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THE ANALYSIS OF THE PEBBLE-BED MODULAR REACTOR THERMAL-FLUID CYCLE USING A NETWORK CODE.
G.P. Greyvenstein*, P.G. Rousseau** and C.G. du Toit****
School for Mechanical and Materials Engineering
Potchefstroom University for CHE Private Bag X6001, Potchefstroom 2520, South Africa
Abstract
The Pebble Bed Modular Reactor (PBMR) power plant is currently being developed by PBMR (Pty) Ltd in South Africa in association with ESKOM and other industrial partners. This high temperature gas cooled reactor (HTGR) plant is based on a three-shaft Brayton cycle with helium gas as coolant. This is a complex thermal-fluid system consisting of many interacting components such as pipes, valves, heat exchangers, compressors, turbines, pumps, blowers and the nuclear reactor itself. Engineers are faced with two major challenges when carrying out the thermal-fluid design of the PBMR power plant. The first challenge is to predict the performance of all the thermal-fluid components of the plant such as pipes, valves, heat exchangers, turbo machines and the reactor. The second challenge is to predict the performance of the integrated plant consisting of all its sub-systems.
System performance predictions must be done for both steady-state and transient conditions. Steady-state analyses are required to study normal operating conditions and to generate initial values for transient analyses. Transient analyses, in contrast, are required for control studies and for studying operating procedures such as start-up, load rejection and load following, as well as when analysing accident events. The complexity associated with the thermal-fluid design of the cycle requires the use of a variety of analysis techniques and simulation tools. These range from simple one-dimensional models that do not capture all the significant physical phenomena to large-scale three-dimensional CFD codes that, for practical reasons, can not simulate the entire plant as a single integrated model.
Various approaches have been developed to model complete thermal-fluid systems. One approach is to build a custom computer model for a specific system layout or to use commercially available modelling tools such as EES or Aspen Custom Modeller (ACM). An approach that has gained wide acceptance is known as the network approach. With this approach models of standard components are developed that can be interconnected in any arbitrary way. The name “network” is derived from the graphical representation of thermal-fluid systems as networks of interconnected components. With the network approach the system layout can easily be reconfigured without having to change any computer code. This paper gives an overview of one of the most prominent codes that provide a suitable compromise, namely the thermal-fluid network simulation code Flownex. Flownex allows detailed steady state and transient thermal-fluid simulations of the complete power plant, fully integrated with core neutronics and controller algorithms. This is illustrated through several examples, including the PMBR power plant.
* Dean, Faculty of Engineering ** Director, Research *** Director, School for Mechanical and Materials Engineering
Potchefstroomse UniversiteitvIr Christelike Hoër Onderwys
Mechanical and MaterialsEngineering
THE ANALYSIS OF THE PEBBLE-BED MODULAR REACTOR
THERMAL-FLUID CYCLE USING A NETWORK CODE
GP Greyvenstein, PG Rousseau and CG du Toit
Mec
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Mat
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Eng
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SCOPE
• Pebble-bed Modular Reactor Main Power System • Flow Network or Integrated Systems CFD Approach• Implicit Pressure Correction Method• Reactor Model• Validation• PBMR Load Rejection• Conclusions
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PBMR MAIN POWER SYSTEM
Reactor
HP Turbo Unit
LP Turbo Unit
Power Turbine and Generator
RecuperatorPre-coolerInter-cooler
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PBMR
RXHPC
PBR
HPT LPT
PCIC
PT
LPC
SBS
G
GBPLPBHPB
SIV
SBSIV
PV
CWP
NIV
SBSOV
NEV
R
SCHEMATIC LAYOUT OF MPS
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PBMR: ISSUES
• Complex thermal-fluid system consisting of many interacting components.
• Performance of all the thermal-fluid components must be predicted.
• The performance of the integrated plant must be predicted.
• System performance predictions must be done for both steady-state and transient conditions.
• The system performance predictions can be done using a network or integrated systems CFD approach.
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Pump
PipeOrifice Compressor
Turbine
Reservoir
Heat exchanger Diffuser
Node NodeElement
NETWORK APPROACH
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1Reactor_Core (R)
3
Reactor_Outlet_Connection_to_Core_Outlet_Pi
pe (FP)
7 Core_Outlet_Pipe (FP)
9CM
11
HPT_Diffuser (FP)
13
HPT_Outlet_Pipe (FP)
17
Low_Pressure_Turbine (T)
CM19
LPT_Diffuser (FP)
21LPT_Outlet_Pipe (FP)
27PT_Intake (FP)
29
Power_Turbine (T)
31PT_Diffuser (FP)
35
PT_Outlet_Contraction (FP)
39
Recuperator_LP (H)RX
41
Pre-cooler_outer_bundle (H)CX
43
Pre-cooler_inner_bundle (H)CX
47
PC_Outlet_Contraction (FP)
51
LPC_Intake (FP)
53CM
55
LPC_Diffuser (FP)
57
LPC_Outlet_Pipe (FP)
61
Intercooler_outer_bundle (H)CX
63
Intercooler_inner_bundle (H)CX
67
IC_Outlet_ducting(FP)
71
HPC_Intake (FP)
73CM
75
HPC_Diffuser (FP)
