On the multiple steady flow states in spindle shaped geometry of bridge foundations

Abstract

Flow hysteresis in a channel with a supercritical flow in the vicinity of a spindleshaped bridge foundation (SSBF) with a change in flow rate has been investigated in a laboratory for the first time. Two spindle-shaped bridge foundations with diameters of 9 and 6.5 cm, which are placed at distances of 1.5 and 1 meter from the gate, have been used. The critical depth ranges between 0.027 and 0.0528 meters, and the used flow rates range from 250 to 600 liters/min. The flow regimes in the vicinity of the bridge foundations are classified based on the relative depths and Froude numbers created in sections B and C according based on the Froude number at the vena contracta. Sections B and C are near the bridge foundation and the flow passing through the center of the bridge foundation, respectively. The increase and subsequent decrease in velocity leads to different flow states. In some cases, two different behaviors can be seen from the flow with similar laboratory conditions. Hysteresis manifests in the range of Froude number 2.697 similar to 5.0. As the bridge foundations approach the valve, the hysteresis area becomes wider. Changes in the flow regime under the same conditions, called hysteresis, should be considered in designs. Also, with hysteresis, the relative residual energy and the downstream Froude number increased by 57.36% and 72.31%, respectively.