Prediction of Hydraulic Jumps on a Triangular Bed Roughness Using Numerical Modeling and Soft Computing Methods
This study investigates the characteristics of free and submerged hydraulic jumps on the triangular bed roughness in various <i>T</i>/<i>I</i> ratios (i.e., height and distance of roughness) using CFD modeling techniques. The accuracy of numerical modeling outcomes was checke...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/23/3135 |
| _version_ | 1797507459694198784 |
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| author | Mehdi Dasineh Amir Ghaderi Mohammad Bagherzadeh Mohammad Ahmadi Alban Kuriqi |
| author_facet | Mehdi Dasineh Amir Ghaderi Mohammad Bagherzadeh Mohammad Ahmadi Alban Kuriqi |
| author_sort | Mehdi Dasineh |
| collection | DOAJ |
| description | This study investigates the characteristics of free and submerged hydraulic jumps on the triangular bed roughness in various <i>T</i>/<i>I</i> ratios (i.e., height and distance of roughness) using CFD modeling techniques. The accuracy of numerical modeling outcomes was checked and compared using artificial intelligence methods, namely Support Vector Machines (SVM), Gene Expression Programming (GEP), and Random Forest (RF). The results of the FLOW-3D<sup>®</sup> model and experimental data showed that the overall mean value of relative error is 4.1%, which confirms the numerical model’s ability to predict the characteristics of the free and submerged jumps. The SVM model with a minimum of Root Mean Square Error (RMSE) and a maximum of correlation coefficient (<i>R</i><sup>2</sup>), compared with GEP and RF models in the training and testing phases for predicting the sequent depth ratio (<i>y</i><sub>2</sub>/<i>y</i><sub>1</sub>), submerged depth ratio (<i>y</i><sub>3</sub>/<i>y</i><sub>1</sub>), tailwater depth ratio (<i>y</i><sub>4</sub>/<i>y</i><sub>1</sub>), length ratio of jumps (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>L</mi><mi>j</mi></msub><mo>/</mo><msubsup><mi>y</mi><mn>2</mn><mo>*</mo></msubsup></mrow></semantics></math></inline-formula>) and energy dissipation (Δ<i>E</i>/<i>E</i><sub>1</sub>), was recognized as the best model. Moreover, the best result for predicting the length ratio of free jumps <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><msub><mi>L</mi><mrow><mi>j</mi><mi>f</mi><mo>/</mo></mrow></msub><msubsup><mi>y</mi><mn>2</mn><mo>*</mo></msubsup></mrow></semantics></math></inline-formula>) in the optimal gamma is <i>γ</i> = 10 and the length ratio of submerged jumps <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><msub><mi>L</mi><mrow><mi>j</mi><mi>s</mi><mo>/</mo></mrow></msub><msubsup><mi>y</mi><mn>2</mn><mo>*</mo></msubsup></mrow></semantics></math></inline-formula>) is γ = 0.60. Based on sensitivity analysis, the <i>Froude number</i> has the greatest effect on predicting the (<i>y</i><sub>3</sub>/<i>y</i><sub>1</sub>) compared with submergence factors (<i>SF</i>) and <i>T</i>/<i>I</i>. By omitting this parameter, the prediction accuracy is significantly reduced. Finally, the relationships with good correlation coefficients for the mentioned parameters in free and submerged jumps were presented based on numerical results. |
| first_indexed | 2024-03-10T04:48:48Z |
| format | Article |
| id | doaj.art-d4c4269b8f5843a0b43d2ef2a8fa4433 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T04:48:48Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d4c4269b8f5843a0b43d2ef2a8fa44332023-11-23T02:46:34ZengMDPI AGMathematics2227-73902021-12-01923313510.3390/math9233135Prediction of Hydraulic Jumps on a Triangular Bed Roughness Using Numerical Modeling and Soft Computing MethodsMehdi Dasineh0Amir Ghaderi1Mohammad Bagherzadeh2Mohammad Ahmadi3Alban Kuriqi4Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Maragheh 8311155181, IranDepartment of Civil Engineering, Faculty of Engineering, University of Zanjan, Zanjan 537138791, IranDepartment of Civil Engineering, Faculty of Engineering, Urmia University, Urmia 5756151818, IranDepartment of Civil