4th Japanese-European Two-Phase Flow Group Meeting Kanbaikan, Kyoto 24 - 28 September 2006

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INTRODUCTION

Foreword

In this paper, the main outcomes of a ten-year research activity on pool boiling in microgravity, carried out at Low Gravity and Thermal Advanced Research Laboratory (LOTHAR) of Pisa University, are resumed. Reference is made also to the other parallel researches on pool boiling in microgravity carried out worldwide. The activity at LOTHAR has been characterized since the beginning by the application of electric forces as a replacement of the lacking buoyancy in microgravity: therefore, a part of the paper deals with the effect of electrostatic fields on boiling. The reported results were obtained in several microgravity experimental campaigns: two in the dropshaft of JAMIC, Japan, four ESA parabolic flights, one sounding rocket (MASER-8), and finally a longer campaign in orbital flight, using the ESA facility FluidPac [1], on the Russian satellite FotonM2. The main features of the above research up to 2001 have been described by Di Marco and Grassi [2].

Boiling experiments in microgravity

The removal of vapor from a heated surface in boiling heat transfer is strongly affected by the buoyancy that lifts the bubbles away from the surface, giving way to fresh liquid to reach it. In the lack of gravity, bubbles reside close to the surface, coalescing in a large mass of vapor that is difficult to condense, due to the low surface to volume ratio, and prevent the liquid to reach the surface. These conditions may lead to impairment of heat transfer performance and anticipated dryout of the surface, precluding application of boiling heat

transfer in micro-g. Several experimental campaigns conducted worldwide, and recently reviewed by Kim [3], Ohta [4] and Di Marco [5] showed the potential of boiling heat transfer in microgravity, along with the limitations outlined above. Due to the space and power constraints, intrinsic in microgravity campaigns, experiments in this field were often limited to small surfaces or low heat rates.

The application of an electric field may provide an additional volume force able to replace buoyancy, to reduce the size of detaching bubbles and to lead them away of the surface, restoring efficient heat transfer conditions. The effectiveness of this technique was already demonstrated by several experiments carried out in microgravity, both in gas-liquid systems [6, 7] and in boiling systems [2,8].

Electric field effects on boiling

The most generally accepted expression for the volumic electric force that acts on a fluid, to be included in the momentum equation, is [9]

20 0

1 1grad grad2 2

re F r

T

E E⎡ ⎤⎛ ⎞∂ ε

=ρ − ε ε + ε ρ⎢ ⎥⎜ ⎟∂ρ⎢ ⎥⎝ ⎠⎣ ⎦F E (1)

Only the first term (Coulomb's force) depends on the sign of the electric field. It is present when free charge buildup occurs and in such cases it generally predominates over the other electrical forces. The following two terms depend on the gradient of the electric field and of the dielectric constant (related to thermal gradients or phase discontinuities), and on the magnitude of E2, thus being independent of the field polarity. In particular, the second term is a body force due to non-homogeneities of the dielectric constant and the third term is caused by non-uniformities in the electric field distribution.

POOL BOILING IN MICROGRAVITY:

OLD AND RECENT RESULTS

Paolo Di Marco

LOTHAR (LOw gravity and THermal Advanced Research laboratory) Dipartimento di Energetica “L. Poggi”, Università di Pisa, via Diotisalvi 2, 56126 Pisa (Italy)

Tel +39-050-2217107 - Fax +39-050-2217150 - e-mail: lothar@ing.unipi.it

Abstract The main outcomes of a ten-year research activity on pool boiling in microgravity, carried out at Low Gravity

and Thermal Advanced Research Laboratory (LOTHAR) of Pisa University, are resumed. A large part of the paper deals with also the effect of electrostatic fields on microgravity boiling, which has been always the main research theme of this group. The reported results were obtained in several microgravity experimental campaigns, mainly during one sounding rocket (MASER-8), and one orbital flight, on the Russian satellite FotonM2, and refer to wire and plate heaters in FC-72, subjected to the action of strongly non-uniform and nearly uniform electrostatic fields, respectively. Long term steady state nucleate boiling seems to be possible in microgravity, especially in subcooled conditions, though impaired bubble removal and coalescence lead to an increase of void fraction, and could degrade nucleate boiling heat transfer and anticipate CHF. It has been shown that the addition of an appropriate electric field widens the nucleate boiling region (increase of CHF) and the heat transfer coefficient becomes almost insensitive to gravity. These effects are more marked on wires than on plates, where, due to the different field geometry, a higher voltage is needed to attain the same effect, and demonstrate the progressive dominance of electric forces over buoyancy.

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It is worth to pay some attention to the derivative ( )/T

∂ε ∂ρ , appearing in the third term of Eq.(1). If the fluid is considered incompressible, coherently this term should be dropped off; this is the approach pursued e.g. by Korteweg and Helmholtz [10]. However, it can be also retained in a sort of analogous of Boussinesq approximation. For non-polar liquids, according to Clausius-Mossotti equation, the derivative can be expressed as

( 1) ( 2)3

r r r

T

⎛ ⎞∂ε ε − ε +ρ =⎜ ⎟∂ ρ⎝ ⎠

(2)

while for gases this term is always very close to zero [9]. No general expression for polar fluids seems to exist, to the author’s best knowledge.

