This model uses a single fuel node and two coolant nodes to derive the thermal output equations.
$$\frac{d\Delta T_F}{dt}=\frac{fP_0}{m_FC_{PF}}\Delta n+\frac{hA}{2m_FC_{PF}}(\Delta T_{\theta 1}+\Delta T_{\theta 2}-2\Delta T_F)$$
$$\frac{d\Delta T_{\theta 1}}{dt}=\frac{(1-f)P_0}{m_CC_{PC}}\Delta n+\frac{hA}{m_CC_{PC}}(\Delta T_F-\Delta T_{\theta 1})+\frac{\dot{m_C}}{m_C}(\Delta T_{CL}-\Delta T_{\theta 1})$$
$$\frac{d\Delta T_{\theta 2}}{dt}=\frac{(1-f)P_0}{m_CC_{PC}}\Delta n+\frac{hA}{m_CC_{PC}}(\Delta T_F-\Delta T_{\theta 1})+\frac{\dot{m_C}}{m_C}(\Delta T_{\theta 1}-\Delta T_{\theta 2})$$
Where \(P_0\) is the initial reactor power, \(f\) is the fraction of the total power produced in the fuel, \(h\) is the heat transfer coefficient from the fuel to the coolant. \(A\) is the heat transfer area, \(m_F\) is the mass of the fuel, \(C_{PF}\) is the specific heat of the fuel, \(m_C\) is the mass of the coolant, \(C_{PC}\) is the specific heat of the coolant, \(\dot{m}_C\) is the core mass flow rate.
- chenComprehensiveRealTimeHardwareIntheLoop2020
Backlinks: