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Ski jump and plunge pool
Published in Willi H. Hager, Anton J. Schleiss, Robert M. Boes, Michael Pfister, Hydraulic Engineering of Dams, 2020
Willi H. Hager, Anton J. Schleiss, Robert M. Boes, Michael Pfister
Terminal jet deflectors are essentially a generalized form of ski jumps, with the particularity of transverse jet deflection in addition to the streamwise take-off into the atmosphere. These poorly studied structures are often employed as terminal elements of bottom outlets (Chapter 8), including a jet deflection of some 45° to realign the flow to the tailwater. A particular problem relies on flow choking, given that the high-speed flow may break down if the deflector geometry is too abrupt, so that a hydraulic jump may develop at the takeoff location, resulting in a hydraulic drop rather than in a trajectory jet. As for the ski jump, the scour hole is then too close to the dam structure, undermining its foundation by the drop flow. Two main jet deflectors are presented below, one for small and the other for higher supercritical approach flows.
Open Channel Flow
Published in Ahlam I. Shalaby, Fluid Mechanics for Civil and Environmental Engineers, 2018
9.14C Applications of the governing equations for real open channel flow include the analysis and design of uniform (see Section 9.14; also see Example Problems 5.2, 5.11, and 5.12) and nonuniform (see Section 9.15) flow (generated by controls such as a break in channel slope, a hydraulic drop, or a free overfall). Furthermore, in the analysis and design of an open channel flow system, there may be channel friction (resistance) or controls (break in channel slope, hydraulic drop, or free overfall) in the open channel flow that will determine the significance of a major head loss and a nonuniform surface water profile. Explain the application of the governing equations (integral vs. differential) for the case of a straight channel section without flow-measuring devices.
Open Channel Flow
Published in Herman Depeweg, Krishna P. Paudel, Néstor Méndez V, Sediment Transport in Irrigation Canals, 2014
Herman Depeweg, Krishna P. Paudel, Néstor Méndez V
A rapidly varied flow is also known as a local phenomenon; examples are the hydraulic jump and the hydraulic drop. Spatially constant flow occurs when the average velocity is the same in all points; when the velocity changes along or across the flow, the flow is spatially variable. A clear example of a spatially varied flow is the flow through a gradual contraction or in a canal with a constant slope receiving inflow over the full length. Spatially varied flow shows some inflow and/or outflow along the reach under consideration; the continuity equation should be adapted to this situation. Examples are side channel spillways, main drainage canals and quaternary canals in irrigation systems. Figure 2.4 gives some typical locations in canals and rivers where gradually and rapidly varied flow might occur.
A well-balanced and positivity-preserving SPH method for shallow water flows in open channels
Published in Journal of Hydraulic Research, 2021
Kao-Hua Chang, Tsang-Jung Chang, Marcelo H. Garcia
A prismatic rectangular channel flow simulation, which involves a hydraulic jump and a hydraulic drop, as conducted by Zhou and Stansby (1999), was adopted to address the ability of the proposed 2D model in the third case. The 30.5-m long and 1.4-m wide rectangular channel, which consists of two reaches, was designed. The length of the first reach with a flat slope is 14.5 m, while the length of the second reach with a steep slope of 0.03 is 16 m. To perform the simulation, 18,872 fluid particles at the initial time, a time step of 0.005 s, and a Manning roughness coefficient of 0.019 were established to perform the simulation. The inflow water velocities and surface level are given at u = 3.57 m s−1, v = 0 m s−1 and zs = 0.54 m due to supercritical inflow, while no outflow boundary conditions are prescribed because of critical outflow. Figure 5 shows the simulated distribution of water depth in the domain and the profile of water-surface level along the central longitudinal line. A hydraulic jump occurs near x = 5 m and changes to a hydraulic drop near x = 7.5 m, and the flow remains uniform to the outflow boundary. A comparison of the proposed 2D SPHSW and 2D FVSW proposed by Zhou and Stansby (1999) is shown in Fig. 5b. A consistent profile of the water-surface level illustrates that the proposed 2D model can capture complex open channel flows with hydraulic jump and hydraulic drop.
Analysis of the water surface profiles of spatially varied flow with increasing discharge using the method of singular points
Published in Journal of Hydraulic Research, 2021
In Test 3 (Fig. 11c), lateral inflow involves only the central portion of the laboratory flume (3.10 m ≤ x ≤ 5.38 m), and line ψ(h, x) = 0 is then discontinuous at the upstream and downstream ends of this stretch. Moreover, lateral inflow intensity is higher than in the previous tests (qin ≅ 12.184 · 10−3 m2 s−1). A supercritical flow in a steep channel ensues freely from the opening of the sluice gate with a characteristic S3-profile (a contraction coefficient equal to 0.61 is considered at the vena contracta for the computation of the profile). The supercritical flow (with increasing discharge) that enters in the central portion of the channel (affected by lateral inflow) is not able to occupy the entire inflow stretch up to the downstream end (x = 5.38 m). In addition, no singular points occur in this channel stretch since lines ψ(h, x) = 0 and ϕ(h, x) = 0 (and the transitional profile) do not intersect. Therefore, a control section takes place at x = 5.38 m, where the critical state occurs since the downstream channel is steep. This implies that the influences of two controls (namely, the gate at x = 1.9 m, which produces a supercritical flow downstream, and the hydraulic drop at x = 5.38 m, which produces a subcritical flow upstream) cause the formation of a hydraulic jump. This jump is located at x = 3.504 m and is characterized by a height of approximately 0.067 m. The flow remains supercritical downstream of the critical section, despite the change in bottom slope at x = 6.15 m, and the flow profile is again composed by the sequence of a S2-profile and a M3-profile. The comparison between the computed longitudinal profile and the experimental data shows that the predicted hydraulic jump is located slightly upstream of the observed one; moreover, the water surface elevation along the S2-profile (which takes place in 5.38 m ≤ x ≤ 6.15 m) is underestimated by the 1D numerical model (Fig. 11c).