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THERMAL-HYDRAULIC IN NUCLEAR REACTOR GS Trần Đại Phúc THERMAL-HYDRAULIC IN NUCLEAR REACTOR Summary I Introduction I.1 Safety Functions & Requirements I.2 Basis of thermal-hydraulic core analysis I.3 Constraints of the thermal-hydraulic core design II Energy from nuclear fission III Fission yield IV Decay heat V Spatial distribution of the heat sources VI Coolant flow and heat transfer in fuel rod assembly VII Enthalpy distribution in heated channel VIII Temperature distribution in channel in single phase IX Heat conduction in fuel assembly THERMAL-HYDRAULIC IN NUCLEAR REACTOR Summary X Axial temperature distribution in fuel rods XI Void fraction in boiling channels XI.1 Homogeneous Equilibrium Model (HEM) XI.2 Drift-flux model XI.3 Sub-cooled boiling region XII Heat transfer to coolant XII.1 Single phase XIII Two-Phase flow XIV Pressure drops XIV.1 Single-phase flows a) The Darcy Weisbach equation b) The Moody diagram XIV.2 Two-phase flows THERMAL-HYDRAULIC IN NUCLEAR REACTOR Summary XV Critical Heat Flux (CHF) XV.1 Departure from Nucleate Boiling (DNB) XV.2 Dry-out XV.3 Protection against boiling crisis A Fuel temperature B Reactor core coolant mass flow rate C Hydro-dynamic stability of the reactor core D.Technology of the DNBR or Critical Heat Flux ratio and Mixing effect D.1.Technology of the DNBR a) Critical Heat Flux (CHF) – Correlation E)Definition of the DNBR F) Mixing effect between sub-channels THERMAL-HYDRAULIC IN NUCLEAR REACTOR Summary G) Uncertanties relative to the manufacturing parameters H) Effect of the eccentricity of the fuel pellets and the ovality of the cladding on the CHF I) Effect of the manufacturing tolerances of the spacer grids on CHF J) Effect of the fuel rod bowing in the reactor on the CHF k)Correlation between the heat transfer and the void coefficient to the radial distribution of the nuclear power l)E Hydro-dynamic instability m)F Defect of distribution of the rate at pressure-vessel inlet n)G Pressure drops in the pressure-vessel o)H Hydraulic forces p)I Hydraulic Dimensioning of the internal components THERMAL-HYDRAULIC IN NUCLEAR REACTOR Summary J Thermal effects during the normal transients K Uncertainties a) Statistical approach b) Deterministic approach c) Uncertainties relative to computer code and mixing coefficient d) Justification of the statistic combination of the uncertainties e) Uncertainties relative to the manufacturing tolerances f) Uncertainty relative to the design computer code g) Uncertainty of the transient conditions versus the steady state conditions L Temperatures of the fuel pellet and the cladding THERMAL-HYDRAULIC IN NUCLEAR REACTOR Summary M Hydraulic a) Uncertainties related to the pressure-drops in the reactor core and in the pressure-vessel b) Uncertainties due to the defect of the repartition of the inlet mass flow rate c) Uncertainties relative to the mass flow rate d) Uncertainties relative to the hydraulic forces e) Uncertainties relative to the hydraulic dimensioning of the internal components N Methods of analysis and study data N.1 Methods utilized to analyse the transients O Hot channel factors XVI.1 Radial power distribution THERMAL-HYDRAULIC IN NUCLEAR REACTOR Summary XVI.2 Axial power distribution XVI.3 Heat transfer in nuclear fuel rods bundles a)Laminar Flow b) Single-Phase Turbulent Flow c) Nucleate Boiling Flow d) Boiling Crisis e)Quenching in Rod Bundles f) Steam and water cross-flows g) Ballooning and grid effects h) Cold rod effects XVI.4 Limitations of power distribution XVI.5 Reactivity coefficients XVI.6 Reactivity control a) Safety requirements THERMAL-HYDRAULIC IN NUCLEAR REACTOR Summary b) Functional criteria c) Design requirements d) Tests e) Design basis f) The maximal control insertion of the reactivity g) Shutdown margin h) Sub-criticality i)Description of the functional aspects of the design of the systems j)The command system of the control rods clusters k) Chemical & Volume Control System (CVCS) & Emergency Boration System (EBS) l) Emergency Core Coolant System (ECCS) THERMAL-HYDRAULIC IN NUCLEAR REACTOR Summary n) Evaluation of the design XVI.6 Fuel temperature coefficient (Doppler effect) XVI.7 Moderator coefficient XVI.7a Density moderator coefficient XVI.7b Void moderator coefficient XVI.7c Heat flux limitations XVI.7.d The behaviour of the DNB correlations XVI.7e Requirements relative to the instrumentation