## 1 Introduction  
Rapid development of electronic industries has resulted in higher heat fluxes of electronic devices, and more effective and environmentally friendly methods are required to face the challenges associated with thermal management. Pulsating heat pipes (PHPs), as a kind of two-phase passive heat transfer device, have drawn wide attention due to their advantages of excellent heat transfer capability, simple structure, low cost, and high flexibility [1]. However, the thermal-hydraulic behavior of the PHP is complex, and thus it is difficult to predict the thermal performance of the PHP. To date, several approaches have been developed to theoretically investigate the thermal performance of PHP, including artificial neural networks (ANNs) [2, 3], computational fluid dynamics (CFD) [4, 5], and numerical analysis. The numerical approach, which considers mass, momentum, and energy equations, can not only predict the transient performance of the PHP, but also help researchers to understand the operation mechanism. Several numerical models have been proposed for predicting the heat transfer performance of the PHP, and Table 1 shows the typical numerical models used in the past 10 years for predicting the heat transfer performance of the PHP [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. From Table 1, it could be seen that the numerical models had been improved to get closer to the actual operation of the PHP by considering local pressure losses in the bend [6, 14] or the dynamics of the liquid film [13, 15] or the heterogeneous and homogeneous phase changes in the PHP [11; 15]. However, due to the complexity of the operating mechanism, there are still a number of problems that must be overcome in numerical investigations. For example, the calculation on capillary force was one of the problems needed to be overcome in the numerical investigation. It was found that the capillary force had significant effects on the flow motion of the working fluid inside the PHP in previous experimental investigations [17; 18]. However, in the numerical models shown in Table 1, the dynamic contact angles were usually assumed to be zero, and the capillary force was ignored. Only [PERSON] et al. [16] considered the effect of the capillary force on the flow motion of the working fluid in their numerical investigation. [PERSON] et al. [16] assumed that the advancing contact angle and the receding contact angle were 45\({}^{\circ}\) and 25\({}^{\circ}\), respectively. But the advancing and receding contact angles of the working fluid change with the flow motion of the working fluid during operation [19], and therefore, the calculation of the capillary force should be improved. In addition, the simulation on the coalescence of vapor plugs was another problem needed to be overcome. During the operation of PHP at high heat input, more bubbles are generated in the PHP, different bubbles are contacted, and the coalescence of vapor plugs can be observed in the PHP [20]. Figure 1 shows the coalescence of vapor plugs during visual experiments in our previous work [21]. However, the coalescence of vapor plugs was usually neglected in some numerical models [6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16], and long vapor plugs were hardly simulated in PHPs which made the simulation results on flow characteristics deviate from the actual results. Meanwhile, bubbles were assumed to only generate at particular positions of the PHP [9; 10], which affected the pressure distribution in the PHP and further influenced the flow and heat transfer characteristics. In addition, the necessary superheat for bubble generation changed with the thermophysical properties of the working fluids and the local heat flux. Thus, assuming the superheat as a constant brought some errors to the calculation on the latent heat transfer. The numerical simulations needed to be improved to simulate the bubble generation without a large amount of subjective fitting parameters by the researchers.