Analytical solutions for vortex flow at the tangential inlet of a vertical dropshaft

Abstract

Vertical dropshafts with tangential intake structures are often used in urban drainage systems to route surface flow into underground systems. Vortex flow driven by a tangential inlet is the typical flow pattern in the vertical dropshaft. However, analytical solutions of the key hydraulic transition from chute flow to vortex flow have not been investigated, and theoretical guidelines of the vortex dropshaft are not available. In the present study, a series of theoretical analytical solutions are proposed to determine the circumferential flow generated at the vertical dropshaft inlet. The contraction ratio of the tapering chute, dropshaft size, and flow depth at the joint section determines the vortex flow performance in the vertical dropshaft. Based on the free surface drop height, theoretical criteria are proposed to describe the spiral movement intensity in the vertical dropshaft. Systemic experiments for different vortex dropshaft models are tested, and the experimental observations agree with the theoretical analysis. The present investigation provides a general reference for a tangential dropshaft inlet design that can smoothly route rotational flow down a vertical dropshaft.