*3.1. Experimental Model*

In order to study the emptying process in a pipeline, an experimental facility was developed (see Figure 4) at the Civil Engineering, Research and Innovation for Sustainability (CEris) Center, in the Hydraulic Lab of Instituto Superior Técnico (IST), University of Lisbon, Portugal. The experimental facility consisted of a set of transparent PVC pipes with 7.3 m length and nominal diameter of 63 mm (*DN*63). An air valve (*AV*1) was installed at the highest point of the pipeline with a pressure transducer (*PT*1) to measure the absolute pressure. The air valves *S*050 and *D*040 (manufacturer A.R.I.) and different air pocket sizes were tested for showing the effect on the hydraulic behaviour. There were four ball valves (*BVs*). *BV*1, *BV*2 and *BV*4 were opened, consequently permitting the movement of the water column. *BV*3 and manual valve (*MV*1) were closed and represented the system configuration extremities. The two manual ball valves (*MBVs*) identified as *MBV*1 and *MBV*2 with nominal diameter of 25 mm (*DN*25) at the downstream ends were used to control the outflow conditions. These valves have the same level as the horizontal pipes *<sup>L</sup>*1,2 and *L*2,2. Two free-surface small tanks were used to collect the drainage water. The PicoScope system was used for absolute pressure data recording. The frequency of the pressure data collection was 0.0062 s. The length of the emptying columns were measured by using a Sony Camera DSC-HX200V (Sony Corporation, Minato, Tokyo, Japan) for decomposing frames for each second. The water velocities were measured with an Ultrasonic Doppler Velocimetry (UDV) device with a transducer for 4 MHz frequency (MET FLOW, Lausanne, Switzerland). The transducer was located on the horizontal pipe with an angle of 20◦. To measure the water velocities, all other facilities were turned off in the Hydraulic Lab to avoid the noise, and seeding was used inside the water in order to ge<sup>t</sup> appropriate measurements.

**Figure 4.** The pipe system and its components.

The emptying process of the experimental facility was started by an opening maneuver at the same time as valves (*MBV*1) and (*MBV*2). Consequently, the two emptying columns started the emptying procedure until reaching the horizontal pipes when the drainage is practically stopped, and part of the two water columns remain inside the installation because the gravity term is zero in both pipe reaches.

Equations (8)–(14) were used to simulate the emptying process of this experimental facility. The gravity terms were computed for the two emptying columns. For the emptying column 1, it depends on:

• If the air-water interface located on the sloped pipe reaches *θ* = 30◦ (*Le*,<sup>1</sup> ≤ *<sup>L</sup>*1,1 + *<sup>L</sup>*1,2 and *Le*,<sup>1</sup> > *L*1,2), then:

$$\frac{\Delta z\_{\mathfrak{e},1}}{L\_{\mathfrak{e},1}} = \left(1 - \frac{L\_{1,2}}{L\_{\mathfrak{e},1}}\right) \sin(\theta\_{1,1}).\tag{18}$$

• If the air–water interface located on the horizontal pipe reaches *θ* = <sup>0</sup>◦(*Le*,<sup>1</sup> > 0 and *Le*,<sup>1</sup> ≤ *L*1,2), then:

$$\frac{\Delta z\_{\mathfrak{e},1}}{L\_{\mathfrak{e},1}} = 0.\tag{19}$$

The gravity term for emptying column 2 is similar in emptying column 1.

### *3.2. Experimental Results and Model Verification*

Ten experimental tests are selected as shown in Table 1, where two different air valves and five air pocket sizes were defined. The air valve *D*040 admits large quantities of air during the emptying process, and it has a diameter of 9.375 mm and *Cadm* of 0.375 according to the vacuum curve presented by the manufacturer. The air valve *S*050 is not recommended for vacuum protection because it has a smaller orifice of 3.175 mm. The manufacturer does not present a vacuum curve because it is used specially for relief in pressurized systems. Consequently, the *Cadm* was calibrated during the tests with a value of 0.303. The selection of the appropriate air valve size is of utmost importance. The initial air pocket lengths were 0.001, 0.540, 0.920, 1.320 and 2.120 m. To avoid a numerical problem in the proposed model, a minimum air pocket size around of 1 mm is imposed instead of 0 mm.


**Table 1.** Characteristics of tests.

In the model, a constant friction factor of *f* = 0.018 was used. Valves *MBV*1 and *MBV*2 were modeled by using a synthetic maneuver, with a flow factor of *K*1 = *K*2 = 1.4 × 10−<sup>3</sup> m3/s and a valve maneuvering time (*Tm*) of 1.6 s. The flow factor represents the local losses due to the opening of the valve and the reduction from *DN*63 to *DN*25. The expansion of the air pocket was modeled by using a polytropic model in adiabatic conditions (*k* = 1.4) because the event occurs very quickly.

According to the results, there are two types of behaviours that depend on the air valve: (1) air valve *S*050 (see Figure 5) and (2) air valve *D*040 (see Figure 6). In all tests, the proposed model can predict the subatmospheric pressure pattern. Test No. 1 and Test No. 6 were selected in order to compare results.

