Developed Three-dimensional model for extract stage-discharge relationship in straight multi-stage compound channels
ABSTRACT
Introduction
In natural rivers and certain urban channels, when flood events occur, the flow diverts from the main channel and inundates the surrounding floodplains. These particular configurations are termed compound channels. Floodplains can exhibit both symmetrical and asymmetrical patterns. Depending on geometric factors, lateral slope, and differences in elevation, multiple floodplains can manifest on each side of the main channel. These intricate structures are known as multi-stage compound channels. Multi-stage compound channels not only possess enhanced flow conveyance capabilities compared to simpler classic compound channels but also their second or third floodplains may offer prospects for recreational utilization or landscape enhancement within urban settings. Historically, the examination of flow parameters and the computation of conveyance capacities for compound sections were carried out using conventional methodologies, such as divided channel methods and traditional flow resistance equations like Manning, Chezy, Darcy-Weisbach, and others. However, these approaches often disregarded the momentum exchange arising from interactions between the main channel and floodplains, as well as the impact of secondary flows. Consequently, the estimated flow rates for compound sections tended to be higher than actual values. Sellin (1964) played a pioneering role in acknowledging the interaction between the main channel and floodplains, laying the groundwork for subsequent investigations into the evolution of conventional techniques. In contrast to the extensive research on classic compound channels, multi-stage compound channels have received limited attention and exploration in the scientific literature.
Methodology
In this research, a numerical solution of the Navier-Stokes equations using the finite volume method and The RNG k-ε turbulence model has been employed to simulate various hydraulic characteristics of multi-stage compound channels. These characteristics encompass the three-dimensional flow pattern, distribution of transverse velocity, secondary flows, turbulence energy, and the stage-discharge relationship. The RNG k-ε turbulence model is adept at reproducing rotational flows and large vortices, addressing the limitations of the standard k-ε model in representing non-circular channels at corner locations and rotational flows.
To verify the validity of this mathematical model, laboratory data obtained from a channel with a three-stage asymmetric rectangular compound section (Singh, 2021) were utilized. The experimentation carried out in a channel featuring a main section width of 0.445 meters. On one side of the main section, two floodplains of widths 10 and 20 centimeters were established. The bed of the main channel was constructed using glass, while the bed of the first and second floodplains were covered with a uniform layer of syntetic grass to introduce channel roughness.The channel itself is 20 meters in length, with a longitudinal slope of 0.003. The total height and width of the channel are 0.5 and 0.745 meters, respectively. The bankful height is set at 0.0425 meters. The flow rate within this channel varies between 20 and 60 liters per second.
Results and discussion
Overall, the comparison of the three-dimensional model's computational results with experimental data in terms of the positions and values of maximum and minimum velocities indicates the satisfactory accuracy of the proposed mathematical model in this study.
The turbulence intensity and momentum exchange at the interface between the first and second floodplains are lower compared to the interface between the main channel and the first floodplain. This discrepancy is attributed to the greater velocity difference at the interface plane of the main channel and the first floodplain. The influence of secondary currents at the main channel and first floodplain interface diminishes as the water level rises. However, significant secondary currents persist at the boundary between the first and second floodplains across all investigated relative depths. This underscores the significance of flow dispersion in contrast to convection in the second floodplain, particularly in cases of shallow relative depths.The highest flow velocity is observed at the midpoint of the main channel, inclined toward its right wall, situated far from the channel bed and close to the water surface. The computed transverse profiles of stream-wise velocity are satisfactorily accurate in both the main channel and floodplains (especially the second floodplain). Nevertheless, the modeling error is relatively notable at the interface of the main channel and the first floodplain. Predicting flow discharge for this channel using the mathematical model yields an average error of approximately 3.9% and a maximum error of 6.2%.
Conclusion
Due to the lack of experimental data on height and width variations of the second floodplain and their impact on flow characteristics, expressing the effects of these conditions is challenging. Further research involving precise laboratory measurements is required to comprehensively understand the influence of these changes.
Considering that one of the applications of multi-stage compound channel is in urban areas and the first floodplain has a smaller width and is designed with the aim of increasing the channel conveyance capacity, and the second floodplain is intended to beautify the urban landscape and use it as a recreational and tourism environment. Therefore, it usually has tree vegetation. In addition to creating high shear stresses in the bed of the second floodplain, this causes high energy loss and a significant decrease in the conveyance capacity of the multi-stage compound channel. Therefore, it is recommended to design rivers or manmade flood control channels in the urban areas in the form of multi-stage compound channels so that the first floodplain is to be significantly increase the conveyance capacity of the channel and the second floodplain is for urban and public landscapes. This provides nearby people to escape from the danger zone during severe urban floods.
Key words: finite volume method,quick method, RNG K-ε, multi-stage compound channel, stage-discharge relationship