Recently, emptying processes have been studied in experimental facilities in pipelines, but there is a lack regarding applications in actual pipelines, which permits establishing the risk of collapse because of sub-atmospheric pressure occurrence. This research presents a mathematical model to simulate the emptying process of water supply networks, and the application to a water emptying pipeline with nominal diameter of 1000 mm and 578 m long which is located on the southern of Cartagena, Bolívar Deparment, Colombia. In the application, both pipes and the air valve data manufacturer were considered. The behavior of all hydraulic and thermodynamic variables is considered. Results show that is crucial to know sub-atmospheric pressure values to prevent the collapse of the pipeline. The application of the mathematical model confirms that the hydraulic system is well designed depending on air valve sizes and maneuvering of drain valve.
An air pocket's behaviour inside of a pipeline during transient conditions is of great importance due to its effect on the safety of the hydraulic system and the complexity of modeling its behaviour. The emptying process from water pipelines needs more assessment because the generation of troughs of subatmospheric pressure may lead to serious damage. This research studies the air pocket parameters during an emptying process from a water pipeline. A well-equipped experimental facility was used to measure the pressure and the velocity change throughout the water emptying for different air pocket sizes and valve opening times. The phenomenon was simulated using a one-dimensional (1D) developed model based on the rigid formulation with a non-variable friction factor and a constant pipe diameter. The mathematical model shows good ability in predicting the trough of subatmospheric pressure value as the most important parameter which can affect the safety of hydraulic systems.
Over the past few years, there has been significant interest in the importance of reversible hydro-pumping systems due to their favorable flexibility and economic and environmental characteristics. When designing reversible lines, it is crucial to consider dynamic effects and corresponding extreme pressures that may occur during normal and emergency operating scenarios. This research describes essentially the turbine operation, although various boundary elements are mathematically formulated and presented to provide an understanding of the system complexity. Different numerical approaches are presented, based on the 1D method of characteristics (MOC) for the long hydraulic circuit, the dynamic turbine runner simulation technique for the behavior of the power station in turbine mode and the interaction with the fluid in the penstock, and a CFD model (2D and 3D) to analyze the flow behavior crossing the runner through the velocity fields and pressure contours. Additionally, the simulation results have been validated by experimental tests on different setups characterized by long conveyance systems, consisting of a small scale of pumps as turbines (at IST laboratory) and classical reaction turbines (at LNEC laboratory). Mathematical models, together with an intensive campaign of experiments, allow for the estimation of dynamic effects related to the extreme transient pressures, the fluid-structure interaction with rotational speed variation, and the change in the flow. In some cases, the runaway conditions can cause an overspeed of 2–2.5 of the rated rotational speed (NR) and an overpressure of 40–65% of the rated head (HR), showing significant impacts on the pressure wave propagation along the entire hydraulic circuit. Sensitivity analyses based on systematic numerical simulations of PATs (radial and axial types) and reaction turbines (Francis and Kaplan types) and comparisons with experiments are discussed. These evaluations demonstrate that the full-load rejection scenario can be dangerous for turbomachinery with low specific-speed (ns) values, in particular when associated with long penstocks and fast guide vane (or control valve) closing maneuver.
Air pockets generated during emptying operations in pressurized hydraulic systems cause significant pressure drops inside pipes. To avoid these sudden pressure changes, one of the most widely used methods involves the installation of air valves along the pipeline route. These elements allow air exchange between the exterior and the interior of the pipe, which alleviates the pressure drops produced and thus prevents possible breaks or failures in the structure of the installation. This study uses a mathematical model previously validated by the authors in smaller installations to simulate all hydraulic variables involved in emptying processes over time. The purpose of these simulations is the validation of the mathematical model in real large-scale installations, and to do this, the results obtained with the mathematical model are compared with actual measurements made by the partner company. The hydraulic system selected for the study is a pipeline with a nominal diameter of 400 mm and a total length of 1020 m. The results obtained from the mathematical model show great similarity with the experimental measurements, thus validating the model for emptying large pipes.
Studying sub-atmospheric pressure patterns in emptying pipeline systems is crucial because these processes could cause collapses depending on the installation conditions (the underground pipe covering height, type, fill, and pipeline stiffness class). Pipeline studies have focused more on filling than on emptying processes. This study presents an analysis of the following variables: air pocket pressure, water velocity, and water column length during the emptying of an irregular pipeline without an air valve by two-dimensional computational fluid dynamics (2D CFD) model simulation using the software OpenFOAM. The mathematical model predicts the experimental values of the study variables. Water velocity vectors are also analysed within the experimental facility, assessing the sensitivity of the drain valve to different openings and changes in water column length during the hydraulic phenomenon.