77HPCe_Holes_to_Manifold (FP)
79
Maintanence_Valve (V)RD
83 RX(HP)_Inlet_Pipes (FP)
85RX
87 RX(HP)_Outlet_Pipes(a) (FP)
89
Core_Inlet_Pipes(e) (FP)
91
Reactor_Annular_Pipes (FP)
93
Reactor_Gas_Inlet_Plenum_Holes (FP)
95Control_Rod_Cooling_flow_connection (FP)
102CX
104CX
109CX
111CX
78P
113
Manifold_to_HPTe_Leakage (L)RD
78P
116RD
119HPC_Bypass_Valve_(HPB) (V)
120
LPC_Bypass_Valve_1_(LPB1) (V)
121
Gas_Cycle_Bypass_Valve_1_(GBP1) (V)
78P
133
Manifold_to_HPTi_Leakage (L)RD
78P
135
RX_bypass_valve_(1 TO 4)_(RBP1) (V)
136Reactor_Plenum_Reduction_Area (FP)
137 Reactor_Outlet_Slots (FP)
138
Control_Rod_Bypass(filled) (FP)
140
Control_Rod_Bypass(empty) (FP)
142
Leakflow_from_Control_Rod_to_Outlet_Manifold (FP)
RD
144
Inside_Cavity_Slots_to_Core (FP)RD
146Reactor_Outside_
Cavity (FP)
148 Reactor_Leak_into_Manifold (FP)
RL
150HPT_Intake (FP)
152
LPT_Intake (FP)
158
RX(LP)_to_PC_connection (FP)
160
Annular_flow_path_to_IC (FP)
162
Annular_flow_path_. . ._to_IC_core (FP)
163
Recuperator_Outlet_Pipe (FP)
165
Core_Inlet_Pipes(a) (FP)
167Core_Inlet_Pipes(b) (FP)
169
Core_Inlet_Pipes(c) (FP)
171
Core_Inlet_Pipes(d) (FP)
174
175
LPC_Bypass_Valve_Pipe2 (FP)
178
LPC_Bypass_Valve_Pipe1 (FP)
180Bypass_Valve_Pipe (FP)
181 HPCe_to_HPCi_Leakage (L)
RD
78P
182
Manifold_to_LPTi_Leakage (L)
RD
183
LPCe_to_LPCi_Leakage (L)RD
184 Casing_cooling_flow (L)RD
56185
LPCe_to_PT_casing_flow (FP)
186
PTi_to_Basket_leak (L)RD
188
188 25%_casing_cooling_flow (L)
RD190
190 75%_casing_cooling_flow (L)
RD
192
Basket_to_PTe_leak (L)RD
194
PT_internal_fp2 (FP)
RD
196
196 Buffer_to_gaspath_leak (L)
197
197 ECLS_upper (L)
198
ECLS_lower (L)
300
ECLS_to_PToutlet (L)RD
301
dummy
303
HPS_supply_line (FP)RD
305
PTG_Shaft_Labyrinth_Seal(a) (L)
307
307 PTG_Shaft_Labyrinth_Seal(b) (L)
309
PT_top_volume_to_PTe
(FP)
78P
310
Shaft_valve (V)RD
153312
Pipe_RXe_to_SBSi_2 (FP)
314
SBS_Isolation_valve_2(SBSV2) (V)
316
SBS_Blower2 (CM)
M
CM327 318
Pipe_SBSe2_to_RX_manifold (FP)
153319
Pipe_RXe_to_SBSi_1 (FP)
321
SBS_Isolation_valve_1(SBSV1) (V)
323
SBS_Blower1 (CM)
M
CM327 325
Pipe_SBSe1_to_RX_manifold (FP)
326
SBS_Inline_valve_1_(SIV1) (V)
78P
329
HP_coolant_valve_1_(HCV1) (V)78
P330
LP_coolant_valve_1_(LCV1) (V)
332SBS_Labyrinth_Seal2 (L)
334SBS_Labyrinth_Seal1 (L)
336
RX(HP)_Outlet_Pipes
(b) (FP)
338 RX_inlet_header_pipe (FP)
340
PC_Impingement_plate(FP)
341HPC_Bypass_Control_Valve_(HPBC) (V)
342
LPC_Bypass_Control_Valve[LPBC] (V)
343
SBS_Bypass_valve_(SBP) (V)
344
SBS_Bypass_Control_Valve_(SBPC) (V)
345
LPC_Bypass_Valve_2_(LPB2) (V)
346
LPC_Bypass_Valve_3_(LPB3) (V)
347
348
349
350
351
352
353 Gas_Cycle_Bypass_Valve_8_(GBP8)(V)
78P
354
HP_coolant_valve_2_(HCV2) (V)
78P
355
LP_coolant_valve_2_(LCV2) (V)
356
SBS_Inline_valve_2_(SIV2) (V)
357
SBS_Inline_valve_3_(SIV3) (V)
78P
361
78P
362
78P
363
364
HPC_Bypass_Control_Valve_Pipe (FP)
365LPC_Bypass_Control_Valve
_Pipe2 (FP)
366
LPC_Bypass_Control_Valve_Pipe1 (FP)
368
PT_1st_stg_stator (FP)
370
370 PT_1st_stg_rotor_inlet (FP)
371
371 Inlet_1st_stg_throat (FP)
373
373 25%_rim_cooling_flow (L)
RD
375
375 75%_rim_cooling_flow (L)
RD
376
Rim_cooling_flow (L)RD
377
OD_u_ECLS_backup_lab (L)
380
380 ID_u_ECLS_backup_lab (L)56 381
PT_internals_cooling flow
(FP)
383
PT_internal_fp1 (FP)
RD
387
Inlet_to_SBS_Blower1 (FP)
388
SBS_Blower1_Outlet_Diffuser (FP)
390
Outlet_From_SBS_Blower1 (FP)
393
Inlet_to_SBS_Blower2 (FP)
394
SBS_Blower2_Outlet_Diffuser (FP)
396
Outlet_From_SBS_Blower2 (FP)
78P
1702
Basket_ventilation_flow (L)RD
1703Reactor_Outlet_Pipe_to_CCS (FP)
1705
CCS_Splitting_Restrictor (FP)RD
1707
CCS_Outlet_Pipe_to_Reactor (FP)
2Reactor_Core_Outlet
H
4
6
Reactor_Outlet_Manifold
8 10 12
HPT_Diffuser_Volume
16 18 20
LPT_Diffuser_Volume
26
PT_Inlet_Volume
28 30
34
PT_Diffuser_Volume
38RX(LP)_Inner_Vess
el_Volume40PC_Inlet_Volume
42
46
PC_Outlet_Volume
5052545658
IC_Inlet_Volume
62
66
IC_Outlet_Volume
707274
76HPC_Diffuser_Volume
78
Manifold
P82
RX(HP)_Inlet_Plenum
84RX(HP)_Core_Inlet
86
88 RX(HP)_Outlet_Plenum
90
Reactor_Inlet_Manifold
92
Reactor_Gas_Inlet_Plenum_Volume1
94Reactor_Gas_Inlet_Plenum_Volume2
96
98
Void_above_the_Reactor_Core
H
99IC_Waterside_Inlet
PT
103
105
IC_Waterside_OutletM
106
PC_Waterside_Inlet
PT110 112
PC_Waterside_Outlet
M
139141
143
Reactor_Inside_Cavity
T
145
Reactor_Upper_Volume
T
147
Reactor_Lower_Volume
T
149HPT_Intake_Volume
151
LPT_Intake_Volume
153
RX_Outer_Volume
159161
164
166
168
170172
173
176 177
179
187
187 Turbine_casing_temp
T
189PT_casing_volume
191
PT_basket_volume
195
PT_Inner_Volume
199
302
HPS_outlet_purified
MT304
Generator_Volume
306
308
308 Volume_on_top_of_PT
311
HPS Extraction
M
313315
Inlet_Volume_To_SBS_Blower2
317
320322
Inlet_Volume_To_SBS_Blower1
324
327RX_Outer_Annulus_Volume
328
333SBS_Motor_Casing_Volume2
335
SBS_Motor_Casing_Volume1
337Inlet to RX(HP)_Outlet_Pipes(b)
339
367
369
372 374
374 Turbine_rim_temp
T
378
378 u_ECLS_OD_volume
379
379 u_ECLS_ID_volume382 384
386389
SBS_Blower1_Dump_Volume
391
SBS_Blower1_Dump_Volume
392395
SBS_Blower2_Dump_Volume
397
SBS_Blower2_Dump_Volume
398
1700 1701
1704CCS_Volume1
1706
Reactor
LP Turbo Unit
Power Turbine
Pre-cooler
Recuperator
Start-UP Blower System
HP turbo Unit
Intercooler
MPS NETWORK MODEL
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SHELL-AND-TUBE SUBNETWORK
Discretization of a section of a shell-and-tube heat exchanger
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NETWORK SOLUTION METHODS
• Methods can be broadly classified as explicit and implicit.
