Transcript 슬라이드 1 - http://hydrogen.kaist.ac.kr

Chapter 4: Core Thermal Design and Analysis
Hee Cheon NO
Nuclear System/Hydrogen Lab.
KAIST
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Contents
4.1 Technical Specifications and Setpoint Methodology
4.1.1 Standard review plan and Regulatory guides
4.1.2 Best-estimate methodology statistical tolerance limits
4.1.3 Technical Specification and Setpoint Methodology
4.1.4 Software package for Technical Specification analysis
4.2 Core Thermal Design
4.2.1 Power peaking factor
4.2.2 Power distribution control
4.2.3 Fuel centerline temperature limit
4.2.4 DNB limits: Improved DNBR Analysis Methodology
4.2.5 Practice of PWR core thermal design
4.3 Core Thermal Analysis
4.3.1 Overview of subchannel analysis
4.3.2 Subchannel Analysis: Fluid Model of COBRA -ⅢC
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4.1 Core thermal design regulatory guides
 Reactor design: The reactor core and associated coolant,
control, and protection systems shall be designed with
appropriate margins to assure that specified acceptable
fuel design limits (SAFDL) are not exceeded during and
condition of normal conditions, including the effects of
anticipated operational occurrences(AOO).
 Fuel system Design: A fuel failure criterion should be
given for each known failure mechanism. Such criteria
should address as follows:
Overheating : DNB or dryout, fuel melting, hydrodynamic
flow instability(premature boiling crisis)
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2. Reactor design regulatory guides
Thermal – Hydraulic Design: DNB correlation should be
established such that there should be 95% probability at a
95% confidence level that the hot rod in the core does
not experience DNB for normal operation conditions and
AOO. There should be at least 99.9% of the fuel rods in
the core which would not be expected to experience
departure from nucleate boiling or boiling transition for
normal operating conditions
Ex: W-3 correlation : Limiting DNBR=1.3
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2. Reactor design regulatory guides
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2. Reactor design regulatory guides

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2. Reactor design regulatory guides
 Example of DNBR application of 95/95 concept:
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15
n 1
n 1
x ( M / P)   xi  0.99133; S ( M / P)  [ ( xi x )2 / (15  1)]1/2  0.0541
K95/95  5.27049exp(15 / 21.50779)  2.624
lim it DNBR( P / M )  1 / [ x ( M / P)  K95/95S ( M / P)]  1 / (0.99133  2.624 *0.0541)  1.17734
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CHF evaluation
Example of CHF evaluation
Energy balance : q( z )  m( h( z )  hin )
Definition of x ( z ) : x ( z )  (h( z )  h f ) / h fg  h( z )  h fg x ( z )  h f
q( z )  m( h( z )  hin )  m( h fg x( z )  h f  hin )  m( h fg x( z )  hsub )
 qDNB ( z  L)  mxDNB ,L h fg  mhsub
x ( z )  q( z ) / ( mh fg )  hsub / h fg  4q ''( z ) z / (GDeh fg )  hsub / h fg
 xDNB ,L ( z  L)  4 q '' DNB L / (GDe h fg )  hsub / h fg  q '' DNB  q '' DNB ( xDNB ,L )
z
where q( z )   q ' ( z )dz  q ''( z ) z * Pw ; m  GA f  GDe Pw / 4;
in
q( z ) / m  4q ''( z ) z / GDe
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4.1 Core thermal design regulatory guides
 Technical specification: The reactor core and associated
coolant, control, and protection systems shall be
designed with appropriate margins to assure that
specified acceptable fuel design limits (SAFDL) are not
exceeded during and condition of normal conditions,
including the effects of anticipated operational
occurrences(AOO).
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2. Reactor design regulatory guides
 Safety limits:
PWR core safety limits
Damage of fuel rod
Accidents
LOCA
Transients
(cladding
overheating)
uniform strain of
cladding < 1%,
MDNBR<limit DNBR
<1204C(2200F)
peak cladding
temperature
local maximum oxidation of <17%; LOCA
of cladding
embrittlement
cladding
maximum fuel centerline No incipient melt
temperature
MDNBR
MDNBR >
design MDNBR limit
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2. Reactor design regulatory guides
 Safety limits:
 Shutdown margin (SDM): margin to criticality in the situation with all
control rods inserted and the strongest control rod withdrawn. SDM is
initial subcriticality for the steam line break accident analysis. sufficient
boron concentration to assure shutdown without control rod movement;
 Fuel enrichment: current enrichment limits around 5 wt% U235; Neither
benchmarks of code performance nor the bases for extrapolating code
performance in the enrichment
range of 5-10 wt% have been well established.
 Fuel melting: the transition from the solid to the liquid phase of UO2 is
accompanied by an increase (~13%) in volume; neither allow molten
fuel to contact the cladding nor produce local hot spots~<82 kW/m.
 RIA cladding failure: maximum radially averaged fuel enthalpy of 280
cal/g and DNB; failures from PCMI and CHF
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2. Reactor design regulatory guides
 Technical Specification & Setpoint Development:
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2. Reactor design regulatory guides
 Technical Specification & Setpoint Development:
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2. Reactor design regulatory guides
 Technical Specification & Setpoint Development:
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2. Reactor design regulatory guides
 Technical Specification & Setpoint Development:
LSSS
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2. Reactor design regulatory guides
 Technical Specification & Setpoint Development:
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2. Reactor design regulatory guides
 Technical Specification & Setpoint Development:
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2. Reactor design regulatory guides
 Technical Specification
& Setpoint Development:
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2. Reactor design regulatory guides
 Technical Specification & Setpoint Development:
Core Analysis Code Package
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3. Core hydraulic design analysis
 Unit cell concept and ttoal pressure drop with spacer grids:
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3. Core hydraulic design analysis
 total pressure drop in the core channel
 pressure drop in spacer grid and at inlet and outlet
 frictional pressure drop
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3. Core hydraulic design analysis
pressure drop in spacer grid: Rehme's correlation
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4. Fuel thermal design analysis
Fuel centline temperature limit: fuel thermal analysis
methodology
• Issue of the fuel melting: the molten fuel may contact the
cladding leading to cladding overheating.
• Fuel centline temperature limit: during condition II events,
the maximum fuel centerline temperature should not
exceed the fuel incipient melting temperature.
• The fuel centerline temperature directly depends on the
local power generation rate, q’(z) with the small effects of
gap conductivity and melting temperature depending on
burnup.
• The local power generation rate with the incipient melting
temperature at the fuel center ranges from 18 to 21kw/ft.
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5. Core thermal design analysis
 power peaking factor: why do we need it?
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5. Core thermal design analysis
 power peaking factor
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5. Core thermal design analysis
 Example of power peaking factor for rated power of
3411Mwth from secondary side heat balance
Energy from fuel : 3411Mwth*0.974=3322Mwth
# of active feet of fuel rods (considering densification, swelling, thermal expansion)
L fuel ,total  193 Ass * 254rods / Ass *11.97active ft / rod  610,150 ft
'
qcore
 3,322,314kw / 610,150 ft  5.44kw / ft
q'peak  11.64kw / ft : lim ited cons tan t by design criteria
'
Fq  q'peak / qcore
 11.64 / 5.44  2.14
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5. Core thermal design analysis
 estimation of power peaking factor