This study presents a detailed analysis of the morphological evolution of beaches in the Bocagrande sector of Cartagena de Indias, Colombia, over more than a decade, based on periodic monitoring of six beach profiles. The beaches in this area are in bays constrained by headlands and promontories located at both ends of each bay. Changes in shoreline position, dry beach widths, and the surf zone were evaluated using aerial photographs, orthophotos, satellite imagery, and field data, together with sediment size determined through granulometric analysis. The results indicate that the beaches exhibit characteristics of wave-dominated, exposed systems, with sediments classified as fine sand that tend to increase in grain size toward the northern sector of the bay. A cyclical variation in the shoreline was observed, with average retreats and advances ranging from 5 to 10 m, depending on the climatic season. Dry beach widths ranged from 10 to 90 m, decreasing toward the north. Differences in morphology between profiles and shoreline variation are attributed to the climatic season, profile location within the bay, and proximity to a coastal structure and its particular type. Beach profiles were fitted to conceptual equilibrium profile models using traditional equations, which yielded a coefficient of determination of 0.76; when machine learning algorithms were applied, this value improved to 0.99. This study provides an important baseline for future morphological assessments and coastal management efforts in the city and places with similar characteristics, particularly considering ongoing shoreline protection projects.
The emptying procedure is a common operation that engineers have to face in pipelines. This generates subatmospheric pressure caused by the expansion of air pockets, which can produce the collapse of the system depending on the conditions of the installation. To avoid this problem, engineers have to install air valves in pipelines. However, if air valves are not adequately designed, then the risk in pipelines continues. In this research, a mathematical model is developed to simulate an emptying process in pipelines that can be used for planning this type of operation. The one-dimensional proposed model analyzes the water phase propagation by a new rigid model and the air pockets effect using thermodynamic formulations. The proposed model is validated through measurements of the air pocket absolute pressure, the water velocity and the length of the emptying columns in an experimental facility. Results show that the proposed model can accurately predict the hydraulic characteristic variables.
Water losses in water distribution systems are typically analysed using extended period simulations, where its numerical resolution is commonly achieved using the gradient method. These models assume that adjustments to regulating valves occur, either manually or automatically, over an extended period of time, then the system inertia can be neglected. This research introduces the development of a rigid water column model for analysing water leakages in single pipelines, which can be employed to account for regulation valve adjustments in shorter time periods, thereby providing greater accuracy when assessing water losses. The application to a case study is presented to analyse pressure variations and leakage flow patterns over 30, 60, and 180 s. A comparison between the extended period simulation and rigid water column model is presented in order to note the order of magnitude on leakages when the system inertia is not considered. The results confirm that is crucial for water utilities the consideration of inertial system to simulate adequately opening and closure manoeuvres in water distribution systems, since according to the case study the extended period simulation can overestimated or underestimated the total leakage volume in percentages of 37.1 and 55.2 %, respectively.
The prediction of the pressure inside the air pocket in water pipelines has been the topic for a lot of research works. Several aspects in this field have been discussed, such as the filling and the emptying procedures. The emptying process can affect the safety and the efficiency of water systems. Current research presents an analysis of the emptying process using experimental and computational results. The phenomenon is simulated using the two-dimensional computational fluid dynamics (2D CFD) and the one-dimensional mathematical (1D) models. A backflow air analysis is also provided based on CFD simulations. The developed models show good ability in the prediction of the sub-atmospheric pressure and the flow velocity in the system. In most of the cases, the 1D and 2D CFD models show similar performance in the prediction of the pressure and the velocity results. The backflow air development can be accurately explained using the CFD model.
This study examines the impact of sub-atmospheric pressures in water pipelines during emptying manoeuvres with air admitted. Previous research has looked at this issue but has not studied it in detail. This research presents a two-dimensional model using the OpenFOAM software to analyse different emptying manoeuvres in a single pipeline with entrapped air. The results show the sensitivity of the ball valve opening percentage, which show that absolute pressure drop can reduce to 23% for each 5% of ball valve opening percentage. The influence of the size of the entrapped air pocket and different air-admission orifices was also analysed. The numerical model showed that the selection of the percentage and times of opening drainage valves in pipelines with air-admission orifices is crucial in controlling sub-atmospheric pressure conditions. Finally, this study demonstrates the ability of the two-dimensional model to show the sensitivity of hydraulic drainage parameters in pipelines with entrapped air.
