In many areas of the world water distribution systems are operated intermittently. The alternate filling and emptying of the pipe network leads to effects, which have negative impacts on water meter accuracy. For example, air that is present in the pipe network due to the emptying process must exit the network during the subsequent filling process. A part of this air is discharged through service connections and, thus, through water meters. In this paper, a study is presented in which the measurement error of single-jet and multi-jet water meters due to the filling process of an empty pipe is investigated experimentally. From the start of air flow to the steady-state flow of water, several causes of measurement errors can be distinguished, such as pure air flow, the impact of the water front on the impeller, the existence of two-phase flow or unsteady flow conditions. For both meter types, it has been discovered that the measurement error is mainly caused by the air flow. The experimental results show that up to 93% of the air volume in the pipe is registered by the water meters. Based on these results, an approach for estimating the measurement error for both meter types is presented.
In water supply systems, single- and multi-jet water meters, which cumulatively determine the volume of water flowing through, are used to measure delivery to the customer. Both water meter types have an impeller on the inside which is set in rotational motion by a single or multiple water jets that flow against the impeller tangentially. The impeller's revolutions are transmitted via gears to a roller counter which displays the volume that flowed through. While all the water flows through the impeller of single-jet water meters, part of the water in a multi-jet water meter goes around the impeller via an adjustable bypass. By variably dividing both flows, multi-jet meters can also be calibrated (Arregui et al. 2006).
The accuracy requirements and tolerated limits of error for water meters are regulated in ISO 4064 (2014). The error tolerance is divided into an upper and lower zone with error limits of ±2% and ±5%, respectively. These error limits only apply to calibration in state-approved test facilities. Maximum error limits, which are double those for calibration, i.e. ±4% and ±10%, respectively, apply when installed. A precondition for an accurate measurement is that water meters are used in line with their conceptual design. Among other things, the water meter must be completely filled with water and vented (DVGW worksheet W 406 2012; ISO 4064 2014).
However, in many regions of the world, water distribution systems are operated intermittently. The distribution systems are thus filled with water for a limited time and are not constantly under pressure (De Marchis et al. 2010; Klingel & Nestmann 2014). To guarantee constant water supply for domestic use, consumers store the water in private tanks. Especially in development countries with high water scarcity and flat-rate tariffs being used by the supply system operator, the consumers try to obtain a higher amount of water by keeping the service connections constantly opened. Hence, the pipe network is partially or completely drained after a supply period, before being refilled in the subsequent period (Farley & Trow 2003; Totsuka et al. 2004; Kingdom et al. 2006).
If an air-filled distribution system is filled with water, a two-layer water front spreads out in the distribution mains from the entry point. A first, higher speed front forms on the lower side of the pipe and a second lower speed front forms on the upper side of the pipe. Atmospheric pressure is present in the pipe in front of the first (lower) water front. Between the first and second front, the pressure increases linearly, with the pressure within the air volume over the first front being equal to the pressure in the water-filled area (Liou & Hunt 1996; Guizani et al. 2006; Hou et al. 2014). The advancing front pushes the air present in the system out of the pipe network through, amongst others, service connection pipes. This part of the air flows through the domestic water meters, thus causing them to work contrary to their initial design (Van Zyl 2011).
While some causes of measurement inaccuracies of water meters used in intermittently operated water supply systems have already been exhaustively analysed, such as meter under-registration due to the use of domestic storage by Feldtmann (1985), Rizzo & Cilia (2005), Cobacho et al. (2008) and Tamari & Ploquet (2012), increased wear of water meters by Arregui et al. (2007) and Criminisi et al. (2009), as well as deposits in water meters by Arregui et al. (2005), there exist no studies on the extent to which an air flow or a two-phase flow of air and water falsifies water meter measurements. Thus, the authors developed an experimental set-up to analyse measurement errors of water meters during the filling of a pipe under atmospheric pressure. Since the characteristics of single-jet water meters (Q3 = 2.5 R80H) have been described in Walter et al. (2017), this article presents the measurement error of multi-jet water meters (Q3 = 4 R80H) and compares the results of both meter types. The study's parameters are the air volume Vair before the water meter and pipe pressure p1,stat. Since the water meter casing can either be dry or contain an initial amount of water, the basic correlation between measurement error, pipe pressure, and air volume for dry and wet casings is presented.
