FEM Analysis of Hagen-Poiseuille Law Pressure Distribution

[Parker678]

Hello,

I am doing a project which includes attempting to map a theoretical pressure distribution across a capillary tube. I am trying to do a finite element analysis using Hagen-Poiseuille's Law to map the theoretical pressure distribution before I move onto using a SolidWorks Flow Simulation. The problem is that, I keep getting values that seem way too high and suggest things that I believe are not possible for the problem (like supersonic flow).

A basic physical description of the problem: There is a 5 ft section length of capillary tube, which is held at a constant Pressure of 10 psig across its length. Then at time t = 0 the tube is pierced at one end so that the pressure at that point is atmospheric Pressure. I would like to be able to use Finite Element Analysis utilizing Hagen-Poiseuille's Law to create a pressure distribution across the capillary tube for each time step.

Some dimensions about the scenario:

CAPILLARY TUBE DIMENSIONS: Length = 1.524 m, Diameter = 0.00635 m. I am wanting to break this up into 5 sections (dx = 0.3048 m) for the finite element analysis.

Pressure = 68947.6 Pa (10psig) ***For time = 0, I have assumed that the pressure drop across section 1 is 10 psig, and there is no change in pressure from the subsequent sections, it will be clearer in the image I attach

Gas = Air (R_air = 287.06 J/(kg*K))

Time_step = 8.89e-04 s ***I have been assuming this time step based on how long itwould take a pressure wave at the speed of sound to travel one section length (0.3048m)
I am going to attach an image below of some of my hand calculations because I think it will illustrate better than I can in my text. I would greatly appreciate any insight!

 

[Future Bruno]

Thank you! From your description, it appears that you are trying to simulate a shock wave traveling through the capillary tube. If this is the case, then you need to use a different approach than Hagen-Poiseuille's Law. Hagen-Poiseuille's Law assumes that the flow is steady and laminar, which is not the case in a shock wave scenario. Instead, you will need to use a numerical method such as finite difference or finite volume methods to solve the equations of motion for the shock wave. These methods will allow you to capture the transient behavior of the shock wave traveling through the tube.