Hello Stressers,

I am doing a comparison for wave loading between Caesar II and another beam element software. For simplicity, I only consider the drag force by setting Cd=1 and all other factors such as Ca=0, Cl=0, and Marine growth and density=0. Also, to make it more simple I did not consider the current in the input but only the water depth= 95.33 ft, wave height=16.4 ft wave period 11.1 sec, wave kinematics factor=1 and direction cosines X=1 and Z=0. The wave theory I use is Stream Function order 11. All this information are the same for both software including the wave theory.

The difference I can see is that the other software's output for wave forces is Fx and Mz while Caesar II have Fx, Fz, Mx, and Mz. Both values for Fx and Mz for both software are almost the same only some minor difference maybe in the non-linear calculation of particle velocity, there is a small difference between two software. My only question is the Fz and Mx component, where it came from?

My example is a simple cantilever beam with fixed end and free end oriented downward (20 ft long, 12.75 in OD and 0.626 in thick). Coordinate of the first node is the same for both software especially the Y coordinate.

Thanks in advance for your answer to my query. Just correct me if I made any wrong statement.

Cheers,

If you specify Ca=0 and Cl=0 CAESAR calculate values depending on flow speed. It is not zero

Thanks for the reply. This means that maybe the lift force is the z component in the output. How to set the lift force to zero say for a vertical pipe.

Anyway, maybe I'm missing something in my results interpretation between two software.

Any other opinion is greatly appreciated. Just correct me if there are error in my interpretation.

Thanks & Warm Regards,

Hello,

I've tried setting Cd=0 also and still got some value in the output of CII. I think you're right, CII calculate values based on flow speed. Need to understand more for this approach of CII because the other software spits out 0 values when I set Cd=0 also.

Any other opinion is greatly appreciated. Just correct if I have some misinterpretation in the result.

Cheers!!

If you leave the coefficients blank, then CAESAR II will determine their proper value during the analysis as a function of the load case (based on the Keuligan Carpenter and Reynolds numbers).

The force you refer to is actually a transverse force; this force acts perpendicular to the pipe axis and the direction of flow. For a vertical pipe this transverse force will be horizontal.

If you really want to zero something out, try a coefficient value of 0.001.

Nice tip Richard for setting 0.001 for those values that I want to zero out such as Cl=0.001 and Ca=0.001. It works now, the output is now Fx and Mz only with all other components almost zero. Now I understand how Caesar II works regarding setting these coefficients. This means Caesar can automatically calculate these coefficients based on the given data.

Theoretically speaking, is it correct to say that for a vertical pipe there is no lift (Cl=0.001) and only buoyant force in the vertical direction going up? Or there is a lift with the area being the diameter of pipe (Pi*D^2/4)? Can this be captured in the software?

Any other opinion is greatly appreciated.

Please correct me if I have a wrong interpretation in my statement.

Cheers!!

Is it correct to say that for vertical segment of pipe, we must set the lift coefficient Cl=0.001 since the software will report a tranverse lift instead of vertical lift if we leave it as blank or set some value say Cl=0.6?

Or maybe we can consider lift for vertical pipe by using the projected area diameter of pipe (pi*D^2/4)?

Just a thought.

Any opinion is greatly appreciated.

Cheers!!!

I suddenly had a question
Richard, if the pipe is vertical and flow velocity is horizontal, then in which direction transverse force will act. Left or right? How Caesar choose direction?

Left or right? This is the reason I don't like the term "lift", "transverse" is a much better term.

For all pipes, regardless of orientation, buoyancy is "up", and automatically included in the "W" (weight) primitive when a WAVx primitive is included in any of the load cases.

The drag (Cd), inertia (Cm), and transverse (Cl) forces are determined based on Morrison's equation as a function of these coefficients. If the input for these coefficients is left blank (which is typically recommended), the software will determine their values based on the Keuligan Carpenter and Reynolds numbers.

