flow, reattachment and recirculation the numerical model usually predicts a turbulent viscosity near the wall that is too high and a viscous sublayer that is [too] thin.....The additional emperical terms [E-terms, several in this particular model] are added to account for the nonequilibrium dissipation processes. These terms help by adjusting the turbulent dissipation rate from the fully turbulent region to the viscous sublayer." Cho and Goldstein: An improved low-Reynolds-number k-\epsilon turbulence model for recirculating flows. Note that the Yap-term produce a similar effect, and that the Launder-Sharma model shouldn't be used without this correction added to its \epsilon-eq. - especially if you would like to predict heat transfer.

Regards Jonas

John C. Chien June 6, 2000 09:17

Re: The effect of E term in the EPSILON equation
(1). Many many years ago, when I was still a student, I remembered that my advisor made a comment, " What is the dissipation of the dissipation of the kinetic energy? " I guess, he had hard time finding a physical model for it.(2). I think, it is not quite on the physics side. It is easier to understand it by thinking as a math model. (3). Some are using this E-term, but not every model has it, I think. (4). By the way, my point was, it's up to you to add or substract terms, if it improves the results. There is a long list of names already in the low Reynolds number models, it is ideal place to make one's name and model known. (5). Why is the turbulence in separated flows different from other flows, so that an improved model is required with additional terms? What is missing is the physics. Can you add extra terms to the Navier-Stokes equations? The answer is NO, because it represents the conservation law. (6). Except the turbulence kinetic energy (k) equation (which can be derived systematically from conservation law), the rest of the equations related to the "length scales" (such as epsilon, omega, kl, etc) are just model equations.

Jonas Bredberg June 6, 2000 09:56

Re: The effect of E term in the EPSILON equation
Similar to the k-eq, it is quite possible to derive an exact equation for the dissipation equation. Involving four! production terms, two transport terms, a diffusion term and a dissipation term. However the MODELLED \epsilon-eq. as well as the MODELLED k-eq. is another story. Truely agree that Navier-Stokes is the solution to CFD - however it is not that easy to solve these coupled equations. Until DNS makes real progress we are sadly restricted to models, which should be and generally is based on physics rather than maths. The Yap-term does not change anything in attached flows, merely changing the turbulent length scale in non-equilibrium flows, and hence improve the physics of the Launder-Sharma model. It is really questionable to develop a model that fails simple testcase however yield accurate result for a certain case. That is not turbulence modelling, rather curve-fitting.

John C. Chien June 6, 2000 10:31

Re: The effect of E term in the EPSILON equation
(1). I agree with you. (2). It is a good idea to use the physics to simplify the math models. I think, turbulence modeling is still a wide open field. It controls the modern cfd development and applications. (3).Perhaps the numerical experiments such as DNS will provide some useful insight into the physics of turbulence in the future and guide the development of new models. (if the results are valid and useful) (4). By the way, "Curve Fitting" is easier to understand, but 20 years ago, researchers in turbulence modeling field had invented a better name for it already. It is called "Numerical Optimization". (5). So, the modern turbulence models were all derived through this numerical optimization phase as the final step in the process. There is nothing wrong with it. I must say that, most of these numerical optimization were systematically carried out, under some physical constraints.( law of wall, wake decay,etc..) (6). I think, more test data and simulation are needed to improve the understanding of the turbulent flows. And I think, physics has to be based on the test data or observation (and simulation as well).

Duane Baker June 7, 2000 02:37

Re: The effect of E term in the EPSILON equation
Hi Jonas,

good comments!

I am interested in learning more about the prediction of hear transfer in separated flows as it is one of those cases where the poor numerical predictions do look reasonable to the untrained eye (usually the customer). The real danger is that the under-predicted separation in the physical device can seriously affect performance. What are some good references that lean to the industrial/practical side?


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