NPP Simulators for Education Workshop - Passive PWR Models
Wilson Lam ([email protected]) CTI Simulation International Corp. www.cti-simulation.com
Sponsored by IAEA
Learning Objectives Understand the scope of the simulation of a passive PWR reactor.
Describe approximations made in the math models for the simulation.
Describe the difference between lumped parameter models and distributed parameter models.
Explain reactivity as a global reactor concept and not a zone concept (i.e., it is not precisely correct to speak in terms of zone reactivity)
Understand the origins of decay heat and how it is modeled in the CTI desktop simulations.
Understand the origins of delayed neutrons and how they are modeled in the CTI simulation.
Control Rods Reactivity
Reactor Protection System
Neutron Flux
Xenon Reactivity
Doppler Reactivity
Coolant Temperature Reactivity
Control Rods Position In core
Fuel Rod Thermal Output
Flux shapes Changes
Coolant Pumps Dynamics & Coolant Flow
Core Inlet Enthalpy & Pressures at Cold Legs
Core Primary Coolant Heat Transfer & Hydraulics
Downcomer Flow & Inlet Enthalpy
Steam Flow Rate
Coolant Enthalpy & Pressures at Hot Legs
SG Dome Pressure
Feedwater Flow & Enthalpy
Reactor Power Control
Boiler Pressure Control
Boiler Drum Water Level Control
Turbine Generator & Unit Power
Condenser
Feedwater Heaters
PWR Modeling Diagram
Other Reactivity Effects -Boron injection/removal
Reactor Model
Primary Coolant Heat Transfer to SG
Point Kinetic Reactor Model
dndt
=∆K − β
Λ⋅ n + Σ
i=1
m
λi ⋅Ci
dCi
dt= βi ⋅
nΛ− λi ⋅Ci for I = 1….m
Where ΔK = (Ke - 1) / Ke Λ = / Ke
Spatial Kinetic Model for Pressurized Water Reactor Nodal approach based on Avery’s coupled
region kinetics theory
12 point kinetics models to simulate the 12 reactor zones in core.
Each zone reactor model based neutron balance DE , and 6 different neutron delay groups.
Reactivity changes in each zone reactor - a function of (a) control rods position, (b) zonal concentration of Xenon (c) zonal fuel temp (d) zonal moderator temp. (e) boron conc. (f) zone reactivity coupling effects.
Reactivity due to zone couplings are calculated separately for each zone using
Sum up all the effects for any particular zone, and enter as one of the reactivity change for that zone.
Total power from the 12 zone reactors are summed up and then divided by 12 to get normalized overall power.
∆ Λρ α
λ
ij i ij ij
i i
m mZONEjm
i
KNN l
C
N= +
=
∑1 1
6
1
2
3
4
5
6
87
Gray Rods Worth to Reactor Zones, as a function of Rods Position
0
0.2
0.4
0.6
0.8
1
1.2
0 20 40 60 80 100 120
% Withdrawn from Core
Nor
mal
ized
Rod
s W
orth
UPPER ZONES
MIDDLE ZONES
LOWER ZONES
Dark Rods Reactivity Worth to Reactor Zones, as a function of Rods Position
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
0 20 40 60 80 100 120
% Withdrawn from Core
Nor
mal
ized
Rod
s W
orth
UPPER ZONES
MIDDLE ZONES
LOWER ZONES
The decay heat calculation within each zone assumes 3 separate decay product groups
The decay heat from each zone used to calculate zone coolant temperature and fuel temp in each zone.
P = Nflux - Σ (γi. Nflux- Di) dDi/dt = λi. (γi. Nflux- Di) γi = fission product fraction for Decay Group I λi = decay time constant for Decay group i
The average fuel energy equation is given by:
)( cff
fff TTUAPdt
dTCV −−=ρ …………………(5.7-1)
Where
ρf = volume average fuel density Vf = fuel volume in one zone Cf = average fuel specific heat capacity Tf = average fuel temperature Tc = average coolant temperature P = reactor power U = overall heat transfer coefficient
A = overall heat transfer area for fuel channel
The average core coolant energy equation is given by:
)( cfooiio
cc TTUAhWhWdt
dhV −+−=ρ …………..(5.7-2)
Where
ρc = volume average coolant density Vc = coolant volume in one zone hi = average coolant specific enthalpy at inlet of the zone ho = average coolant specific enthalpy at outlet of the zone A = overall heat transfer area for fuel channel zone U = overall heat transfer coefficient Tf = average fuel temperature Tc = average coolant temperatureWi = coolant mass flow rate at fuel channel zone inletWo = coolant mass flow rate at fuel channel zone inlet
Reactor Zone 1
Reactor Zone 2
Average ReactorFlux Calculation
Flux Mapping
Reactor Zone 12
Zone 3 to 12
To Display
Reactor Zone 1 Flux
Reactor Zone 14 Flux
Reactivity Change due toGrey rods, Dark rodsshutdow n rods, Xenon and fueltemperature
Fig. 1 - Spatial Kinetic Reactor Model
reactivity changes due to temperature change, xenon poisoning and voiding arewithin each reactor zone
coupling is modelled between each neighbouring zones according to prescribed formula
ReactorPow erControls
Reactor Zone 1 Flux
Zone Decay Heat
Zone Decay Heat
Zone Decay Heat
Zone Fuel & Coolant T
Zone Fuel & Coolant T
Zone Fuel & Coolant T
PWR Core Modeling Flow & Pressures in zone calculated by Hydraulic Flow Network
SG1
SG2
Lower Plenum
Upper Plenum
HL1
HL2
CL1
CL2
CL3
CL4
Channel 1
Channel 2
Channel 3
Channel 4
Lower Zones
Middle Zones
Upper Zones
Reactor Core
The fuel heat transfer calculations (equation 5.7-1, 5.7-2) start with the lower zones, withzones inlet temperatures derived from the core lower plenum temperatures; with coolantflows derived from hydraulic flow network computation at the lower plenum. Afterobtaining the lower zone coolant outlet temperatures and average fuel temperatures, thecalculations proceed to the middle zones, and then to the upper zones accordingly.
