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Nuclear Engineering and Design 235 (2005) 153–164

Computational Fluid Dynamics for nuclear applications:from CFD to multi-scale CMFD

G. Yadigaroglu∗

Swiss Federal Institute of Technology-Zurich (ETHZ), Nuclear Engineering Laboratory, ETH-Zentrum, CLT CH-8092 Zurich, Switzerland

Received 17 November 2003; received in revised form 1 June 2004; accepted 31 August 2004

Abstract

New trends in computational methods for nuclear reactor thermal–hydraulics are discussed; traditionally, these have beenbased on the two-fluid model. Although CFD computations for single phase flows are commonplace, Computational Multi-FluidDynamics (CMFD) is still under development. One-fluid methods coupled with interface tracking techniques provide interestingopportunities and enlarge the scope of problems that can be solved. For certain problems, one may have to conduct “cascades”of computations at increasingly finer scales to resolve all issues. The case study of condensation of steam/air mixtures injectedfrom a downward-facing vent into a pool of water and a proposed CMFD initiative to numerically model Critical Heat Flux(CHF) illustrate such cascades. For the venting problem, a variety of tools are used: a system code for system behaviour; aninterface-tracking method (Volume of Fluid, VOF) to examine the behaviour of large bubbles; direct-contact condensation canb©

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. Introduction

Thermal–hydraulic computations for the design andhe simulation of transients in Light Water ReactorsLWR) have been conducted the last decades withainly one-dimensional (1D), two-phase flow tools;

he large system codes that have been developed andontinuously improved during this time have been theajor, universally used tools.

∗ Tel.: +41 1 632 4615; fax: +41 1 632 1166.E-mail address:[email protected].

The very first two- or multiphase system acomponent analysis system codes were basethe equal-velocities, equal-phase-temperathomogeneous-equilibrium model; RELAP4/MOwas a prominent example in this category (EG&G,1978). In reality, most two-phase flows of interestfar from homogeneous. Separated-flow models, wthe two phases are allowed to have different avevelocities (and temperatures) followed; in this caseaverage-velocity ratio is typically derived from soempirical correlation. The drift-flux model (Zuber andFindlay, 1965), characterizing this velocity ratio witwo parameters having a clear physical significa

029-5493/$ – see front matter © 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.nucengdes.2004.08.044

154 G. Yadigaroglu / Nuclear Engineering and Design 235 (2005) 153–164

became the dominant, almost universal tool. Thereare cases, however, where the velocity ratio cannot bedetermined from the local, necessarilymixture-based,flow conditions, the phases are no longer intimatelycoupled, and the approach breaks down; this is thecase, for example, when the two phases flow in oppo-site directions, each driven by a different driving force.The two-fluid (six-equation) model was introduced todeal with these situations; it is based on the so-calledinterpenetrating-media approachand is widely usedtoday. This is the level of development currentlyimplemented and used in most system codes, suchas the RELAP5 (Carlson et al., 1990; RELAP5 CodeDevelopment Team, 1995) and TRAC (LANL, 1986)families originating from the US and CATHARE(Micaelli et al., 1988) from France. The United StatesNuclear Regulatory Commission is producing theUSNRC consolidated code based on the previous UScodes (Mahaffy et al., 2000); advanced code develop-ments are also taking place in Europe and elsewhere.

As noted above, most of the two-phase safety anal-ysis work is still performed today with 1D systemcodes: all flows are assumed to take place in 1D ductsand are described with their cross-sectional-averageparameters, such as void fraction, velocity, enthalpy,etc. There are situations, however, e.g., steam–waterflows in an open core, flows through the steam genera-tor tube bundle, flows in the downcomer of PWRs, etc.that are clearly three-dimensional (3D). Developmentsare needed in this area, partly to clarify certain issuesa useo ysiso erd as-s uta-to )O id,i usu-a

