Calculate the work done by pressure rupturing a spherical containment

Click For Summary

Discussion Overview

The discussion revolves around calculating the work done by pressure in rupturing a spherical containment, specifically focusing on a simulation involving a time-dependent pressure applied to a spherical mesh. Participants explore the relationship between pressure, area, displacement, and energy in the context of the rupture process.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant describes a simulation where a time-dependent pressure (p=10*t) is applied to a spherical mesh, aiming to calculate the energy introduced by this pressure during the rupture.
  • Another participant suggests that the energy needed to rupture the sphere should equal the energy required to increase the internal pressure from zero to the rupture pressure.
  • Some participants request clarification on the specifics of the simulation and the calculations involved, particularly regarding the energy needed to tear the sphere into parts.
  • There is a discussion about the relevance of post-rupture dynamics and the necessity of understanding material properties to simulate the rupture accurately.
  • One participant likens the energy accumulation in the system to that of a compressed spring, suggesting that the energy of the expanding air dissipates with distance from the center of the sphere.
  • Questions arise regarding how the energy needed to rupture the sphere is determined, including inquiries about the material properties and thickness relevant to the rupture process.
  • A participant mentions that the simulation outputs the energy required for rupture, indicating the material is considered elastic.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and agreement on the calculations and concepts involved. Some agree on the need for clarity regarding the energy calculations, while others raise questions about the assumptions and properties of the materials involved. The discussion remains unresolved with multiple competing views on how to approach the problem.

Contextual Notes

Limitations include the dependence on specific material properties, the assumptions made about the pressure application, and the lack of consensus on the method for calculating displacement and energy. The discussion also highlights the need for more background information on the simulation parameters.

miraboreasu
Messages
24
Reaction score
0
I am post-processing a simulation.

A spherical is meshed by many little triangles. A time-dependent pressure (p=10*t) is equally applied to the inner surface of a spherical in the normal direction all the time. After t1=0.1s, the spherical is broken, and each little triangle is disconnected.
Assuming during t1, p is constantly 1 (10*0.1). My ultimate goal is to calculate the energy brought by p to this system

My idea is to use p*area*displacement for 1 triangle, then do the same thing for all other triangles

Here is what I have from the simulation (for one triangle).
Nodal coordinates (vector in x,y,z) for three vertices of the triangle
p1: 2.48309 2.51276 2.45388
p2: 2.4875 2.50415 2.45103
p3: 2.47773 2.50283 2.45452
Nodal velocities (vector in x,y,z) for three vertices of the triangle
v1: -11.352 4.68846 -58.9501
v2: -10.2788 -1.54017 -60.6666
v3: 12.043 6.94501 -34.1632
Nodal displacements (vector in x,y,z) for three vertices of the triangle
d1: -0.00023 0.000131 -0.00071
d2: -0.00025 6.02E-05 -0.00066
d3: -0.00027 0.000148 -0.00066

I write the following MATLAB code to compute the area of this triangle from nodal coordinates
'''
p1=[2.48309 2.51276 2.45388];
p2=[2.4875 2.50415 2.45103];
p3=[2.47773 2.50283 2.45452];

edge12=p2-p1;
edge13=p3-p1;

area = 0.5*norm(cross(edge12,edge13),2)
'''

Then I use p*area to get the force, but I don't know how to get the right (or approximated) displacement, since force should be in the same direction as displacement, what I have is the Nodal displacements shown above.

Any idea to figure out the energy brought by p to this system during t1? It will be great if the answer is explained in detail
 
Physics news on Phys.org
That should equal the amount of energy that is initially needed to increase the internal pressure of the sphere from zero (respect to atmospheric pressure) to the rupture pressure.
 
  • Like
Likes   Reactions: berkeman
Lnewqban said:
That should equal the amount of energy that is initially needed to increase the internal pressure of the sphere from zero (respect to atmospheric pressure) to the rupture pressure.
Can you please be more specific? Assume I know the energy needed to tear the sphere into parts, which is E.
Besides, the data I provide is all I have. What should I use to calculate it?
 
Welcome to PF.

miraboreasu said:
A spherical is meshed by many little triangles. A time-dependent pressure (p=10*t) is equally applied to the inner surface of a spherical in the normal direction all the time. After t1=0.1s, the spherical is broken, and each little triangle is disconnected.
Assuming during t1, p is constantly 1 (10*0.1). My ultimate goal is to calculate the energy brought by p to this system
Could you please say more about what you are trying to simulate/calculate? If you are wanting to calculate how much energy you need to use to compress a gas to rupture a spherical enclosure, the post-rupture dynamics seem irrelvant to me. You would need to simulate the strength and deformation of the enclosure based on the material properties of the enclosure material, and the properties of the gas that is going to cause the rupture.

The more background that you can give us about your project and simulation, the better we can help you. :smile:
 
berkeman said:
Welcome to PF.Could you please say more about what you are trying to simulate/calculate? If you are wanting to calculate how much energy you need to use to compress a gas to rupture a spherical enclosure, the post-rupture dynamics seem irrelvant to me. You would need to simulate the strength and deformation of the enclosure based on the material properties of the enclosure material, and the properties of the gas that is going to cause the rupture.

The more background that you can give us about your project and simulation, the better we can help you. :smile:
Hey berkeman,

I am post-process my simulation. My simulation is to add a dynamic loading to a sphere surface. I know the energy needed to tear the sphere into parts.

I know how much pressure is added, since it is added as a boundary condition. Under this pressure, the sphere is broken into triangle as it was meshed, and I have these data from the output of the simulation
Nodal coordinates (vector in x,y,z) for three vertices of the triangle
p1: 2.48309 2.51276 2.45388
p2: 2.4875 2.50415 2.45103
p3: 2.47773 2.50283 2.45452
Nodal velocities (vector in x,y,z) for three vertices of the triangle
v1: -11.352 4.68846 -58.9501
v2: -10.2788 -1.54017 -60.6666
v3: 12.043 6.94501 -34.1632
Nodal displacements (vector in x,y,z) for three vertices of the triangle
d1: -0.00023 0.000131 -0.00071
d2: -0.00025 6.02E-05 -0.00066
d3: -0.00027 0.000148 -0.00066

I want to know the total energy brought into this system by my boundary condition pressure p
 
miraboreasu said:
Can you please be more specific? Assume I know the energy needed to tear the sphere into parts, which is E.
Besides, the data I provide is all I have. What should I use to calculate it?
Energy in = energy out

It is like a compressed spring: elastic energy is accumulated, and then, released.
Nothing else will separate the little triangles.
Once detached, they should move radially out at same speed than liberated air.

The energy of the expanding air should dissipate with the square of the radial distance from the center of the sphere.
...Or so I believe. :smile:
 
miraboreasu said:
I am post-process my simulation. My simulation is to add a dynamic loading to a sphere surface. I know the energy needed to tear the sphere into parts.
How do you know the value of that energy? What were your calculations/simulations to tell you that? What is the material and its thickness? What are its properties that are germaine to its rupturing?
 
berkeman said:
How do you know the value of that energy? What were your calculations/simulations to tell you that? What is the material and its thickness? What are its properties that are germaine to its rupturing?
The simulation outputs this energy. It is considered an elastic material.