Fig 8 - uploaded by Bryan W Karney
Content may be subject to copyright.
Different components of energy in the reservoir pipe system with friction: (a) f 1⁄4 0 . 01 ; (b) f 1⁄4 0 . 02 ; (c) f 1⁄4 0 . 03
Source publication
A global energy-auditing approach is used to describe the complex transient flow associated with sudden pressurization of a confined pipe system containing entrapped air pockets. The key concept is that the greatest pressures following pressurization are directly related to the amount of energy absorbed by the air pockets. The energy approach leads...
Citations
... where a and c are the coefficients of the head (H) versus discharge (Q) curve of the pumping system, and R is the relative rotational speed of the pumping system given by R = N 2 /N 1 , with N 2 as the actual rotational speed and N 1 as the rated rotational speed. The H versus Q curve of the pumping system is assumed to be represented by H = aQ 2 + cR 2 [38]. ...
Water conveyance systems are notorious for incurring considerable energy expenditures, either as losses of gravitational potential energy or as increased electricity consumption. Entrapped air pockets, originating from ineffective or nonexistent air management schemes, are common and often significant contributors to these energy costs. This work summarizes the detrimental influence of entrapped air on the energetics and conveyance capacity of pressurized pipelines and identifies those conditions that typically result in temporary or persistent air accumulations. Gravity and pumped lines are considered and gravity lines are shown to be more prone to the negative effects of entrapped air. In addition, initially robust air management strategies can gradually degrade if poorly adjusted to evolving circumstances. The paper critically assesses two common air management strategies: through employing air valves or by air removal by hydraulic means—that is, by considering a line’s configuration along with an attempt to predict the necessary flow conditions for the hydraulic removal of entrapped air.
... The rapid filling process may not properly push the air above the free surface flow toward the boundaries so that an air pocket can be entrapped in the systems. As indicated in the literature (e.g., Malekpour et al. 2016;Wylie and Streeter 1993), in the presence of an air pocket, the maximum induced transient pressure head can be significantly larger than the driving pressure head. In addition, based on observations, Wright et al. (2017) showed that the pressurized air pocket is mainly responsible for the geyser formations, which is contrary to previous studies such as Guo and Song (1990), in which the geyser was only linked to the inertial surge. ...
... Air pockets influence the dynamics of unsteady pipe flows in several circumstances of pipeline operation: filling, draining, water hammer events, and pipe bursts [8][9][10][11]. The transient behaviour of a system containing air is often complex because of air-water interactions and the marked difference between the properties of air and water [12,13]. To explore the relevance of entrapped air during unsteady pipe flows in hydraulic systems, experimental tests have been conducted in a variety of locations, including at the hydraulics laboratory of the Instituto Superior Técnico, University of Lisbon. ...
The risks associated with unsteady two-phase flows in pressurized pipe systems must be considered both in system design and operation. To this end, this paper summarizes experimental tests and numerical analyses that highlight key aspects of unsteady two-phase flows in water pipelines. The essential dynamics of air–water interactions in unvented lines are first considered, followed by a summary of how system dynamics change when air venting is provided. System behaviour during unsteady two-phase flows is shown to be counter-intuitive, surprising, and complex. The role of air valves as protection devices is considered as is the reasonableness of the usual assumptions regarding air valve behaviour. The paper then numerically clarifies the relevance of cavitation and air valve performance to both the predicted air exchanges through any installed air valves and their role in modifying system behaviour during unsteady flows.
... Air entrapped in pipes has been a problem that causes (i) increases in the absolute pressure of the system, (ii) vibrations in the system due to abrupt changes in velocity, and (iii) corrosion due to temperature changes [2]. When it comes to filling processes, the water that enters the system by means of a hydraulic impulsion begins to occupy the space occupied by the air, generating the compression of the air pocket, which causes overpressures [3][4][5][6]. ...
