Multi-objective optimization of stepped spillway and stilling basin dimensions

Abstract In the present paper, an optimization procedure is proposed for stepped spillway design dimensions, which leads to maximum energy dissipation rate and minimum construction cost considering independently the chute cost and stilling basin cost. Three independent objective functions are thus simultaneously satisfied. The procedure involves four main tools: The multi-objective particle swarm optimization method (MOPSO) to find Pareto solutions in one run, the K-means clustering algorithm to reduce the size of the obtained non-dominated solutions, the pseudo-weight vector approach (PWV) to facilitate the decision making and to select some adequate solutions, and finally, CFD simulations to analyze the retained optimal solutions. The suitability of the proposed procedure is tested through an example of application. As results, a set of twenty solutions with different satisfaction levels are found and compared to existing solutions. A multi-objective optimization problem may have many different solutions, the originality of the present work lies in the proposed procedure which explores several possible ones and reduces their number to give help for the decision making. Furthermore, an approximate expression of spillway total cost is also derived as a function of flow energy dissipation rate.

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Study on the Best Depth of Stilling Basin with Shallow-Water Cushion

Water ◽

10.3390/w10121801 ◽

2018 ◽

Vol 10 (12) ◽

pp. 1801

Author(s):

Qiulin Li ◽

Lianxia Li ◽

Huasheng Liao

Keyword(s):

Energy Dissipation ◽

Shallow Water ◽

Froude Number ◽

Flow Regime ◽

Dissipation Rate ◽

Hydraulic Jump ◽

Energy Dissipation Rate ◽

Main Stream ◽

Stilling Basin ◽

Key Factor

The depth of the stilling basin with shallow-water cushion (SBSWC) is a key factor that affects the flow regime of hydraulic jump in the basin. However, the specific depth at which the water cushion is considered as ‘shallow’ has not been stated clearly by far, and only conceptual description is provided. Therefore, in order to define the best depth of SBSWC and its relationship between the Froude number at the inlet of the stilling basin, a large number of experiments were carried out to investigate SBSWC. First of all, 30 cases including five different Froude numbers and six depths were selected for which large eddy simulation (LES) was firstly verified by the experiments and then adopted to calculate the hydraulic characteristics in the stilling basin. Finally, three standards, based on the flow regime of hydraulic jump, the location of the main stream and the energy dissipation rate, were proposed to define the best depth of SBSWC. The three criteria are as follows: (1) a complete hydraulic jump occurs in the basin (2) the water cushion is about 1/10–1/3 deep of the stilling basin, and (3) the energy dissipation rate is more than 70% and the unit volume energy dissipation rate is as high as possible. It showed that the best depth ratio of SBSWC (depth to length ratio) was between 0.1 and 0.3 and it also indicated the best depth increased with the increase in Froude number. The results of the work are of significance to the design and optimizing of SBSWC.

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Interactive evolutionary multi-objective optimization and decision-making on life-cycle seismic design of bridge

Advances in Structural Engineering ◽

10.1177/1369433218770819 ◽

2018 ◽

Vol 21 (15) ◽

pp. 2227-2240 ◽

Cited By ~ 3

Author(s):

Yu-Jing Li ◽

Hong-Nan Li

Keyword(s):

Decision Making ◽

Life Cycle ◽

Seismic Design ◽

Life Cycle Cost ◽

Pareto Front ◽

Optimization Procedure ◽

Multi Objective Optimization ◽

Seismic Capacity ◽

Preference Information ◽

Multi Objective

Considering future seismic risk and life-cycle cost, the life-cycle seismic design of bridge is formulated as a preference-based multi-objective optimization and decision-making problem, in which the conflicting design criteria that minimize life-cycle cost and maximize seismic capacity are treated simultaneously. Specifically, the preference information based on theoretical analysis and engineering judgment is embedded in the optimization procedure. Based on reasonable displacement ductility, the cost preference and safety preference information are used to progressively construct value function, directing the evolutionary multi-objective optimization algorithm’s search to more preferred solutions. The seismic design of a reinforced concrete pier is presented as an application example using the proposed procedure for the global Pareto front corresponding with engineering designers’ preference. The results indicate that the proposed model is available to find the global Pareto front satisfying the corresponding preference and overcoming the difficulties of the traditional multi-objective optimization algorithm in obtaining a full approximation of the entire Pareto optimal front for large-dimensional problems as well as cognitive difficulty in selecting one preferred solution from all these solutions.