As to the direction of these forces, well that depends on the velocity and acceleration vectors. In a water column, subjected to wave motion, both the velocity and acceleration of the water particles behave in an oscillatory elliptical fashion. Therefore the direction of the forces varies based on where a particular point of interest is in the wave (crest, trough, etc).

For the question above, is the transverse (lift) force left or right? Sometimes it is to the left and sometimes to the right, the velocity vector does change direction based on the wave position. Similarly, for a horizontal pipe, the transverse force can be sometimes up and sometimes down. (This is why I don't like the term "lift", that word implies the force is always up - which is not correct.)

Thanks Richard for clearing my thought. I was confused by the word lift. But in the example of one of the beam element software they set Cl=0 for vertical segment of pipe. Anyway, it is just an example, it is still up to the analyst to properly set-up the correct wave forces and their direction.

Just correct me if I have made a wrong statement.

Cheers!!

This is the definition of lift force in one of the beam element software.

"A body resting on the sea bed is subjected to a vertical force, known as the lift force."

This is the one that confuses me.

Any other opinion is greatly appreciated.

Cheers!!!

My initial thought:

A wave forms due to one "blob" of water colliding with a different "blob" of water moving at a different velocity. The kinetic energy is converted to potential energy, and therefore, you get an equal increase in height of the fluid minus the compressibility of the fluid (and we all know how compressible water is).

Depending on the depth of the pipe and the height of the colliding "blobs" of liquid, the force against a body in it could be in any of the 6 directions. (Depending on the size of the body, I'm fairly certain it could also impart meaningful moment.)

Since we assume the floor itself is also incompressible, the pipe probably isn't going to flex downwards as far as beam analysis is concerned.

Therefore, we should check to see if the buoyancy plus "blob collision lift" causes harm to our pipe.

Thanks Michael for that very nice information. That means for a vertical segment of pipe there will also be a transverse lift force perpendicular to the plane of flow direction and pipe element centerline in either left or right.

That was indeed a meaningful explanation Michael.

Any other opinion is greatly appreciated. Just correct me if I have some wrong statement.

Thanks & Warm Regards,

This is another definition of lift force I found on the internet and I think is more generalized definition:

"The lift force is defined as the force acting normal to the
plane formed by the velocity vector and the element's axis."

Any other opinion is greatly appreciated.

Cheers!!!

Exactly! Therefore, as the velocity vector switches direction from positive to negative, the transverse force also shifts its direction from positive to negative.

"The lift force is defined as the force acting normal to the plane formed by the velocity vector and the element's axis."

The normal to the plane can have two directions!

Which of these two directions CAESAR II use? Is it possible to predict in which of these two directions transverse force will act?

For example we have horizontal pipe and water velocity is horizontal too.
On first pipe CAESAR II can apply transverse force in up direction, but on the second pipe it can be applied down? It is random? Or there's a rule?
For example "transaverse force direction will be always up. For vertical pipe it will be always by +X direction".

How to check the direction of transverse force in each pipe for each wave load?

The direction of the transverse force won't change from pipe to pipe. The direction changes as the velocity vector changes. For example, assume you have run of pipe in the +X direction, and the wave direction is in +Z.

When the wave crest is over the pipe the velocity vector is in +Z. Therefore +X cross +Z yields -Y, so the transverse force is down. Later, when the wave trough is over the pipe, the velocity vector is in -Z. So +X cross -Z yields +Y, so the transverse force is up.

The same evaluation can be applied to a vertical pipe. This is why I said above sometimes the transverse force is to the right and sometimes to the left.

In classic aero(hydro)dynamics, a force is applied to an obstruction, perpendicular to the direction of flow, in the direction of whichever flow is moving more quickly, e.g. an aero(hydro)foil.

I guess if it's on the seabed, it probably has a very low velocity under it due to drag and the velocity above it is whatever it is. I can buy that logic.

Depending on the size of the pipe and how it's buried, it could have two zones of recirculation, thereby making a half-ellipse shape.

In terms of (normal, new) pipe just sitting in the water at arbitrary depth, I'd expect for there to be no lift.

Richard, thank you! Now it's clear