A numerical solution to the onset of boundary layer separation in the flow around a circular cylinder independent of the size of the flow domain*

The onset of boundary layer separation in the flow around a circular cylinder is studied as a numerical experiment using Galerkin finite elements. The flow domain is carefully chosen  to ensure undisturbed flow conditions deep inside  both in the streamwise and transverse direction. Since there has never been a numerical experiment that ensures undisturbed flow conditions deep inside a domain, a criterion is introduced that allows the implementation of such an analysis. Using a constant entrance distance from the forward stagnation point, we vary the blockage ratio in such a way to reveal an exponential behavior in the change of the Reynolds number where boundary layer separation occurs. In addition, we are able to measure the angle as well as the length of separtion and check if these magnitudes exhibit a limit that is reached in an exponential fashion as well. Indeed, we are going to show that the Reynolds number, the separation angle and the length of separation of the eddy reach a limit as the flow domain grows. We show that this kind of analysis is possible only if the size of the domain in the transverse direction is of the order of 80 millions dimensionless units and five times greater in the streamwise direction, which justifies the use of supercomputing facilitites to enable this kind of research. It is further discussed how this work complements the previous research in the field by verifing research of other workers and pointing out shortcomings, as this is the first time that such an analysis has been performed with a flow domain of such dimensions.