Probably you know that a pressurizer is a component of a nuclear plant which have the task to mantain the pressure constant in the primary circuit.
A way to get the pressurizer dimension is consider the maximum amount of mass of water entering and exiting the volume due to the increase or decrease of temperature in the core.
To proceed we need these data (what i used):
— Volume of primary system (150 m^3)
— Maximum insurge and outsurge core temperature variation (+10/-20 °C)
— Nominal pressure (155 bar)
— Radius of pressurizer (1 m)
— Heaters power (1000 kW)
— Heaters height (1 m)
— Sprayers max flow rate (40 kg/s)
The main hypotesis are two:
- Adiabatic pressurizer
- Constant sprayer flowrate/heaters power during the transient
INSURGE
m_{f2} = m_I + \dot{m}_{spray}\Delta t_I + m_{f1} + m_{v1}
m_{f2}u_{f2} = m_Ih_I + \dot{m}_{spray}\Delta t_Ih_s + m_{f1}u_{f1} + m_{v1}u_{v1}
m_{f2}v_{f2} = m_{f1}v_{f1} + m_{v1}v_{v1}
OUTSURGE
m_{f2} + m_{v2} = -m_O + m_{f1} + m_{v1}
m_{f2}u_{f2} + m_{v2}u_{v2}= -m_Oh_O + m_{f1}u_{f1} + m_{v1}u_{v1} + \dot{Q}_{heaters}\Delta t_O
m_{f2}v_{f2} + m_{v2}v_{v2} = m_{f1}v_{f1} + m_{v1}v_{v1}
Internal energy (u) enthalpy (h) and specific volume (v) are found using XSteam script (Matlab) considering that the vapor at equilibrium condition (initial and final states) is at saturation temperature, and for the fluid you can consider a mean temperature between the hot leg T (at the bottom of the pressurizer) and the saturation one (on the interface with vapor).
Input and output mass depend on the average variation of the fluid densities in the primary circuit, we can evaluate them in this way:
m_{I/O} = |V_{primary}\Delta \rho|
After the calculation of the height we can compute the heat exchange with environment by the simple cunductive formula:
\dot Q = (\dot Q)_{vapor} + (\dot Q)_{liquid} = \frac{T_{sat}-T_{out}}{R_{tot,v}} + \sum_i \frac{T_{i}-T_{out}}{R_{tot,dz}}Where Ti is linearly increasing from T hot leg up to Tsat.