A mathematical model for the assessment of the pressure head maxima that air pockets within a pipeline can originate on start-up is presented. This model is based on a general model addressing the filling of a pipeline with several air pockets published by the authors. Here the simulation of the operation of a discharge valve in order to control the peak pressure following the pump start-up is included. Also, in order to correctly model reverse flow through the pump use is made of the dimensionless Suter curves. Water movement is modelled through rigid column theory and air - water straight cross section moving interfaces are considered. Because of the huge pressure values that the very rapid compression of the air can cause, and in order to avoid pipe breaks, practical engineers must lend great attention to this problem.
The decision making process when deciding which strategy to adopt must be based, in any activity, on good information. Broadly speaking, we can say that to elaborate a model of a network of water distribution consists in organizing adequately the available...
This work aims to study in detail the methods of experimental characterization of air valves. In the first part, different experimental techniques are compared to the measurements made in the Air Valves Test Bench built by Bermad CS at its factory in Evron (Israel). The second part deals with the study of a collection of commercial air valves from different manufacturers. Finally, the Wylie and Streeter discharge coefficient Cd for air valve characterization [1] has been obtained. The results have been also compared with a simplified proposed model representation of the air valve.
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.
En el campo del agua existe una enorme diversidad de actividades e intereses y, por tanto, de áreas de trabajo. Los problemas que se plantean en estas áreas son auténticos problemas de ingeniería y, como consecuencia, las ayudas que ciertas técnicas de Matemática Aplicada pueden prestar son realmente importantes. Por un lado, es preciso disponer de herramientas de análisis que permitan realizar simulaciones fiables de los distintos modelos que se plantean analizando diversas configuraciones, modos de funcionamiento, estados de carga, etc. con los que estudiar instalaciones ya existentes a partir de los datos básicos que las caracterizan. Se trata de procesos deterministas cuya plasmación matemática es a través de conjuntos acoplados de distintos tipos de ecuaciones, algebraicas, diferenciales ordinarias y en derivadas parciales, típicamente no lineales, para los que se precisan técnicas numéricas específicas. Además, dada la incertidumbre a que están sometidos muchos de los datos (especialmente en configuraciones ya existentes), resulta, con frecuencia, necesario resolver problemas inversos de gran envergadura, en donde, además, otras técnicas (estadísticas, mínimo cuadráticas, etc.) son de gran interés. Por otra parte, se necesita diseñar para realizar configuraciones nuevas. Con frecuencia, la ausencia de datos iniciales y la disposición de conjuntos limitados de restricciones de tipo diverso (algunas difícilmente objetivables), hacen de los procesos de diseño verdaderos problemas de optimización, en donde los métodos clásicos fracasan con frecuencia y para los que técnicas más actuales basadas en redes neuronales, algoritmos genéticos, teoría difusa, teoría del caos, etc. Se hacen imprescindibles. En este documento se presentan los aspectos matemáticos más importantes que se necesitan en algunos de los puntos del ciclo integral del agua haciendo hincapié de manera especial en los temas de mayor actualidad.
Pipelines with irregular profiles exhibit a number of peculiarities that cannot be ignored, such as the likely accumulation of air at elevated points. To avoid the risks inherent to the air pockets use is made of air valves, which admit and release air. In any case, air into the pipe must be eventually vented out. But, to avoid undesirable overpressures it must be vented in a controlled way, since, with or without air valves, an air pocket between two liquid columns may cause important peak pressures, especially on the installation start-up. In this paper, the filling of a pipeline with air valves installed at the elevated points and with entrapped air is modelled. The aim is to predict the transient phenomena likely to occur and assess the peak pressures that can be developed. To analyze the behavior of n trapped air pockets in a pipeline of irregular profile with vi air valves, use is made of the so-called rigid model. In this paper, boundary conditions for the most critical function of air valves (the outlet air phase) are reviewed. The isothermal behavior, proposed by standard literature, of the trapped air into the pipe is compared with the adiabatic process, a more realistic approach for fast transients.
The growing concern on improving the use of water in distribution systems, requires increasing the quality and the reliability in such systems. This paper presents a series of techniques aimed at reducing water losses and increasing the efficiency in the supply. The...
Based on our wide experience in continuous professional development (CPD) through traditional activities and hands-on experience on several commonly used Learning Management Systems, we have integrated both concepts and developed a simple, yet effective e-learning approach to help professionals in the water field to fill the gap between their sometimes not updated background and the new features that characterize the water field in the present days.We argue that this task can make use of the same approach that is essential to the knowledge discovery process, to which the e-learning process boils down to.In this contribution we present the work performed at the Polytechnic University of Valencia, within the Multidisciplinary Team of Fluid Modelling, on web systems to support technology enhanced learning specifically addressed to professionals in the Water field.Our approach hinges on the joint use of the online as well as the offline characteristics of the e-learning process and puts to work together in a synergic way both traditional and technology-based learning know-how.As a result, a number of distance courses have been produced that are used for Engineering CPD across the globe, since many professionals worldwide, mainly from Spanish speaking countries, have followed our courses.We present the evolution of our system and the results obtained from testing and evaluating the prototype during the last three years.We have identified issues significant to users in order to better manage the system and changes required to adapt our system to organizational processes and context.Feedback received from trainees indicates both the validity of our approach and the feasibility of implementing e-learning materials to contribute to CPD in the water field in particular and in any field in general, since the methodology herein presented can be exported in a straightforward manner.
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.
Air valves characterization is critical for proper design of pipeline systems, mainly for the processes of filling and emptying. However, knowing this capacity is not a simple matter. Technical information provided by manufacturers is often insufficient or inaccurate. Moreover, experimental determination of the behavior of these elements requires large infrastructures either for pumping air either for storage it. In this paper an alternative methodology for testing air valves is presented. The procedure is based on testing the elements using water instead of air, measuring the flow through the element for different differential pressures. Subsequently, the application of techniques based on the hydrodynamic similarity allows extrapolating the performance characteristics of these valves with air. Finally, the proposed methodology has been validated with four air valve models. These valves have been tested with water. Later, the results obtained by similarity are compared with those obtained from tests in specialized laboratories.
