Dear forum ,
This is going to be a long question, but I hope some of you will get interested.
Duct - SB625 N08904 (titanium), 6mm thick and 1620, 1470 and 1220mm in diameter at different sections.
The ducting in question is supposed to be used in a brine recalculation system and consists of a relatively short suction duct L/D = +/-7, an axial pump and a relatively short discharge duct L/D = +/-6.
To present a better picture, the suction duct is mostly vertical and is connected between the evaporator outlet (via a tied bellow, nuts on outside only) and the pump inlet nozzle (positive suction). The pump (imagine 90deg very rigid elbow) is sitting on the baseplate supported with 6 dumpers. The mostly horizontal discharge duct connects onto the heat exchanger also via a tied bellow (nuts on outside only).
Both ducts are supported with a couple of spring hangers.
This system was installed a year ago but they still have not managed to get it operating.
Original design was done by another stress engineer who had supported the pumps on very soft springs. The vibrations were too excessive, so the client wanted to consider removal of the springs under the pumps and fixing them rigidly. I have done the analysis, but due to the pressure thrust (from bellows) the calculated nozzle loads on the pump were excessive. The bellows could not be removed due to rigidity of the system.
And this is how we came up with the dumper solution, not as soft as original springs, but also not too rigid. In Caesar everything looked right.
Then new dumpers were installed.
The vibrations are not so much of the problem, but now the ducting is excessively and nonlinearly displacing. I have analyzed the actual displacements measured at each spring / dumper, but they are impossible to simulate in Caesar(by playing with density and/or additional concentrated forces that might have been missed in the model). My first conclusion was that there is a “soft point” that has yielded, but the client is confident that there are no problems with the duct. On my side, I am confident in supporting and spring sizing since the spring's and dumper's operating and cold loads balance the total weight of the system. Then only explanation could be that the stiffness matrix created in Caesar is incorrect and local membrane stresses / deflections are governing the behavior of the system.
Can anyone tell me if Ceasar is the right tool to model and analyse the system as above or did we waste all this time while FEA is the only option.

Maybe someone else has performed a similar analysis and can offer their advice. However, CAESAR II utilizes a 3D Beam Element in formulating the stiffness matrix. This element is incapable of addressing local effects. In CAESAR II you have a centerline or stick model, where the behavior is dominated by bending associated with the deflection of the node points. The 3D Beam Element can not be used to evaluate shell behavior.

Buckling and localized plate phenomena will not be adressed by ANY BEAM ELEMENT MODEL (pipe stress programs are all beam element analysis programs following the B31 codes).

So your tool is not able to adress these phenomena. However your problems may have nothing to do with the limitations of CAESAR II.

My first impression is that you have to be kidding me! Springs and EJs!!!! Your pump must be quite delicate and fragile so as to require a zero load design.

Its quite possible that the combination of EJs and pressure pulsations during operation may then result in pulsing loads that are the source of your problem. If the pressure swings from + to - for instance the single nut rods will slack off for sure.

So I would try to get rid of the EJ's and leave the pump on springs. Also I would look into a visco damper by Gerb for the pump base for interim dynamic loads.

Thanks for your response. Just a few clarifications.
I am trying to see if the system can work with minimum changes. The pump (cast steel) is not so delicate and it is perhaps the strongest part of the system. The vendor did not provide allowables, but so far was approving loads up to 50kN (each load component). Either with a rigid support of the pumps or by removing EJs these loads increase over 150kN which is not acceptable.
The pressure pulsations are negligible since the pump head is only 3m. The velocities are also quite low but I have added the load at the elbows to account for the change in momentum. I have also transferred more fluid weight to the lower horizontal parts of duct on account of the vertical duct.
The system starts displacing “abnormally”(according to Caesar) already during the filling (SG=1). Then when is heated (100degC), during the recirculation, SG increases to 1.2.
What is interesting is that the displacements on the horizontal discharge duct springs (system's low point) are more then double the Caesar values, while the displacements on the suction duct springs are less then half the Caesar values (system's high point). It looks like the duct is opening up.

The basic question is: Is there a criteria based on L/D and D/t if Caesar is the right tool or not?

Why considering pressure thrust for the nozzles (coming from bellows) when the bellows are tied?

Hello RS.
I think that what you need to evaluate if it is safe to operate the system under the circumstances that you are describing. I mean that sometimes the displacements and the vibrations are things that you have to acknowledge and learn to live with these. The codes normally tries to tell you where are the limits of acceptable conditions. Dynamic measurements should be taken on field, amplitudes, frequencies and forces should be measured with the system working. This company has already spent a lot of money in this system (titanium and expansion joints!!!) so I don’t think they are going to object trying new test field measurements. From these measurements then you can conclude if the system is going to survive with these conditions or not. Even further, you can take the corrections required to correct the system if necessary
Regarding if CAESAR II is or is not the right tool for your modeling is up to you. As a general approach I would say that this kind of software is intended for structural systems in which one of the dimensions in prevailing over the 2 others. If your case is in the limit that length and diameter are in close order of magnitude, then, you need another tool. One thing that you should keep in mind is that the system in the computer is a model and the real thing is on the field and not viceversa, so if after measuring in field you cannot get the same results in the computer then you know that the software does not fit your requirements…


Regards,

To: Michael Bau
Servus,
Why? Because these EJs are nutted or restrained on one side only. If the pressure was varying from + to - the EJs might actually "contract". In these types of cases the EJ needs to be restrained from pressure thrusts both ways or nutted on either side of the flange.