Experimental set-up and test procedure
The experimental set-up is represented schematically in Figure 1. A 15 m high water tower with two branches at its foot supplies the measuring section. The first branch goes through valve S3 and a pump to a water-filled tank, thus making the water level in the tower steplessly adjustable. The second branch goes through valve S1 to the measuring section of the experimental rig. Pressure sensor P1 measures pressure p1 in front of valve S1, while sensor P2 measures pressure p2 in front of the water meter. When valve S1 is closed, the water level in the water tower or hydrostatic pressure p1,stat is measured. With the opening of valve S1 at the time tp1,start, the water column begins to move and pressure p1 drops abruptly. When the water front reaches P2 at the time tp2,start, there is a sudden increase of pressure p2. If there is no further change in pressure p2, the unsteady movement of the water column has ended and thus a steady-state flow with constant flow rate is reached at the time tp2,const.
The air volume Vair in front of the water meter can be varied using hoses of different lengths LS. This study used calibrated, dry-running single- and multi-jet water meters manufactured by ZENNER International GmbH & Co. KG of type ETKD-N for size Q3 = 2.5 and MTKD-N for size Q3 = 4, respectively, and accuracy class R80H. The water meter determines volume Vwm, which comprises a mix of air and water. An optical sensor detects the throughput of each rib of the water meter's low-flow indicator as impulse Ij, so that the flow Qwm(t) can be calculated from the rotation frequency. The flow can be stopped by closing valve S2. The resulting pressure surge at the time tp2,wh is also measured by P2.
A tank with diameter Dt stores the entire volume of water Vt that flows out of the measuring section. Pressure sensor P3 helps to detect the water level in the tank. The analogue signals of the measuring instruments are recorded and digitized synchronously with a 1,000 Hz sampling frequency by an analogue-to-digital converter with a 12-bit resolution. The experimental set-up is consistent with ISO 4064 (2014) standards.
Determination of measurement error
During an event, i.e. from the start of air flow up to steady-state water flow through the water meter, several causes of measurement errors all adding up to Etotal can be defined. Once the water front starts moving, air inevitably flows through the water meter. The volume is recorded by the water meter when air flows exclusively is defined as measurement error Eair. Using the experimental setup described, all additional causes of measurement errors can only be partially differentiated from one another and are therefore integrated under measurement error Erest. This contains errors arising from the water front impacting the impeller (impulse from an abrupt change in density), air bubbles entering the front of the water column (two-phase flow), the unsteady flow condition (inertial forces of the impeller's rotation), the steady-state flow condition (permissible measuring error according to ISO 4064), and the abrupt stoppage of flow (wake behaviour; only relevant in the experiment).
The illustrated test procedure was conducted for hose lengths of LS = 1, 2, 3, 5, 10, 15, 20 and 25 m that resulted in air volumes of Vair = 0.48, 0.78, 1.08, 1.67, 3.17, 4.66, 6.15, and 7.65 L for single-jet water meters. For multi-jet water meters Vair increases by additional 0.07 L due to the larger volume of the water meter casing. On account of the impeller rotating at very high speeds while air flows through and the filling process of service connections in intermittently operated water distribution systems being consistently marked by small pressures or pressure gradients, pressures p1,stat = 0.1 bar up to a maximum of 1.0 bar were analysed in steps of 0.1 bar. If the casing of the water meter is not completely dry, the movement of the impeller is disturbed by the initial water in the casing. This affects the starting behaviour of the impeller and leads to additional dependence of measurement error Eair on pressure p1,stat. Therefore, measurements were also conducted for the listed volumes using wet casings. Based on the differing geometry of both meter types, single-jet water meters were tested up to p1,stat = 0.5 bar, while multi-jet water meters were tested up to p1,stat = 1.0 bar. Three measurements were conducted for each parameter combination to calculate the mean value.
RESULTS AND DISCUSSION
Compared to the total measurement error Etotal, error Erest results in low values that mostly fluctuate around zero and may be positive or negative. For all tested combinations of Vair and p1,stat there was a positive mean value of Erest,mv = +0.10 L and a negative mean value of Erest,mv = −0.14 L. Regarding the low values of Erest it can be concluded that, Etotal depends substantially on measurement error Eair, which is described below in more detail.
