Characterization of exchange flow in vertical pipes of circular and square cross-sections under unstable density gradient

Abstract

The exchange flows in a buoyancy driven forced flow in vertical pipes of circular and square cross-sections were studied experimentally and the flow structure was examined by proper orthogonal decomposition (POD) analysis. The experiments were carried out in the vertical pipes issuing into a still brine water environment and the flow fields were visualized by the laser-induced fluorescence (LIF) technique. The flow visualization study showed that the critical inflow condition was deviated from the purging boundary due to the influence of hysteresis, and they are shifted to the high Froude numbers in the square pipe compared to the circular one. The POD analysis of the exchange flow indicates that the fluctuating energy is increased in the lower POD modes due to the formation of large-scale structure of the exchange flow. It is found from the analysis that the exchange flow in the low Reynolds number is promoted at the corners of the cross section in the square pipe, while it is randomly distributed in the circular pipe. This corresponds to an increased critical Froude number in the square pipe than that of the circular pipe, which is due to the presence of exchange flow through the corners. With increasing the Reynolds numbers, the flow becomes turbulent and the scale of the exchange flow is decreased and restricted to the near-wall region, while the location of the exchange flow becomes random along the pipe wall irrespective of the cross-sectional shape of the pipes.