In this work we investigate the present capabilities of CFD for wall boiling. The computational model used combines the Euler/Euler two-phase flow description with heat flux partitioning. Very similar modelling was previously applied to boiling water under high pressure conditions relevant to nuclear power systems. Similar conditions in terms of the relevant non-dimensional numbers have been realized in the DEBORA tests using Dichlorodifluoromethane (R12) as the working fluid. This facilitated measurements of radial profiles for gas volume fraction, gas velocity, liquid temperature and bubble size.
Robust predictive capabilities of the modelling require that it is validated for a wide range of parameters. In previous studies (Krepper and Rzehak, 2011, 2013) it was shown that a careful calibration of correlations used in the wall boiling model is necessary to obtain agreement with the measured data. We here consider tests under a variety of conditions concerning liquid subcooling, flow rate and heat flux. It is investigated to which extent a set of calibrated model parameters suffices to cover at least a certain parameter range.
In the paper the potential of the application of a population balance model is demonstrated. The measured gas bubble size profiles show an increase of the bubble size with increased distance from the heated wall caused by bubble coalescence. Furthermore the model framework is shown to be able to describe a shift from wall peak to core peak in the radial gas volume fraction profiles with increasing inlet temperature respective decreasing subcooling temperature, which was observed in some test series.
References
1.
ANSYS., 2010. ANSYS CFX-Solver Theory Guide, Release 13 ANSYS Inc.
2.
BartolomejG.G.ChanturiyaV.M., 1967. Experimental study of true void fraction when boiling subcooled water in vertical tubes, Thermal EngineeringVol. 14, pp. 123–128, translated from TeploenergetikaVol. 14, 1967, 2,pp. 80–83.
3.
BasuN.WarrierG. R.DhirV. K., 2005. Wall Heat Flux Partitioning During Subcooled Flow Boiling: Part 1–Model Development, Journal of Heat Transfer, 127, 131.
4.
BouckerM.GuelfiA.MimouniS.PéturaudP.BestionD.HervieuE., 2006. Towards the prediction of local thermal-hydraulics in real PWR core conditions using NEPTUNE_CFD software, Workshop on Modeling and Measurements of Two-Phase Flows and Heat Transfer in Nuclear Fuel Assemblies, KTH, Stockholm, Sweden – 10–11 October 2006.
5.
BurnsA.D.FrankT.HamillI.ShiJ.-M., 2004. The Favre averaged drag model for turbulence dispersion in Eulerian multi-phase flows, 5th Int. Conf. on Multiphase Flow, ICMF′2004, Yokohama, Japan, 2004.
6.
v. Ceumern-LindenstjernaW.-C. B., 1977. Bubble departure diameter and release frequencies during nucleate pool boiling of water and aqueous NaCl solutions, in HahneE.GrigullU. (ed.), Heat transfer in Boiling, Academic Press and Hemisphere.
7.
CieslinskiJ. T.PolewskiJ.SzymczykJ. A., 2005. Flow Field around Growing and Rising Vapour Bubble by PIV Measurement, Journal of Visualization, 8, 209.
8.
ColeR., 1960. A photographic study of pool boiling in the region of the critical heat flux, AIChE JournalVol. 6, pp. 533–542.
9.
DrewD. A.PassmanS. L., 1998. Theory of Multicomponent Fluids, Springer.
10.
FrankT.ZwartP.KrepperE.PrasserH.-M.LucasD., 2008. Validation of CFD models for mono- and polydisperse airDwater two-phase flows in pipes, Nuclear Engineering and Design, 238, 647–659.
11.
GarnierJ.ManonE.CubizollesG.2001. Local measurements on flow boiling of refrigerant 12 in a vertical tube, Multiphase Science and Technology, 13, pp. 1–111.
12.
GriffithP.WallisJ.1960. The Role of Surface Conditions in Nucleate Boiling, Chemical Engineering Progress Symposium Series, 56, 49.
13.
HanC.-Y.GriffithP., 1965. The Mechanism of Heat Transfer in Nucleate Pool Boiling, Int. J. Heat Mass Transfer, 8, 887.
14.
HongK. T.ImadojemuH.WebbR. L.1994. Effects of oxidation and surface roughness on contact angle, Exp. Therm. Fluid Sci, 1994, 8, 279.
15.
IshiiM.HibikiT., 2011. Thermo-fluid dynamics of two-phase flow. Springer, 2nd ed.
16.
IshiiM.ZuberN., 1979. Drag coefficient and relative velocity in bubbly, droplet or particulate flows, AIChE J.25, 843–855.
17.
IveyH. J., 1967. Relationships between bubble frequency, departure diameter, and rise velocity in nucleate boiling, International Journal of Heat and Mass Transfer, 10, 1023.
18.
JonesS.EvansG.GalvinK.1999. Bubble nucleation from gas cavities – a review, Adv. Colloid interface Sci, 80, 27.
19.
KaderB.A.1981. Temperature and concentration profiles in fully turbulent boundary layers, Int. J. Heat Mass Transfer24, pp. 1541–1544.
20.
KandlikarS.MizoV.CartwrightM.1995. Investigation of bubble departure mechanism in subcooled flow boiling of water using high-speed photography, Convective flow boiling international conference, April 30–May 5.
21.
KlausnerJ. F.MeiR.ZengL. Z., 1997. Predicting stochastic features of vapor bubble detachment in flow boiling, International Journal of Heat and Mass Transfer, 40, 3547.
22.
KolevN. I., 2006. Uniqueness of the Elementary Physics Driving Heterogeneous Nucleate Boiling and Flashing, Nuclear Engineering and Technology, 38, 175.
23.
KoncarB.MavkoB.2010. Wall function approach for boiling two-phase flowsNuclear Engineering and Design, 2010, 240, 3910.
24.
KrepperE.RzehakR.LifanteC.FrankT.2013. CFD for subcooled flow boiling: Coupling wall boiling and population balance models, Nuclear Engineering and Design255, 330–346.
25.
KrepperE.RzehakR., 2011. CFD for subcooled flow boiling: Simulation of DEBORA experiments, Nuclear Engineering and Design, 241, 3851–3866.
26.
KrepperE.BeyerM.LucasD.SchmidtkeM.2011. A population balance approach considering heat and mass transfer – Experiments and CFD simulations, Nuclear Engineering and Design241, 2889–2897.
27.
KrepperE.LucasD.FrankT.PrasserH.-M.ZwartP.2008. The inhomogeneous MUSIG model for the simulation of polydispersed flows, Nuclear Engineering and Design, 238, 1690–1702.
28.
KrepperE.KoncarB.EgorovY., 2007. Modelling of subcooled boiling – concept, validation and application to fuel assembly design, Nuclear Engineering and Design237, 716–731.
29.
KurulN.PodowskiM.Z., 1990. Multidimensional effects in forced convection subcooled boiling, Proc. 9th Int. Heat Transfer Conf., Jerusalem, Israel.
30.
KurulN.PodowskiM., 1991. On the modeling of multidimensional effects in boiling channelsANS Proceedings of 27th National Heat Transfer Conference, Minneapolis, MN.
31.
LeeS.LaheyR.Jr.JonesO, 1989. The prediction of two-phase flow turbulence and phase distribution using a k-εe model. Jpn. J. Multiphase Flow3, 335.
32.
LifanteC.ReitererF.FrankTh.BurnsA., 2011. Coupling of wall boiling with discrete population balance model, The 14th International Topical Meeting on Nuclear Reactor Thermalhydraulics, NURETH-14, Toronto, Ontario, Canada, September 25–30, 2011, NURETH14–087.
33.
LoS., 2000. Recent advances in CFD for industrial multiphase flows, Industrial CFD and the Move Towards Multiphase Flow Simulations, 8 Nov 2000, University of Warwick.
34.
LucasD. M.FrankT.LifanteCZwartP.BurnsA., 2011. Extension of the inhomogeneous MUSIG model for bubble condensation. Nuclear Engineering and Design241, 4359–4367.
35.
LucasD.PrasserH.-M.2007a. Steam bubble condensation in sub-cooled water in case of co-current vertical pipe flow, Nuclear Engineering and Design, 237, 497–508.
36.
LucasD.KrepperE.PrasserH.-M., 2007b. Use of models for lift, wall and turbulent dispersion forces acting on bubbles for poly-disperse flows. Chem. Eng. Science62, 4146–4157.
LuoH.SvendsenH.F., 1996. Theoretical model for drop and bubble break-up in turbulent flows, AIChEJ, 42, 5, pp. 1225–1233.
39.
ManonE.2000. Contribution à l'analyse et à la modélisation locale des écoulements boillants sous-saturés dans les conditions des Réacteurs à Eau sous Pression, PhD thesis, Ecole Centrale Paris, Nov. 2000.
40.
MenterF. R., 1994. Two-equation eddy-viscosity turbulence models for engineering applications, AIAA-Journal, Vol. 32, No. 8.
41.
MenterF. R., 2009. Review of the shear-stress transport turbulence model experience from an industrial perspective, International Journal of Computational Fluid Dynamics23, p305.
42.
MikicB.B.RohsenowW.M., 1969. A new correlation of pool-boiling data including the fact of heating surface characteristics, ASME Journal of Heat TransferVol. 91, pp. 245–250.
43.
MitrovicG.StephanK., 1980. Gleichgewichtsradien von Dampfblasen und Flüssigkeitstropfen, Wärme- und Stoffübertragung13, p171.
