Hydraulic diameter

IBC · July 26, 2021, 14:11

Hi,

What would be the equation for the hydraulic diameter of a square inlet in a 2d geometry?

Thank you

LuckyTran · July 26, 2021, 14:27

What is the context? If the geometry is 2D then there is no such thing as a square inlet. Why do you need to know what is the hydraulic diameter?

IBC · July 26, 2021, 19:35

I need the hydraulic diameter for the velocity boundary condition. I am using turbulence intensity and hydraulic diameter. It is a 2D geometry representing an oven. It is like a 2D box with an inlet and outlet. I was using --- (2*width*height)/(width + height).

LuckyTran · July 27, 2021, 04:16

If you have a square cross section, the sides are equal and the hydraulic diameter is equal to the length of the side of the square. So why is width and height even being mentioned... Is the hypothetical inlet of this 3D oven geometry not a square cross section or what is going on?

IBC · July 27, 2021, 09:38

Rectangular cross-section.

LuckyTran · July 27, 2021, 14:17

Quote:

Originally Posted by IBC

Hi,

What would be the equation for the hydraulic diameter of a square inlet in a 2d geometry?

Quote:

Originally Posted by IBC

Rectangular cross-section.

Is this an out of season april fool's joke?

What you really need to apply as a BC are intensity and length scale. So just think about what your turbulent length scale is. Since you've chosen to two-dimensionalize a 3D geometry, there is no straightforward answer. More technically, you need to provide BC's for k and epsilon or k and omega or whatever your turbulence model is.

IBC · July 27, 2021, 15:31

It was not a joke.

Maybe I didn't explain the question very well. I won't bother you anymore.

Thank you

obscureed · July 27, 2021, 15:50

This isn't a bad question at all. The point is that the real, 3D inlet has a hydraulic diameter, which can be used to estimate the turbulent parameters of the inflow. Then the inlet and the inflow can be represented in a 2D simulation.

So, in 3D, the hydraulic diameter of any duct cross-section is defined as (4*area/perimeter). The factor 4 ensures that a cylindrical duct has a hydraulic diameter equal to its circular diameter. (Slightly strangely, it also means that a W*W square has hydraulic diameter W.) So, for a rectangular cross-section W*H, the hydraulic diameter is 2*W*H/(W+H).

The whole point of all this might be to get an estimate of the typical turbulent lengthscale. If the aspect ratio of the duct becomes extreme, maybe W<(H/5) or W<(H/10) or similar, then there won't be any turbulent structures across the larger dimension. In this case, a better estimate of the turbulent lengthscale might be just the smaller dimension. But if W<<H, the formula for hydraulic diameter approaches (2*W) anyway, which is good enough. This gives some confidence that the formula has some validity for all aspect ratios.

IBC · July 27, 2021, 15:59

Make sense. Then, I am calculating the hydraulic diameter correctly.

Thank you for your help.

LuckyTran · July 28, 2021, 11:35

For square and close to square ducts it is not an issue. But in the case of a very wide aspect ratio duct, the hydraulic diameter is twice the gap distance. This means, if you use the hydraulic diameter, you'll get a length scale that is too large and eddies technically don't even fit in the gap. All the confusion can be avoided if you just remember that the hydraulic diameter is not a boundary condition, it's just a convenient tool implemented to help you get a turbulent length scale. But actually, the turbulent length scale isn't even the boundary condition you are applying. You are applying values of the transported variables in your (probably two-equation) turbulence model.

In my opinion, 2W is not "good enough" when it is geometrically non-realizable.

July 26, 2021, 14:11	Hydraulic diameter	#1
IBC New Member Join Date: Jul 2021 Posts: 23 Rep Power: 4	Hi, What would be the equation for the hydraulic diameter of a square inlet in a 2d geometry? Thank you

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July 26, 2021, 14:27		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,674 Rep Power: 66	What is the context? If the geometry is 2D then there is no such thing as a square inlet. Why do you need to know what is the hydraulic diameter?

July 26, 2021, 19:35		#3
IBC New Member Join Date: Jul 2021 Posts: 23 Rep Power: 4	I need the hydraulic diameter for the velocity boundary condition. I am using turbulence intensity and hydraulic diameter. It is a 2D geometry representing an oven. It is like a 2D box with an inlet and outlet. I was using --- (2widthheight)/(width + height).

July 27, 2021, 04:16		#4
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,674 Rep Power: 66	If you have a square cross section, the sides are equal and the hydraulic diameter is equal to the length of the side of the square. So why is width and height even being mentioned... Is the hypothetical inlet of this 3D oven geometry not a square cross section or what is going on?

July 27, 2021, 09:38		#5
IBC New Member Join Date: Jul 2021 Posts: 23 Rep Power: 4	Rectangular cross-section.

July 27, 2021, 15:31		#7
IBC New Member Join Date: Jul 2021 Posts: 23 Rep Power: 4	It was not a joke. Maybe I didn't explain the question very well. I won't bother you anymore. Thank you

July 27, 2021, 15:50		#8
obscureed Senior Member Join Date: Sep 2017 Posts: 246 Rep Power: 11	This isn't a bad question at all. The point is that the real, 3D inlet has a hydraulic diameter, which can be used to estimate the turbulent parameters of the inflow. Then the inlet and the inflow can be represented in a 2D simulation. So, in 3D, the hydraulic diameter of any duct cross-section is defined as (4area/perimeter). The factor 4 ensures that a cylindrical duct has a hydraulic diameter equal to its circular diameter. (Slightly strangely, it also means that a WW square has hydraulic diameter W.) So, for a rectangular cross-section WH, the hydraulic diameter is 2WH/(W+H). The whole point of all this might be to get an estimate of the typical turbulent lengthscale. If the aspect ratio of the duct becomes extreme, maybe W<(H/5) or W<(H/10) or similar, then there won't be any turbulent structures across the larger dimension. In this case, a better estimate of the turbulent lengthscale might be just the smaller dimension. But if W<<H, the formula for hydraulic diameter approaches (2W) anyway, which is good enough. This gives some confidence that the formula has some validity for all aspect ratios.

July 27, 2021, 15:59		#9
IBC New Member Join Date: Jul 2021 Posts: 23 Rep Power: 4	Make sense. Then, I am calculating the hydraulic diameter correctly. Thank you for your help.

July 28, 2021, 11:35		#10
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,674 Rep Power: 66	For square and close to square ducts it is not an issue. But in the case of a very wide aspect ratio duct, the hydraulic diameter is twice the gap distance. This means, if you use the hydraulic diameter, you'll get a length scale that is too large and eddies technically don't even fit in the gap. All the confusion can be avoided if you just remember that the hydraulic diameter is not a boundary condition, it's just a convenient tool implemented to help you get a turbulent length scale. But actually, the turbulent length scale isn't even the boundary condition you are applying. You are applying values of the transported variables in your (probably two-equation) turbulence model. In my opinion, 2W is not "good enough" when it is geometrically non-realizable.