The effect of water hammer on a confined air pocket towards flow energy storage system

initial head of air pocket inside CAV

peak head of air pocket

initial head of HT₁

initial head of pipe

peak head of pipe

stored head inside the air pocket as pressure

initial pressure of the air pocket

pressure after transient action in the air pocket

maximum pressure of the air pocket

average velocity

pipe diameter

kinematic viscosity of fluid

initial value

HT

hydro-pneumatic tank

PT

pressure transducers

BV

ball valve

MV

manual valve

CV

check valve

CAV

compressed air vessel

VFR

volume fraction ratio

WH

water hammer

Re

Reynolds number

Entrapped air within a water flow is of great importance since the maximum pressure that can be attained is much higher than a full-filled water flow due to the high compressibility of air. In addition, the entrapped air is capable of causing changes in the turbulence pattern during the pressurization phase that alters the shear stress at the wall. Any mixture of air and water changes the bulk properties of the fluid, such as the flow density and the elasticity, due to the pressurization of the air pocket (Lauchlan et al. 2005). Many researchers have studied the effect of entrapped air in pressurized systems to investigate its various effects, studying aspects such as different initial pressures and sizes of the air pocket, surrounding conditions and the length of the water column (Martin 1976; Cabrera et al. 1992; Martin 1996; Lee & Martin 1999; Zhou et al. 2002; Lee 2005; De Martino et al. 2008; Martins et al. 2009; Martins 2013). Martins (2013) studied the effect of entrapped air in pressurized vertical and inclined experimental pipe systems and found that the peak pressure can be much higher in the air-water condition than in the water-only condition. The author tried to define the effect of the change in initial pressure of the air pocket on the maximum pressure of the air pocket in rapid void pressurization tests and concluded the highest pressure was attained when the initial pressure within the air pocket was the atmospheric pressure. Accordingly, the maximum pressure increases until a peak value and then decreases as the void fraction increases gradually (Martins 2013).

The behavior of air pockets in pressurized systems under transient flow conditions is also very important due to the unpredictability of behavior and the complexity of analysis. Air volumes are also able to absorb and control high pressures induced by transient events. Various transient control devices can be used in pressurized systems, e.g., surge tanks, air chambers (vessels) and special relief valves. For that purpose in some cases, air vessels are more preferable because they can work under a wider range of pressure, they can be installed in diverse possible locations, they have small volumes and then they are more economic. Therefore, it is easy to apply them and their functionality is better (Chaudhry et al. 1985). The main role of an air vessel is to maintain the maximum and minimum pressures within the design limit of each system. In an air vessel there is a compressed air pocket above the water surface (Chaudhry et al. 1985). In this case, the pressure and the water level variation in the air vessel can affect the safety and efficiency of the system operation. Disclosing various aspects of an air pocket in a confined compressed vessel may increase knowledge regarding its behavior and yield easier and more reliable utilization for different purposes. Nowadays, the water hammer (WH) issue has become more important because of increasing concerns on the conveying capacity and system complexity of pressurized systems. Much research can be pointed out in design, stability and operation of air vessels. First studies of air vessels supposed a rigid water column, showing that the rigid column assumption is reliable if the maximum and minimum oscillations of pressure are less than half of the maximum pressure surge induced by instantaneous closure of a valve (De Martino & Fontana 2012). Stephenson (2002) used the rigid column assumption for calculation of both air volume and vessel volume in case of a pump failure. Kim et al. (2015) presented a work to investigate the behavior of an air pocket inside an air vessel and its dependence on parameters such as polytropic exponent, discharge coefficient, wave speed and initial size of the air pocket. Yang et al. (1992) presented a study about the stability of large oscillations in closed surge chambers using the direct method of Liapunov considering the nonlinear terms. This work suggests that the critical area is a product of Svee's law and a factor greater than unity.

In addition, an air pocket shows the ability for energy storage. There is a rising rate of researches in renewable energy sources (RES) because of emerging problems such as environmental impacts, scarcity and economic aspects related to the fossil sources. Although the RES are abundant, their availability over time is an obstacle to engage them effectively. Compressed air energy storage (CAES) systems which take advantage of storage vessels either above or under-ground are promising and low-cost tools with high energy capacity (Proczka et al. 2013). In this system the energy is stored as pressure within an air pocket which can be recovered by air pocket expansion. Zhang et al. (2013) presented a study on an advanced adiabatic compressed air energy storage (AA-CAES) system coupled with the air storage vessels. They studied four air vessels and showed that each vessel presents distinct characteristics of the charge and discharge process. Grazzini & Milazzo (2008) presented a study of a CAES system and showed a magnitude of heat recovery and resulting energy recovery efficiency of 72%.

Conventional CAES systems depend on fuel or other energy storage plants to store and recover the energy, unlike the solution herein proposed. Current work uses WH to convert the kinetic energy of flow known as ‘flow energy’ to potential energy. The mentioned potential energy is stored in a compressed air vessel (CAV) as compressed air for later use. The compressed air, in an action similar to CAES systems, can be expanded in order to recover the stored energy. In fact, this research was intended to provide information concerning practical approaches for storing energy in the form of compressed air in a vessel. To address this, the WH phenomenon was analyzed experimentally, with two generations of an experimental apparatus. The proposed case is able to store high-pressure created by a pressure surge inside an air vessel, which can be used to drive a micro-hydro turbine or to elevate water as a ram pump. The proposed system can be used in liquid conveyance systems as a lateral system to take a portion of main flow for storing energy. The separated flow will be returned to the main conduit after a WH action.

