[Inderjeet Singh]

Hello All,

I want to clarify the significance of the three turbulence parameters -

1. Turbulent Kinetic Energy
2. Turbulence Intensity
3. Turbulent Dissipation rate


I want to know how they inter-relate with each other and how they have impact on the heat transfer and pressure drop in means (say) - Higher T.K.E gives higher Heat transfer rate or something like that.

[LuckyTran]

Turbulence intensity is just a normalized turbulent kinetic energy (normalize k by a mean velocity scale). So you can ignore that. It is a powerful tool to help you interpret your results. Or, you can interchange k and turbulence intensity but they mean the same thing.

Just look at the RANS equations and you will see that it's all mean flow variables and a turbulent viscosity (because we have used Boussinesq hypothesis to model the turbulence). Basically, you just need to figure out what the turbulent viscosity is, and whether it is greater or lower. Then invoke the heat-mass-momentum transfer analogy.

The relationship between k and epsilon is exactly the turbulence model. Unfortunately it differs from model to model. But you can take a look at the standard k-epsilon model as a starting point.

https://www.cfd-online.com/Wiki/Stan...-epsilon_model

Also note you can see where to get the turbulent viscosity, it goes like k^2/epsilon. This isn't a universal truth but it should give you a feel for the result that you're looking for. Of course, in reality the real heat transfer and pressure drop are whatever they need to be to satisfy physical laws. These are just (hasty) generalizations.

k and epsilon are related through coupled transport equations (coupled partial differential equations). epsilon doesn't appear in the k-equation explicitly (it appears via the turbulent viscosity in the production term). k appears all over the place in the epsilon equation. Both appear in the turbulent viscosity (which makes its way back to the k equation). Turbulent viscosity affects momentum, which affects both k and epsilon. They are related in a big loop. But if you just want to know what is the influence on heat transfer and pressure drop, just freeze the velocity field and you see that the only free parameter is the turbulent viscosity. This result shouldn't be a surprise, because that's exactly what the Boussinesq hypothesis/assumption is.

Of course, we know that there is more to heat transfer and pressure drop than just viscosity! It depends on the flow obviously. But this gives you a way to proceed.

[Inderjeet Singh]

Thanx @LuckyTran for your reply..

I guess your answer is of too much depth i guess.. But i understood the basic relationships between k and e. Lets not go towards the transport equations side..

I was expecting a very basic answer and for that let me try and explain you the case once again in more detail-

Lets say i am investing a fluid flow in a duct with heat flux as well.. with k-e model. Say from 5 different cases (A1, A2, A3, A4, A5) , let's assume i obtained maximum Heat transfer coefficient and Pressure drop in case A3.

And i have to justify the obtained results (higher heat transfer coefficient and higher pressure drop in case A3) with the contour plots of Turbulence Kinetic Energy and Turbulence Dissipation Rate.


How there trend need to be ? Will the highest H.T case (A3) will have maximum Scale value of T.K.E. and T. Dissipation Rate or it's not necessary ???


are the Heat transfer and turbulent Kinetic Energy Proportional to each other ?? Can other cases get a higher T.K.E value than A3 ?

[LuckyTran]

I think you dismissed the basic answer too quickly. It lies in the heat-momentum analogy.

Can you explain heat transfer using tke? Yes and no. Yes there is a trend. Yes because the turbulent viscosity is proportional to k. Via the Boussinesq hypothesis the influence of turbulence can be explained as laminar-like with an enhanced viscosity (the turbulent viscosity). The Reynolds analogy also tells you that the heat transfer analogous and proportional to the momentum transfer (the wall friction or the pressure drop).

Trends do not explain everything. So my answer is also no because you are looking at field variables and asking how they affect surface properties. It's like asking if the maximum temperature in the universe can explain global warming. There are a many ways that other combinations can have more heat transfer at less pressure drop, otherwise heat transfer engineers would have run out of jobs already. You can easily imagine that you can have infinite turbulence but no heat transfer if the fluid is at the same temperature as the surface. Imagine you are a molecule on the surface, your interaction with the flow is limited to only the fluid near the surface. If the turbulence and high k occurs in regions far away from the surface, the surface cannot know.