## 1 Introduction  
With economic development, the demand for energy in human society is increasing, placing significant pressure on the environment. In response, attention has turned to renewable energy sources. Among these, solar energy is the most widely utilized, and tank energy storage is a crucial method for harnessing solar energy. Tank energy storage can be categorized into two forms: dual-tank storage, where hot and cold working fluids are stored separately, and single-tank storage, where hot and cold working fluids coexist. Due to its lower manufacturing costs and environmental benefits, single-tank energy storage is more widely applied [1]. This type of tank, also known as a thermocline storage tank, separates the hot and cold working fluids using a thermocline. Under the influence of gravity, the hot working fluid is positioned at the top, while the cold working fluid remains at the bottom [2; 3]. Thermal stratification within storage tanks has consistently been a focal point of research in the relevant field, as enhancing thermal stratification can improve both the charging and discharging efficiency of the system [4]. The thickness of the thermocline is a key factor affecting the efficiency of energy storage in a single tank. For a given volume, a thicker thermocline indicates more severe fluid mixing, resulting in lower energy storage efficiency [5]. To improve energy storage efficiency, numerous researchers have investigated the temperature stratification within storage tanks. [PERSON] et al. designed four different shapes of obstacles within the storage tank. Through experimental analysis, they concluded that Type a obstacles improved stratification more effectively. They also noted that the position of the obstacles influences the stratification effect [6]. [PERSON] et al. studied the energy storage effects of obstacles with central openings. By comparing numerical simulations with experimental results, they determined the optimal hole diameter, installation position, and flow rate for the best stratification effect [7]. [PERSON] et al. investigated the impact of different baffle configurations on energy storage in horizontal solar water tanks. Through experimental results analysis, they identified the baffle combination that achieved the best stratification effect [8]. [PERSON] et al. studied the stratification characteristics of 12 different shapes of obstacles in storage tanks. Through numerical calculations and experiments, they concluded that obstacles with central perforations exhibited the best stratification performance [9]. [PERSON] et al. designed a special type of baffle that can automatically float up and down. The edges of the baffle contact the tank wall, preventing convection between cold and hot water, thereby making stratification influenced only by thermal conduction. The results showed that this device can improve stratification, and baffles with lower thermal conductivity result in a thinner thermocline [10]. [PERSON] et al. studied the installation of different numbers of perforated obstacles in storage tanks, using the Richardson number to evaluate stratification effectiveness. They found that increasing the number of obstacles can significantly improve stratification quality, but the optimal flow rate varies with the number of baffles [11]. [PERSON] et al. numerically simulated the charging and discharging of heat storage tanks, revealing the change rule of the thickness of the thermocline layer in the process of discharging and charging, and the greater the number of discharging times, the greater the thickness of the thermocline layer [12]. [PERSON] et al. designed four different structures of elbow water inlet devices. Compared to traditional elbow designs, the sintered bronze conical diffuser showed better improvement in stratification. They also noted that at low flow rates, the stratification effect is better when the nozzle is closer to the top of the tank [13]. [PERSON] et al.