[windfire]

Hello everyone,
i use CFX to simulate waterhammer, Courant number is less than 0.5 in the first two cycle ,when transient run after a two cycle of the pressure, Courant number increase suddenly and large than one, the rusult begin to oscillate, What could cause this? thank you!


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[ghorrocks]

Could be due to many things. It could be real, it could be a numerical artefact. If numerical artefact it could be divergence, too big a time step, and many others.

I recommend you use adaptive time steps homing in on 3-5 coeff loops per iteration. That tends to work better than Courant number for CFX.

[windfire]

thank you for rely this question,i have used adaptive time steps, the pressure oscillate better when Courant less than 0.5, due to no-slip condition at the
hydraulically smooth pipe wall, pressure should not increase with time in thoery, but pressure increase with time actually, What could cause this? thank you!

[ghorrocks]

It could be vortex shedding, transition to turbulence or one of the many flow instabilities. And yes, they can build up over time as they get themselves going.

If you are confident your transient simulation is well converged and accurate then the effect is real. Have a look at the transient results and you should see some form of transient flow happening.

[windfire]

Thank you Glenn,

i have changed initial time step from 0.001 to 0.01, the pressure oscillation begin to decrease, then i set up to 0.1, the pressure oscillation drop very fast in sevel time steps,because i simualte water hammer occurred in a horizontal pipe, outlet flow discharge sudden drop to zero in 0.5s, the time step have such a strong influence the results of the calculation? what could cause this? thank you!

[ghorrocks]

As you increase the time step size you are resolving the transient terms with less and less accuracy, and then some of the transient effects are either not present or muffled.

You need to do a sensitivity analysis where you make the time step size smaller (not bigger!) until the result converges. Or even better, use adaptive time stepping, homing in on 3-5 coeff loops per iteration and it will find the correct time step for you.

[evcelica]

Is a water hammer simulation one where the acoustic Courant number is more critical, and the standard Courant number is meaningless? Pressure waves and such would tell me yes.
I performed a helium relief analysis which had pressure waves and I had to use time steps which related to the Courant number using the speed of sound in the fluid, not the fluid velocity itself. My standard Courant number was always 0.00, I have never seen that acoustic Courant number before in the output, why does it show up for you?

[ghorrocks]

That is a good point Erik. You are correct, the acoustic Courant number (which is also known as the Courant-Lewy-Friedrichs or CFL number) is the important parameter for defining the time step. And I must admit that I am not sure the 3-5 coeff loops per iteration approach adequately handles this.

Many years ago I did lots of work on pressure waves in compressible flow and I used either a CFL number of around 0.5 or a time step size calculated to give CFL of approximately 0.5. I have not checked the 3-5 coeff loops per iteration approach gives reasonable time step sizes for this class of simulation.

Erik correctly points out that the incompressible Courant number (usually known as Courant Number) is meaningless in these type of flows and should not be used.

[evcelica]

CFL number of 0.5 sounds about right for what I did as well. I was initially shooting for ~1, but noticed it was always hovering around half of that. I believe I did have to use a maximum time step setting. Adaptive time stepping would increase too much and I would have time steps that would not converge, then it would decrease the time step and bounce back and forth at this unstable maximum. Setting the maximum time made it much more smooth and the simulation ran much faster.

[ghorrocks]

For water hammer simulations the acoustic velocity is usually far greater than any fluid velocity, which means a fixed time step size gives pretty much constant CFL number for the entire simulation. In addition, second order time differencing looses significant accuracy when the time step size changes. This meant that for a lot of my work just using a fixed time step, calculated to give a CFL of around 0.5 was best. (Reference: https://opus.lib.uts.edu.au/handle/2100/248 and section 5.2.6 looks at time step size in a shock tube simulation. Note that this was done on CFX 4, which is quite different to the current CFX - but the time step required for good modelling of compressible flows is similar)

Note that first order time differencing is not so badly affected by time step size changes, but second order is quite sensitive to it.

[windfire]

Thank you all, i have made sensitivity analysis of time step, but all results seems to make me satisfy, i also simulated water hammer occurred in a 3m pipe , but this model get a stable results, is it length of pipe influence results more obvious?

PS:Attach Files is stable results of 3m, i decrease discharge of previous model,i found that the stability also strengthen.

[ghorrocks]

Please post your output file and an image showing the results. A comparison between the 3m pipe stable results and the unstable results would be good.