NASA 2004 PP
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Transcript of NASA 2004 PP
Motivation: System Integration
Steam
Generator &
Electrical:
Pressure
Vessel &
Piping
Core Design:
neutronics
thermal
hydraulics
Mechanical
Pumps, valves
turbines
System
Integration
(Control
Engineering)
DETAILED MODELS DETAILED MODELS
DETAILED MODELS DETAILED MODELS
References
Scoping Calculations of Power Sources for Nuclear Electric Propulsion, ORNL CR-191133, 1994 50 MW 4-year reactor example data
Brayton Power Conversion System Parametric Design Modeling for NEP, NASA contractor report CR-191135, 1993 500 kWe Brayton PCU
Modular Modeling System (MMS): A Code for the Dynamic Simulation of Fossil and Nuclear Power Plants: Overview and General Theory, EPRI CS/NP-2989, 1983
Preliminary Results of a Dynamic System Model for a Closed-Loop Brayton Cycle Coupled to a Nuclear Reactor, Steven Wright, Sandia National Lab.
“Dynamic Analysis and Control System Design for an Advanced Nuclear Gas Turbine Power Plant”, a dissertation in Mechanical Engineering,
MIT 1990.
Reactor Kinetics Equations
output nr, relative reactor power
input r(t), reactivity from control devices
feedback from temperature, etc
b is fraction of neutrons that are “delayed”
1,...6i cndt
dc
cnt
dt
dn
irriir
ir
6
1i
ir
r
b
br
reactor power response to 10 cents without temperature feedback
0 1 2 3 4 5 6 7 8 9 101
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4power response of reactor without feedback to 10 cents
seconds
rela
tive r
eacto
r pow
er
br 1.0t
Scoping Calculations of Power Sources for Nuclear Electric Propulsion, ORNL CR-191133, 1994
50 MW, four year life 82.24 cm diameter, 75.37 cm height 82.92% enriched Uranium 5871 fuel pins, 6.4 mm diameter Tantalum-181 clad, 0.6355 mm Tungsten liner, 0.127 mm Uranium-Nitride fuel, 4.826 mm Lithium coolant, 16.139 kg/s
2.75 g/s per fuel pin 500 oK inlet temperature, 1200 oK outlet
temperature
Reactor Fuel Pin Equations: for 30 axial nodes, k
ccinkpk
ckcc
kk
ck
f
kfk
ff
kff
C/T)k(TcmR
)k(T)k(T
dt
)k(Td
dt
)k(dT
C/R
)k(T)k(T
R
)k(T)k(T
dt
)k(dT
C/R
)k(T)k(TQ
dt
)k(dT
Fuel (Tf) Clad (Tk) Coolant (Tc)
Tc(k)
Tc(k-1)
Rk Rf Cc Ck Cf
Fuel temperature response to 10% step change in power
0 1 2 3 4 5 6 7 8 9 10900
905
910
915
920
925
930
935
940
945Fuel temperature response to 10% step in power
seconds
tem
pera
ture
(K
)
SIMULINK Reactor Model
reactor power response to 10 cents WITH temperature feedback
0 2 4 6 8 100.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14power response of reactor with feedback to 10 cents
seconds
rela
tive r
eacto
r pow
er
reactor temperature response to 10 cents WITH temperature feedback
0 2 4 6 8 10901.9
902
902.1
902.2
902.3
902.4
902.5
902.6
902.7
seconds
tem
pera
ture
(K
)
temperature response of reactor with feedback to 10 cents
Brayton Power Conversion System Parametric Design Modeling for NEP, NASA contractor report CR-191135, 1993
500 kWe unit
Helium-Xenon with cp=0.5 cal/g-K
Compressor inlet
375 oK, 1339.18 kPa
Turbine inlet
1144.69 oK, 2355.46 kPa
Lithium Intermediate Heat Exchanger
1166.7 inlet, 1111.1 oK outlet temperatures
(considerably smaller DT than 50 MW reactor)
Brayton Code Model
Duct 6
Duct 5
Duct 4
Duct 2
Duct 3
Duct 1
Gas Cooling
Aux Cooling
IHX
Turb Comp Generator
Recuperator
16
1
5
6 7
13 14
15
10
8
12
9
Brayton Code data
Temperatures, K 375.00 500.67 500.67 500.67 500.67 500.67 871.19 869.82 1144.44 1141.69 1141.69 939.33 936.58 566.05 566.05 375.00 375.00