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present as well as the new generations of reactors.Current trends are towards multi-dimensional, -scale,-physics approaches for such analyses. Such com-putational developments are possible now, thanks tothe opportunities offered by the tremendous increasein computing power, the maturity of state-of-the-artComputational Fluid Dynamics (CFD) methods (stillapplied today mainly to single-phase flow problems)and the emergence of Computational Multi-FluidDynamics (CMFD) methods (Yadigaroglu, 2003a). Ifsuch developments are pursued vigorously and suc-cessfully, it is likely that we will be doing simulationsin the future with increasingly sophisticated numericalmethods and modelling approaches and in much greaterdetail than in the past. These could lead to improve-ments in the design of the new generations of reactorsand to the elimination or reduction of certain remaininguncertainties in safety analysis (Bestion, 1992).

1.2. Scope of this paper

Papers dealing with the trends in numerical sim-ulation for LWR safety were presented at theFISA(2001) conference (Yadigaroglu et al., 2003) and byYadigaroglu and Lakehal (2003). The first paper wasessentially limited to the application of CFD methodsto single-phase flow situations in the primary systemand the containment. We also illustrated there the use of“cascades” of CFD studies conducted with increasingdegree of sophistication and detail to clarify key is-s haseC -t tudyt ulti-p andt fer-e ,2

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nd partly to remove conservatisms imposed by thef 1D tools. As an example, we can cite the analf counter-current flow limitations in the downcomuring the refill phase of PWRs where penalizingumptions are made in the absence of 3D compions; see for example,Weiss et al. (1986)and detailsf the 2D/3D program byDamerell and Simons (1993.ne should also note that in the two- (or multi-)flu

nterpenetrating-media system codes turbulence islly ignored.

.1. The needs, the challenges and thepportunities

The nuclear thermal–hydraulics communityacing today interesting challenges. These includereation of the new computational tools that willsed for improved and more detailed analysis of

ues. In the present paper, we move from single-pFD to ComputationalMulti-Fluid Dynamics applica

ions. We also discuss and illustrate with a case she approach consisting of addressing complex mhase flow problems involving a range of space

ime scales with “cascades” of computations at difnt scales now, the multi-scale approach (Yadigaroglu003b).

Although the development of three-dimensioultiphase system simulation tools (system coeeded to address some of the situations mentibove is a very important issue, it is not consideere. We can only say that the introduction of CMethods will be an automatic step in this direct

ince such tools are by their nature multi-dimensioather than 1D.

It is evident that the development of new comational tools must be accompanied by experime

G. Yadigaroglu / Nuclear Engineering and Design 235 (2005) 153–164 155

work that will provide the data needed for validation ofthe new tools. This is a difficult task, since detailed, of-ten 3D data will be needed. To collect such data, the ex-perimenters would have to take advantage of advancesin instrumentation, miniaturization and coupling of thesensors with sophisticated data processing equipmentand software. Although the experimental work is cer-tainly very important, it is beyond the scope of thispaper that concentrates on the computational aspects.

2. Two-fluid versus one-fluid,interfacial-tracking formulations

It is worth recalling the basic premise of the two-fluid model at this point. The two-fluid conservationequations are based on an averaging procedure thatallows both phases to co-exist at any point, accord-ing to a certain “phase-indicator function” or essen-tially a probability that leads to the definition of thelocal instantaneous void fraction: this is also referredto as the “interpenetrating media” approach. Conserva-tion equations are written for each phase; these containphase interaction terms that specify the mass, momen-tum and heat exchanges between the phases. The ve-locity ratio and any thermal disequilibrium between thephases are no longer specified externally via correla-tions or assumptions but determined by the momen-tum and energy exchanges between the phases and thewalls. With the two-fluid model, also referred to as thes ulti-fl ser-v ovesa

eenc (andl on-c es ofm s), thec andp ia,t esc imesc thea nott iss reat

2004) is a partial remedy to this problem since the de-tailed modelling of bubble interactions provides someinformation of the flow regime and the distribution ofthe phases; developments in this area are underway.