The rapid filling process in pressurized pipelines has been extensively studied using mathematical models. On the other hand, the application of computational fluid dynamics models has emerged during the last decade, which considers the development of CFD models that simulate the filling of pipes with entrapped air, and without air expulsion. Currently, studies of CFD models representing rapid filling in pipes with entrapped air and with air expulsion are scarce in the literature. In this paper, a two-dimensional model is developed using OpenFOAM software to evaluate the hydraulic performance of the rapid filling process in a hydraulic installation with an air valve, considering different air pocket sizes and pressure impulsion by means of a hydro-pneumatic tank. The two-dimensional CFD model captures the pressure evolution in the air pocket very well with respect to experimental and mathematical model results, and produces improved results with respect to existing mathematical models.
... Safety problems arise when pipes containing entrapped air undergo rapid filling and studies in this area date back to more than fifty years (Streeter and Wylie 1967). Theoretical analysis and one-dimensional (1D) mathematical models have been developed in order to predict peak pressures, which are based upon the equations of continuity, momentum and thermodynamics of air (Martin 1976;Cabrera et al. 1992;Zhou et al. 2002b;Lee 2005;Zhou et al. 2011b;Malekpour et al. 2015;Tijsseling et al. 2015;Huang and Zhu 2020a & b). The assumption that a distinct vertical air-water interface maintains throughout the filling process has been adopted in these models. ...
... As explained, V denotes the water column velocity at a time when the air pressure is equal to reservoir pressure. Malekpour et al. [17] analyzed the energy conversion of a transient flow in a reservoir-pipe system and derived an equation for the water column velocity in terms of initial air and water column lengths, reservoir pressure, and the air pressure. However, a simple equation for the cases with constant water column length assumption is derived here. ...
... As can be seen, V is a function of p L L ⁄ . Note that a similar function can be found in [17] (Equation (20)). Therefore, Equations (10) and (11) show that the frequency and the damping of the air pressure distribution increase as the reservoir pressure increases and as the product of the air and water lengths (L L) decreases. ...
This paper studies the air pressurization problem caused by a partially pressurized transient flow in a reservoir-pipe system. The purpose of this study is to analyze the performance of the rigid column model in predicting the attenuation of the air pressure distribution. In this regard, an analytic formula for the amplitude and frequency will be derived, in which the influential parameters, particularly, the driving pressure and the air and water lengths, on the damping can be seen. The direct effect of the driving pressure and inverse effect of the product of the air and water lengths on the damping will be numerically examined. In addition, these numerical observations will be examined by solving different test cases and by comparing to available experimental data to show that the rigid column model is able to predict the damping. However, due to simplified assumptions associated with the rigid column model, the energy dissipation, as well as the damping, is underestimated. In this regard, using the backward Euler implicit time integration scheme, instead of the classical fourth order explicit Runge–Kutta scheme, will be proposed so that the numerical dissipation of the backward Euler implicit scheme represents the physical dissipation. In addition, a formula will be derived to calculate the appropriate time step size, by which the dissipation of the heat transfer can be compensated.
... One-dimensional rigid-column models RCMs have been developed in numerous studies for rapid filling in empty pipes (Martin 1976;Cabrera et al. 1992;Zhou et al. 2002b;Lee 2005;Tijsseling et al. 2015;Malekpour et al. 2015). The RCM, within its range of validity, is widely believed to be convenient, efficient, and reliable for calculating pressure oscillations induced by rapid filling of pipes containing entrapped air (Abreu et al. 1991Guarga et al. 1996;Malekpour 2014). ...
Uncontrolled filling is often seen in storm sewers under wet weather conditions. This study develops a rigid-column model for rapid filling in a partially filled horizontal pipe with entrapped air. Numerical solutions compare very well with experimental measurements from earlier studies. Parametric analysis is conducted by nondimensionalizing the governing equations, and two typical scenarios are numerically investigated in detail: one with a fixed air pocket length and the other with a fixed air pocket volume under different tailwater depths. For the cases with a fixed air pocket length, the peak pressure becomes greater as the tailwater depth increases when the length ratio of the water column and the air pocket is large, whereas the trend is reversed when the length ratio is small. And the critical length ratio is system-dependent. In cases with a fixed air volume, the peak pressure is monotonically reduced with the increase in the tailwater depth. The proposed model can also be adapted for rapid filling with ventilation and surges in closed-conduit flows.
