1

XIX UIT National Heat Transfer Conference, Modena, I, June 25-27, 2001, invited paper

INTRODUCTION

Premise

Several times in the past we have been asked to deliver akeynote lecture on boiling in microgravity (Di Marco &Grassi, 1997, 2000a, 2000b), thanks to the politeness of ourcolleagues. Most of the times we dedicated these lectures toshow a general picture of the work done by the internationalcommunity in this field, and the interested reader can easilyrefer to the previously quoted papers. The approach followedin the present article is rather different. This is motivated bythree main reasons:• most relevant, the quite crucial moment for the “space

community” in connection with the ongoing constructionof the International Space Station and the next MinisterialEuropean Space Conference (to be held next autumn) thatwill make quite fundamental decisions for the future spaceactivity;

• the effort that one of the authors (Grassi) is performing tomake “Heat Transfer” accepted by the European (ESA)and the Italian (ASI) Space Agencies as a self consistenttopic1;

• the need of people like us, involved in low gravity researchsince a long time, to discuss our findings opinions andfuture work within a highly qualified scientificenvironment and to increase the interest for this sort of

1 The following results have been achieved: the institution of an

ESA Topical Team on Boiling (as one of the most relevant heattransfer mode, including also condensation) chaired by Pisa and theinclusion of “thermal control” as one of the topics to be addressed byASI in the next calls for proposals.

unique opportunity of experimentation (weightless testcampaigns).

Owing to this, we dedicate the rest of this chapter todescribe the reasons which led us to get involved in theresearch that we have been pursuing since around twelveyears. Some more details can be found in (Grassi & Legros,2001).

Heat transfer an exciting challenge for low gravityscience and technology.

A large debate (not yet completely concluded, Trusler,1996) took place in the past with regard to the mechanisms ofheat transfer and in particular on heat conduction in gases.According to Brush (Brush, 1988) Benjamin Thompson,Count of Rumford “..made a more important contribution tothe development of science by his researches (published in thelast decade of the 18th century) on the various modes of heattransfer; he helped to make this subject one of the majorscientific concerns of the 19th century.” Unfortunately hisconclusions were affected by the problem of distinguishingbetween the contribution of conduction and convection.Around sixty years later Gustav Magnus, after his experiments(still affected by convective flows) on heat exchange inhydrogen, concluded that “…this gas can transmit heat fromparticle to particle, in other words conduct it…”2. The realstep forward was made by James Clerk Maxwell who

2 This statement might be misleading: Magnus did not recognize

the possibility of molecular motion and attributed this particleinteraction to molecular radiation. In addition he could not exclude afurther influence of radiation in his experiments.

WHY WEIGHTLESNESS EXPERIMENTS ON BOILING HEAT TRANSFERAND WHAT WE LEARNED UNTIL NOW

P. Di Marco and W. Grassi*

LOTHAR (LOw gravity and THermal Advanced Research laboratory)Dipartimento di Energetica “L. Poggi” – Università di Pisa – Italy

* Phone: +39.050.569646 Fax +39.050.830116 E.mail: w.grassi@ing.unipi.

ABSTRACTThis paper refers to a long-term research, begun more than ten years ago, about heat transfer in reduced gravity

and/or in the presence of an electric field and summarises the main results and the main conclusion achieved sofar. After a somehow detailed analysis of the impact of heat transfer on modern society and of the motivation oflow gravity research on this subject, the authors describe their own research work on the effects of gravitationaland electric forces on single-phase convection and pool boiling. This research has the twofold aim to investigateon the basic mechanism of natural convective heat transfer, and to identify technological devices to made itpossible also in the lack of buoyancy. It has been experimentally shown that the application of an external electricfield enhances any kind of convective heat transfer around a heated wire: the enhancement can be modulated byvarying the value of the applied voltage. Critical heat flux is enhanced as well. In reduced gravity, heat transferperformance is generally degraded to a various extent: the application of a sufficiently intense electric fieldrestores the same value of heat transfer coefficient and critical heat flux measured in normal gravity conditions,thus demonstrating the progressive overwhelming of the electrical force on the buoyancy one.

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introduced a kinetic theory of heat conduction (1860).3 Thisnotwithstanding, Maxwell treated this subjects quiteincidentally, due to his pessimism about the possibility ofmeasuring gas thermal conductivity experimentally: “…Itwould be almost impossible to establish the value of theconductivity of a gas by direct experiment, as the heatradiated from the sides of the vessel would be far greater thanthe heat conducted through air, even if currents could beentirely prevented …”. Such an opinion was caused by someerrors Maxwell made, that led him to heavily underestimatethe gas conductivity, as pointed out by Clausius (for airMaxwell gave a value of 10-7 of that of copper while aftercorrection Clausius estimated it as 1/1400 that of lead)4 5.Dueto the lack of experimental data Narr (1871), Stefan (1872)and Kundt and Warburg (1875) tried to set up a satisfactorymethod to perform measurements. In particular the latterauthors decided to perform low-pressure tests to stronglyreduce convective motions without affecting the conductivityvalue, according to Maxwell’s theory.

At this point we might wonder how much the abovescientists would appreciate the chance of getting rid of gravityand how beneficial would this possibility be to make that longprocess shorter and easier. Asking such a question is whathistorians call historical anachronism, but it is easy to imagineweightless experiments to measure thermal conductivity offluids.

In any case, the heat transfer science was not only heatconduction in gases. It was fundamental to formulate thePrinciples of Thermodynamics, Planck’s radiation theory,quantum physics etc. Nowadays it also plays a key role for on-earth and space technology and has a crucial impact on socialand economic development of modern countries. Toemphasise this we should make a step behind and brieflydiscuss some major challenges issued by the future societydevelopment.

Sustainable development

“Sustainable development” with all its implications, isprobably the most important problem that modern society hasto cope with. The attention of the world is focussed on theclimate change that can be induced by the anthropogeneticactivity with particular regard to the production of greenhousegasses (CO2, CH4, NO2, CFC’s..). They are mostly, 80% in theUS (Murray, 1999), associated to energy and heat transfertechnology. The first step was the Montreal protocol (1987),later on reinforced in London (1990) and Copenhagen (1992),aimed at eliminating the production of ozone depleting gasseslike CFCs. These gasses are mainly employed in refrigerationtechnology for an investment in the related equipment of about75 billion Euro per year. The transition to HCFC and HFCwith a lower or nil Ozone Depletion Potential could partiallysolve the problem. Anyway the last revision of the KyotoProtocol imposed the elimination of several of these transitionsubstances (HCFC22 in particular) within 2030 at the latest,

3 Maxwell adopts the concept of mean free path proposed byClausius two years before.

4 Maxwell recognized his mistake with a very appreciable fairplay, unfortunately not so common nowadays: “ ..It is ProfessorClausius, of Zurich, that we owe the most complete dynamical theoryof gases,…there were several errors in my theory of the conductionof heat in gases which Clausius has pointed out in an elaboratememoir on the subject”.

