We are using a code where the divergence of velocity is neglected in the stress tensor for a low Mach approximation. We inject a pure helium plume in an air cavity. In PIV experiments the flow is more turbulent than in CFD corse DNS calculations. Kolmogorov scale is evaluated to be around 0.1mm. Mesh cell is around 0.3mm. We performed Smagorinsky LES and coarse DNS calculations. L2 norm convergence is estimated better than 7% of error. We wonder whether the Approx 20% of differences between experimental PIV measurements could be attributed to that neglected Div(u) term in the stress tensor, or not sufficiently converged DNS (or exp. problem). Has someone examples of the importance of this div U term in turbulence development ? Best regards?
Dear Gilles,
As far as I know, in incompressible flow the term you mentioned should be equal to zero. I have attached the full-term equation for convenient.
Regards
Dear Ehsan
You are perfectly right if we are incompressible, that is using Boussinesq approximation. But we are using low Mach approximation, where Pressure is assumed uniform in space (possibly varying with time) and given by perfect gas law, but density is varying with time and space. This Div U term is not 0 in this case.
Hence my question about this term's importance.
Best regards
Dear Gilles:
1) you wrote about strong buoyancy, are you sure you can apply Bousinnesq linearization model?
2) Why are you considering that the PIV measurements is the "ideal solution" to compare with? Maybe experimental people would like to consider a DNS solution as their ideal solution...I suggest to consider the "discrepancy" between the two set of data, not an assessed error.
3) Consider how the experimental measurements are post-processed to compute the statistics you are using for comparison.
4) I don't think that the lack in the compression/expansion of volume is relevant in the onset of turbulence. On the other hand, the Stokes hypothesis could be used independently from the assumption on the div v term.
5) Even if you are not resolving exactly up to the Kolmogorov scale, if the numerical method is accurate there are evidence you can get quite good result resolving up to the Taylor microscale of the flow.
In conclusion, I also suggest to show here some plot of the comparisons.
Regards
Dear Filippo
1 - I am not applying the Boussinesq model as I said but Low Mach approximation.
2 - of course, but I can consider a DNS solution as reference only if I am sure there is no problem with the code, hence my question about the importance of div U problem in the stress tensor.
3 - experiments and DNS are post processed the very same way since both produce exactly the same kind of data.
4 - I don't understand what you mean in this section ?
5 - I will produce plots, how do you calculate the Taylor microscale of the flow ?
Thx for the information.
Regards
The stress tensor in the Newtonian model writes as
T = [-p+(lambda+2/3mu)div v]I+2mu D0
therefore if lambda+2/3mu=0 is assumed, also if the flow is not divergence-free this term has no relevance.
Taylor microscale can be estimated by means of the autocorrelation.
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