• Explicit methods are especially suited for solving fast transients, but stability governed by Courant number which dictates short time steps.
• Very slow when solving steady-state or slow transient problems.
• Implicit methods not governed by Courant number and are especially suited for steady-state and slow transient problems.
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NETWORK SOLUTION METHODS
• Generally much slower than explicit methods when solving fast transients.
• In the design of the PBMR plant the concern is mostly slow transients and steady-state solutions.
• The method used in the case of the PBMR is the Implicit Pressure Correction Method, which is suitable for both steady-state and transient analyses, slow and fast transients, gas and liquid flows, and for adiabatic and non-adiabatic flows.
• The method is embodied in the network or systems CFD code Flownex.
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GOVERNING EQUATIONS
• Mass conservation
( ) 0VAt A xρ ρ∂ ∂+ =
∂ ∂
• Momentum conservation
2( ) ( ) cos 02
f V VV V A p gt A x x D
ρρ ρ ρ θ∂ ∂ ∂+ + + + =
∂ ∂ ∂
• Energy conservation
0 0( ) ( ) 0h p VAh qt A x
ρ ρ∂ − ∂+ − =
∂ ∂
Fully conservative form of conservation equations:
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GOVERNING EQUATIONS
• Mass conservation
( ) 0V
t xρρ ∂∂
+ =∂ ∂
• Momentum conservation
2
cos 02 2
o o
o o
f V Vp TV p Vgt p x T x D
ρρρ ρ θ∂ ∂∂+ + + + =
∂ ∂ ∂
• Energy conservation
( ) ( ) 0o oh Vhp qt t xρ ρ∂ ∂∂
− + − =∂ ∂ ∂
For compressible gas flows:
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SOLUTION ALGORITHM
Conservation of mass:
Branch 1
1
2
j ik 1
2
J
Branch 2
Branch j Branch 1
1
2
j ik 1
2
J
Branch 2
Branch j
1
2
j ik 1
2
J
Branch 2
Branch j
Control surface
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1
2
j ik 1
2
J
Branch 2
Branch j
Control volume
Branch 1
1
2
j ik 1
2
J
Branch 2
Branch j
Control volume
Branch 1
SOLUTION ALGORITHM
Conservation of momentum:
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SOLUTION ALGORITHM
Conservation of energy:
1
2
j ik 1
2
J
Branch 2
Branch j
Control volume
Branch 1
1
2
j ik 1
2
J
Branch 2
Branch j
Control volume
Branch 1
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REACTOR MODEL
Horizontalinlet slots
Control rodchannels
Centralreflector
Pebble bed
Verticalriserchannels
Core barrelannulus
Core barrel
Gas inletmanifold
Corestructures
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REACTOR MODEL
• Gas flow channels and/or leak flow paths connected to inner and outer perimeters of core.
• Heat transfer and flow through core structures.• Fluid flow and heat transfer, including radiation and
convection in cavities between core structures.• Variable porosity.• Radial as well as axial power profiles.• Heat generation in core structures.
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Conservation of mass for gas:
{ } 0V A
d dV V n dAdt
ερ ε ρ+ =∫ ∫ i
Conservation of momentum for gas:
( ){ }V A V V
d V dV n V V n dA gdV B dVdt
ερ ε ρ ερ ε+ − = −∫ ∫ ∫ ∫σi
Conservation of energy for gas:
{ } ( )bfV A V
d E dV n EV V q dA g V q dVdt
ερ ε ρ ερ+ − + = +∫ ∫ ∫σi i
GOVERNING EQUATIONS
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Expressed in axi-symmetric cylindrical coordinates
Continuity:
( ) ( ) ( )1 0r zru ut r r zερ ερ ερ∂ ∂ ∂
+ + =∂ ∂ ∂
GOVERNING EQUATIONS
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GOVERNING EQUATIONSMomentum in radial direction:
( ) ( )
2
21
o or r zz
o o
rr zr r r
T pu u u V put z r T r p r
p r g Br r r z r
θθ
ρερ ερ ε
ετε ε τ ετ ερ ε
⎡ ⎤∂ ∂∂ ∂ ∂⎛ ⎞+ − = − +⎢ ⎥⎜ ⎟∂ ∂ ∂ ∂ ∂⎝ ⎠ ⎣ ⎦∂ ∂ ∂
− + + − + −∂ ∂ ∂
Momentum in axial direction:
( ) ( )
2
21
o oz z rr
o o
rz zz z z
T pu u u V put r z T z p z
p r g Bz r r z
ρερ ερ ε
ε ε τ ετ ερ ε
⎡ ⎤∂ ∂∂ ∂ ∂⎛ ⎞+ − = − +⎢ ⎥⎜ ⎟∂ ∂ ∂ ∂ ∂⎝ ⎠ ⎣ ⎦∂ ∂ ∂
− + + + −∂ ∂ ∂
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GOVERNING EQUATIONS
Energy:
( ) ( ) ( ) ( )
( )
[ ]( ) [ ]( )
1
1
1
o o r o z
r r z z bf
rr r rz z zr r zz z
h r h u h u pt r r z t
T Trk k g u g u qr r r z z
r u u u ur r z
ερ ε ρ ερ ε
ε ε ερ
ε τ τ ε τ τ
∂ ∂ ∂ ∂+ + =
∂ ∂ ∂ ∂∂ ∂ ∂ ∂⎛ ⎞ ⎛ ⎞+ + + + +⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠∂ ∂
+ + + +∂ ∂
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GOVERNING EQUATIONS
For the pebble-bed:
1B L
V Vρ ⋅
Thus momentum in radial direction:2
2o or
ro o
T pu V p yg B pt T r p r r r
ρ εερ ε ε ερ ε∂ ∂∂ ∂ ∂
= − − − − −∂ ∂ ∂ ∂ ∂
Thus momentum in axial direction:2
2o oz
zo o
T pu V p yg B pt T z p z z z
ρ εερ ε ε ερ ε∂ ∂∂ ∂ ∂
= − − − − −∂ ∂ ∂ ∂ ∂
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GOVERNING EQUATIONS
Darcy-Weisbach pipe momentum:
Therefore momentum in radial direction:2
2 2r ro or
ro o
u uT pu V p y pgt T r p r r r
ρρ ερ ρ βε
∂ ∂∂ ∂ ∂= − − − − −
∂ ∂ ∂ ∂ ∂
2
2 2o o
o o
f V VT pV V p ygt T s p s s D
ρρρ ρ∂ ∂∂ ∂=− − − −
∂ ∂ ∂ ∂
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GOVERNING EQUATIONS
Energy:
( ) ( ) ( ) ( )
( )
1
1
o o r o z
r r z z bf
