**3. Results**

### *3.1. Tests with Closed BV*

When the BV is closed, the WH allows the observation of the storage ability of each AP. This type of transient action is important in protection vessels and also in SS-CAES applications. The measured pressure shows that the AP is able to retain an amount of pressure as stored energy after finishing the tests due to the compressibility and confinement effects. Figure 2 shows the pressure change for different velocities of an AP = 3 cm (VFR = 4.75%). The pressure related to the first peak is called "peak pressure" and is referred by P1p. As in Figure 2, an amount of pressure has been stored in the air pocket after the test which is called "stored pressure" and is shown by Ps. Graphs show a large growth in the peak pressure with increasing Re, while similar growth does not occur in the stored pressure. As it can be seen in Figure 2, from Re of 36,000 to 155,000, the peak pressure is changed from 1.33 bar to 6.25 bar. However, the stored pressure in the AP varied from 2.33 bar to 4.51 bar. Previous work [17] showed that either decreasing the VFR or increasing the Re will amplify the peak pressure considerably. Similar behavior exists for the stored pressure change, i.e., stored pressure with direct correlation to the flow velocity, but this is in contrast to the VFR. Results show that decreasing the VFR will continuously increase the stored amount of energy. For the VFR = 4.75% shown in Figure 2, the pressure change during 5WH and 9WH tests starts by increasing steeply and eventually ends up at the final stored pressure with smaller increases. The final magnitude of the stored pressure is also directly related with Re.

When comparing the stored pressure and peak pressure, in most of the tests the magnitude of the stored pressure is higher than the peak pressure, as expected. However, in some tests related to small AP and high Re, the amount of peak pressure is extremely high and even after the pressure storage cycles, the stored pressure remains smaller than the peak pressure. Some general rules can be stated based on results from these tests for all the Re and VFR as shown in Figure 3:


**Figure 2.** *Cont.*

**Figure 2.** Pressure change in the air pocket (AP) for different water hammer (WH) events and Reynolds number (Re) for the volume fraction ratio VFR = 4.75%.

**Figure 3.** Comparison of the final stored pressure (Ps) with the first peak (P1p).

As a logical expectation, the final stored pressure should be higher in the 9WH test in comparison to the 5WH test as a consequence of more WH events. Nevertheless, graphs show higher pressure storage magnitudes in 9WH tests when Re is low while for higher Re, the recorded pressure magnitudes of 9WH tests become less than or equal to 5WH pressure magnitudes. Large AP lengths of 20 cm and 40 cm (VFR > 30%) do not obey this rule; in other words, for these two APs, the recorded pressure of 9WH is always higher than for 5WH values. A comparison of the pressure magnitudes of 9WH and 5WH is presented in Figure 4, demonstrating the non-conforming behavior of a small VFR and high Re values.

**Figure 4.** Comparison between the first peak for 5WH and 9WH as a function of Re and VFR.

Figures 5 and 6 show the route of change in pressure recorded from 1WH, 5WH and 9WH tests for AP lengths of 10 cm and 40 cm (VFR of 15.84% and 63.35% respectively) in order to demonstrate the behavior of an AP in more detail. For small values of VFR, as in Figures 4 and 5, pressure variation shows irregular steps during the WH events. In the case of low Re values, small and almost equal steps have been recorded for all VFR. The larger values of Re show big increments at first WH steps and fast dissipation steps at the final events. In addition to irregular steps, considerable higher stored pressure was not recorded for the 9WH in comparison with the 5WH test, representing behavior against the usual expectation for obtaining higher stored pressure as a consequence of more WH events. On the other hand, the magnitude of pressure steps remains nearly constant for every Re value related to a high VFR in measurements similar to Figure 6. Furthermore, in this range, the stored pressure of 9WH tests always stays larger than the 5WH stored pressure, as explained before. Accordingly, 1WH tests are shown to be regular and constantly increasing in the stored pressure when increasing the Re number.

**Figure 5.** *Cont.*

**Figure 6.** *Cont.*

**Figure 6.** Pressure change in the AP for various WH events and Re for the VFR = 63.35%.

In fact, the rules for changing the stored pressure with VFR and Re are the same in all the tests, as stated below and shown in Figure 7:


**Figure 7.** Stored pressure change against Re and VFR for various WH tests.

Finally, the curves in Figure 7 show that for the VFR < 15%, the stored pressure of all three groups of tests, i.e., 1WH, 5WH and 9WH do not show a substantial difference in magnitude and the WH events do not appear to play an important role in pressure storage. However, for VFRs > 15%, the stored pressure is significantly higher for 5WH and 9WH than for 1WH tests, showing the importance of number of WH events.

