## 1 Introduction
designed an equalizer for the improvement of stratification, invoked Richardson number, filling efficiency and mixing number to evaluate the energy storage efficiency, and demonstrated the functionality of the equalizer in improving stratification through simulation and experimental comparison [14]. [PERSON] et al. established a one-dimensional model to analyze the cooling and heating of tanks with radial plate structure, and the numerical results were compared with the experimental data, and the correctioncoefficients were introduced to improve the prediction accuracy of the one-dimensional numerical model [15]. [PERSON] et al. investigated household water tanks, focusing on the design of the inlet device. Their research revealed that storage tanks equipped with baffles near the inlet device exhibited higher thermal efficiency compared to other tanks. Specifically, the effective utilization rate of solar energy in tanks with baffles increased by 3% compared to those without baffles [16]. [PERSON] et al. designed a household storage tank equipped with thermal diodes and partitions, aiming to improve thermal stratification. The study results indicated that the partitions and diodes within the tank effectively promoted stratification. Furthermore, the distance between the partitions, as well as the length and diameter of the diodes, were found to have a direct impact on the stratification [17]. [PERSON] et al. analyzed the energy storage efficiency and exergy efficiency during the thermal storage process in tanks. They found that combining the Peclet number and Fourier number with a small amount of real measurement data can accurately predict stratification. They also noted that exergy efficiency is primarily concentrated in the upper half of the tank [18]. [PERSON] et al. used a two-dimensional numerical method to predict the growth process of the thermocline in storage tanks under static conditions. Both experimental and computational results indicated that the height-to-diameter ratio of the tank affects the thickness of the thermocline, with tanks having a height-to-diameter ratio of 1 showing the best stratification effect [19]. [PERSON]. [PERSON] et al. used a one-dimensional numerical model to predict the behavior of the thermocline in storage tanks. Compared to three-dimensional models, this model can produce results more quickly and meets accuracy requirements in most cases [20]. [PERSON] et al. designed a new radial plate diffuser, and both numerical and experimental results confirmed that the device can improve the lamination inside the box, and pointed out that the Reynolds number and the Froude number are important references for evaluating the delamination [21]. [PERSON] et al. studied the thermal stratification characteristics inside storage tanks with encapsulation layers. They found that both the flow rate and the direction of the inlet affect internal thermal stratification. Properly controlling the flow rate and the direction of the jet can promote internal stratification [22]. [PERSON] et al. comparatively studied the stratification effect of slotted inlet devices versus perforated inlet devices and found that slotted inlets are suitable for high flow rates and low temperature differentials, while perforated inlets are more advantageous for low flow rates and large temperature differentials [23]. To evaluate the thermal stratification behavior within thermocline storage tanks, previous research has utilized various methods and parameters [24; 25]. Most of these approaches involve analyzing the transient temperature evolution inside the tank. Currently, the thickness and temperature gradient of the thermocline layer have been widely adopted as metrics for assessing the level of stratification [21]. Previous research has demonstrated that installing obstacles and designing inlet devices within storage tanks can enhance stratification. Compared to other shapes of internal obstacles, many researchers prefer perforated obstacles for their superior stratification improvement.