Water

Research

25 pages, 4635 KiB

Open AccessArticle

Influence of Entrapped Air on Hydraulic Transients During Rapid Closure of a Valve Located Upstream and Downstream of an Air Pocket in Pressurised Pipes

by Oscar Pozos-Estrada

Water 2025, 17(7), 927; https://doi.org/10.3390/w17070927 - 22 Mar 2025

Viewed by 208

Abstract

This paper examines the dual impact of trapped air on fluid transients in pressurised conduits, highlighting both its beneficial and detrimental impacts. This research analyses transient pressures caused by rapid valve closure in pipelines that contain air pockets and small bubbles dispersed within [...] Read more.

This paper examines the dual impact of trapped air on fluid transients in pressurised conduits, highlighting both its beneficial and detrimental impacts. This research analyses transient pressures caused by rapid valve closure in pipelines that contain air pockets and small bubbles dispersed within the liquid phase, by a hydraulic jump occurring at the downstream edge of the pockets. Experiments and numerical simulations were conducted with the valve positioned at the ends of the test section on both the inflow and outflow sides. A numerical model utilising the four-point centred scheme and method of characteristics was developed to resolve the governing equations of two-phase flow and was experimentally validated. The results indicate that entrapped air significantly influences hydraulic transients. When the valve is positioned downstream, air pockets and bubbles reduce pressure transients, illustrating a favourable effect. Conversely, when the valve is positioned upstream, adverse pressure transients occur, highlighting a detrimental impact. These outcomes underscore the importance of considering trapped air in pipeline systems, as its existence can either mitigate or exacerbate transient pressures depending on the configuration of the pipeline. The research highlights the significance of considering entrapped air in the design and evaluation of pressurised conduits to improve performance and prevent adverse effects. Full article

(This article belongs to the Special Issue Transient Flows: Mathematical Models, Laboratory Tests, Protection Elements and Systems)

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14 pages, 3637 KiB

Open AccessArticle

Two-Dimensional Transient Flow in a Confined Aquifer with a Cut-Off Curtain Due to Dewatering

by Guangcheng Li, Huiming Lin, Min Deng, Lu Wang, Jianxiao Wang, Fanshui Kong, Yushan Zhang and Qinggao Feng

Water 2025, 17(4), 601; https://doi.org/10.3390/w17040601 - 19 Feb 2025

Viewed by 347

Abstract

Long, narrow, deep excavations commonly encountered in practice, such as those for subway stations, require effective groundwater management to prevent disasters in water-rich areas. To achieve this, a cut-off curtain and pumping well are typically employed during long, deep foundation pit dewatering. The [...] Read more.

Long, narrow, deep excavations commonly encountered in practice, such as those for subway stations, require effective groundwater management to prevent disasters in water-rich areas. To achieve this, a cut-off curtain and pumping well are typically employed during long, deep foundation pit dewatering. The unsteady groundwater flow behavior in the confined aquifer must consider the influence of the cut-off curtain during dewatering. This paper establishes a two-dimensional analytical model to describe transient groundwater flow in a confined aquifer with a cut-off curtain. Both the dewatering well pumped at a steady discharge inside the pit and the cut-off curtain are partially penetrating in the anisotropic confined aquifer. With the help of the Laplace and Fourier cosine transformations, the semi-analytical drawdown solution for the model is derived and validated against numerical solution and unsteady pumping test data. It is shown that the inserted cut-off curtain depth and the structural parameters of the pumping well significantly affect the drawdown inside the pit. Sensitivity analysis reveals that, regardless of whether the observation is made inside or outside the curtain, the drawdown is very sensitive to the change in pumping rate, aquifer thickness, storage coefficient, and horizontal hydraulic conductivity. Additionally, drawdown near the cut-off curtain outside the pit is sensitive to the vertical hydraulic conductivity of the aquifer, the width of the pit, and the interception depth of the cut-off curtain, while drawdown far from the curtain outside the pit is not sensitive to the location and length of the well screen. Full article

