WATER HAMMER CAUSED BY AIR RELEASE IN THE OPERATION OF PIPELINE FILLING

V. Amoruso, G. Discipio, V. Iacobellis and A. F. Piccinni

Dipartimento di Ingegneria Civile e Ambientale - Politecnico di Bari

Via E. Orabona, 4, 70125, Bari, Italy

Tel.: +39-080-5963321; Fax: +39-080-5963414;

E-mail: v.iacobellis@poliba.it

Abstract: In this paper, results of a numerical investigation performed over a large range of possible values of hydraulic and geometrical parameters are reported with the aim of  providing a design criteria for the air release valve and for the optimization of pipeline filling time within the constraints imposed by the upsurge containment.

By means of a mathematical model, accounting for the elasticity of the water column, we analyzed the water hammer phenomenon due to the flow stoppage which occurs when the liquid column strikes the plate of an automatic air vent device, after complete exhaustion of the air pocket.

Results of the numerical experiments highlight different interesting features of the phenomenon. In particular we found that a smaller orifice allows to reduce the upsurge pressures which, on the other hand, result to increase with the filling rate.

 The initial volume of the air pocket, which in the considered scheme is determined by the pipeline diameter is practically not influent on the upsurge pressures for values of filling rates less than 0.6 times the maximum filling rate. Above such threshold the upsurge pressures increase with the initial air volume.

By the light of the presented results we propose a design chart that allows to chose the optimal filling rate, as a function of the hydraulic and geometrical characteristic of the pipeline and of the maximum allowed overpressures.

Keywords: pipe flow, air valve, water hammer, pipeline operations

1  INTRODUCTION

The presence of entrapped air in pipelines designed to carry water or other liquids, may cause considerable problems and loss in line efficiency with reference to steady state conditions as well as to operations for hydraulic control and regulation. Among these, particular remark has to be given to the start up operation of the system and initial filling of pipeline when dangerous transient pressures may arise following the rapid exhaustion of air from an air release valve. In order to avoid such situation, the technical practice suggests to proceed with very slow filling rates. In this way the rate of air exhaustion and the corresponding velocity of the water column are also reduced together with the upsurge pressures due to the sudden stoppage of the water column following the complete expulsion of the air pocket through the air release orifice of an automatic air valve. With particular reference to long adduction pipelines over large scale aqueduct systems, the transient state and the time of operation need to be investigated in order to improve and better define the control procedures and design criteria.

In the last century many researchers (Veronese, 1937, Benfratello, 1958, De Martino et al., 1985, Roth and Nucera, 1988, Viparelli, 1989, Gisonni, 1998) faced causes and phenomena involved in the transient which develops during the air release ad after complete exhaustion of the air pocket. Their work clarified the main theoretical aspects and the mathematical modeling.

In this paper, results of a numerical investigation performed over a large range of possible values of hydraulic and geometrical parameters, with reference to a schematic installation, are reported with the aim of  providing design criteria for the air release valve and for the optimization of pipeline filling time within the constraints imposed by the upsurge containment.

2  THEORETICAL ANALYSIS

We referred to the geometric layout of the experimental pipeline of Albertson and Andrews (1971), Figure 1, which considers the pipeline filling operation performed with an air release valve placed in a peak of the pipeline and with the air vent initially open and allowing the air release. By means of a mathematical model, accounting for the elasticity of the water column, we analyzed the water hammer phenomenon due to the rapid flow deceleration which occurs when the liquid column strikes the automatic device which instantaneously closes after complete exhaustion of the air pocket.

Fig. 1  Schematic layout of the analyzed pipeline system.

The governing equations are obtained assuming the fluid as slightly compressible, linearly elastic and slightly deformable walls of the conduit and computing the head losses during the transient-state by means of the steady-state formula. The continuity and momentum equations give the following set of partial differential equations:

                                                          (1)

where A is the cross sectional area of the pipeline, g is gravitational acceleration, c is celerity, J represents the distributed head losses, Q is the discharge and h is the pressure head.

The solution of this equation set was performed by the method of characteristics with initial and boundary conditions hereafter described assuming the discharge pipeline as divided into a number of reaches, the quantities without any subscripts as referred to the generic node placed at distance s from the pipeline upstream end.

Boundary conditions:

- at the first pipe section corresponding to the gate valve position:

                            H=H₀                                (2)

where H is the total pressure head and the subscript ‘o’ is referred to the gate valve section (s=0) and

                t > 0                            (3)

where Q_o,o is the discharge obtained with gate valve completely open, y is then meant as the ratio between the filling velocities respectively referred to the partial and complete opening of the gate valve. Equation (3) describes an instantaneous operation of the gate valve opening operation.

The boundary conditions at the air valve position at time before complete exhaustion of the air pocket can be written as:

                                       (4)

where subscripts u and d refer to the upstream and downstream nodes respectively, z is the coordinate vertical direction, positive upward, as in figure 2, W(z) is the horizontal cross sectional area of the interface between the air pocket and water.