Pressures, KPA 1339.18 1874.86 1874.86 2410.53 2410.53 2398.48 2379.17 2367.28 2362.54 2355.46 1867.82 1380.19 1376.05 1359.47 1352.68 1345.91 1339.18
Brayton Code data
duct dimensions Duct 1 diameter, cm 12.91509 Length, cm 193.7263 Duct 2 diameter, cm 14.96846 Length, cm 224.52680 Duct 3 diameter, cm 18.38337 Length, cm 275.75050 Duct 4 diameter, cm 22.70933 Length, cm 340.64000 Duct 5 diameter, cm 17.61942 Length, cm 264.29120 Duct 6 diameter, cm 15.94148 Length, cm 239.12220
MMS component equation set: mass, momentum, energy
r
r
r
rr
r
rr
r
r
P/hu uses dt
dPV
dt
dVhWqhmhm
V
1
dt
dh
hP,f uses dt
dVhWqhmhm
Vdt
d
dt
dP
K
mPP
L
A
dt
md
mmV
1
dt
d
oosooii
o
Ph
osooii
ho
o
2i
oii
oio
Ideal Gas Assumption
RT
1
P
TRc
P
h
RT
P
Tch
hP
2pP
h
p
r
r
r
SIMULINK “duct” model
duct model equation implementation
function sys=mdlDerivatives(t,x,u,V,L,Af,cp,R,K,mo) delp=u(1)-x(1); rhoo=x(1)/(R*x(2));rhoi=u(1)/(R*u(2));rhobar=(rhoo+rhoi)/2; if mo==0 if delp<=0 mdi=0; else mdi=K*sqrt(delp*rhobar); end else xd(3)=Af/L*(u(1)-x(1)-(u(3)/K)^2/rhobar); %Vi=x(3)/rhoi/Af;Vo=u(3)/rhoo/Af; this term creates numerical %problems and is neglected. %xd(3)=xd(3)+(x(3)*Vi-u(3)*Vo)/L mdi=x(3); end drholdt=(mdi-u(3))/V; Tbar=(u(2)+x(2))/2; Pbar=(u(1)+x(1))/2; dp=1/(R*Tbar); dh=-Pbar/(R*cp*Tbar^2); term1=(mdi*cp*u(2)-u(3)*cp*x(2)+u(4)-cp*Tbar*V*drholdt); xd(1)=(rhobar*drholdt-dh/V*term1)/(dh+dp*rhobar); xd(2)=(term1/(rhobar*V) + xd(1)/rhobar)/cp; sys=xd'
Duct model response to set change in inlet pressure
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 22.35
2.4
2.45
2.5
2.55
2.6x 10
6 outlet pressure response to inlet pressure step, duct 1
time in seconds
pre
ssure
in p
ascal
Response without the dynamic form of the momentum equation
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 22.38
2.4
2.42
2.44
2.46
2.48
2.5x 10
6 outlet pressure response to inlet pressure step, duct 1
time in seconds
pre
ssure
in p
ascal
Interconnecting the duct components to form a loop
Interconnecting ducts to form a heat exchanger
Compressor and Turbine models from performance data
A representation of Wright’s data
Mass flow
Speed 1
Speed 2
Pressure ratio
compressor
turbine
Speed 1
A linear generalization of Wright’s data
1.2 1.4 1.6 1.8 22
4
6
8
10
12
14
16m
ass f
low
kg/s
pressure ratio
compressor/turbine performance characteristics
compressor
turbine
Maps that execute
1.2 1.4 1.6 1.8 22
4
6
8
10
12
14
16
compressor
turbine
50000 RPM
50000 RPM
Compressor/Turbine Thermal model
T4s
T3
T2 T2s
T
s
T1
T4
Compressor Thermal equations
Compressor
Turbine
1s22
12
1s2
k1k
1
21s2
1
s2k1k
1
2
T)1(TT
TT
TT
P
PTT
T
T
P
P
s4334s43
43
k1k
4
3
3s4
s4
3k1k
4
3
TTTTTT
TT
P
P
TT
T
T
P
P
SIMULINK compressor block
poscope
mdo mdi
Pi
Ti
mdo
N
Po
To
mdi
J
compressor2
ToTi
Pi
N J
SIMULINK Compressor model
4J
3mdi
2To
1Po
1/s
po
(u(1)-u(2))*u(3)*cp
mdot*cp*deltat
mp*u(1)+u(2)
mdot
(u(1)-u(2))*2500000
flow equalizer
mn*u(1)+b
Yint
u(3)*(u(1)/u(2))^((k-1)/k)
T2s(u(1)-(1-eta)*u(2))/eta
T2
u(2)/u(1)
Pr
4N
3mdo
2Ti
1Pi
SIMULINK model of CBC
Compressor-recuperator subsystem
turbine – IHX subsystem constant heat input
Flow response to speed step transient 28000->30000 RPM
10 10.2 10.4 10.6 10.8 11 11.2 11.4 11.6 11.86.5
6.6
6.7
6.8
6.9
7
7.1
7.2
7.3flow response to speed step 28000->30000
time (sec)
flow
(kg/s
)
Turbine inlet temperature to speed step transient 28000->30000 RPM
0 2 4 6 8 10 12 14 16 18 201100
1105
1110
1115
1120
1125
1130
1135
1140