Equation (1) is of little use when an interface (and hence a discontinuity in εr) is present. In this case, it is useful, according to continuum mechanics, to consider the volumic electric force as the divergence the Maxwell’s electric stress tensor

dive e=F T (3)

where the components of Te, according to [9], depend on the local intensity of electric field, the fluid density and its variation with temperature

20

0 2r

ik r i k r ikT

Et E E⎡ ⎤⎛ ⎞ε ∂ε

= ε ε − ε − ρ δ⎢ ⎥⎜ ⎟∂ρ⎝ ⎠⎣ ⎦ (4)

The resulting electric force acting on both sides of the interface S can thus be expressed as

DEP e

S

dS= ⋅∫∫F n T (5)

The electric force can also be included into the local equilibrium equation of the interface, namely [11]

, ,

, ,

' ( ) ( ) ( )( ) 2

A B A B d A d B

e A e B s

m p pK

− = − + ⋅ − +

+ ⋅ − − ∇ σ − σ

v v n n T Tn T T n

(6)

Several effects may arise from the additional normal and tangential electric action on the interface, like increase in bubble internal pressure, bubble distortion, net electric force on bubbles, and alterations of capillary oscillation wavelength.

It must also be considered that the presence of bubbles may substantially alter the local electric field distribution with respect to the one in the absence of bubbles, and also these effects should be carefully evaluated by means of a coupled fluid-dynamic and electrostatic computation. Besides, a correct evaluation of the local value of electric field at the interface relies on the adoption of appropriate boundary conditions on it, and the problem is still debated [12], [13].

Some simplification, however, is possible. In the absence of free charge, and in the limiting assumptions outlined later, the net force acting on a ellipsoidal gas bubble can be expressed as [9]

( )3 2

01 1

grad6 1

rg rfDEP eq rf

rg rf

d En n

ε − επ= ε ε

ε + − εF (7)

The constant n1, which can be calculated with an elliptic integral related to the eccentricity of the bubble, is equal to 1/3 for a perfect sphere, while n1>1/3 for an oblate ellipsoid [9]. This force can be considered to obtain a simple model for bubble detachment in the presence of an electric field, as done for instance by Herman et al. [7], Baboi et al. [14], Danti et al. [15]. It is worth noting that, as E2 is proportional to the electric

field energy, Eq.(7) indicates the tendency of the bubbles to migrate towards the zones of less electrostatic energy.

The validity of Eq.(7), however, stands on several restrictions [8], [16]: the dielectric must be isotropically, linearly and homogeneously polarizable, and both fluids must have zero conductivity; most remarkably, the bubble must be small enough to obtain the amount of polarization by approximating the field as locally uniform. These drawbacks were removed by Karayiannis and Xu [12], Zaghdoudi and Lallemand [13], Cho et al. [17], Iacona et al. [18] who developed more general relationships in the form of Eq.(5).

Another factor to be accounted for is the time required to the electric field in reaching its equilibrium distribution in the medium, which is linked to the diffusion of the electric charge. This is ruled by the so-called charge relaxation equation [19]

( )D 1+ - grad = 0D

FF et

ρρ σ ⋅ τ

τE (8)

where τ = ε0 εr /σe is referred to as charge relaxation time. This time has to be compared with a characteristic one of the system, tc, in this case the bubble cycle period. Although no real fluid is either perfectly conducting or perfectly insulating, if τ >> tc the fluid can be considered insulating, and on the contrary if τ << tc the fluid can be modeled as conducting. To give an order of magnitude, τ is lower than 0.1 s for kerosene and transformer oil, higher than 20 s for R113, and about 150 s for FC-72.

In any case, with some care, Eq.(7) can be retained at least as a first approximation of the dielectrophoretic force on a bubble. If a small bubble is immersed in a liquid of higher electrical permittivity, a net force arises, driving it towards the zone of weaker electric field. This force has generally a little magnitude, however in the absence of buoyancy it might be an important tool for phase separation. The gradient of the square of electric field intensity (grad E2) in the unperturbed liquid is a good parameter for a first characterization of the EF actions on bubbles. It can be used for a first screening of the most suitable EF geometrical configuration, to evaluate the requested voltage and the capability of a particular EF geometry to direct the individual gas bubbles as desired. However, Eq.(7) seems to give zero-force when the bubble is immersed in a uniform electric field, but this situation requires a deeper analysis, as outlined in the following.

