UNIVERSITY OF PITTSBURGH
Secondary Side of the
Steam Generator (SSG)
Design Basis Document
SimulinkTM Thermal Hydraulic Model
Scott E Fortune
4/25/2011
1
SSG Model
Table of Contents
X.1
Model SSG ........................................................................................................................................ 3
X.1.1
System Scope of Simulation ..................................................................................................... 3
X.1.1.1
Simulation Description ......................................................................................................... 3
X.1.1.2
Equipment and Functions Not Simulated ............................................................................. 4
X.1.2
Software Communication and Hierarchy Diagram ................................................................... 4
X.1.3
Mathematical Description ......................................................................................................... 5
X.1.3.1
Secondary Side of the Steam Generator................................................................................ 5
X.1.3.2
Primary-to-Secondary Heat Transfer .................................................................................... 7
X.1.3.3
Steam Control System........................................................................................................... 9
X.1.3.4
Feedwater Control System .................................................................................................. 10
X.1.3.5
SG Water Level................................................................................................................... 11
X.1.3.6
Turbine Pressure Calculation .............................................................................................. 12
X.1.4
Constants Derivation ............................................................................................................... 12
X.1.4.1
Secondary side of the SG constants .................................................................................... 12
X.1.4.2
Primary-to-secondary heat transfer constants ..................................................................... 12
X.1.4.3
Steam control system constants .......................................................................................... 13
X.1.4.4
Feedwater control system constants .................................................................................... 13
X.1.4.5
SG water level constants ..................................................................................................... 14
X.1.4.6
Turbine pressure constants .................................................................................................. 14
X.1.5
GUI Interfaces ......................................................................................................................... 14
X.1.5.1
Screen Displays ................................................................................................................... 15
X.1.5.2
Screen Controls ................................................................................................................... 15
X.1.6
X.1.6.1
X.1.7
Program Description and Simulink model .............................................................................. 16
Simulink Model and Matlab Functions ............................................................................... 16
References ............................................................................................................................... 34
2
SSG Model
X.1
Model SSG
This section documents the development of a SimulinkTM based thermal hydraulic model for the
Secondary Side of the Steam Generator (SSG) for an Advanced Passive Pressurized Water Reactor
(PWR).
X.1.1 System Scope of Simulation
The scope of the SSG simulation includes the development of a lumped node model of the secondary side
of the steam generator, the primary-to-secondary heat transfer model and control systems for main
feedwater (FW), outlet steam flow and steam generator (SG) water level. This model will approximate
the performance of the U-tube SGs of the AP1000™ Advanced PWR design (Reference 3).
X.1.1.1 Simulation Description
The SSG model provides transient responses to secondary side conditions, including changes in
secondary liquid mass, steam mass, pressure, and temperature. In addition, the secondary temperature is
used in conjunction with primary side conditions to calculate thermal resistances and overall primary-tosecondary heat transfer.
The secondary side of the steam generator is modeled as a single lumped node at saturated conditions
with feedwater (FW) input, steam output, and primary heat input. The model is designed for a load
follow simulator; i.e., the core power is driven by the demand from the turbine generator. Therefore, the
outlet steam flow is set by the user and drives the heat transfer and secondary conditions calculations.
As stated above, the steam outlet/turbine control system determines the outlet steam flow rate based on
user input. The ability to model turbine trip exists, and a maximum flow rate can be input. This flow rate
would correspond to the maximum flow rate enabled by the steamline integral flow restrictors.
The FW control system is based on maintaining the desired SG water level. A lead/lagged SG water level
signal is compared to the reference SG water level, and the FW flow rate is adjusted accordingly to
reestablish the desired level. The user is also able to input FW flow as a function of time and the
capability exists to trip the main feedwater pumps.
The SG water level calculations are performed to estimate the water level corresponding to the secondary
fluid mass. As the shape of the SG varies widely by elevation, the SG was split into three regions to
achieve a simple yet more accurate estimate of water level; from the top of the tubesheet to the lower
narrow range (NR) level tap, between the upper and lower NR level taps, and from the upper NR level tap
to the top of the SG. The volume within each these regions was estimated. The secondary fluid mass is
converted to a volume based on the density of the fluid, and the overall volume of the fluid is compared to
the volumes within each of the three regions to establish an equivalent water level. Note that this water
level does not explicitly address transient conditions and therefore is most representative during steady
state conditions.
The primary-to-secondary heat transfer model calculates the heat transferred based on the difference
between the secondary side saturation temperature and an average primary side SG temperature based on
the SG inlet and SG outlet enthalpies. Calculations are performed to determine the primary film thermal
resistance and tube wall metal thermal resistance. The Primary Reactor Coolant (PRC) System model
3
SSG Model
provides the SG inlet and SG outlet enthalpies, primary pressure, and primary flow rate, which are used to
calculate necessary properties for the heat transfer and thermal resistance calculations.
A calculation of first stage turbine pressure is performed based on applying a correction factor to the
outlet steam pressure as determined during calibration runs.
X.1.1.2 Equipment and Functions Not Simulated
The SSG is a lumped node model for the SG, meaning that detailed modeling of primary and secondary
separators, feedwater rings, and other SG features does not exist. The boundaries of the SSG model are
the outlet steam nozzle, the feedwater inlet, and the primary-to-secondary interface through the SG Utubes; therefore, secondary systems beyond the steam outlet nozzle are not explicitly modeled (e.g., SG
safety and relief valves, steamline isolation valve, the turbine or associated control systems), safety
systems such as auxiliary feedwater and secondary trips (e.g., low SG water level, low steamline pressure,
etc.) are not modeled, and only simplified control systems for the feedwater system and SG level control
exist.
X.1.2 Software Communication and Hierarchy Diagram
The SSG model is a Simulink model that requires additional SSG-specific Matlab™ scripts and inputs
from the PRC model and outputs information to the GUI, PRC, and PPX models.
A hierarchy diagram of the system is contained in Figure X.1.2-1 below illustrating the SSG interfaces
with other systems and external files.
PRC
SSG
Initialization
File
PPX
SSG
GUI
Secondary side
of the SG
Matlab Scripts
• SSG_solution
• SSG_props
• SSG_primprops
4
SSG Model
X.1.3 Mathematical Description
X.1.3.1 Secondary Side of the Steam Generator
X.1.3.1.1
Model Description
The secondary side of the steam generator is a single lumped node model with transient calculations
performed based on the conservation of the following; fluid mass, vapor mass, total volume, and energy.
Feedwater inlet flow and steam outlet flow are modeled, as is primary-to-secondary heat transfer. This
model is based on a simplified secondary model developed by Dr. David Aumiller.
The solution technique involves a system of linear equations integrated over a time step to solve for the
change in fluid mass, vapor mass, and pressure. For simplicity, the system is assumed to be at saturated
conditions.
X.1.3.1.2
Assumptions and Approximations
The secondary side is approximated as a single lumped node at saturated conditions. In order to simplify
the system of linear equations, it is assumed that both the vapor and liquid phases in the secondary side
are at equilibrium; this assumption enables the densities and enthalpies to be expressed as a function of
pressure alone and reduces the number of system unknowns. Additionally, to approximate the derivatives
of density and enthalpy in terms of pressure, a forward/backward step linearized solution technique was
employed with a fixed change in pressure of 0.25 bar.
