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Determination of the time period for averaging of the velocity field at periodic flow

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Old   December 18, 2018, 12:24
Question Determination of the time period for averaging of the velocity field at periodic flow
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Hi everyone,

I have a question regarding the field average of the velocity field.

I use a quite simple setup of a flow past a circular cylinder at Reynolds number Re=100. The case is two-dimensional and for mesh generation I use blockMesh with a depth of one cell in the z direction. In addition, I use extrudeMesh to collapse the front patch into the back patch to get a truly two-dimensional geometry. I use the solver simpleFoam. At this Re the flow shows the Kármán vortex street with vortex shedding.

I need to calculate the field average of the U (velocity) field using function objects “fieldAverage” (mean U for each cell over time). The averaging works fine, but I try to figure out the proper time for running the averaging of the field after the periodic flow in the wake of the cylinder is fully developed.

Therefor I have two basic ideas:

1) As the vortex shedding frequency is equal to the oscillation frequency of the lift coefficient of the cylinder, I also use the functionObject “force coefficients” to calculate the lift coefficient.
Using fft (fast Fourier transform) to analyze the plot of the lift coefficient over time I can calculate the frequency of the vortex shedding and the periodic time. Then I could use a multiple of this period as the timespan for averaging. Thereby I should get a result that is independent from the state of the flow (U field) at the start of the averaging.

I am not entirely sure whether this is a proper way to determine the averaging time and I would prefer a method that allows a more quantitively way to indicate that the averaging was executed for a sufficient amount of time. I am aware that deviation decreases as the time for averaging is increased, but I still would like to implement it in a way that allows to monitor the progress (ideally by a single parameter).

2) Therefor I was wondering if there is a better way e.g. by using some other function objects for averaging. Does it make sense to calculate the average of U over the time and all cells and if so, how could that be done? Is there another method that is typically used to determine the averaging time for a periodic flow?

I am quite new to OpenFOAM and could really use the help. Any comments or ideas would be much appreciated. Thanks in advance!

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