At the core upper plenum, the coolant temperatures from the 4 lumped channels are mixed by flowturbulence, and the temperatures at the hot legs will be the coolant mixing temperatures at the upper plenum
Steam Generator Model
Lumped Parameter Model
More Detailed Distributed Parameter Model Add more dynamic details - drum,
downcomer, U-tubes heat transfer, riser etc. Depends on training needs or boiler design
evaluation requirements etc. Multi-Nodal Thermal-hydraulic Model
A2
X01
A3
A4
A5
A6
A7
A8
A1
B8
B7
B6
B5
B4
B3
B2
B11
2
3
4
5
6
7
8 9
10
11
12
13
14
15
16
HNC_X01 NHC_X02
X01
NHB NHA
Wp1, Tp1 Wp2, Tp2
Wf, Hf
Weq
Wr1 Wr2Wr, Hl
Wrh, Hrh Wr.(1-X), Hl Wr.(1-X), Hl
Wr.X, Hg
X2
Ws, Hs
Pd
Multi-Nodal Thermalhydraulic Model
Thermalhydraulic of Feedwater System
BOP Processes
Main Steam Utilization: main steam piping; mass and energy distributions.
Turbine Generator Condenser & Condensate Extraction Feedwater & Feedwater Heating Electrical Systems
Reactor Power Cycle - Rankine Cycle
saturation line T
S
T1
T2
P1
P2
QR
1
2 3
4
5
1-2: Turbine Expansion 2-3: Steam condensed in condenser 3-4: FW pump condensate to boiler 4-5: FW heated up by reactor thermal power 5-1:Sat. water vaporizes to sat. steam.
Wnet
S1 S2
Reactor Power Cycle
Turbine shaft work WT= H1 - H2
Pumping work WP= H4 - H3
Heat input Qin= H1- H4
NPP Efficiency = Net Work Output/Energy In η =
WT −WP
Qin
=WNET
Qin
Turbine Generator
throttle valve HP Stage blading
Moisture Separator/ Reheater
LP Stages
• Number of turbine stages for turbine expansion • Steam expansion is a isentropic expansion: • Stage efficiency does not change
P.V γ = C where γ =
Cp
Cv
Condenser
1st stage
Turbine Model
Ws = kttv Attv (
Pttv
Tttv
) 1− (φ − φcr
1−φcr
)2
Assuming choked flow to HP Cylinder, the turbine steam flow through the throttle valve is :
where is the throttle valve pressure ratio φ =
P1st
Pttv
φcr
Pttv
Tttv
kttv
= Upstream pressure at turbine throttle valve
= Upstream temperature at turbine throttle valve
= turbine throttle valve flow coefficient
= critical pressure ratio (superheat steam = 0.547)
P1st = turbine 1st stage pressure
Attv = cross-section float area of turbine throttle valve
Turbine Model (cont’d)
The relationship between the 1st stage temperature and throttle valve temperature is given by:
T1st = Tttv .φk−1
k
The turbine expansion equation is used to determine the pressure stage relationship:
P2
P1
= (1− (Ws
k1st
)2 )k
1+ k
k = constant, 1.3 for superheated steam
k1st= stage expansion coefficient
Turbine Model (cont’d) H
S
H1
H2
P1
P2
inlet enthalpy H1
outlet enthalpy H2
isentropic outlet enthalpy Hs
saturation line
turbine expansion line
Mollier Diagram for turbine expansion
∆Hs η.∆Hs
S1
H2 = H1 −η.∆Hs
H2 = H1 −η.(H1 − H (P2 ,S1))
Turbine Model (cont’d)
PTB =Ws(H1 − H2 )Turbine mechanical power:
Pe = PTB when TG connected to large grid For grid island situation:
Electrical Power:
Pe = Peb(1+α PFδ f )where Peb = island load;
δ f = turbine frequency deviation
α PF = power/frequency coefficient Frequency swing equation:
d(δ f )dt
= −De
2I(δ f ) +
fs
2I(PTB − Pe )
De = generator damping constant I = turbine inertia constant fs = turbine synchronous frequency
Approach to Main Steam & Turbine Modeling Use Compressible Hydraulic Flow Network
and Turbine Stages Algorithms
X1 N1 N2 N3 N4 N5 N61 2 N73 N84 X65
Gov Valve
Prim SH Sec SH
Main SteamHdr
X2 X3 X4 X5
#1 HP FWHeater
#2 HP FWHeater
Deaerator LP Heater
Condenser
Boiler DrumPressure
Thermalhydraulic network models used for Passive Cooling System – single phase & two phase
Explain the Passive Cooling Systems
Go to the Passive PWR Simulator Manual P.59, Section 4.20
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