Eair for single-jet water meters and dry casing
In Figure 2(a) Eair is plotted for various pressures p1,stat dependent on the air volume Vair using a dry meter casing. Eair is relatively independent of pressure p1,stat for p1,stat ≥ 0.2 bar and, therefore, depends only on air volume Vair. The measurement error increases continuously with an increase in air volume. Starting at Vair = 1.08 L a linear relationship between Vair and Eair is recognisable. Eair decreases nonlinearly for smaller volumes and must inevitably end at zero, since there is no air volume in front of the water meter tp1,start = tp2,start and, thus, Eair = 0 is valid.
Occasionally, measurement error Eair for p1,stat = 0.1 bar is comparatively low. A reason for this may be the relatively unstable build-up of the water front. For lower pressures p1,stat and, thus, lower flow rates, the front shows a more marked development and both layers of the front form with a greater distance between them. Once the forward layer of the front reaches the pressure sensor P2 at time tp2,start, pressure p2 rises and the recording of air flow stops. Therefore, the air volume above the first layer is not contained in volume Eair. Consequently, it can be inferred that the conclusions drawn here regarding Eair are valid for p1,stat ≥ 0.2 bar.
The mean values Eair,mv,d of all measurements with p1,stat ≥ 0.2 bar from Figure 2(a) are plotted in Figure 2(b). The gradient of Eair,mv,d in the linear range, and thus the deviation in volume due to the medium of air, is 96%. In addition, a linear function Eair,mv,d,lin with the same gradient but running through the origin is illustrated. The vertical offset of the curve Eair,mv,d compared to Eair,mv,d,lin can be explained by the starting resistance of the impeller which leads to an additional deviation in volume. When air flow starts, the inertial forces of the impeller and the register must be overcome. Thus, the front part of the air column flows through the water meter being under-registered. The vertical distance between Eair,mv,d and Eair,mv,d,lin therefore constitutes the mean value of the volume ΔEinert not registered due to the inertial forces of the impeller (ΔEinert = 0.57 L in the linear range).
An air volume Vair < 1.08 L results in a non-linear relationship between air volume and measurement error. The decline of ΔEinert for small air volumes can be explained by the compression of the air that inevitably occurs directly in front of the water front. This leads to a density and pressure gradient in the air column. For short hose lengths LS, this compressed part of the air column flows through the water meter while the impeller starts up. Additional acceleration occurs as a result of the pressure gradient, thus letting the impeller start turning earlier. The specific approximations for the linear and non-linear range of Eair,mv,d can be found in Figure 2(b).
Eair for single-jet water meters and wet casing
Dependent on the air volume Vair, measurement error Eair in Figure 2(c) is plotted for various pressures p1,stat using a wet meter casing. Eair,mv,d, the mean value error curve for a dry casing from Figure 2(b), is also plotted. Compared to Eair,mv,d, a significantly smaller volume Eair results from p1,stat = 0.1 bar. Starting from a pressure of p1,stat = 0.3 bar, abruptly larger volumes Eair are recorded, which come closer to Eair,mv,d with increasing pressure. Volumes of Eair for p1,stat = 0.2 bar, are partly in the range of the results for p1,stat = 0.1 and 0.3 bar. Hence, the error curve can be divided in an upper and a lower range with p1,stat = 0.2 bar being the border between the ranges. In spite of the additional dependence on pressure, there is mostly also an approximately linear relationship between Vair and Eair.
The speed of the water front and thus, the speed of the air column depends on pressure p1,stat. For measurements with p1,stat= 0.1 bar, the speed of the air column at the beginning is too low to push a significant part of the water out of the casing. As a result, the rotational motion of the impeller is affected by the initial water during air flow, which is resulting in very low values for Eair. When p1,stat ≥ 0.3 bar the speed is high enough to carry a part of the water out of the casing. Larger volumes are registered for Eair as a result of the freer rotational motion of the impeller. With increasing pressure, a larger part of the water is displaced from the casing, thus suggesting a correlation between Eair and p1,stat.
The mean values Eair,mv,w of all measurements using a wet casing for the range above and below 0.2 bar is illustrated in Figure 2(d). The specific approximations are also given in each case, in which only the approximations in the upper range, analogous to a dry meter casing, must be divided into two sections. With a wet casing, the average error curves for small air volumes can also be described sufficiently using linear approximations.