X.1.3.1.3
Description of Equations and Variables
The derivation of the model for the secondary side of the steam generator begins with the conservation of
mass for the liquid and vapor phases:
𝑑
(𝑀 ) = 𝑊𝐹𝑊 (𝑡) − Γ
𝑑𝑡 𝑆𝐹
𝑑
(𝑀 ) = Γ − 𝑊𝐺 (𝑡)
𝑑𝑡 𝑆𝑉
(1)
(2)
Where,
MSF
WFW

MSV
WG
=
=
=
=
=
Mass of fluid in secondary side of the SG
Feedwater flow rate
Vapor generation term
Mass of vapor in secondary side of the SG
Outlet steam flow rate
Next, the total volume must be conserved on the secondary side, therefore the conservation of volume
equation becomes:
𝑀
𝑀
𝑑𝑀𝑆𝑉
𝑑𝜌
𝑑𝑀𝑆𝐹
𝑑𝜌
𝑑 ( 𝜌𝑆𝑉 ) 𝑑 ( 𝜌𝑆𝐹 )
𝜌𝑉 − 𝑀𝑆𝑉 𝑉
𝜌𝐹 − 𝑀𝑆𝐹 𝐹
𝑉
𝐹
𝑑𝑡
𝑑𝑡
𝑑𝑡
𝑑𝑡
+
=0=
+
(3)
𝑑𝑡
𝑑𝑡
𝜌𝑉2
𝜌𝐹2
Where,
V
F
=
=
Density of the secondary steam
Density of the secondary fluid
5
SSG Model
Finally, the conservation of energy equation is considered, where the liquid, vapor, and structural energies
are considered along with the net primary-to-secondary heat transfer, the heat addition from the FW inlet
flow, and the heat extraction from the steam outlet flow:
(𝐶𝑉)𝑆𝑀
𝑑(𝑇𝑠𝑎𝑡 ) 𝑑(𝑀𝑆𝐹 𝐻𝐹 ) 𝑑(𝑀𝑆𝑉 𝐻𝑉 )
+
+
= 𝑄𝑛𝑒𝑡 (𝑡) − 𝑊𝐺 𝐻𝐺 + 𝑊𝐹𝑊 𝐻𝐹𝑊
𝑑𝑡
𝑑𝑡
𝑑𝑡
(4)
Where,

C
V
Tsat
HF
HV
Qnet
=
=
=
=
=
=
=
Density of the saturated mixture (kg/m3)
Specific heat of the saturated mixture (kJ/kg°C)
Volume of the saturated mixture (m3)
Secondary side saturation temperature (°C)
Enthalpy of the secondary fluid (kJ/kg)
Enthalpy of the secondary steam (kJ/kg)
Net primary-to-secondary heat transfer (kJ/s)
Applying the chain rule on the derivatives of fluid and vapor energy:
𝑑(𝑀𝑆𝐹 𝐻𝐹 ) 𝑑𝑀𝑆𝐹
𝑑𝐻𝐹
=
𝐻𝐹 + 𝑀𝑆𝐹
𝑑𝑡
𝑑𝑡
𝑑𝑡
(5)
𝑑(𝑀𝑆𝑉 𝐻𝑉 ) 𝑑𝑀𝑆𝑉
𝑑𝐻𝑉
=
𝐻𝑉 + 𝑀𝑆𝑉
𝑑𝑡
𝑑𝑡
𝑑𝑡
(6)
Using the assumption that both phases are in equilibrium at the saturation temperature allows the
enthalpies and densities to be expressed as functions of pressure, as can the saturation temperature term in
the structural component of the conservation of energy equation. The result is a system of four equations
with four unknowns (, MV, MF, P), which can be solved for by integrating over one time step. The
resulting linear system is written as:
Δt
−Δ𝑡
0
[ 0
0
1
1
𝜌𝑉
𝐻𝑉
1
0
1
𝜌𝐹
0
0
Γ
𝑀𝑉 𝑑𝜌𝑉 𝑀𝐹 𝑑𝜌𝐹
𝛿𝑀
−( 2
+ 2
)
[ 𝑉]
𝜌𝑉 𝑑𝑃
𝜌𝐹 𝑑𝑃
𝛿𝑀𝐹
𝑑𝐻𝑉
𝑑𝐻𝐹
𝑑𝑇𝑠𝑎𝑡
𝛿𝑃
𝐻𝐹 (𝑀𝑉
+ 𝑀𝐹
+ (𝜌𝐶𝑉)𝑆𝑀
)]
𝑑𝑃
𝑑𝑃
𝑑𝑃
𝑊𝐹𝑊 Δ𝑡
−𝑊𝐺 Δ𝑡
=[
] (7)
0
(𝑄𝑛𝑒𝑡 + 𝑊𝐹𝑊 𝐻𝐹𝑊 − 𝑊𝐺 𝐻𝐺 )Δ𝑡
This model could be further expanded to take into account tube rupture flow into the secondary side,
feedline break flow out and steamline break, safety and relief valve and steam dump flow out by
substituting the following for the right hand side of Equation (7):
6
SSG Model
(𝑊𝐹𝑊 + 𝑊𝑇𝑅 − 𝑊𝐹𝑅 )Δ𝑡
−(𝑊𝐺 + 𝑊𝑆𝑅 )Δ𝑡
[
] (8)
0
(𝑄𝑛𝑒𝑡 + 𝑊𝐹𝑊 𝐻𝐹𝑊 + 𝑊𝑇𝑅 𝐻𝑇𝑅 − 𝑊𝐹𝑅 𝐻𝐹𝑅 − 𝑊𝐺 𝐻𝐺 − 𝑊𝑆𝑅 𝐻𝑆𝑅 )Δ𝑡
Where,
WTR
WFR
WSR
HTR
HFR
HSR
=
=
=
=
=
=
Tube rupture mass flow rate into the secondary side (kg/s)
Feedline rupture mass flow rate out of the secondary side (kg/s)
Net safety and relief valve, steam dump, and steamline break mass flow rate (kg/s)
Enthalpy of fluid entering secondary side due to tube rupture (kJ/kg)
Enthalpy of the fluid exiting through the feedline rupture (kJ/kg)
Enthalpy of the vapor exiting through the safety and relief valves, steam dump, or steamline break (kJ/kg)
X.1.3.1.4
Malfunctions
As the secondary side model is a simplified version only meant to allow proper execution of the detailed
primary side model, there are no pre-programmed malfunctions available for this version of the
PANTHER simulator code. The ability to specify feedwater as a function of time exists, as well as the
ability to trip the feedwater pumps and turbine; however, as the model is a simplified lumped node
representation, the accuracy of the plant response to these transients cannot be guaranteed. Further
generations of the PANTHER simulation code will allow for more detailed secondary transients, such as
steamline and feedline ruptures, tube ruptures, loss of feedwater pumps, loss of external electrical load,
feedwater malfunctions, load increases, or inadvertent opening of safety or relief valves.
X.1.3.2 Primary-to-Secondary Heat Transfer
X.1.3.2.1
Model description
The primary-to-secondary heat transfer calculation is performed based on the primary-to-secondary
temperature difference, the available tube bundle heat transfer area and calculated thermal resistances.
The thermal resistances considered in the model are the primary side film resistance and the tube metal
resistance.
X.1.3.2.2
Assumptions and Approximations
The secondary film resistance is neglected in the model. This simplification was made due to the
secondary side being modeled as a single lumped node, therefore an explicit secondary side tube bundle
flow is not modeled and an explicit film resistance calculation cannot be performed. The primary film
resistance is calculated using the Dittus-Boelter correlation.
The primary side temperature is approximated as the temperature corresponding to the primary pressure
and average primary SG enthalpy (as calculated by averaging the SG inlet and SG outlet enthalpies).
Therefore, asymmetric and local heating and cooling effects are not explicitly included.
The thermal resistances are not modeled to take into account excessive voiding, primary side dryout, or
reverse heat transfer. Modifications to the resistance calculations would be required to accurately model
these phenomena.
X.1.3.2.3
Description of Equations and Variables
The primary heat transfer equation utilized in the primary-to-secondary heat transfer calculation is the
following:
7
SSG Model
𝑄 = 𝑈𝐴(𝑇𝑝𝑟𝑖𝑚 − 𝑇𝑠𝑒𝑐 )
(9)
Where,
Q
U
A
Tprim
Tsec
=
=
=
=
=
Net heat transfer (kJ/s)
Heat transfer coefficient (W/m2°C)
Surface area available for heat transfer (m2)
Average primary fluid temperature in SG node (°C)
Secondary side fluid temperature (°C)
The heat transfer coefficient is the reciprocal of the total thermal resistance. Since the primary film
resistance and tube metal resistance are in series, the total thermal resistance is simply the sum of the
individual thermal resistances.
