Research

17 pages, 5221 KiB

Open AccessArticle

Numerical Simulation of Cavitation Bubble Collapse inside an Inclined V-Shape Corner by Thermal Lattice Boltzmann Method

by Yu Li, Jingyi Ouyang, Yong Peng and Yang Liu

Water 2024, 16(1), 161; https://doi.org/10.3390/w16010161 - 31 Dec 2023

Viewed by 1003

Abstract

Cavitation happening inside an inclined V-shaped corner is a common and important phenomenon in practical engineering. In the present study, the lattice Boltzmann models coupling velocity and temperature fields are adopted to investigate this complex collapse process. Based on a series of simulations, [...] Read more.

Cavitation happening inside an inclined V-shaped corner is a common and important phenomenon in practical engineering. In the present study, the lattice Boltzmann models coupling velocity and temperature fields are adopted to investigate this complex collapse process. Based on a series of simulations, the fields of density, pressure, velocity and temperature are obtained simultaneously. Overall, the simulation results agree with the experiments, and they prove that the coupled lattice Boltzmann models are effective to study cavitation bubble collapse. It was found that the maximum temperature of bubble collapse increases approximately linearly with the rise of the distance between the single bubble center and the corner. Meanwhile, the velocity of the micro-jet increases and the pressure peak at the corner decreases correspondingly. Moreover, the effect of angle of the V-shaped wall on the collapse process of bubbles is similar to the effect of distance between the single bubble center and the corner. Moreover, with the increase in bubble radius, the maximum temperature of bubble collapse increases proportionally, the starting and ending of the micro-jet are delayed and the pressure peak at the corner becomes larger and also is delayed. In the double bubble collapse, the effect of distance between two bubble centers on the collapse process of bubbles is discussed in detail. Based on the present study, appropriate measures can be proposed to prevent or utilize cavitation in practical engineering. Full article

(This article belongs to the Special Issue Hydraulic Engineering and Modelling: Numerical Modelling and Simulation)

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20 pages, 13214 KiB

Open AccessArticle

A Dimension-Reduced Line Element Method for 3D Transient Free Surface Flow in Porous Media

by Yuting Chen, Qianfeng Yuan, Zuyang Ye and Zonghuan Peng

Water 2023, 15(17), 3072; https://doi.org/10.3390/w15173072 - 28 Aug 2023

Cited by 1 | Viewed by 753

Abstract

In order to reduce the numerical difficulty of the 3D transient free surface flow problems in porous media, a line element method is proposed by dimension reduction. Different from the classical continuum-based methods, homogeneous permeable pores in the control volume are conceptualized by [...] Read more.

In order to reduce the numerical difficulty of the 3D transient free surface flow problems in porous media, a line element method is proposed by dimension reduction. Different from the classical continuum-based methods, homogeneous permeable pores in the control volume are conceptualized by a 3D orthogonal network of tubes. To obtain the same hydraulic solution with the continuum model, the equivalent formulas of flow velocity, continuity equation and transient free surface boundary are derivable from the principle of flow balance. In the solution space of transient free surface flow, the 3D problem is transformed into 1D condition, and then a finite element algorithm is simply deduced. The greatest advantage of the line element method is line integration instead of volume/surface integration, which has dramatically decreased the integration difficulty across the jump free surface. Through the analysis of transient free surface flow in the unconfined aquifer, trapezoidal dam, sand flume and wells, the transient free surface locations predicted from the proposed line element method generally agree well with the analytical, experimental and other numerical data in the available literatures, the numerical efficiency can also be well guaranteed. Furthermore, the hydraulic anisotropy has significant effect on the evolution of free surface locations and the shape of depression cones in spatial. The line element method can be expanded to model the 3D unsaturated seepage flow, two-phase flow and thermos problems in porous media because of the similarity between the similarity of Darcy’s law, Buckingham Law and Fourier’s law. Full article

(This article belongs to the Special Issue Hydraulic Engineering and Modelling: Numerical Modelling and Simulation)

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16 pages, 4846 KiB

Open AccessArticle

The Comparison of Seven Models to Simulate the Transport and Deposition of Polydisperse Particles under Favorable Conditions in a Saturated Medium

by Zhike Zou, Lei Yu, Yalong Li, Shuyao Niu, Linlin Fan, Wenbing Luo and Wei Li

Water 2023, 15(12), 2193; https://doi.org/10.3390/w15122193 - 10 Jun 2023

Viewed by 1318

Abstract

Polydisperse particles are ubiquitous in both the natural and engineered environment, and the precise prediction of the transport and capture of polydisperse particles in a saturated medium is crucial. Several efforts (Yao model, RT model, TE model, MPFJ model, NG model, MHJ model, [...] Read more.

