Exploratory NEP modeling
Robert M. Edwards
Penn State
814.865.0037
rmenuc@engr.psu.edu
Motivation: System Integration
Steam
Generator &
Electrical:
Pressure
Vessel &
Piping
Core Design:
neutronics
thermal
hydr...
References
 Scoping Calculations of Power Sources for Nuclear Electric Propulsion,
ORNL CR-191133, 1994
 50 MW 4-year re...
Reactor Kinetics Equations
 output nr, relative reactor power
 input r(t), reactivity
 from control devices
 feedback ...
reactor power response to 10 cents
without temperature feedback
0 1 2 3 4 5 6 7 8 9 10
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1...
Scoping Calculations of Power
Sources for Nuclear Electric
Propulsion, ORNL CR-191133, 1994
 50 MW, four year life
 82.2...
Reactor Fuel Pin Equations:
for 30 axial nodes, k
  ccinkp
k
ckcc
k
k
ck
f
kfk
f
f
kff
C/T)k(Tcm
R
)k(T)k(T
dt
)k(Td
dt
...
Fuel temperature response to
10% step change in power
0 1 2 3 4 5 6 7 8 9 10
900
905
910
915
920
925
930
935
940
945
Fuel ...
SIMULINK Reactor Model
reactor power response to 10 cents
WITH temperature feedback
0 2 4 6 8 10
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
power r...
reactor temperature response to 10
cents WITH temperature feedback
0 2 4 6 8 10
901.9
902
902.1
902.2
902.3
902.4
902.5
90...
Brayton Power Conversion System
Parametric Design Modeling for NEP,
NASA contractor report CR-191135, 1993
 500 kWe unit
...
Brayton Code Model
Duct 6
Duct 5
Duct 4
Duct 2
Duct 3
Duct 1
Gas
Cooling
Aux
Cooling
IHX
TurbComp Generator
Recuperator
16...
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...
Brayton Code data
 duct dimensions
 Duct 1 diameter, cm 12.91509
 Length, cm 193.7263
 Duct 2 diameter, cm 14.96846
 ...
MMS component equation set:
mass, momentum, energy
 
 
 
r






r

r

r
r





 r

...
Ideal Gas Assumption
RT
1
P
TRc
P
h
RT
P
Tch
h
P
2
pP
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*...
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 2
2.35
2.4
2.45
2.5
2.55
2.6
x 10
...
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 2
2.38
2.4
2.42
2.44
2.46
2...
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...
A linear generalization of
Wright’s data
1.2 1.4 1.6 1.8 2
2
4
6
8
10
12
14
16massflowkg/s
pressure ratio
compressor/turbi...
Maps that execute
1.2 1.4 1.6 1.8 2
2
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
   
























...
SIMULINK compressor block
poscope
mdo mdi
Pi
Ti
mdo
N
Po
To
mdi
J
compressor2
ToTi
Pi
N J
SIMULINK Compressor model
4
J
3
mdi
2
To
1
Po
1/s
po
(u(1)-u(2))*u(3)*cp
mdot*cp*deltat
mp*u(1)+u(2)
mdot
(u(1)-u(2))*2500...
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 11.8
6.5
6.6
6.7
6.8
6.9
7...
Turbine inlet temperature to speed
step transient 28000->30000 RPM
0 2 4 6 8 10 12 14 16 18 20
1100
1105
1110
1115
1120
11...
Net power output response to speed
step transient 28000->30000 RPM
0 2 4 6 8 10 12 14 16 18 20
1
1.02
1.04
1.06
1.08
1.1
1...
CBC with reactor model
turbine
exhaust
recuperator
exhaust
high
pressurePi
Ti
md0
N
mdRx
rho
Po
To
mdi
J
nr
turbine_ihx
rh...
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
...
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 11.8
6.5
6.6
6.7
6.8
6.9
7
7....
turbine inlet temperature Response
to speed step 28000 to 30000 RPM
0 5 10 15 20 25 30 35 40 45 50
1130
1132
1134
1136
113...
Reactor power Response to
speed step 28000 to 30000 RPM
0 5 10 15 20 25 30 35 40 45 50
1
1.005
1.01
1.015
1.02
1.025
1.03
...
net power output Response to
speed step 28000 to 30000 RPM
0 5 10 15 20 25 30 35 40 45 50
1.06
1.07
1.08
1.09
1.1
1.11
1.1...
Simplified generator model
added:  
I
PP
2
dt
d outin
2 


Speed Response to step -15%
step decrease in load
0 50 100 150 200 250 300 350 400 450 500
2.8
2.9
3
3.1
3.2
3.3
3.4
3.5
3...
Turbine Inlet Temperature
response to -15% in load
0 50 100 150 200 250 300 350 400 450 500
1100
1105
1110
1115
1120
1125
...
Reactor Power Response to
-15% step in load
0 50 100 150 200 250 300 350 400 450 500
1
1.05
1.1
reactor power response to ...
Net Power Output response to
-15% step in load
0 50 100 150 200 250 300 350 400 450 500
9
9.2
9.4
9.6
9.8
10
10.2
10.4
10....
Summary, exploratory NEP
modeling approach
 representative fuel pin from a 50 MW four
year core
 500 kWe CBC
 MMS equat...
Possible Improvements
 T=f(h,P), r=f(h,P), h=f(T,P)
 compressor/turbine performance maps
 mass flow as a function of sp...
of 49

NASA 2004 PP

Published on: Mar 3, 2016
Source: www.slideshare.net


Transcripts - NASA 2004 PP

  • 1. Exploratory NEP modeling Robert M. Edwards Penn State 814.865.0037 rmenuc@engr.psu.edu
  • 2. Motivation: System Integration Steam Generator & Electrical: Pressure Vessel & Piping Core Design: neutronics thermal hydraulics Mechanical Pumps, valves turbines System Integration (Control Engineering) DETAILED MODELSDETAILED MODELS DETAILED MODELS DETAILED MODELS
  • 3. 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.
  • 4. 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,...6icn dt dc cn t dt dn irri ir ir 6 1i i r r   b   br   
  • 5. reactor power response to 10 cents without temperature feedback 0 1 2 3 4 5 6 7 8 9 10 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 power response of reactor without feedback to 10 cents seconds relativereactorpower   br 1.0t
  • 6. 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
  • 7. Reactor Fuel Pin Equations: for 30 axial nodes, k   ccinkp k ckcc k k ck f kfk f f kff C/T)k(Tcm R )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(T Q dt )k(dT                                   Fuel (Tf)Clad (Tk)Coolant (Tc) Tc(k) Tc(k-1) Rk Rf Cc Ck Cf
  • 8. Fuel temperature response to 10% step change in power 0 1 2 3 4 5 6 7 8 9 10 900 905 910 915 920 925 930 935 940 945 Fuel temperature response to 10% step in power seconds temperature(K)
  • 9. SIMULINK Reactor Model
  • 10. reactor power response to 10 cents WITH temperature feedback 0 2 4 6 8 10 0.98 1 1.02 1.04 1.06 1.08 1.1 1.12 1.14 power response of reactor with feedback to 10 cents seconds relativereactorpower
  • 11. reactor temperature response to 10 cents WITH temperature feedback 0 2 4 6 8 10 901.9 902 902.1 902.2 902.3 902.4 902.5 902.6 902.7 seconds temperature(K) temperature response of reactor with feedback to 10 cents
  • 12. 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)
  • 13. Brayton Code Model Duct 6 Duct 5 Duct 4 Duct 2 Duct 3 Duct 1 Gas Cooling Aux Cooling IHX TurbComp Generator Recuperator 16 1 5 6 7 1314 15 10 8 12 9
  • 14. 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
  • 15. 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
  • 16. MMS component equation set: mass, momentum, energy       r       r  r  r r       r    r r          r        r P/huuses dt dP V dt d VhWqhmhm V 1 dt dh hP,fuses dt d VhWqhmhm Vdt d dt dP K m PP L A dt md mm V 1 dt d oo sooii o Ph o sooii ho o 2 i oi i oi o    
  • 17. Ideal Gas Assumption RT 1 P TRc P h RT P Tch h P 2 pP h p   r    r  r 
  • 18. SIMULINK “duct” model
  • 19. 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'
  • 20. 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 2 2.35 2.4 2.45 2.5 2.55 2.6 x 10 6 outlet pressure response to inlet pressure step, duct 1 time in seconds pressureinpascal
  • 21. 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 2 2.38 2.4 2.42 2.44 2.46 2.48 2.5 x 10 6 outlet pressure response to inlet pressure step, duct 1 time in seconds pressureinpascal
  • 22. Interconnecting the duct components to form a loop