𝑈=
1
𝑅𝑡𝑜𝑡𝑎𝑙
=
1
1
=
1
1
𝑅𝑝𝑓 + 𝑅𝑡𝑤
+
ℎ𝑝𝑓 ℎ𝑡𝑤
(10)
Where,
Rtotal
Rpf
Rtw
hpf
htw
=
=
=
=
=
Total thermal resistance (m2°C/W)
Primary film thermal resistance (m2°C/W)
Tube wall thermal resistance (m2°C/W)
Primary fluid heat transfer coefficient (W/m2C)
Tube wall heat transfer coefficient (W/m2C)
The primary thermal resistance is calculated using the Dittus-Boelter correlation. Per Reference 1,
utilizing the Dittus-Boelter correlation, the heat transfer coefficient equation becomes:
ℎ𝑝𝑓 𝐷
= 0.023 ∙ 𝑅𝑒 0.8 𝑃𝑟 0.4
𝑘𝑝𝑓
(11)
Where,
hpf
D
kpf
Re
Pr
=
=
=
=
=
Primary film heat transfer coefficient (W/m2°C)
Hydraulic diameter (m)
Fluid thermal conductivity (W/m°C)
Reynolds number for the primary fluid flow
Prandtl number for the primary fluid flow
Using the definitions for the Reynolds and Prandtl numbers, and the approximation that the average fluid
velocity is equal to the mass flow rate divided by the density and cross-sectional flow area, Equation (11)
can be rearranged to be in terms of h.
8
SSG Model
𝑘𝑝𝑓
𝐷
0.4
0.8
𝑘𝑝𝑓
𝐷𝑣𝜌
𝐶𝑃 𝜇
= 0.023 ⋅ (
) (
) ∙
𝜇
𝑘𝑝𝑓
𝐷
ℎ𝑝𝑓 = 0.023 ∙ 𝑅𝑒 0.8 𝑃𝑟 0.4 ⋅
ℎ𝑝𝑓
ℎ𝑝𝑓 = 0.023 ⋅ (
ℎ𝑝𝑓
𝐷𝜌 𝑊 0.8 𝐶𝑃 𝜇
⋅ ) (
)
𝜇 𝜌𝐴
𝑘𝑝𝑓
0.4
∙
𝑘𝑝𝑓 0.6 𝑊 0.8 𝐶𝑝 0.4
= 0.023 ⋅ 0.2 ∙ ( ) ( )
𝐷
𝐴
𝜇
𝑘𝑝𝑓
𝐷
(12)
Where,
v

µ
Cp
W
A
=
=
=
=
=
=
Fluid velocity (m/s)
Fluid density (kg/m3)
Fluid viscosity (kPa/s)
Specific heat (J/kg°C)
Primary mass flow rate (kg/s)
Primary cross sectional flow area (m2)
Next, the heat transfer coefficient of the tube wall is calculated simply using the wall thickness divided by
the thermal conductivity of the metal (per Reference 1).
ℎ𝑡𝑤 =
𝐿
𝑘𝑡𝑤
L
ktw
=
=
(13)
Where,
Thickness of the tube walls (m)
Thermal conductivity of the tube metal (W/m°C)
X.1.3.2.4
Malfunctions
There are no malfunctions associated with this system.
X.1.3.3 Steam Control System
X.1.3.3.1
Model description
The steam control system calcules the SG outlet mass flow rate based on a user-defined load fraction.
Additionally, the capability to model a turbine trip exists, along with the ability to set a flow floor and
ceiling.
X.1.3.3.2
Assumptions and Approximations
The simplified steam control system takes the desired turbine load fraction and applies this to the nominal
mass flow rate to calculate the SG outlet mass flow rate. Due to variance in the outlet steam enthalpy the
actual turbine power demand may not exactly equal the user-defined fractional load.
X.1.3.3.3
Description of Equations and Variables
The calculation performed by Simulink to calculate the steam outlet mass flow rate corresponds to the
following equation:
9
SSG Model
𝑊𝑠𝑡𝑚 = (1 − 𝑇𝑇) ∙ 𝐹 ⋅ 𝑊𝑛𝑜𝑚 , 0 ≤ 𝑊𝑠𝑡𝑚 ≤ 𝑊𝑚𝑎𝑥
(14)
Where,
Wstm
TT
F
Wnom
Wmax
=
=
=
=
=
Steam outlet mass flow rate (kg/s)
Turbine trip signal (0 for not tripped, 1 for tripped)
Turbine load fraction (fraction of nominal)
Nominal steam outlet mass flow rate (kg/s)
Maximum allowable steam outlet mass flow rate (kg/s)
X.1.3.3.4
Malfunctions
There are no malfunctions currently modeled for this system.
Future versions of the code should consider malfunctions such as an accidental opening of a SG safety or
relief valve, an excessive increase in turbine load, a loss of external electrical load, and a steamline
rupture.
X.1.3.4 Feedwater Control System
X.1.3.4.1
Model description
The FW control system calcules the FW inlet mass flow rate based on the user-defined turbine load
fraction and also to maintain the desired SG water level. Additionally, the capability to model FW pump
trips exists, along with the ability to set a flow floor and ceiling.
X.1.3.4.2
Assumptions and Approximations
The simplified FW control system calculates a flow correction based on SG water level deviation that is
applied to the nominal mass flow rate to calculate the FW inlet mass flow rate. The feedwater control
valve is not explicitly modeled.
X.1.3.4.3
Description of Equations and Variables
The calculation performed by Simulink to calculate the FW inlet mass flow rate corresponds to the
following equation:
𝑊𝑓𝑤 = (1 − 𝐹𝑇) ∙ 𝐹 ⋅ 𝑊𝑛𝑜𝑚 , 0 ≤ 𝑊𝑓𝑤 ≤ 𝑊𝑚𝑎𝑥
(15)
Where,
Wfw
PT
F
Wnom
Wmax
=
=
=
=
=
FW inlet mass flow rate (kg/s)
FW pump trip signal (0 for not tripped, 1 for tripped)
Turbine load fraction (fraction of nominal)
Nominal FW inlet mass flow rate (kg/s)
Maximum allowable FW inlet mass flow rate (kg/s)
X.1.3.4.4
Malfunctions
There are no malfunctions currently modeled for this system.
Future versions of the code should consider malfunctions such as a malfunction of the feedwater control
system that results in increased FW flow, loss of main FW, and a feedline rupture such that SG inventory
drains from the rupture.
10
SSG Model
X.1.3.5 SG Water Level
X.1.3.5.1
Model description
The SG water level system calculates the equivalent secondary water level based on the secondary fluid
mass. The calculation is performed for each of the three simplified regions of the secondary side as
discussed in Section X.1.1.1. The system also calculates a heat transfer area fraction that adjusts the
available tube bundle heat transfer area to compensate for the degradation of heat transfer capability due
to the secondary side level dropping below the top of the tube bundle.
X.1.3.5.2
Assumptions and Approximations
The secondary side is approximated as three separate volumes. The shape and makeup of the SG varies
widely with elevation; therefore, in order to produce a more realistic equivalent water level, the SG is
split into three regions. The lower region mainly consists of the downcomer and tube bundle, the middle
region mainly consists of the primary separators and feedring region, and the upper region consists of the
secondary separators and steam dome.
X.1.3.5.3
Description of Equations and Variables
The SG water level system relies upon simply arithmetic and linear interpolation to determine the
equivalent SG water levels and the heat transfer area fraction. Note that none of the contributions can be
less than zero.
𝑉𝑓 =
𝑀𝑓
(16)
𝜌𝑓
𝑉𝑓
𝐸,
𝐿1 = {𝑉1 1
𝐸1 ,
𝑉𝑓 ≤ 𝑉1
(17)
𝑉𝑓 > 𝑉1
(𝑉𝑓 − 𝑉1 )
(𝐸2 − 𝐸1 ),
𝐿2 = { 𝑉2
(𝐸2 − 𝐸1 ),
𝑉𝑓 ≤ (𝑉2 − 𝑉1 )
(18)
𝑉𝑓 > (𝑉2 − 𝑉1 )
(𝑉𝑓 − 𝑉1 − 𝑉2 )
(𝐸𝑚𝑎𝑥 − 𝐸2 ),
𝐿3 = {
𝑉𝑡𝑜𝑡
(𝐸𝑚𝑎𝑥 − 𝐸2 ),
𝐿𝑡𝑜𝑡 = 𝐿1 + 𝐿2 + 𝐿3
(20)
𝑉𝑓 ≤ (𝑉𝑡𝑜𝑡 − 𝑉2 − 𝑉1 )
(19)
𝑉𝑓 > (𝑉𝑡𝑜𝑡 − 𝑉2 − 𝑉1 )
Where,
Mf
f
V1
V2
Vtot
Vf
E1
E2
Emax
L1
L2
L3
=
=
=
=
=
=
=
=
=
=
=
=
Current secondary fluid mass (kg)
Secondary fluid density (kg/m3)
Volume of lower SG region (m3)
Volume of middle SG region (m3)
Total volume of the SG secondary side (m3)
Current secondary fluid volume (m3)
Elevation of top of lower SG region (m)
Elevation of top of middle SG region (m)
Elevation of top of upper SG region (m)
Water level height contribution from lower SG region (m)
Water level height contribution from middle SG region (m)
Water level height contribution from upper SG region (m)
11
SSG Model
X.1.3.5.4
Malfunctions
There are no malfunctions associated with this system.
