Discussion Forum

February 8, 2012 10:52am UTC

Hagen–Poiseuille flow

I would like to use Comsol for a microfluidics project I'm working on. As this is my first time working with Comsol I am trying to simulate a simple problem to compare the simulation with analytical results.
The Hagen-Poiseuille flow problem is a solution to a simple fluidic problem, the flow of a liquid through a circular tube. More infor here: http://en.wikipedia.org/wiki/Hagen%E2%80%93Poiseuille_equation

I've set up the simulation as follows:
The geometry is 2D axisymmetric (radius is 15, length is 800)
The material is water
The physics is laminar flow (spf)
I use incompressible flow as my physical model
And define the inlet and outlet
The inlet pressure is 100 Pa, the outlet pressure is 0 Pa
The mesh is 'physics controlled' and normal

I run the simulation and to obtain the flow rate I apply a surface integration spf.U with Dataset 'solution 1'.
The result for this particular simulation is: flow rate = 5.593e-11 M3/s

The problem is that the analytical result is different. I've put it in Matlab to make sure it isn't me. The result is a factor of 22 too high.

r = 15e-6; % radius
dP = 100; % Pressure
Nu = 0.001; % viscosity
L = 800e-6; % Length
Fr = (pi*r^4*dP)/(8*Nu*L) % Hagen-Poseiulle equation for flow rate

Fr = 2.4850e-012 M3/s

I've triple checked these results but I cannot find why they don't match up. A factor 22 indicates that something's wrong, either on the theory side, or on the simulation side. Because I've just started with Comsol I would like to ask anyone to look over this model and see if something is evidently wrong. If anyone can give me suggestions why the analytical model is not correct I would like to hear it as well.

Thanks in advance

Reply  |  Reply with Quote  |  Send private message  |  Report Abuse

February 10, 2012 4:36am UTC in response to Jaap Verheggen

Re: Hagen–Poiseuille flow

You are calculating the integration over the wrong surface. You should do a line integration over the top or bottom line of U*2*pi*r. You can also integrate over the same line, just U and select “Compute surface integral” in the Integration settings. That way COMSOL internally adds the 2*pi*r term for you.

Nagi Elabbasi
Veryst Engineering

Reply  |  Reply with Quote  |  Send private message  |  Report Abuse

February 15, 2012 9:32am UTC in response to Nagi Elabbasi

Re: Hagen–Poiseuille flow

May i know why you recommend to use U*2*pi*r? as in my opinion, U is only represent for the radial velocity, not the whole model velocity.

and by default, comsol give us spf.U which calculate 3D velocity.

I thought we should use spf.U rather U, as it represent the velocity in 3D domain.

sorry, i am just curious, and hope you can evaluate more.

Reply  |  Reply with Quote  |  Send private message  |  Report Abuse