1. Chapter 6 Subchannel Analysis
POST-CHF HEAT TRANSFER
Following the occurrence of CHF, a regime of transition boiling may be observed
During transition boiling, a film of vapor prevents the liquid from coming in direct contact with the heating surface resulting in a steep rise in temperature
The film itself is not stable causing repetitive wetting and dryout of the heating surface resulting in an oscillatory surface temperature

2. CHF (Critical Heat Flux)
Definition of CHF
Critical Heat Flux (CHF) is the fuel cladding surface heat flux at which either DNB(Departure from Nucleate Boiling) or LFD(Liquid Film Dryout) occurs
Consequence of CHF
Heat flux controlled system (core)
Rapid increase of clad temperature
Cladding failure
Temperature controlled system (SG)
Sudden decrease of HTC
Decrease of heat flux
CHF design criteria
There will be at least a 95% probability that CHF will not occur on the limiting fuel rods during normal operation and operational transients at a 95% confidence level.

3. CHF & Flow Regime - LFD

4. CHF Mechanism – LFD Issues Liquid Film Dryout (LFD) under Annular Flow
Selection of annular flow initiation conditions (entrainment fraction, OAF criteria)
Modeling of deposition & entrainment rates

5. CHF & Flow Regime - DNB

6. CHF Mechanism – DNB Plausible DNB Mechanisms
Bubble crowding and vapor blanketing near the wall
Macrolayer dryout underneath vapor blanket
Prediction of DNB Heat Flux in Rod Bundles
Phenomenological approach
CHF lookup table method
Subchannel approach with empirical correlations
SR-1 correlation:

7. MAJOR ROLE OF SUBCHANNEL ANALYSIS CODE

8. Reactor Pressure Vessel (Integral-type)

9. SUBCHANNEL CONFIGURATION

10. CLASSIFICATION OF TH CODES

11. TH CODE – SYSTEM ANALYSIS
System Codes
The System Code Deals With The Overall Reactor System Including Generic Components Models And Special Process Models
Generally One-dimensional Approach
3-dimensioanl Core Dynamics Model (MARS)
RELAP5, RETRAN, TRAC, MARS

12. 1D Module (RELAP5) SYSTEM CODE - MARS Internal, Implicit
MASTER &
COBRA-III/CP
1D Module
(RELAP5)
Internal, Implicit
Coupling – Consolidation
3D Module
(COBRA-TF)
CONTEMPT
& CONTAIN
External, Explicit
Coupling with DLL
GUI: QuickWin or NPA

13. TH CODE – CORE ANALYSIS Porous Body Approach
Control Volume is Composed of Both Fluid and Solid
3-dimensional Approach
COMMIX Code Developed By ANL
(From Todreas & Kazimi, 1990)

14. Boundary-Fitted Coordinate Approach
TH CODE – CORE ANALYSIS
Boundary-Fitted Coordinate Approach
A Subchannel is Divided Into a Number of Fine Meshes
BODYFIT Code Developed by ANL

15. Application of subchannel analysis codes
SUBCHANNEL CODE
Functions
Calculate detailed TH conditions in subchannels (flow, enthalpy, pressure, and void fraction within subchannels)
Minimum DNBR or maximum fuel temperature
Application of subchannel analysis codes
To evaluate available and required thermal margins
To evaluate the number of failed rods due to DNB during accidents

16. WORLD-WIDE SUBCHANNEL ANALYSIS CODES
Developer
Spatial
Hydraulic
2- Model
Thermal
Remark
THINC-IV W
2-D
Homo. / Slip
Equil.
W3R, WRB (Perturbation method)
TORC CE
CE-1
COBRA-3CP
KWU
ERB-3 (MAT method)
COBRA-IV-I
PNL
External dimension control
VIPRE-01
PNL(EPRI)
EPRI-1 (recirculation)
FLICA
CEA
3-D
Slip
Part. Non-Equil.
OMEGA-1
ASSERT-4
AECL
Drift-Flux
Non-Equil.
Horizontal, Low G or flow reversal
THERMIT-2
MIT
Two-Fluid
FIDAS
PNC
Dryout, 3-Field model
COBRA-TF
3-Field model
VIPRE-02
PWR SLB and BWR stability
MATRA
KAERI
PWR & Advanced reactors, Void drift