                                    (5)

where U is the volume of the air pocket;

                                            (6)

describes the thermodynamical transformation of the air in the pocket with exponent n assumed equal to the safety value of 1.41 and p_a is the absolute pressure of air in the pipe. Q_a is the volumetric rate of the jet issuing the orifice and depends on the air pressure p_a. In particular p_a has a physical upper limit in a critical value p_c

              p_c =  p_atm / 0.527                             (7)

where p_atm is the atmospheric pressure. When p_a equals p_c the air jet occurs in sonic condition and its flow rate Q (m³/s) is found as equal to (Roth and Nucera, 1988):

                                             (8)

where w is the orifice area (m²).

For values of p_a less then the critical value, we have

                       (9)

After complete exhaustion of the air pocket we consider

Q_a=0                                   (10)

The above-defined set of conditions allows the analytical representation of the unsteady flow, following the sudden stoppage of the water column. The initial conditions are defined in all nodes as static conditions with gate valve closed, air vent open and air pocket confined in the peak of the pipeline (with z = 0) as in Figure 2. The gate valve at the end of the pipeline is considered always closed.

The model found a preliminary validation by means of the experimental data provided by experimental results (De Martino et al., 1985) obtained by the equipment schematically introduced by Kolp, as quoted by Albertson and Andrews, (1971). The transient was then analyzed for different hydraulic and geometrical configurations, in particular the ratio of the filling rate (y), the diameter of the pipeline (D), the diameter of the orifice (d), covering the entire range of the ratio d/D in real installation, and the static pressure head H₀.

Fig. 2  Air pocket placed in the peak of the pipeline at the initial condition

3  RESULTS AND CONCLUSION

Results of the numerical experiments highlight different interesting features of the phenomenon. In particular, comparing the data in figure 3a, b and c it is possible to observe that a smaller orifice allows to reduce the maximum upsurge pressures H_max which, on the other hand, result to increase with the filling rate (represented by y) and the total head H₀. Also, results show that if the air release valve is closed, the upsurge pressures are less than or equal (for high opening ratios) to those obtained in analogous other conditions but open air valve. Of course such a solution can not be considered acceptable due to the necessity of expel the entrapped air.

The initial volume of the air pocket, in the considered scheme is only determined by the pipeline diameter D and by the angle a (see Figure 3). The angle a was also varied within a large range covering technical values, showing a negligible influence on the maximum upsurge. Also the initial volume of the air pocket resulted practically not influent on the upsurge pressures for values filling rate less than 0.6Q_o,o  (y=0.6), as one can deduce by the inspection of figure 4 where H_max is represented versus the pipeline diameter D. Also, above y=0.6 the maximum upsurge pressures H_max increase with the initial air volume.

By the light of the presented results we propose a design methodology, based on a chart (figure 5) that allow to chose the optimal rate ratio to be used in the filling operation and the diameter of the air valve, as a function of the other hydraulic and geometrical characteristic of the pipeline and of the maximum allowed overpressures.

References

Albertson, M.L., and J.S., Andrews, Transients caused by air release, in “Control of flow in closed conduits”, Edited by J.P. Tullis, Fort Collins, Colorado, 1971.

Benfratello, G., Sulle sovrappressioni che si suscitano alla fine del riempimento delle tubazioni mobili, in Italian, L’Acqua, 5, 1958.

De Martino G., M. Giugni and M. Viparelli, La presenza dell’aria nelle condotte, in Italian, Idrotecnica, 1, 1985.

Gisonni, C., Confronto teorico-sperimentale di transitori in condotte in pressione causati da fuoriuscita d’aria, in Italian, XXVI Convegno di Idraulica e Costruzioni Idrauliche, Catania, 1998.

Roth, G., and D., Nucera, Sull’utilizzo di metodi di calcolo numerico nell’analisi di fenomeni transitori attraverso sfiati, in Italian, XXI Convegno di Idraulica e Costruzioni Idrauliche, L’Aquila, 1988.

Veronese A., Sul moto delle bolle d’aria nelle condotte d’acqua, in Italian, L’Energia Elettrica, 1937.

Viparelli, M., Sull’espulsione di sacche d’aria da condotte idriche, in Italian, Atti dell’Accademia Pontaniana, Napoli, 1989

Fig. 3  Maximum pressure head at the air vent, versus static pressure head,
for different ratios of the filling rate, D = 300 mm and, a) d = 30 mm; b) d = 24 mm; c) d = 18 mm.

Fig. 4  Maximum pressure head versus pipeline diameter D for different ratios of
the filling rate; d/D =0.06 and, a) H₀=90 m; b) H₀=120 m.

Fig. 5  Design chart: dependence of the ratio H_max/H₀ on d/D for
different ratios of the filling rate and a=30°.