X.1.3.6 Turbine Pressure Calculation
X.1.3.6.1
Model description
This portion of the system calculates an estimated 1st stage turbine pressure based on the turbine load
demand and the secondary saturation pressure. This calculation is performed by subtracting a correction
factor from the secondary saturation pressure that is determined using a Simulink lookup table.
X.1.3.6.2
Assumptions and Approximations
The correction factors were determined based on calibration runs performed using the SSG model in a
standalone configuration. Adjustments may be required when the model is integrated.
X.1.3.6.3
Description of Equations and Variables
The system utilizes a Simulink lookup table and simple arithmetic. No explanation of equations is
required.
X.1.3.6.4
Malfunctions
There are no malfunctions associated with this system.
X.1.4 Constants Derivation
The following is a description of the constants concerning initial conditions, boundary conditions,
geometric data and material properties data that are used in the SSG model.
X.1.4.1 Secondary side of the SG constants
The initial fluid mass, vapor mass and saturation pressure for the secondary side were obtained iteratively
through calibration runs. The default values correspond to a power level of 100% and a primary side
vessel average temperature of 300°C and are included in the SSG initialization file.
X.1.4.2 Primary-to-secondary heat transfer constants
Required constants for the primary-to-secondary heat transfer subsystem are based on information
available from Revision 18 of the Design Control Document (Reference 3) and engineering judgment.
The AP1000 design includes 2 vertical U-tube SGs. SG geometric and performance data is provided in
Tables 5.4-4 and 5.4-5 of Reference 3. Table X.1.4.2-1 contains a summary of the key parameters used
for the primary-to-secondary heat transfer constants.
Table X.1.4.2-1 – SG data for primary-to-secondary heat transfer model
Description
Total heat transfer surface area
Tube outer diameter
Tube wall thickness
Number of SG tubes
Value
123,538 ft2 (11,477 m2)
0.688 in (0.2097 m)
0.040 in (0.0122 m)
10,025
Source
Ref. 3, Table 5.4-4
Ref. 3, Table 5.4-4
Ref. 3, Table 5.4-4
Ref. 3, Table 5.4-4
12
SSG Model
Using the values from Table X.1.4.2-1, the primary flow area and hydraulic diameter can be calculated as
follows:
𝐴𝑝𝑟𝑖𝑚 =
𝜋𝐷 2
∙𝑁
4
(21)
𝐴𝑝𝑟𝑖𝑚 = 2.405 m2
4 ∙ 𝐴𝑝𝑟𝑖𝑚
𝐷𝐻−𝑝𝑟𝑖𝑚 = √
𝜋
(22)
𝐷𝐻−𝑝𝑟𝑖𝑚 = 1.750 m
Where,
Aprim
D
N
DH-prim
=
=
=
=
Primary cross sectional flow area (m2)
Tube inner diameter (m)
Number of tubes
Primary side of the tube bundle hydraulic diameter (m)
Per Reference 3, the tube material is Inconel 690. Publicly available data for Inconel 600 has been used;
the makeup of these materials is largely the same and any differences in the conductivity data would have
only a second order impact on the heat transfer. The Inconel 600 thermal conductivity data was retrieved
from Reference 2, and is shown below.
Table X.1.4.2-2 – Tube wall thermal conductivity data
Primary side temperature (°C)
21
93
204
316
427
Thermal conductivity (W/m°C)
14.8E-3
15.7E-3
17.4E-3
19.2E-3
20.9E-3
X.1.4.3 Steam control system constants
The nominal steam flow rate is based on the value found in Tier 2, Chapter 15, Table 15.0-3 of
Reference 3. Slight adjustments to the value were made to assist in achieving steady state operation of
the model.
X.1.4.4 Feedwater control system constants
The nominal feedwater flow rate, temperature, and pressure are based on information found in Tier 2,
Chapter 15, Table 15.0-3 of Reference 3. Slight adjustments were made either due to conversion factors
or for assisting in achieving steady state operation of the model. Table 15.0-3 also presents the nominal
steam outlet pressure; however, the FW enthalpy calculation was performed at an arbitrarily increased
pressure to account for head effects.
13
SSG Model
X.1.4.5 SG water level constants
The parameters for the SG elevations are based on Reference 3 and engineering judgment. The level tap
elevations can be estimated from information in Figure 5.1-4 of Reference 3. For the SG volumes, an
approximate secondary side volume was assumed that is marginally larger than that presented in
Table 5.4-5. The split of the secondary side into three separate regions was based on the following logic.
The lower region is made up of the downcomer and the tube bundle region, and is also located in the
more narrow section of the SG. Therefore, this area would have a smaller height-to-volume ratio. The
middle region contains the primary separators and region between the deck plates. This is in the widest
section of the SG and also has more open space; therefore, a larger portion of the SG volume is within
this region. Finally, the upper region consists mainly of the secondary separators and steam dome, so
there is again a more significant amount of empty space.
The only calculations the secondary volumes and elevations are used in are the secondary water level
calculations. The water level calculations are used for display in the GUI, but more importantly in the
feedwater control system as the driver for changes in feedwater flow. Since it is SG water level deviation
that drives the FW control system, the actual level value is not of great significance. Furthermore, as this
is only a simplified secondary side with no secondary protection systems or malfunctions, the only use for
the NR and WR level indications will be to indicate transient conditions on the secondary side. Based on
this, the estimated volume and elevation values provide reasonable representations that are sufficient for
the purposes of this model.
An arbitrary nominal level of 15 m was chosen. It provids reasonable performance and therefore is
acceptable for the purposes of the simplified secondary model.
X.1.4.6 Turbine pressure constants
The data for the adjustment factor for calculating the 1st stage turbine pressure was based on iterative runs
during the calibration phase. These runs were performed with the SSG in a standalone configuration; e.g.,
with fixed primary boundary conditions. Validation of these values is required after the system has been
fully integrated.
X.1.5 GUI Interfaces
The primary focus of the initial version of the PANTHER code is the primary side of the plant; however,
provided on the next page is a proposed GUI for the SSG.
14
X.1.5.1 Screen Displays
The SSG GUI is shown in the following figure. It consists of an animated display of the secondary water level within each steam generator,
numerical displays of key output parameters (steam outlet mass flow rate, secondary saturation pressure, secondary saturation temperature, FW
inlet mass flow rate, NR water level and WR water level) and graphs of key parameters (secondary saturation pressure, steam outlet mass flow
rate, FW inlet mass flow rate, and NR water level).
Steam Outlet Mass Flow Rate
60
50
40
30
20
10
0
0
20
40
60
80
100
Steam outlet mass flow rate (kg/s)
Secondary Saturation Pressure (bara)
Secondary Saturation Pressure
70
1010
1000
990
980
970
960
950
940
930
920
910
0
20
40
80
100
80
100
SG NR Water Level
FW Inlet Mass Flow Rate
64
1010
1000
990
980
970
960
950
940
930
920
910
SG Water Level (% NR span)
FW Inlet Mass Flow Rate (kg/s)
60
Time (sec)
Time (sec)
62
60
58
56
54
52
50
0
20
40
60
Time (sec)
80
100
0
20
40
60
Time (sec)
Figure X.1.5.1-1: SSG GUI Screen
X.1.5.2 Screen Controls
The simplified secondary side model does not require any screen controls; however, for later versions of the PANTHER simulator code, the ability
to vary the turbine load, initiate turbine or pump trips, vary feedwater temperature, vary SG level, vary FW flow, and vary outlet steam flow
should be included.
15
X.1.6 Program Description and Simulink model
The SSG model is a Simulink model that requires additional SSG-specific Matlab™ scripts and inputs
from the PRC model and outputs information to the GUI, PRC, and PPX models.
X.1.6.1 Simulink Model and Matlab Functions
The Simulink portion of the SSG model is divided into a number of subsystems focusing on a specific
secondary function. Each subsystem is described in Sections X.1.6.1.1 through X.1.6.1.14.