1145turbine inlet temperature to speed step 28000->30000
time (sec)
tem
pera
ture
(K
)
Net power output response to speed step transient 28000->30000 RPM
0 2 4 6 8 10 12 14 16 18 201
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16x 10
6 net power output to step in speed 28000 30000
time (sec)
pow
er
(watt
s)
CBC with reactor model
turbine
exhaust
recuperator
exhaust
high
pressurePi
Ti
md0
N
mdRx
rho
Po
To
mdi
J
nr
turbine_ihx
rho
mdot
Pi
Ti
mdo
N
Po
To
mdi
J
compressor-recuperator
Scope9
Scope8
Scope7
Scope6Scope5Scope4
Scope3
Scope2
Scope1
Scope
Output Point1
Output PointN
Input Point2
Input Point1
Input Point
turbine-ihx with reactor model
5
nr
4
J
3
mdi
2
To
1
Po
Pi
Ti
mdo
N
Po
To
mdi
J
turbine2 -3.797e04
q2
-1.892e04
q
mdot
Ti
peak
Tout
Tf max
Tf av g
Tkav g
Tcav g
rhof b
neppin
Tg
Ti
mdot
Q
TiRx
ihxts
Pi
Ti
mdo
q
Po
To
mdi
ihx_shell
Pi
Ti
mdo
q
Po
To
mdi
duct3
Pi
Ti
mdo
q
Po
To
mdi
duct2
Scope7
Scope6
Scope5
Scope4
Scope3Scope2
Scope1
Scope
1/0.646
Gain2
109.61
Gain1
.5
Gain
rho (dk) nr
6-delayed
groups
6
rho
5
mdRx
4
N
3
md0
2
Ti
1
Pi
mass flow Response to speed step 28000 to 30000 RPM
10 10.2 10.4 10.6 10.8 11 11.2 11.4 11.6 11.86.5
6.6
6.7
6.8
6.9
7
7.1
7.2
7.3flow response to step in speed to 30000 RPM
seconds
flow
(kg/s
)
turbine inlet temperature Response to speed step 28000 to 30000 RPM
0 5 10 15 20 25 30 35 40 45 501130
1132
1134
1136
1138
1140
1142turbine inlet temperature to step in speed to 30000 RPM
seconds
tem
pera
ture
(K
)
Reactor power Response to speed step 28000 to 30000 RPM
0 5 10 15 20 25 30 35 40 45 501
1.005
1.01
1.015
1.02
1.025
1.03
1.035power response of reactor to step in speed to 30000 RPM
seconds
rela
tive r
eacto
r pow
er
net power output Response to speed step 28000 to 30000 RPM
0 5 10 15 20 25 30 35 40 45 501.06
1.07
1.08
1.09
1.1
1.11
1.12
1.13
1.14
1.15x 10
6
seconds
net pow
er
outp
ut (w
atts)
net power output to step in speed to 30000 RPM
Simplified generator model added:
I
PP2
dt
d outin2
Speed Response to step -15% step decrease in load
0 50 100 150 200 250 300 350 400 450 5002.8
2.9
3
3.1
3.2
3.3
3.4
3.5
3.6x 10
4 speed response to -15% step in load
time (sec)
speed (
RP
M)
Turbine Inlet Temperature response to -15% in load
0 50 100 150 200 250 300 350 400 450 5001100
1105
1110
1115
1120
1125
1130
1135
1140
1145turbine inlet temperature to -15% step in load
time (sec)
tem
pera
ture
(K
)
Reactor Power Response to -15% step in load
0 50 100 150 200 250 300 350 400 450 5001
1.05
1.1
reactor power response to -15% step in load
time (sec)
rela
tive r
eacto
r pow
er
Net Power Output response to -15% step in load
0 50 100 150 200 250 300 350 400 450 5009
9.2
9.4
9.6
9.8
10
10.2
10.4
10.6x 10
5 Net power output to -15% step in load
time (sec)
pow
er
(watt
s)
Summary, exploratory NEP modeling approach
representative fuel pin from a 50 MW four year core
500 kWe CBC
MMS equation set not suitable for low pressure drops and flows
simplified compressor/turbine performance curves
results consistent with Wright
more study needed
Possible Improvements
T=f(h,P), r=f(h,P), h=f(T,P)
compressor/turbine performance maps mass flow as a function of speed and Pr
efficiency as a function of speed and Pr
add component metal heat capacities
data for another Brayton unit full power steady state temperatures and pressures around
the unit
component dimensions, masses, heat capacities
more detail on the generator, electrical power distribution system, and ion propulsion