5 For a more detailed discussion of these and several other aspectsthe reader is referred to the valuable paper by Bush already quoted.

while the new regulations of the European Union (CE n.2037/2000) are much more severe on this respect. Due to this,the use of “natural” fluids like ammonia6 is stronglyencouraged by some authors (IIF, 1997). After a rather longprocedure (Rio de Janeiro, 1992, Kyoto, 1997, and BuenosAires, 1998) some decision was made, at a world level, withregard to greenhouse gasses (among which also CFC areincluded). Most of the industrialised countries are todaycommitted to fulfil the Kyoto protocol directions, thusreducing the production of climate altering gasses. Inparticular the European Union is committed to reduce CO2emissions of 7% within 2010. The 17th Congress of the WorldEnergy Council (Sfligiotti 1998), held in Houston in 1998, hasbeen focused on how technology could face the challenges ofenergy supplying and use for the next fifty years. It made theconclusion that: “…The increased efficiency in the use ofenergy constitutes the most immediate, wide and economicopportunity of reducing resource consumption andenvironment degradation … Efficiency should becomemandatory in any aspect of the energetic business …”.

In addition the Fifth Framework Programme7 (funded foraround 15 billion Euros) includes within its 4 thematicprogrammes “Energy Environment and SustainableDevelopment”.

As most of the energy-dedicated equipment involves heattransfer, the enhancement of heat exchange performancesbecomes mandatory.

Space technology development

Satellite services play an essential role in the human kinddaily life. They include communications and broadcastings,global positioning systems (GPS) for aeroplanes, ships andcars, meteorological forecasts, earth observation etc. A trendtowards more sophisticated use of satellites is easilyforeseeable (like, for example, Real Time EmergencyManagement via Satellite, REMSAT project, whose firstdemonstration was held on 13-14 May 2000 with the aim ofhelping bring a forest fire under control). Furthermore there isa strong interest in deep space exploration and in situresources utilisation on Mars and Moon. All the relatedequipment undergoes thermal requirements as stringent assevere are the conditions of the surrounding environmentwhere they should operate. For example on the ESA Web siteone reads about the Mars Express8 thermal control: “…thespacecraft has to provide a benign environment for theinstruments and on-board equipment. That means keepingsome parts of the spacecraft warm and other parts cold. Twoinstruments.... have infrared detectors that need to be kept atvery low temperatures (about –180°C)….. But the rest of theinstruments and on-board equipment function best at roomtemperatures (10 – 20°C).” In this case the chance of makingexperiments in a low gravity environment is fundamental totest heat transfer equipment suited for space applications.

6 Besides being already used in earth technology, ammonia is alsoused in the secondary cooling loop of the Russian segment of theInternational Space Station.

7 Framework programme of the European Union that defines thestrategic priorities for research and technological development for theperiod 1998-2002. Among its goals we enumerate, for example:increasing of industrial competitiveness, job opportunities creationand quality of life.

8 Mars Express is a spacecraft designed to take a payload ofscientific instruments, a data relay system for communicating withEarth and a lander to Mars. Its launch is foreseen for June 2003.

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Heat Transfer and Fluid Physics

There is a fortunate large convergence of goals betweenearth and space technology requirements discussed above:• on earth, more effective thermal equipment means less

energy consumption and a consequent reduction ofenvironmental pollution;

• for space, it leads to lighter and more compact equipmentand can better match the increasing need of dissipatinglarger heat fluxes. This need is clearly demonstrated byHughes satellite HS 702 that produces a power of 18kWand the new one HS 702, to date under design, which willhave a power production of 25kW (Dorheim, 2000).

Within the field of fluid physics the most effective heatexchange technologies are those involving phase change andin particular boiling and condensation. Their use on earth isvery widespread and includes power generation plants, coolingof electronics, building air conditioning, food conservation etc.Their importance in daily life and their impact on economics isquite well established. For instance it has been estimated (IIF1997) that up to 25% of the total food world production isinterested by refrigeration (home refrigerators included). Inorder to stress the importance of two phase mixtures, and inparticular of bubble behaviour in space, we can report a fewsentences written in an amusing paper appeared in the NewScientist Journal (Mullins, 1997): ”In space gas bubbles affecteverything from rocket fuel and life-support systems to humandigestion and excretion… in space bubbles do not rise and socan block tubes that carry liquid. They cannot be bled away…because there is not enough gravity to separate gas fromvapour… NASA astronauts on the shuttle recently asked forthe amount of gas in fizzy drinks to be reduced…they hadtrouble burping. But if bubbles were to block pipes carryingliquid in a life support system, the problem could bedisastrous. The Russians are designing a gas turbine powersystem (much more energy efficient than photovoltaic cells)that will keep equipment working and astronauts alive on theISS. Solar rays will boil a liquid and the vapour used to powera turbine to generate electricity… but its success, andultimately astronauts lives, will depend on understandingbubble behaviour”.

BOILING IN THE ABSENCE OF WEIGHT

One never fully appreciates how much his way of thinkingis conditioned by his daily life on earth, until he starts dealingwith the preparation of low gravity experiments or having funon a parabolic flight. We are so used to think in terms ofgravity that it is often difficult even to conceive theories (andexperiments) not accounting for its effect.

Thus the very first contribution of undertaking a research inweightless conditions consists in changing our mental attitude,long before than simply giving the opportunity of a veryspecial experimental approach.

Whoever has been even occasionally involved in boiling orcondensation heat transfer has easily learnt how much usualcorrelations are affected by the acceleration of gravity, g. Onthe other hand, gravity on earth (for our normal purposes) ispractically constant and its force is the dominating force inseveral cases. Now one can wonder whether the use of g incorrelations always catches the real physical nature ofphenomena and how much the presence of gravity leads tounderestimate some other small scale effect that could play afundamental role in phase change heat transfer. Herein we will

devote our attention just to boiling. The main physical aspectsin which gravity acceleration could be involved aresummarized in Tab.1

Table 1: Boiling phenomena affected by gravity.

