What Is the Correct Non-Dimensional Time Scaling in CFD for 2D Channel Flow?

[member 428835]

Hi PF!

I'm running a CFD software that non-dimensionalizes the NS equations. The problem I'm simulating is a 2D channel flow: relaxation oscillations of an interface between two viscous fluids, shown here. I'm trying to see what they are non-dimensionalizing time with, which is evidently just $\tau$ shown here.

Thinking about my problem, quantities that involve time are $g,\mu,\sigma$. However, I'm setting $g=0$ and trying assume inviscid flow so $\mu \ll 1$. This makes me think for my problem $\tau = \sqrt{\rho l^3 / \sigma}$. Do you agree?

 

[boneh3ad]

The proper dimensionless scaling depends on application. I can't honestly tell you what your software package uses, but the scaling you provide does look like a good building block for producing the Weber number in your final dimensionless equation, which would be appropriate here.

 

[member 428835]

The proper dimensionless scaling depends on application. I can't honestly tell you what your software package uses, but the scaling you provide does look like a good building block for producing the Weber number in your final dimensionless equation, which would be appropriate here.

Not sure why I missed this until now? The issue with the Weber number is the velocity, which I compute with the surface tension (it's the only temporal component since we look at an inviscid fluid). Any other ideas?

Apologies for the late reply.