The absence of topological information about the in-terfaces is not a shortcoming in many two-phase flowproblems, but there are situations where the two phasesare sharply separated (at a large scale, such as the scaleof the channel) and full understanding of the situationrequires knowledge of the position and geometry ofthe interface. This could be, for example, the case ofinjection of subcooled water in a pipe with stratifiedflow; clearly one needs to know the characteristics ofthe steam–water interfaces to estimate the rate of con-densation taking place there.

The injection of a large bubble from a vent is anothersituation where the shape and extent of the liquid–gasinterface are important; we will deal with this problemas a case study in this paper. Although the two-fluidmodel could, in principle, deal with the vent dischargeand similar problems,in practiceit cannot. Indeed, onecould imagine starting the vent flow problem with thevolume occupied by gas characterized as a region ofvoid fraction one, and the liquid volume as a regionof void fraction zero. Numerical diffusion will veryquickly mix the two phases, however, and the interfacewill lose its sharpness and disappear. The implemen-tation of interface tracking methods, discussed next, isnecessary to get solutions for such problems.

There are also cases where prediction of the locationa thed ionst facet oft andb

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ix-equation approach (or more generally the muid model), each phase, controlled by its own conation equations (three for each field or phase), mnd develops independently.

Although the presence of the interfaces has bonsidered during the local averaging processed to the definition of the local interfacial area centration that provides the area for the exchangass, momentum and energy between the phase

haracteristics of the interfaces (their exact shapeosition) are “lost” with the interpenetrating-med

wo-fluid formulation. The topology of the phasannot be obtained and consequently the flow regannot be determined, except by correlation withverage flow conditions; the two-fluid 1D model canell if, for example, at a 30% void fraction, the flowtratified or bubbly. The addition of an interfacial aransport equation to the two-fluid equations (seeIshii,

nd topology of the phases, leading essentially toefinition of the flow pattern is needed. Other situat

hat are good candidates for application of interracking methods are those for which the stabilityhe interface plays an important role: the stabilityreak-up of jets are good examples.

. One-fluid formulation and interface trackingethods

As mentioned above, tracking of the interfaceecessary in certain situations. The various inter

racking methods are typically associated with a “ouid” description of the two-phase flow: while in two-fluid, interpenetrating-media formulation the cervation equations were appropriately averagedxample, over volume)for each phaseand sets of con


Fig. 1. The classical two-fluid vs. the one-fluid/interfacial-trackingapproach.

servation equations for each phase resulted, in the one-fluid formulation, a unique set of conservation equa-tions is used for the entire computational domain, butthe fluid properties such as density and viscosity varysharply when we move from one phase into the other.The differences between the two approaches are illus-trated inFig. 1.

The position of the interface is tracked first using avariety of procedures (e.g., seeLakehal et al., 2002).Interface tracking methods can be Lagrangian or Eu-lerian. The most frequently employed Eulerian inter-face tracking methods are the Volume of Fluid (VOF)method (e.g.,Hirt and Nichols, 1981; Rider and Kothe,1998) and the Level Set (LS) method (e.g.,Osher andSethian, 1988; Sussman et al., 1994; Osher and Fed-kiw, 2001; Sethian and Smereka, 2003). In Lagrangianmethods (e.g.,Unverdi and Tryggvason, 1992; Tryggvason et al., 2001), particles are typically used to trackthe movements of the interface. The relative merits ofVOF and LS as well as other possibilities are discussedby Lakehal et al. (2002). The next step involves the so-lution of the unique set of conservation equations overthe entire computational domain. Numerical difficul-ties arise here due to the sharp variation of the fluidproperties across the interfaces. A number of methodshave been proposed to deal with this problem. In someof these, the sharp variation of the fluid properties issmeared in a narrow band of fluid on both sides of theinterface. The second-gradient approach developed byJamet et al. (2001a, 2001b)is particularly interestingi am-i de-t the

interested reader is referred to available reviews (McHyman, 1984; Sethian, 1996; Shyy et al., 1996; Sethianand Smereka, 2003).

