Drag Coefficient of a trapezoidal bar

[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.

 

[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

 

[SteamKing]

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.

 

[Chestermiller]

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

 

[venkiee]

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

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

 

[Chestermiller]

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

http://www.aerospaceweb.org/question/aerodynamics/q0231.shtml

 

[SteamKing]

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

It's not going to matter much to the C_D 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 C_D 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 C_D 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.

 

[boneh3ad]

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.

 

[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.

 

[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.

 

[SteamKing]

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.

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.

 

[venkiee]

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.

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

A typical Jacket

http://www.richtechusa.com/upload/1335591599199121.jpg

 

[SteamKing]

Thanks for the info.

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

 

[venkiee]

Thanks for the info.

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

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

 

[SteamKing]

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.

 

[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?

 

[SteamKing]

Second question, is this a pipeline lying on the seabed or is something elevated above the seabed?

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.

 

[boneh3ad]

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.

 

[JBA]

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.

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.

 

[SteamKing]

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

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.

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.)

 

[JBA]

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.)

Actually,the sea floor of the 7 mile region outward form the East coast of Saudi Arabia in the Arabian Gulf is composed of a cemented crushed coral seabed is as hard as concrete; and in that area the production subsea pipelines are laid directly on the top of that surface. I spent 14 years in the offshore E&C industry; and, at one point, I was required to design a complete water flood and crude gathering piping system for the offshore Berri Field platforms located there which included anchoring at all riser and subsea manifold points with adjoining expansion loops and studies for determining the pipeline weight coating required for one segment of the lines that was transverse to the predicted 100 year wave forces in one critical area.
Similarly, on the Ju'Aymah Crude Export Terminal, the two parallel 56 inch diameter pipelines running 7 miles from the loading onshore pumping and storage facility to the offshore loading platform and buoy's, 6 miles of those lines were left on the seabed surface with only 1 mile approaching the beach landing being trenched using hundreds of pounds of TNT.

 

[venkiee]

Some Literature I found

 

[venkiee]

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.

I mentioned clearly that It's a fixed Jacket Structure.
Sacrificial anodes are attached to the Jacket to avoid corrosion of steel under water.

But when the anodes are attached to the tubular members, the members attract additional drag and inertia forces due to shape change. for this kind of shape in an open channel flow, there is no drag coefficient defined in any literature.

Hence I asked if there can be any assistance to do a calculation to ascertain this CD value for a trapezoidal bar attachment.

 

[SteamKing]

I mentioned clearly that It's a fixed Jacket Structure.
Sacrificial anodes are attached to the Jacket to avoid corrosion of steel under water.

But when the anodes are attached to the tubular members, the members attract additional drag and inertia forces due to shape change. for this kind of shape in an open channel flow, there is no drag coefficient defined in any literature.

Hence I asked if there can be any assistance to do a calculation to ascertain this CD value for a trapezoidal bar attachment.

Seems like there's a discussion in the linked paper of the drag due to the anodes and how it affects the overall drag of the tubular to which it is attached.
The actual numbers are dependent on the characteristics of the flow, however.

 

[venkiee]

Another Paper I found...

 

[JBA]

The fact that the design and successful application of conventional jacket structures in some of the most severe oceanic wave regions around the world for many years and multiple orientations of the jacket members relative to wave orientations simply caused me to wonder why the drag of an anode in one particular flow orientation was one of special interest.

 

[venkiee]

The fact that the design and successful application of conventional jacket structures in some of the most severe oceanic wave regions around the world for many years and multiple orientations of the jacket members relative to wave orientations simply caused me to wonder why the drag of an anode in one particular flow orientation was one of special interest.

As the anodes contribute around 5% to 8% of jacket weight, they play a significant role in increase of wave loads and the pile head reactions. In Well head jackets (usually light) the gravity loads contribute only 30% while environmental loads occupy rest 70%.

The increase in CD CM has a major role in pile head forces up to 10% in general.. If you don't add CD CM for that anodes.. you can notice the difference

This is a big topic of discussion... can't be explained in few words...

 

[SteamKing]

As the anodes contribute around 5% to 8% of jacket weight, they play a significant role in increase of wave loads and the pile head reactions. In Well head jackets (usually light) the gravity loads contribute only 30% while environmental loads occupy rest 70%.

The increase in CD CM has a major role in pile head forces up to 10% in general.. If you don't add CD CM for that anodes.. you can notice the difference

This is a big topic of discussion... can't be explained in few words...

I think this is why the engineers at Petronas decided to do model testing. A purely analytical solution appears to be unlikely; therefore, the gap in the theory must be filled by model testing.

There may be a research project, using CFD, which can be developed from this question to 1) confirm the model test results obtained by Petronas, and 2) develop a numerical method of analysis of such a problem should phase 1) turn out satisfactory.

 

[JBA]

I understand, actually, I have overseen the installation of a number of such jackets in relatively shallow waters off the coast of west Africa, but that was decades in the past.