**Figure 5.** Comparison between computed and measured absolute pressure oscillation patterns (air valve S050): (**a**) Test No. 1; (**b**) Test No. 2; (**c**) Test No. 3; (**d**) Test No. 4; (**e**) Test No. 5.

Figure 5a shows Test No. 1 (air pocket size of 0.001 m) where the absolute pressure quickly reaches the minimum subatmospheric pressure of 9.61 *mH*20 at 1.69 s. Then, the absolute pressure pattern starts to increase slowly until it reaches the atmospheric condition. The duration of the hydraulic event is 40.3 s. In contrast, when the air valve *D*040 is used, small troughs of subatmospheric pressure occur and the hydraulic event is very short. Figure 6a shows the results for Test No. 6 (air pocket size of 0.001 m) where the absolute pressure decreases quickly until it reaches the minimum subatmospheric pressure of 10.16 *mH*20 at 1.82 s and then increases again until it reaches the atmospheric condition (10.33 *mH*20). The duration of the hydraulic event is 8.13 s. Figures 5 and 6 show that the pressure drop is linear due to the opening of the valves *MBV*1 and *MBV*2. Then, subatmospheric pressure is presented and the water flow starts to decrease since the air valve can admit a better ratio of the air flow. Consequently, the pressure pattern rises.

**Figure 6.** Comparison between computed and measured absolute pressure oscillation patterns (air valve D040): (**a**) Test No. 6; (**b**) Test No. 7; (**c**) Test No. 8; (**d**) Test No. 9; (**e**) Test No. 10.

In more complex and large systems, an air valve similar to *S*050 cannot be recommended as a protection device during the emptying process because, depending on the conditions of the installation, the subatmospheric pressure can reach excessively low values. Engineers should select an air valve similar to *D*040 for minimizing problems associated with the pressure drop to subatmospheric value.

The density of the air pocket is validated with the measurements of the absolute pressure, since these variables are related, because the temperature of the air pocket remains practically constant. Therefore, the results are similar considering an isothermal process (*k* = 1.0).

Figure 7 presents the evolution of the length of emptying columns 1 and 2 for Test No. 2 and Test No. 7. Figure 7a shows the results for Test No. 2 (air valve *S*050) where the emptying column 1 reached

the horizontal pipe at 28 s, while the emptying column 2 reached it at 29 s. This difference of 1 s was caused because the valves *MBV*1 and *MBV*2 were not opened exactly at the same time. In contrast, Figure 7 shows the results for Test No. 7 (air valve *D*040), where practically the two emptying column reached the horizontal pipe in 5 s because the hydraulic event in this case is faster. In both tests, the proposed model predicted the length of emptying columns. It is important to note that when the emptying column reaches the horizontal pipe *θ* = 0◦, the proposed model cannot be applied because air–water interface is parallel to the horizontal pipe direction (as a stratified flow).

**Figure 7.** Comparison between computed and measured length of emptying columns: (**a**) Test No. 2 (air valve *S*050); (**b**) Test No. 7 (air valve *D*040).

Figure 8 shows the comparison between computed and measured water velocity for Test No. 3 and Test No. 8. In both tests, the water velocity in emptying column 1 is practically the same as in emptying column 2 (*ve*,<sup>1</sup> ≈ *ve*,2). In addition, in all tests from 0 s to 1.6 s, the water velocity is induced by the opening of the valves *MBV*1 and *MBV*2. In this range of values, the measurements are not adequate because the system starts resting and the UDV cannot detect the suspended small seeding particles because of no reflection. However, after 1.6 s, the proposed model can predict adequately and give information about the system behaviour. Figure 8a presents the results for Test No. 3 (air valve *S*050) where the maximum water velocity is rapidly reached at 1.39 s, with a value of 0.076 m/s. According to the measurements, the maximum value is 0.0775 m/s at 1.30 s, which is very close to the proposed model. After the maximum value is attained, the water velocity decreases linearly until it reaches a value of 0 m/s at 34 s. The oscillations around 2 s are caused after the complete opening of valves *MBV*1 and *MBV*2. The water velocity range is very low during the emptying procedure with the air valve *S*050. Consequently, the UDV device with a transducer of 4 MHz frequency cannot detect appropriately the evolution of the water velocity. It records water velocity with intervals of 0.015 m/s. Figure 8b shows the comparison between computed and measured water velocities for the air valve *D*040 where the water velocity reaches its maximum value of 0.324 m/s at 1.77 s. According to the measurements, the maximum value is 0.32 m/s at 1.78 s, which is quite similar to the proposed model. After this maximum, the water velocity starts to decrease until the end of the event. During this range, the UDV device can measure appropriately the evolution of the water velocity. The volume of admitted air by *D*040 is almost the same as the water volume drained by valves *MBV*1 and *MBV*2 since the minimum subatmospheric pressure is 10.22 *mH*20, practically the atmospheric pressure.

**Figure 8.** Comparison of water velocity between computed and measured values: (**a**) Test No. 3 (air valve *S*050); (**b**) Test No. 8 (air valve *D*040).