(This article belongs to the Special Issue Transient Flows: Mathematical Models, Laboratory Tests, Protection Elements and Systems)

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12 pages, 1498 KiB

Open AccessArticle

MOC-Z Model of Transient Cavitating Flow in Viscoelastic Pipe

by Giuseppe Pezzinga

Water 2024, 16(11), 1610; https://doi.org/10.3390/w16111610 - 4 Jun 2024

Viewed by 1304

Abstract

In this paper, a unitary method for the solution of transient cavitating flow in viscoelastic pipes is proposed in the framework of the method of characteristics (MOC) and a Z-mirror numerical scheme (MOC-Z model). Assuming a standard form of the continuity equation allows [...] Read more.

In this paper, a unitary method for the solution of transient cavitating flow in viscoelastic pipes is proposed in the framework of the method of characteristics (MOC) and a Z-mirror numerical scheme (MOC-Z model). Assuming a standard form of the continuity equation allows the unified treatment of both viscoelasticity and cavitation. An extension of the MOC-Z is used for Courant numbers less than 1 to overcome a few cases with numerical instabilities. Four viscoelastic models were considered: a Kelvin–Voigt (KV) model without the instantaneous strain, and three generalised Kelvin–Voigt models with one, two, and three KV elements (GKV1, GKV2, and GKV3, respectively). The use of viscoelastic parameters of KV and GKV models calibrated for transient flow tests without cavitation allows good comparisons between experimental and numerical pressure versus time for transient tests with cavitation. Whereas for tests without cavitation, the mean absolute error (MAE) always decreases when the complexity of the model increases (from KV to GKV1, GKV2, and GKV3) for all the considered tests, this does not happen for tests with cavitation, probably because the decreasing capacity of parameter generalization for the increasing complexity of the model. In particular, in the examined cases, the KV model performs better than the GKV1 and the GKV3 models in three cases out of five, and the GKV2 model performs better than the GKV3 model in three cases out of five. Furthermore, the GKV2 model performs better than the KV model only in three cases out of five. Full article

(This article belongs to the Special Issue Transient Flows: Mathematical Models, Laboratory Tests, Protection Elements and Systems)

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19 pages, 12948 KiB

Open AccessArticle

Development of Pipeline Transient Mixed Flow Model with Smoothed Particle Hydrodynamics Based on Preissmann Slot Method

by Yixin Yang, Hexiang Yan, Shixun Li, Wenke Song, Fei Li, Huanfeng Duan, Kunlun Xin and Tao Tao

Water 2024, 16(8), 1108; https://doi.org/10.3390/w16081108 - 12 Apr 2024

Cited by 2 | Viewed by 1690

Abstract

The accurate modeling and understanding of complex transient mixed pipe flows is crucial for the optimal design and safe and efficient operation in pipeline systems such as urban drainage systems. Currently, the predominant approach for modeling free-surface-pressurized flows relies on grid-based numerical schemes, [...] Read more.

The accurate modeling and understanding of complex transient mixed pipe flows is crucial for the optimal design and safe and efficient operation in pipeline systems such as urban drainage systems. Currently, the predominant approach for modeling free-surface-pressurized flows relies on grid-based numerical schemes, with comparatively limited capability for exploring its complex phenomena. This study proposed a novel one-dimensional numerical model that integrates the smoothed particle hydrodynamics (SPH) method with the Preissmann slot method (PSM) to explore transient mixed flows in pipeline systems, with better potential capability for exploring more mixed flow phenomena. Empirical parameters of the proposed SPH-PSM model were optimized for improving the numerical accuracy and stability, and the applicable range for these empirical parameters was recommended. The performances of the proposed model were evaluated by different flow regimes, including one free surface case, one fully pressurized case, and two transient mixed-flow cases. The simulation results of different flow regimes demonstrated a high level of agreement with the reference data, indicating the good capability of the SPH-PSM model in simulating complex flow regimes in pipeline systems. Therefore, the proposed SPH-PSM model can be an alternative way for modeling, exploring, and understanding the complex transient mixed flows in pipeline systems. Full article