... Despite the RCFM predicting accurately the main hydraulic and thermodynamic draining maneuvers in water pipelines [16], the numerical resolution is still complex since the utilizing of specialized math software suitable for solving a complex system composed of algebraic-differential equations [2,13,[17][18][19][20] is necessary. In this sense, when the inertial term of the water movement equation is neglected, then the resolution of the system is easier compared to the RCFM since water columns can be modeled using algebraic equations (Bernoulli's equation) [21][22][23]. ...
The draining operation involves the presence of entrapped air pockets, which are expanded during the phenomenon occurrence generating drops of sub-atmospheric pressure pulses. Vacuum air valves should inject enough air to prevent sub-atmospheric pressure conditions. Recently, this phenomenon has been studied by the authors with an inertial model, obtaining a complex formulation based on a system composed by algebraic-differential equations. This research simplifies this complex formulation by neglecting the inertial term, thus the Bernoulli’s equation can be used. Results show how the inertial model and the simplified mathematical model provide similar results of the evolution of main hydraulic and thermodynamic variables. The simplified mathematical model is also verified using experimental tests of air pocket pressure, water velocity, and position of the water column.
... In the emptying process, the air pocket volume increases when the size of the water column decreases, causing pressure drops within the pipes (Coronado-Hernández et al. 2018;Fuertes-Miquel et al. 2019b;Laanearu et al. 2012). The opposite occurs in the filling process; in this case, the length of the water column increases, and the air pocket volume decreases, which generates substantial overpressures inside the pipe (Zhou, Liu, and Karney 2013a;Zhou and Liu 2013b;Malekpour, Karney, and Nault 2016). These overpressures and pressure drop that are generated during the filling and emptying processes, respectively, may cause ruptures or collapses (Fuertes-Miquel et al. 2019a). ...
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.
... Recently, draining and filling processes have been investigated using inertial models for the water phase [14,15] and a polytropic law for the air phase [5,8]. Some researchers have used elastic models, where the elasticities of water and pipe have been considered [4,16], and others have used rigid column models to simulate the water phase because the elasticity of air is much higher compared to those of water and pipes [2,7]. Inertial models have been validated in several experimental setups and demonstrated that both models presented a good agreement regarding experimental tests [7,9]. ...
... • The air-water interface is simulated using a piston flow model [2,16]. Sections 2.1 and 2.2 present the mathematical formulations of the draining and filling processes using the quasi-static flow model, respectively. ...
... Although real pipelines present a horizontal air-water interface, the considered hypothesis has been implemented by many researchers to obtain a suitable approximation of this phenomenon [1,4,8]. The air-water interface can be modelled as follows [5,16]: ...
Inertial models have been used by researchers to simulate the draining and filling processes in water pipelines, based on the evolution of the main hydraulic and thermodynamic variables. These models use complex differential equations, which are solved using advanced numerical codes. In this study, a quasi-static flow model is developed to study these operations in hydraulic installations. The quasi-static flow model represents a simplified formulation compared with inertial flow models, in which its numerical resolution is easier because only algebraic equations must be addressed. Experimental measurements of air pocket pressure patterns were conducted in a 4.36 m long single pipeline with an internal diameter of 42 mm. Comparisons between measured and computed air pocket pressure oscillations indicate how the quasi-static flow model can predict extreme values of air pocket pressure for experimental runs, demonstrating the possibility of selecting stiffness and pipe classes in actual pipelines using this model. Two case studies were analysed to determine the behaviour of the quasi-static flow model in large water pipelines.
