Estimation of Discharge Coefficients for Free-Flowing Compound Weirs with Upstream Horizontal Flow Contraction

Abstract

Compound weirs have been used as adjustable structures to divert flow, for example, through river branches at the river bifurcations. For this purpose, a wide variety of weir configurations can be used including asymmetric configurations that have not been studied in the literature yet. A proper one-dimensional representation of flow over these structures is needed as the effect they have on the river are generally added as subgrid energy losses to the river hydrodynamic models. In this study, an experimental study was conducted to estimate the correct representation of compound weirs at varying weir configurations and flow conditions. In the experimental campaign, eight weir configurations were used with six discharge values. Upstream flow depths at each case were recorded and their relationship with the flow rate and weir configuration was analyzed. A 1D model was proposed to estimate flow rates when the upstream flow depths are known. The proposed correction to the well-known Kindsvater and Carter approach was applied to modify the discharge coefficient when nonuniform geometries are used that cause horizontal flow contraction. To estimate and validate the proposed correction, additional numerical simulations using computational fluid dynamics (CFD) were conducted to estimate the detailed flow field upstream of the nonuniform weirs. Surface particle image velocimetry (SPIV) measurements were also conducted to validate the CFD model. The corrected 1D model predicted the flow rates at 48 cases covering uniform to highly nonuniform weir geometries with a maximum of 9.7% and a mean of 2.45% deviation from the measurements. Additional tests on the performance of the proposed model validated its effectiveness in various nonuniform geometries at low flows. However, when substantial changes are made to the geometry, such as the removal of buttresses, the model may require calibration to maintain its accuracy.