Phenomena includinggravity

Heat transfer and fluiddynamics

Bubble detachment diameterand frequency

Nucleate boilingFilm boiling (bubbledetaching from the liquid-vapour interface)

Bubble terminal velocity Transition from singlebubble to fully nucleateboiling regime

Bubble and drop oscillations Bubbly flowsSprays

Bubble coalescence Vertical coalescence:transition from singlebubble to column regimes

Liquid-vapour interfaceinstability

Mechanism leading to CHFaccording to thehydrodynamic theory and toKatto’s theoryTransition boilingMinimum film boiling pointMFBStable film boilingTransition from filmwise todropwise condensation andviceversaCounter current flowlimiting condition, CCFL

The boiling process involves extremely complicated, non-linear physical processes, operating over length scales rangingfrom 10nm to 1m or more. Strictly speaking it is intrinsically anon-stationary, non-equilibrium process, although it shows asort of “regularity” only on a statistic basis.

As a consequence, a satisfactory description of the wholephenomena in terms of conservation and constitutiveequations (plus obviously boundary and initial conditions) isunaffordable at present. Thus engineering design is still basedon simplified correlations of experimental data, with limitedrange of validity. Over the next years increase in computingpower will make it feasible to replace, or at least supplement,the correlations by large-scale models. The development ofsuccessful models depends on advances in understanding thephysics of boiling: experiments in low gravity can play afundamental role by modifying the balance between gravity-dependent forces and other interacting forces. This is why,from the very pioneering, but somehow solitary, work of a fewscientists in the past (like, for example, Prof. Merte in the USand Prof. Straub in Europe), we passed to a very alive andincreasing interest of the boiling community in this sort ofexperimentation, nowadays.

The statistic nature of boiling as a whole has someconsequences for low gravity experiments. For example itimplies that a sufficiently large number of bubbles must existon the heating surface, that appropriate time and spaceaverages of the phenomenon must be taken into account andthat a steady fluid dynamic and thermal regime, both in thebulk fluid and in the heater, must take place. While all theseconditions can be easily attained on earth (in some cases, likeflow boiling, on a large length scale), a great care has to be

4

paid to their fulfilment during low gravity experiments. This isbecause of the intrinsic limitations in size, power and time (incase of short duration tests9) of the different experimentalconditions available on low gravity platforms to date.Therefore any experimental apparatus to fly has to be properlydesigned to match the above constraints. Otherwise we canonly speak of vapour bubbles behaviour, but not of boiling.

One more mandatory requirement has to be the gravityrelevance of the proposed experiment. Roughly this, forinstance, means that, whenever field forces other than gravityare recognised to be absolutely prevailing in the phenomenon,there is not enough scientific motivation for its testing in lowgravity. This might be the case for strongly forced flow, whichare already used in some space application (i.e. in the Russiansegment of the International Space Station) just thanks to theirinsensitivity to the force of gravity.

LESSONS WE LEARNED FROM EXPERIMENTSCONDUCTED IN WEIGHTLESS CONDITIONS

Our team in Pisa is conducting a broad spectrum of studieson the effects of force fields on single-phase convection andboiling. In general, the main force fields we can refer to are:gravitational, electric, magnetic and acoustic fields. In thesecase we can adopt a twofold viewpoint:• Gravity, on earth, is likely to mask the effects of the other

force fields (scientific motivation for low gravityexperiments);

• The force fields can be used to replace the gravity force inspace applications (technological motivation for lowgravity experiments).

At present we have a large amount of data related to theinfluence of the former two fields for a cylindrical geometry,and we are at an advanced stage of preparation of anexperiment on flat surfaces to be flown next year on the

9 Drop towers and drop shafts: 5 to 10 seconds. Parabolic flightson airplanes: 20 seconds for each parabola. Sounding rockets: from 6(Texus and Maser) to 15 (Maxus) minutes.

Russian satellite Foton 13. In addition a co-operation hasstarted with the University of Timisoara for a joint work onmagnetic force fields. Furthermore we defined a collaborationwith Alenia Aerospazio to develop a heat exchanger for spaceapplication. Unfortunately the start up of this project has beenheavily delayed for beaurocratic reasons.

In the following we will deal with the effect of gravity andelectric fields on single-phase convection and pool boiling.

Experimental apparatus and procedure

The basic experimental set-up we have been using for ourtests is shown in Fig.1. Of course it has been adapted fromtime to time, depending on the particular environment where ithas been used (laboratory, aeroplane parabolic flight, soundingrocket, drop shaft) It consists of an aluminium vesselcontaining the test section, heated by Joule effect by a directcurrent up to 12 A. A bellows, connected to the main vessel,was operated by pressurised nitrogen in the secondary side, tocompensate for volume variation due to thermal dilatation andvapour production, and to maintain the pressure constant. Themain vessel had windows to allow visualisation of thephenomenon by means of video cameras (both normal andhigh speed camera). An external heating system, asserved to aPID controller, kept the fluid temperature constant within ±0.1K.

Experiments were carried out using a horizontal platinumwire of several diameters ranging from 0.2 to 0.6-mm andabout 45-mm in length, which served as both a resistanceheater and a resistance thermometer. In case of bubblingexperiments the wire has been substituted with a capillarytube, with a small hole on its lateral surface to inject nitrogenbubbles into the liquid.

The electric field was obtained by imposing a d.c. voltagedrop (up to 30 kV) between an 8-rod cylindrical “squirrelcage”, of 60 mm diameter and 200 mm length, surrounding theheater, and the heater itself. It was shown that the length of thecage is sufficient to avoid side effects along the active part ofthe heater. The analysis showed also that, up to 10 mm fromthe wire axis, the field has the same 1/r trend as the one

Fig. 1. Sketch of the experimental apparatus.

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generated by a solid cylindrical electrode surrounding theheater, although with a lower intensity. The use of such asmall test section is due to the above mentioned limitation inspace, power and time (a little thermal inertia is required)imposed by flight experiments constraints. So far we havebeen using used three fluids: R113, FC72 (3M) and Vertrel XF(Dupont). The first and second fluid are non-polar with arelative dielectric constant equal to around 2, while the third ispolar with an estimated constant around 9, but itsthermophysical properties are hardly available. Differentoperating pressures as well as different values of liquidsubcooling have been tested.

