### 12.5.2. Averaging

Unsteady simulations with scale resolution require special care in postprocessing and averaging. Engineers are usually interested only in time-averaged results and not in the details of the unsteady flowfield. It is therefore important to follow a systematic approach when computing such quantities.

The typical process is to start from a RANS solution (or reasonable initial condition). When switching to any SRS model, the flow will require some time to statistically settle into a new state for the following reasons:•

- The resolved turbulence requires some time to develop and be transported through the domain.

- The global flow topology might change from the initial (RANS) solution.

- Other physical effects might require longer start-up times (such as multi-phase).

•The general strategy is therefore to run the simulation for some start-up time , before activating the averaging process (or initiating the acquisition of, for example, acoustics information). When should this process be started and how long does it take until the flow is statistically steady? This is the stage where any increase in would not change the averaged solutions. Unfortunately depends strongly on the flowfield and no general guidelines can be given. For some flows, the flow develops quickly (in a few thousand time steps). For others it takes tens of thousands of steps to reach that point. However, a first estimate can be obtained by estimating throughflow time, . This is the time that the mean flow requires to pass one time through the domain where is the length of the domain and is the mean flow velocity. The turbulence statistics typically require several (3-5) throughflow times to establish themselves. Again, this is just a rough estimate and can depend on the particular flow.

In order to determine more systematically, one must monitor the simulation. It is advisable to monitor some local and some global quantities.•

- Continuously inspect the solution visually with the aid of regular images and updated animations.

- Inspect solution variables at monitor points in the critical zone of simulation (pressure, velocity, temperature, and so on) as a function of time. The amplitude and frequency of local oscillations should become regular before the averaged statistics can be gathered.

- Monitor global quantities (forces on body, massflow, integrated swirl, and so on). Interesting quantities are often those that would be zero for RANS (spanwise forces, and so on) as they are sensitive to the SRS characteristics. They also help to evaluate the overall symmetry of the solution (they should fluctuate around zero) and to determine slow transients (quantities that fluctuate around zero but with low overlaid frequencies).

•Only when all indicators show that the flow is no longer changing statistically (meaning only the details of the turbulence structures are a function of time) should the averaging be activated. It is important to document the number of steps that have already occurred when averaging was started and how many steps have been averaged. With respect to averaged quantities:•

- Monitor time-averaged quantities and ensure that they are not “drifting.” They will drift initially, but should then settle to an asymptotic value.

- Ensure that they satisfy the symmetry conditions of the flow. Any asymmetry is an indicator of non-convergence (exceptionally, there are flows that develop physical asymmetries despite a symmetric set-up. Example: some symmetric diffusers separate from one side and stay attached on the other).

- Ensure that the averaged quantities are smooth.

- In zonal/embedded simulations, check if averaged quantities are reasonably smooth across RANS-LES interfaces (they will never be perfectly smooth, but should also not change drastically).

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