XVI.7.f Operations at high linear power XVI.7.g Other criterion XVIII The corresponding core protection channels XVIII.1 Limiting conditions of operation XVIII.2 PWR nuclear instrumentation 10 THERMAL-HYDRAULIC IN NUCLEAR REACTOR Schematic view of the fuel rod supported by spacer grid 404 THERMAL-HYDRAULIC IN NUCLEAR REACTOR Displacement of fuel rod versus excitation force 405 THERMAL-HYDRAULIC IN NUCLEAR REACTOR Vibration mode and amplitude of fuel rod 406 THERMAL-HYDRAULIC IN NUCLEAR REACTOR B) Creep Laws The best estimate creep law form formulation of Inconel 718 and Zy-4 (see following figure) used in the model is: ε = [Aln(1 + wФt) + BФt]exp(-Q/T)σ/E With: - Φt: fluence(>1MeV) of springs and dimples - E: Young modulus of Inconel 718 or Zy-4 - A, w, B: constants (≠ for Inconel 718 or Zy-4) - Q: Activation Energy (≠ for Inconel 718 or Zy-4) - T: temperature (≠ for Inconel 718 or Zy-4) 407 THERMAL-HYDRAULIC IN NUCLEAR REACTOR Zircaloy & Inconel 718 creep laws 408 THERMAL-HYDRAULIC IN NUCLEAR REACTOR C) Grid growth law Best estimate grid growth law form used for Zy4 grids in the model is : ε = (at +b)Фtn With - Φt : fluence(>1MeV) of the grid - a, b, n : constants - T : temperature of the grid As Inconel 718 grids are in a position with few fluence (bottom and top grids), in this study, no growth is considered for these grids 409 THERMAL-HYDRAULIC IN NUCLEAR REACTOR Zircaloy-4 & Inconel 718 growth laws 410 THERMAL-HYDRAULIC IN NUCLEAR REACTOR Comparison between calculations & measurements of spring force relaxation versus burn-up 411 THERMAL-HYDRAULIC IN NUCLEAR REACTOR APPENDIX: Major thermal-hydraulic parameters      FZ = Maximal flux in a reactor core channel/ Mean flux in the same channel of the reactor core For PWR, FZ = 1.67 (value equal to the one in the hot and mean channel To characterize the reactor channel receiving the most higher power, one calculates two types of following factors upon one interested to the integrated power in a channel or to the local power: The enthalpy elevation: FΔH, serving for the analysis of the DNB, to define the fluid state in the hot channel: FΔH = Maximum enthalpy increase in the channel/Mean enthalpy increase in the reactor core 412 THERMAL-HYDRAULIC IN NUCLEAR REACTOR       Hot spot factor utilized in the analysis of the accidents and CHF analysis and to characterizing the maximal local power of the hot rod: FQ = Maximal local power/ Mean power of the reactor core Nota: These factors are the product of the “nuclear” factors included the uncertainties of the factor called “engineering” factor: FΔH = FQR + FΔHE FQR: Mean power of the hot fuel (which belong in general to the hot channel) is defined as FΔHN: FΔHN > FQR N 413 THERMAL-HYDRAULIC IN NUCLEAR REACTOR       FΔHN (partial power) = FΔH (full power) x [1 + 0.2 (1 – p)] p: power fraction FΔHN is generally included an uncertainty of %¨, thus for a typical fuel management: FΔHN = 1.435 x 1.08 = 1.55 The FΔHE is decomposed in factors; there is only one , noted (FΔHE, 1), related to the fuel enrichment and to the weight of the fuel: FΔHE = FΔHE, 1), = 1.021 414 THERMAL-HYDRAULIC IN NUCLEAR REACTOR  Hot factors for LOCA analysis:  FQ = FNZ x FQN  x ( Nuclear factors) factor) FUN (Uncertainty factor) x (Engineering  FZN: Axial power distribution  FQN: Radial power distribution  FUN: Uncertainty factor affecting the FQN  F QE FQE: Engineering factor relative to the diameter, to the density and the enrichment of the fuel pellet 415 THERMAL-HYDRAULIC IN NUCLEAR REACTOR   FZN resulted to the maximal admissible value FQ, the others parameters having the imposed values: FQN = 1.435  FUN = 1.05  FQE = 1.03   Nota: These historical definition of FQ is maintained by conservatism; a more rigourous definition must taken into account the bowing effect of the fuel rod With FQB: Flux increased due to the fuel rod bowing, there conservative because FQ > FQ’ 416 with some millimeters THERMAL-HYDRAULIC IN NUCLEAR REACTOR   FZN resulted to the maximal admissible value FQ, the others parameters having the imposed values: FQN = 1.435  FUN = 1.05  FQE = 1.03   Nota: These historical definition of FQ is maintained by conservatism; a more rigourous definition must taken into account the bowing effect of the fuel rod With FQB: Flux increased due to the fuel rod bowing, there conservative because FQ > FQ’ 417 with some millimeters THERMAL-HYDRAULIC IN NUCLEAR REACTOR THANKS FOR YOUR ATTENTION 418