Stepped spillways are consisting of some steps, which started from top crest of weirs to the down stream of spillways. These structures are used now because of their efficiency in dissipating energy of flow, and their benefits in economical aspects. This kind of spillways is also used in agriculture because of air entrance along them and natural purification of water. This study was carried out to find a mathematical model for estimating the relative dissipation of energy by making 10 physical models of stepped spillways in a laboratory flume. The models were built up to 31 steps, and data was collected by passing many different discharges through them. Effective parameters such as: a, N, Hdam, Yc, and (h, l) were obtained by data analysis and then some important and effective dimensionless parameters for geometric optimization of the stepped spillways were found using a dimensionless technique and analyzing the results. There was a relation between the relative dissipating energy and some dimensionless parameters like yc/h, Hdam/yc. Results showed that the best physical model for dissipating the energy was 15 step spillways. Finally, the geometric optimized formula were proposed for mentioned spillway by analyzing the obtained parameters.

Comparison of Hydraulic Behavior of Flow over Stepped Spillway and Chute SpillwayExtended AbstractBackground and Objectives Stepped spillways are convenient and economical options for high dams compared to other types of spillways because of their special abilities such as construction procedure compatibility with the Roller Compacted Concrete Dams (RCC Dam) technology, the ability of self-aeration of flow and reduction the stilling basin dimensions at the downstream dam toe due to significant energy dissipation. Depending on the discharge rate, step height and slope, three flow regimes can be identified on stepped spillways: nappe, transition, and skimming flow. Nappe flow occurs for relatively low discharge rates and lower slopes. Transition flow with a range of intermediate flow rates has a chaotic flow motion with intense splashing. Skimming flow occurs for relatively higher discharge rates and steeper slopes, is characterized by a flow over the pseudo-bottom formed by small vortices between steps. On a stepped spillway, the steps act as macro roughness elements, contributing to enhanced energy dissipation and significant aeration. In a skimming flow, the upstream flow motion is nonaerated, and the free surface appears smooth and glossy up to the inception point of free-surface aeration. In this developing flow region, a turbulent boundary layer grows until the outer edge of the boundary layer interacts with the free surface and air entrainment takes place. In recent decades, much research has been done on various flow regimes over the stepped spillway, the way they dissipate energy and the impact of the geometry of the steps on flow structure. In this research, hydraulic performance of skimming flow over Zhaveh stepped spillway has been studied and qualitative and quantitative comparison of flow between stepped and chute spillways has been presented.Methodology A 2D numerical models of spillway has prepared using FLUENT 6.3.26 software, k-e RNG turbulence model and Mixture multiphase flow method to simulate and calculate the hydraulic characteristics of the energy dissipation of spillways. The softwares to create the spillways geometry and mesh were SOLIDWORKS and GAMBIT respectively. The meshes in the tank section were quadrilateral and due to irregular geometry and the presence of stairs, meshes in the spillway and chute section were tri / pave. The boundary conditions were velocity inlet for inlet flow, free pressure inlet for free surface flow, outlet pressure for outflow and wall for floor and stairs. The numerical model has been calibrated applying experimental data extracted from the physical model of the Zhaveh spillway. It is stepped spillway with a height of 85 m and located on the Zaveh river at the junction of the Gavrood and Gheshlagh rivers at 35 km south of Sanandaj city. The spillway with a crest length of 55 m and a side slope of 1.2V:1H (50.19 degrees) located on the body of the Zhaveh dam. Findings The results indicated in addition to agreement between laboratory and numerical data, having steps alongside the chute spillway can reduce significantly the length of the boundary layer which is developed from the spillway crest and encountered with the flow surface from where the flow air entrainment is initiated. So the inception point related to air entrainment is located further upstream. Analysing the flow pattern indicated that due to aeration after the inception point, the flow depth and velocity in stepped spillway increases and decreases respectively compared to a chute spillway. Flow aeration causes the cavitation index to become much higher than the critical value (0.2) in the entire stepped spillway thus the risk of cavitation occurrence and the relevant damages are reduced considerably. While it was observed that the possibility of cavitation occurrence was high on the chute spillway (without steps) starting from 56 m downstream of the spillway crest. As a result, cavitation erosion was more likely expected on the chute spillway surface. Also for design discharge, the flow energy was effectively dissipated alongside the stepped spillway in comparison to chute spillway with a discrepancy of 46%.Conclusion The application of the stepped spillway would be more appropriate and economical than the chute spillway due to the various advantages mentioned above and also there is no risk of cavitation on the Zaveh stepped spillway, while in the end of the chute spillway Corresponding to it, we may encounter cavitation erosion.

