Bifurcation Behavior of Flow in a Mixed-Geometry Tube Array

Abstract The work reported here pertains to the (nonlinear) dynamics of flows in mixed-geometry tube arrays. Helical coil steam generator tube bundles differ from U-bend tube steam generator tube bundles in two key features, (i) the presence of tube curvature and (ii) the non-uniformity or mixed-symmetry of the tube pattern at a given (azimuthal plane) normal to the tube axis. The present work focuses only on the latter feature. We therefore study the flow dynamics in a mixed-symmetry straight tube array (with no curvature). Flow in tube arrays having simple symmetry (square or triangular patterns) is characterized by flow periodicities for which corresponding Strouhal numbers are easily determined. This study is carried out for a mixed-geometry (combination of inline and triangular pattern) tube array, having a transverse spacing ratio of 1.3 and a longitudinal spacing ratio of 1.5. The array studied here was subjected to water cross-flow. The URANS equations were used for the CFD simulations. Lift and drag forces on the surface of the cylinders were extracted from the simulations. The results showed how the mixed-geometry tube array behaved as the Reynolds number ranged from 2,800 to 13,700. For low Reynolds numbers, the periodic behavior of the lift and drag coefficients started to change as a result of period-doubling bifurcations. As the flow Reynolds number exceeded (Re ≈ 8, 000), further bifurcations led to intermittency in the lift and drag forces on the tubes. With increasing velocity, the intermittent bursts of energy became more frequent and occurred after shorter time intervals, eventually leading to apparently chaotic dynamics. The results demonstrate that the stable periodic dynamic behavior, common in symmetrical arrays, breaks down in the case of the mixed-geometry array studied here. Practically the results suggest that Strouhal number characterization of flow in (symmetrical) tube arrays may not hold (for wide ranges of Re) for mixed geometry tube arrays due to flow bifurcations and possible transition to chaos. This would have implications for the flow-periodicity-induced resonance normally encountered for symmetrical arrays.