FEM Analysis of Hagen-Poiseuille Law Pressure Distribution

In summary, you need to use a different numerical method to solve the equations of motion for a shock wave traveling through the tube.
  • #1
Parker678
1
0
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!
 

Attachments

  • FEAhandcalc.pdf
    1.7 MB · Views: 350
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  • #2
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.
 

1. What is FEM analysis?

FEM analysis, or Finite Element Method analysis, is a numerical technique used to solve complex engineering problems involving stress, heat transfer, and fluid flow. It uses a discretized model of the problem to approximate the behavior of a system and obtain a solution.

2. What is the Hagen-Poiseuille law?

The Hagen-Poiseuille law, also known as the Poiseuille's law, is an equation that describes the laminar flow of a fluid through a cylindrical pipe. It states that the volume flow rate of the fluid is directly proportional to the pressure difference, the fourth power of the radius of the pipe, and inversely proportional to the length and viscosity of the fluid.

3. How is FEM analysis used to study pressure distribution in the Hagen-Poiseuille law?

FEM analysis can be used to model the fluid flow in a pipe and calculate the pressure distribution along the length of the pipe. This is done by dividing the pipe into small elements and solving the equations for each element, taking into account the boundary conditions and properties of the fluid. The results from each element are then combined to obtain the overall pressure distribution of the system.

4. What factors affect the pressure distribution in the Hagen-Poiseuille law?

The pressure distribution in the Hagen-Poiseuille law is affected by several factors, including the fluid's viscosity, the length and diameter of the pipe, and the velocity of the fluid. Additionally, the pressure distribution may also be influenced by external factors such as changes in temperature or the presence of obstacles in the pipe.

5. What are the limitations of FEM analysis in studying the Hagen-Poiseuille law?

While FEM analysis is a powerful tool for studying complex fluid flow problems, it does have some limitations. One limitation is that it assumes a steady-state flow, which may not be accurate for certain situations. Additionally, the accuracy of the results depends on the quality of the mesh used in the analysis and the assumptions made in the model. Therefore, it is important to validate the results with experimental data.

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