Stepped gabion spillways have many applications in dam structure, river engineering and soil conservation works. These types of weirs have more flexibility in respect to rigid (impervious) type and are more stable against water pressure. Energy dissipation through this weir is high due to over flow and inflow from steps, so the cost of stilling basin construction can be reduced. Flowing water through the body of weir is one of its important characteristics that make flow condition more complex. Most of the researches until now were on rigid stepped weir in large dams and there are a few studies on gabion stepped spillways. The purpose of this study is to investigate flow over and through the gabion stepped spillway body and determine energy dissipation rate. For this purpose 8 physical gabion stepped spillways with 3 different porosities 38 to 42 percent and two slopes 1:1 & 1:2 (V:H) were made and iron plate on each horizontal or vertical step was used to study the effect of step pervious on energy dissipation. Results show that at higher discharge, energy dissipation is more in pervious (gabion) spillway. In fact at higher discharge or skimming flow regime, energy dissipation divided in to over flow and inflow through the spillway body. In this situation energy dissipation through the spillway body have more effect on total energy dissipation. Thus in skimming flow regime, gabion stepped spillway will have greaterenergy dissipation. At lower discharge, energy dissipation is more in impervious stepped spillway. In this condition other rank belongs to gabion, step with vertical plate and step with horizontal plate respectively. Gabion with higher porosity had bigger energy dissipation and with increasing in discharge, their differences tend to zero. Slope decreasing from 1:1 to 1:2 causes more energy dissipation.

Stepped ogee spillways are one of the most widely used types of dams that are used in most dam construction projects, including small and large dams. The inception point of aeration on these spillways is an important place in determining the range of single-phase and two-phase flow, which characterize the areas at risk of cavitation. In this paper, the effect of roughness on the location of the inception point of flow aeration (IPFA) on the stepped Ogee spillways was investigated. For this purpose, the surface of the steps of a laboratory model was covered with gravel with specific granulation. The result indicated that by roughing the surface of steps, the displacement of IPFA moves towards the crest (upstream) and the length of non-aerated area on the stepped spillways is decreased by about 15 percent. The results declared that there is a direct exponentially relation between flow rate and displacement IPFA. At low flow rates, most of the flow turbulence is due to the roughness created by the geometry of the steps, hence the role of surface roughness is negligible, while with increasing flow rate, its role in increasing the flow turbulence increases, and its effect on displacement of IPFA becomes obvious. At a given flow, the length of the non-aerated is decreased with increasing roughness.In this study, the effect of surface roughness of steps on the displacement of IFPA was investigated experimentally. To this end number of laboratory experiments were programmed. To investigate the objective of this study, a stepped ogee spillway in which its horizontal part of steps was covered by gravel with given grain size. The results declared that three factors including the flow rate, the roughness caused by steps dimension (ks), and the roughness of steps surface (ns) are effective in the displacement of IPFA. In this study, the change in the size of the steps and the longitudinal slope of the stepped chute on the displacement of IPFA has not been investigated because it has already been studied by other researchers. There is a direct exponential relationship between the discharge and the IPFA (length of the non-aerated area on the stepped ogee spillway). As the flow rate increases, the location of this point is transferred downstream exponentially. With the increase of flow, the role of roughness in IPFA displacement became clearer and the reason is the increase of its role in creating and increasing flow turbulence. On average, surface roughness can be about 15% effective in reducing the displacement of IPFA.

In this study, experimental procedure and laboratory works have been conducted to investigate the energy loss rate on stepped spillway, using inclined steps together with end sill. To have a more elucidated investigation inclined steps with different slopes (Horizontal, 7, 10, and 12 degrees with respect to the horizon) and end sill with different thicknesses (5 and 10 mm) and heights (6, 8, 10, and 15 mm) were used to determine the impact of these parameters on the relative energy loss. Results show that using inclined steps together with end sill has a considerable effect on the energy loss of both nappe (30 liter/sec) and skimming (90 liter/sec) flows; however, energy dissipation in nappe flows is greater than that in skimming flows. Energy loss resulted from end sills with smaller thicknesses is higher than that of end sills with greater thicknesses. Comparison of the results of the current survey with similar studies reveals that the approach used in the current investigation is more efficient than previous ones.