The whole set of pool boiling regimes, except for transitionboiling, has been analysed, included single phase convectionprior to boiling inception. Moreover gas bubbling has beenperformed. All this has been done both on earth and in lowgravity. In the following pages we will shortly report the mainresults obtained. For each of the analysed heat transfer regimewe will summarise the most relevant result obtained withregard to the scientific (Fundamentals) and the technological(Technology) point of view.

Single phase convection

Two parabolic flight campaigns were partly dedicated tothis subject, respectively using R113 and FC72 as test fluid. Avery good agreement exists between the related sets ofexperimental results. The following discussion mainlydescribe the FC72 data (Di Marco & Grassi, 1998). Some testswere run at constant heat flux during the entire parabolas.Thus we could collect data both in the low and in the highgravity phases. Other tests were performed increasing the heatflux linearly with time during the low gravity phase. Part ofthese tests led to the onset of nucleate boiling. No significanttests of natural convection were carried out in low gravity inthe absence of electric field: in such conditions, transientconduction to the surrounding fluid or transition to boilingmay occur. In this case, tests in microgravity resulted in a veryearly onset of nucleate boiling.

Constant heat flux tests. – Figures 2 and 3 show the trend ofthe heat transfer coefficient, with the wall heat flux keptconstant, and vertical acceleration versus time for an appliedvoltage of 1.5 and 3 kV, respectively. Natural convection isstill influenced by gravity in the former case, while thephenomenon is independent of the value of gravity within thedata accuracy in the latter. In Fig.4, the trends of the heattransfer coefficient versus time at different values of theapplied electric field, for a constant heat flux of 20 kW/m2, arecompared. The weightless phase starts at 0 s, and the recoveryone starts at around 20 s. The heat transfer coefficientincreases with the value of the electric field and is independentof gravity for an applied voltage larger than 3 kV.

Variable heat flux tests. - During these tests the heat fluxwas increased linearly, starting from 0 at the onset of lowgravity, and then it was kept at a constant value at thebeginning of the recovery phase (enhanced gravity). Ratesfrom 100 to 175 kW/m2 s were adopted. The heat transfercoefficient increased with the heat flux during themicrogravity phase and remained constant through thefollowing recovery and levelled flight phases, i.e. when theheat flux was no longer increased and the gravity accelerationpassed from 10-2 to 1.8 g0, and later on to g0. A comparison

-40 -20 0 20 40t (s)

0

500

1000

1500

2000

α (W

/m2 K

)

V = 1.5 kV

V = 3 kV

V = 5 kV

V = 7 kV

V = 10 kV

Constant qq = 21.3 kW/m2

normal g macro g micro g macro g

Fig. 4. Trend of the heat transfer coefficient vs. time (duringa parabola) for different high voltage values. The lowgravity phase is located within 0 and 20 seconds.

-40 -20 0 20 40 60t (s)

-0.5

0.0

0.5

1.0

1.5

2.0

g

0

200

400

600

800

1000

1200

1400α

(W/m

2 K)

α

az

Fig. 2. Heat transfer coefficient and gravity acceleration forq = 21.3 kW/m2, V = 1.5 kV, FC72.

-40 -20 0 20 40 60t (s)

-0.5

0.0

0.5

1.0

1.5

2.0

g

0

200

400

600

800

1000

1200

1400

α (W

/m2 K

)

α

az

Fig. 3. Heat transfer coefficient and gravity acceleration forq = 21.3 kW/m2, V = 3 kV, FC72.

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done with steady state conditions (constant heat fluxconditions included) proved that, thanks to the low thermalinertia of the heater, quasi-steady conditions were reached ateach step. Finally, the data obtained in normal gravity duringpre-flight and in-flight tests were compared with thoseobtained in microgravity. It further proved that the heattransfer coefficient in the presence of an electric field, beyonda certain threshold, is independent of gravity. Besides, thepresence of an electric field greatly improves the heat transfer.Enhancements up to 4-fold in the heat transfer coefficientcould be obtained, with respect to zero-field conditions.

Fundamentals. Once an electric field is applied to a fluid anelectrical force arises, that reads

ρ∂ε∂ρ+ε−ρ=

TEe EE grad

21grad

21 2EF (1)

The first RHS term (Coulomb's force) depends on the signof the electric field and is present when charge build-upoccurs. In many cases it predominates over the other electricalforces. The second term is a body force due to non-homogeneities of the dielectric constant (e.g. related tothermal gradients) and the third term is caused by non-uniformities in the electric field. The last term of the RHS ofEq.(1) is irrotational and can be lumped with pressure in theNavier-Stokes equations. Thus, in an incompressible flow, theonset of convection is only affected by the first two terms inthe RHS of Eq.(1). Even in poorly conducting fluids, as theone considered here, charge build-up may occur (Di Marco &Grassi, 1993).

On earth, the electric force usually adds to gravityenhancing the heat exchange between the heater and the fluid(Jones, 1978; Di Marco & Grassi, 1993; Di Marco et al.,1997). Relations have been proposed of the form (Jones, 1978)

)()( 21 ElPrFGrPrFNu += (2)

to evaluate the contribution of the electric force to naturalconvection. If the EHD effect is solely attributed to thedielectrophoretic forces, El is defined as

2

22

'µ

∆∂

ε∂

ρ=ETL

TEl (3)

accounting for the effect on ε of temperature variations inspace. If the charge build-up mechanism dominates (dc field),the El number is expressed as

2

22

"µ

∆∂σ∂

τρ=ETL

TElE

(4)

In the absence of gravity and interfaces, the electric force isthe only body force that promotes the motion of a pure liquid,thus allowing convection heat transfer to occur. A preliminarystudy on EHD enhancement of natural convection in R113 inmicrogravity condition was performed in a former parabolicflight campaign (Di Marco et al., 1997) for the first time inweightless experiments.

The comparison with correlations of the type reported inEq.(4) is at present awkward, since no reliable data for thevalue of ∂σΕ/∂T, appearing in El”, are available for the testedfluid. It is anyway evident that the second term in the right-hand side of Eq.(2), F2, dominates the heat transfer startingfrom relatively low values of the applied potential. Theavailability of “zero-g” allows for evaluating this term, thuschecking the reliability of such kind of correlations.

Technology. The application of an electric field stronglyenhances convection on earth, in agreement with theconclusions shown in the literature. Besides we demonstratedthat it can be used to obtain rather large (same as on groundfor high fields) heat transfer coefficient in space application,independent of the acceleration level, with no need ofpumping devices In addition the value of this coefficient canbe easily adjusted by simply tuning the high voltage value.Another remarkable result is that, in case of static fields, aquite small power consumption is needed. In fact in our teststhe energy consumption in the high voltage circuit wasnegligible: the related electric current was always below thesensitivity threshold of the ammeter (5 µA), thus allowing toestimate that the power absorption did not exceed 50 mW

Fig. 5. Heat transfer coefficient at normal gravity for different pressure and applied electric fields. R113.

