Entrapped air pockets in water pipelines play a significant role in influencing transient over-pressures during filling procedures. Several research is focused on highlighting the attenuation of pressure peaks in pipes with single air pockets. This research studies the air-water interaction during rapid water filling processes in an irregular pipeline and air pockets in different branches, and how the trapped air can attenuate the over-pressure peaks. A three-dimensional computational fluid dynamics (CFD) model was developed, and numerical results of the model were validated through experimental measurements. For a given initial air pocket condition upstream of the high point, the maximum air pocket over-pressure was 11% to 32% lower when the descending pipe segment initially contains air compared to when it contains water. In sum, it was found that entrapped air pockets at high points of water pipelines can help mitigate transient over-pressures considering specific initial hydraulic conditions prior to filling operations.
The start-up process of water-distribution networks has been extensively investigated in recent years, particularly regarding the pressure surges that may occur during such transient events. In this context, researchers have concentrated on exploring physical formulations capable of describing the behaviour of the two interacting phases—water and air—typically resolved through numerical approaches. This paper presents an analytical solution to the nonlinear mathematical model governing the start-up of water pipelines containing a trapped air pocket. The model adopts the rigid water column approximation for the liquid phase and a polytropic gas law to account for the compressibility of the air. The resulting system can be formulated as a second-order nonlinear differential equation. The analytical approach consists of transforming the governing equation into a first-order linear ordinary differential equation, in which the square of the water front velocity is expressed as a function of the water column length. This transformation yields a closed-form solution expressed as a special integral series. The required integrals are evaluated using binomial expansions and incomplete gamma functions, enabling the derivation of a general solution valid within alternating intervals of monotonic motion. A practical application involving an 800 m pipeline is presented. Furthermore, the proposed solution is validated against experimental measurements, demonstrating the accuracy and effectiveness of the analytical approach in capturing the system’s transient behaviour.
Spanish Abstract: El vaciado de agua es una operación común que los ingenieros deben afrontar en conducciones presurizadas. Este proceso genera depresiones causadas por la expansión de las bolsas de aire, las cuales pueden producir el colapso del sistema dependiendo las condiciones de instalación. Para evitar este problema, se deben instalar válvulas de aire (ventosas) a lo largo de la conducción. Sin embargo, si las válvulas de aire no han sido dimensionadas adecuadamente, entonces el riesgo en las conducciones continúa. En este trabajo se presenta el modelo matemático desarrollado por los autores para simular el proceso de vaciado, el cual puede ser empleado para el planeamiento de este proceso. Finalmente, se presenta la resolución de un ejemplo de aplicación en donde se muestra la evolución de las variables hidráulicas que intervienen en el proceso tales como: caudal de agua, longitud de la columna de vaciado, presión en la bolsa de aire, densidad en la bolsa de aire y caudal de aire admitido por la válvula de aire.
Air pockets in water distribution networks can cause various operational issues, as their expansion during drainage operations leads to sub-atmospheric conditions that may result in pipeline collapse depending on soil conditions and pipe stiffness. This study presents an analytical solution for calculating air pocket pressure, water column length, and water velocity during drainage operations in a pipeline with an entrapped air pocket and a closed upstream end. The existing system of three differential equations is reduced to two first-order nonlinear differential equations, enabling a rigorous analysis of the existence and uniqueness of solutions. The system is then further reduced to a single secondorder nonlinear ordinary differential equation (ODE), providing an intuitive framework for examining the physical behaviour of the hydraulic and thermodynamic variables. Furthermore, through a change of variables, the second-order ODE is transformed into a first-order linear ODE, facilitating the derivation of an analytical solution. The analytical solution is validated by comparing it with a numerical solution. Additionally, a practical application demonstrates the effectiveness of the developed tool in predicting the extreme pressure values in the air pocket during the water drainage process in a pipe, within a controlled environment.
