[jonasa97]

Good evening,

I have come across two conflicting definitions of the length scale:

L = k^1.5 / e (from the CFX documentation)
L = 0.09 * k^1.5 / e (from Wilcox and the wiki)

where L is the length scale, k is the turbulence kinetic energy, and e is the turbulence dissipation rate (epsilon).

The turbulence kinetic energy transport equation (including model coefficients) is identical between the two sources, and therefore an absorption of the constant "0.09" into epsilon seems unlikely (as has been suggested here for conflicting length scale definitions using k and omega).

Wilcox explicitly states that L is the integral length scale (determined via the autocorrelation method). This would suggest that we can use experimentally-measured length scales (following Wilcox's definition above) to determine boundary conditions of k and e. This seems to conflict with the CFX definition, however, unless the CFX length scale is not equivalent to the integral length scale (having been divided by the constant 0.09). This would be equally confusing, because specifying length scale directly (in CFX) based on experimentally-measured length scales would then be incorrect.

How do experimentally-measured length scales relate to the CFX length scale? Does the constant 0.09 get absorbed into the length scale or is there something else I missed?

Thanks in advance for any insights!

[ghorrocks]

Doesn't that just mean the Wilcox/wiki definition of length scale is different to the CFX definition of length scale by the 0.09 factor? But as for the question of how you relate an experimentally measured length scale to a turbulence model length scale - you would have to have a close read of the literature to work that out I fear.

[jonasa97]

Thank you for taking the time to engage with my question.

Originally Posted by ghorrocks

Doesn't that just mean the Wilcox/wiki definition of length scale is different to the CFX definition of length scale by the 0.09 factor?

Yes, it would seem that the length scale in CFX is 11 times larger than the Wilcox/wiki length scale. I found this very confusing, however, because Wilcox claims (p 49; Eq 2.57 in the 3rd Edition) that the factor "0.09" was chosen specifically such that the expression is equal (not proportional) to the integral length scale (computed via a single point auto-correlation or directly from a spatial correlation). Obviously this won't be exact, but one would hope it yields a length scale with the right order of magnitude. Therefore, deviating from this purportedly "calibrated" definition of the length scale by a factor of 11 would seem imprudent. However, I'm not sure which definition to trust anymore, because the literature (Spalding and Launder, 1974) does not support Wilcox's claim that the turbulence length scale is equal to the integral length scale, choosing (in contradiction to Wilcox) to call "L" a "length representing the macroscale of turbulence". I will compare DES auto-correlation integral length scales to equivalent RANS results to see what the coefficient should be.

[jonasa97]

The DES time series was unfortunately too short to determine the integral time scale accurately.

It occurred to me, however, that the integral time/length scale is not necessarily proportional to the local eddy size. One such example is a flapping shear layer, which may have a natural frequency several times lower than the passing frequency of eddies. I suppose this highlights the complexities of translating integral length scales into turbulence length scales for RANS modeling.

[ghorrocks]

Your posts show you are doing some good research into this issue and are working out some of the finer details. So you know more about this issue than I do. In fact your posts are a good summary so we can keep up with you

Why can't you run the DES simulation longer to see if you can get an integral time scale?

[jonasa97]

The DES took approximately 3 months of wall time to get where it is now, so keeping it running is unfortunately not an option.

For clarification: it is technically possible to determine an integral time scale from the DES time series (i.e. auto-correlation crosses zero). The resultant timescales are, however, not well converged (I have assessed this by calculating the timescale for subsets of the DES time series). Overall, the unconverged integral time scale data is extremely noisy, and unfortunately looks nothing like the corresponding RANS time scales (entirely different distribution in space). Therefore - even if provided with converged DES integral time/length scales - I don't think that comparing these to RANS length scales would offer any useful insights. In truth, I think that this actually demonstrates that the proportionality constant in question does not exist.

[ghorrocks]

Out of interest, how long did the RANS simulation take?

How isotropic is your turbulence? Also, how long has it had to develop - is it close to the source/trigger, or has it had a while to form a energy cascade?

[jonasa97]

Originally Posted by ghorrocks

Out of interest, how long did the RANS simulation take?

The DES has 31 million cells and models the unresolved turbulence with k-omega SST. The test case ran on a server with two Xeon E5-2697 v3 CPUs (28 cores total). The DES took 3 months (~2200 hours) for approximately 5 flow-through periods (including startup transient). The RANS simulation which was used to initialize the DES (i.e. same mesh) converged in less than 60 hours.

Originally Posted by ghorrocks

How isotropic is your turbulence? Also, how long has it had to develop - is it close to the source/trigger, or has it had a while to form a energy cascade?

The test case was for a combustor simulator (massively separated swirling flow). The flow passes through a swirler, which is highly accelerating (from a few meters per second to Mach ~0.3), so any upstream turbulence would only have a very limited influence on the turbulence downstream of the swirler. The region of interest is located approximately 4 swirler diameters downstream of the swirler itself. The turbulence at this location was very anisotropic (judging from the Reynolds stress tensor).

[Opaque]

By any chance, have you read the following paper

https://public.lanl.gov/livescu/fram...etal_FTC15.pdf

Pay attention to their definition of length scale, and how it relates to your concerns.

It is all about context, and interpretation.

[jonasa97]

Originally Posted by Opaque

By any chance, have you read the following paper

https://public.lanl.gov/livescu/fram...etal_FTC15.pdf

I have not come across this paper - thank you for the suggestion.

[ghorrocks]

Correct me if I am wrong here, but all the definitions of length scale you have quoted so far in this thread have assumed isotropic turbulence. You have just stated your flow is strongly swirling, which means it will be strongly anisotropic. So you will have problems comparing length scale from any isotropic turbulence model (eg k-e, SST) or any length scale definition which assumes isotopy to simulations which are anisotropic (eg your DES model)

[jonasa97]

Originally Posted by ghorrocks

Correct me if I am wrong here, but all the definitions of length scale you have quoted so far in this thread have assumed isotropic turbulence. You have just stated your flow is strongly swirling, which means it will be strongly anisotropic. So you will have problems comparing length scale from any isotropic turbulence model (eg k-e, SST) or any length scale definition which assumes isotopy to simulations which are anisotropic (eg your DES model)

Yes, swirling flow certainly wasn't an ideal test case for deducing the correct scaling factor (considering different distributions of length scales altogether), but unfortunately it was the only scale-resolving simulation in my possession. For context, I am trying to deduce the proportionality constant between L, k, and epsilon for a sanity check on a different test case altogether (but one I do not have DES data for).

[jonasa97]

I found the answer by chance today. This paper (see Appendix A) seems to suggest that the correct relation is:


L = 0.32*k^1.5 / e


Naturally, the applicability will depend on how the integral length scale is defined.