[Dno]

Greetings,
I'm trying to simulate water flowing in a closed channel with width >>>> height. Both top and bottom walls have a no slip condition. Inlet and outlet are coupled with a periodic (cyclic) boundary condition, aswell as both walls to the sides (see the attached image). For this case, what's the hydraulic diameter?

[sbaffini]

https://en.m.wikipedia.org/wiki/Hydraulic_diameter

Spoiler: it's twice the height

[Dno]

Thanks for the quick reply! I saw one person using H/2 on a paper and got slightly confused, thought I could be missing something. I suppose the person forgot to multiply the dynamic radius by 4 and didn't notice

[flotus1]

The way I see it, the main purpose of the "hydraulic diameter" concept, is having an estimate for the characteristic length, in cases where the choice is not obvious.
If I understood correctly, you are dealing with the flow between two parallel, infinite plates. My choice for characteristic length would be the distance between the plates.

Of course, simply applying the formula for hydraulic diameter in rectangular channels yields 2H. My argument against it would be: why use a hydraulic diameter, although the choice for characteristic length is obvious.

[sbaffini]

To be more accurate, if your question was about the typical length scale used for this flow, then the answer would have been H/2 as you found in that paper. Yet, this is not the hydraulic diameter for this case.

[FMDenaro]

This is a case wherein the equivalence with the hydraulic diameter is not well posed. It is not a 2D case where you can assume an area H*1 and is not a 3D case where the area is H*W. Being the spanwise direction periodically repeated (or in your case W>>H) the area would be undefined (->+Inf). There is only a specific geometric lenght, the heigh.

[Dno]

Originally Posted by sbaffini

To be more accurate, if your question was about the typical length scale used for this flow, then the answer would have been H/2 as you found in that paper. Yet, this is not the hydraulic diameter for this case.

Yes, it would indeed be the characteristic length. I'm trying to get an appropriate L value to calculate the Reynolds number.

[flotus1]

As long as you know which characteristic length was used, the exact value doesn't matter.
Say you want to compare your results to some publication that used Re=500: look up which definition of characteristic length they used, and adjust yours accordingly.
And the other way around: you want to publish some data for a certain Re, don't forget to mention how you chose the characteristic length.
The flow itself is invariant to the choice of characteristic length.

[Dno]

My intention was to analytically calculate Re number and pressure drop for a case where top and bottom plates are flat and then use this value as a benchmark for 2 simulations:

- both plates are flat and;
- bottom plate has riblet-like structures, that in theory should reduce drag/pressure drop.

If my analytically calculated pressure loss is off by a decent amount, due to a poorly evaluated Re, it would be hard to validate the model.

[FMDenaro]

Originally Posted by Dno

My intention was to analytically calculate Re number and pressure drop for a case where top and bottom plates are flat and then use this value as a benchmark for 2 simulations:

- both plates are flat and;
- bottom plate has riblet-like structures, that in theory should reduce drag/pressure drop.

If my analytically calculated pressure loss is off by a decent amount, due to a poorly evaluated Re, it would be hard to validate the model.

In this kind of test-cases, the Reynolds number is based on half-height but be aware you will find the literature where the u_tau velocity is used. Depending on pressure-driven or mass-driven forcing, you can have difference.