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

Water ◽  
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.

scholarly journals Study on the Best Water Cushion Depth of Stilling Basin with Shallow-Water Cushion at Different Froude Numbers

2017 ◽  
Author(s):  
Qiulin Li ◽  
Lianxia Li ◽  
Huasheng Liao ◽  
Jingjing Wei ◽  
Shengyin Jiang ◽  
...  
Keyword(s):  
Shallow Water ◽  
Flow Velocity ◽  
Froude Number ◽  
Flow Regime ◽  
Hydraulic Jump ◽  
Length Ratio ◽  
Flow Profile ◽  
Critical Flow Velocity ◽  
Stilling Basin ◽  
Study Results

The water cushion depth of stilling basin with shallow-water cushion 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 be stated clearly for now, and only conceptual description is provided. This paper attempts to specify the best water cushion depth based on the flow regime of hydraulic jump and underflow speed; namely, in case of critical hydraulic jump in the basin, the best water cushion depth is located where the minimum distance to the bottom plate of the stilling basin is 1/5~1/4 of the water cushion depth. The theoretical analysis indicates, at different inclinations of discharge chute (θ) and depth ratios of inlet (m), instead of monotonic change, the Froude number (Fr) at inlet of the stilling basin with shallow-water cushion firstly reduces and then increases as the flow velocity at discharge chute inlet (V) increases; the parameters of inflection point (critical flow velocity and critical Fr) increase as the inclinations of discharge chute (θ) and depth ratios of inlet (m) increase. Such regularity is the theoretical basis for selecting representative study cases. The reliability of the large eddy simulation calculation results are verified by a model test; in the paper, 30 cases including five different Froude numbers and six shallow-water cushion depths are selected, for calculating the hydraulic factors such as flow profile, flow regime and flow velocity in the stilling basin with shallow-water cushion; and the varying pattern between the best depth of stilling basin with shallow-water cushion (depth-to-length ratio) and the inflow Froude number is obtained which indicates that the best depth of stilling basin with shallow-water cushion varies little as the change of the Froude number before reaching the critical Froude number; however, the best depth-to-length ratio of stilling basin with shallow-water cushion increases as the Froude number increases after the critical Froude number is reached. The study results in this paper are of reference significance to design and calculation of the stilling basin with shallow-water cushion.

scholarly journals SPH Simulation of Hydraulic Jump on Corrugated Riverbeds

2019 ◽  
Vol 9 (3) ◽  
pp. 436 ◽  
Author(s):  
Shenglong Gu ◽  
Fuping Bo ◽  
Min Luo ◽  
Ehsan Kazemi ◽  
Yunyun Zhang ◽  
...  
Keyword(s):  
Energy Dissipation ◽  
Dissipation Rate ◽  
Hydraulic Jump ◽  
Numerical Study ◽  
Energy Dissipation Rate ◽  
Vortex Pattern ◽  
Particle Hydrodynamics ◽  
Sph Model ◽  
Smoothed Particle ◽  
Sph Simulation

This paper presents a numerical study of the hydraulic jump on corrugated riverbed using the Smoothed Particle Hydrodynamics (SPH) method. By simulating an experimental benchmark example, the SPH model is demonstrated to predict the wave profile, velocity field, and energy dissipation rate of hydraulic jump with good accuracy. Using the validated SPH model, the dynamic evolvement of the hydraulic jump on corrugated riverbed is studied focusing on the vortex pattern, jump length, water depth after hydraulic jump, and energy dissipation rate. In addition, the influences of corrugation height and length on the characteristics of hydraulic jump are parametrically investigated.

scholarly journals Multi-objective optimization of stepped spillway and stilling basin dimensions

2021 ◽  
Author(s):  
Fatiha Lebdiri ◽  
Abdelghani Seghir ◽  
Ali Berreksi
Keyword(s):  
Decision Making ◽  
Energy Dissipation ◽  
Dissipation Rate ◽  
Clustering Algorithm ◽  
Optimization Procedure ◽  
Energy Dissipation Rate ◽  
Stepped Spillway ◽  
Multi Objective Optimization ◽  
Stilling Basin ◽  
Multi Objective

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.

scholarly journals A Novel Analytical Method for Evaluating the Characteristics of Hydraulic Jump at a Positive Step

Water ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2005
Author(s):  
Milad Mohammadi ◽  
Mohammad Nazari-Sharabian ◽  
Moses Karakouzian
Keyword(s):  
Experimental Data ◽  
Energy Dissipation ◽  
Dissipation Rate ◽  
Hydraulic Jump ◽  
Rectangular Channel ◽  
Theoretical Models ◽  
Energy Dissipation Rate ◽  
Flow Depth ◽  
Jump Length ◽  
Positive Step

We present a new method to evaluate the hydraulic jump characteristics in a horizontal rectangular channel with a positive step. We considered the flow curvature effect and the free surface’s small rise at the A-type hydraulic jump’s end. First, we present a novel method to give jump length estimation based on the similarity of the jump and the turbulent wall-jet, considering the pressure gradient. Then, considering the jump as a curvilinear flow and using a one-dimensional momentum equation, we present an accurate expression for the conjugate flow depth regarding the initial Froude number and step height. Finally, we compute the jump’s energy dissipation rate. Compared to the theoretical models for conjugate flow depth in a hydraulic jump, the proposed equation in this study fit the experimental data better, even for high steps and large initial Froude numbers. However, for low Froude numbers (F1 < 5), the equation was less accurate in estimating the jump length. Regarding the jump’s energy dissipation rate, the results agreed well with the experimental data from previous investigations. However, it is noted that the increased energy dissipation rate dwindled in larger Froude numbers.

The evolution of turbulent bursts: the b—ε model

1994 ◽  
Vol 5 (4) ◽  
pp. 537-557 ◽  
Author(s):  
M. Bertsch ◽  
R. Dal Passo ◽  
R. Kersner
Keyword(s):  
Partial Differential Equations ◽  
Energy Dissipation ◽  
Energy Density ◽  
Differential Equations ◽  
Dissipation Rate ◽  
Turbulent Energy ◽  
Energy Dissipation Rate ◽  
Self Similar ◽  
Similar Solutions ◽  
Semi Empirical

We study the semi-empirical b—ε model which describes the time evolution of turbulent spots in the case of equal diffusivity of the turbulent energy density b and the energy dissipation rate ε. We prove that the system of two partial differential equations possesses a solution, and that after some time this solution exhibits self-similar behaviour, provided that the system has self-similar solutions. The existence of such self-similar solutions depends upon the value of a parameter of the model.

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