Menu

Discussion Forum

New Discussion
Filter

Discussion Closed This discussion was created more than 6 months ago and has been closed. To start a new discussion with a link back to this one, click here.

Average pressure at the meniscus

Posted Jul 9, 2020, 7:55 a.m. EDT Fluid & Heat, Results & Visualization 1 Reply

Harsha Desu
Send Private Message Flag post as spam

Please login with a confirmed email address before reporting spam

Hello, I am new to comsol and working on the capillary flow using Lamiar flow phase field method. Is it possible to calculate the average pressure at the meniscus exactly. Meniscus is an isosurface with constant volume fraction(0.5). I am able to construct a cut plane and get an average value of pressure along the cut plane. But meniscus is not a straight plane, so getting average pressure is difficult. Is it possible to use the meniscus surface as a cut plane and get the average value of pressure? The pressure at the meniscus is different at different points. So, is there any way to find pressure across the meniscus.

1 Reply Last Post Jul 9, 2020, 8:38 a.m. EDT
Alexis Prel
Send Private Message Flag post as spam

Please login with a confirmed email address before reporting spam

Posted: 4 years ago Jul 9, 2020, 8:38 a.m. EDT
Updated: 4 years ago Jul 9, 2020, 9:19 a.m. EDT

Hello Harsha,

This is an interesting question. I do not have a full answer that would work out of the box in COMSOL, but I see two work-arounds. Hopefully someone with more experience can provide a better solution

  1. Export the volume fraction and pressure fields, then work out the problem in python
  2. Compute an approximated average using a Gaussian as a substitute for the Dirac distribution

I will focus on solution n°2:

The point is that you are interested in the quantity

where is the volume fraction field, is the pressure field and is the meniscus area

The idea is to approximate with a narrow normal distribution

So for small enough, you can take . Where has the dimension of u and is to be interpreted as the width of a small averaging window around the meniscus value .

So, I would define this expression in COMSOL using the usual integration operators, then trace this quantity has a function of . As it get smaller, should converge, until becomes too small compared to the mesh spacing I presume.

I wish I knew a more efficient answer to your question.

Hello Harsha, This is an interesting question. I do not have a full answer that would work out of the box in COMSOL, but I see two work-arounds. Hopefully someone with more experience can provide a better solution 1. Export the volume fraction and pressure fields, then work out the problem in python 2. Compute an approximated average using a Gaussian as a substitute for the Dirac distribution I will focus on solution n°2: The point is that you are interested in the quantity P_{avg} = (1/S) \times \iiint \delta\left(\phi(\vec{x} - \frac{1}{2}\right) \times P(\vec{x}) d^3\vec{x} where \phi(\vec x) is the volume fraction field, P(\vec x) is the pressure field and S is the meniscus area S = \iiint \delta\left(\phi(\vec{x}) - \frac{1}{2}\right) d^3\vec{x} The idea is to approximate \delta with a narrow normal distribution \delta(u) = \lim_{\sigma \to 0} \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{u}{\sigma}\right)^2} So for \sigma small enough, you can take \delta(u) \simeq \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{u}{\sigma}\right)^2}. Where \sigma has the dimension of u and is to be interpreted as the width of a small averaging window around the meniscus value \phi_m = 1/2. So, I would define this expression in COMSOL using the usual integration operators, then trace this quantity has a function of \sigma. As it get smaller, P_{avg} should converge, until \sigma becomes too small compared to the mesh spacing I presume. I wish I knew a more efficient answer to your question.

Note that while COMSOL employees may participate in the discussion forum, COMSOL® software users who are on-subscription should submit their questions via the Support Center for a more comprehensive response from the Technical Support team.

Suggested Content