Confusion about hydraulic diameter

[kfoh]

Hi all,

I currently design a multitube heat exchanger. In this heat exchanger multiple tubes are put in parallel, while the flow goes in parallel, so not with baffels for cross flow (due to very stringent pressure drop reqs). The tubes will be longitudinally finned.
I currently struggle a bit with the calculation of the heat transfer coefficient. I model the heat exchanger as a double pipe exchanger with the equivalent heat transfer surface area of the entire device.
The question I do have now is the following:
I do calculate the Reynoldsnumber with the hydraulic diameter of the entire tube bank within the shell to obtain the heat transfer coefficient of the plain tubes. For calculation of the heat transfer coefficient I now am in doubt which hydraulic diamter to use. Shall I use the same as for the calculation of the heat trasnfer coefficient of the plain tubes? Or shall I calculate it based on the area between the ribs? The flow speed is kept the same, such that also the reynoldsnumber is only dependent on the hydraulic diamter.

I am really confused about the hydraulic diameter and its use in the Nusselt number and Reynoldsnumber definition.

thank you for your hints!

 

[racookpe1978]

What is the closest distance between the tubes?
Between the outermost tubes and the HX wall?
What is the ID of each of the tubes?
I think you will find there are two different hydraulic flows going on: One inside the tubes, and the second outside of the tubes, around and between the tubes. You seem to be assuming the two are the same.

 

[DesertEagle01]

Could you post a sketch of your arrangement and the hydraulic diameters you are currently assuming?

 

[kfoh]

Hey,
thank you for your responses. I'm sorry that I didn't reply instantly since I was very busy in the last time.
I am aware that the flow inside the tubes and the one outside of it are of course different. I am confused about the hydraulic diameter purely on the outside. As you can see in the sketch I did, there are differnt flows in the outside as well. There is a macro flow between all the tubes, as well as the flow around the tubes between the fin compartments.

The hydraulic diamteres I am currently assuming is for the tube flow twice its radius.
For the outside flow I am currently assuming a hydraulic diameter of the form of D_h=4A/P, where A is the free flow cross secitonal area and P the wetted perimeter of the flow.
the inner radius of the tubes is currently 0.0075m, the thickness is 1mm and the outer Shells radius is 0.13.

 

[georgeverghese]

kfoh,

The treatment for shellside dp in this type of HX is given in chapter 16 of Process Heat Transfer by DQ Kern - you have to refer to fig 16.10 on page 525 to get the corresponding shellside friction factor.

Pls note the value of shellside hydraulic diameter for the purposes of dp calculation is different from that for shellside h in this treatment by DQ Kern.

Your formula for Dh for shellside is correct; for shellside dp calculation, the value for P = wetted perimeter for shell id + wetted perimeter for fins + wetted perimeter of exposed tube OD.