X.1.6.1.1
Secondary Side of the Steam Generator (SSG_Solution) Simulink Model
The inputs and outputs to the SSG_Solution subsystem are displayed below. See Table X.1.6.1.1-1 for a
description of the inputs and outputs. This subsystem calculates the secondary side transient response
based on secondary side properties, FW inlet flow, steam outlet flow, and primary-to-secondary heat
addition.
Figure X.1.6.1.1-1 – Inputs and outputs of SSG_Solution subsystem
The SSG_Solution subsystem detail is shown in Figure X.1.6.1.1-2, with a detailed description of the
model following.
16
SSG Model
Figure X.1.6.1.1-2 – SSG_Solution Subsystem
The SSG_Solution subsystem creates a vector of inputs for the secondary solution Matlab function that
consists of the following; vapor generation rate (unitless), total secondary vapor mass (kg), total
secondary liquid mass (kg), secondary saturation pressure (bar), net primary-to-secondary heat transfer
(kJ/s), feedwater flow rate (kg/s), feedwater enthalpy (kJ/kg), outlet steam flow rate (kJ/kg), steam
enthalpy (kJ/kg), and the time step size (s). This vector is then fed to the external Matlab script
SSG_solution.m (discussed in Section X.1.6.1.2), which calculates the change in vapor generation rate,
liquid mass, vapor mass, and pressure per time.
These changes per time are then fed to an integrator block, which converts them to overall values. The
initial values for the integrator block are read from the initialization file and are based upon values
determined during calibration tests. Note that the pressure units used in the model in general are Pa;
however, the thermodynamic properties lookup routine requires that pressures be input in the units of
bara. Therefore, the initial condition pressure is converted from Pa to bara before being fed to the vector
concatenation. The integrator block then outputs a 4x1 matrix, which is then separated into the individual
variables. Before the parameters are output, a check is first performed using switches to ensure that the
masses and pressure have not gone below 0. This would not only be an aphysical phenomenon, but it
would also lead to code instability. The parameters are then output to the higher level SSG Simulink
model.
Table X.1.6.1.1-1 summarizes the variables of the SSG_Solution subsystem.
17
SSG Model
Table X.1.6.1.1-1 – SSG_Solution Subsystem Variables
Variable Name
Variable Description
PSG_SSG_Qnet
Net primary-to-secondary heat
transfer
SSG_FW_MassFlow
Feedwater inlet mass flow rate
Units
kJ/s
SSG_FW_Enthalpy
SSG_Steam_MassFlow
Feedwater enthalpy
Steam outlet mass flow rate
kJ/kg
kg/s
SSG_Steam_Enthalpy
Outlet steam enthalpy
kJ/kg
dt
vapor_genrate
Time step size
Internal process variable for the
vapor generation rate
Internal process variable for the
total secondary steam mass
Internal process variable for the
total secondary liquid mass
Internal process variable for the
secondary side pressure
Initial condition for the vapor
generation term of the solution
Initial condition for the
secondary vapor mass
Initial condition for the
secondary fluid mass
Initial condition for the
secondary pressure
Vapor generation term calculated
by SSG_Solution
Total secondary side vapor mass
calculated by SSG_Solution
Total secondary side fluid mass
calculated by SSG_Solution
Secondary side saturation
pressure calculated by
SSG_Solution
s
-
Originating System
SSG – internally calculated variable, from
SSG_HeatTransfer
SSG – internally calculated variable, from
SSG_FWControlSystem
Boundary condition from initialization file
SSG – internally calculated variable, from
SSG_SteamControlSystem
SSG – internally calculated variable, from
calculation SSG_Props
Boundary condition from initialization file
Internal to SSG_Solution
kg
Internal to SSG_Solution
kg
Internal to SSG_Solution
bara
Internal to SSG_Solution
-
Initial condition from initialization file
kg
Initial condition from initialization file
kg
Initial condition from initialization file
Pa
Initial condition from initialization file
-
SSG – calculated by SSG_Solution
kg
SSG – calculated by SSG_Solution
kg
SSG – calculated by SSG_Solution
kg
SSG – calculated by SSG_Solution
steam_mass
liquid_mass
steam_pressure
SSG_Gamma0
SSG_Mv0
SSG_Mf0
SSG_P0
SSG_VaporTerm
SSG_VaporMass
SSG_FluidMass
SSG_Steam_Pressure
kg/s
X.1.6.1.2
SSG_Solution Matlab Functions
The Matlab function SSG_solution.m is required to execute the SSG_Solution subsystem. The following
is the code and associated description.
First, the function name, outputs, and required inputs are defined. Note that the vapor generation term,
which would be the first term in the input vector, is not used in any calculations and therefore a “~” is
input in the input definitions. The expected units of each of the inputs are defined.
function B = SSG_solution(~,Mv,Mf,p,Q,wfw,hfw,wg,hg,dt)
% Mv %kg
% Mf %kg
% p
%bar
% Q
%kJ/s
% wfw %kg/s
% hfw %kJ/kg
18
SSG Model
% wg
% hg
% dt
%kg/s
%kJ/kg
%s
Next, function handlers are created for determining the thermodynamic properties of the water and steam.
Function handlers are created to determine the following properties solely as a function of pressure;
density of saturated fluid, density of saturated steam, enthalpy of saturated fluid, enthalpy of saturated
steam, saturation temperature, isobaric specific heat of saturated vapor, and isobaric specific heat of
saturated steam.
% define the functions for saturated steam
XrhoF_p = @(p)XSteam('rhoL_p',p);
XrhoV_p = @(p)XSteam('rhoV_p',p);
XhF_p = @(p)XSteam('hL_p',p);
XhV_p = @(p)XSteam('hV_p',p);
Xt_p = @(p)XSteam('Tsat_p',p);
XCpV_p = @(p)XSteam('CpV_p',p);
XCpF_p = @(p)XSteam('CpL_p',p);
Next, a user-defined function “deriv” is utilized to determine the required properties as a function of
pressure and as a differential equation varying pressure. The function “deriv” is described further below
in this section. Calculated quantities that are not required are discarded through use of the “~” symbol in
the output variable locations.
% compute density, enthalpy, and
dp = 0.1;
%generic
%
[rf,rfp] = deriv(XrhoF_p,p,dp);
[hf,hfp] = deriv(XhF_p,p,dp);
[rv,rvp] = deriv(XrhoV_p,p,dp);
[hv,hvp] = deriv(XhV_p,p,dp);
[~,tsatp] = deriv(Xt_p,p,dp);
[CpV,~] = deriv(XCpV_p,p,dp);
[CpF,~] = deriv(XCpF_p,p,dp);
steam derivatives
dp of 0.1 bar.
%[kg/m^3, kg/m^3/bar]
%[kJ/kg, kJ/kg/bar]
%[kg/m^3, kg/m^3/bar]
%[kJ/kg, kJ/kg/bar]
%[~, degC/bar]
%[kJ/kg*degC, ~]
%[kJ/kg*degC, ~]
For the saturated mixture/structural energy properties, a weighted average of the saturated fluid and
saturated vapor properties is calculated, with the properties weighted based on mass fraction. A constant
is then calculated which represents (𝜌𝐶𝑉)𝑆𝑀 .
rhoavg = (rf*Mf+rv*Mv)/(Mf+Mv); %[kg/m^3]
Cpavg = (CpF*Mf+CpV*Mv)/(Mf+Mv); %[kJ/kg*degC]
Vtot = (Mf/rf)+(Mv/rv);
%[m^3]
con1 = rhoavg*Cpavg*Vtot;
Finally, the matrices are built corresponding to Equation (7) in Section X.1.3.1.3. The solution is then
performed by setting the unknown parameters matrix (B) equal to the left hand side matrix (M) divided
by the right hand solution matrix (N). This gives a 4x1 matrix, which must then be transposed to a 1x4 in
order to be able to be separated by the demux Simulink block when returned to the SSG_Solution model.
% setup the matrices
M = [ dt ,
0 ,
1 ,
0 ;...
%[ s, -, -, -;
-1*dt ,
1 ,
0 ,
0 ;...