44.
MorelC., 1997. Turbulence modeling and first numerical simulations in turbulent two-phase flows, Technical Report CEA/Grenoble, France.
45.
PflegerD.BeckerS., 2001. Modelling and Simulation of the Dynamic Flow Behaviour in a Bubble Column. Chem. Eng. Sci., 56, pp.1737–1747.
46.
PrinceM.J.BlanchH.W., 1990. Bubble coalescence and break-up in air-sparged bubble columns, AIChEJ, 36, No 10, pp. 1485–1499.
47.
PolitanoM.CarricaP.ConvertiJ., 2003. A model for turbulent polydisperse two-phase flow in vertical channelsInternational Journal of Multiphase Flow, 29, 1153.
48.
PopeS.B., 2000, Turbulent Flow, ISBN 0521 59125 2.
49.
RamstorferF.BreitschädelB.SteinerH.BrennG.2005. Modelling Of The Near-wall Liquid Velocity Field In Subcooled Boiling Flow Proceedings of HT2005, ASME Summer Heat Transfer Conference 2005, San Francisco, California, USA,.
50.
RanzW.E.MarshallW.R., 1952, Evaporation from drops, Chemical engineering progressVol. 48No. 3, pp. 141–146.
51.
RzehakR.KrepperE.2013. CFD Modeling of Bubble-induced Turbulence, International Journal of Multiphase Flow55, 138–155.
52.
SatoY.SadatomiM.SekoguchiK., 1981. Momentum and heat transfer in two-phase bubble flow-I, Int. J. of Multiphase Flow, vol. 7, pp. 167–177, 1981.
53.
SchmidtkeM., 2008. Investigation of the dynamics of fluid particles using the Volume of Fluid Method, PhD-ThesisUniversity Paderborn, (in German).
54.
SituR.HibikiT.IshiiM.MoriM., 2005. Bubble lift-off size in forced convective subcooled boiling flow, International Journal of Heat and Mass Transfer, 48, 5536.
55.
TolubinskyV.I.KostanchukD.M., 1970. Vapour bubbles growth rate and heat transfer intensity at subcooled water boiling; Heat Transfer 1970, Preprints of papers presented at the 4th International Heat Transfer Conference, Paris, Vol. 5, Paper No. B–2.8.
56.
TomiyamaA.TamaiH.ZunI.HosokawaS., 2002. Transverse migration of single bubbles in simple shear flows, Chemical Engineering Science, 2002, 57, 1849–1858.
57.
TroshkoA. A.HassanY. A., 2001. A two-equation turbulence model of turbulent bubbly flows, International Journal of Multiphase Flow, 27, 1965.
58.
UnalH., 1976. Maximum bubble diameter, maximum bubble-groth time and bubble-groth rate during the subcooled nucleate flow boiling of water up to 17.7 MN/m2, International Journal of Heat and Mass Transfer, 1976, 19, 643del ValleM.KenningD., 1985. Subcooled flow boiling at high heat flux, International Journal of Heat and Mass Transfer 28, 1907.
59.
WellekR.M.AgrawalA.K.SkellandA.H.P., 1966. Shapes of liquid drops moving in liquid media, AIChE Journal, vol. 12, pp. 854–860.
60.
WhiteF.M., 1991. Viscous fluid flow, McGraw-Hill Inc.
61.
WintertonR.1984. Flow boiling: Prediction of bubble departure, International Journal of Heat and Mass Transfer, 27, 1422.
62.
WintterleT.2004. Development of a numerical boundary condition for the simulation of nucleate boiling at heated walls, Diploma ThesisUniversity Stuttgart, IKE – 8– D- 014.
63.
YaoW.MorelC., 2002. Prediction of parameters distribution of upward boiling two-phase flow with two-fluid models, 10th International Conference on Nuclear Engineering ICONE-10-22463, Arlington, April 14–18.
64.
YeohG. H.TuJ.Y., 2005. A unified model considering force balances for departing vapour bubbles and population balance in subcooled boiling flow, Nuclear Engineering and Design, Vol. 235, pp. 1251–1265.
65.
YeohG. H.TuJ. Y., 2010. Computational Techniques for Multiphase Flows — Basics and Applications, Butterworth-Heinemann, Elsevier Science and Technology.
66.
ZengL.Z.KlausnerJ.F.BernhardD.M.MeiR., 1993. A unified model for the prediction of bubble detachment diameters in boiling systems – II. Flow boiling, Int. J. Heat Mass Transfer, Vol. 36, pp. 2271–2279,.
67.
ZunI.1980. The transverse migration of bubbles influenced by walls in vertical bubbly flow, Int. J. Multiphase Flow, Vol. 6, pp. 583–588.
