AIR INLET VALVE AS A PROTECTION DEVICE  AGAINST WATER HAMMER

A. Castorani, A. Di Santo and A. F. Piccinni

Dep. Civil and Environmental Engineering

Polytechnic of Bari – Italy

Abstract: This paper reports the results of a theoretical and experimental investigation to prove the effectiveness of an air inlet valve as a protection device against water hammer in delivery mains of pumping stations where, upon sudden stopping of pumps, cavitation conditions may occur close to the station. Theoretical research has proved that the valve, though simple and of very low cost, can considerably reduce pressure rise resulting from unsteady flow and the first experimental results fully confirm the forecasts of the theoretical model.

1    INTRODUCTION

Pumping stations for sewage present greater management problems because of the low reliability of devices for the protection against unsteady flow, the operation of which is challenged by the quality of the fluid to be conveyed. Experiences have proven that the use of air chambers, a classical protection system, is extremely expensive due to continuous maintenance required for air volume control devices. To face the problem of stopping and starting of pumps, inverters (Fiori et al., 1996) can be useful but they don’t solve the problem of sudden stopping of the station due to blackout; on the other hand, fly-wheels are no longer proposable since they require a starting torque  incompatible with cost-effective management of the works. Thus, the use of mechanical devices like “water hammer” valves, by-passes, or the like, may apply to reduce unsteady flow phenomena.

An air inlet valve can efficiently reduce water hammer following on cavitation conditions close to delivery mains in pumping stations.

The operation principle is to let air enter into the pipeline during the pressure drop stage, upon sudden stopping of pumps, and to retain it at the successive stage with the occurrence of the backward wave that will tend to compress it: it will behave as the air volume in the air chamber. Investigation on this type of valve was carried out both theoretically, through mathematical models to determine the peculiarities of the phenomenon, and experimentally in the laboratory; a good agreement with the forecasts of the model was found.

2    DESCRIPTION OF THE PHENOMENON

Consider a classical pumping station,  as represented in Fig. 1, except the presence of a valve, close to the pipe and downstream of the non-return valve protecting the pumps, situated on the upper generatrix of the same pipe that is closed when the pressure in the pipe is higher than atmospheric and opens, to let the air come in, when the pressure in the pipe drops below atmospheric. If, upon sudden stopping of pumps, hydrodynamic conditions of a pressure lower than atmospheric do occur at the initial section of the pipe, the air inlet valve opens and the air enters the conduit. In that case absolute pressure will be between 0 and atmospheric pressure and the flow will be positive or different from zero. The entrance of air will create an air pocket zone that will continuously increase and expand as long as the flow at the initial section is positive. When the initial section starts having hydrodynamic conditions with negative flow rates, pressure progressively rises. The air pocket continues to expand until the value of pressure is equal to or greater than atmospheric pressure and the air inlet valve closes.  From that moment, the subsequent hydrodynamic conditions, with negative flow rate, provoke the compression of the air trapped in the pocket until it reaches the maximum pressure value corresponding to zero flow rate. At that moment, air expansion starts in the pocket and causes positive flow and a decrease in pressure: if such pressure drops again below atmospheric pressure the air inlet valve opens again, otherwise an oscillatory movement with successive compressions and expansions of air similar to the one occurring in the air chamber starts.  This oscillation subsequently attenuates because of internal friction of the system.

Fig. 1    Definition sketch of the pump-discharge system

3    THE MATHEMATICAL MODEL

We will not deal here with the mathematical model representative of the unsteady flow phenomena, but with the boundary conditions describing the phenomena of air entrance and compression close to the delivery main.

When the ratio of the absolute air pressure to the pressure at the vena contracta exceeds 0.527, the outflow conditions of the orifice no longer depend on the downstream parameters: the velocity through the orifice is constant and equal to the sound velocity under the prevailing temperature and pressure conditions. Different formulas depending if it is a subsonic (P₂/P₁ > 0.527) or sonic regime (P₂/P₁ ≤ 0.527) then calculate the air discharge. Moreover, the processes downstream of the orifice are different depending if the outflow occurs in subsonic regime, in that case the reversible adiabatic process law is applicable, or in sonic regime, since in this case a chock wave which is an irreversible process is generated.

