CFL influence on turbulence decay
 

Hi,

I am working on a spectral element code, flow in a sudden expansion pipe.

I ran a simulation with polynomial order N=5 at Reynolds number Re= 2000, I found turbulence inside my pipe which stays there forever and this matches with the real physics and some literature.

for same Re, I increased the order of my polynomial from N = 5 to N = 7 this in turn increased my CFL number, This time the turbulence decayed completely and became steady flow.

So I reduced the time step DT to get the CFL number same like that of the 1st simulation (N=5) and I found that the turbulence occurs but takes a little more longer time to decay

I reduced the time step Dt much more lower to have a CFL = 0.036 and found that the whole pipe became turbulent.

Could some tell me what is the effect CFL number on laminar to turbulent transition ?? why did the turbulence decay when I increased my order from N=5 to N =7 ?

This is a classic problem with high-order methods. When you increase the order, you are removing most of the dissipation which can trigger turbulence. This is a well-known problem with spectral methods. The fix that has been suggested is to perform simulations on a coarse grid with say p=3 or p=5 and let the turbulence develop. Interpolate the obtained results to the grid for p=7 and continue simulations.

Are you performing DNS? If so, are you sure that you used time and space steps enough small to resolve physical scales?
No matter in a CFL value if the time step is at the level of the Kolmogorov time scale, otherwise the effect is in an implicit filtering.

Thanks Harishg and FMDenaro !!!

I am wondering if increasing the total time would help. You suggestion mentioned a coarse grid, which in return might produce larger time step and larger total time, if CFL and iteration steps are not changed.

Moreover, if high-order as high as p=7 methods removing most of the dissipation that would trigger turbulence, is it less realistic for higher order methods?

Best,
Shawn

The idea is that the initial condition has some sort of perturbation to trigger turbulence similar to the physical occurrence of turbulence due to some instability in the flow. So it is not about being realistic. It is about tripping the flow to become turbulent. Experiments use trip wires and we need some form of numerical trip wire.

I got what you mean. Yes it is. Thank you for your response.