Prioritizing Design Parameters for Stepped Chutes and Shear Stress Distribution

Abstract

Stepped chutes offer high efficiency in decreasing flow velocity due to roughness; however, negative impacts may still be experienced by the receiving water body into downstream. These effects might be mitigated if geometric and hydraulic parameters governing the structure are well addressed. Herein, five influential parameters were developed, i.e., longitudinal slope S (S = tan θ), discharge (Q), pool height above steps (hp), chute width (W), and chute height (H), employing a three dimensional (3D) numerical model. Through 600 simulations, two regression models were developed for predicting depth-averaged velocity at the last step Vd (m/s) and critical length Lc (cm) at the downstream where the maximum velocity occurs, using response surface methodology (RSM) based on the mixed-level full factorial design. The prediction data obtained by developed regression models were agreeable with actual data with coefficient determination (R2) of about 0.95, highlighting the accuracy and ability of the models for the prediction of Vd and Lc. Additionally, the analysis of variance (ANOVA) was used to prioritize the impact of the studied parameters on Vd and Lc. Results highlighted that among geometric parameters, W and S had a significant influence on Vd and Lc; however, the impact of W was more pronounced. Using a regression model for Lc, a cross section was obtained, and the shear stress distribution of the downstream was compared with that of the last step and sidewalls. The shear stress patterns showed that the maximum value shifted from the side walls to the downstream between the lower and higher slopes. Further, the longitudinal distribution of shear stress at the downstream revealed that geometric and hydraulic characteristics played a negligible role in the changing pattern of shear stress. The results of this study reveal the dynamic behavior of the given structure where different geometric options are available for structure design.