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NUCLEATE BOILING

The nucleate boiling regime extends from boiling inceptionup to the so called critical heat flux (CHF). Preliminaryground experiments suggest a favourable effect of the electricfield reducing the temperature overshoot at the onset ofboiling (Carrica et al., 1995 ). This notwithstanding we did notperform yet a systematic study of the effect of gravitationaland electric forces on this point. Thus this aspect will not betreated here. On the other hand nucleate boiling has beenrather extensively studied. Test with R113, at normal gravityand different system pressures (atmospheric pressure included)are shown in Fig. 5 (Carrica et al., 1995 ). Boiling is enhancedby the electric field at low heat flux and marginallydeteriorated at the higher heat fluxes.

A complete data set showing the combined influence onnucleate boiling of gravity and electric field is shown in Fig.6(Di Marco & Grassi, 1996) for FC72. Video records showedthat the vapour pattern (bubble size and velocity) isdramatically altered by the variation of the acceleration.Surprisingly, such a change is not reflected in an appreciablechange of boiling performances, i.e. in the location of therelated curve on the q” vs. ∆Tsat plane, as shown in Fig.6.

For the tested geometry we can in general state that both theelectric and the gravity field do not have any major effect onthe nucleate boiling heat transfer coefficient, while theyheavily modify the vapour pattern at the wall. In fact thepresence of an electric field reduces bubble size and increasestheir detachment frequency. Gravity has a similar effect so thatin low gravity bubbles grow to very large diameters. Throughappropriate combinations of electric and gravity forces it ispossible to control bubble size and frequency. All this can beclearly observed in Fig.7. In this figure the bubble size can be,at least qualitatively, appreciated with reference to length ofthe boiling wire (the amperometric contacts are clearly visibleon the left and right sides of the photos).

Fundamentals The electric field affects many boilingfeatures such as bubble shape, detachment diameter, frequencyand number of nucleation sites. Also the fluid flow around thebubble, and thus the thermal field, can be modified accordingto what has been previously said about natural convection.Moreover changes in physical properties, like surface tensionand wettability, can be expected, even if they are usuallydiscounted. Generally speaking, the volume of the detachingbubbles decreases at increasing value of the group

σε

=LEGE

20 (5)

The detachment volume shows also a separate dependenceon εl for non polar fluids, with an increasing prolate bubbleeccentricity versus the liquid permittivity. Furthermore, incase of non uniform electric fields, a net force acts on thebubbles that, for a tiny spherical bubble, can be given as

20

2E 2

2 Er llg

lgb ∇εε

ε+εε−ε

π=F (6)

This force tends to move the bubble towards regions withweaker electric field intensity. Therefore its effect depends onhow it is directed with respect to gravity. For example, forupward oriented surface and field strength decreasing from thesurface outwards, it accelerates the bubble growth anddetachment, while the opposite occurs for downward orientedsurface. To account for the relative magnitude of this forcereferred to the buoyancy force, a new dimensionless group canbe introduced:

g

EG

gllg

lgleb, ))(2(2

)(3 20

b

E

ρ−ρε+ε

∇εεε−ε==

FF

(7)

For a cylindrical heater, like the one studied herein, thisforce tends to increase the circumferential symmetry of the

5 10 15 20 25 30 35∆T

sat (K)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

q" (M

W/m

2 )

V = 0 kV , µ g

V = 1 kV , µ g

V = 7 kV , µ g

V = 10 kV , µ g

V = 0 kV , 1 g

V = 1 kV , 1 g

V = 5 kV , 1 g

V = 7 kV , 1 g

V = 10 kV , 1 g

Solid symbols: micro-g data Open symbols: ground data

Fig. 6. Boiling curves in normal gravity and in low gravity for different applied voltages, FC72, atmospheric pressure

8

boiling heat transfer and bubbles can detach also from thelower side of the heating surface.

The overall effect of the electric field on nucleate boiling isstill not completely established. The general opinion is eitherthat there is no practical influence or that a little enhancementof the heat exchange takes place (Jones, 1978).

However, Baboi et al. (1968) have reported an increase inboiling performance at low heat fluxes. For higher fluxes, theyhave asserted quite weakly that "there is no effect on therelative heat exchange coefficient, but on further increase ofthe heat flux, the latter decreases somewhat".

For geometries similar to the present one, Cooper (1990)proposed a correlation providing an electric field enhancementof the heat transfer coefficient decreasing with increasing heatflux. This correlation was obtained by fitting old data sets(Baboi et al., 1968; Choi, 1962; Bonjour et al., 1962).

A more recent paper (Uemura et al., 1990), on saturatedpool boiling of R113 on a flat, horizontal, upward facingsurface, reports a little enhancement at very low heat fluxes.Beyond this range of fluxes all the data (with and withoutelectric field) collapse on a single curve.

In the absence of applied electric field, Straub et al (Straubet al., 1990) noted a very weak influence of gravityacceleration on pool boiling on wires. On the contrary, Oka etal (Oka et al., 1995) reported a significant dependence ongravity of boiling heat transfer on flat plates at high heat flux;the surface overheating was also affected by the variation ofdirection of the residual gravity in the micro-g phase. Theimportance of having a statistically meaningful number ofbubbles on the heater in order to be able of dealing withboiling (as a process) is worth stressing once more. Thishappened in our case, as clear from the pictures of Fig.7. Thecontribution of the electric field to this aspect is absolutelyfavourable as it increases the bubble number decreasing theirsize: thus “the heater behaves as a very large (in some casespractically infinite) surface if compared to bubbles diameter”.In addition bubbles can “escape” in any direction from a small(not necessarily a wire) cylinder. All this is generally not truefor a flat heater, where horizontal coalescence is likely tooccur. This, joined with some local field gradient (e.g. at thesurface edge), can make bubbles slide along the surface with abeneficial effect on the heat transfer. Anyway the behaviour offlat surfaces needs a much deeper insight. Among the otherthings it is worth emphasising that they are much more(respect to cylinders) sensitive to g-jitter10 . Thus bubbles canbe either pushed toward the surface or moved away from it.

