[Julian121]

I am evaluating the performance of a compressor at an operating point by a transient simulation.

The image shows the mass flow signal at the inlet.

The boundary condition at the outlet is static pressure.

At this operating point, what value of the mass flow should be used to draw the performance map?

Should I take an average over some time periods?

[ghorrocks]

What you do from here is up to you. If you decide that those transients are small and fast enough that it would just average out, then feel free to take the mean over a few cycles. If you decide that those transients are going to affect the way the system behaves then you need to think about how that can be dealt with.

[Julian121]

Could you please explain more?

Are you talking about the convergence in transient simulations?

How can I measure the effect of the transients?

[ghorrocks]

If you are modelling an aircraft and you get a signal in the lift at 100Hz frequency then you can safely average it to get the average lift. The 100Hz would just vibrate the aircraft.

But if the signal is 0.1Hz then that will cause the whole aircraft to climb and dive, so you better have a think about whether that climb and dive is going to cause other effects.

[Julian121]

Why does stationary components like IGV or Stator have blade passing frequency? Aren't they stationary?

[ghorrocks]

The IGV and stator will create a wake which will interact with the rotor blades as they pass and this will generate a signal.

[Julian121]

Which one of local or global parameters is better to assess the convergence of a transient simulation?

In the CFX manual, it is said that variable should be averaged over the time interval required to pass 1 pitch to decide about the convergence. Does it have to be exactly one pitch?

[ghorrocks]

That depends on what you are doing, that is why you are given the option of choosing what is appropriate for you.

The averaging time does not need to be exactly one period, but things get complex if you compare results where you use different averaging times. For instance if the parameter is low in the first half of the cycle and high in the second half, if you average over 1.1 cycles you could get 0.5 periods of low, 0,5 periods of high and another 0.1 of low. This will bias the average downwards.

[Julian121]

I am using the transient blade row method and I have selected 40 time steps per a passing period.

The signal shows the absolute pressure for a probe at mid span mid chord of the rotor.

Here if I use the averaging time as 40 time steps, the averaging is not constant. (image1)

But if I use larger time steps such as 480 time steps (12 passing periods), the averaging does not change. (image2)

Is it correct to assume the simulation is converged and use the large interval?

[ghorrocks]

If the cycle average is not over an exact cycle it can be misleading, we discussed that in the previous post.

You would expect that averaging over 12 cycles will reduce the variations by a factor of about 12, and I can see some variation there so it is probably just 1/12 of the single cycle variation. In other words they are both behaving as expected.

But whether this is converged or not is up to you. It depends on what you expect and what you are doing with it.

[Julian121]

My main requirement is to calculate the global pressure ratio and draw a performance map with and without a casing treatment.

However, I am not sure whether the transient simulation is enough converged or I should run it longer.

The image1 shows the global pressure ratio and the average over exact 1 passing period (40 time steps) has been added.

Image2 is just the average.

It seems that the average is somewhat repeating itself. Does it signify anything?

[ghorrocks]

Image 2 shows the averaged signal seems to be a decaying signal. You would think for most applications you could just take the average of it.

Also note the size of the decaying signal, it appears to be 0.1% peak to peak. Surely you are not looking for 0.1% accuracy? Call it 1.009 or 1.01, it does not matter; and that covers the entire range of the variation you are seeing.

For future reference - getting CFD results of turbulent flows under 10% accuracy requires care, and under 1% requires extremely thorough validation and verification. So most people are happy with 10% errors. And a lot of preliminary design work is done on acceptable errors much larger than that.

[Julian121]

I was thinking that the average over a cycle must reach a constant value to get convergence.

As you said since the average varies between 1.009 – 1.01, it does not matter.

Is it correct?

[ghorrocks]

This is basic numerical analysis - you will never get a numerical approach to converge completely. There will always be some residual left. So you have to decide how much error/residual you are happy to live with and stop iterating when you have gone far enough. So convergence in a numerical approach (like CFD) requires you to define a level of accuracy you are happy with.

You can define that tolerance to be anything you like. Just remember that if it is loose your results will be inaccurate and if it is tight then you are using time and resources to get accuracy you don't need. What the appropriate balance is between these two factors is different for each application.

But having said that, your results have converged to within 0.1% and there is no way the result of your model is accurate to within 0.1%, so you have definitely converged tighter than you need to.

[Gert-Jan]

Originally Posted by Julian121

I was thinking that the average over a cycle must reach a constant value to get convergence.

As you said since the average varies between 1.009 – 1.01, it does not matter.

Is it correct?

You can try to achieve deep convergence to feel confident but this is all fake. CFD is like doing experiments: there will always be an uncertainty. You better get used to it.