First of all, you need to assess that the time averaging has been computed for a sufficiently long period, that must be controlled by the averaged variables that do no longer depend on time. However, the starting of the time averaging must be done after that the numerical solution has correlated, that is after that the arbitrary initial condition is disregarded by the solution. You must avoid to average during the numerical transient.

Finally, the presence of two or more separated regions in the averaged field could be also a correct solution, that must be checked from the literature as well as you need to check the response of the solution to a grid refinement. Are you performing a 3D model? What about the Re number and the formulation you are using?

Hello sir,

1- First of all, I want to thank you for your quick response, I have a :

- 2D simulation with an inlet velocity of 30 m / s.

- the jet frequency is 30 Hz and their amplitude is around 100 m / s.,

-Simulation time: 30 periods of the jet (T)

- The number of time step / T: 160,

- Mean flow on the last 5 periods of the jet(after establishing the flow).

For more details, I use URANS with the K-W-SST turbulence model. I have plotted the average value of the coefficient of friction over the last 5 periods, this indicates to me the existence of a single zone (see image above) the curve with the color in red presents the case without control and the curve with blue color presents the case with control.

2- ((First of all, you need to assess that the time averaging has been computed for a sufficiently long period, that must be controlled by the averaged variables that do no longer depend on time)). How can I check this?

Best regrads,

SERRAR

Start your simulation and monitor the total kinetic energy in time. Then, when you see that the level of the KE oscillates around a mean value, the numerical transient ended and you have a condition of energy equilibrium so that you can start to compute the time averaging. You need to cumulate the time averaging for several characteristic turn-over time. Again, you can monitor the u^2 and v^2 total components integrated in time. When they are constant you have the final mean fields.

However, let me say that the 2D URANS makes no real sense, you could directly solve the steady RANS equation if you are interested in the recirculation zone.

Thank you, sir,

I will implement your recommendation, and I will present here when I find the solution.

I mean sir, that at first, I launched the simulation in steady-state without jet, and then I drew the streamlines and the coefficient of skin friction ... to see the length of attachment, in the second phase I add the synthetic jet and I launch the simulation in transient flow.