Scour holes formed downstream from a stepped spillway may affect the safety and stability of a structure. The development of such scour hole can cause failure of the structure by undermining the riverbed, thus it is important to develop criteria that result in understanding how such a scour hole can develop. The literature contains many studies dealing with energy dissipation, aeration and oxygen transfer in stepped spillways. However, their downstream scour hole depth and geometry is not well documented. In this study, a physical model is employed to study the impact of offtake channel base angle of stepped spillways on the scour hole. The area of the longitudinal profile of the scour hole is used to evaluate the amount of scour at downstream from the stepped spillways. Experimental results showed that the takeoff angle of 30o is the optimum angle which gives minimum longitudinal area and maximum depth of the scour hole.

Using stepped spillway due to its low cost and high efficiency is increasingly on the rise. Hence, the studies in this area are associated with the growth and attention from dam engineers but most of these studies were including stepped spillway with uniform step height while the non-uniform step heights can also be considered as an option in some cases. In this study, a physical model of Herat dam for stepped spillway with 1.3 m height and a slope of 19.2o were used for the verification of numerical models then, three types of stepped configurations using computational fluid dynamics in ANSYS CFX software for range of 1.54#dc/h # 16.15 tested. Two-phase flow simulation for each configuration and all of the discharge took place and results in the case of flow pattern, energy dissipation and aeration point were compared. The results showed minimum difference in energy dissipation for nappe regime flow and maximum difference for skimming regime flow.

A stepped spillway consists of steps that start from near the crown and continue to downstream heel. Generally, the amount of energy dissipation in stepped spillway is more than the one of flat spillways (with no steps) with the same dimensions. The high amount of energy dissipation caused by steps allows reducing the depth of drilling of downstream stilling basin, length of stilling basin, and the height of sidewalls. This way, a considerable economic saving is achieved in the implementation of dams. Since spillways help reduce flow rate and increase intake airflow rate, they can be referred to as a combination of a spillway and an energy dissipater. Some of the studies on stepped spillways are as follows: Launder and Spalding (1972); Olsen and Kjellesvig (1998); Chen et al. (2002); Tabbara et al. (2005); Dermawan et al. (2010); Sori and Mojtahedi. 2015; Haji azizi et al. (2016) So far, the studies on stepped spillways have been mostly on experimental and physical models. However, experimental and physical models are costly and sometimes have limitations such as required space and a large number of tests. This necessities consideration of further mathematical and numerical models. Several numerical models can be introduced to analyze flow on a stepped spillway. CFX is one of the numerical models. CFX has been known as one of the most robust software for fluid flow analysis and heat transfer. The finite volume method (FVM) is a numerical method to solve the governing differential equations, which is capable of simulating complexities of a turbulent flow on a spillway appropriately. On the other hand, CFX numerical model uses the coupled model, which increases the speed to achieve results considerably as compared to other numerical models. This research aims at simulating a stepped spillway using CFX numerical model and assessing the amount of energy dissipation under geometric parameters (such as spillway height, spillway gradient, number of steps, and height of steps) and hydraulic parameters (such as flow rate). The difference between this research and other studies can be attributed to the coherence and correlation in studying various components (geometric and hydraulic parameters) and the ability of CFX numerical number in replacing some of the costly and time-consuming tests.

In this paper, the issue of energy losses in Gabion Stepped Spillway and the effect of grain size on stone materials on it have been investigated. Laboratory models of the L r= 1/5 scale overflows for steps 2 and 3 were 40 and 60 cm high, respectively. The stone materials were prepared as round stones from borrowed sources based on the scale model with dimensions of 4, 6 and 8 cm, equivalent to the normal size of the stones used in gabion structures. The models were installed in a 50 cm wide hydraulic flow with a discharge capacity of up to 65 liters per second. The results show that energy losses in rocks with a diameter of 4 cm are higher than in other cases. Also, by increasing the number of steps from 2 to 3 steps in Gabion Weirs, the efficiency of Energy losses increases. In all cases, the efficiency of energy losses in these overflows decreases with increasing flow rate. Construction of gabion stairwells up to 3 steps will increase the efficiency of energy losses in the laboratory environment and consequently in nature.