# Drag Coefficient of a trapezoidal bar

1. Feb 2, 2016

### venkiee

I have a peculiar problem of calculating a trapezoidal bar (used as sacrifical anode) in offshore substructures. Can anyone advise me how to calculate the Cd value of such a section. Flow is along the length of the bar.

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2. Feb 2, 2016

### venkiee

Size of trapezium cross section is a=185mm b=265mm h=234mm and length of the bar is 3000mm
the item is in sea water

3. Feb 2, 2016

### SteamKing

Staff Emeritus
Since the flow is along the length of the bar, the drag coefficient is probably going to be close to the stagnation value for a flat plane perpendicular to the flow. The shape of the cross-section of the bar (or anode) will have very little contribution to whatever the true drag coefficient is.

The total drag of various appendages like anodes and whatnot is usually pretty low as a fraction of total drag, unless there are some unusual circumstances.

If you want to reduce the drag of your anode, you'll probably have to fair the ends in some manner so that the cross-section at the end is not wholly perpendicular to the direction of the flow.

4. Feb 2, 2016

### Staff: Mentor

It seems to me that there is going to be substantial drag along the length of the bar as well as at the leading face. The length is more than 10x the cross sectional dimensions. What is the free stream velocity of the water flow going to be along the bar?

Chet

5. Feb 2, 2016

### venkiee

Actually it is a sacrificial anode welded on a tubular underwater for an offshore structure. I's appreciate if can advise how to calculate its drag coefficient CD value

6. Feb 2, 2016

7. Feb 2, 2016

### SteamKing

Staff Emeritus
It's not going to matter much to the CD that the cross section of the anode is a rectangle, a trapezoid, a circle, or whatever. You have a flat surface which is perpendicular to the flow. The CD is going to be in the range 0.82 - 1.28, with the lower number being for flow end onto a long cylinder and the higher number being for flow directly onto a flat plate:

These CD values don't account for an anode being attached to a larger diameter tubular. It depends on your particular application if you need really precise drag figures or if an order of magnitude figure will suffice. If you really need to have a precise figure, probably a model test would be required, unless you know someone who could make an analysis using CFD.

8. Feb 2, 2016

Also keep in mind that these are estimates for shapes in a free stream. For a shape bolted to a larger shape, there will be quite a different answer. One fewer surface will be exposed to the flow, but all of the other surfaces are subject to whatever level of turbulence is in the boundary layer on the larger shape, which can increase drag pretty substantially.

9. Feb 2, 2016

### JBA

Generally, for offshore installations, other than some type of underwater vehicle, the longitudinal drag on an item such as your anode would not be expected to be a substantial element relative the size of the structure it is protecting based upon the fact that, generally, the size of an anode is relative to the surface area and therefore size of the structure it is protecting.

10. Feb 2, 2016

### venkiee

This is how my attachment looks. Tube has its own CD factor. But when an anode is attached to it, for increased CD on the tubular, the attachment has to be considered for analysis purpose to calculate wave drag on main tubular. My question is the anode part. There are no clear guidelines how to calculate CD CM for such attachment as individual...

Appreciate detailed explanation and method.

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• ###### trap.jpg
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11. Feb 2, 2016

### SteamKing

Staff Emeritus
It's not clear how big a structure these anodes are protecting, nor how many anodes there are attached to the structure in this manner. If the flow is along the length of the anode, that suggests it's also along the length of the tubular, which should generate less resistance than if the flow was normal to the side of the tubular.

12. Feb 2, 2016

### venkiee

This is how it would look like on a fixed jacket structure @ many places

A typical Jacket

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13. Feb 2, 2016

### SteamKing

Staff Emeritus
Thanks for the info.

Are you trying to evaluate the wave forces on the jacket structure after it has been installed?

14. Feb 2, 2016

### venkiee

While providing the CD CM values for members, if they are tubular, it is straight forward. If there is an attachment to it (like anodes) the CD CM need to be modified to counter the added mass and drag forces.

Hence, when the jacket is in installed / operating condition in sea water, this situation arises. There are no clear cut indications how to arrive a CD CM for attached anode. That's why I am asking...

It should be like what is shown in figure above for a trapezoidal bar

15. Feb 2, 2016

### SteamKing

Staff Emeritus
I'm afraid you'll have to do a literature search on how other offshore engineers have handled this analysis.

By Googling "wave drag of anodes on tubulars", there are several papers which come up where engineers have done model tests to determine the coefficients you are looking for. These papers are behind paywalls, unfortunately.

Most of the design guides from the major classification societies don't seem to address the influence of anodes on tubular wave loads, so you'll either have to increase the wave loads on a bare tubular by a certain factor or try to extract some meaningful data from one of these papers.

16. Feb 3, 2016

### JBA

From how you have described your problem it appears that the "tubular structure" is longitudinal to the direction of the imposing wave direction and you are treating this as a fully submerged object being subjected a longitudinal fluid flow drag on the structure and it's anode(s). Is that a true statement of your process?
Second question, is this a pipeline lying on the seabed or is something elevated above the seabed?

17. Feb 3, 2016

### SteamKing

Staff Emeritus
It's not a pipeline.

From the pitchers the OP posted, it's a jacket erected offshore, like to support an oil production platform. The anodes are affixed to the tubular structural members to mitigate corrosion from seawater. It appears the OP is trying to evaluate wave loads imposed on the fixed structure, as if to perform a structural analysis.

18. Feb 3, 2016

This problem doesn't have an analytical solution and doesn't really have any sort of easy approximation as far as I can see. The drag on each tube and the drag on the trapezoid will not add linearly, i.e. the total drag won't be the drag on one plus the drag on the other in their own right. In reality, bolting the trapezoid onto the tube will fundamentally change the flow field. You are probably best off performing an experiment or simulating it.

19. Feb 3, 2016

### JBA

From the statements with the pictures he does not state that his application is a jacket structure, only that the anode arrays are similar to what is shown on the structures tube members. No offence intended, only clarification. Hopefully Venkiee will resolve this question.

20. Feb 3, 2016

### SteamKing

Staff Emeritus
I think the application is indeed on a jacket. Pipelines can be buried under the seabed, and no one needs to calculate wave forces acting on a pipeline, which they are required to do for fixed platform installations offshore, especially if the structure is being classed by one of the marine classification societies (ABS, DNV-GL, etc.)