h r h u h u pt r r z t
T Trk k g u g u qr r r z z
ερ ε ρ ερ ε
ε ε ερ
∂ ∂ ∂ ∂+ + =
∂ ∂ ∂ ∂∂ ∂ ∂ ∂⎛ ⎞ ⎛ ⎞+ + + + +⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠
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GOVERNING EQUATIONS
Conservation of energy for pebble:
( ) 22
1 sinsinv s
Tc T kr qt r r rρ θ
θ∂ ∂ ∂⎡ ⎤⎛ ⎞= +⎜ ⎟⎢ ⎥∂ ∂ ∂⎝ ⎠⎣ ⎦
Convective, conductive and radiative heat transfer between pebbles:
10 eff eff fbT Trk k q
r r r z z∂ ∂ ∂ ∂⎛ ⎞ ⎛ ⎞= + +⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠
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GOVERNING EQUATIONS
Conservation of energy for reflector blocks:
( ) ( )
( ) ( )
11 1
1 1
v
fs
Tc T r kt r r r
Tk qz z
ε ρ ε
ε ε
∂ ∂ ∂⎛ ⎞⎡ ⎤− = −⎡ ⎤ ⎜ ⎟⎣ ⎦ ⎢ ⎥∂ ∂ ∂⎣ ⎦⎝ ⎠∂ ∂⎛ ⎞⎡ ⎤+ − + −⎜ ⎟⎢ ⎥∂ ∂⎣ ⎦⎝ ⎠
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DICRETIZATION
Pebble bed Core structures
Pebble surfacetemperature
Pebble internalsolid mass
temperatures
Core structureSolid masstemperatures
Conductionelements
Effectiveconduction
and radiation inpebble bed
Core and core structures solid elements
Horizontalinlet slots
Control rodchannels
Centralreflector
Pebble bed
Verticalriserchannels
Core barrelannulus
Core barrel
Gas inletmanifold
Corestructures
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DICRETIZATION
Horizontalinlet slots
Control rodchannels
Centralreflector
Pebble bed
Verticalriserchannels
Core barrelannulus
Core barrel
Gas inletmanifold
Corestructures
Pebble bed Core structures
Pebble bedvoid volumes
Pebble bedflow resistance
elements
Inlet slot flowresistanceelements
Riser channelflow resistanceelements
Inlet manifold
Riser channels, inlet slots and pebble bed flow paths
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DICRETIZATION
Control rod channel flow paths
Pebble bed Core structures
Control rodchannel flowresistanceelements
Horizontalinlet slots
Control rodchannels
Centralreflector
Pebble bed
Verticalriserchannels
Core barrelannulus
Core barrel
Gas inletmanifold
Corestructures
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DICRETIZATION
Integrated networkHorizontalinlet slots
Control rodchannels
Centralreflector
Pebble bed
Verticalriserchannels
Core barrelannulus
Core barrel
Gas inletmanifold
Corestructures
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T = 323 K
m = 5kg/s
Convection at 373 K
Radiation at 373 K
Composite layer reservoir
Node 1
Node 2
Node 3
VALIDATION
Heat transfer through a composite reservoir wall
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VALIDATION
322
324
326
328
330
332
334
336
338
340
342
0 50 100 150 200 250 300 350 400 450 500
Time [s]
Tem
pera
ture
[K]
Bench Node 1 Bench Node 2 Bench Node 3FN Node 1 FN Node 3 FN Node 332
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VALIDATION
5000 m
0.5 mHelium
5000 kPa
107ºC
2000 m
Measuring point
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VALIDATION
0.00
1000.00
2000.00
3000.00
4000.00
5000.00
6000.00
7000.00
8000.00
9000.00
10000.00
0.00 10.00 20.00 30.00 40.00 50.00 60.00
Time (sec)
Tota
l Pre
ssur
e[kP
a]
Benchmark solution Flownet solution34
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VALIDATION
Pebble-bed micro model35
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VALIDATIONPBMM
RXHPC
HS
HPT LPT
PCIC
PT
LPC
CT
SBS
PTC
GBPLPBHPB
SIV
SBSOV
PTCV
PV
ELC
CWP
NIV
SBSIV
NEV
Schematic layout36
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VALIDATION
PBMM network model37
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VALIDATION
0
5
10
15
20
25
30
35
40
50 150 250 350 450 550 650
HPT inlet temperature [oC]
Pres
sure
incr
ease
ove
r SIV
[kPa
]
Measured Predicted
Pressure difference across system inline valve38
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1Reactor_Core (R)
3
Reactor_Outlet_Connection_to_Core_Outlet_Pi
pe (FP)
7 Core_Outlet_Pipe (FP)
9CM
11
HPT_Diffuser (FP)
13
HPT_Outlet_Pipe (FP)
17
Low_Pressure_Turbine (T)
CM19
LPT_Diffuser (FP)
21LPT_Outlet_Pipe (FP)
27PT_Intake (FP)
29
Power_Turbine (T)
31PT_Diffuser (FP)
35
PT_Outlet_Contraction (FP)
39
Recuperator_LP (H)RX
41
Pre-cooler_outer_bundle (H)CX
43
Pre-cooler_inner_bundle (H)CX
47
PC_Outlet_Contraction (FP)
51
LPC_Intake (FP)
53CM
55
LPC_Diffuser (FP)
57
LPC_Outlet_Pipe (FP)
61
Intercooler_outer_bundle (H)CX
63
Intercooler_inner_bundle (H)CX
67
IC_Outlet_ducting(FP)
71
HPC_Intake (FP)
73CM
75
HPC_Diffuser (FP)
77HPCe_Holes_to_Manifold (FP)
79
Maintanence_Valve (V)RD
83 RX(HP)_Inlet_Pipes (FP)
85RX
87 RX(HP)_Outlet_Pipes(a) (FP)
89
Core_Inlet_Pipes(e) (FP)
91
Reactor_Annular_Pipes (FP)
93
Reactor_Gas_Inlet_Plenum_Holes (FP)
95Control_Rod_Cooling_flow_connection (FP)
102CX
104CX
109CX
111CX
78P
113
Manifold_to_HPTe_Leakage (L)RD
78P
116RD
119HPC_Bypass_Valve_(HPB) (V)
120
LPC_Bypass_Valve_1_(LPB1) (V)
121
Gas_Cycle_Bypass_Valve_1_(GBP1) (V)
78P
133
Manifold_to_HPTi_Leakage (L)RD
78P
135
RX_bypass_valve_(1 TO 4)_(RBP1) (V)
136Reactor_Plenum_Reduction_Area (FP)
137 Reactor_Outlet_Slots (FP)