The ultimate goal, namely to capture the geometryof the interfacesand to resolve sufficiently well theregion near the interface and the gradients there, sothat heat and mass transfer can be computed, is muchmore elusive. Interface tracking methods, although notlimited in theoryto consideration of turbulence in thefluids by methods such as Direct Numerical Simulation(DNS), arein practicenot adequate for this. Indeed,the scales needed to consider turbulence are typicallyorders of magnitude smaller than those used for theresolution of the interfaces in practical problems.The next best alternative would be a combination ofLarge-Eddy Simulation (LES) with interface trackingmethods. Efforts in this direction are underway in ourlaboratory.

It is, however, possible to conduct DNS studiesofturbulent flowsin certain relatively simple two-phaseflow situations, for example, for countercurrent flowsof two phases separated by a “simple” deformable in-terface. An example of such an application will bediscussed in the case study below. This situation alsoappears in the so-called Pressurized Thermal Shockscenario when emergency coolant (subcooled water) isinjected in a pipe containing stratified layers of satu-rated water and steam and produces rapid condensationbut also sudden cooling of the pipe walls; for recentprogress in this area, seeYao et al. (2003).

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n this respect, since it is based on the thermodyncs of the interface. We will not elaborate on theails of the one-fluid/interface tracking techniques;

. Addressing the problems at a multiplicity ofcales

Sometimes, one attempts to fully understanituation by considering a “cascade” of problemarious scales with a corresponding panoply andrchy of tools. For the nuclear systems that motivuch developments, the behaviour of the entire sys typically obtained using a system code based owo-fluid approach and operating at scales compao the dimensions of the system and its componocal phenomena, or the behaviour of parts ofystem, may need then to be addressed at the mesevel, with tools considering smaller scales and metailed description of phenomena. Finally, one meed to obtain wall and interfacial momentum, h


Fig. 2. The computational cascade.

and mass transfer laws by performing studies at thesmallest possible scale, for example, via DNS ofturbulence; such level of spatial resolution is indeedneeded to resolve the gradients determining transfersat the interfaces. An example of such an approach willbe given in the case study already mentioned.

In other words, certain problems may have to beaddressed with a cascade of computations. At eachlevel of the scale hierarchy, the physics of the flow maybe amenable to numerical prediction by scale-specificstrategies. Cross-scale interactions (feed-forward andfeedback between micro-, meso-, macro-scales) re-quire merging of the solutions delivered by scale-specific approaches at each level of the scale hierarchy,as sketched inFig. 2. Such approaches are among thegoals of the NURESIM project proposal prepared forexecution during the Euratom Sixth Framework Pro-gramme (Latrobe et al., 2003).

Pushing the computations and the scales consid-ered to the nanoscale level, Molecular Dynamics (e.g.,Mouriyama, 2000) is the ultimate tool in CFD andCMFD. We will only mention here, as a relevant exam-ple, the possibility of investigating phenomena such asthe vaporisation of an ultra-thin liquid layer on a hotmetallic surface by Molecular Dynamics simulations(Pan et al., 2002). In this case, the forces acting betweenall combinations of pairs of wall and fluid molecules aremodelled and the evolution of the system is simulatednumerically; the results ofPan et al. (2002)showed re-semblance to our knowledge of the vaporisation of as

5. Case study: condensation of large bubbles ina pool of water

The case study discussed below was motivated bythe need to understand certain phenomena taking placein passive Boiling Water Reactor (BWR) containments,in particular the containment of the ESBWR (Rao andGonzalez, 1998). The situation of interest is the con-densation of large bubbles injected into a pool of waterfrom a large downwards-pointing vent having a rela-tively shallow immersion depth. The bubbles contain amixture of steam and non-condensable gases.

