# Research on the Dynamic Characteristics Analysis and Power Control Method of Heat Pipe Reactors
## 2 Dynamic Modelling of HPR
### Design of Heat Exchanger  
A heat pipe heat exchanger (HE) is similar to a shell and tube heat exchanger, and the cooling fluid flows through the condensing section of the heat pipe in the circular flow channel, as shown in Figure 4. The MegaPower does not give specific design parameters for the heat pipe heat exchanger, so this paper requires a combination of existing design parameters and reasonable assumptions to determine the core parameters of the heat exchanger. For this heat exchanger, the most important parameters are the SCO\({}_{2}\) flow rate and the flow channel width, which are subject to certain constraints. First, the unit used to express the flow rate of the cooling mass \(\dot{m}\) is kg/s. The HE should be able to export the heat from the core, and the heat generated by the core under steady-state initial conditions \(P_{full}\) should be equal to the heat removed by the cooling mass:  
\[P_{full}=\dot{m}(h_{out}-h_{in}) \tag{4}\]  
where \(h_{out}\) and \(h_{in}\) are the specific enthalpy of SCO\({}_{2}\) at the outlet and inlet, respectively. Although the MegaPower project has described the inlet and outlet temperatures, inlet pressure, and overall pressure drop of the heat exchanger SCO\({}_{2}\), there is no specific analysis of the feasibility [2]. In contrast, the SCO\({}_{2}\) Brayton cycle conversion system of Sandia National Laboratories (SNL) [30] has passed experimental verification after years of development, so the inlet and outlet parameters of the SNL heat exchanger are used in this paper as the boundary conditions for the heat exchanger model at a steady state under full power. The inlet temperature \(T_{in}=698\) K, the outlet temperature \(T_{out}=810\) K, the inlet pressure \(P_{in}=13612\) kPa, and the heat exchanger pressure drop \(DP=113\) kPa. Secondly, determine the width of the flow channel. It is mainly restricted by two aspects: one is the constraint of the size of the heat pipes in the core, and the other is the constraint of the wall temperature of the condenser section of the heat pipes. The center distance between two adjacent flow channels is consistent with the center distance between adjacent heat pipes in the reactor core. There is the following relationship among the center distance between two adjacent flow channels \(\delta\), the radius of heat pipes \(r_{hp}\), and the width of flow channel \(d\):  
\[2d<\delta-2r_{hp} \tag{5}\]  
Figure 4: Schematic diagram of heat pipe heat exchanger. When analyzing the thermal safety characteristics of MegaPower HPR in references [31; 32], the cooling fluid is air. The use of different cooling fluids will change the convective heat transfer conditions on the surface of the condensation section of the heat pipe, but it will not directly affect the heat transfer in the core. In order to keep the full power steady state temperatures of the fuel, monolith, and heat pipe consistent with the references, it is necessary to keep the wall temperature of the condensation section of the heat pipes unchanged before and after switching to cooling medium, that is, Equation (6):  
\[P_{full}=\frac{T_{c,w}-T_{a}}{R_{ref}} \tag{6}\]  
where \(T_{c,w}\) is the wall temperature of the condensing section of the heat pipe. \(T_{a}\) is the average temperature of the cooling fluid, which is the arithmetic average of the inlet and outlet temperatures. The reference thermal resistance \(R_{ref}\) is the convective heat transfer resistance that satisfies the condition of keeping the wall temperature of the condensing section of the heat pipe constant, calculated from the literature [32]. According to the above two constraints, an iterative calculation method can be designed to determine the parameters of heat exchanger, as shown in Figure 5.  
During the circulation, the Reynolds number \(Re\) is determined by the mass flow rate \(\dot{m}\), hydraulic diameter \(D_{h}\), flow path cross-sectional area \(A\), and the dynamic viscosity \(\mu\).