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5. Core thermal design analysis
 Envelope of limiting peak local power
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5. Core thermal design analysis
 enthalpy rise hot channel factor
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5. Core thermal design analysis
 enthalpy rise hot channel factor
burnup
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5. Core thermal design analysis
CHF concept
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5. Core thermal design analysis
CHF correlation(W-3)
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5. Core thermal design analysis
MDNBR concept
"
"
"
DNBR( z)  qDNB
( z) / qactual
( z); MDNBR  qDNB
/ q"peak
MDNBR design limit=1.3
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5. Core thermal design analysis
Core thermal margin Analysis Procedure
MDNBR failure limit=1.0
MDNBR design limit=1.3
MDNBR trend after
Rx pump trip
Rx trip time
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5. Core thermal design analysis
DNBR and MDNBR evaluation
"
"
DNBR( z )  qDNB
( z ) / qactual
( z );
"
Design lim it : MDNBR  qDNB
/ q"peak  1.3  Design DNBR lim it
"
"
"
MDNBR  qDNB
/ q"peak  qDNB
/ ( Fq q 'core )  (qDNB
Ntotal , fuel Lactive
fuel
) / ( Fq Qth )
"
qDNB
/ Fq
where
"
0.22
qDNB
 C ( P)(G /106 ) M ( P ) Tsub
; Jens  Lottes CHF correlation
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Note : qDNB
, Fq  MDNBR 
1.Fq  axial / radial power flattening
issues : loading scheme, high fluence in Rx vessel
"
2.qDNB
 higher primary mass flow rate  higher pumping power (~ m3p )
"
qDNB
 higher mixing by spacer grids  higher pumping power
issue : high power loss by higher pumping power
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5. Core thermal design analysis
Example of CHF evaluation
Energy balance : q( z )  m( h( z )  hin )
Definition of x ( z ) : x ( z )  (h( z )  h f ) / h fg  h( z )  h fg x ( z )  h f
q( z )  m( h( z )  hin )  m( h fg x( z )  h f  hin )  m( h fg x( z )  hsub )
 qDNB ( z  L)  mxDNB ,L h fg  mhsub
x ( z )  q( z ) / ( mh fg )  hsub / h fg  4q ''( z ) z / (GDeh fg )  hsub / h fg
 xDNB ,L ( z  L)  4 q '' DNB L / (GDe h fg )  hsub / h fg  q '' DNB  q '' DNB ( xDNB ,L )
z
where q( z )   q ' ( z )dz  q ''( z ) z * Pw ; m  GA f  GDe Pw / 4;
in
q( z ) / m  4q ''( z ) z / GDe
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5. Core thermal design analysis
CHF evaluation(modified Biasi correlation)
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5. Core thermal design analysis
Determination of limit DNBR
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5. Core thermal design analysis
Example of limit DNBRs for DNB correlations
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5. Core thermal design analysis
Determination of limit DNBR nominal at 95% confidence
level
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5. Core thermal design analysis
 Determination of limit DNBR nominal
at 95% confidence level
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5. Core thermal design analysis
 Determination of limit DNBR nominal
at 95% confidence level
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5. Core thermal design analysis
 Determination of norminal
values & uncertainty of
parameters
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5. Core thermal design analysis
Example of two DNBR design methods for Loss of flow
transient
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5. Core thermal design analysis
Core thermal design procedure
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5. Core thermal design analysis
Example of enginnering Fq
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6. Subchannel Analysis
Overview of subchannel analysis
- Based on the subchannel control volume where fluid channels and fuel rods with the
interconnection of neighbor channels
- Through the interconnection of neighbor channels thermal and momentum mixings by
turbulent-induced and pressure-induced crossflows are considered
- Slip-equilibrium model
- The size of each subchanne: a single fluid channel to several assemblies.
- The fuel rod heat transfer model is coupled with the fluid subchannel analysis method.
- one buffer zone surrounding the hot channels is accurate enough to the hot channels
Numerics:
- fully implicit scheme: no stability limitation on space or time steps
- grid-based marching scheme: computation starts from the inlet grid to the top gridplane by grid-plane so that the pressure on each grid plane may be uniform allowing
pressure equalization through crossflows;
- valid where the axial upward flow is dominant.
