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CHT in rectangular pipe with cylindrical pins

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Old   November 21, 2019, 07:47
Default CHT in rectangular pipe with cylindrical pins
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Hello,

I am trying to build a 1D model of CHT in a rectangular pipe with cylindrical pins. The idea is to compare it with a baseline case with no pins. The next step would be to construct the 3D CFD model.

The geometry consists of a rectangular metal pipe of thickness "t" and length "L", which has a rectangular cross section of sides "a" and "b". The interior of the pipe contains a grid of staggered cylinders of diameter "d", which cross the full height of the pipe. The geometry is shown in the two following images for clarity:




The fluid will evacuate a heat source modeled as constant along the length of the tube. There are namely 2 parameters of interest: the temperature of the metal at the exit section (so maximum metal temperature), and the pressure drop along the pipe from entrance to exit.


I have several questions concerning the heat transfer.

1. Considering the baseline case (no pins in the interior), the heat transfer coefficient between the solid and fluid is modeled with experimental correlations widely available in the literature. These correlations are normally functions of the Reynolds number. For this specific problem the characteristic length is normally taken as the hydraulic diameter. What determines the characteristic length of the problem?

2. Considering the case with the interior pins. Are there any available experimental correlations for the HTC/Nusselt Number that deal with flow inside of a pipe with cylindrical pins (or other types of obstacles)?

3. If a correlation does exist, what value should be chosen as the characteristic length this time? Should it still be the hydraulic diameter? Or is a small correction needed for the presence of the cylindrical pins?

4. If no experimental correlation exists, is it correct to consider the heat transfer as the superposition of two independent cases for which correlations exist? In this case I would consider the baseline case (flow inside a rectangular pipe) and cross-flow in a staggered bank of pins. In what way could I combine them to produce a feasible end result?

5. As far as the prediction of the results go, I expect the addition of the pins to increase the pressure drop along the pipe in relation to the baseline case, but to increase the heat transfer. This would be a consequence of the increase in surface area introduced by the pins. However, how would the HTC be affected?

Thanks in advance
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Old   November 21, 2019, 09:02
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1. The characteristic physics determines the characteristic length.
2. Some exist. But a pipe with pin fins could mean a pipe with only a few rows of pin fins or a pipe with many many rows of pin fins.
3. Whichever one fits. Or just look at the correlation. If you've ever seen these correlations, there's a lot more than just Reynolds number in them. You'll find the pi pitch, pin relative diamter, etc.
4. Is it correct? No. Convection is highly non-linear because the navier-stokes equations are non-linear in velocity. Do people do it anyway? All the time. The first row of a pin fin bank behaves very much like a pin in cross-flow. However, for closely spaced pin fins, you can't use a simple cylinder in crossflow correlation because of the blockage effect. But after a few rows, it starts to adopt its fully developed characteristics. It's a lot like predicting developing heat transfer in a pipe: you need to know the entrance region, the fully developed region and how to go in-between.
5. See Reynolds analogy.
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Old   November 21, 2019, 09:51
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Quote:
Originally Posted by LuckyTran View Post
1. The characteristic physics determines the characteristic length.
2. Some exist. But a pipe with pin fins could mean a pipe with only a few rows of pin fins or a pipe with many many rows of pin fins.
3. Whichever one fits. Or just look at the correlation. If you've ever seen these correlations, there's a lot more than just Reynolds number in them. You'll find the pi pitch, pin relative diamter, etc.
4. Is it correct? No. Convection is highly non-linear because the navier-stokes equations are non-linear in velocity. Do people do it anyway? All the time. The first row of a pin fin bank behaves very much like a pin in cross-flow. However, for closely spaced pin fins, you can't use a simple cylinder in crossflow correlation because of the blockage effect. But after a few rows, it starts to adopt its fully developed characteristics. It's a lot like predicting developing heat transfer in a pipe: you need to know the entrance region, the fully developed region and how to go in-between.
5. See Reynolds analogy.
Thanks for the response.

A couple of follow up questions regarding your answers:

1. In this sense, what is characteristic physics referring to? Would the characteristic length change if I want to focus more on the flow rather than the heat transfer? How can I quantify the physics change from the baseline pipe to the pipe with interior pins.

2. Where would be a good place to start to look for these correlations? Are there any databases? It seems like I might be using the wrong terminology, because the search for "heat transfer in rectangular pipe with cylindrical pins" does not give me the results that I'm looking for. I would be interested in all sorts of correlations (developing region with few pins, and downstream with the flow along the pins "fully developed")

3. Ok, so from what I understand, the correlation that I find will need to explicitly state whether the characteristic length is the hydraulic diameter, the pin diameter, or some other representative length from the domain.

4. So, if I don't find any suitable correlations, in theory, considering the fully developed case, I could use a careful combination of flow inside pipe and flow across staggered bank tube. I should just take the results with a grain of salt.
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Old   November 21, 2019, 10:42
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1. Heat transfer and flow go hand-in-hand. Again, see the Reynolds analogy. Flow is the mechanism for advection/convection in the first place. Actually a much better characteristic length is the boundary layer thickness. Consider what the boundary layer thickness looks like in different scenarios and you should have a better of idea of what makes a characteristic length a characteristic length. At the end of the day, the characteristic length is a number chosen for its convenience more than anything else.

2. Handbooks. ASME also has a ton of papers because trailing edge cooling in turbine blades is a bunch of pin fins in all sorts of shaped channels. A dissertation.

3. Not only that but the correlation will have multiple parameters at the exact same time. For example, Re^n*(P/e)^m**(S/d)^k*blahblahblah. It's not about having just 1 characteristic length.
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