Polydisperse particles are ubiquitous in both the natural and engineered environment, and the precise prediction of the transport and capture of polydisperse particles in a saturated medium is crucial. Several efforts (Yao model, RT model, TE model, MPFJ model, NG model, MHJ model, and MMS model) were developed to obtain accurate correlation equations for the particle capture probability (single-collector removal efficiency), but the applicability of the existing models to the entire porous medium and the retention characteristic of the polydisperse particles are still unclear. In this study, sand column experiments were undertaken to investigate the transport and capture processes of the polydisperse particles in the saturated medium. The mass density was employed to quantize the effects of particle polydispersity and incorporated into the depth-dependent deposition rate. The experimental results showed that the polydisperse particles formed a hyper-exponential retention profile even under favorable conditions (no repulsion). The excellent agreement between the results obtained from the MMS model and the experimentally observed results of the breakthrough curves (BTCs), as well as the retention profiles demonstrated the validation of the MMS model, as the correlation coefficient and the standard average relative error were 0.99 and 0.005, respectively. The hyper-exponential retention profile is caused by the uneven capture of the polydisperse particles by the porous medium. This study highlights the influences of particle polydispersity on particle transport and capture in a saturated porous medium. Full article

(This article belongs to the Special Issue Hydraulic Engineering and Modelling: Numerical Modelling and Simulation)

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13 pages, 2347 KiB

Open AccessArticle

Hamiltonian Additional Damping Control for Suppressing Power Oscillation Induced by Draft Tube Pressure Fluctuation

by Yun Zeng, Shige Yu, Fang Dao, Xiang Li, Yiting Xu and Jing Qian

Water 2023, 15(8), 1479; https://doi.org/10.3390/w15081479 - 10 Apr 2023

Viewed by 959

Abstract

The power oscillation induced by pressure fluctuation in the draft tube of the hydraulic turbine is one of the limiting factors preventing the Francis turbine from operating in the vibration zone. At the present power grid with a high proportion of renewable energy [...] Read more.

The power oscillation induced by pressure fluctuation in the draft tube of the hydraulic turbine is one of the limiting factors preventing the Francis turbine from operating in the vibration zone. At the present power grid with a high proportion of renewable energy resources, we try to improve the load regulation ability of the hydropower units by extending the stable operation zone to the vibration zone. By the mathematical modelling of pressure fluctuation, this paper gives an analytical expression of the power oscillation. We derive the extended Hamiltonian model of the hydropower unit where power oscillation is external excitation. Secondly, the damping injection method introduces some desired interconnection and damping matrices as the Hamiltonian damping factor into the additional damping control. Finally, through theoretical analysis and experimental simulation, this research discusses the resonance characteristics of pressure fluctuation and power oscillation, the equivalent analysis between the damping factor and equivalent damping coefficient, and the control design of vibration zone crossing during the start-up. Simulation results show that when r₂₅ = 1.3, the minimum power oscillation amplitude is 0.5466, which is equivalent to an increase in D by 20. The maximum oscillation amplitude decreases by 4.6%, and the operation limited zone is reduced by 10.1%. The proposed additional damping control can effectively suppress the power oscillation and expand the regulation range. Full article

(This article belongs to the Special Issue Hydraulic Engineering and Modelling: Numerical Modelling and Simulation)

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20 pages, 8218 KiB

Open AccessArticle

Two-Phase MPM Simulation of Surge Waves Generated by a Granular Landslide on an Erodible Slope

by Kai-Li Zhao, Liu-Chao Qiu, Tang-Jin Yuan, Yang Wang and Yi Liu

Water 2023, 15(7), 1307; https://doi.org/10.3390/w15071307 - 26 Mar 2023

Cited by 1 | Viewed by 1624

Abstract

A high-speed debris flow sliding into a reservoir can cause a huge disaster. Consequently, predicting landslide movement accurately and its potential interaction with water is crucial. This paper developed a computational model based on a two–layer two–phase material point method (MPM) to simulate [...] Read more.