(This article belongs to the Special Issue Transient Flows: Mathematical Models, Laboratory Tests, Protection Elements and Systems)

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12 pages, 2395 KiB

Open AccessArticle

Analyzing Water Leakages in Parallel Pipe Systems with Rapid Regulating Valve Maneuvers

by Vicente S. Fuertes-Miquel, Alfonso Arrieta-Pastrana and Oscar E. Coronado-Hernández

Water 2024, 16(7), 926; https://doi.org/10.3390/w16070926 - 22 Mar 2024

Cited by 3 | Viewed by 2035

Abstract

Water utilities face the challenge of addressing physical leaks generated from the aging of water distribution systems and the need for more innovative practices to manage water infrastructure efficiently. Water leakages are typically modeled using extended period simulations based on Bernoulli’s equation. However, [...] Read more.

Water utilities face the challenge of addressing physical leaks generated from the aging of water distribution systems and the need for more innovative practices to manage water infrastructure efficiently. Water leakages are typically modeled using extended period simulations based on Bernoulli’s equation. However, this approach must be revised since traditional methods do not appropriately simulate variations induced by regulating valves. In this study, the authors developed a mathematical model based on the mass oscillation equation, which is well-suited for predicting water leakages while accounting for system inertia from regulating valves. This approach is versatile and can be applied to all parallel pipe systems. A comprehensive practical application involving two parallel pipes has been conducted. The aim is to provide engineers and designers with a tool to assess the total volume of water leaks caused by regulating valves in real-world water distribution networks. Furthermore, the study includes a comparative analysis with a single pipe configuration to illustrate how parallel systems lead to increased leaks in contrast to simpler pipe setups. Full article

(This article belongs to the Special Issue Transient Flows: Mathematical Models, Laboratory Tests, Protection Elements and Systems)

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30 pages, 6346 KiB

Open AccessArticle

Application of Machine Learning Coupled with Stochastic Numerical Analyses for Sizing Hybrid Surge Vessels on Low-Head Pumping Mains

by Ahmed M. A. Sattar, Abedalkareem Nedal Ghazal, Mohamed Elhakeem, Amgad S. Elansary and Bahram Gharabaghi

Water 2023, 15(19), 3525; https://doi.org/10.3390/w15193525 - 9 Oct 2023

Viewed by 2791

Abstract

In surge protection, low-head profiles are deemed a challenge in pump failure events since they are prone to severe negative pressure surges that require an uneconomical surge vessel volume. A hybrid surge vessel with a dipping tube can provide required protection with reasonable [...] Read more.

In surge protection, low-head profiles are deemed a challenge in pump failure events since they are prone to severe negative pressure surges that require an uneconomical surge vessel volume. A hybrid surge vessel with a dipping tube can provide required protection with reasonable economic volume. This work presents novel analyses for the hybrid surge vessel and develops a simple model for its optimum sizing using a stochastic numerical approach coupled with machine learning. Practical ranges for correct sizing of vessel components, such as ventilation tube, inlet/outlet air valves, and compression chamber, are presented for optimal protection and performance. The water hammer equations are iteratively solved using the hybrid surge vessel’s revised boundary conditions within the method of characteristics numerical framework to generate 2000 cases representing real pump failures on low-head pipelines. Genetic programming is utilized to develop simple relations for prediction of the hybrid vessel initial and expanded air volumes in addition to the compression chamber volume. Moreover, the developed model presented a classification index for low-head pipelines on which the hybrid vessel would be most economical. The developed model yielded good prediction error statistics. The developed model proves to be more accurate and easier to use than the classical design charts for the low-head pumping mains. The model clearly showed the relation between various hydraulic and pipe parameters, with pipe diameter and static head as the most influencing parameters on compression chamber volume and expanded air volume. The developed model, together with the classification indices, can be used for preliminary surge protection sizing for low-head pipelines. Full article