During the filling process in pressurized hydraulic systems, sudden pressure changes generated inside the pipes can cause significant damage. To avoid these excessive overpressures, air valves should be installed to allow air exchange between the inside and outside during the filling process. This study presents a mathematical model to analyse the hydraulic transients during filling processes. This model, which has already been validated in small laboratories, is now applied to real large-scale systems that consist of DN400 and DN600 pipelines from Empresa Mixta Metropolitana S.A (EMIMET – Group Global Omnium), which is the company that manages the water supply of the metropolitan area of Valencia (from the Drinking Water Treatment Station to the municipalities). The mathematical model for large pipes is validated by comparing the experimental measurements and the results of model.
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.
This research evaluates Battery Energy Storage Systems (BESS) and Compressed Air Vessels (CAV) as complementary solutions for enhancing micro-grid resilience, flexibility, and sustainability. BESS units ranging from 5 to 400 kWh were modeled using a Nonlinear Autoregressive Neural Network with Exogenous Inputs (NARX) neural network, achieving high SOC prediction accuracy with R2 > 0.98 and MSE as low as 0.13 kWh2. Larger batteries (400–800 kWh) effectively reduced grid purchases and redistributed surplus energy, improving system efficiency. CAVs were tested in pumped-storage mode, achieving 33.9–57.1% efficiency under 0.5–2 bar and high head conditions, offering long-duration, low-degradation storage. Waterhammer-induced CAV storage demonstrated reliable pressure capture when Reynolds number ≤ 75,000 and Volume Fraction Ratio, VFR > 11%, with a prototype reaching 6142 kW and 170 kWh at 50% air volume. CAVs proved modular, scalable, and environmentally robust, suitable for both energy and water management. Hybrid systems combining BESS and CAVs offer strategic advantages in balancing renewable intermittency. Machine learning and hydraulic modeling support intelligent control and adaptive dispatch. Together, these technologies enable future-ready micro-grids aligned with sustainability and grid stability goals.
In hydraulic engineering, some researchers have developed different mathematical and numerical tools for a better understanding of the physical interaction between water flow in pipes with trapped air during emptying processes, where they have made contributions on the use of simple and complex models in different application cases. In this article, a comparative study of different experimental and numerical models existing in the literature for the analysis of trapped air in pressurised pipelines subjected to different scenarios of emptying processes is presented, where different authors have develope, experimental, one-dimensional mathematical and complex computational fluid dynamics (CFD) models (two-dimensional and three-dimensional) to understand the level of applicability of these models in different hydraulic scenarios, from the physical and computational point of view. In general, experimental, mathematical and CFD models had maximum Reynolds numbers ranging from 2670 to 20,467, and it was possible to identify that the mathematical models offered relevant numerical information in a short simulation time on the order of seconds. However, there are restrictions to visualise some complex hydraulic and thermodynamic phenomena that CFD models are able to illustrate in detail with a numerical resolution similar to the mathematical models, and these require simulation times of hours or days. From this research, it was concluded that the knowledge of the information offered by the different models can be useful to hydraulic engineers to identify physical and numerical elements present in the air–water interaction and computational conditions necessary for the development of models that help decision-making in the field of hydraulics of pressurised pipelines.
<p>Debido a las bolsas de aire que hay en el interior de las tuberías durante los procesos de llenado y vaciado, se producen depresiones o sobrepresiones en el interior de las mismas, capaces de producir serios daños en las instalaciones. Para analizar todas las variables hidráulicas en las maniobras de llenado y vaciado, se opta por la aplicación de un modelo matemático, el cual es capaz de simular con exactitud el comportamiento de ambos fluidos, tanto la columna de agua como la bolsa de aire. El modelo propuesto por los autores ya ha sido validado en pequeñas instalaciones de laboratorio. En este trabajo, se pretende validar el modelo matemático en una instalación real de grandes dimensiones. Concretamente, se trata de una conducción de diámetro DN400, ubicada en Massamagrell (Valencia), donde se analizan las maniobras de llenado y de vaciado. Finalmente, se comparan los resultados que proporciona el modelo con las mediciones realizadas por la Empresa Mixta Metropolitana S.A. (EMIMET), obteniéndose una similitud muy aceptable.</p>
