STUDY OF FLOW CHARACTERISTICS AND ENERGY DISSIPATION ON CASCADE OF STEPS

Abstract

Analysing flow behavior and predicting energy loss is a vital part of designing the cascade of steps for various applications. As far as the practical application of a cascade of steps is concerned, it is used as an auxiliary spillway, rainwater drainage system, waterways to drain out excess water, etc. The flowing water has high potential energy, which is converted into kinetic energy throughout its entire length, therefore, the rate of energy dissipation is higher. Thus, the present study is focused on finding different flow behaviors and aerated flow parameters using experimental, numerical, and soft computing methods. Various combinations of channel geometry such as slopes (26.6o, 23.12o) and widths (0.52m, 0.28m, 0.23m) have been added to predict energy dissipation and other flow properties. It includes the experimental study of six models with different configurations from Model 1 to Model 6. An experimental flow has been conducted for two flow regimes, such as nappe flow and lower limit of transition flow with 0.201≤yc/h≤0.685 (8.93×10-3 m2/s ≤qw≤56.15×10-3 m2/s) and skimming flow from 0.910≤yc/h≤1.28 (86.08×10-3 m2/s ≤qw≤143.43×10-3 m2/s) with the Froude’s number of steps varying from 1.536≤Fs ≤ 2.616. A numerical investigation of four distinct configurations was also investigated using the k-ε turbulent model to incorporate more variables that could not be captured in the experimental research. Further, a total 450 number of experimental datasets were collected from the literature from the skimming flow regime and 63 from the nappe flow regime. Without applying any physics or statistics for data-driven modeling, five clusters as per the physics of flow behavior are considered as PBC-1, PBC-2, PBC-3, PBC-4, and PBC-5. To predict energy dissipation under nappe flow, a rational model is proposed in the present study. The model utilizes a sequence of momentum equations to predict flow conditions on a control volume basis. To validate the model, a series of experiments were conducted on the cascade of steps under nappe flow regime (0.201≤yc/h≤0.466) for two different slopes 26.6o, and 23.12o. According to the literature, these slopes have been selected close to the stated optimum slope of 21.8o. The proposed model predicts energy dissipation within an error band of ±5%. Evaluation of other theoretical models in the literature indicates deviation from the experimental results by ±17%. The better performance of the present model is because it detects the behavior of each jet at different steps and integrates this behavior while developing energy dissipation relationships. Thus, the proposed approach offers a framework for predicting energy dissipation downstream of the stepped channel under the nappe flow regime by utilizing the concept of drop iv structure while accounting for the variations observed in the stepped channel due to the presence of pool. Further, various combinations of channel geometry, such as slopes (26.6o, 23.12o) and widths (0.52m, 0.28m, 0.23m) have been added to assess different flow behaviors. A series of tests were carried out on a stepped channel for 0.201≤yc/h≤0.685 (8.93×10-3 m2/s ≤qw≤56.15×10-3 m2/s). In this study, a series of experiments were conducted on a flat stepped channel for two different slopes 26.6o, and 23.12o. Several flow behavior experiments have been conducted, taking all configurations into account. The change of depth-average air concentration has been studied, and the fluctuations have been recorded. Models 1 and 2 have optimal Cmean values within the yc/h range of 0.35 to 0.4, Models 3 and 4 within the range of 0.3 to 0.35, and Models 5 and 6 within the range of 0.2 to 0.3. According to this study, the wider channel is preferable for aeration due to its higher Cmean values. In the current observation, Cmean for step edges spans from 0.325 to 0.672 for model 2. Four alternative methodological approaches were developed for predicting energy dissipation rate based on flow behavior. In order to obtain the best results, a few semi-empirical methods are evaluated in addition to the MNLR expressions that are suggested using a variety of input parameters (approach-1,2). Out of these, the semi-empirical methods were more accurate in predicting energy dissipation than other expressions. However, the assessment revealed that the semi-empirical