Genetic Programming Approach for Estimating Energy Dissipation of Flow over Cascade Spillways
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RESEARCH PAPER
Genetic Programming Approach for Estimating Energy Dissipation of Flow over Cascade Spillways Farzin Salmasi1 · Mohammad Taghi Sattari1 · Morteza Nurcheshmeh2 Received: 30 September 2017 / Accepted: 9 November 2020 © Shiraz University 2020
Abstract In this study, the hydraulics of cascade spillways were investigated by conducting a series of laboratory experiments; twenty different cascade spillways tested in a horizontal laboratory flume. A wide range of discharge values, three weir slope angles (15, 25 and 45 degrees), and different step numbers ranged from 3 to 50 on ogee surface were considered. Some data-based models were developed to explain the relationships between hydraulic parameters. Multiple regression equations were developed based on dimensional analysis theory to compute energy dissipation over cascade spillways. For testing the robustness of developed data-based models, genetic programming (GP) was used as a new computing technique. A GP approach was developed to relate the input and output (energy dissipation) variables. It was found that formulation based on the GP approach in solving energy dissipation problems over cascade spillways is more successful than the method based on the regression equation. Keywords Cascade · Energy dissipation · Genetic programming · Spillway Symbols B Spillway width E1 Energy at the downstream of spillway before hydraulic jump E0 Total energy at the upstream of spillway ΔE Difference between energy at the upstream and at downstream of the spillway (ΔE = E0 − E1) √ Fr Supercritical Froude number = V1 ∕ gy1 g Acceleration due to gravity h Each step height Hw Total spillway height from flume bed l Each step length q Discharge per unit width Q Discharge * Farzin Salmasi [email protected] Mohammad Taghi Sattari [email protected] Morteza Nurcheshmeh [email protected] 1
Department of Water Engineering, Faculty of Agriculture, University of Tabriz, Tabriz, Iran
School of Engineering and Applied Sciences, Western Kentucky University, 1906 College Heights Blvd#21082, Bowling Green, KY 42101, USA
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S Spillway slope (V: H) Va Approach velocity = q/y V1 Velocity at the toe of the spillway y0 Depth of flow about 0.60 m distance from upstream in spillway above the spillway crest y1 Depth before hydraulic jump at the spillway toe y2 Depth after hydraulic jump
1 Introduction The design of cascade/stepped spillways has been known for at least 3500 years, but at the beginning of the 20th century, breakthroughs in the design of hydraulic jump-stilling basins led to disuse of stepped spillways (Felder and Chanson 2011). With developing several new, and more efficient construction techniques [(e.g., roller-compacted concrete (RCC)], design of stepped spillways regained interest in the 1980s (Chanson 2001). This was associated with a substantial amount of physical modeling research (Felder and Chanson 2009; Chamani and Rajaratnam 1999). Cascade spillways (Figs. 1, 2) have many applications in dam structures, river engin
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