In conclusion we can state, at present, that according tomost of the studies about fully nucleate boiling (thus not thesingle bubbles region) heat transfer does not exhibit a majorsensitivity to electrical and gravitational forces. As theseforces strongly affect the vapour fluid dynamics, it is possibleto infer that fluid dynamics is not the dominating mechanismin fully developed nucleate boiling.

Technology. In any case the above findings mean that fullydeveloped nucleate boiling is a very effective heat transfermeans also for space applications. This is a very good newsfor space thermal devices improvement, but can we keepboiling stable without buoyancy, i.e. without a force liftingbubbles away from the heating surface? In general the answeris as follows. Steady-state long-term nucleate pool boiling canbe attained in micro-g. The possibility is higher with largersubcoolings and low heat fluxes. A debate is still open on thepossibility of maintaining it indefinitely, and on the roleplayed by fluid properties and size and shape of the solidsurface. At the present state of knowledge it would beadvisable to keep the liquid at least slightly subcooled.Moreover the electric field can help removing vapour from theheater, thus directing vapour towards appropriate regions(vapour management).

10 G-jitter represents the time variation of the acceleration with

respect to its mean value. In parabolic flights it may be of the order ofthe mean value. According to the authors’ experience it is muchlower in sounding rocket (no effect of air turbulence to becompensated, of course) and in drop-shafts.

(A)

(B)

(C)

(D)

(E)

Fig. 7. Vapour patterns vs. gravitational and electric fieldsfor FC72 and wall heat flux of 100 kW/m2:(A) 2g0, 0kV; (B) 1g0, 0kV; (C) 0.02g0, 0kV;(D)0.02g0, 10kV; (E) 1 g0, 10kV.

9

Critical heat flux

The critical heat flux, CHF, represents the maximum valueof heat flux that a boiling surface can “safely” reach, once wallheat flux is the controlled variable. Beyond this point the walltemperature can suddenly and dramatically rise, eventuallycausing the physical burnout of the heater. Therefore it is animportant limit to the boiling performances of any apparatus.To understand the mechanisms leading to CHF and to findappropriate means for improving its value constitutefundamental issues for enhancing the effectiveness of any heatexchange equipment.

Fundamentals - The interpretation of this phenomenon isstill controversial. Several approaches have been attemptedamong which we can recall: the bubble coalescence model(proposed by Rohsenow and Griffith in 1956), thehydrodynamic theory (proposed by Zuber in 1959 andmodified in 1973 by Lienhard & Dhir for finite size heaters),the macrolayer theory, (defined by Haramura & Katto in1983) which anyhow implies the hydrodynamic instability ofvapour stems and the hot spot theory (proposed by Unal et al.,1992). Unfortunately, only the model of the hydrodynamictheory has been extended to the case of boiling with an electricfield (by Johnson in 1968 and refined by Berghmans, 1976).For a detailed discussion on the whole matter the reader canrefer to ( Di Marco & Grassi, 2000a; Di Marco & Grassi,1997; Carrica et al., 1995; Di Marco & Grassi, 1993).

At present, it is unclear if just one mechanism determinesthe occurrence of critical heat flux (CHF) in any geometricaland thermodynamic condition. Regardless of the previously

quoted models, critical heat flux data on flat plates have beenoften correlated in the so-called Zuber-Kutatelatze form

refCHF qKq = (8)

where

( )[ ] 25.05.0gffggref ghq ρ−ρσρ= (9)

In Eq.(8) if the heater is large with respect to the Taylorwavelength, K (often referred to as Kutatelatze number) is aconstant: K can vary in the range 0.119-0.157, and for flatplates was assumed 0.131 by Zuber and 0.149 by Lienhard.

Pool boiling on wires and small bodies has been extensivelystudied in a number of papers in the 60-70s. A non-trivialdependence of critical heat flux on the diameter of the wirehas been reported. The most suitable group to scale the effectof the diameter is the so called dimensionless length, i.e. thesquare-root of the Bond number

L

gf

lRg

RBoR =−

==σ

ρρ )(' (10)

and it is assumed that the factor K is a decreasing function ofR’: K=K(R’). This means that gravity and heater size have asort of interchangeable role, as a change in their value has thesame qualitative effect on R’. Thus “large” heaters become“small” at low gravity and viceversa. For large heaters (R’above a critical value R’c) the proposed mechanism is thevapour – liquid interface instability, that proved to be theleading mechanism also for film boiling. For small heaters(R’<R’c) hydrodynamics no longer dominates the phenomenonand the vapour front propagation mechanism comes into play.

0.01 0.10 1.00R'

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0K

/0.1

31

FC72, 1g, p=0.75

FC72, 1g, p=1.1

FC72, 1g, p=1.6

FC72, 0.02g, p=1.1

FC72, 0.4g, p=1.1

FC72, 1.5g, p=1.1

Hong (1993) FC-72, 1g

R113 data, 1g

Hong (1993) R113, 1g

Elkassabgi (1988) R113, 1g

Sun (1970) correlationHong (1993) correlation

Mohan-Rao (1976) corr., C=1.5

Sun 90% data bounds

Range of R113 micro-g data

Fig. 8. Values of K in Eq.(8) and comparison with available correlations. All the data not countersigned with areference belong to the present authors. The symbol p represents the system pressure in bar

10

In this case the effects of surface tension and liquid and wallthermophysical properties play a major role. For exampleR’c=0.07 – 0.1 was proposed in the past.

Once an electric field is applied it influences the physics ofthe vapour-liquid interface instability. Consequently therelation for the heat flux becomes

uE

u

CHF

ECHF

qq

λλ

= 0"

0,

", (11)

Where λu0, λuE, represent the instability wavelength withoutfield and in the presence of the field, respectively. Accordingto Johnson (1968)

33** 2

0 ++=λλ ElEl

uE

u (12)

with the electric influence number given by

) -(

=

g l

20*

gE

El Ieq

σρρ

εε(13)

where EI is the electric field at the gas-liquid interface and εeqan equivalent relative electric permittivity. The proper value ofεeq to be used mostly depends on the actual physical situation,as discussed in (Di Marco & Grassi, 1994). Equation (12) isstrictly valid for a plane interface only, although it can beextended to cylindrical geometry.

The available CHF data are reported in the K-R’ plane inFig.8 together with the most commonly accepted correlations.It is worth mentioning that a reduction in the Kutatelatzenumber, K, does not directly imply a corresponding reductionin the value of critical heat flux: since qref (a function of fluidproperties) increases with pressure. The overall effect is anincrease of CHF with pressure and a reduction with decreasinggravity .