Entrapped air pockets can cause failure in water distribution systems if air valves have not been appropriately designed for expelling air during filling manoeuvres performed by water utilities. One-dimensional mathematical models recently developed for studying this phenomenon do not consider the effect of blocking columns inside water pipelines. This research presents the development of a mathematical model for analysing the filling process in a pipeline with an undulating profile with various air valves, including blocking columns during starting-up water installations. The results show how different air pocket pressure peaks can be produced over transient events, which need to be analysed to ensure a successful procedure that guarantees pipeline safety during the pressure surge occurrence. In this study, an experimental set-up is analysed to observe the behaviour of two blocking columns during filling by comparing the air pocket pressure pulses.
For the design of stormwater pumping stations, there is often uncertainty regarding the selection of an appropriate rainfall event to determine the required pumping capacity and temporary storage volume for managing extreme events of a given magnitude. To account for the risk of system failure, the return period is considered, as recommended based on the size of the catchment’s drainage area or other considerations, depending on the local regulations of a country. This study focused on analysing the direct runoff volume from the catchment, the storage volume required for the operation of the pumping system, and the order of magnitude of the design flow rate. The results indicate that a rainfall event with a duration of at least twice the time of concentration should be used. The design flow rate should range between 50% and 70% of the peak discharge, and designing for flow rates near the peak is not advisable, as it can lead to intermittent pump operation and result in an oversized installed capacity. The methodology developed in this research was applied to the Coastal Protection Project located in the city of Cartagena, Colombia, which includes a 2045.6-m-long box culvert with a cross-sectional area of 2 × 2 m, and three pumping stations, each equipped with three pumps rated at 0.75 m3/s, for a total installed capacity of 6.75 m3/s.
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 $$\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>%</mml:mo> </mml:math> , respectively.
The Hybrid Smart Energy Community (HySEC) model is an integrated framework for optimizing hybrid renewable energy systems, unifying BIM, IoT, and data-driven modeling, as an innovative approach for the energy transition. A Revit—Twinmotion BIM model, enriched with topographic, CAD, and real-image data, enhances spatial accuracy and stakeholder communication, while a digital–physical architecture linking sensors, gateways, edge devices, and cloud platforms enables decentralized peer-to-peer communication and real-time monitoring. The framework is applied to a smart energy community composed of a hydropower–wind–solar PV system serving six buildings (48.8 MWh/year), supported by high-resolution hourly Open-Meteo data. A NARX neural network trained on 8760 hourly observations achieves an MSE of 2.346 at epoch 16, providing advanced predictive capability. Benchmarking against HOMER demonstrates clear advantages in grid exports (15,130 vs. 8274 kWh/year), battery cycling (445 vs. 9181 kWh/year), LCOE (€0.09 vs. €0.180/kWh), IRR (9% vs. 6%), payback (8.7 vs. 10.5 years), and CO2 emissions (−9.4 vs. 101 tons). These results confirm HySEC as a conceptually flexible solution that strengthens energy autonomy, supports heritage site rehabilitation, and promotes sustainable rural development.
Air pockets can become trapped at high points in pipelines with irregular profiles, particularly during service interruptions. The resulting issues, primarily caused by peak pressures generated during pipeline filling, are a well-documented topic in the literature. However, it is surprising that this subject has not received comprehensive attention. Using a model developed by the authors, this paper identifies the key parameters that define the phenomenon, presenting equations in a dimensionless format. The main advantage of this study lies in the ability to easily compute pressure surges without the need to solve a complex system of differential and algebraic equations. Numerous cases of filling operations were analysed to obtain dimensionless charts that can be used by water utilities to compute pressure surges during filling operations. Additionally, it provides charts that facilitate the rapid and reasonably accurate estimation of peak pressures. Depending on their transient characteristics, pressure peaks are either slow or fast, with separate charts provided for each type. A practical application involving a water pipeline with an irregular profile demonstrates the model’s effectiveness, showing strong agreement between calculated and chart-predicted (proposed methodology) values. This research provides water utilities with the ability to select the appropriate pipe’s resistance class required for water distribution systems by calculating the pressure peak value that may occur during filling procedures.
No abstract is provided for this article.