Engineering, Faculty of Engineering, Shabestar Branch, Islamic Azad University, Shabestar 1584743311, IranCERIS, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisbon, PortugalThis study investigates the characteristics of free and submerged hydraulic jumps on the triangular bed roughness in various <i>T</i>/<i>I</i> ratios (i.e., height and distance of roughness) using CFD modeling techniques. The accuracy of numerical modeling outcomes was checked and compared using artificial intelligence methods, namely Support Vector Machines (SVM), Gene Expression Programming (GEP), and Random Forest (RF). The results of the FLOW-3D<sup>®</sup> model and experimental data showed that the overall mean value of relative error is 4.1%, which confirms the numerical model’s ability to predict the characteristics of the free and submerged jumps. The SVM model with a minimum of Root Mean Square Error (RMSE) and a maximum of correlation coefficient (<i>R</i><sup>2</sup>), compared with GEP and RF models in the training and testing phases for predicting the sequent depth ratio (<i>y</i><sub>2</sub>/<i>y</i><sub>1</sub>), submerged depth ratio (<i>y</i><sub>3</sub>/<i>y</i><sub>1</sub>), tailwater depth ratio (<i>y</i><sub>4</sub>/<i>y</i><sub>1</sub>), length ratio of jumps (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>L</mi><mi>j</mi></msub><mo>/</mo><msubsup><mi>y</mi><mn>2</mn><mo>*</mo></msubsup></mrow></semantics></math></inline-formula>) and energy dissipation (Δ<i>E</i>/<i>E</i><sub>1</sub>), was recognized as the best model. Moreover, the best result for predicting the length ratio of free jumps <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><msub><mi>L</mi><mrow><mi>j</mi><mi>f</mi><mo>/</mo></mrow></msub><msubsup><mi>y</mi><mn>2</mn><mo>*</mo></msubsup></mrow></semantics></math></inline-formula>) in the optimal gamma is <i>γ</i> = 10 and the length ratio of submerged jumps <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><msub><mi>L</mi><mrow><mi>j</mi><mi>s</mi><mo>/</mo></mrow></msub><msubsup><mi>y</mi><mn>2</mn><mo>*</mo></msubsup></mrow></semantics></math></inline-formula>) is γ = 0.60. Based on sensitivity analysis, the <i>Froude number</i> has the greatest effect on predicting the (<i>y</i><sub>3</sub>/<i>y</i><sub>1</sub>) compared with submergence factors (<i>SF</i>) and <i>T</i>/<i>I</i>. By omitting this parameter, the prediction accuracy is significantly reduced. Finally, the relationships with good correlation coefficients for the mentioned parameters in free and submerged jumps were presented based on numerical results.https://www.mdpi.com/2227-7390/9/23/3135artificial intelligenceenergy dissipationFLOW-3Dhydraulic jumpsbed roughnesssensitivity analysis |
| spellingShingle | Mehdi Dasineh Amir Ghaderi Mohammad Bagherzadeh Mohammad Ahmadi Alban Kuriqi Prediction of Hydraulic Jumps on a Triangular Bed Roughness Using Numerical Modeling and Soft Computing Methods Mathematics artificial intelligence energy dissipation FLOW-3D hydraulic jumps bed roughness sensitivity analysis |
| title | Prediction of Hydraulic Jumps on a Triangular Bed Roughness Using Numerical Modeling and Soft Computing Methods |
| title_full | Prediction of Hydraulic Jumps on a Triangular Bed Roughness Using Numerical Modeling and Soft Computing Methods |
| title_fullStr | Prediction of Hydraulic Jumps on a Triangular Bed Roughness Using Numerical Modeling and Soft Computing Methods |
| title_full_unstemmed | Prediction of Hydraulic Jumps on a Triangular Bed Roughness Using Numerical Modeling and Soft Computing Methods |
| title_short | Prediction of Hydraulic Jumps on a Triangular Bed Roughness Using Numerical Modeling and Soft Computing Methods |
| title_sort | prediction of hydraulic jumps on a triangular bed roughness using numerical modeling and soft computing methods |
| topic | artificial intelligence energy dissipation FLOW-3D hydraulic jumps bed roughness sensitivity analysis |
| url | https://www.mdpi.com/2227-7390/9/23/3135 |
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