nuclear reactors, bau, 1st semester, 2007-2008 (saed dababneh). 1 reactor model: one-group reactor r...
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Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
1
Reactor Model: One-Group
Reactor
R
H
• Briefly, we go through project 3.
01 2
2
2
Bdzdr
rrr
)()(),( zrzr
0
22
2
2
coscos0
0
H
zz
dz
d
dr
dr
dr
d
z
xy
r
)()( 00 rCYrAJ
Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
2
Reactor Model: One-Group
0)(0 CxYx n
00 4048.20)4048.2( RJ
Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
3
Reactor Model: One-Group
Reactor
R
H
z
xy
r
000 cos)
4048.2(
H
z
R
rAJ
Criticality condition?
Criticality condition?
Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
4
Reactor Model: One-Group
x
aa/2
Core
zReflected Slab ReactorReflected Slab Reactor
bb
Re
flect
or
Re
flect
or
),()(),()(
),()(),(1
trrDtrr
trrtrtv
a
f
For steady-state, homogeneous, 1-D
0)()(
0)()()(
2
2
2
2
xdx
xdD
xdx
xdD
RRa
RR
CCa
Cf
CC
C
C Core
R Reflector
)2
()2
(),2
()2
(,0)2
(BCa
Ja
Jaa
ba CRCRR
Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
5
Ra
RR
RRR
C
Ca
CfC
mCm
CC
DL
L
xba
A
DBxBAx
2
2
)(2sinh
)()cos()(
Reactor Model: One-Group
Verify.
RR
R
RCmCC
mC
RR
CmC
L
bA
L
DaBABD
L
bA
aBA
cosh)2
sin(
sinh)2
cos(
BC
RR
RCmC
mC
L
b
L
DaBBD coth)
2tan(
Criticality condition.Criticality condition.
Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
6
Reactor Model: One-Group
RR
RCmC
mC
L
b
L
DaBBD coth)
2tan(Criticality condition.Criticality condition.
• For bare slab CC was / 2.• Smaller core for reflected reactor.• Save fuel.
Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
7
Criticality “Calculation”• Can we solve “real” reactor problems analytically?• The previous discussion provides understanding of the concepts but also indicates the need for computational techniques.computational techniques.
• Assume:
• Adjust parameters so that = 0 (Steady-state).
• What parameters and how to adjust them?
),()(),()(),()(),(1
trrDtrrtrrtrtv af
)(),( retr t
)()()()()()()( rrDrrrrrv af
Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
8
)()()()()()()( rrDrrrrrv af
Criticality “Calculation”
• Fixed design and geometry the free variable is the fuel.
• As we did earlier (be guided by HW 21):As we did earlier (be guided by HW 21):
)()()()()()( rrk
rrrrD ffudge
a
221 LBDk af
a
ffudge
operators are ,1
FMFK
Mfudge
Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
9
Criticality “Calculation”
221 LBk af
fudge
FK
Mfudge
1
• Build an algorithm.• “Guess” (reasonably) initial kfudge and (or ) for the zeroth iteration.• Calculate the initial source term.• Iterate:
converges.flux until .....on so and
get 1
. and Guess
0
101
11
10
00
01
00
S
Skk
FS
k
SF
kM
k
Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
10
Criticality “Calculation”• Or:
• If for example k > 1, take action to reduce source or increase absorption.• How?How?
volume
ii
volume
i
volume
i
volume
i
i
dVSk
dVS
dVM
dVF
k
M
Fk
1
sinks
sourcesfission
1
1
1
1
Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
11
Reactor Kinetics Reactor Kinetics Reactor kinetics refers to the manipulation of parameters that affect k and to the subsequent direct response of the reactor system. Examples are:
• Absorber rods or shim movements to compensate for fuel burnup. • Safety scram rods to rapidly shutdown the chain reaction. • Control rods to provide real-time control to keep k = 1 or to maneuver up and down in power.• …..
Reactor Dynamics Reactor Dynamics Reactor dynamics refers to the more indirect feedback mechanisms due to power level effects and other overall systems effects such as:
• Temperature feedback. • VoidVoid feedback. • Pump speed control (affects water density and temperature). • …
How to Adjust Criticality
Negative or positive reactivity.reactivity.
Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).
12
How to Adjust Criticality
Before all:Before all:
Core Design Core Design The transient response of the reactor to the above direct and indirect changes in basic parameters is highly dependent on the design details of the reactor. Sample issues are:
• Where should the control rods be placed for maximum effectiveness? • Will the power go up or down if a void is introduced into the reactor? • Will the power go up or down if core temperature goes up? • How often should the reactor be refueled? • and so on...