17. Subchannel Equations

18. GENERAL PROCEDURE FOR SUBCHANNEL EQUATIONS

19. LOCAL INSTANT EQUATION
Generalized integral balance
Reynolds transport theorem
Local instant phase equation
Mass 1
Linear momentum
Energy

20. (RANS) TIME AVERAGING Time averaging operator Time perturbations
Time averaging of Linear Momentum Equation
(RANS)

21. TWO FLUID MODEL (Practical Form)
Mass conservation
Momentum conservation
Energy conservation

22. MIXTURE MODEL Mass conservation Momentum conservation
Energy conservation

23. CLASSIFICATION OF FLOW EQUATIONS
S. Fabic, Adv. Nucl. Sci. Tech. 10, (1977)

24. Subchannel Integral Balance Equations

25. Subchannel Control Volume – Mass, Energy, Axial momentum

26. DEFINITIONS
Operators
Variables

27. Subchannel integral balance (Mass)
Time-averaged mixture equation
Subchannel integral balance equation (including spatial perturbation of mass)
Divergence theorem

28. Subchannel integral balance (Mass)
Subchannel integral balance equation (Mass)

29. Subchannel integral balance (Energy)
Time-averaged mixture equation
Subchannel integral balance equation

30. MIXTURE ENTHALPY & FLOW ENTHALPY
Slip parameter
Rewrite energy equation
HEM (Homogeneous Equilibrium Model)

31. Subchannel integral balance (Axial Momentum)
Time-averaged mixture equation (axial momentum)
Subchannel integral balance equation (axial momentum)

32. AXIAL MOMENTUM FLUX TERM
Area average for each phase
Axial momentum flux term
Momentum velocity
Rewrite axial momentum equation

33. Subchannel Control Volume – Lateral momentum

34. Subchannel integral balance (Lateral Momentum)
Time-averaged mixture equation (lateral momentum)
Subchannel integral balance equation (lateral momentum)

35. LATERAL MOMENTUM FLUX TERM
Rewrite lateral momentum equation

36. SUMMARY OF SUBCHANNEL EQUATIONS (for subchannel i )
Mass conservation
Energy conservation
Axial momentum conservation
Lateral momentum conservation

37. Constitutive Models & Closure

38. SUBCHANNEL LATERAL TRANSFER
Diversion crossflow due to pressure difference
Forced crossflow due to spacers such as wire-wrap or helical fin
Turbulent mixing due to eddy motion of fluid
Forced mixing due to turbulent promoters such as mixing vanes
Viscous transfer due to molecular diffusion
Void drift due to the tendency of the two-phase system to approach equilibrium condition

39. EVOLUTION OF COBRA CODES
Code Capability
COBRA-II
COBRA-IIIC
COBRA-IIIC/MIT
COBRA-IV-I
Subchannel Representation
BWR multiple closed channels
PWR assembly/subchannel
Multi-stage calculation No
Yes
Hydrodynamic Capability
Transient
Homogeneous/Non-homogeneous
Thermal equilibrium/Non-equilibrium
Lateral pressure difference
Flow reversal
Natural circulation
Flow blockage
Homogeneous
Equilibrium
                                                          
Minor blockage
                                            
Substantial blockage
                                                                                                          
                                                                                                    
Total channel blockage
Fuel/Thermal-Hydraulic Models
Single/two-phase mixing
Coolant void fraction
Two-phase friction factor
Gap conductance
Fuel conductivity
Critical Heat Flux
Axial conduction
Wall conduction
Heat transfer correlation
input/input
homo./mod. Armand/slip/Levy
homo./Armand
input
temperature dependent
homo./mod. Armand/slip
BAW-2/W-3
input/Beus or input
homo./Levy/mod. Armand/Smith
homo./Armand/Baroczy
detailed MATRO package
BAW2/W3/CISE-4/Hench-Levy
BEEST package
homo./Levy/mod. Armand
both in fuel and coolant
RELAP-4 package

40. TURBULENT MIXING MODEL
Equal-mass exchange model

41. TURBULENT MIXING MODEL
Equal-volume exchange model
Void drift with equal-volume exchange model

42. THERMAL ANALYSIS OF FUEL ELEMENT
Energy equation (Temperature)
Heat conduction equation (for Fuel temperature calculations)
Steady, 1-D, Plate-type fuel