expression produced accurate results taking two fundamental parameters, such as yc/h (critical depth to step height) and w/l (width to step length) into consideration. The energy dissipation strategy that is described here attained precise prediction among different approaches. However, other approaches are producing good results with an error rate of ±30%. This technique provides a reference for predicting energy dissipation downstream of the cascade of steps by taking geometry and flow parameters into account. A few more details of higher discharge are treated separately with 0.910≤yc/h≤1.28 (86.08×10-3 m2/s ≤qw≤143.43×10-3 m2/s). According to the findings, the mean air concentration is somewhat higher in slope 23.12o, indicating that as the slope lowers, the mean air concentration increases at the final step edge. The mean air concentration for the current research data did not reach equilibrium at 26.6° slope, but it did at 23.12° slope. The few fundamental studies on different input parameters revealed that, Cmean depends on the different combination of input parameters such as qw√gsinθ (hcosθ)3,ych,θ,and ΔHTyc. Few MNLR and MLR expressions were developed out of which the MLR expression using input parameters wh,θ,and ΔHTyc can be able to capture the flow variations with CC of 0.945. Different combinations of input parameters also v been studied which show that the combination of KDh,w,q𝑤2gΔHT3,θ,wh,and N can observe the flow variations in an appropriate way within an error rate of ±10%. The variation of friction factor is also studied for all the configurations using the Darcy-Weisbach friction factor which ranges from 0.0096 to 0.414 including all the configurations. Further, few numerical studies have been conducted using four slopes and it is observed that the pressure fluctuations will be more both positive and negative for 30o slope. The TKE variations show that, from slope of 30o to 20o oscillating seesaw patterns have been observed. Some of the limitations of the numerical study have also been observed that the k-𝜀 turbulent model with VOF sharp interface is weak in capturing the air-water flow data. The energy dissipation statistics indicate that the 30° slope has the lowest energy dissipation rate, whereas slopes 26.6o and 23.12o both exhibit comparable outcomes. A single data-driven model and cluster-based models are compared to get a better understanding of the flow behavior of stepped channels. Clusters are proposed based on methods and location of measurement of air-water flow, and different levels of porosity are used in pool steps. Subsequently, these clusters of data are processed using a variety of machine learning models, such as Random Forest (RF), REPTree, and Kstar model, along with three hybrid algorithms of Additive Regression (AR), Random Subspace (RS), and Weighted Instance Handler Wrapper (WIHW). Results indicate a significant improvement with the clusters derived using physics-based clustering and modeling. Interestingly, the physics-based clusters with the AR-RF hybrid model predicted the energy dissipation rate more accurately, with CC of 0.9885, RMSE of 0.026705, and MAE of 0.02192 during testing, than other models and existing empirical formulae. Results indicate a significant improvement with the physics-based clustering and modeling. It is interesting to note that the physics-based clusters using the AR-RF hybrid model were able to predict the energy dissipation more accurately than the data-driven model, with a relative increase of CC by 1.68% and NSE (Nash-Sutcliffe efficiency) by 3.36%, and a decrease of RMSE (Root-Mean-Squared-Error) and MAE (Mean-Absolute-Error) by 32.06% and 31.13%, respectively. For the nappe flow regime, multiple AI tools such as Random Forest (RF), Random Tree (RT), M5P (M5 model trees), M5Rules, Feed-forward Neural Networks (FFNNs), Gradient Boosting Machine (GBM), Adaptive Boosting (AdaBoost), and Support Vector Machines kernel-based model (SVM-Pearson VII Uni-versal Kernel, Radial Basis Function) are tested in the present study using various combinations of datasets from the present study as well as from literature. Out of all the models, the GBM model performed better than other AI tools in both the field of energy dissipation of stepped channels, with a coefficient of vi determination (R2) of 0.998, root mean square error (RMSE) of 0.00182 and mean absolute error (MAE) of 0.0016 during testing.