Two- and three-dimensional analyses of transient flows considering the air–water interaction have been a challenge for researchers due to the complexity in the numerical resolution of the multiphase during emptying in pressurized water pipelines. The air–water dynamic interaction of emptying processes can be analyzed using thermodynamic and hydraulic laws. There is a lack in the current literature regarding the analysis of those phenomena using 3D models. In this research, several simulations were performed to study the complex details of two-phase flows. A 3D model was proposed to represent the emptying process in a single pipeline, considering a PVoF model and two-equation turbulence model. The model was numerically validated through 12 experimental tests and mesh sensitivity analysis. The pressure pulses of the air pockets were evaluated and compared with the experimental results and existing mathematical models, showing how the 3D models are useful for capturing more detailed information, such as pressure and velocity patterns of discrete air pockets, distribution of air and water velocity contours, and the exploration of temperature changes for an air pocket expansion.
The study of draining processes without admitting air has been conducted using only steady friction formulations in the implementation of governing equations. However, this hydraulic event involves transitions from laminar to turbulent flow, and vice versa, because of the changes in water velocity. In this sense, this research improves the current mathematical model considering unsteady friction models. An experimental facility composed by a 4.36 m long methacrylate pipe was configured, and measurements of air pocket pressure oscillations were recorded. The mathematical model was performed using steady and unsteady friction models. Comparisons between measured and computed air pocket pressure patterns indicated that unsteady friction models slightly improve the results compared to steady friction models.
The analysis of filling processes in pressurized pipelines has been conducted using a steady friction model in the implementation of governing equations. This research is focused on the case of a filling process of a single pipeline without an air valve. Three equations were used to represent the phenomenon: (i) a rigid water column approach, which describes the water movement along the water system; (ii) a piston flow model, which assumes a perpendicular air-water interface to the main direction of the pipe; and (iii) a polytropic model for representing the thermodynamic behaviour of an entrapped air pocket. This research studies the filling processes occurrence using equations of steady and unsteady friction models, where Moody, Wood, Hazen-Williams, and Swamee-Jain equations are analysed. The analysis is applied to a case study of a single pipe of a total length of 1000 m with an internal diameter of 595 mm variation of pressure surges in the implementation of these formulations. Results confirm that there is a minimum discrepancy between steady and unsteady friction models since values of pressure surges pattern are similar.
This study presents a methodology for the digitalisation process for analysing transient flow phenomena in a U-tube. It comprises several layers, including the characterisation of liquid oscillation dynamics, image segmentation for experimentally determining variations in the meniscus position, and the integration of machine learning techniques with analytical solutions. The position, velocity, and acceleration of the meniscus are obtained using image-processing methods and subsequently compared with the corresponding analytical predictions. The proposed methodology accurately represents the existing hydraulic conditions, incorporating both Newtonian and Ogawa friction models. To assess model performance, the index of agreement was employed to compare analytical and experimental results. The findings indicate a systematic error of 2.2 mm ± 3 pixels when using the Ogawa friction model, which corresponds to the best model for predicting this hydraulic behaviour. Finally, the implementation of machine learning techniques demonstrates considerable potential for predictive analysis, with statistical measures showing coefficients of determination above 0.997 and consistently low Root Mean Square Error values.
Draining operations using pressurised air can produce sub-atmospheric pressures that pose a significant risk to structural integrity, given the pipe stiffness class. This research presents a modelling strategy for predicting water velocities during the occurrence of this phenomenon. The proposed approach combines a physically based hydraulic formulation with machine learning techniques for making this prediction. A calibrated rigid water column model is first employed to reproduce the transient interaction between the expanding air phase and the draining water column. Input parameters include pipe bridge height varying from 0.5 to 3.0 m, a valve loss dimensionless coefficient ranging from 2.0 to 14.0, and an initial water column length between 163.0 and 286.3 m. Subsequently, a Monte Carlo scheme is used to generate a representative dataset. A total of 28 models were assessed, among which a wide neural network demonstrated superior predictive capability, achieving root-mean-square error values between 0.043 and 0.056 m/s and coefficients of determination ranging from 0.996 to 0.997 for the validation and testing stages, respectively. Sensitivity analyses indicate that the minor loss coefficient governs the water velocity response, whereas geometric features such as the pipe bridge height exert a comparatively minor influence.