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6. Subchannel Analysis
Overview
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6. Subchannel Analysis
Assumptions of subchannel analysis
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6. Subchannel Analysis
Codes of subchannel anlysis
·COBRA series
·TORC : CE
·LYNX : B&W
·VIPRE : EPRI
*Note : THINC(W) : porous-body code
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6. Subchannel Analysis
Continuity equation
 (  Ax )i / t  mi  mi 1  wij xi  w'ji xi  wij' xi
 mi  (mi  mi / xxi )  wij xi  w'ji xi  wij' xi
 mi / xxi  wij xi  w'ji xi  wij' xi
where
w'ji  wij'  turbulent mass flow rateunit axial length
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6. Subchannel Analysis
Energy equation
Vi [(  e)vi  (  e)li ] / t  Ai xi [(  hu) vi  (  hu)li ] / x
 qi' xi  wij h*xi  w'ji h j xi  wij' hi xi  c ji (T j  Ti )xi
where
e  int ernal energy
h*  donor enthalpy
qi'  linear heat generation rateat i
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6. Subchannel Analysis
Energy equation
(  h ) vi  (  h )li  (  h )i  i hˆi  i (hˆi  hi )  i hˆi   i h fgi
(  uh ) vi  (  uh )li  hˆi (mi / Ai )
where
 i h fgi   i ( hˆi  hi )
mixture density   i  (  ) vi  (  )li
mixture enthalpy  hi  [(  h ) vi  (  h )li ] / i
flowing quality  xˆi  (  u ) vi / [(  u )vi  (  u )li ]
flowing enthalpy  hˆi  [(  uh ) vi  (  uh )li ] / [(  u ) vi  (  u )li ]  xˆi hvi  (1  xˆi )hli
[(  uh )  (  uh ) ]  hˆ ( m / A )
vi
li
i
i
i
 (  i hˆi   i h fgi ) / t   (  i hˆi ) / t   (  i h fgi ) / t
 [  i  h fgi ( i / hˆi )]hˆi / t  hˆi  (  i ) / t   i h fgi / p )(p / t )
~ [  i  h fgi ( i / hˆi )]hˆi / t   i''hˆi / t  ( mi / (ui'' Ai ))hˆi / t
where
 (  i hˆi ) / t   i  ( hˆi ) / t  hˆi  ( i ) / t
 i h fgi / t  h fgi  i / t   i h fgi / t  h fgi ( i / hˆi )(hˆi / t )   i (h fgi / p )(p / t )
 i''  [  i  h fgi ( i / hˆi )]  mi / (ui'' Ai ); mod ified density
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6. Subchannel Analysis
Energy equation
Ai xi [(  hu)vi  (  hu)li ] / x  Ai xi [hˆi (mi / Ai )] / x  xi [hˆi mi ] / x
 x m hˆ / x  x hˆ m / x  x m hˆ / z  hˆ [V  / t  x w ]
i
i
i
i i
i
i
i
i
i
i
i
i
ij
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6. Subchannel Analysis
Axial momentum
pAf   w Aw  p( / 4) De 2   w De   De c f  u 2 / 2  p  4c f (x / De )  u 2 / 2
F x  pAf   w Aw  Af f (x / De )  u 2 / 2  ( Af / 2) f (x / De )( u ) 2
 ( Af / 2) f (x / De )(m / Af ) 2 :1 flow
 ( Af / 2) f  (x / De )(m / Af ) 2 : 2 flow
where   fritional 2 multiplier
c f / f : Fanning / Darcy friction factors
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6. Subchannel Analysis
Axial momentum
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6. Subchannel Analysis
transverse momentum equation
F xl  Cw(sx);
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6. Subchannel Analysis
transverse momentum equation
xi sij ijturbulent  xi sij t  ( du / dy )ij  xi sij t  (u j  ui ) / lij
sij ijturbulent   t  sij (u j  ui ) / lij  wij' (u j  ui )  wij'   t  sij / lij   sijG
where
 t : eddy diffusivity
   t / (lij u )  TDC (input )  0.038 forW design application
G, u : average axial mass flux / velocity
lij  (u j  ui ) / ( du / dy )ij  mixing length
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