43. CLOSURE OF EQUATIONS
Unknowns
Equations

44. Algorithm & Code Structure

45. ALGORITHM (IMPLICIT SCHEME)
Boundary conditions:
Specify inlet flow distribution
(or, uniform overall pressure drop)
Specify enthalpy distribution
Zero inlet crossflow
Uniform pressure at exit

46. CODE STRUCTURE

47. CODE STRUCTURE

48. Applications Analysis of experimental data – code validation
Thermal margin analysis

49. CODE VALIDATION METHOD
Comparison with experimental data
Channel-wise flow and enthalpy distributions data under adiabatic/diabatic conditions
Flow distribution data under blockage conditions
Void fraction distribution data
CHF and thermal mixing data
Code sensitivity study
TH models, analysis models, numerical schemes
Comparison with reference code results for benchmarking problems

50. EXPERIMENTAL DATA FOR CODE VALIDATION
MATRA
COBRA-4
TORC
THINC-4
VIPRE-01
WH Zion-1 Core exit Temp. ○
CNEN 4x4 mixing (velocity)
CU 4x4 exit flow & enthalpy
GE 3x3 mixing
WH 14x14 blockage
CE inlet jetting
ORNL 19-rod
ISPRA 16-rod mixing
PNL 7x7 blockage - water
PNL 2x6 buoyancy
FRIGG 36-rod (two-phase DP)
FRIGG 36-rod (void)
ANL void
Martin void
Long cylinder conduction
Fuel T meas. Halden IFA-432
GE 4x4 transient CHF
CU 19-rod CHF
GE 4x4 CHF
CU/W 3x4 & 4x4 CHF

51. VALIDATION: SINGLE-PHASE VELOCITY DISTRIBUTION
PNL Flow Blockage Tests (single-phase)

52. VALIDATION: TWO-PHASE VELOCITY & ENTHALPY
GE 9-rod Bundle Tests (Two-phase)
Two-phase mixing model
Equal mass exchange model (EM) for COBRA-IV-I
Equal volume exchange & void drift model (EVVD) for MATRA

53. VALIDATION : SUBCHANNEL VOID DISTRIBUTION
Phase-I Ex-1 (Test , 58, 61)
OECD/NRC BFBT benchmark
During the benchmark exercise-1, we have calculated steady-state subchannel void distributions for the TS-4, which was also used for this transient experiments. As shown in this figure, the hot rods were located at the peripheral region of the test bundle.
From the analyses, it was found that the subchannel void distribution was reasonably predicted by MATRA code. MATRA tends to under-predict the void fraction as the exit quality increases.
The standard deviation is about 3 to 4% for all cases. From this result it was conceived that the prediction capability of void distribution is similar to the three different quality conditions, even though there is a systematic bias of the cross sectional averaged void fraction(, and it may be possibly due to the void fraction correlation used in MATRA code).
(P-M) %
X=5%
X=12%
X=25%
Mean
-0.9
-2.1
-5.0
Std. dev.
3.4
3.3
3.7
Bundle cross-section (8X8)

54. THERMAL MARGIN ANALYSIS : SMART
SMART Core
(57 FA)

55. Schematic Diagram of REX-10
REX-10 Core
11x11 Fuel Assembly
ThO2
Control Rod
Schematic Diagram of REX-10
UO2 IT

56. APPLICATION TO GAS-COOLED REACTOR
Multichannel test (JAERI, 1986)
HTTR-type GCR application
(Ref. Nuclear Engineering Design 236, , 2006)

57. Input & Output

58. Geometry & power distributions
MATRA INPUT
Geometry & power distributions
Axial power distribution
Channel geometry (flow area, heated & wetted perimeter, gap size, etc.)
Spacer grid (location, loss coefficient)
Rod geometry (diameter, peaking factor)
Operating conditions
System pressure, inlet temperature, flow rate, average heat flux
Model selection
Correlations & models
Solution scheme (implicit, explicit)
Numerical solution parameters
Boundary conditions
Convergence criteria
Acceleration & damping factors
Number of axial nodes and time steps

59. Input mirror & calc. parameters Channel results
MATRA OUTPUT
Input mirror & calc. parameters
Channel results
Results for channel exit
Results for bundle average
Results for each channel (DP, h, r, c, a, flow, area, etc.)
Crossflow results
Crossflow between channel i and j
Rod results
Results for each rod (q”, DNBR, HTC, Tfluid, Tclad, Tfuel)
CHF summary
Summary of CHF data (z, q”, MDNBR, rod no., Channel no.)