Fig. 2    Representative model of air inlet valve

In our specific case, referring to Figure 2, we consider the case of air entrance in a conduit through an orifice, when, because of a pressure drop, the air inlet valve opens. In the conduit, an absolute pressure P₂ lower than atmospheric will prevail, whereas outside of it the absolute pressure P₁ equal to atmospheric will prevail. If P₂/P₁ > 0.527 the regime will be subsonic and the flow rate close to the air-water interface will be given by the relationship (Di Santo e Piccinni; 1997):

                      (1)

When the pressure drop in the pipe reduces the pressure ratio below the critical threshold (P₂/P₁<0.527), the entrance of air occurs in sonic regime and the mass flow through the orifice is constant, even if P₂ continues to decrease, since the pressure P_c is constant and equal to 0.527 m of water column. In this case the equation is:

                               (2)

Equations (1) and (2) within the limits of their own domain of applicability, define the boundary conditions applicable for the description of the entrance of air into the pipe.

4    ANALYSIS OF THE PHENOMENON THROUGH THE MATHEMATICAL MODEL

The phenomenon was analysed using a mathematical model for studying the unsteady flow in elastic regime, to understand how some typical parameters of the pumping station affect it and especially the values of absolute maximum H_max and minimum H_min pressure rises. The investigated parameters are: regime flow rate Q₀ or the regime velocity V₀; length L of the delivery main; absolute pressure close to the station under static conditions H_s; size of the orifice of the air inlet valve, assumed to be equal to the size of the valve, represented by the diameter of the latter.  A wide range of values of these parameters were investigated; to be noticed that, though the results are presented quantitatively for some special cases, they are qualitatively valid in the whole investigated range. 

    Figures 3a, 3b, 3c illustrate the patterns of H_max, H_min and W_max, where W_max is the maximum value the air pocket reaches during the evolution of the phenomenon, as a function of Q₀, for one of the examined cases.

Fig. 3    Variability of H_max (a), W_max (b) and H_min (c) with regime flow rate Q₀.

It is evident that maximum pressure rise decreases when the flow rate, or the velocity, increases. This occurs because when velocity increases, the value of the initial pressure drop and, consequently, the amount of air sucked in the time unit increase. On the other hand, the duration of the suction stage is also related to the period of mass oscillation that takes place during the process in a way similar to that of air chambers. It increases with the volume of air, so that, globally, the total volume of sucked air increases, thus allowing the system to have a greater capacity to attenuate unsteady flow pressure rises - as it is also the case in air chambers where if the initial air volume in the chamber increases, the pressure rise value decreases - and, in our case, this effect prevails over the tendency of the pressure rise to increase due to increased initial velocity.

Figures 4a, 4b, 4c represent the effect of the change in size of the air inlet valve orifice.
The peculiarity of the maximum pressure rise diagram (Fig. 4a) is its tendency to converge towards a lower threshold value with the increase in diameter of the valve orifice. The graph of figure 4b shows that with the increase in diameter d the volume of air pocket tends to a maximum and, correspondingly, the value of minimum pressure in the pipe, as from Figure 4c, tends to a value close to atmospheric pressure.

Fig. 4    Variability of H_max (a), W_max (b) and H_min (c)  versus orifice diameter d.

Remember that the law representing the suction of air into the pipe is different depending if the suction occurs in sonic or subsonic regime. In figure 4c, two fields in the diagram of minimum pressure corresponding to 5.3 m of absolute pressure are identified. Notice that for orifice diameter values greater than the said pressure value and that provoke the entrance of air in subsonic regime, there are no great variations in the decrease of maximum pressure rise or in the increase of the maximum value of the air pocket. But, greater diameters limit the value of minimum pressure. This behaviour, the same as those previously illustrated, was observed in the whole investigated range with the variations in the typical parameters of the plant. If we assume, as a design parameter, that the minimum absolute pressure in the pipe is exactly equal to 5.3 m, through equation (1) and considering the continuity equation in a discrete form at the initial section of the pipe - supposing that at the instant immediately after the stopping of the station the velocity value is almost equal to the regime one - we define, as a function of the regime velocity, the valve size to pipe size ratio, that is:

                              (3)

5    LABORATORY TESTS

In the laboratory of Water Engineering of the Polytechnic of Bari, some experimental trials were carried out to check the results of the theoretical investigation.

We used a slightly modified previously existing experimental plant schematically represented in Fig. 5.

We used a welded steel DN 53 mm pipe extending, through a quadrangular spiral with bends large enough to be neglected, over a total length of 341 m. The pipe takes water from a pumping station that can deliver a maximum flow rate of 3.5 l/s with a head of approximately 22.0 m. Lower flow rates can be obtained by partial closure of the ball valve downstream of the non-return valve protecting the pump. The suction pipe of the pump is 4 m long and withdraws water under head from a tank with a free water level at about 0.5 m. On such a pipe, a Woltman type flow meter is installed. The pipe ends in a raised tank where the free water surface is kept constant through a weir located at 4.33 m above the laboratory floor, from which water flows back to the previous tank.

Fig. 5    Representation of the experimental installation.

