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

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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?
 
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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.
 
boneh3ad said:
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.