(This article belongs to the Special Issue Transient Flows: Mathematical Models, Laboratory Tests, Protection Elements and Systems)

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18 pages, 2530 KiB

Open AccessArticle

Smoothed Particle Hydrodynamics Simulations of Porous Medium Flow Using Ergun’s Fixed-Bed Equation

by Carlos E. Alvarado-Rodríguez, Lamberto Díaz-Damacillo, Eric Plaza and Leonardo Di G. Sigalotti

Water 2023, 15(13), 2358; https://doi.org/10.3390/w15132358 - 26 Jun 2023

Cited by 2 | Viewed by 2432

Abstract

A popular equation that is often employed to represent the relationship between the pressure loss and the fluid flow in fluidized or packed granular beds is the Ergun equation, which is an extension of Darcy’s law. In this paper, the method of Smoothed [...] Read more.

A popular equation that is often employed to represent the relationship between the pressure loss and the fluid flow in fluidized or packed granular beds is the Ergun equation, which is an extension of Darcy’s law. In this paper, the method of Smoothed Particle Hydrodynamics (SPH) is used to numerically study the flow field across a rectangular channel partially filled with a porous layer both at the Representative Elementary Volume (REV) scale using the Ergun equation and at the pore scale. Since the flow field can be estimated at the REV scale with a much lower cost compared to the pore scale, it is important to evaluate how accurately the pore-scale results can be reproduced at the REV scale. The comparison between both scales is made in terms of the velocity profiles at the outlet of the rectangular channel and the pressure losses across the clear and porous zones for three different arrays of solid grains at the pore scale. The results show that minimum differences in the flow structure and velocity profiles between the REV and the pore scale always occur at intermediate values of the porosity (

ϕ = 0.44

and 0.55). As the porosity increases, the differences between the REV and the pore scale also increase. The details of the pressure losses are affected by the geometry of the porous medium. In particular, we find that the pressure profiles at the REV scale match those at the pore scale almost independently of the porosity only when the grains are uniformly distributed in a non-staggered square array. Full article

(This article belongs to the Special Issue Transient Flows: Mathematical Models, Laboratory Tests, Protection Elements and Systems)

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15 pages, 6277 KiB

Open AccessArticle

Application of Newton–Raphson Method for Computing the Final Air–Water Interface Location in a Pipe Water Filling

by Dalia M. Bonilla-Correa, Óscar E. Coronado-Hernández, Vicente S. Fuertes-Miquel, Mohsen Besharat and Helena M. Ramos

Water 2023, 15(7), 1304; https://doi.org/10.3390/w15071304 - 26 Mar 2023

Cited by 4 | Viewed by 5475

Abstract

The estimation of thermodynamic behavior during filling processes with entrapped air in water pipelines is a complex task as it requires solving a system of algebraic-differential equations. A lot of different numerical methods have been used for this purpose in literature including the [...] Read more.

The estimation of thermodynamic behavior during filling processes with entrapped air in water pipelines is a complex task as it requires solving a system of algebraic-differential equations. A lot of different numerical methods have been used for this purpose in literature including the rigid water column (RWC) model. The main advantage of the RWC model is its acceptable accuracy with very low computational load. In that context, this research presents the computation of critical points of the physical equations that describe the phenomenon. These points provide information about the final position of the air–water interface. The Newton–Raphson method was then applied to obtain a unique equation that can be used by engineers to directly compute variables such as air pocket pressure and water column length at the end of the hydraulic event. A case study was analyzed to compare the results of the mathematical model with the obtained equation for computing critical points. Both methods provided the same values for the water column length at the end of the hydraulic event. A sensitivity analysis was conducted to identify dependent and non-dependent parameters for evaluating the critical points. The proposed formulation was validated through an experimental set of data. Full article

(This article belongs to the Special Issue Transient Flows: Mathematical Models, Laboratory Tests, Protection Elements and Systems)

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