There is still space for more research studying the air pocket behavior inside a CAV for pressure controlling and energy storage purposes. To study this issue a specific CAV was developed in an experimental facility at the Civil Engineering, Research, and Innovation for Sustainability (CEris) Center, a research center of Instituto Superior Técnico (IST), the engineering faculty of the University of Lisbon, Portugal. The authors tried to reveal the effect of WH caused by an instantaneous closure of a valve on the pressure variation of a CAV, for various sizes of air pockets and different flow velocities inside the pipe system. Proper analysis based on dimensionless parameters is presented and discussed.

The experimental model was developed by improving the previous system of Martins (2013) in the CEris Center. Two types of the experimental models, i.e., system 1 and system 2 are used in this study. Two hydro-pneumatic tanks (HT₁ and HT₂) were considered in the system as a means to provide initial pressure and water required for different tests. Each tank has the volume of 1 m³. A set of transparent PVC pipes with 8 m length, nominal diameter of 63 mm (DN63), and a nominal pressure of 16 bar (PN16) is used to conduct water from HT₁ towards HT₂. A hydro-pneumatic CAV is installed on the highest point of the pipe and three pressure transducers identified as PT₁, PT_2, and PT₃ are installed along the pipe to measure the pressure. A high-speed camera (500 fps) is used to capture the air-water interface during each transient flow. A trigger provides the electrical means to activate all measuring equipment. The experimental pressure data are acquired using a pico-scope system. The trigger controls the actuation of valves and the start of recording by the camera allowing a perfect synchronization of data collection. Then, the starting times of the experimental tests and hydrodynamic simulations coincide. There are four ball valves (BVs), identified as BV₁, BV₂, BV₃, and BV₄ to create different transient flow conditions in different pipe sections.

The maximum capability for storing energy corresponded to a low VFR when the VFR was less than 0.20. However, the air volume also demonstrated storage capabilities for VFRs exceeding 0.30. The minimum storage capacity occurred for VFRs from 0.20 to 0.30.

where is the initial pressure of the air pocket and is the pressure after the transient action.

For VFR = 0, in the absence of the air and consequently its compressibility effect, pressure fluctuations are restricted and the damping occurs more or less after 0.2 s (Figure 8). However, this can be a dangerous case, especially at higher Reynolds number since the hydrostatic pressure of the water column within the CAV is high and the ability of the mass absorption from the pipeline is very low, and the probability of a rupture in the pipeline seems to be high in this case. Beyond the VFR = 0, a regular manner of the CAV with respect to VFRs and the Reynolds numbers can be seen in Figure 9. Hence, some conclusions can be addressed, as follows. (i) Increasing the value of VFR decreases the pressure fluctuations for each individual Reynolds number. This is due to higher interaction between the air and water column within the CAV in lower VFRs. (ii) For each individual VFR, the damping period is proportional to the Reynolds number, e.g., in the case of VFR = 0.0317, while the fluctuation dissipates after about 0.27 s for Re = 36,000, this dissipation occurs after about 0.9 s for Re = 115,000, indicating the significance of the WH phenomenon in higher Reynolds numbers. (iii) Due to the higher compressibility effect of the air at higher VFRs, the damping period of the pressure fluctuation increases with the VFR. From the perspective of the imposed normal stress and air vessel safety, longer damping periods can be preferred since the pressure variation and dissipation occur gradually.

Fluctuations of the pressure become smaller by increasing the VFR and decreasing the Reynolds number. This reduction for higher VFRs is due to the higher compressibility effect of the air, which allows higher amounts of flow mass absorption in the CAV. Pressure fluctuations for all Reynolds numbers become minimum in the case of high VFR in the tested VFR range.

The attenuation of the Reynolds number role on the development of the maximum pressure can be noticed with the increasing of the VFR number, due to higher ability of the CAV in the mass absorption. On the other hand, a pressure jump is seen for the Reynolds numbers of 115,000, 132,000 and 155,000 in the case of VFR = 0.0317, due to the higher incoming flow mass demand and the lower air compressibility effect. This reveals that by increasing the Reynolds number, the compressibility effect of the CAV and consequently the VFR value should be increased for the hydraulic pipeline design point of view.

This research showed the ability of an air pocket in system 1 to store energy in the form of compressed air volume. Results also demonstrate how decreasing the VFR can affect the peak pressure in an air pocket. CAES systems with a very low VFR would be troublesome with respect to the effect of the size of the air pocket on the pressure increasing. An efficient VFR was analyzed and because of the interface behavior, the VFRs less than 0.20 would be preferable for use in storing energy in system 1. Likewise, the proposed characteristics parameters showed the ability of the experimental apparatus to store energy in a CAV by compression of different sizes of air pockets. The parameter demonstrated a quasi-linear relationship between the maximum pressure of the CAV and the pipe system. Small VFRs had different behavior that arose from their lower damping capability. Consequently, the pressure in the air pocket was closer to the pressure inside the pipe, and the maximum pressure in both was higher for small VFRs. Thus, it is possible to select an efficient VFR for converting kinetic energy to potential energy that can be stored in an air pocket. An efficient VFR must integrate high pressure storage with stable behavior of the air-water interface.

Accordingly, a laboratory study was carried out in system 2 in order to investigate the performance of an air vessel (CAV) in pressure control during a WH phenomenon. Experiments were performed over a wide range of VFRs and Reynolds numbers. It was revealed that the value of the VFR and the Reynolds number had a significant role in the pressure rising control during a WH event. In addition, increasing the VFR value (compressibility effect), allows a higher absorption of the flow mass during a WH event. Finally, the performance of a CAV in WH control depends on the VFR and flow velocity.

The authors gratefully acknowledge the support of the Center for Hydro-Systems Research (CEHIDRO) in the CEris Center, a research center of IST, the engineering faculty of the University of Lisbon, for providing the experimental facilities for conducting the tests and financial support for the first author under grant number of HR Serviços no. 2714.