###### Abstract  
In this study, curved risers stepped spillways models based on the increasing angle of suspension were tested to check for improvement in energy dissipation and pressure distributions. Four fourteen-steps stepped spillway models with a slope 1:0.84 were selected, using [PERSON]'s number non-dimensional similarity. The risers of steps were made curved, based on three angles of suspensions, i.e., 30\({}^{\circ}\), 60\({}^{\circ}\), and 90\({}^{\circ}\). The simulations were performed by FLOW 3D software and by the turbulence model Renormalization Group (RNG) for discharges between 0.020 and 0.068 m\({}^{3}\)/s followed by the model calibration. The 3D Reynolds-averaged Navier-Stokes equations were solved, which included sub-grid models for air entrainment, density evaluation, and drift-flux, to capture free-surface flow over the stepped spillway. It was estimated that curving the risers increases the energy dissipation up to three percent for lower flow rates, whereas it has no significant impact on energy dissipation for higher flow rates. It was found that in simply stepped spillway lower steps dissipate more energy as compared to curved risers stepped where energy dissipation is shifted to higher steps. On the other hand, curved risers stepped spillways showed lower values of negative pressures as compared to the simply stepped spillway. It was seen that a higher energy dissipating step as experienced more negative pressures as compared to the lower energy dissipating step. stepped spillways; flow 3D; energy dissipations; pressure profiles; cavitation +
Footnote †: journal: Medical  
found that stepped spillways provide more resistance to flow [11]. Studies on lower scale models have found that energy dissipation is more in stepped spillways, as compared to ooge smooth spillways. The authors in [12; 13] calculated the pressure profiles along the vertical and horizontal surfaces of the steps for a model stepped spillway and found that vertical surfaces of the steps are subjected to negative pressures. The authors in [14] used the k-e turbulence model to study a model stepped spillway using FLUENT software to plot pressure profiles on the horizontal and vertical surface of the steps. The authors in [15] used ADINA software to simulate the turbulence flow over the stepped spillways of various step configurations. The authors in [16] performed model experiments to check the aeration efficiency of stepped spillways, in particular the effects of varying chute angle and step height. The authors in [17] did an experimental study on stepped spillway, using Froude number similitude in large size experimental facilities, using 10 configurations, which included smooth steps and steps with devices to enhance the energy dissipation. The authors in [18] did model studies on steeply sloped spillways, with high velocity flows, to investigate cavitation damage, along with formulation of mathematical expression to calculate the location of the inception point. The authors in [19] did model studies to look for energy dissipation due to the production of turbulence due to steps. They concluded that energy dissipation during the skimming flow is at a maximum for low discharge as compared high flow rates. The authors in [9] investigated the stepped spillways with non-uniform heights and found that there was no improvement in energy dissipation instead there was more turbulence for smaller flow rates. The authors in [20] studied stepped spillway models with stones and gabions and found that energy dissipation improved as compared to horizontal steps. The authors in [21] did laboratory experiments in order to determine the cavitation potential during the flow across the stepped spillway, along with an investigation into the relationship between cavitation index and friction factors. The authors in [22] studied the impact of inclined steps and inclined steps with end sills on energy dissipation. It was found that energy dissipation considerably increased.