From the system (macro-scale) point of view, one isinterested in finding out whether there is direct commu-nication between the exit of the vent and the surface ofthe pool; in this case, condensation will not take place inthe pool, something that should be avoided. For the realplant vent diameters and flow rates, experimentation ata scale of 1:1 was too expensive to consider. So, therewas a strong incentive to develop and assess computa-tional techniques capable of providing the answer. Thephenomena of interest are the growth of the bubble atthe vent, its rise and eventual break-up (meso-scale).Predicting bubble break-up is important since, afterbreak-up, the smaller bubbles condense very rapidly.Assessing the rate of condensation is important dur-ing the growth and rise phases of the large bubbles,in particular in the presence of non-condensables thatdegrade the rate of condensation (micro-scale). In thiscascade of analyses, the system code provides bound-a iledm cialh closet hreel t bef

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imilar macroscopic system.
ry conditions for the local analyses and the detaicroscopic-level investigations provide the interfaeat, mass and momentum transfer laws needed to

he problem at the intermediate level. Clearly, the tevels of analysis are coupled and information mused back and forth from one level to the other.

.1. VOF simulations of downwards injection fromvent

Meier et al. (2002)produced VOF simulations fohe injection of air bubbles into water; these mimicell experimental findings, in spite of the fact that there conducted in axisymmetric geometry (Fig. 3).he real situation is only partly axisymmetric; mubbles, after a roughly axisymmetric initial groweriod, tilt to one side or the other and also develop

muthal instabilities that lead to their break-up. Th


Fig. 3. Bubble formation from injection of air through a downward-facing vent. High-speed video images (bottom) and VOF computations (top)(Meier et al., 2002).

details could not of course be simulated with axisym-metric computations, but were reproduced in later 3Dwork mentioned below. The axisymmetric computa-tions reproduced, however, fairly well the characteris-tic frequency of appearance of bubbles at the exit ofthe vent, as well as their size and shape at break-up.Fig. 3 shows a number of frames from both experi-mental recordings and the corresponding VOF simula-

tions.Electronic Annexes 1 and 2show a sample exper-imental recording and an animation from a VOF com-putation. The small-scale experiment (injection froma 5-cm diameter, downwards facing vent) was set upto verify the computations (Meier, 1999; Meier et al.,2000).

Very recently,Liovic (2003) simulated the Meierdownwards vent data with a 3D VOF technique (Liovic


Fig. 4. Three-dimensional VOF simulation of downwards injectionof air showing azimuthal instabilities (experimental recording at thebottom) (Liovic, 2003).

et al., 2002). Fig. 4 shows a frame from his com-putations. The surface instabilities that create the az-imuthal ripples present in the experimental recordingsare clearly visible now. The 3D computations require,however, much greater computing power and time.

5.2. Heat and mass transfer at the condensinginterface

The simulation of the condensation of the steamcontained in the large bubbles requires the implemen-tation of heat and mass transfer capability in the VOFcode used. Although this is possible (e.g.,Welch and

Wilson, 2000), Meier et al. (2002)andLiovic (2003)could not compute the behaviour of bubbles contain-ing also steam for lack of a condensation heat and masstransfer law and because of difficulties in the integra-tion of such a law within the VOF computations.

The difficulties inherent to the heat and mass trans-fer physics of the problem can be clearly shown in thiscase study: for Prandtl and Schmidt numbers typical ofthe present situation, the thickness of the regions overwhich the noncondensable gas concentration and liq-uid and vapour temperature gradients are significant isa fraction of a millimetre (Meier, 1999) and resolutionof these boundary layers is not possible at the scale atwhich the VOF simulations are performed. Thus, heatand mass transfer cannot be computed properly withthe resolution of the fields used for the VOF compu-tations. Other ways must be found for determining theinterfacial exchange laws and incorporating them intothe VOF simulation.

