## 1 Introduction  
Energy storage is a driving force for the development of renewable and sustainable energy infrastructure. Compressed air energy storage (CAES) has attracted progressively more attention in recent years [1]. Many branches of compressed air energy storage such as adiabatic CAES (A-CAES) [2; 3; 4], isothermal CAES (I-CAES) [5], isobaric CAES (I- CAES) [6], sub-critical liquid air energy storage (SC-LAES) [7], supercritical CAES (SC-CAES) [8], and underwater CAES (UW-CAES) [9; 10], have been explored. UW-CAES is a flexible-scale energy storage technology that can store compressed air in deep-water air accumulators. It is particularly suitable for energy storage from offshore platforms, offshore renewable energy facilities, islands, and coastal cities [11; 12; 13; 14]. As renewable energy grows rapidly, achieving carbon compliance and carbon neutralization is the goal of all countries [15]. This trend will further promote the rapid development of UW-CAES in the next few decades. Many researchers have started working on the structural design, system modeling, application scenarios, and energy efficiency of UW-CAES [16; 17; 18; 19; 20]. However, less attention has been paid to the underwater gas transmission process along the long pipelines, a key factor restricting the development of UW-CAES. In the transport of underwater gas, the transmission pipe wall temperature decreases with the increase in water depth. The heat exchange between the pipe wall and seawater causes the gas temperature in the pipe to gradually decrease, and condensation takes place when the dew point pressure is reached [21]. The liquid is formed in the pipeline and it falls due to the action of gravity, leading to liquid accumulation in the low-lying part of the pipeline [22; 23]. Driven by the flowing gas, a complex and troublesome slug flow is formed, and this adversely affects pipeline transportation, as displayed in Figure 1.  
Liquid accumulation often forms in low-lying pipelines, and hilly terrain pipelines are the most common in pipeline transportation. Many scholars have researched the slug flow pressure in a hilly terrain pipeline [24]. This provides a reference value for the study of ZNLF in a UW-CAES hilly terrain pipeline. The conditions that are required for ZNLF to occur include the accumulation of all liquid in the lowest parts of the pipe, then a portion of the liquid is cut off by the flowing gas, and the rest circulates in the upward pipe section to form ZNLF [25; 26]. [PERSON] et al. [27] carried out liquid accumulation flow experiments with inner diameters of 25.8 mm and 51.2 mm and inclination angles of 1\({}^{\circ}\), 5\({}^{\circ}\), and 9.2\({}^{\circ}\). From the experimental pressure drop data, the amount of liquid accumulation in the pipe depended on the inclination angle and gas flow. Blowing out all liquid accumulation required a relatively high gas flow. In addition, the study clearly showed that the presence of liquid accumulation increases the pressure loss of the natural gas pipeline. Based on [PERSON] et al. 's experiment (1981), [PERSON] and [PERSON] [28] proposed a slug flow pressure drop prediction model in the middle of an inclined pipeline under ZNLF. Experiments with inclination angles of 1\({}^{\circ}\), 5\({}^{\circ}\), and 9.2\({}^{\circ}\) were carried out on 26 mm and 51 mm pipes. Following that, [PERSON] et al. [29] performed experimental and theoretical studies on the pressure in upward pipes under ZNLF. The pressure experimental data of four upward inclination angles (1\({}^{\circ}\), 2\({}^{\circ}\), 5\({}^{\circ}\), and 9\({}^{\circ}\)) were obtained. A prediction model for the average liquid holdup and pressure gradient of the liquid accumulation exit velocity under ZNLF was developed. Compared with the experimental data and model of [PERSON] and [PERSON] (1986), [PERSON] et al. 's prediction model results were good match with the experimental data. ZNLF is a special state in the pipeline, and there are few studies on pipeline fluidity in this state.