To keep a pressurized system in a safe and stable condition during transient events, controlling the pressure along a pipe from the transient source position plays a major role. For that purpose, the pressure inside the pipe at the PT2 point is measured and its maximum value is named Pp. Figure 8 shows the change of maximum pressure in the pipe system for different Re values. Although the CAV does not have any discharge to the main pipe of the system, results in Figure 8 show that increasing the AP size will significantly decrease the pressure peak inside the pipe (Pp), specifically for higher Re. All WH events show the same behavior. Since the safety of pressurized systems under transient conditions matters most for high Re, a high VFR seems to be a better option to control pressure surge. However, smaller CAVs are more economic and easier to apply. Regarding this concern, Figure 8 shows the constant magnitude of pressure for the VFR > 30%.

**Figure 8.** Pressure change inside the pipe at PT2 against the VFR for different Re and WH events.

The water level in the CAV will rise during the WH tests as a consequence of pressure increasing by each WH action. The rising height of the water level is called Δh, a parameter that is calculated with Re and the VFR. The Δh shows a wide range of change from lower to higher values of Re and VFR (Figure 9).

**Figure 9.** Water level change (Δh) in the CAV against the VFR for different Re.

The Δh magnitude starts at around 1.2 cm for a small VFR and goes up to around 28 cm for the biggest VFR and Re in the 9WH case. The VFR > 30% showed good performance as presented in Figure 8 for controlling the pressure surge in the pipe system. Since, for the purpose of controlling the pressure surge by a CAV, only one WH can occur, the Δh remains in an acceptable range for the worst case, i.e., remains below 20% of the CAV length.

Figures 10 and 11 present average velocities (Vavg) for different Re for the 1WH and 9WH tests, where Vavg around zero indicates a WH occurrence. Since the Vavg does not show less than zero values, it can be concluded that the velocity vectors in reverse direction are not significant compared to the remaining flow. When repeating the WH to store energy in an AP, it is important to preserve the required flow rate in the pipe. During the "closed BV tests", the flow rate downstream of the system is not altered.

**Figure 10.** Average velocity for different Re during 1WH tests.

**Figure 11.** Average velocity for different Re during 9WH tests.

### *3.2. Tests with Open BV*

In these series of tests, the BV located in the lower level of the CAV is left open to discharge water into an open water tank (Figure 1). The water level should be adjusted before each test to have the predefined AP length. Since the CAV is completely confined, opening the BV before starting a test does not affect the water level in the CAV because of an emerging vacuum state in the AP. After each upsurge in the AP induced by the WH, a volume of water was dislodged. After finishing the test, the water level in the CAV returns to the initial level. In fact, no change takes place in the water level when comparing the start and end of each test. As a result, the pressure of the AP returned to initial pressure at the end of every WH. Figure 12 demonstrates the pressure changing way for 5WH and 9WH tests for AP length of 3 cm (VFR = 4.75%). The results from 1WH tests are not presented in Figure 12 since they do not make a sensible change in the measured parameters. The discharged volume of water at the end of the test is shown in each graph too. The peak pressure is almost constant during the repetition of WH and the magnitude of peak pressure is approximately equal to the tests with closed

BV presented in Figure 3. As expected, by increasing the Re value, the magnitude of discharged water from the CAV rises.

**Figure 12.** Pressure change in the AP and discharged water volume for 5WH and 9WH events, different Re and VFR = 4.75%.

Figure 13 shows the amount of discharged water volume after each test for different VFR, Re and WH events. There is a fast increase in discharging water volume for small VFR while it rises slowly for bigger VFR. Working with a small VFR needs more attention due to its high sensitivity to the pressure. Figure 13 shows that the discharged water volume for 9WH is considerably higher than for 5WH. In "open BV tests" the 9WH event creates a constant discharge from the CAV, while for the 5WH the discharge is not constant. In fact, the AP acts as a means of pressure storage and recovery, as a regulating flow system that adjusts the outflow from the CAV to create a constant discharge (see Supplementary Materials).

**Figure 13.** Discharged water volume against the VFR for different Re and WH events.

After finishing the "open BV tests", the discharge from the CAV stops and the water level returns to the initial level. For the VFR > 32% (AP length > 20 cm), the 9WH test leads to a constant discharge from the CAV which is less evident for the 5WH test. A high VFR shows very useful capability. This range of VFR seems to be very effective in SS-CAES systems when connected to the main water conveyance system.