A high-speed debris flow sliding into a reservoir can cause a huge disaster. Consequently, predicting landslide movement accurately and its potential interaction with water is crucial. This paper developed a computational model based on a two–layer two–phase material point method (MPM) to simulate surge waves generated by granular landslides on an erodible slope. By comparing granular landslide on a rigid and erodible slope, the effect of the slope erodibility on the process of landslide movement and the waves generated is investigated. The model takes full account of the large deformations, fluidisation and settlement of granular material in soil–water interactions. The numerical model is validated by comparing the simulated results with experimental data. The influences of internal friction angle, density, elastic modulus, Poisson ratio and dilatancy angle on wave height are also studied. The validated model was then used to investigate the surge waves generated by dry and saturated granules sliding along a rigid and erodible slope. The results show that both the erodible slope and saturated granular slide can increase the first wave crest height generated by the landslide. Full article

(This article belongs to the Special Issue Hydraulic Engineering and Modelling: Numerical Modelling and Simulation)

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17 pages, 8492 KiB

Open AccessArticle

A Simple Line-Element Model for Three-Dimensional Analysis of Steady Free Surface Flow through Porous Media

by Qianfeng Yuan, Dong Yin and Yuting Chen

Water 2023, 15(6), 1030; https://doi.org/10.3390/w15061030 - 08 Mar 2023

Cited by 2 | Viewed by 1354

Abstract

Considering the fact that only pores can transport water, pores in the homogeneous control volume are conceptualized as a three-dimensional orthogonal network of line elements, which is in contrast to the continuum hypothesis in traditional numerical approaches. The related flow velocity, hydraulic conductivity [...] Read more.

Considering the fact that only pores can transport water, pores in the homogeneous control volume are conceptualized as a three-dimensional orthogonal network of line elements, which is in contrast to the continuum hypothesis in traditional numerical approaches. The related flow velocity, hydraulic conductivity and continuity equation equivalent to the continuum model are formulated based on the principle of flow balance. Subsequently, the unified form for flow velocity and continuity equation is established based on the local coordinate system, and a finite line-element method is developed, in which three-dimensional steady free surface flow is reduced to one-dimensional form, and the numerical difficulty is greatly decreased. The proposed line-element model is validated by the good agreements of free surface locations with other methods through steady flow in a rectangular dam and a right trapezoidal dam, respectively. It is found that the proposed line-element model is not heavily dependent on the mesh size and penalty parameter. Steady free surface flow on the left bank abutment slope of the Kajiwa Dam in Southwestern China is further evaluated, and a parabolic variational inequality algorithm based on the continuum model is also employed for comparison. The consistent results indicate that the proposed line-element model can capture the steady free surface flow behavior as well as the continuum-based method. Moreover, the proposed line-element model can rapidly achieve accurate solutions whether for simple examples or for complicated engineering applications. Full article

(This article belongs to the Special Issue Hydraulic Engineering and Modelling: Numerical Modelling and Simulation)

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11 pages, 1682 KiB

Open AccessArticle

Hydrogeological Parameter Estimation of Confined Aquifer within a Rectangular Shaped Drop Waterproof Curtain

by Yi Li, Wentao Xie, Hongwei Wang, Bin Peng, Feng Xiong and Chun Zhu

Water 2023, 15(2), 356; https://doi.org/10.3390/w15020356 - 15 Jan 2023

Viewed by 1672

Abstract

For the dewatering of deep excavation, the existing man-made waterproof curtain has a significant influence on flow response in confined aquifers; the effect of the waterproof curtain must be considered when using the field data for hydrogeological parameter estimation. In this study, a [...] Read more.

