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

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.

CHF & Flow Regime - LFD

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

CHF & Flow Regime - DNB

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:

MAJOR ROLE OF SUBCHANNEL ANALYSIS CODE

Reactor Pressure Vessel (Integral-type)

SUBCHANNEL CONFIGURATION

CLASSIFICATION OF TH CODES

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

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

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)

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

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

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

Subchannel Equations

GENERAL PROCEDURE FOR SUBCHANNEL EQUATIONS

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

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

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

MIXTURE MODEL Mass conservation Momentum conservation Energy conservation

CLASSIFICATION OF FLOW EQUATIONS S. Fabic, Adv. Nucl. Sci. Tech. 10, 365-404 (1977)

Subchannel Integral Balance Equations

Subchannel Control Volume – Mass, Energy, Axial momentum

DEFINITIONS Operators Variables

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

Subchannel integral balance (Mass) Subchannel integral balance equation (Mass)

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

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

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

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

Subchannel Control Volume – Lateral momentum

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

LATERAL MOMENTUM FLUX TERM Rewrite lateral momentum equation

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

Constitutive Models & Closure

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

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

TURBULENT MIXING MODEL Equal-mass exchange model

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

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

CLOSURE OF EQUATIONS Unknowns Equations

Algorithm & Code Structure

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

CODE STRUCTURE

CODE STRUCTURE

Applications Analysis of experimental data – code validation Thermal margin analysis

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

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

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

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

VALIDATION : SUBCHANNEL VOID DISTRIBUTION Phase-I Ex-1 (Test 4101-55, 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)

THERMAL MARGIN ANALYSIS : SMART SMART Core (57 FA)

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

APPLICATION TO GAS-COOLED REACTOR Multichannel test (JAERI, 1986) HTTR-type GCR application (Ref. Nuclear Engineering Design 236, 164-178, 2006)

Input & Output

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

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.)