The space within the two dotted curves represents a furtherlarge amount of data mainly obtained at normal gravity(changing either fluid properties or heater diameters) or in acentrifuge. The symbols with no references are experimentalresults due to the present authors with different gravity levels.It can be seen that the correlation of Sun & Lienhard (1970), is

still acceptable up to R’ = 0.08 although it underestimatesslightly the data for fluorocarbons for high R’. A differentvalue of the constant or of the exponent might yield betterresults. The modification proposed by Hong et al. (1993)provides better results for intermediate values of R’, but worstperformance in the range 0.06 < R’< 0.3.

For R’> 0.08, the data obtained in reduced or enhancedgravity lies in the range of most of the other experimental data.Thus it seems that the Bond number is a suitable parameter toscale the effect of gravity for R’> 0.08. However, it should benoted that the data obtained with higher system pressuresystematically lie below the others: a secondary effect of thisvariable should not be excluded.

The situation appears to be drastically different for R’<0.04:the data obtained in low gravity are very well separated fromthe ones of thinner wires, corresponding to the same value ofR’, obtained in normal gravity. Thus, it must be concluded thatthe Bond number (or the equivalent parameter R’) is not ableto scale adequately both the effects, and separate groupscontaining the gravity acceleration and the wire diameter seemto be needed. Alternatively, the mechanism itself of CHFcould be different in the two situations. The correlation byMohan-Rao & Andrews (1976) is able to fit the data obtainedfor fluorocarbons in microgravity, and could be consideredacceptable up to R’ = 0.2, but it is not able to predict the dataobtained in normal gravity on thin wires for the same fluids.

The trend of critical heat flux data versus the applied highvoltage, for FC72 at atmospheric pressure, are shown in fig. 9.Similar trends have been obtained for R113 and, on ground,for Vertrel XF. These results clearly demonstrate that• CHF is very sensitive to gravity and undergoes a strong

reduction with a decrease of the above acceleration;• the electric field is very effective in improving CHF both

on ground and in low gravity;• for large enough electric fields the values of the critical

heat flux on earth and in weightless conditions becomeindistinguishable.

Figure 10 reports the same data as Fig.9 butadimensionalised with respect to the critical heat flux(corresponding to g0 and to low g) at zero high voltage. Thisallows for concluding that the relative enhancement of CHF is

0 2 4 6 8 10High voltage (kV)

0

200

400

600

800q"

CH

F(kW

/m2 )

micro-g

1 g

Fig. 9. Critical heat flux values vs. high voltage for FC72 onground and in low gravity.

0 2 4 6 8 10High voltage (kV)

0

1

2

3

4

5

q"C

HF /

q" C

HF,

0kV

micro-g

1 g

Correlation, Eq.(14)

Fig. 10. Dimensionless (respect to the corresponding flux at0kV) critical heat flux at low g and on ground vs. theapplied high voltage, for FC72.

11

larger at low g than on earth.The above trends are very well fitted by the following

relation, deriving from hydrodynamic theory, obtained bycombination of Eqs. (11-12)

33 + + =

2**

0

ElElqq

CHF

ECHF (14)

with ) -(

=

g l

20*

gEEl l

σρρεε

(15)

In El*, the electric field E is calculated at a distance fromthe wire of the order of the bubble size. This is done as anattempt to obtain the value of the field actually present at the“liquid-vapour” interface. These conclusions seem to hold forthe whole range of tested acceleration (g/g0=1.5, 1, 0.4 and0.02). The data obtained during a sounding rocket experiment(g/g0=10-4) are still under evaluation. So far these results withelectric field seem to support the validity of the hydrodynamictheory to some extent and for the tested geometry. It is worthrecalling that, in this case, bubbles become much smaller withthe increasing of the field. Thus the ratio between the heatersize and the bubbles one becomes larger. Probably, in thiscase, we should refer to a modified R’, that becomes larger forthe effect of the electric field.

Technology – The importance of the achieved results fortechnology are quite clear. As already said the location ofCHF on the boiling curve defines the extension of the nucleateboiling regime. We established that this region narrows whengravity decreases. Conversely the same region widens with theapplication of an electric field both on ground and inweightless conditions. Therefore the CHF value can becontrolled by simply controlling the applied voltage. Withregard to space it offers an active technique for improving theperformances of some heat transfer equipment with a verylimited energy consumption.

FILM BOILING

Film boiling was studied both for gaining a betterunderstanding of the mechanism leading to CHF and in viewof its technological importance in processes like metaltreatment and power production (e.g. the suppression of filmboiling in large boilers). Very recent data we obtained in lowgravity are being processed at present.

Carrica et al. (1996) performed experiments of film boilingof R113 on a platinum wire, 0.2 and 0.3 mm diameter. For thefirst time, it was clearly identified that the electro-hydro-dynamic (EHD) enhanced film boiling regime cannot besustained indefinitely in this configuration. A second transitiontakes place for large enough wire superheat, bringing thesystem back to a film boiling regime which is practicallyunaffected by the presence of the field. A weak evidence ofthis can be also found in the data by Jones and Schaeffer(1976). Later on, a confirmation that the application of anelectric field has a poor influence on film boiling performanceat high wall superheats was found by Di Marco et al. (1997),who adopted R113 and Vertrel as testing fluids. For both thetested wire diameters, data were obtained in saturated andsubcooled (10 K) conditions, at pressures of 0.075, 0.115, 0.16MPa and with an applied high voltage ranging from 0 to 10kV.

Fig. 12. First film boiling regime, monodimensionaloscillatory pattern; p = 115 kPa; d = 0.2 mm; V = 0kV; q = 400 kW/m2; ∆Tsat = 449 K.

Fig. 13. EHD enhanced film boiling regime,multidimensional oscillatory pattern; p = 115 kPa; d= 0.2 mm; V = 7 kV; q = 400 kW/m2; ∆Tsat = 201 K.

Fig.14. Second film boiling regime, independent of appliedvoltage; monodimensional oscillatory pattern; p =115 kPa; d = 0.2 mm; V = 7 kV; q = 850 kW/m2;∆Tsat = 781 K.

0 200 400 600 800 1000∆ T sat ( K )

0

500

1000

1500

2000

q" (k

W/m

2 )

V = 0 kV

V = 2 kV

V = 5 kV

V = 7 kV

V = 10 kV

D = 0.2 mmp = 115 kPa

Fig. 11. Film boiling curves at different electric field levels.