138
Control_Rod_Bypass(filled) (FP)
140
Control_Rod_Bypass(empty) (FP)
142
Leakflow_from_Control_Rod_to_Outlet_Manifold (FP)
RD
144
Inside_Cavity_Slots_to_Core (FP)RD
146Reactor_Outside_
Cavity (FP)
148 Reactor_Leak_into_Manifold (FP)
RL
150HPT_Intake (FP)
152
LPT_Intake (FP)
158
RX(LP)_to_PC_connection (FP)
160
Annular_flow_path_to_IC (FP)
162
Annular_flow_path_. . ._to_IC_core (FP)
163
Recuperator_Outlet_Pipe (FP)
165
Core_Inlet_Pipes(a) (FP)
167Core_Inlet_Pipes(b) (FP)
169
Core_Inlet_Pipes(c) (FP)
171
Core_Inlet_Pipes(d) (FP)
174
175
LPC_Bypass_Valve_Pipe2 (FP)
178
LPC_Bypass_Valve_Pipe1 (FP)
180Bypass_Valve_Pipe (FP)
181 HPCe_to_HPCi_Leakage (L)
RD
78P
182
Manifold_to_LPTi_Leakage (L)
RD
183
LPCe_to_LPCi_Leakage (L)RD
184 Casing_cooling_flow (L)RD
56185
LPCe_to_PT_casing_flow (FP)
186
PTi_to_Basket_leak (L)RD
188
188 25%_casing_cooling_flow (L)
RD190
190 75%_casing_cooling_flow (L)
RD
192
Basket_to_PTe_leak (L)RD
194
PT_internal_fp2 (FP)
RD
196
196 Buffer_to_gaspath_leak (L)
197
197 ECLS_upper (L)
198
ECLS_lower (L)
300
ECLS_to_PToutlet (L)RD
301
dummy
303
HPS_supply_line (FP)RD
305
PTG_Shaft_Labyrinth_Seal(a) (L)
307
307 PTG_Shaft_Labyrinth_Seal(b) (L)
309
PT_top_volume_to_PTe
(FP)
78P
310
Shaft_valve (V)RD
153312
Pipe_RXe_to_SBSi_2 (FP)
314
SBS_Isolation_valve_2(SBSV2) (V)
316
SBS_Blower2 (CM)
M
CM327 318
Pipe_SBSe2_to_RX_manifold (FP)
153319
Pipe_RXe_to_SBSi_1 (FP)
321
SBS_Isolation_valve_1(SBSV1) (V)
323
SBS_Blower1 (CM)
M
CM327 325
Pipe_SBSe1_to_RX_manifold (FP)
326
SBS_Inline_valve_1_(SIV1) (V)
78P
329
HP_coolant_valve_1_(HCV1) (V)78
P330
LP_coolant_valve_1_(LCV1) (V)
332SBS_Labyrinth_Seal2 (L)
334SBS_Labyrinth_Seal1 (L)
336
RX(HP)_Outlet_Pipes
(b) (FP)
338 RX_inlet_header_pipe (FP)
340
PC_Impingement_plate(FP)
341HPC_Bypass_Control_Valve_(HPBC) (V)
342
LPC_Bypass_Control_Valve[LPBC] (V)
343
SBS_Bypass_valve_(SBP) (V)
344
SBS_Bypass_Control_Valve_(SBPC) (V)
345
LPC_Bypass_Valve_2_(LPB2) (V)
346
LPC_Bypass_Valve_3_(LPB3) (V)
347
348
349
350
351
352
353 Gas_Cycle_Bypass_Valve_8_(GBP8)(V)
78P
354
HP_coolant_valve_2_(HCV2) (V)
78P
355
LP_coolant_valve_2_(LCV2) (V)
356
SBS_Inline_valve_2_(SIV2) (V)
357
SBS_Inline_valve_3_(SIV3) (V)
78P
361
78P
362
78P
363
364
HPC_Bypass_Control_Valve_Pipe (FP)
365LPC_Bypass_Control_Valve
_Pipe2 (FP)
366
LPC_Bypass_Control_Valve_Pipe1 (FP)
368
PT_1st_stg_stator (FP)
370
370 PT_1st_stg_rotor_inlet (FP)
371
371 Inlet_1st_stg_throat (FP)
373
373 25%_rim_cooling_flow (L)
RD
375
375 75%_rim_cooling_flow (L)
RD
376
Rim_cooling_flow (L)RD
377
OD_u_ECLS_backup_lab (L)
380
380 ID_u_ECLS_backup_lab (L)56 381
PT_internals_cooling flow
(FP)
383
PT_internal_fp1 (FP)
RD
387
Inlet_to_SBS_Blower1 (FP)
388
SBS_Blower1_Outlet_Diffuser (FP)
390
Outlet_From_SBS_Blower1 (FP)
393
Inlet_to_SBS_Blower2 (FP)
394
SBS_Blower2_Outlet_Diffuser (FP)
396
Outlet_From_SBS_Blower2 (FP)
78P
1702
Basket_ventilation_flow (L)RD
1703Reactor_Outlet_Pipe_to_CCS (FP)
1705
CCS_Splitting_Restrictor (FP)RD
1707
CCS_Outlet_Pipe_to_Reactor (FP)
2Reactor_Core_Outlet
H
4
6
Reactor_Outlet_Manifold
8 10 12
HPT_Diffuser_Volume
16 18 20
LPT_Diffuser_Volume
26
PT_Inlet_Volume
28 30
34
PT_Diffuser_Volume
38RX(LP)_Inner_Vess
el_Volume40PC_Inlet_Volume
42
46
PC_Outlet_Volume
5052545658
IC_Inlet_Volume
62
66
IC_Outlet_Volume
707274
76HPC_Diffuser_Volume
78
Manifold
P82
RX(HP)_Inlet_Plenum
84RX(HP)_Core_Inlet
86
88 RX(HP)_Outlet_Plenum
90
Reactor_Inlet_Manifold
92
Reactor_Gas_Inlet_Plenum_Volume1
94Reactor_Gas_Inlet_Plenum_Volume2
96
98
Void_above_the_Reactor_Core
H
99IC_Waterside_Inlet
PT
103
105
IC_Waterside_OutletM
106
PC_Waterside_Inlet
PT110 112
PC_Waterside_Outlet
M
139141
143
Reactor_Inside_Cavity
T
145
Reactor_Upper_Volume
T
147
Reactor_Lower_Volume
T
149HPT_Intake_Volume
151
LPT_Intake_Volume
153
RX_Outer_Volume
159161
164
166
168
170172
173
176 177
179
187
187 Turbine_casing_temp
T
189PT_casing_volume
191
PT_basket_volume
195
PT_Inner_Volume
199
302
HPS_outlet_purified
MT304
Generator_Volume
306
308
308 Volume_on_top_of_PT
311
HPS Extraction
M
313315
Inlet_Volume_To_SBS_Blower2
317
320322
Inlet_Volume_To_SBS_Blower1
324
327RX_Outer_Annulus_Volume
328
333SBS_Motor_Casing_Volume2
335
SBS_Motor_Casing_Volume1
337Inlet to RX(HP)_Outlet_Pipes(b)
339
367
369
372 374
374 Turbine_rim_temp
T
378
378 u_ECLS_OD_volume
379
379 u_ECLS_ID_volume382 384
386389
SBS_Blower1_Dump_Volume
391
SBS_Blower1_Dump_Volume
392395
SBS_Blower2_Dump_Volume
397
SBS_Blower2_Dump_Volume
398
1700 1701
1704CCS_Volume1
1706
Reactor
LP Turbo Unit
Power Turbine
Pre-cooler
Recuperator
Start-UP Blower System
HP turbo Unit
Intercooler
MPS NETWORK MODEL
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LOAD REJECTION
• Initially the plant operates at maximum power and at time t=0.9 s the generator power is reduces by 50 percent.
• The generator speed is controlled by a PID controller that adjusts the bypass flow by opening and closing a control valve.
• Following figures shows the variation in turbine temperatures and the variation in compressor temperatures during the transient.
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LOAD REJECTION
500
550
600
650
700
750
800
850
900
950
0 2 4 6 8 10 12
Time (s)
Tem
pera
ture
(ºC
)
HPin LPin PTin PTout
Turbine temperatures
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LOAD REJECTION
0
20
40
60
80
100
120
0 2 4 6 8 10 12
Time (s)
Tem
pera
ture
(ºC
)
LPin LPout HPin HPout
Compressor temperatures42
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Conclusions
• IPCM method as embodied in systems CFD code Flownex is capable of simulating complex thermal-fluid systems consisting of many interacting components.
• Flownex can predict performance of complex systems for both steady-state and transient conditions.
• Flownex can therefore be used to predict the performance of the integrated PBMR plant.
43
1
[1] TITLE: • My co-authors and colleagues are Proff Gideon Greyvenstein and Pieter
Rousseau [2] SCOPE: • Give a brief overview of PBMR main power system or power conversion unit
to sketch the context and put what will be said in context. • An overview of the essence of the network approach • A very brief introduction to the implicit pressure correction method which
forms the heart of the network code Flownex being used • Discussion of the reactor model as an example of the models incorporated in
the network code Flownex • Discuss a few validation cases to test / demonstrate the validity or fitness for
purpose of the code • An illustration of one scenario for the PBMR [3] PBMR MAIN POWER SYSTEM: • The slide shows a solid CAD representation of the main power system of the
proposed PBMR nuclear power plant currently under development in South Africa.
[4] SCHEMATIC LAYOUT OF MPS: • This slide shows a schematic layout of the main power system illustrating the
various components that from the system. [5] PBMR ISSUES: • High temperature gas reactors are complex thermal-fluid systems consisting
of many interacting components such as pipes, valves, heat exchangers, compressors, turbines, pumps, blowers and the nuclear reactor itself.
• Engineers are faced with two major challenges when carrying out the thermal-hydraulic design of a HTR power plant. The first challenge is to predict the performance of all the thermal-hydraulic components of the plant such as pipes, valves, heat exchangers, turbo machines and the reactor. The second challenge is to predict the performance of the integrated plant consisting of all its sub-systems
• System performance predictions must be done for both steady-state and transient conditions. Although it is obvious why steady-state analyses are required it is not so obvious why transient analyses are required. Transient analyses are required for control studies and for studying operating procedures such as start-up, load rejection and load following. It is also required when analyzing accident events.
2
• An approach that has gained wide acceptance is known as the network approach. With this approach models of standard components are developed that can be interconnected in any arbitrary way. The name “network” is derived from the graphical representation of thermal-fluid systems as networks of interconnected components. With the network approach one can easily reconfigure the system lay-out without having to change any computer code
[6] NETWORK APPROACH:
• With the flow network approach elements such as pipes, compressors, valves are denoted by circles while nodes, which are the end points of elements, are denotes as squares. Elements can be connected in any arbitrary way at common nodes to form a network as shown. An important feature of the model is that elements such as pipes, heat exchangers and the reactor, although depicted on the systems level as single elements or pairs of elements, can be discretized into sub-networks. Networks can therefore be embedded within networks thereby enabling the model to treat complex elements as distributed systems rather than lumped systems.
[7] MAIN POWER SYSTEM NETWORK MODEL:
• This slide shows a representation of the network model that was set-up to simulate the behaviour and performance of the PBMR under various conditions. The model is also used to test various control strategies.
[8] SHELL-AND-TUBE SUBNETWORK:
• As had been said, an important feature of the model is that elements such as pipes, heat exchangers and the reactor, although depicted on the systems level as single elements or pairs of elements, can be discretized into sub-networks.
• The network approach therefore allows for the discretization of more complex components such as shell and tube heat exchangers. The figure shows the discretization of part of a shell and tube heat exchanger. Larger circles and squares denote flow elements and nodes respectively while smaller circles and squares denote convective heat transfer links and metal temperatures respectively. The metal nodes can also be linked to form conductive paths.
[9] + [10] NETWORK SOLUTION METHODS:
3
• Flow network problems can be characterized in terms of their time dependence as steady-state or transient problems while transients in turn can be characterized as fast or slow. Flow problems can also be characterized in terms of fluid type i.e. gas or liquid flow. Another classification is adiabatic, non-adiabatic or isothermal flow. Methods for solving flow network problems can be broadly classified as explicit or implicit.
• Explicit methods such as the Method of Characteristics (MOC) are especially suited for solving fast transients in isothermal liquid flows while the Lax-Wendroff method are suitable for solving fast transients in gas flow problems. The stability of explicit methods is, however, governed by the ∆t-∆x relationship, which makes it very slow when solving steady-state or slow transient problems. The ∆t-∆x relationship also pose serious limitation when solving networks where both liquids and gasses can be present in different parts of the network.
• Implicit methods on the other hand are not governed by the ∆t-∆x relationship which means that longer time steps can be used. This makes implicit methods especially suited for solving steady-state or slow transient problems. A draw-back of implicit methods, however, is that they are generally much slower than explicit methods per time step which make them slower than explicit methods when solving fast transient.
• Method used in Flownex is known as the Implicit Pressure Correction Method (IPCM) and is suitable for both steady-state and transient analysis; for both slow and fast transients; for both liquid and gas flows; and for both adiabatic and non-adiabatic flows.
[11] GOVERNING EQUATIONS: • The equations governing transient flow through a variable area duct are the
continuity, the momentum and the energy equations. These equations are given in conservative form where h0 is the total enthalpy.
[12] GOVERNING EQUATIONS (for compressible flows): • In order to eliminate the convective acceleration term in the momentum
equation we first use the mass conservation equation to write the momentum equation in the non-conservative form. We then use principles in gas dynamics to replace the static pressure with the total pressure and total temperature.
[13] SOLUTION ALGORITHM:
4
• The discretized equations are obtained by integrating the equations for the conservation of mass, momentum and energy (which for a pipe are partial differential equations) over control volumes.
• The slide shows the control volume for the conservation of mass at nodal point.
[14] SOLUTION ALGORITHM: • This slide shows the control volume for the conservation of momentum over
an element. [15] SOLUTION ALGORITHM: • This slide shows the control volume for the conservation of energy. • The iterative solution procedure is then as follows:
i) Derive a set of algebraic equation using second order time integration of the mass, momentum and energy equations.
ii) Guess an initial pressure field. iii) Calculate the mass flows in all elements using the initial pressures in the
momentum equation. iv) Test for continuity at all nodes. v) Adjust the nodal pressures to ensure that continuity is satisfied at all
nodes. vi) Update the mass flows using the new updated pressure field. vii) Treat the updated pressure field as new initial pressures and repeat steps
(iii) to (vi) until convergence. viii)Solve the energy equation. ix) Repeat (iii) to (viii) until convergence. x) Move to next time step and repeat (ii) to (ix).
[16] REACTOR MODEL: • Flownex currently contained a simplified model for the pebble bed nuclear
reactor. The purpose of the model was not to do detail reactor design, but rather to allow for the integrated simulation of the reactor together with the PCU within acceptable computer simulation times.
• Recent developments in the design and layout of the PBMR reactor have given rise to the need for the simulation of a wider range of reactor phenomena, even within a simplified model, since these will influence the boundary values for the integrated plant simulations.
5
• Therefore, a need exists for the development of a new, more comprehensive pebble-bed reactor model that can still provide relatively quick integrated plant simulations, but including the phenomena listed in the following slide.
[17] REACTOR MODEL: • The presence of a central reflector column that implies that the core itself has
an annular rather than a cylindrical shape. • The addition and extraction of gas via purpose provided channels and/or leak
flow paths along the inner or outer perimeters of the core. • The simulation of heat transfer and fluid flow through porous and solid core
structures surrounding the core. • The simulation of fluid flow and heat transfer, including radiation and natural
convection, in purpose provided cavities between core structures with a two-dimensional rather than one-dimensional nature.
• The ability to take into account variations in porosity throughout the core. • The ability to specify normalised radial power distribution profiles within the
different axial layers in the core. • The ability to take heat generation that may occur in any of the core
structures into account. [18] GOVERNING EQUATIONS (integral): • The conservation equations in integral form for mass, momentum, and energy
for the fluid in the pebble-bed reactor can written as shown in the slide. [19] GOVERNING EQUATIONS (cylindrical mass): • If it is assumed that the properties of the fluid are continuous and sufficiently
differentiable, then the conservation equations in integral form can be transformed into an equivalent set of partial differential equations through the divergence theorem. The equation for the conservation of mass can be expressed in axi-symmetric cylindrical coordinates as shown in the slide.
[20] GOVERNING EQUATIONS (cylindrical momentum): • The equation for the conservation of momentum in the radial direction can be
obtained as axi-symmetric cylindrical coordinates. The continuity equation can be extracted from it, the dynamic head can be added and subtracted and the static pressure can be converted to the total pressure. This then leads to the equation shown in the slide.
• The same can be done to obtain the corresponding equation for the conservation of momentum in the axial direction.
[21] GOVERNING EQUATIONS (cylindrical energy):
6
• The equation for the conservation of energy in terms of the total specific enthalpy can be obtained in axi-symmetric cylindrical coordinates as shown in this slide.
[22] GOVERNING EQUATIONS (porous momentum): • For flow through a porous medium, such as the pebble-bed, it has been found
that the convective terms and diffusive or shear stresses terms may be neglected if dimensionless particle (pebble) resistance is much larger then one. For the pebble-bed the value is approximately 1470.
• The momentum equations may be reduced to the equations shown in the slide.
• Taking a close look at the convective terms in the momentum equations shown earlier reveals that these terms have been written in terms of the vorticity. The above conclusion therefore implies that the average (or macroscopic) flow can be assumed to be irrotational.
[23] GOVERNING EQUATION (pb vs pipe): • This slide shows the correspondence between the momentum equations for
the pebble-bed and a pipe. [24] GOVERNING EQUATIONS (reduced energy): • It can be shown that the contributions of the viscous dissipation terms are
negligible compared to the other terms in the energy equation. The energy equation can therefore be simplified to become as shown in the slide.
[25] GOVERNING EQUATIONS (pebble and convective): • It is assumed that the temperature distribution in a pebble is the same in all
radial directions. The equation for the conservation of energy in the pebble can therefore be written in one-dimensional spherical coordinates as shown in the slide.
