Vessel Instrumentation - SRV Tailpipe
06. SAFETY RELIEF VALVE TAILPIPE CALCULATIONS
The Safety Relief Valve (SRV) tailpipe calculations involve teperature and pressure calculations. The temperature calculations are based on use of the Mollier diagrams. An approximation of steam specific heat is made using the diagrams. The metal temperature is calculated using a heat sink/source model. The heat sink/source model uses the basic equation:
Ttp = Ttp + Δt * ( Qst + Qtm + Qmsl - Qdw ) / ( CMcp * Mtp )
where
- Δt :: Time, program delta
- CMcp :: Specific heat for tailpipe metal
- Mtp :: Tailpipe metal mass (constant)
- Qdw :: Heat rate of tailpipe metal to drywell
- Qmsl :: Heat rate of main steam lines to tailpipe conductance
- Qst :: Heat rate of steam to tailpipe metal
- Qtm :: Heat rate of tailpipe metal conductance
- Ttp :: Tailpipe metal temperature
(06-1)
06.1 Tailpipe Pressure, Enthalpy Properties
The tailpipe pressure is calculated as a simple relation of flow and delta pressure. The calculation is:
Ptp = Psnk + Kdp * Wsrv * Wsrv
where
- Kdp :: Constant, SRV flow vs. delta pressure
- Ptp :: Pressure in tailpipe at temperature sensor
- Psnk :: SRV sink pressure, usually wetwell water
- Wsrv :: SRV mass flow
(06.1-1)
The tailpipe saturated steam temperature and enthalpy (based on pressure) is calculated using the saturated tables:
TVtp = f ( Ptp )
HVtp = f ( Ptp )
where
- HVtp :: Saturated enthalpy of vapor at tailpipe pressure
- Ptp :: Pressure in tailpipe at temperature sensor
- TVtp :: Saturated temperature of vapor at tailpipe pressure
(06.1-2)
06.2 Tailpipe Steam Temperature
The tailpipe superheated steam temperature is calculated using an approximation of steam specific heat. The steam temperature is:
TStp = TVtp + ( HStp - HVtp ) / Cp
where
- Cp :: Specific heat of superheated steam at low enthalpies and pressures
- HStp :: Actual enthalpy of vapor at tailpipe
- HVtp :: Saturated enthalpy of vapor at tailpipe pressure
- TStp :: Actual temperature of vapor at tailpipe pressure
- TVtp :: Saturated temperature of vapor at tailpipe pressure
(06.2-1)
See Simplifications for the rationale behind the constant value for Cp. The equation may actually multiply by inverse of Cp.
06.3 Tailpipe Heat Transfer
The tailpipe superheated steam transfers heat to the metal based on convective heat transfer principles. The heat transfer from steam to metal is represented by:
Qst = Kht * ( abs ( Wsrv ) ** Kcv ) * TStp - Ttp
where
- Kht :: Constant, heat transfer from tailpipe steam to tailpipe metal
- Kcv :: Constant, convective heat transfer exponent, about 0.8 for turbulent flow
- Ttp :: Tailpipe metal temperature
- TStp :: Actual temperature of vapor at tailpipe pressure
- Wsrv :: SRV mass flow
(06.3-1)
The convective heat transfer exponent for turbulent flow is taken from reference 1.
The tailpipe heat transfer from metal to drywell is represented by:
Qdw = Kdw * ( Ttp - Tdw )
where
- Kdw :: Constant, heat transfer from tailpipe metal to drywell
- Qdw :: Heat rate of tailpipe metal to drywell
- Ttp :: Tailpipe metal temperature
- Tdw :: Drywell temperature
(06.3-2)
06.4 SRV Sink Pressure and Aperture
The instrumentation system calculates a sink pressure and aperture for the SRVs. The sink pressure and aperture functions are based on the following :
Qst = Kht * ( abs ( Wsrv ) ** Kcv ) * TStp - Ttp
where
- Kht :: Constant, heat transfer from tailpipe steam to tailpipe metal
- Kcv :: Constant, convective heat transfer exponent, about 0.8 for turbulent flow
- Ttp :: Tailpipe metal temperature
- TStp :: Actual temperature of vapor at tailpipe pressure
- Wsrv :: SRV mass flow
(06.4-1)
The convective heat transfer exponent for turbulent flow is taken from reference 1.
The tailpipe heat transfer from metal to drywell is represented by:
Qdw = Kdw * ( Ttp - Tdw )
where
- Kdw :: Constant, heat transfer from tailpipe metal to drywell
- Qdw :: Heat rate of tailpipe metal to drywell
- Ttp :: Tailpipe metal temperature
- Tdw :: Drywell temperature
(06.4-2)