Suppression of three-dimensional flow instabilities in tube bundles

We study the generation of three-dimensional vorticity in tightly packed tube bundles. In particular, our goal is to investigate which conditions (if any) enable the flow to remain two-dimensional for Re>180. We calculated two- and three-dimensional flow through periodic rotated square tube bundles with tight packing, P/D=1.5, using a high resolution pseudo-spectral code with penalization. The tubes are cylinders whose response is modelled as a rigid harmonic oscillator forced by the flow-induced lift. We find that at Re=200 tube motion completely suppresses the three-dimensional instability. At Re=1000 tube motion does not suppress the three-dimensional instability, although the flow does have increased spanwise correlation and the Strouhal number for the two- and three-dimensional flows is approximately the same. The tight packing alone does not suppress the three-dimensional instability. Three-dimensional vorticity drastically reduces fluid forces acting on the tube compared with an equivalent two-dimensional flow.