To: RS
If the systems displacements when it is cold with negligible pressure does not match the W+H only displacements from CAESAR II, especially as it concerns the spring settings then it is most likely that the beam element model is not correct statically. Whenever springs are introduced to a system, the statics of the model must be as correct as possible otherwise the springs seetings will be incorrect.

Obviously I am not reviewing the work but here are some things to consider....
1)Have the CG for Motor, Coupling and Pump been placed correctly in X, Y, and Z,?

2)Are all the weights accurately accounted for Frame, Pump, coupling etc.

I would expect the beam element model results to match closely the results in the field with the system in-operative. After heat and pressure affects come into the picture the beam elements model solutions to high D/T ratio pipe come into question.

This is particularily true when D/T exceeds 100. Also check the notes from B31.3 SIF appendix you will find a cautionary note on this.

Dear All,
I would like to add my opinion regarding the loads being calculated on the pump. Bear in mind that the pressure thrust of the duct core area is not acting at the pump flange but at the pump impeller / casing.Caesar calculates the total thrust based on the effective area of the expansion joint as it does not know whether the two ends of the expansion joints are attached to a solid area ( blind flange ) or a hollow area ( pump casing / vessel nozzle etc. ). The actual pressure thrust acting at the pump flange is P * Annulus Cross Sectional Area of the convolutions. In order to get the correct piping loads at the pump flange the Pressure field has to be modified in the Caesar expansion joint input. Input Pressure = P * Annulus Cross Sectional Area of the convolutions / Effective area of the expansion joint. ( Annulus cross sectional area = pi* ( Do^2 - Di^2 ) / 4 , wherein Do = OD of the convolutions , Di = ID of the convolutions ). This will give you the correct pressure thrust on the pump flange.
Also please check if the differential pressure thrust at the pump impeller coming from suction and discharge is causing any problem. In normal cases due to the pump being fixed this does not cause any problem but in this case, since the pump is free to displace it can.

Regards.

Thanks to everyone for such a wonderful response.
P Massabie, I agree with you proposal, but before I go any further into dynamics, I am not sure about one thing. If I take the cold case and model in the measured displacements (dx, dy and dz) instead of springs I will be creating fixed points that are forcing the ducting into a position that is not “natural” according to the Caesar, but it is “natural” in reality. Are the calculated stresses going to be realistic?
John, as an indication of how different the Caesar and real thing is, I had to add 2500kN concentric force (the whole system is less then half of this weight) at the discharge duct in order to achieve the field displacements. So it is no longer question that I might have forgotten the coupling or base or even the pump weight (I have not of course. Actually, I have moved all the liquid weight from the vertical duct and even the water column in the vessel above onto the pump base, like the deep shaft mining aplications.).
Rajesh, regarding the pressure thrust, I have different approach. I do not think that the pump nozzle is the weakest point and that this is why the pump manufacturer specifies the allowable loads there. What is relevant is the total load transferred onto the pump base and / or coupling and resulting displacements, whatever might be his criteria, via the nozzle that presents the battery limit between piping and equipment.

Hello RS,
If your model is not "naturally" matching the reality I think, then, that your model is not good at all. Be aware: I am not seeing that you or the software is not good. I'm referring to the model: Something is missing or not accurately modeled. As we go deeper in the subject more I think that the tool is not adequate for your problem. But before disregarding the software try increasing the number of nodes in you model. Is my understanding that for approaching to the exact solution to a cantilever beam you need at least three elements in the model so, probably, increasing the number of nodes would help to get the real movements of the pipe (But, again, this is a far anticipation)

RS

The allowables at the flange face are there to limit distortion of the pump casing, so that you don't get excessive shaft misalignment and all the reliability problems that go along with it.

So, while it is the case that your total load on the base plate would be the full PxA of the duct, that's not the load you're worried about. As Rajesh pointed out, the nozzle load is going to be K*dx + P*Aconvolutions. (Stiffness of joint * Thermal Expansion + Pressure * Net Area of the Convolutions)

I find it very hard to believe, based on the system that you describe, that the pump has any need to be on springs. I would hope that your upstream evaporator and downstream heat exchanger are anchored close to the nozzles that go to/from the pump. In that case, your thermal expansion to deal with should be almost exclusively axial relative to each duct. Your expansion joints should be designed to be soft enough to keep the K*dx force down when the joint compresses.

By putting the pump on springs, all you're going to insure is that the suction joint in the vertical doesn't do anything as the pressure thrust will keep the joint fully extended against the nuts and the thermal expansion pushes the springs down as well. Your horizontal outlet joint is going to be deflected to give you a downward slope from the exchanger back to the pump. Unless that joint is a universal, it's not going to want to deal well with that lateral deflection and the stiffness is probably going to put a mighty big moment on your pump discharge nozzle.