Hydraulic investigation of finite crested stepped spillways

In this paper, the hydraulic properties of the finite-crested stepped spillway (FCSS) including discharge coefficient (Cd) and the ratio of energy dissipation (EDR) were experimentally investigated. Results indicated that the Cd of the FCSS changes between 0.9 and 1.2, while the ratio of the upstream head to the length of the crest (hup=Lc) changes between 0.25 and 1.8. The hup=Lc is the main parameter affecting the Cd. The value hup=Lc equal to 0.6 is a good criterion for designing the crest of the FCSS. At this point, the Cd of FCSS is about 1.0. The performance of FCSS regarding the EDR changes between 95 and 40 percent. By increasing the discharge of flow and skimming flow formation, the performance of the FCSS related to energy dissipation is dramatically decreased.


INTRODUCTION
Water resources management, especially flood control, is one of the most important actions for the development of human societies. River engineering projects and dam construction projects are among these measures (Patel et al. ; Mehta & Yadav ). Spillways are one of the most costly and important components of the flood evacuation systems of dams. A spillway usually consists of guide walls, approach channel, crest, chute, and an energy dissipator placed at the toe of the chute. The proper performance of the spillway depends on the optimal design of all its components. For example, the proper design of the guide walls could remove cross waves and helps the smooth transfer of flow from the dam's reservoir to the approach channel (Parsaie et al. ). The crest is the main part of the spillway in determining its discharge capacity (Parsaie ). As the flow passes over the crest and flows into the chute, its velocity increases rapidly, which in turn leads to a decrease in pressure. As a result, the potential for occurrences of cavitation is increased significantly (Parsaie et al. ). On the other hand, the high kinetic energy of the flow may cause scouring downstream of chutes (Rajaratnam & Chamani ; Chamani & Rajaratnam ; Rashki Ghaleh Nou et al. , ). The best approach to remove the cavitation is aeration and the reduction of flow velocity. One of the best ideas to reduce or eliminate the cavitation is to step up the chute. Besides, in some cases, it has been observed that steps have been used as aerated structures that eliminate cavitation with more confidence (Pfister et al. ; Pfister & Hager ).
A typically stepped spillway is made of a flat crest and a stepped chute (Roushangar et al. ). The use of this structure, due to its hydraulic properties, has been welcomed by many hydraulic engineers. Investigators have divided the flow regime on stepped spillways into three classes as nappe, transition, and skimming flow. Reviewing the literature shows that most researches have focused on the mechanism of energy dissipation.
Recently finite-crested weirs have been investigated by few numbers of investigators. The finite-crest weirs are categorized as the short crested weirs that their crest length is more than the sharp-crest weir and is less than the broadcrest weirs. Based on the reports, the C d of finite-crest weirs is more than the broad and sharp-crested weirs In other words, in this study, the finite-crested stepped spillways are proposed and their hydraulic properties including the C d and its ability in energy dissipation is investigated.

Dimensional analysis
The sketch of FCSS is shown in Figure 1 (1) As presented in Equation (2), the C d is proportional to the velocity of approached flow (V), water density (ρ), acceleration due to gravity (g), dynamic viscosity (μ), surface tension (σ), P, L c , and h up . Using the Buckingham П theorem as the dimensional analysis technique, the involved dimensionless parameters in C d are derived and given in Equation (3). Notably, the ρ, V, and h up are considered as repetitive parameters.
where F r , W e and R e are the Froude, Weber, and Reynolds numbers, h up =L c is the ratio of the head of the flow over the crest (at enough distance from the crest) to the length of the crest named the relative upstream head, and P=h up is the ratio of the height of FCSS to the flow head over the crest. For evaluation of the performance of FCSS in terms of energy dissipation of flow, the Bernoulli equation is applied at its upstream (Equation (4)) and downstream (Equation (5)). To determine the performance of the FCSS concerning energy dissipation, it is enough to minus the H dwn from the H up (Equation (6)).
where EDR is the energy dissipation ratio. The factors involved in the energy dissipation of the flow passing through the FCSS are seen in Equation (7). Using the Buckingham Π theorem, the dimensionless parameters affecting the energy dissipation of flow on the FCSS are derived as Equation (8).  Table 1.

RESULTS AND DISCUSSION
In this section, the results obtained in this study are pre-   The examination of Figure 3 shows