Abstract

Channel expansions are common in both natural and engineered open channels. They connect a relatively narrow upstream section of channel with a large downstream section of channel. Due to increasing cross-sectional dimensions in an expansion, the flow decelerates. Under steady flow conditions flow deceleration results in an increase in water pressure and hence an adverse pressure gradient. This often triggers flow separation and turbulent eddy motion, and causes energy losses in the flow. When conservation of flow energy is required, the issue of energy losses becomes important, a consideration which has motivated this study. The focus of this study is on subcritical flow, a typical flow seen under a wide range of flow conditions. This study aims to quantify the energy losses in a lateral expansion and to further investigate how effective a hump fitted on the channel-bed of the expansion is at reducing energy losses.
This study adopted the experimental approach. Using a recirculating laboratory flume, experiments of flow in expansions with or without a hump were performed to measure flow depth, pressure, and cross-sectional mean velocities. These measurements were analysed using the energy concept for direct estimates of the energy loss coefficient. Without the hump, measured water pressures showed adverse gradient in the expansion, opposing the approaching flow. Estimates of the energy loss coefficients ranged from 0.46 to 0.62. These results would be useful for the design of channel expansions, and for calibrating and validating numerical hydrodynamics models. The presence of the hump has been shown to accelerate the flow, convert adverse to favourable pressure gradient, and lower the energy loss coefficients by more than 50% when compared with the corresponding values without the hump.
So far no satisfactory theory has been established for determining the energy loss coefficient for a given expansion. In this study, the momentum concept is combined with the energy concept in order to derive a theoretical expression for the energy loss coefficient. When applying the momentum concept to flow in an expansion, the pressure forces may be evaluated using the hydrostatic approximation, as supported by experimental evidence from this study. The theoretical expression involves extra parameters whose values are obtained based on the experimental data. It has been shown that the theoretical and experimental values for the energy loss coefficient are in good agreement. This theoretical expression can easily be extended to study channel expansions of different configurations.