Investigation of bed shear force and boundary layer thickness in the abrupt expanding stilling basin with negative step

Hydraulic jump is a phenomenon that occurs due to the change of current from supercritical to subcritical. In water-depleting buildings, or relaxation ponds, methods are usually used to control the jump in the ponds, which can be used to stabilize, control, and reduce the length and depth of the secondary hydraulic jump. In a stilling basin, different main variables such as floor geometry (including initial and final steps, etc.), plan geometry (including gradual or sudden divergence), bed roughness (to increase shear force) and change in flow rate (by adding It is localized or extracted from water) causes a change in the dimensions of the hydraulic jump or a reduction in the destructive energy of the initial flow.

The experiments were conducted in a flume with Plexiglas bed and walls, which was 8.0 m in length, 0.40 m in width, and 0.60 m in depth. It was connected to a hydraulic circuit allowing for recirculation of discharge. The discharge in the flume was obtained from an overhead tank. The discharge was measured by a calibrated magnetic flow meter located in the supply line with ±5% accuracy. Water entered the flume under a vertical sluice gate, 1.2 m deep. The supercritical depth was controlled by the upstream sluice gate, while the tailwater depth was controlled by the downstream sluice gate. The point gauge with an accuracy of 1 mm was used for the measurement of the depth of water at various locations in the flume. In each experiment, the flow velocity was measured by using a pitot tube in several sections of the jump length. In this study, the expansion ratio is considered in the range of 0≤B≤2, and the height of steps are 0≤B≤6. In total, 108 experiments have been conducted in the range of Froude numbers of 4.9 to 9.5 and discharge 30 to 50 (L⁄s).

In this study, the velocity profiles were measured in the jumps on abrupt expanding channel with a negative step. The velocity profile variations are similar to that of a wall jet, so the boundary layer growth and the maximum velocity, um, decrease with increasing longitudinal distance (x) from the beginning of the jump. To investigate the similarity of these velocity profiles, the length scale (b); the value of y at which (u=0.5u_m ) and ∂u⁄(∂y<0) was determined. Results shows the dimensionless velocity profiles for all expanding data and the negative step in experiments in which velocity profiles are measured. The maximum velocities in the sudden divergent channel and the eternal negative bed step occur at higher points than in the classical wall nozzle.In addition, the results shows the shear force coefficient ε increasing with the Froude number. The shear force coefficient for hydraulic jump in a abrupt expanding channel is 14 times that of hydraulic jump in a rectangular channel, While the negative step reduces the shear force coefficient, which has not been mentioned in any research. As can be seen from the results, the shear force coefficient, in addition to the landing number, also depends on the parameters of divergence ratio, relative step height and conjugate depth ratio.

In the present study, the velocity and shear force profiles in the hydraulic jump in an abrupt expanding channel with a negative step were investigated. In general, the shear stress coefficient of the bed increases with increasing Froude number. The values of shear force coefficient are presented using laboratory data as a function of landing number, divergence ratio and relative height of the step. The shear stress coefficient of the bed in an abrupt expanding channel with a negative step is 14 times that of the classical case. The velocity profiles at different stages of the hydraulic jump in an abrupt expanding channel with a negative step are similar to the classical mode. However, the maximum velocity in these experiments is higher than that of the classic wall jet, and the thickness of the boundary layer is greater when jumping in a sudden divergent channel with a negative step. The value of the dimensionless border layer (δ/b) in the present study was equal to 0.57, which is higher than the corresponding value in the classical case (0.16).