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1-D Fully Developed Turbulent Pipe flow

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Old   January 14, 2020, 19:01
Default 1-D Fully Developed Turbulent Pipe flow
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Sharat Chandrasekhar
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Is it possible to obtain meaningful velocity profiles for fully developed pipe flow with one-dimensional (radial coordinate only) finite difference simulations using the k-epsilon class of turbulence models ?

I know that this can and has been done using mixing length models, but wanted to check with the experts on this forum before embarking on a fool's errand.

Thanks
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Old   January 14, 2020, 21:52
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Quote:
Originally Posted by RruffPaw View Post
Is it possible to obtain meaningful velocity profiles for fully developed pipe flow with one-dimensional (radial coordinate only) finite difference simulations using the k-epsilon class of turbulence models ?

I know that this can and has been done using mixing length models, but wanted to check with the experts on this forum before embarking on a fool's errand.

Thanks
I am not sure to understand what do you mean for “pipe flow” and 1D radial direction... Do you want to express the velocity law U+(r+)? This is a classical theory, why do you want to use FDM?
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Old   January 15, 2020, 06:53
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Is it possible to obtain meaningful velocity profiles for fully developed pipe flow with one-dimensional (radial coordinate only) finite difference simulations using the k-epsilon class of turbulence models ?
Yes. It may not be particularly informative with respect to the velocity profile though because it will simply follow from a linear shear stress. If you know the wall stress from your boundary conditions then the details of the turbulence model becomes irrelevant to the velocity profile.
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Old   January 16, 2020, 16:33
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It can be done, and I actually suggest it as a useful toy model to learn dealing with turbulence models and/or wall functions.

The same holds, obviously, for other simple settings, like the simpler channel or the boundary layer.

The latter however is more interesting because it is the basis for some wall function approaches.

However, it depends from what you want to do.

Along the same lines, if you extend the approach to the 2D section you can use it as inflow generator (but to be useful you would need it for unstructured 2D grids)
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Old   January 16, 2020, 18:10
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I am not sure to understand what do you mean for “pipe flow” and 1D radial direction... Do you want to express the velocity law U+(r+)? This is a classical theory, why do you want to use FDM?
Hello, I'm trying to solve for the complete velocity profile, not just the near wall region, in a concentric annulus.
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Old   January 16, 2020, 18:13
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Yes. It may not be particularly informative with respect to the velocity profile though because it will simply follow from a linear shear stress. If you know the wall stress from your boundary conditions then the details of the turbulence model becomes irrelevant to the velocity profile.
What I'm actually trying to do is construct the complete velocity profile in a concentric annulus. I know the flow rate and hence the Reynolds number based on the bulk velocity. So, the wall shear stress must follow from mass conservation for which I need to integrate the entire velocity profile over the domain.
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Old   January 16, 2020, 18:14
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It can be done, and I actually suggest it as a useful toy model to learn dealing with turbulence models and/or wall functions.

The same holds, obviously, for other simple settings, like the simpler channel or the boundary layer.

The latter however is more interesting because it is the basis for some wall function approaches.

However, it depends from what you want to do.

Along the same lines, if you extend the approach to the 2D section you can use it as inflow generator (but to be useful you would need it for unstructured 2D grids)
Thanks! It will be nice to see how it compares to the Mixing Length model which is actually not bad for confined flow in conduits.
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Old   January 17, 2020, 06:03
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Consider that for the k-epsilon family of models you are going to need a wall function, even if in 1D. So, what you will see is how this performs more than how the k-epsilon performs. As a matter of fact, most wf models actually mimic the mixing length model, so you might not see any specific difference.

Maybe try the k-omega family or the Spalart-Allmaras.
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