% s, -, -, -;
0 , 1/rv , 1/rf, -1*(Mv/(rv*rv)*rvp+Mf/(rf*rf)*rfp);... % -, m^3*bar/kg,
m^3*bar/kg, m^3/bar
0 ,
hv ,
hf , (Mv*hvp+Mf*hfp+con1*tsatp)];
% -, kJ/kg, kJ/kg, kJ]
N = [ wfw*dt; -wg*dt; 0; (Q+wfw*hfw-wg*hg)*dt];
19
SSG Model
B = M\N;
D = transpose(B);
B = D;
return
end
The “deriv" function enables the computation of a derivative in a discrete, linearized manner. It first
evaluates the desired function using the given data, and returns the value. It then computes the derivate
by evaluating the desired function at a point one step forward and one step backward as determined by the
input step size (h). The derivative is then computed as the slope between these points. To mitigate
problems with the calling functions, a check is performed to see if a non-numeric answer has been
returned; if so, the value is generically set to 0 to prevent the code from crashing.
function [y,y_] = deriv(func,x,h)
%This function enables computing the derivative in a discrete, linearized
%manner
y = func(x);
y2 = func(x+h);
y1 = func(x-h);
if isnan(y)==1
y=0;
end
if isnan(y2)==1
y2=0;
end
if isnan(y1)==1
y1=0;
end
y_ = (y2-y1)/2/h;
return
end
X.1.6.1.3
Primary-to-Secondary Heat Transfer (SSG_HeatTransfer)
The inputs and outputs to the SSG_Solution subsystem are displayed below. See Table X.1.6.1.3-1 for a
description of the inputs and outputs. This subsystem calculates the net primary-to-secondary heat
transfer based on primary and secondary conditions. In addition, associated thermal resistances are also
calculated based on primary conditions.
20
SSG Model
Figure X.1.6.1.3-1 – Inputs and outputs of SSG_HeatTransfer subsystem
The SSG_HeatTransfer subsystem detail is shown in Figures X.1.6.1.3-2 through X.1.6.1.3-4.
Figure X.1.6.1.3-2 – SSG_HeatTransfer Subsystem Part 1
21
SSG Model
This portion of the SSG_HeatTransfer subsystem obtains takes the inputs provided to the subsystem and
either directs them to a “To” block for ease of use in other parts of the subsystem (as with the inlet/outlet
enthalpies, primary flow rate and secondary temperature) or uses them to calculate other necessary
variables. Primary pressure is provided by the PRC system in the units of Pascale, but needs to be
converted to bar for use in the thermodynamic property lookup routine.
The SG inlet and outlet enthalpies from the primary side are obtained from the PRC system model. These
enthalpies are then averaged to obtain a reasonable approximation of the average enthalpy of the primary
side SG node. This average enthalpy is used in conjunction with the primary pressure input to calculate
other necessary input parameters using the SSG_primprops.m Matlab script. The parameters calculated
will be used in the overall heat transfer equation as well as to calculate the thermal resistances. The
primary temperature is used as an input to a lookup table for the thermal conductivity of the tubes. Per
the AP1000™ Design Control Document, Revision 18 (Reference 3), the tube material is Inconel 690.
Publicly available data for Inconel 600 (Reference 2) was used under the assumption that it would
reasonably approximate the performance of Inconel 690.
Figure X.1.6.1.3-3 – SSG_HeatTransfer Subsystem Part 2
The next step is to calculate the thermal resistances for use in the overall heat transfer equation. The
primary film thermal resistance and tube wall resistance are calculated based on Equations (12) and (13)
from Section X.1.3.2.3. As the resistances occur in series, the primary film and tube wall resistances
were added to obtain the overall thermal resistance.
22
SSG Model
Figure X.1.6.1.3-4 – SSG_HeatTransfer Subsystem Part 3
The final step is to calculate the overall primary-to-secondary heat transfer based on Equation (9) using
the parameters calculated within and the provided heat transfer area parameters. The heat transfer area
portion of the solution addresses heat transfer degradation due to SG tube bundle uncovery by adjusting
the available heat transfer area based on the fraction of the tube bundle that is uncovered.
Table X.1.6.1.3-1 summarizes the variables of the SSG_HeatTransfer subsystem.
Table X.1.6.1.3-1 – SSG_HeatTransfer Subsystem Variables
Variable Name
Variable Description
Units
SSG_PRC_EnthIn
Primary side SG inlet enthalpy
kJ/kg
SSG_PRC_EnthOut
Primary side SG outlet enthalpy kJ/kg
SSG_PRC_Pressure
Primary side pressure
Pa
SSG_PRC_Flow
Primary side SG inlet mass flow kg/s
rate
SSG_Primary_Dh
Primary side SG hydraulic
m
diameter (tube total hydraulic
diameter)
SSG_Primary_FlowA
Primary side tube flow area
m2
(total of all tubes)
SSG_Tube_Thickness
Thickness of the tube walls
m
SSG_HT_AreaFrac
Fraction of the tube bundle
surface area available for heat
transfer
SSG_MaxHTA
Maximum tube bundle surface
m2
area available for heat transfer
SSG_Steam_Temp
Secondary saturation
°C
temperature to be used in heat
transfer calculation
PSG_SSG_Qnet
Net primary-to-secondary heat
kJ/s
transfer
hprim_in
Internal process variable for
kJ/kg
primary SG inlet enthalpy
hprim_out
Internal process variable for
kJ/kg
primary SG outlet enthalpy
Pprim
Internal process variable for
bara
primary pressure
Wprim
Internal process variable for
kg/s
primary flow rate
hprim_avg
Internal process variable for
kJ/kg
average primary SG enthalpy
Originating System
PRC
PRC
PRC
PRC
From initialization file
From initialization file
From initialization file
SSG – internally calculated variable, from
SSG_WaterLevel
From initialization file
SSG – internally calculated variable, from
SSG_Solution
Output from SSG_HeatTransfer
Internal to SSG_HeatTransfer
Internal to SSG_HeatTransfer
Internal to SSG_HeatTransfer
Internal to SSG_HeatTransfer
Internal to SSG_HeatTransfer
23
SSG Model
Table X.1.6.1.3-1 – SSG_HeatTransfer Subsystem Variables
Variable Name
Variable Description
Units
Tprim_avg
Internal process variable for
°C
primary fluid temperature
ktube
Internal process variable for
W/m°C
tube wall thermal resistance
rho
Internal process variable for
kg/m3
primary fluid density
Cp
Internal process variable for
kJ/kg°C
primary fluid isobaric specific
heat
mu
Internal process variable for
Pa/s
primary fluid dynamic viscosity
k
Internal process variable for
W/m°C
primary fluid thermal
conductivity
Tsec
Internal process variable for
°C
secondary temperature for use
in overall heat transfer
calculation
Rpf
Internal process variable for
W/m2°C
primary film thermal resistance
Rtube
Internal process variable for
W/m2°C
tube wall thermal resistance
Rtotal
Internal process variable for
W/m2°C
total thermal resistance
Originating System
Internal to SSG_HeatTransfer
Internal to SSG_HeatTransfer
Internal to SSG_HeatTransfer
Internal to SSG_HeatTransfer
Internal to SSG_HeatTransfer
Internal to SSG_HeatTransfer
Internal to SSG_HeatTransfer
Internal to SSG_HeatTransfer
Internal to SSG_HeatTransfer
Internal to SSG_HeatTransfer
X.1.6.1.4
SSG_HeatTransfer Matlab Functions
The Matlab function SSG_primprops.m is required to execute the SSG_HeatTransfer subsystem. The
following is the code and associated description.
First, the function name and inputs are defined. Note that the pressure is input in bara, as required by the
thermodynamic property lookup routines.
function D = SSG_primprops(p,h)
%p given in bar
Next, the function handlers for the thermodynamic property lookups are defined. The properties for
saturated temperature, density, isobaric specific heat, dynamic viscosity, and thermal resistance are
defined. These calculations are then performed, and the results are output as a 1x4 matrix to the higher
level SSG system.
% define the functions for saturated steam
XT_ph = @(p,h)XSteam('T_ph',p,h);
Xr_ph = @(p,h)XSteam('rho_ph',p,h);
XC_ph = @(p,h)XSteam('Cp_ph',p,h);
Xm_ph = @(p,h)XSteam('my_ph',p,h);
Xtc_ph = @(p,h)XSteam('tc_ph',p,h);
% calculations
Tprim = XT_ph(p,h);
rho
= Xr_ph(p,h);
24
SSG Model
cp
mu
k
= XC_ph(p,h);
= Xm_ph(p,h);
= Xtc_ph(p,h);
%hV = 2789.63;
D = [Tprim rho cp mu k];
return
end
X.1.6.1.5
Calculation of secondary properties (SSG_props)
The inputs and outputs to the SSG_props routine are shown below.