For the dewatering of deep excavation, the existing man-made waterproof curtain has a significant influence on flow response in confined aquifers; the effect of the waterproof curtain must be considered when using the field data for hydrogeological parameter estimation. In this study, a closed-form analytical solution for constant discharge pumping in a confined aquifer within a rectangular-shaped drop waterproof curtain is obtained by making use of the image method coupled with the superpose principle. A straight-lined method is presented to determine the value of the hydraulic parameters of the confined aquifer and the application of the obtained results is illustrated by the usefulness of a field pumping test in Wuhan, China. The results show that the predicted drawdowns developed by the estimated parameters are in good agreement with the measured drawdown in the field. The proposed solution and parameter estimation are reliable and can provide important help for the design of dewatering in deep foundation pit engineering. Full article

(This article belongs to the Special Issue Hydraulic Engineering and Modelling: Numerical Modelling and Simulation)

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15 pages, 5889 KiB

Open AccessArticle

Impact of Geometrical Features on Solute Transport Behavior through Rough-Walled Rock Fractures

by Xihong Chuang, Sanqi Li, Yingtao Hu and Xin Zhou

Water 2023, 15(1), 124; https://doi.org/10.3390/w15010124 - 29 Dec 2022

Viewed by 1308

Abstract

The solute transport in the fractured rock is dominated by a single fracture. The geometric characteristics of single rough-walled fractures considerably influence their solute transport behavior. According to the self-affinity of the rough fractures, the fractal model of single fractures is established based [...] Read more.

The solute transport in the fractured rock is dominated by a single fracture. The geometric characteristics of single rough-walled fractures considerably influence their solute transport behavior. According to the self-affinity of the rough fractures, the fractal model of single fractures is established based on the fractional Brownian motion and the successive random accumulation method. The Navier–Stokes equation and solute transport convective-dispersion equation are employed to analyze the effect of fractal dimension and standard deviation of aperture on the solute transport characteristics. The results show that the concentration front and streamline distribution are inhomogeneous, and the residence time distribution (RTD) curves have obvious tailing. For the larger fractal dimension and the standard deviation of aperture, the fracture surface becomes rougher, aperture distribution becomes more scattered, and the average flow velocity becomes slower. As a result, the average time of solute transport is a power function of the fractal dimension, while the time variance and the time skewness present a negative linear correlation with the fractal dimension. For the standard deviation of aperture, the average time exhibits a linearly decreasing trend, the time variance is increased by a power function, and the skewness is increased logarithmically. Full article

(This article belongs to the Special Issue Hydraulic Engineering and Modelling: Numerical Modelling and Simulation)

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14 pages, 2504 KiB

Open AccessFeature PaperArticle

A Comprehensive View of the ASM1 Dynamic Model: Study on a Practical Case

by Carlos Costa

Water 2022, 14(7), 1046; https://doi.org/10.3390/w14071046 - 26 Mar 2022

Cited by 4 | Viewed by 3353

Abstract

The ASM1 model was elaborated by the IWA Task Group for Mathematical Modelling, with the aim of explaining and predicting the output values of organic matter concentration in activated sludge processes, especially for domestic wastewaters. In recent years, ASM1 has been completed with [...] Read more.

The ASM1 model was elaborated by the IWA Task Group for Mathematical Modelling, with the aim of explaining and predicting the output values of organic matter concentration in activated sludge processes, especially for domestic wastewaters. In recent years, ASM1 has been completed with new components and extended to other biological processes, including biological membrane reactors, activated carbon filters, and microalgae bioreactors. In this article, the essentials of this model are studied by outlining the original topics that were formulated in the model, and by using a practical example of a wastewater treatment plant (WWTP), which can clarify the application of the ASM1. A protocol of approximation between the dynamic model and the experimental data for the COD effluent concentration is presented, based on three steps of tuning and fine tuning, and the corrected values of the kinetic parameters Y_H and μ_H_,_max are calculated in accordance with the minimum error. In the simulation procedure, the baseline and dynamism are controlled, comparing them to the experimental data line, and the values obtained for the kinetic parameters are Y_H = 0.60 and μ_H_,_max = 0.40 d⁻¹. The kinetic parameters reflect the activity of the mixed community of microorganisms in the WWTP. Full article

(This article belongs to the Special Issue Hydraulic Engineering and Modelling: Numerical Modelling and Simulation)

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