New empirical equations to assess energy efficiency of flow-dissipating vortex dropshaft

Abstract

Vortex structures are generally considered the common energy-dissipating infrastructures in order to convey urban surface waters. During transferring wastewater in such urban networks, the major proportion of water energy is dissipated and additionally, the hydraulic performance of these infrastructures is evaluated on the basis of the dissipation of energy efficiency in the vortex dropshaft. Over the last decade, the literature review of vortex structures demonstrated that there is no reliable mathematical expression to predict energy efficiency although various experimental investigations were done to evaluate the hydraulics of vortex structures. In this research, robust numerical models based on conceptions of Artificial Intelligence (AI) methodologies (i.e., classification, non-parametric analysis, and evolutionary computing) were developed by using 144 experimental data extracted from a physical model of vortex dropshaft. Through analysis of experiments, three main factors, called flow Froude number (Fr), the ratio of sump height (Hs) to shaft diameter (D), and the ratio of drop total height (L) to shaft diameter (D) were determined to estimate the efficiency of flow energy dissipation. The numerical models were calibrated/trained by different algorithms such as multi/single-objective optimization strategies (e.g., Particle Swarm Optimization [PSO] and Multi-Objective Genetic Algorithm [MOGA]). Various statistical tests, known as quantitative assessments for training and testing stages of AI models, demonstrated that Evolutionary Polynomial Regression (EPR) had the best performance (Coefficient of Correlation [R] = 0.9736, Root Mean Square Error [RMSE] = 0.5923, and Mean Absolute Percentage Error [MAPE] = 0.5035) and followed by MT (R = 0.9665, RMSE = 0.7039, and MAPE = 0.6225), GEP (R = 0.9113, RMSE = 1.0803, and MAPE = 0.9535), and MARS (R = 0.8337, RMSE = 1.6473, and MAPE = 1.1010). Additionally, expressions given by AI models provided more accurate predictions of energy dissipation efficiency when compared with a regression-based equation (R = 0.9113, RMSE = 0.7039, MAPE = 0.6225) from the literature. Additionally, variations of three effective factors versus the predicted responses (values of energy dissipation efficiency given by AI models) were in coincidence with experimental observations. Overall, this study proved that the usability of mathematical expressions could provide new insights for experts to assess the hydraulic evaluation of vortex structures before their physical and prototype models are constructed.