CFD-Modelling of subcooled boiling and Applications in the Nuclear Technology
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1 CFD-Modelling of subcooled boiling and Applications in the Nuclear Technology Eckhard Krepper Jahrestagung Kerntechnik 2011 Fachsitzung: CFD-Simulationen zu sicherheitsrelevanten Fragestellungen Text optional: Institutsname Prof. Dr. Hans Mustermann Mitglied der Leibniz-Gemeinschaft
2 Contents 1. Motivation 2. Critical heat flux 3. Critical heat flux and fuel element design 4. CFD-Modelling of wall boiling actual state of the art 5. Application on modelling of a heat channel 6. Planned experiments in HZDR The work is funded by Federal Ministry of Education and Research Folie 2
3 Fuel assembly Length: about 4 m 9 x 9 up to 15 x 15 fuel rods per assembly typical rod diameter: 9 mm typical distances of rod centres: 12 mm rods are fixed by spacers axial distance about 0.5 m tasks of the spacers: insurance of the rod distance influence on the flow field to enhance the permissible heat flux Folie 3
4 Boiling curve [e.g. 1998_Dhir] maximum or critical heat flux heat flux log(q) Nukiyama point TW controlled q controlled minimum heat flux q controlled Leidenfrost point wall superheat log(t W -T sat ) single-phase convection nucleate boiling (partial vs developed) [1998_Dhir] transition boiling (partial film boiling) (stable) film boiling Folie 4
5 Boiling regimes with constant wall heat flux q w [W/m 2 ] A [m 2 ] H ( z) H x( z) = H H ( z ) = H z [m] G in in [kg/m 2 s] H in [J/kg] fg in + f qwph z GA z 0, H f x, H q 3 q 2 q 1 Single phase convection DNB q w Subcooled film boiling Subcooled nucleate boiling H f x=0 Sat. film boiling Mist evaporation Sat. nucl. boiling Forced convective boiling dryout H v x=1 H x Folie 5
6 Flow Regimes in a Channel with Dryout Mist flow Post-dryout heat transfer Dryout Annular flow Evaporative liquid film Slug flow Nucleate boiling Bubbly flow Singlephase flow Convection Folie 6
7 Flow Regimes in a Channel with DNB Inverted annular flow Film boiling Bubbly flow Single-phase flow Nucleate boiling Convection Departure from nucleate boiling (DNB) Folie 7
8 Importance of Critical Heat Flux for Fuel Assemblies Integrity of fuel rods has to be insured during operation and accidents the heat flux has to stay below the critical heat flux The critical heat flux depends on fluid properties flow conditions geometry Advanced FA designs can allow higher permissible heat fluxes Verification of improvements in the critical heat flux require expensive measurements Folie 8
9 Examples of Mixing Vane Design swirl-type split-type W. K. In et al.2008, Numerical Computation of Heat Transfer Enhancement of a PWR Rod Bundle with Mixing Vane Spacers, Nuclear Technology, Vol. 161, pp , Folie 9
10 Measurement of CHF by experiments Examples HTRF (NY/USA, ODEN, FRIGG Västeras/Sweden, Westinghouse) KATHY (Karlstein, AREVA) Measurement of integral values Dependent on geometry and thermal hydraulic parameters Pressurizer Measurements of CHF Direct contact condenser 450 P el. 9,5MW High pressure coolers 5MW PWR Test Vessel p 185 bar 10 MW Void Fraction Measurement Device P 15 MW el. Circulation pump Water steam seperator Control valve BWR Test Vessel p 110 bar To conenser Feed water Control valve Downcomer W all Tem peratur ( C ) Time (s) Rod 7 Rod 17 Rod 1 Natural Circulation Loop Folie 10
11 Prediction of CHF Empirical correlations W-3 correlation Tong (1967) Correlation of Levitan (1975) etc. Valid only for a certain geometry in a narrow range of thermal hydraulic parameters Look-up tables 10000s of data points gained by experiments Interpolation Valid only for a certain geometry in a slightly extended range of thermal hydraulic parameters All these methods depend on geometry Folie 11
12 Modeling of CHF independent on geometry Only possible by CFD methods Calculation of the phenomena on mesoscale Modeling of the phenomena on microscale (Closure relationships) Folie 12
13 Qwall CFD concept modelling subcooled boiling at a heated wall Constant pressure given T sat Overall heat flux Q w given Heat flux partition: Q w = Q f + Q e + Q q Q f - single phase convection Q e - evaporation Q q - quenching: (departure of a bubble from the heated surface cooling of the surface by fresh water) Calculation of Q f, Q e, Q q and T wall by iteration Kurul/Podowski, 1991 QQ QE QF G Folie 13
