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Local Nusselt Number analysis in structured Pipes

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Old   August 11, 2023, 08:53
Question Local Nusselt Number analysis in structured Pipes
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Max E.
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Hello together,

I am analysing a rib-structured pipe flow with heated walls with constant Heat flux in ensight. The CFD was done in fluent in a transient RSM-BSL model at Re=50000 with periodic boundary conditions over 1 rib. Note that the image attached shows 2 ribs, this is only a periodic condition set in ensight, the flowfiled was calculated over only one instance.

One topic of analysis is maxima and minima as well as local Nusselt Number distribution. I am working of the definition for the Nusselt Number Nu=\frac{\partial T*}{\partial y*}_{y=0}. T* given as T*=\frac{T_{wall}-T}{T_{wall}-T_{ref}} . As my pipe is short i used T_inlet as T_ref. y* is given as y*=\frac{y}{D_{pipe}}. However, as the ribs have a complex surface, the relevant direction for the Heat flux will not always be \partial y* (see attached image).

I have computed the wall normal vector field, as they should be the relevant directions for Heat Flux. I tried to then map the cartesian temperature gradient to the Wall normal vector field usign dot WallNormalVector. This brings me into the issue of my Nusselt Number being of the dimension \frac{1}{m}. I realize the Wall normal vector field needs to be normalised by a characteristic length, but struggle to understand if the diameter of the pipe is appropriate, given the normal vector field isnt simply in radial direction. Any clarification for this would be very appreciated.

Additionally, the values for NU I am receiving are way too large, and sometimes also negative. This seems impossible for a wall with constant heat flux. When evaluating the global Nusselt Number via the averaged wall temperature as \overline{Nu}=\frac{\dot{q}*D_{pipe}}{\lambda_{0}*(T_{Wall}-T_{ref})}* I receive something in the Order of \overline{Nu}\approx 600. The maxima and minima for the local one however range from -115000 to 20000.

I am not clear if T* needs to be defined different when evaluating the local Nusselt number compared to the global Nusselt Number, as in plugging the local wall temperature into the definition vs. the averaged one.

I am also unsure If I need to convert my cartesian Temperature gradient into a cylindrical one before proceeding. This should clear up any issues of the sign of the gradient changing depending on if its on the top or the bottom of the pipe.

Thank you for your patience and for reading through my wall of text, I hope someone can give me an insight where I am stuck.
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Last edited by Mpee93; August 11, 2023 at 09:04. Reason: Latex Syntax
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calculus, heat tranfer, nusselt calculation, structured pipe

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