Figure X.1.6.1.5-1 – Inputs and outputs of SSG_props subsystem
This routine takes the calculated secondary saturated pressure and performs a thermodynamic property
lookup using the Matlab script SSG_props.m. The output from this is a 1x3 matrix, which is then split
into three individual parameters (saturated temperature, fluid density, and saturated steam enthalpy).
Table X.1.6.1.5-1 summarizes the variables of the SSG_Props subsystem.
Table X.1.6.1.5-1 – SSG_Props Subsystem Variables
Variable Name
Variable Description
SSG_Steam_Pressure
Secondary side saturation
pressure
SSG_Steam_Temp
Secondary side saturation
temperature
SSG_FluidDensity
Secondary side saturated fluid
density
SSG_Steam_Enthalpy
Secondary side saturated steam
enthalpy
Units
Bar
°C
Originating System
SSG – internally calculated variable, from
SSG_Solution
Output from SSG_Props
kg/m3
Output from SSG_Props
kJ/kg
Output from SSG_Props
X.1.6.1.6
SSG_Props Matlab Functions
The Matlab script SSG_props.m performs a thermodynamic property lookup similar to that performed by
the script SSG_solution.m (see Section X.1.6.1.2). The primary difference is that the derivative of the
properties is not required, so this script simply calls the thermodynamic property lookup script XSteam to
calculate the saturation temperature, liquid density, and steam enthalpy based on the secondary saturated
pressure.
function C = SSG_props(p)
%p given in bar
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SSG Model
% define the functions for saturated steam
Xt_p = @(p)XSteam('Tsat_p',p);
XrhoL_p = @(p)XSteam('rhoL_p',p);
XhV_p = @(p)XSteam('hV_p',p);
% calculations
tsat = Xt_p(p);
rhoL = XrhoL_p(p);
hV = XhV_p(p);
%hV = 2789.63;
%degC
%kg/m^3
%kJ/kg
C = [tsat rhoL hV]; %[degC, kg/m^3, kJ/kg]
return
end
X.1.6.1.7
Steam/Turbine Control System (SSG_SteamControlSystem)
The inputs and outputs to the SSG_SteamControlSystem subsystem are displayed below. See
Table X.1.6.1.7-1 for a description of the inputs and outputs. This subsystem calculates the outlet steam
mass flow rate based on initialization parameters.
Figure X.1.6.1.7-1 – SSG_SteamControlSystem Inputs and Outputs
The SSG_SteamControlSystem subsystem detail is shown in Figure X.1.6.1.7-2.
Figure X.1.6.1.7-2 – SSG_SteamControlSystem Subsystem
The SSG_SteamControlSystem subsystem calculates the steam outlet mass flow rate based on
considering whether the turbine is tripped, the user-defined turbine load fraction, and the nominal mass
26
SSG Model
flow rate. The calculated mass flow rate is then compared to ensure it falls within the allowable range of
flows as defined by the user.
First, the turbine trip signal is read. A value of 0 indicates that the turbine is not tripped and a value of 1
is then passed to the calculation of the load fraction. A value of 1 indicates that the turbine is tripped, and
the Addition block then outputs a value of 0 to the calculation of the load fraction, causing the mass flow
rate to go to zero. The load fraction block takes the load fraction from the turbine trip signal and
multiplies that by the fractional load fraction from the user-defined turbine load fraction. These
multiplied together generate the overall turbine load, which is then multiplied by the nominal mass flow
rate. A pair of switches then perform a comparison to ensure that the calculated mass flow rate is below
the user-defined maximum (controlled by initialization parameter SSG_Steam_MaxFlow) and a
minimum of 0.
Table X.1.6.1.7-1 summarizes the variables of the SSG_SteamControlSystem subsystem.
Table X.1.6.1.7-1 – SSG_SteamControlSystem Subsystem Variables
Variable Name
Variable Description
Units
Originating System
SSG_Turbine_Trip
Turbine trip signal (0 if turbine
SSG initialization file. Note that in future
not tripped, 1 if turbine tripped)
versions of the PANTHER simulator code
this signal will originate from the PPS
system
SSG_Turbine_Load
Turbine load fraction
fraction
SSG initialization file. Note that in future
versions of the PANTHER simulator code
this signal will originate from the PCS
system
SSG_Steam_NomFlow Nominal outlet steam mass flow kg/s
SSG initialization file.
rate
SSG_Steam_MassFlow Outlet steam mass flow rate
kg/s
Output from SSG_SteamControlSystem
SSG_Steam_MaxFlow Maximum allowable outlet
kg/s
SSG initialization file.
steam mass flow rate
X.1.6.1.8
SSG_SteamControlSystem Matlab Functions
The SSG_SteamControlSystem subsystem does not use any Matlab functions.
X.1.6.1.9
Feedwater Control System (SSG_FWControlSystem)
The inputs and outputs to the SSG_FWControlSystem subsystem are displayed below. See
Table X.1.6.1.9 -1 for a description of the inputs and outputs. This subsystem calculates the inlet FW
mass flow rate based on various initialization parameters, control parameters, and a calculation of SG
water level deviation.
27
SSG Model
Figure X.1.6.1.9-1 – SSG_FWControlSystem Inputs and Outputs
The SSG_FWControlSystem subsystem detail is shown in Figures X.1.6.1.9-2 and X.1.6.1.9-3.
Figure X.1.6.1.9-2 – SSG_SteamControlSystem Subsystem Part 1
The SSG_SteamControlSystem subsystem calculates the FW inlet mass flow rate based primarily on
maintaining the programmed SG water level. This calculation is performed by subtracting a lead/lagged
current SG water level signal from the desired SG water level. This deviation is then normalized by
dividing by the desired SG water level to create a fractional deviation, and a gain of 100 is then applied to
increase the magnitude of the correction signal to create a faster system response. This level correction
factor is then fed to Part 2 of the subsystem described below.
Figure X.1.6.1.9-3 – SSG_SteamControlSystem Subsystem Part 2
The FW inlet mass flow rate is calculated based on considering whether feed pumps are tripped, the userdefined FW load fraction, the water level correction factor and the nominal mass flow rate. The
calculated mass flow rate is then compared to ensure it falls within the allowable range of flows as
defined by the user.
First, the FW pump trip signal is read. A value of 0 indicates that the FW pumps are not tripped and a
value of 1 is then passed to the calculation of the flow fraction. A value of 1 indicates that the FW pumps
are tripped, and the Addition block then outputs a value of 0 to the calculation of the flow fraction,
28
SSG Model
causing the mass flow rate to go to zero. The flow fraction block takes the flow fraction from the FW
pump trip signal and multiplies that by the flow correction fraction. This flow correction factor is a sum
of the FW demand fraction, which is set equal to the turbine load fraction in order to ensure conservation
of mass, and the SG water level correction. These multiplied together generate the overall FW inlet flow
demand, which is then multiplied by the nominal mass flow rate. A pair of switches then perform a
comparison to ensure that the calculated mass flow rate is below the user-defined maximum (controlled
by initialization parameter SSG_FW_MaxFlow) and a minimum of 0.
Table X.1.6.1.9-1 summarizes the variables of the SSG_FWControlSystem subsystem.
Table X.1.6.1.9-1 – SSG_FWControlSystem Subsystem Variables
Variable Name
Variable Description
Units
SSG_FW_Trip
FW pump trip signal (0 if
turbine not tripped, 1 if turbine
tripped)
Originating System
SSG initialization file. Note that in future
versions of the PANTHER simulator code
this signal will originate from the PPS
system
SSG initialization file. Note that in future
versions of the PANTHER simulator code
this signal will originate from the PCS
system
SSG initialization file.
SSG_Turbine_Load
Turbine load fraction (used to
drive FW flow demand fraction)
fraction
SSG_FW_Flow
Nominal inlet FW mass flow
rate
Current SG water level
kg/s
Desired SG water level
Inlet FW mass flow rate
Lead time constant for current
SG water level signal
Lag time constant for current
SG water level signal
Initial condition for lead/lag
controller for SG water level
signal
FW correction factor based on
SG water level deviation
Maximum allowable inlet FW
mass flow rate
m
kg/s
s
SSG – internally calculated variable, from
SSG_WaterLevel.
SSG initialization file.