Measurements of the instantaneous rate of conden-sation at the surface of large bubbles are difficult andavailable experimental data refer to rather simple situa-tions like the condensation of small spherical bubbles.In the absence of experimental information specific tothe problem in hand, one can try to apply correlationsderived from the solution of simple problems approxi-mating the situation locally at the interface of the largecondensing bubble.Davis and Yadigaroglu (2004)solved with a combination of classical analytical tech-niques augmented with numerical computations thep on al ion.

mm vis

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roblem of condensation of pure steam impingingiquid surface and creating a stagnation-flow situat

Fig. 5 shows how the solution to this probleay approximate the more complex reality. Da

ig. 5. The direct-contact condensing flows considered byDavis andadigaroglu (2004)is shown on the right. The vent flow situation thould be simulated is shown on the left.


and Yadigaroglu covered a wide range of parametersand could correlate their results for further use.Gerner and Tien (1989)presented a similar butaxisymmetric solution for two impinging stagnationjets over a flat interface which, however, also took intoaccount non-condensables. The remaining challengeis to “link” such correlations to the computed flowconditions on both sides of the interface. Indeed, thetheoretical solution is given in terms of the potentialflow velocity outside the boundary layer created bythe impinging flow. One has to link via an appropriatealgorithm the computed flow conditions on bothsides of the interface (in the liquid and the gas,at some distance from the interface) to the ideal-ized, corresponding, theoretical potential flow velo-cities.

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5.3. DNS of turbulent condensing flow

As the last resort, one can rely on DNS of turbu-lence in the flow to elucidate the fundamental lawsof condensation in the presence of non-condensables.DNS computations can be performed in an idealisedconfiguration, in which steam or a steam/air mixtureflow counter-currently over a liquid surface in arectangular box (Fig. 6). The steam condenses on theinterface.Lakehal et al. (2003)and Fulgosi (2004)performed DNSs of condensation of pure, saturated orsuperheated steam on subcooled water in a stratified,counter-current flow situation. First one needs to com-pute and describe the flow and turbulence structure inthe thin diffusive layers on either side of the interface;this is essentially an extension of earlier work per-

ig. 6. The computational domain used for the DNS of countercurrenhe interface (bottom).

t flow of steam and water (top) and variation of the main variables near


formed without condensation byLombardi et al.(1996). Next, the condensation heat transfer laws areobtained from the DNS data (Lakehal et al., 2003). Thefinal steps towards obtaining the interfacial exchangelaws in the presence of noncondensables are underway.

In the work of Fulgosi and co-workers mentionedhere, the DNS computations are conducted sepa-rately in each phase and are coupled with jump con-ditions considering the interfacial exchanges at theliquid–vapour interface. The latter is deformable to acertain extent (small ripples can be accommodated, butno large breaking waves) and its position is contin-uously tracked. The boundary layers on both sides ofthe interface grow in the computational box that has pe-riodic boundary conditions over its bounding verticalplanes. Therefore, special care should be taken to main-tain the correct boundary conditions at the upper andlower horizontal surfaces of the box; the condensationmass flux at the interface should be added and extractedat these boundaries, respectively, to produce steady-state data from which the heat and mass transfer lawscan be extracted. Care should also be taken to properlysimulate the turbulence balances at the boundaries. Theresults obtained so far agree with available experimen-tal data. The work ofFulgosi (2004)provided first-of-a-kind detailed data and produced insights into theeffects of condensation on turbulence in the boundarylayers.

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For DNB at low quality, the microscale work wouldinvolve bubble nucleation at the wall (e.g., VOF or LSwith heat and mass transfer); such computations areat their infancy, but work in this direction has alreadybeen published. For example,Welch (1998), Son et al.(2002)andMathieu et al. (2004)produced computa-tions of bubble growth on a heated wall.