  • 23. Interconnecting ducts to form a heat exchanger
  • 24. 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
  • 25. A linear generalization of Wright’s data 1.2 1.4 1.6 1.8 2 2 4 6 8 10 12 14 16massflowkg/s pressure ratio compressor/turbine performance characteristics compressor turbine
  • 26. Maps that execute 1.2 1.4 1.6 1.8 2 2 4 6 8 10 12 14 16 compressor turbine 50000 RPM 50000 RPM
  • 27. Compressor/Turbine Thermal model T4s T3 T2 T2s T s T1 T4
  • 28. Compressor Thermal equations  Compressor  Turbine                              1s2 2 12 1s2 k1k 1 2 1s2 1 s2 k1k 1 2 T)1(T T TT TT P P TT T T P P      s4334 s43 43 k1k 4 3 3 s4 s4 3 k1k 4 3 TTTT TT TT P P T T T T P P                          
  • 29. SIMULINK compressor block poscope mdo mdi Pi Ti mdo N Po To mdi J compressor2 ToTi Pi N J
  • 30. SIMULINK Compressor model 4 J 3 mdi 2 To 1 Po 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 4 N 3 mdo 2 Ti 1 Pi
  • 31. SIMULINK model of CBC
  • 32. Compressor-recuperator subsystem
  • 33. turbine – IHX subsystem constant heat input
  • 34. 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 11.8 6.5 6.6 6.7 6.8 6.9 7 7.1 7.2 7.3 flow response to speed step 28000->30000 time (sec) flow(kg/s)
  • 35. Turbine inlet temperature to speed step transient 28000->30000 RPM 0 2 4 6 8 10 12 14 16 18 20 1100 1105 1110 1115 1120 1125 1130 1135 1140 1145 turbine inlet temperature to speed step 28000->30000 time (sec) temperature(K)
  • 36. Net power output response to speed step transient 28000->30000 RPM 0 2 4 6 8 10 12 14 16 18 20 1 1.02 1.04 1.06 1.08 1.1 1.12 1.14 1.16 x 10 6 net power output to step in speed 28000 30000 time (sec) power(watts)
  • 37. 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 Point N Input Point2 Input Point1 Input Point
  • 38. 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 Scope3 Scope2 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
  • 39. 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 11.8 6.5 6.6 6.7 6.8 6.9 7 7.1 7.2 7.3 flow response to step in speed to 30000 RPM seconds flow(kg/s)
  • 40. turbine inlet temperature Response to speed step 28000 to 30000 RPM 0 5 10 15 20 25 30 35 40 45 50 1130 1132 1134 1136 1138 1140 1142 turbine inlet temperature to step in speed to 30000 RPM seconds temperature(K)
  • 41. Reactor power Response to speed step 28000 to 30000 RPM 0 5 10 15 20 25 30 35 40 45 50 1 1.005 1.01 1.015 1.02 1.025 1.03 1.035 power response of reactor to step in speed to 30000 RPM seconds relativereactorpower
  • 42. net power output Response to speed step 28000 to 30000 RPM 0 5 10 15 20 25 30 35 40 45 50 1.06 1.07 1.08 1.09 1.1 1.11 1.12 1.13 1.14 1.15 x 10 6 seconds netpoweroutput(watts) net power output to step in speed to 30000 RPM
  • 43. Simplified generator model added:   I PP 2 dt d outin 2   
  • 44. Speed Response to step -15% step decrease in load 0 50 100 150 200 250 300 350 400 450 500 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 x 10 4 speed response to -15% step in load time (sec) speed(RPM)
  • 45. Turbine Inlet Temperature response to -15% in load 0 50 100 150 200 250 300 350 400 450 500 1100 1105 1110 1115 1120 1125 1130 1135 1140 1145 turbine inlet temperature to -15% step in load time (sec) temperature(K)
  • 46. Reactor Power Response to -15% step in load 0 50 100 150 200 250 300 350 400 450 500 1 1.05 1.1 reactor power response to -15% step in load time (sec) relativereactorpower
  • 47. Net Power Output response to -15% step in load 0 50 100 150 200 250 300 350 400 450 500 9 9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 x 10 5 Net power output to -15% step in load time (sec) power(watts)
  • 48. 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
  • 49. 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

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