Effect of the Floating Sphere Objects Flexible Bearing Length on the Characteristic of the Hydraulic Jump

Abstract
Background and Objectives: The hydraulic jump is one of the applicable phenomenons in energy dissipation of rapid flows. The hydraulic jump is one of the rapid varied flows that with converting from the super-critical state of flow to the sub-critical state in a short distance results in sensible energy dissipation and increase of the flow depth. In this experimental study the hydraulic jump is formed on the smooth bed and the bed with attached floating objects. A set of sphere objects with a density lower than the density of the water were attached to the bed, where the bearing length had flexibility. The goal of this study is to investigate the sphere objects bearing length effect on the hydraulic jump length, the relative secondary depth, and relative energy dissipation of hydraulic jump and finally comparing the obtained results with other related work.
Material and Methods: The experiments were performed in a flume with transparent walls, 8 m length, 35 cm width and 40 cm heights. In order to form the hydraulic jump, the height of the walls were extended up to 80 cm in the beginning part of the flume and a shut with 30 degree angle and the height of 40 cm was set up. Then, for modeling the floating objects the size of the applicable diameter of the objects was set to 4 cm. To analyze the effective variables, the dimensional analysis using the Buckingham л-theorem was applied. In total 30 experiments were performed with bearing length and Froude number as variables, where 0 cm, 1.5 cm, 2.5 cm, 3.5 cm, and 4.5 cm were considered as the values of bearing length and 5.1-8.3 was considered as the value interval for the Froude number.
Results: Based on the performed analysis, one of the main achieved results is that the flexibility and the oscillation in the applicable objects as the fixator of the jump results in the increase of energy dissipation while increasing the bearing length, results in the more energy dissipation. However, this effect is more significant for the Froude number between 5.1 - 7.5.
Conclusion: The obtained results show that the energy dissipation using the floating objects in average is around 69% that is approximately 10.2% greater than smooth bed. Additionally, other characteristics of the hydraulic jump were a part of the obtained results based on which, the length of the hydraulic jump and the relative secondary depth, respectively, in average are 35.5% and 19.3% lower than the classic stilling basin. It was observed that the bearing length has a significant effect on characteristics of the hydraulic jump, where as a result of changing the bearing length between the Froude number interval, 5.1-8.3, the jump length and relative secondary depth, respectively, decrease in maximum 19.1% and 15.2% compared to the bearing length of zero that does not have oscillation and in maximum the amount of energy dissipation difference is 10.6% greater than the bearing length of zero.