12

The most striking feature is the clear evidence of a secondboiling transition, separating two distinct film boiling regimes:the first one, at lower wire superheat, was strongly influencedby the presence of the electric field; an increase of the heattransfer coefficient up to 400 % was encountered. The secondfilm regime (taking place at superheats higher than about 550K) was almost unaffected by electrical forces. The transitionpoint moved towards lower superheats with increasing appliedvoltage. All this is shown in Fig.11 for saturated film boilingon a 0.2-mm wire at an operating pressure of 115 kPa. Similartrends were encountered for different pressures, fluids andwire diameters (Carrica et al., 1996; Di Marco et al., 1997;Ciprani et al., 2000)

Visual observation, with the aid of the CCD camera,showed the presence of the following three distinct fluid-dynamic regimes.• For an applied high voltage up to 2 kV, the liquid-vapour

interface had an oscillatory motion and a dominatingwavelength was clearly identifiable (Fig.12).

• With increasing electric field, the wavelength and bubblesize decreased up to a condition in which no dominatingwavelength was identifiable (Fig.13). The oscillatoryphenomenon was likely two-dimensional in theseconditions, with a circumferential oscillationsuperimposing to the axial one. The appearance of theboiling pattern was more similar to the nucleate boilingone. Bubbles started to detach also from the lower part ofthe wire and were of irregular size; lateral coalescencewas observed. The author have also proposed a model forthis transition (Cipriani et al., 2000)

• For high values of the wire superheat, the second filmboiling regime took place (Fig.14). The interfaceoscillated with high values of the wavelength, and bubbleswere larger that in the former two regimes. Thephenomenon was independent of the applied electric fieldin this regime.

Very recently, film boiling regime has been investigatedduring a parabolic flight campaign (Trentavizi, 2001). Thepreliminary data (currently under analysis) indicate that thetwo different regimes persisted even in microgravityconditions. While film boiling at low values of applied electricfield was sensitive to gravity acceleration and it showeddegradation at low values of g, it became insensitive to thevalue of gravity for a high enough applied voltage (over 3 kV).

CONCLUSIONS

In this paper we analysed the main results we achieved sofar about the effect of gravitational and electrical forces onsingle-phase convection and pool boiling heat transfer. Atpresent, mainly due to space and power limitations, only awire geometry was investigated. The outcomes can be veryshortly summarised as follows.♦ Single-phase – It is very much influenced by gravity, as

obvious, as well as by electric fields. The obtained resultscan supply a quite fundamental contribution to theunderstanding of the actual role of the electrical forcesand consequently to improve the existing correlations.Reliable temperature correlations about the temperaturedependence of the electrical properties of the fluids arereally needed to this aim, by means of ad hocmeasurements. For space applications the main result

obtained is the possibility of controlling the heat transfercoefficient by tuning the applied high voltage.

♦ Nucleate boiling – At least for the tested geometry, fullydeveloped nucleate boiling heat transfer is practicallyinsensitive to both the gravitational and electric fields. Onthe other hand the vapour pattern is dramaticallyinfluenced by both of them. This leads to the conclusionthat this regime is not dominated by hydrodynamics. Boththe fields, conversely, act on the extension (heat flux andwall superheat) of the nucleate boiling region, thanks totheir effect on the critical heat flux value.

♦ Critical heat flux – This flux is very sensitive to the twoforce fields examined. It increases both with gravity andelectric fields. As both this forces have an instabilisingeffect on a vapour-liquid interface, this result seems tosupport the hydrodynamic theory, still for the type ofheater tested (geometry, material surface morphologyetc.) and above a certain Bond number. Below this value,the Bond number cannot be considered as the onlyparameter characterising the phenomenon. This is the firsttime that data on this subject are systematically obtainedat different level of acceleration, from low to high gravity.The planned further experimental campaigns in lowgravity on flat geometries will supply some further crucialinformation. The most important feature from thetechnological viewpoint consists in the possibility ofstrongly increasing the CHF value, thus enormouslyimproving the performances of the heat transferequipment.

♦ Film boiling – The related studies confirmed thefundamental action exerted by gravity and electric fieldon the vapour-liquid interface instability, thus givingmany significant pieces of information on thismechanism, that might be fundamental for CHF. Twodifferent film boiling regimes were evidenced: a) one,occurring for lower heat fluxes (and wall superheats)showing a multi-dimensional interface oscillation pattern,with a high sensitivity of the heat transfer process to theelectric forces, b) a second one, for higher heat fluxes,showing a one dimensional interface oscillation regimewhere the heat transfer coefficient keeps quite insensitiveto the electric forces. In microgravity, film boiling inregime a) is quite insensitive to gravity acceleration.

NOMENCLATURE

Bo Bond number, l/lLd wire diameter (m)E electric field intensity (V/m)El* electrical influence number, see Eq.(13)El’ electrical influence number, see Eq.(3)El’’ electrical influence number, see Eq.(4)Fe volumic force (N/m3)g gravity acceleration (m/s2)g0 gravity acceleration, earth value (m/s2)Gr Grashof numberI current intensity (A)K Kutatelatze number, see Eq.(8)lL Laplace length (m)Nu Nusselt numberp pressure (Pa)p pressure (Pa)Pr Prandtl numberq heat flux (W/m2)

13

R radius of the wire (m)r radius (m)R’ dimensionless radius, R/lLT temperature (°C, K)V applied high voltage (V)α heat transfer coefficient (W/m2 K)∆ T temperature difference (K)∆Tsat wire superheat Tw-Tsat (K)ε relative dielectric permittivityε0 vacuum dielectric permittivity (F/m)λu oscillation wavelength (kg/m3)µ dynamic viscosity (Pa s)ρ density (kg/m3)ρΕ free electric charge density (C/m3)σ surface tension (N/m)σΕ electric conductivity (S/m)

Suffixes

0 in the absence of the electric fieldb bubble, buoyancyc criticalCHF peak heat fluxcyl cylinderE in the presence of the electric fieldg vapourI interfacel liquidref referencesat saturatedw heated wall

ACKNOWLEDGEMENTS

Such an activity involved so many people, that it isimpossible to thanks all of them by name. Thus we want tothank all of them as whole, included all our students and ourthird companion Roberto Manetti who followed and assistedus all along our “low gravity adventure”. The fundamentalcontribution of Italian Space Agency (ASI) and EuropeanSpace Agency (ESA), without which this research would notbe possible at all, is gratefully aknowledged.

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