Output from SSG_FWControlSystem
SSG initialization file.
s
SSG initialization file.
m
SSG initialization file.
fraction
Internal to SSG_FWControlSystem
kg/s
SSG initialization file.
SSG_Level
SSG_DesiredLevel
SSG_FW_MassFlow
Tau3
Tau4
SSG_Level0
SGLevel_correction
SSG_FW_MaxFlow
m
X.1.6.1.10
SSG_FWControlSystem Matlab Functions
The SSG_FWControlSystem subsystem does not use any Matlab functions.
X.1.6.1.11
SG Water Level Calculation (SSG_WaterLevel)
The inputs and outputs to the SSG_WaterLevel subsystem are displayed below. See Table X.1.6.1.11 -1
for a description of the inputs and outputs. This subsystem calculates the SG water level based on the
secondary fluid mass and also calculates the fraction of the tube bundle area that is available for heat
transfer.
29
SSG Model
Figure X.1.6.1.11-1 – SSG_FWControlSystem Inputs and Outputs
The SSG_WaterLevel subsystem detail is shown in Figures X.1.6.1.11-2 and X.1.6.1.11-6.
Figure X.1.6.1.11-2 – SSG_WaterLevel Subsystem Part 1
Part 1 of the SSG_WaterLevel subsystem establishes necessary internal parameters for ease of creating
the Simulink model. Additionally, the secondary side fluid volume is calculated by dividing the fluid
mass by the fluid density, which are calculated by the SSG_Solution and SSG_Props subsystems,
respectively.
30
SSG Model
Figure X.1.6.1.11-3 – SSG_WaterLevel Subsystem Part 2
The calculation of the SG water level is based on calculating the equivalent fluid volume in the SG
secondary side. As discussed in Section X.1.3.1.2, the secondary side of the steam generator is separated
into three regions; below the lower NR tap, between the NR level taps, and above the upper NR level tap.
The calculation is performed in three stages, one for each region.
First, the overall secondary fluid volume is divided by the total secondary volume below the lower NR
level tap and multiplied by the elevation of the lower NR level tap. If the current fluid volume is less than
the region volume, the ratio of volumes applied to the lower NR level tap elevation is output from the
switch; if the current fluid volume is greater than the region volume, it indicates that the water level is
above the top of the region and the elevation of the top of the region (lower NR level tap elevation) is
output by the switch.
Next, the second region is analyzed. First, the overall secondary fluid volume is reduced by the volume
of the lower region volume. This is done because the contribution of the volume in the first region has
already been considered in the first portion of the calculation. The same calculation procedure used for
the lower region is then utilized, with the ratio of the current fluid volume less the lower region volume
compared to the second region volume applied to the height of the region (the difference in elevations of
the upper and lower NR level taps). If the result is greater than the region height, the region height is
returned by the switch. A second switch is added to ensure that if the result of the calculation is less than
zero, a zero is returned by the switch.
Finally, the third region is analyzed. Similar to the calculation for the second region, the current
secondary fluid volume is adjusted by the volumes for the lower and middle regions. This is compared
with the third volume region, and the ratio is applied to the height of the third region. As with the middle
region, two switches are utilized to ensure that the maximum height of the region is not exceeded and that
a contribution of less than zero is zeroed out.
The contributions from each of the regions are then added together, and the result is the equivalent
secondary water level.
31
SSG Model
Figure X.1.6.1.11-4 – SSG_WaterLevel Subsystem Part 3
Part 3 of the SSG_WaterLevel subsystem converts the SG water level in meters to NR and WR levels in
terms of percent span. This is performed using linear interpolation based on the current water level and
the location of the upper and lower level taps. The results are returned to the higher level system for
output to the graphical user interface.
Figure X.1.6.1.11-5 – SSG_WaterLevel Subsystem Part 4
Part 4 of the SSG_WaterLevel subsystem calculates the fraction of the tube bundle area that is available
for heat transfer based on the secondary water level. If the water level falls below the elevation of the top
of the tube bundle, the HT area fraction is reduced based on a ratio of the water level to the tube bundle
height. This area fraction is then returned for use in the SSG_HeatTransfer subsystem.
Table X.1.6.1.11-1 summarizes the variables of the SSG_WaterLevel subsystem.
Table X.1.6.1.11-1 – SSG_WaterLevel Subsystem Variables
Variable Name
Variable Description
Units
SSG_FluidMass
Total secondary side fluid
kg
mass
SSG_FluidDensity
Density of the secondary side
kJ/kg
fluid
SSG_Level
Equivalent secondary side
m
water level
SSG_NR_Level
Equivalent secondary side
% NR
water level in terms of narrow
span
range span
SSG_WR_Level
Equivalent secondary side
% WR
water level in terms of wide
span
range span
SSG_HT_AreaFrac
Fraction of tube bundle area
fraction
available for heat transfer (due
to secondary side dry out)
SSG_NR_LowerTapElev Lower NR tap elevation
m
Originating System
SSG – internally calculated variable,
from SSG_Solution
SSG – internally calculated variable,
from SSG_Props
Output of SSG_WaterLevel
Output of SSG_WaterLevel
Output of SSG_WaterLevel
Output of SSG_WaterLevel
SSG initialization file
32
SSG Model
Table X.1.6.1.11-1 – SSG_WaterLevel Subsystem Variables
Variable Name
Variable Description
Units
SSG_NR_UpperTapElev Upper NR tap elevation
m
SSG_V1
Volume of lower region of
m3
secondary side of SG (from the
top of the tube sheet to the
elevation of the lower NR level
tap)
SSG_V2
Volume of middle region of
m3
secondary side of SG (between
the upper and lower NR level
taps)
SSG_Vtot
Total secondary side SG
m3
volume
SSG_WR_LowerTapElev Lower WR tap elevation
m
SSG_WR_UpperTapElev Upper WR tap elevation
m
SSG_MaxTubeElev
Elevation of the top of the tube m
bundle (secondary side, from
the top of the tube sheet)
Originating System
SSG initialization file
SSG initialization file
SSG initialization file
SSG initialization file
SSG initialization file
SSG initialization file
SSG initialization file
X.1.6.1.12
SSG_WaterLevel Matlab Functions
The SSG_WaterLevel subsystem does not use any Matlab functions.
X.1.6.1.13
1st Stage Turbine Pressure Calculation (SSG_TurbinePressure)
The inputs and outputs to the SSG_TurbinePressure subsystem are displayed below. See
Table X.1.6.1.13 -1 for a description of the inputs and outputs. This subsystem calculates the estimated
1st stage turbine pressure for use in turbine power calculations based on the saturated steam pressure.
Figure X.1.6.1.13-1 – SSG_TurbinePressure Inputs and Outputs
The SSG_TurbinePressure subsystem detail is shown in Figures X.1.6.1.13-2.
Figure X.1.6.1.13-2 – SSG_TurbinePressure Subsystem
33
SSG Model
The calculation of first stage turbine pressure is based on an adjustment factor applied to the secondary
side saturation pressure. This adjustment factor comes from a data lookup table based on the turbine
demand fraction. The turbine pressure is returned in the units of both bara and psia.
Table X.1.6.1.13-1 summarizes the variables of the SSG_TurbinePressure subsystem.
Table X.1.6.1.13-1 – SSG_TurbinePressure Subsystem Variables
Variable Name
Variable Description
Units
SSG_Turbine_load
Turbine load demand
fraction
SSG_Steam_Pressure
Secondary side saturated
bara
pressure
SSG_TurbinePres_bar
1st stage turbine pressure
bara
SSG_TurbinePres_psia
1st stage turbine pressure
psia
bar_to_psi
Conversion factor for bara to
n/a
psia
Originating System
SSG initialization file
SSG – internally calculated variable,
from SSG_Solution
Output from SSG_TurbinePressure
Output from SSG_TurbinePressure
SSG initialization file
X.1.6.1.14
SSG_TurbinePressure Matlab Functions
The SSG_TurbinePressure subsystem does not use any Matlab functions.
X.1.7 References
1. Todreas, N.E. and M.S. Kazimi, “Nuclear Systems 1: Thermal Hydraulic Fundamentals,” Taylor
and Francis, 1990.
2. Inconel 600 Technical Data, High Temp Metals, Inc.,
[http://www.hightempmetals.com/techdata/hitempInconel600data.php]
3. AP1000 Design Control Document, Revision 18, available via the United States Nuclear
Regulatory Commission ADAMS reading room.
34