Eair for multi-jet water meters and dry casing
In Figure 3(a) Eair is plotted for various pressures p1,stat dependent on the air volume Vair using a dry meter casing. Unlike the results of the single-jet water meter, there exists a correlation between Eair and p1,stat. With higher pressures p1,stat the gradient of the error curve decreases continuously and error Eair becomes smaller. Analogous to single-jet water meters, each error curve can also be divided into a linear and a non-linear section. The smallest error results from p1,stat = 1.0 bar with a gradient in the linear range of 58% and the highest error results from p1,stat = 0.2 bar with a gradient in the linear range of 150%. The results for p1,stat = 0.1 bar do not follow this behaviour and show slightly smaller values for Eair since the build-up of the water front has an additional influence on Eair.
A possible explanation for the dependence of Eair on p1,stat may be found in the rotational motion of the impeller and the existence of the bypass. The bearing and the axis of the impeller are designed to operate in water, a medium with a density a thousand times higher than air. Especially for high pressures, when the impeller has a high rotational velocity, a vibrational sound can be detected. A vibration of the impeller or the axis would increase the turning resistance of the impeller and, thus, leads to a higher pressure loss for the flow through the impeller. Hence, more air would flow through the bypass, not being registered by the water meter. For very low pressures, an oppositional effect could occur. If, during a low air flow, a smaller air volume flows through the bypass than when the meter is filled with water as a result of e.g. compressible effects, a disproportionate measurement of volume would occur compared to the calibrated state.
Within measurements with the same parameter combination and a dry casing, single-jet water meters have a very high reproducibility of the values for Eair but for multi-jet water meters there is a greater dispersion of the values for Eair. Therefore, several outliners can be observed in the linear section of Eair in Figure 3(a). However, a linear approximation Eair,d,lin for Vair ≥ 1.74 L and a non-linear approximation Eair,d,nonlin for Vair < 1.74 L has been established and plotted in Figure 3(b) to describe Eair as a function of Vair and p1,stat.
Eair for multi-jet water meters and wet casing
Depending on air volume Vair, measurement error Eair in Figure 3(c) is plotted for various pressures p1,stat using a wet meter casing. The error curves for a dry meter casing with p1,stat = 0.2 and 1.0 bar from Figure 3(b) and thus, the upper and lower limits of the error range are also plotted. Compared to these error curves, a significantly smaller volume for Eair is registered for all tested pressures. There is a linear correlation between Vair and Eair and Eair shows no dependence on p1,stat. A sudden rise of the values for higher pressures, as seen for single-jet meters, cannot be observed. This behaviour can be explained by the structure of the measuring chamber of the multi-jet water meter (Figure 1). The measuring chamber is divided into a lower and an upper chamber connected by the impeller. Therefore, the water or the air must flow vertically from the lower chamber to the upper chamber through the impeller. For the initial water in the lower measuring chamber, the velocity of the air flow within the tested pressures is not high enough to lift the water up from the lower chamber. Hence, the rotational motion of the impeller is disturbed while the total volume of air is measured resulting in very low values for Eair.
The mean value Eair,mv,w of all measurements using a wet meter casing is illustrated in Figure 3(d). Here, the specific approximation can be described for the entire range by means of a linear relationship.
This article presents a study in which the influence of a water front driven air flow on the measurement accuracy of single- and multi-jet water meters with dry and wet meter casings was investigated experimentally. The experiment leads to the following conclusions:
The measurement error Erest consists of very low positive and negative values that fluctuate around zero. The total measurement error Etotal thus results significantly from the measurement error Eair. Therefore, Erest can be neglected in Equations (3)–(11) for estimating Etotal.
For single-jet water meters and dry meter casings the measurement error is independent of pipe pressure p1,stat and only depends on the air volume Vair in front of the water meter. Depending on Vair, measurement error Etotal can be estimated using Equations (4) and (5).
For single-jet water meters and wet meter casings, there is an additional dependence on pressure p1,stat, because the initial water in the casing causes a substantial increase of the impeller's starting resistance. This dependence is distinctive for p1,stat = 0.1 bar, but decreases with increasing pressure. Depending on Vair, error Etotal can be approximated using Equations (6)–(8).
For multi-jet water meters and dry meter casings, the measurement error depends on pipe pressure p1,stat and air volume Vair. With higher pressures, the error Etotal becomes continuously smaller. For estimating Etotal depending on p1,stat and Vair, Equations (9) and (10) can be used.
For multi-jet water meters and wet meter casings, there is no dependence on pipe pressure, since, on account of the geometry of the measuring chamber, the initial water remains in the chamber for all tested pressures and affects the rotational motion of the impeller in each case. Depending on Vair, measurement error Etotal can be approximated using Equation (11).