# Research on the Dynamic Characteristics Analysis and Power Control Method of Heat Pipe Reactors
## 1 Introduction
One of the challenges encountered in the modeling of the HPR is related to heat transfer models for high-temperature heat pipes. The modeling methods are divided into the thermal resistance network model method and the two-phase flow model method. And the thermal resistance network modeling method is a fast and approximate method for calculating transient and steady-state heat transfer in heat pipes with low computational complexity [16]. [PERSON] and [PERSON] proposed the first practical thermal resistance network for analyzing the transient processes in heat pipes in 1998. They abstracted the sections of the heat pipe into thermal resistances, while assuming that the heat transfer in the evaporation and condensation sections only occurs in the radial direction and that heat transfer in the adiabatic section only occurs in the axial direction [17]. This method adopts the idea of lumped parameters, which greatly simplifies the heat pipe model and reduces the heat transfer equation of the heat pipe to a set of non-homogeneous linear equations. [PERSON] et al. established the super thermal conductivity model (STCM) based on the thermal resistance network model, which can not only calculate the heat transfer process of the heat pipe but also calculate the flow rates of liquid and gas working fluids [18]. Through introducing the calculation of heat transfer limits, the STCM can analyze the safety margin of the heat pipe. [PERSON] et al. equate the solid region and the liquid region as different thermal resistive, thermal capacitive, or thermal inductive elements, thus establishing a lumped parameter network model of the wick-type heat pipe. The simulation results show that the total thermal resistance of the heat pipe decreases with increasing input heat flux, but there is a lower limit for the total thermal resistance. And the total thermal resistance of the heat pipe is closely related to the thickness and porosity of the wick and the type of working fluid of the heat pipe [19]. During the process of heating up from a cold to a hot state in solid-state reactors such as HPRs, the density of the material in the reactor core increases as its temperature increases, and the distance between the molecules or atoms of the material increases, which results in an increase in the leakage rate of the neutrons. So, the thermal expansion effect of the material causes changes in the HPR's reactivity. Traditional nuclear-thermal analysis is no longer sufficient to meet the requirements of HPR simulation analysis; therefore, some high-fidelity simulation methods are adopted to study the transient phenomena of HPRs nowadays. For example, [PERSON] et al. built a high-fidelity 3D neutronics-thermal elasticity multi-physics coupling model of the HPR KRUSTY using the open-source software OpenMC, Nektar++, and SfePy based on the Monte Carlo and finite element methods [20]. Their calculation results showed that the reactivity change due to thermal expansion accounted for 89.4% of the total reactivity feedback, and even if a limited number of heat pipe failure accidents occurred, the remaining heat pipes could still provide sufficient thermal conductivity to ensure the safety of the core. [PERSON] et al. proposed a coupled calculation method called \"thermalMechanicsFoam\" for solving transient multi-physics fields in HPRs which uses Reactor Monte Carlo (RMC) to calculate the power distribution within the core and cooperates with OpenFOAM to calculate core temperature and expansion [21]. [PERSON] et al. established a transient analysis method combining three-dimensional core heat transfer with two-dimensional heat pipe heat transfer [22]. In the study of the steady-state operating conditions of the HPR, it showed that the isothermal properties of the heat pipe improved the axial and radial heat transfer in the reactor.