Study of Surges in a Large-diameter Subteranean Diversion Channel with Multiple Surge Tanks

Abstract

Complicated surges in a large-diameter subteranean diversion channel with six surge tanks and a pumping station are studied with a nonlinear state equation based on a rigid water column theory.
The state equation consists of flow continuity equations for the tanks and momentum equations for large-diameter pipes with nonlinear resistance.
Under rectangular pulse inputs conditions where the pumped rate of outflow is equated to the total rate of inflow, the state equation and its linearized equation both yield almost identical oscillations of water levels. This shows that effects of pipe resistance on the surges are small, and justifies a free oscillation analysis.
Free oscillation equation has six eigen modes of different periods, including a rigid mode which is excited when the pumped rate of outflow differs from the total rate of inflow. The six modes constitute a variety of surges dependent on different inflow and outflow conditions.
Presence of the rigid mode needs sophisticated pump operations adjusted to real flood inflows.