عنوان مقاله [English]
نویسندگان [English]چکیده [English]
Hydraulic jump is one of the most important phenomena in rapid varied flow which occurs in free surface flow by transforming from supercritical into sub critical flow and causes the depth to be increased in a small distance of flow. Changes in the geometrical parameters of the bed including roughness, the slope of the floor, as well as shape change and their effects on the characteristics of hydraulic jump have always drawn the attention of the researchers.
In the present study, the characteristics of the hydraulic jump formed in contractions and expansions with straight and curved walls were investigated for five Froude numbers of 5.8-9.1. In order to create supercritical flow in the contractions, in all experiments, the opening value of the sliding gate was 2 cm and the width of the upper and lower canals were 80 and 40 cm, respectively, (the convergence ratio equals 0.5). Also, in the experiments concerned with expansions, the opening of the sliding gate was 3 cm and the width of the upper and lower canals equaled to 40 and 80 cm (the divergence ration equals 0.5). An audio flume meter model UFM610P was used to measure the discharge flow of the flume. The accuracy of the flow meter was ±0.02 liters per second and its sensors were installed on the hydration pipe of the flume. Also, a bathometer with the accuracy of ±0.1 was utilized to measure the height of the waves’ surface. In addition, a horizon surface, two-dimensional electromagnetic speedometer with the accuracy of ±0.5 was employed to measure the wave velocity of the different parts of the wave.
The velocity profiles showed that, in all sections, the velocity increased as it got away from the floor and after reaching to its maximum, its value decreased. In fact, the occurrence of hydraulic jump causes intense blending of air and water and formation of eddy currents near the water surface. As a result, the energy of the flow decreases and its velocity value reduces, too. Besides, it was observed that by getting distance from the origin of the jump, the boundary layer extends while the maximum values reduce. On the other hand, negative velocity values were observed in the velocity profiles of contractions near the water surface. This phenomenon is a sign of the overcome of the return flows to the main flow of the canal (near the water surface). Indeed, the entrance of the hydraulic jump to the tightening section caused an increase in the intensity of water and air blending and occurrence of the return flow phenomenon. This situation was observed more with the increase of the Froude number. Furthermore, the velocity value in contraction was higher than its counterpart in expansion for a fixed Froude number in the vertical direction. Also, the results showed that the secondary depth and jump length in contractions were more than expansions for the fixed Froude number while the formed hydraulic jump in contractions had less energy dissipation than expansions. In fact, widening of section intensifies flow energy loss in expansions. However, in contractions, the gradual decrease of the width of the section prevents complete flow energy dissipation. For this reason, energy dissipation or flow from supercritical to subcritical takes longer time and consequently the length of hydraulic jump and the depth of secondary jump increase. On the other hand, the results indicated that the amount of tension faced a sudden drop and reached to a negative value after getting to its maximum value. Considering that Reynolds tensions have a direct relationship with fluctuations of point velocity, the sudden drop of the tension value can be due to the intense blending of air and water in jump surface and after that the reduction of range of fluctuations of point velocity. Therefore, a higher negative value was observed in contractions compared to expansions because of more intense water and air blending. It needs to be noted that the contraction with straight wall had higher negative value. Besides, in both types of the conversions, the highest negative value of the tension was observed in the middle section. Also, in contractions, by getting distance from the origin of the jump, the maximum values of Reynolds tension increase. In fact, the progress of the jump in tightening section increases the fluctuations of point velocity and through this increases the intensity of the tension. However, in expansions, the opposite case happened. On the other hand, by comparing the vertical distributions of velocity and tension in both conversions, it can be found that the site of the occurrence of maximum velocity in different sections of the jump relatively matches the site of the occurrence of the maximum intensity. The values of energy dissipation in the expansions with straight and curved walls were averagely obtained 24.95% and 21.23%, relatively. For the contractions, they were averagely obtained 15.93% and 12.49%. Also, the result showed Reynolds tensions increased in the contraction and decreased in the expansion by increasing the longitudinal distance from the origin of the jump.