Abstract: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.

Transient phenomena during the emptying process of a single pipe with water air interaction.

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This work considers the behaviour of air inside pipes when the air is expelled through air valves. Generally, the air shows isothermal behaviour. Nevertheless, when the transient is very fast, it shows adiabatic behaviour. In a real installation, an intermediate evolution between these two extreme conditions occurs. Thus, it is verified that the results vary significantly depending on the hypothesis adopted. To determine the pressure of the air pocket, the most unfavourable hypothesis (isothermal behaviour) is typically adopted.Nevertheless, from the perspective of the water hammer that takes place when the water column arrives at the air valve and abruptly closes, the most unfavourable hypothesis is the opposite (adiabatic behaviour). In this case, the residual velocity with which the water arrives at the air valve is higher, and, consequently, the water hammer generated is greater.

Genetic algorithms (GA) are optimization techniques that are widely used in the design of water distribution networks. One of the main disadvantages of GA is positional bias, which degrades the quality of the solution. In this study, a modified pseudo-genetic algorithm (PGA) is presented. In a PGA, the coding of chromosomes is performed using integer coding; in a traditional GA, binary coding is utilized. Each decision variable is represented by only one gene. This variation entails a series of special characteristics in the definition of mutation and crossover operations.Some benchmark networks have been used to test the suitability of a PGA for designing water distribution networks. More than 50,000 simulations were conducted with different sets of parameters. A statistical analysis of the obtained solutions was also performed. Through this analysis, more suitable values of mutation and crossover probabilities were discovered for eachcase. The results demonstrate the validity of the method.Optimum solutions are not guaranteed in any heuristic method. Hence, the concept of a "good solution" is introduced. A good solution is a design solution that does not substantially exceed the optimal solution that is obtained from the simulations. This concept may be useful when the computational cost is critical. The main conclusion derived from this study is that a proper combination of population and crossover and mutation probabilities leads to a high probability that good solutions will be obtained.

The filling process in water pipelines produces pressure surges caused by the compression of air pockets. In this sense, air valves should be appropriately designed to expel sufficient air to avoid pipeline failure. Recent studies concerning filling maneuvers have been addressed without considering the behavior of air valves. This work shows a mathematical model developed by the authors which is capable of simulating the main hydraulic and thermodynamic variables during filling operations under the effect of the air valve in a single pipeline, which is based on the mass oscillation equation, the air-water interface, the polytropic equation of the air phase, the air mass equation, and the air valve characterization. The mathematical model is validated in a 7.3-m-long pipeline with a 63-mm nominal diameter. A commercial air valve is positioned in the highest point of the hydraulic installation. Measurements indicate that the mathematical model can be used to simulate this phenomenon by providing good accuracy.

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Filling and emptying processes are common maneuvers while operating, controlling and managing water pipelines systems. Currently, these operations are executed following recommendations from technical manuals and pipe manufacturers; however, these recommendations have a lack of understanding about the behavior of these processes. The application of mathematical models considering transient flows with entrapped air pockets is necessary because a rapid filling operation can cause pressure surges due to air pocket compressions, while an uncontrolled emptying operation can generate troughs of sub-atmospheric pressure caused by air pocket expansion. Depending on pipe and installation conditions, either situation can produce a rupture of pipe systems. Recently, reliable mathematical models have been developed by different researchers. This paper reviews and compares various mathematical models to simulate these processes. Water columns can be analyzed using a rigid water column model, an elastic water model, or 2D/3D CFD models; air-water interfaces using a piston flow model or more complex models; air pockets through a polytropic model; and air valves using an isentropic nozzle flow or similar approaches. This work can be used as a starting point for planning filling and emptying operations in pressurized pipelines. Uncertainties of mathematical models of two-phases flow concerning to a non-variable friction factor, a polytropic coefficient, an air pocket sizes, and an air valve behavior are identified.