The mesoscale computations would deal with thebubbly layer near the wall; bubbly flows have beenalready treated with the interpenetrating-media ap-proach, including (so far rather tentative) RANS mod-els of turbulence (Lance et al., 1999). More advancedapproaches, for example, with LES are being attempted(Milelli et al., 2001); Dean et al. (2004)present inter-esting recent developments in this area. Finally at themacroscale, the entire flow channel would be consid-ered, including the interaction of the wall layer withthe bulk fluid.

For dryout at high quality, the microscale computa-tions would again address the bubbles and nucleation atthe wall; the generation and detachment of waves fromthe liquid film; the impingement of drops and their cap-ture on the liquid film; heat and mass transfer from thesurface of the film and from the wall. VOF, LS and DNScould again be the candidate techniques for such com-putations. At the mesoscale, the global liquid film massbalance and heat and mass transfer from/to the liquidfilm should be considered. Finally, at the macroscale,the overall channel condition should be examined andthe mesoscale results integrated along the channel toa

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. Multi-scale critical heat flux predictions withMFD?

The modelling and computation of the Critical Hlux (CHF) condition has been a very elusive ta

or the last several decades. In spite of the enormumber of publications on the subject, there is stilniversal model and tool for reliable CHF predictionder all conditions. At the European Two-Phase Froup meeting that took place in Stockholm in J002, our French colleagues (Bestion, 2002) proposed

he creation of a CMFD initiative aiming at the predion of the CHF condition; this idea is expanded he

Both subcooled and low-quality Departure from Nleate Boiling (DNB), and high-quality dryout (DOould be attacked with a panoply of CMFD tools aascades of computations at micro-, meso-, and mcales.

rrive at the DO condition.Such an approach is easier to describe than to

lly implement. Although the exercise will not leadull success soon, the trip will certainly be worthffort in terms of fallout and spin-off developments

. Conclusions

Although CFD of single-phase flows has reaccertain degree of maturity, a number of Comp

ionalMulti-Fluid Dynamics (CMFD) methods are snder development. Various situations or phenoman be best addressed at a multiplicity of time/spcales: the micro-, meso-, macro-scales. At eachf the scale hierarchy, the physics of the flow mayest amenable to numerical prediction by scale-spetrategies. Cross-scale interactions (feed-forward


back between scales) require merging of the solutionsdelivered by the scale-specific approaches. Clearly, theway to such multi-scale treatments requires first ad-vances in the corresponding scale-specific methods.

The case study outlined in this paper and the CHFinitiative mentioned illustrate what we have referredto as “cascades” of CMFD methods. To deal with theventing of steam/air mixtures from a vertical downwardvent, we had to address the problem at various scaleswith a variety of tools: system behaviour (in the exam-ple cited here, the flow rate and the composition of themixture entering the vent) with a system code; largebubble behaviour with VOF; finally, the direct-contactcondensation heat transfer law via DNS and analyticalmethods. Cascades of computations at different scaleswould also be needed to arrive at the grand-challenge,the CMFD of CHF.

A number of interesting international collaborativedevelopments are taking place to develop a new gener-ation of tools for safety analysis. Several projects suchas ASTAR and ECORA were conducted in Europe un-der the fourth and fifth FWP (FISA, 2001, 2003) andthe effort is likely to culminate in the sixth FWP, theNURESIM project under preparation.

As illustrated by the examples discussed in thispaper, in the future, safety issues are more likely tobe addressed at a variety of scales with a panoply of(partly) new tools and methods, including CMFD. Nextto the classical, mature system codes, there is indeedalso room for problem-specific computing platforms orc es-s thec

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References

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G tion

H od. 39,

I portencema,

J Thetion

204,

J Then of169,

L rdshase

L irectmo-

odes, working at a multiplicity of scales, when necary considering multiple physics, and coupled tolassical system analysis codes.

cknowledgments

The author is gratefully acknowledging the conutions of his ETH collaborators who performed mf the computations presented in this paper: D. Lal, J. Davis, M. Fulgosi, P. Liovic, and M. Meier. Tlectronic Annexes were produced by M. Meier.

ppendix A. Supplementary data

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