14 Validation: Cross sectional averaged Steam Volume Fractions P=4.5 MPa, D=15.4 mm W/m 2 z [m] Experiment CFX kg/(s. m 2 ) Bartolomej, G.G., Chanturiya, V.M., 1967, Thermal Engineering Vol. 14, pp steam volume fraction [-] Folie 14
15 Cross sectional averaged Temperatures 2.0 T average 1.6 T wall 1.2 z [m] [K] Folie 15
16 Variation of pressure, heat flux and mass flow The larger the generated steam the larger the model deviations Acceptable agreement to the experiments at Pressure MPa heat flux up to 1.2 MW/m 2 mass flow rate at about 1000 kg/(m 2 s) Folie 16
17 Application to a hot channel of a fuel assembly consideration of the channel between 4 rods Calculation of a 0.5 m axial section between two spacers periodic boundary conditions Parameters: pressure 15.7 MPa T sat = 619 K Q wall = W/m 2 V in = 5 m/s, T sub = 12 K Folie 17
18 3. Application to a hot channel of a fuel assembly Simulation of the swirl by given inlet conditions periodic b): V R = 1 m/s c): V R = 2 m/s d): V R = 3 m/s Rod4 Rod1 0.3 periodic [m] Rod3 periodic Rod [-] swirl = V 2 x V 2 x + V + V 2 y 2 z + V 2 z Folie 18
19 3. Application to a hot channel of a fuel assembly Influence of the swirl on the flow in the channel water streamlines vapour streamlines Folie 19
20 3. Application to a hot channel of a fuel assembly Vapour Volume fraction distribution in the cross section at z = m without swirl with swirl (V R = 3 m/s) Folie 20
21 3. Application to a hot channel of a fuel assembly Influence of the swirl on averaged values vapour volume fraction wall superheating heat flux components V R = 3.0 m/s V R = 0.0 m/s Conv Evap Quench z [m] z [m] z [m] V R = 3.0 m/s V R = 0.0 m/s [-] [K] [-] Folie 21
22 3. Application to a hot channel of a fuel assembly Wall superheating at the rod surface [K] z [m] z [m] Φ T sup = T wall -T sat [K] V R = 0 [m/s] V R = 3 [m/s] Φ Folie 22
23 4. Necessary model improvements Improvement of the models necessary Bubble size at departure the larger the departed bubble the larger the evaporation part of heat flux fitting to experiments Tolubinsky calculation of the microscopic mechanisms Unal, Yeoh, Tu Experiments: Observation and measurement of micro phenomena? Gas distribution in the bulk non drag forces Experiments: Measurement of gas and velocity profiles? Bubble size distribution in the bulk Interfacial area influence on condensation/evaporation population balance models (MUSIG) Measurement of bubble sizes? Folie 23
24 4. Necessary model improvements Validation by experiments? Experimental conditions at nuclear reactor parameters: narrow channels (ca. 10 mm) Inconvenient thermal hydraulic parameters of pressure and temperature (15 MPa, 345 C) size of expected bubbles in the range of <1 challenge for measurement Folie 24
25 5. Measurement of profiles Application of Model Fluids enables Up scaling Scaling conditions: Density relation Liquid/Gas Reynolds Number Weber Number replacing water by R12 more convenient experimental conditions: Pressure Temperature tube diameter measurement of profiles becomes possible Water R12 Pressure [MPa] Tsat [ C] Density Liquid [kg/m 3 ] Density Gas [kg/m 3 ] Viscosity [kg/ms] 6.8e-5 9.0e-5 Surface Tension [N/m] 4.5e-3 1,8e-3 D [m] V [m/s] DenLiquid/DenGas Re 5.2e+5 5.2e+5 We 3.3e+3 3.3e+3 Folie 25
26 5. Measurement of profiles Example: DEBORA tests (CEA) Fluid Dichlorodifluoromethane R12 Heated tube D = 19.2 mm over 3.5 m Measurement of profiles for gas fraction, liquid and gas velocities, temperatures, bubble sizes Validation of non drag forces turbulent wall functions flow heat gas fraction Exp CFX liquid and gas velocity U GAS Exp U GAS CFX-11 U LIQUID CFX-11 [-] [m/s] R [m] R [m] Folie 26
27 5. Measurement of profiles Bubble sizes with monodispersed approach bubble size in the bulk db dependent on liquid temperature TL d B d T T d T B1 ( sub sub,2) + B2( sub,1 sub ) = Tsub = Tsat TL Tsub,1 Tsub,2 T Exp CFX [m] d B [mm] R [m] bubble size T-T SAT [K] bubble size dependent on liquid temperature Folie 27
28 Application of a population balance model 1 dispersed phase, 10 size groups: dvf/dd B [mm -1 ] x=3.5 m R=0.095 m R=0.045 m R=0.001 m [m] Exp CFX D B [mm] R [m] bubble size at detachment bubble coalescence near the wall can be described Folie 28
