Physical Intuitions for the k-epsilon Turbulence Model

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SUMMARY

The discussion focuses on the k-epsilon turbulence model, specifically the transport equations related to the production of turbulent kinetic energy (k) and dissipation rate (epsilon). Key inquiries include the relationship between the double contraction of the strain rate tensor and the production of k or epsilon, the significance of the ratio epsilon squared over k in the decay rate of epsilon, and the distinction between epsilon and omega in the k-omega model. Participants seek detailed references beyond basic sources like Wikipedia to deepen their understanding of these complex concepts.

PREREQUISITES
  • Understanding of k-epsilon turbulence model fundamentals
  • Familiarity with strain rate tensor and its applications in fluid dynamics
  • Knowledge of turbulent kinetic energy (k) and dissipation rate (epsilon)
  • Basic principles of the k-omega turbulence model
NEXT STEPS
  • Research advanced texts on k-epsilon turbulence model transport equations
  • Study the mathematical derivation of the double contraction of the strain rate tensor
  • Explore the relationship between epsilon squared and k in turbulence decay
  • Investigate the differences between epsilon and omega in turbulence modeling
USEFUL FOR

Fluid dynamics researchers, aerospace engineers, and anyone involved in computational fluid dynamics (CFD) who seeks to enhance their understanding of turbulence modeling techniques.

Twigg
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Hey all!

I am trying to understand the terms in the source-side of the k-epsilon transport equations. My only reference on this so far has been the wikipedia article (in my defense, it's not in Landau! the gospel has forsaken me :cry:). If you have a reference that goes into gory detail on the transport equations, that'll probably answer my questions.

But my specific questions are:
1) How is the double contraction of the strain rate tensor related to "production of k (or epsilon)"? My gut reaction is that eddy viscosity times strain rate is Reynolds stress, and Reynolds stress contracted with strain rate is somehow like a "turbulent work" thingy, but I'd like to know more. Also that doesn't explain the term in the epsilon transport equation.

2) How is ##\epsilon^2/k## related to the rate of decay of ##\epsilon##? I get the dimensions are right, but is that all there is to it?

3) How is ##\epsilon## different from ##\omega## in the k-omega model?
 

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