• The heat transfer between the surfaces of the pebbles due to contact, convection and radiation can be written in axi-symmetric cylindrical coordinates as shown in the slide.
[26] GOVERNING EQUATIONS (reflector blocks): • Finally the equation for the conservation of energy in the (porous) reflector
blocks is given in axi-symmetric cylindrical coordinates as shown in the slide. • The Zehner-Schlünder correlation is employed to determine effective
conductivity effk between the pebbles, whilst the correlation for the surface heat transfer coefficient proposed by Kugeler et al. is used to determine the heat transfer between the pebbles and the coolant. The heat transfer between
7
the porous reflector blocks and the coolant is determined using the well-known Dittus-Boelter relationship.
• A study of all the equations reveal that they are one-dimensional, or can be written as the sum of two one-dimensional equations. This formulation of the equations allows the reactor to be discretized into a collection of one-dimensional elements (models) that can be incorporated in a general network approach.
[27] DISCRETIZATION (core, structures and solids): • The slide shows a simplified network representation of the solids in the
pebble bed and core structures of the reactor. In the network both the pebble bed and the core structures are each represented by two control volumes in the radial direction and four control volumes in the axial direction.
• In the case of the core structures, the large light grey squares (nodes) represent the mass of the solid material and therefore also the temperatures of the core structure material that is assumed to be homogeneous throughout a control volume. The large grey circles (elements) represent the radial and axial conduction respectively within the core structures.
• In the case of the pebble bed, the large grey squares represent only the outer layer of the pebbles in that control volume and therefore also the surface temperature of all the pebbles in that specific control volume. The inner layers of pebble mass is represented by the smaller grey squares. It will therefore be possible to calculate a temperature distribution profile within the pebbles of each control volume. The small grey circles represent the one-dimensional spherical heat conduction within the pebble while the large grey circles represent the effective conduction and radiation between the pebble surfaces within the bed.
[28] DISCRETIZATION (flow paths): • The slide shows a simplified network representation of the riser channel, inlet
slots and packed bed flow path within the pebble bed and core structures of the reactor.
• The white squares represent the void gas volumes and the circles the flow resistance elements. The node on the bottom right also represents the inlet manifold where it is assumed that the gas is well mixed so that a homogeneous temperature will be obtained.
[29] DISCRETIZATION (control rod flow paths): • The gas flowing in the riser channels, inlet slots and through the pebble bed
does not mix with the gas flowing in the control rod channels. This means
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that a second, separated gas flow network is required to simulate the flow in the control rod channels. This network is shown in the slide as dark grey nodes and elements.
[30] DISCRETIZATION (integrated network): • The interaction between the solid structure network and the respective flow
networks is via fluid/solid surface convection. This interaction is shown schematically in the slide. In the figure the surface convection elements are shown in black, the control rod channel flow network in dark gray, the solid network in light gray and the riser channels, inlet slots and pebble bed flow path in white.
• The slide highlights one of the distinct advantages of employing the network approach rather than the traditional CFD approach. That is that even though the simplifying assumption was made earlier of two-dimensional axi-symmetric geometry, both of the riser channel and control rod channel flow paths that is unmixed, can be simulated together with its interaction with the solid structures. This is accomplished by simply superimposing another network layer on top and adding the correct connectivity via surface convection elements.
[31] VALIDATION (reservoir wall):
• In this example a cylindrical reservoir of with water flowing through at a constant rate of 5kg/s at 323.15 K is considered. The reservoir wall consists of three layers. The outside of the reservoir is exposed to air at 373.15 K.
• Starting at steady state conditions the outside convection temperature is varied with a step function from 273.15 K to 373.15 K with 100-second intervals.
[32] VALIDATION (reservoir wall results): • The slide shows the temperature variation with time for the outside, middle
and inside of the reservoir wall respectively. The IPCM results are compared with an analytical solution. As can be seen the results correlate well.
[33] VALIDATION (pressure wave in pipe): • In this example a pipe with a length of 5000 m and a diameter of 0.5 m is
connected to a reservoir at one end and has valve at the other end. Initially the valve is fully open. The pipe filled with Helium at a pressure of 5000 kPa and a temperature of 107 oC from the reservoir. The valve is then closed in 0.1 seconds. The pressure is measured at point 2000 m downstream from the reservoir.
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[34] VALIDATION (pressure wave in pipe results): • The slide shows the variation in pressure at the measuring point with time.
The solution obtained with Flownex is compared with code based on the Lax-Wendroff approach. The agreement between the results is good.
[35] VALIDATION (PBMM picture): • To test the feasibility of the PBMR power conversion unit and the proposed
control strategies, as well as the validity of the network simulations, a model (pebble-bed micro model) was built of the of proposed main power system. The model was designed, constructed and started-up (commissioned) in 9 months at a cost of USD 1.5 million. The slide shows a picture of the plant. This is the first three shaft closed Brayton cycle in the world that was successfully started up.
• This would not have possible without the network code Flownex. [36] VALIDATION (PBMM layout): • This slide shows a schematic layout of the PBMM cycle. [37] VALIDATION (PBMM network model): • This slide shows a representation of the PBMM network model. [38] VALIDATION (PBMM results): • This slide shows one set of the initial result that was obtained. The graph
shows the comparison between the measured and the predicted pressure difference over the system inline valve. It can be seen that the agreement is good.
• From the validation the tests that had been performed sofar it can be concluded that the network code is fit for purpose.
[39] MPS NETWORK MODEL: • We will now look at how Flownex predicts the behaviour of the PBMR main
power system when a load rejection occurs. • The slide reminds us what the network model for the PBMR main power
system looks like.
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[40] LOAD REJECTION: • Initially the plant operates at maximum power and at time t=0.9 s the
generator power is reduces by 50 percent. • The generator speed is controlled by a PID controller that adjusts the bypass
flow by opening and closing a control valve. [41] LOAD REJECTION (turbine temperatures): • This figure shows the variation in turbine temperatures during the transient
and how the PID controller succeeds in stabilising the turbines. [42] LOAD REJECTION (compressor temperatures): • This figure shows the variation in compressor temperatures during the
transient and how the PID controller succeeds in stabilising the compressors. • It should be remembered that the compressors are each link to a turbine
through a shaft. Simultaneously with the stabilization the Flownex performs the power matching of the coupled compressor-turbine pairs.
[43] CONCLUSIONS:
• IPCM method as embodied in network code Flownex is capable of simulating complex thermal-fluid systems consisting of many interacting components.
• Flownex can predict system performance for both steady state and transient conditions.
• Flownex can predict the performance of the integrated plant.