At a distance of 0.5 m downstream of the ball valve, an upward oriented T fitting of the same diameter as the pipe is inserted; the air inlet valves were mounted on such a diversion. During this early stage of the investigation aimed at checking the peculiarity of the phenomenon rather than at fully defining the influence of all the magnitudes involved, we used a set of commercial “Europa” type non-return valves of different diameters to construct the air inlet valve. For each valve, three tests were performed corresponding to three different regime conditions with initial velocity value equal to about 1.5, 1.0 and 0,5 m/s obtained through the ball valve situated downstream of the pump. For each trial, the regime condition was determined by measuring the flow rate through the flow meter situated upstream and the pressure downstream of the valve  by a Bourdon type precision manometer  and a transducer located at the same section. The steady state conditions being reached, the valve was quickly closed thus provoking the previously described unsteady flow.

The unsteady flow phenomenon was detected by measuring the pressure through the differential pressure transducer with a maximum value of 300 psi, connected to a signal conditioner that, in turn, was connected to an acquisition card mounted on a PC with dedicated software. Data acquisition had a sampling frequency of 200 data per second.

Of course, before performing the trials with the air inlet valve, experiments were made in its absence in order to make a numerical comparison and then assess its benefits. Figure 6 reports the graphs relative to the trials with maximum velocity equal to 1.6 m/s in the absence of the valve and with the presence of a DN 1.5” air inlet valve.

Fig.6    Pressure trace in presence or in absence of a air valve

The illustrated behaviour is a general one. Detailed results are given in table 1.  

Table1    Comparison between experimental results and mathematical model.

The table confirms the validity of the analysis made with the mathematical models, at least for the parameters we could change in the laboratory set up.

Indeed, the area available for the entrance of air doesn’t coincide with the one that can be calculated considering the diameter of the air inlet valve; it should correspond to the surface area of the cylinder left free by the run of the shutter. The attempts made to measure it gave unsatisfactory results since the errors made, at least with the methodologies adopted at this stage, could not allow defining its magnitude correctly. However, it is observed that in all the trials performed, the pressure drop value remained  always above the subsonic operational limit; this implies that the range of the trial had always been of a diameter d greater than the minimum one given by (3).

    From the analysis of the table it is noticed that the value of the initial velocity poorly affects the maximum value of pressure: we are in the range (h_a=0.7) within which  H_max doesn’t change greatly if velocity increases.

    The H_max values are almost constant and tend to increase with the decrease in the diameter of the valve. On the other hand, it is clearly noticed that, in agreement with the theoretical investigation, the H_min value decreases with it.

6    CONCLUSIONS

The theoretical investigation and the first laboratory trials for studying the use of an air inlet valve as a device for protection against water hammer in low head pumping stations have proved the effectiveness of this device. It has high potentiality especially considering  the low installation cost.

Some uncertainties still remain on how the phenomenon actually occurs in the pipe. Further investigations, already scheduled, will allow defining better the design approach of the orifice for the entrance of air into the pipe. In fact, at this stage, since commercial non-return valves were used, it was not possible to study the phenomenal with due accuracy.

Also, experimentation should be extended to real operating pumping stations where the possible advantages and disadvantages of the device could be better investigated.

References

Allievi L.: “Camere d’aria nelle tubazioni prementi” L’elettrotecnica, 1936.

De Martino G., Giugni M., Viparelli M. - “La presenza dell’aria nelle condotte”, Idrotecnica, 1995.

De Martino G., Giugni M., Viparelli M. - “Transitori in condotte idriche causati da fuoriuscita d’aria”, Idrotecnica, 1996.

Di Santo A, Piccinni A.F. – “La valvola di ingresso d’aria come dispositivo di protezione ai fenomeni di moto vario” Giornate di studio in onore del Prof. E. Orabona nel centenario della nascita, Bari, 13-14 ottobre 1997.

Evangelisti G.: “Il colpo d’ariete nelle condotte elevatorie munite di camere d’aria” L’Energia Elettrica 1938.

Fiori G., Fratino U., Piccinni A. F. - “Il controllo del moto vario negli impianti di sollevamento per fognatura”, Scritti in onore di Mario Ippolito; Napoli 16-17 Maggio, 1996.

Fok A.T.K.: “Design charts for air chambers on pump pipe lines” Journal of Hydraulics Division, ASCE 1978.

Graze H.R.: Discussion of “Pressure surge attenuation utilizing an air chamber” by Wood D.J., Journal of Hydraulics Division, ASCE 1971.

Meunier M - “Les coups de bélier et la protection de resaux d’eau sous pression”, Ecole Nationale du Génie, des Eaux et des Forêts, Parigi, 1980.

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