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Length scales in CFD

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Old   September 7, 2022, 17:57
Default Length scales in CFD
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William
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I am relearning the Navier Stokes equations by deriving them again from transport equations. I noted that the fundamental assumption Navier Stokes equations make is that the fluid of interest is a continuum. I understand that for a fluid to be continuum the length scale of interest needs to be much larger than the mean free path of the fluid. It is relatively easy to estimate the mean free path of a fluid, but I am not sure how to find out the length scale of interest in a CFD problem. I guess the question I can come up with now is, what defines the smallest length scale of a typical CFD problem? Are they related to the size of the eddies and things? Thanks!
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Old   September 7, 2022, 18:12
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Quote:
Originally Posted by jinggca View Post
I am relearning the Navier Stokes equations by deriving them again from transport equations. I noted that the fundamental assumption Navier Stokes equations make is that the fluid of interest is a continuum. I understand that for a fluid to be continuum the length scale of interest needs to be much larger than the mean free path of the fluid. It is relatively easy to estimate the mean free path of a fluid, but I am not sure how to find out the length scale of interest in a CFD problem. I guess the question I can come up with now is, what defines the smallest length scale of a typical CFD problem? Are they related to the size of the eddies and things? Thanks!
The smallest lenght scale is dictated by the physics and is the Kolmogorov length scale. If you evaluate the ratio of this lenght to the cell size, you get a non-dimensional number that is the cell Reynolds number. If it is O(1) you have a DNS and all physical lenght scales are resolved by the computational grid size.
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Old   September 7, 2022, 19:10
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I see, thanks for pointing me in the right direction!
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Old   September 7, 2022, 19:22
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A very quick way to estimate Kolmogorov length scale is to figure out your boundary layer thickness and go two orders of magnitude down. Viscous effects dominate the 10% of the boundary layer and 10% of that is your order of magnitude estimate for the viscous length scale.


You'll find out soon enough but the mean free path for air at ambient pressure is nanometer scale. Practical flow devices will have dimensions of milimeters or more. You need to be at crazy vacuum pressures or have a very small device for these scales to be anywhere close to each other.
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