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Numerical Simulation of Stepped Spillways with Front Step Deformation

Mathematical Problems in Engineering ◽

10.1155/2021/7079606 ◽

2021 ◽

Vol 2021 ◽

pp. 1-15

Author(s):

Guodong Li ◽

Haifeng Zhang ◽

Xingnan Li ◽

Lihao Guo ◽

Yanyan Gao ◽

...

Keyword(s):

Numerical Simulation ◽

Energy Dissipation ◽

Water Flow ◽

Dissipation Rate ◽

Energy Dissipation Rate ◽

Maximum Energy ◽

Single Step ◽

Stepped Spillway ◽

Flow State ◽

Front Step

In order to solve the flood discharge problem of both small- and medium-sized warping dams in the Loess Plateau, a stepped spillway scheme, based on an ecological bag, to achieve full-section water flow and energy dissipation has been proposed in this paper. The hydraulic and energy dissipation characteristics of a stepped spillway layout scheme were studied using 3D numerical simulation. As the height of the dams is low and the spillways are short, the research has shown that the traditional single-step layout scheme leads to a low overall energy dissipation rate due to the small amount of energy dissipated in the initial steps. As a result of this, this paper has put forward two kinds of step layout schemes such as the shunt type and the staggered type for the initial steps. Through analysis of the flow state, the pressure distribution, and the total energy dissipation rate, the results have shown that shunt type and staggered type with front step deformation produced an obvious mixing of the water flow, fewer negative pressure areas, and a higher energy dissipation rate. The optimal energy dissipation rate of the staggered type reached 87.75%, and the maximum energy dissipation rate was increased by 27.97%.

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Energy dissipation performance of the trapezoidal stepped spillway

Journal of Engineering Research ◽

10.36909/jer.13649 ◽

2021 ◽

Author(s):

Erdinc Ikinciogullari ◽

Keyword(s):

Energy Dissipation ◽

Dissipation Rate ◽

Energy Dissipation Rate ◽

Stepped Spillway ◽

Base Length ◽

Stepped Spillways

Stepped spillways are a more effective type of spillway in energy dissipation than conventional chute channels. Therefore, the dimensions of the energy breaker at the downstream of the stepped spillways are lower. It is an alternative especially for the downstream pool that cannot be built in sufficient length due to the terrain conditions. In this study, the energy dissipation performance of the trapezoidal stepped spillways was investigated numerically by using Flow3D software. Four different models and three different discharges were utilized for this aim. According to the results, the trapezoidal stepped spillway is more effective up to 30% than classical stepped spillways in energy dissipation. The depth of the trapezoidal step and the bottom base length of the trapezoid significantly affected the energy dissipation rate for the trapezoidal stepped spillway.

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Energy Dissipation in Stepped Spillways with Different Horizontal Face Angles

Energies ◽

10.3390/en12234469 ◽

2019 ◽

Vol 12 (23) ◽

pp. 4469

Author(s):

Peng ◽

Zhang ◽

Yuan ◽

Li ◽

Xie ◽

...

Keyword(s):

Energy Dissipation ◽

Dissipation Rate ◽

Free Water ◽

Energy Dissipation Rate ◽

Field Energy ◽

Stepped Spillway ◽

Turbulent Model ◽

Relevant Research ◽

Unit Discharge ◽

Stepped Spillways

Energy dissipation is one of the most important factors in choosing stepped spillways. However, very few studies have investigated energy dissipation with different horizontal face angles. In this paper, the realizable k-ε turbulent model was used to study the flow field, energy dissipation rates and turbulent kinetic energy and its dissipation rate for different stepped spillways with five horizontal face angles in the skimming flow regions. Results showed that the field and direction of the flow were changed by the horizontal face angles of the stepped spillway, which produced some unique characteristics and thus caused better energy dissipation. The fluctuation of free water surface will be larger with increasing horizontal face angles and the energy dissipation rate decreases with an increasing unit discharge and increases for the enlargement of the horizontal face angles. This conclusion could provide a reference for the relevant research of V shaped stepped spillways.

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