Internal Pressure of an Expanding Pressure Vessel

[Nileo2005]

Hi all. Fist time posting a question, so try to be nice if I mess this whole thing up. I currently am having a problem mapping the stresses and deformation of a closed pressure vessel.
The current method is to just define an internal pressure amplitude on the fluid elements, and that works just dandy with small to no vessel deformation as the internal pressure over time decays negligibly. The problem is when large expansion of the vessel starts to occur.

With the creep effects over time being the target of this testing, this large volumetric expansion is inevitable. Coupled with this volumetric expansion of the vessel, being a closed system, should be an internal pressure decrease due to the ideal gas law, which is not currently represented with the current method.

Does anyone know a way to define a cavity to a certain pressure with a finite amount of fluid or something of the sort? Or possibly to define the internal pressure of the vessel as a function of the current volume, its cvol output, per step? Those are my first two thoughts, but alas my internet forum and book scouring has yeilded bupkus. Thaks in advance!

Oh. by the way, I'm using a compressible fluid like air, ideal and newtonian.

 

[Nileo2005]

Looks like not many people come across this kinda scenario too often.
I think I might have a bit of a break through come about from sifting through pages of user manuals once again. Solution-Dependant Amplitudes. Heres the definition from the manual:

Abaqus/Standard can calculate amplitude values based on a solution-dependent variable. Choose the solution-dependent definition method to create a solution-dependent amplitude curve. The data consist of an initial value, a minimum value, and a maximum value. The amplitude starts with the initial value and is then modified based on the progress of the solution, subject to the minimum and maximum values. The maximum value is typically the controlling mechanism used to end the analysis. This method is used with creep strain rate control for superplastic forming analysis.

Anyone have any experience with this command before? I'm confused because the limited parameters you input, a start, a min, and a max. The definition is "calculate amplitude values based on A solution-dependent variable" and thats all they give you to work with. What solution is your amplitude based off of or where do you choose? Can I make a amplitude based off of a volume output? I haven't a clue where to go next yet again. Thanks!

 

[mrgoldthorpe]

Hi Nileo,

I read your original post and had a few thoughts that led to the paragraphs below, and discarded them. Having read your follow-up, I agree that the manual makes no sense on Solution dependent amplitude. So here goes:

My original idea at your first post was to employ user subroutine DLOAD, making use of say a user field variable (or a common block variable) that tracks the change in volume of the vessel. You do that calculation by accessing the deformed coordinates of the nodes on the inner boundary. Several user subroutines give access to this, so you can perform the calcs and store the result in either a field or state variable or a common block of your own making.

Another idea is rather more "off the wall", but it might give you food for thought. Here, mesh the cavity with material which has the appropriate bulk modulus etc. of the fluid. Give this material zero coefficient of thermal expansion, and give the vessel an appropriate value of thermal expansion. Now set *INITIAL CONDITIONS for the vessel temperature, setting a 'high' initial uniform temparature.

In the first step, set the temparature of the vessel to a lower value, such that the internal pressure due to thermal contraction at the end of the step is the initial value you require.

In the subsequent step(s), use the NLGEOM option so that the volume of the vessel and fluid change appropriately. The vessel volume will change due to creep: relieving the thermal strain you first imposed, but the internal 'fluid' will expand and relax the pressure it imposes on the vessel.

Anyway, just a thought!

 

[Nileo2005]

Hey all. After much deliberation and ruthless sleuthing of example problems, I found a solution to my problem. Defining a surface and assigning a cavity reference node are the first steps, just as I had before. Applying the pressure amplitude boundary condition to the reference node was something I've tried before, just lacking a key factor; even though the step involving the pressure amplitude ended, the last value of the step remained as a constant for the internal pressure of the vessel. op=new in the new step disabled the previous pressure amplitude while retaining the current internal pressure, and that’s when the ideal gas constant comes into play. It will control internal pressure inversely proportional to the volume. w00t! I guess I had it all along; I just didn't turn off that lingering pressure amplitude. It’s always the small crap that gets me...
Just thought I’d conclude on the off chance someone else was encountering the same problem.