29 5. Measurement of profiles Bubble forces At the Euler/Euler-approach no simulation of single bubbles (DNS) but averaged bubble forces dependent on the local flow conditions Drag: Flow resistance in flow direction determines bubble rising velocities (vertikal) essential for velocity of lateral redistribution of bubbles r F D 3 r = C D ρ lα w 4d b g r w l r ( w g r w l ) Nondrag: Forces perpendicular toe the flow direction strong influence on flow pattern in a vertical upward two phase flow: influence on cross sectional gas volume fraction distribution Measurement of the cross sectional gas volume fraction distribution by a wire mesh sensor model validation Folie 29
30 5. Measurement of profiles Nondrag forces: forces perpendicular to the flow direction Lift Force: proportional to the gradient of the liquid flow field direction dependent on the bubble size r r r r F = C ρ α w w ) rot( w ) L L l ( g l l Lift Wall Force: pushes bubbles away from the wall Dispersion Wandkraft r F W ρlα = C r b b W1 CW 2 ) Turbulent Dispersion: r ( w y smoothing of radial volume fraction profiles r F = C TD TD ρ k gradα l l 2 rel r n r Clift BD [mm] Air/Water Folie 30
31 5. Measurement of profiles Lift force: influence of the bubble size Tomiyama: C L = with min[0.288 tanh(0.121re), f ( Eod )] f ( Eod ) f ( Eo ) = Eo Eo d d 2 d Eo d < 4 for 4 < Eo < 10 Eod > Eo d d Eo d 2 g( ρ L ρg ) d H σ = d h = db Eo 0.4 applying the correlation to R12: C L MPa 2.65 MPa d B [mm] Folie 31
32 DEBORA series with increasing inlet temperature P = 1.49 MPa; G = 2000 kg m -2 s -1 ; Q = 75 kw m -2 with increasing inlet temperature gas volume fraction profile changes from wall peak to core peak Measurements [-] T SAT -T IN [K] R [m] [m] T SAT -T IN [K] R [m] gas volume fraction bubble size Folie 32
33 Application of inhomogeneous MUSIG P = 1.49 MPa; G = 2000 kg m -2 s -1 ; Q = 75 kw m -2 ; T SAT T IN = 13.9 K 2 disperse phases, 30 MUSIG size groups dvf/dd B [mm -1 ] x=3.5 m R=0.095 m R=0.045 m R=0.01 m [m] Exp CFX D B [mm] R [m] Gas1 Gas2 bubble size Folie 33
34 Gas volume fraction distribution Gas2 Gas1 2 dispersed gaseous phases, each 10 MUSIG size fractions Folie 34
35 Simulation [-] T SAT -T IN [K] [m] T SAT -T IN [K] R [m] R [m] gas volume fraction bubble size All tests were calculated with the same model parameters Shifting of void fraction maximum towards the core can be reproduced Folie 35
36 Actual state of CFD modelling of wall boiling The described model approaches are implemented in all leading CFD codes Up to now only few applications (but just increasing) numerical effort, numerical problems Validation of microscopic approaches insufficient Validation at practical conditions difficult: narrow channels (ca. 10 mm) difficult thermal hydraulic pressure and temperature parameters (15 MPa, 345 C) size of expected vapour bubbles in the range < 1 mm experimental challenge Folie 36
37 Modellierung, Simulation und Experimente zu Siedevorgängen in Druckwasserreaktoren Model development & Simulation FZ Dresden- Rossendorf TUD, Dept. Fluid Mechanics ANSYS Germany small scale Experiments Univ. Appl. Sci. Zittau / Görlitz TUD, Medical Faculty TUM, Dept. Thermodynamics application-oriented Experimente Karlsruhe Inst. Tech. (KIT) TUD, Dept. Nuclear Engineering RUB, Dept. Energy Systems Folie 37
38 ROFEX ROssendorf Fast Electron beam X-ray tomograph Principle Setup Shielding Elevating device courtesy by U. Hampel F. Fischer Fischer et al., MST 2008 Folie 38
39 Fast x-ray tomography noninvasiv sampling rate up to 1 khz high spatial resolution (<0.5mm) courtesy by U. Hampel F. Fischer Folie 39
40 Concept of fast x-ray tomography Electron beam generator: -150 kev max. energy - 33 ma max. i B - Spot size ma i B Electron optics: - static stigmator - deflection X,Y: 24 full angle up to 10 khz - dynamic lens: 5% of full focal distance to 10 khz - working distance ca. 500 mm Geometry of the bundle segment corrugated bellows CAD view test section CT plane beam generator beam generator high voltage supply Folie 40
41 Concept of a bundle test Favored refrigerant: R134a viscosity surface tension density 1,98 mpa s 72,758,08 mn/m 1200 kg/m³ Geschwindigkeit ct-scanner 200 kw pulsed dc power supply Temperatur Folie 41
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