When a spherical bubble is immersed in a uniform electric field, due to symmetry, no net electric force acts on it, even though its presence may give rise to local EF gradients. However, the electric stresses acting on the upper and lower hemispheres are opposite and balanced, and this may lead to bubble elongation in the direction of the EF. In this way, the surface-to-volume ratio of the bubble may be altered, increasing the phase-change rate. If the bubble sits attached or close to a surface, however, the asymmetry in configuration may originate a net electric force. Henceforth, despite the simple Eq.(7) might be misleading, it may be concluded that net electric forces on bubbles may arise both in uniform (or nearly-uniform) and nonuniform electric field configurations. These forces may press the bubble towards a surface, or conversely detach it, according to the different EF configurations. In some instances, the forces may be attaching in some regions of the heaters and detaching in others [20]. For instance, the EF distribution is reported in Fig.1 for a bubble in FC-72 (εr= 1.76) under the action of an electric field of 10 kV, applied to a ring electrode 3 mm apart of the surface and parallel to it. The resulting electric force is 1.1 mN, compared to a buoyancy of 5.4 mN. For a fluid of higher dielectric

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permittivity, like HFE-7100 (εr= 7.4), the EF action on a detaching bubble can be dramatic, as illustrated in Fig.2.

The same surface force given by Eq.(5) may act on any interface in two-phase flow, and namely on the one that forms on the heater in film boiling, after CHF. It has been shown, e.g. [22] that the action of electric field destabilizes the interface, so that CHF is delayed [23] and the nature of film boiling changes [24]. Hence, the application of an appropriate electric field may increase CHF safety margins and improve film boiling heat transfer, as demonstrated e.g. in [25].

The discussion above addresses the main problems involved in the design of an efficient EF configuration for boiling heat transfer: while a strong gradients of electric field seem preferable, it is difficult to guarantee this kind of distribution over a large surface without creating “hot” and “cold” spots. Pressing the bubble against the surface may give some advantage, in that the microlayer zone under the bubble is enlarged, and so the evaporation heat transfer across it; on the other hand, hindering bubble escape may lead to a slower relaxation layer disruption (and thus less sensible heat removal) and likely CHF reduction. Last but not least, the electrodes should be configured with appropriate vanes to allow an easy vapor escape, and a voltage as low as possible should be adopted to avoid insulation breakdown and electric discharge.

BOILING EXPERIMENTS ON WIRES

In the following the main experimental results are reported, obtained during the sounding rocket Maser 8 campaign, held in

Kiruna, Sweden, in May 1999 [26]. The availability of such a means of experimentation was a fundamental opportunity of having a quite longer period of low gravity (6 minutes compared with 5 or 10 seconds available in drop-towers and drop-shafts and the 20 seconds achievable during parabolic flight), a low value of residual relative gravity g/g0 (10-5 instead of 10-2 of parabolic flight) and a very good quality of acceleration (i.e. a very small g-jitter).

Table 1. Physical properties of FC-72 at 1 bar. Saturation temperature, °C Tsat 56.6 Surface tension, mN/m σ 8.27 Liquid density, kg/m3 ρf 1619.4 Gas density, kg/m3 ρg 13.4 Liquid specific heat, kJ/kg K cp 1098.4 Liquid dynamic viscosity, mPa μ 0.45 Enthalpy of vaporization, kJ/kg hfg 84.5 CHF on an infinite plate (Zuber), kW/m2 q”CHF 136 Relative dielectric constant @ 25°C εr 1.76

GABRIEL experimental apparatus

The GABRIEL experiment consisted in performing pool boiling tests on a 0.2 mm platinum wire in FC-72 (C6F14) a fluoroinert liquid (its relevant physical properties are reported in Table 1) slightly subcooled and at a pressure of 100 ± 3 kPa. in two twin cells. These two cells were used contemporarily, one with an imposed electric field (cell A, applied high voltage of 7kV) and the other without electric field (cell B). The heating sequence and the geometry were the same in the two cells, and allowed for an immediate comparison between the behaviours of these cells, thus stressing the effect of the electric forces on the process. A sketch of one cell is shown in Fig.3. It consisted of an aluminum box containing the test section. A bellows, connected to this vessel and operated by pressurised nitrogen in the secondary side, compensated for volume variations due to vapour production and thermal dilatation of the liquid. The vessel had two windows to allow for visualisation of the phenomenon by means of a video camera, with appropriate back-illumination. Experiments were

Figure 1. Calculated EF trend for a bubble of 0.86 mm diameter

sitting on a surface, ring electrode, 10 kV applied electric potential.

Figure 2. Detached gas bubble shape for nitrogen flow from an orifice in HFE-7100, with applied external electric field, ring electrode (potential on the upper electrode is reported) [21].

I

Vs

P

T1

T2

Peek Insulating Frame

Heater

High voltage rods (squirrel cage)

Pressurecompens.bellows

N2 Exhaust valve

N2 Injection valve

TEST SECTIONSIDE VIEW

Drain/fill valve

heater/cooler

Heater low voltage supply (5V, 20 A)

Sense wires

HEATER DETAIL0.1 / 0.2 mm Pt wire

Copper capillary pipe 1 mm O.D.Insulated sense wire 45 mm

Cage diameter:60 mm

Cage high voltage supply (0-10 kV)

200 mm

Figure 3. Sketch of the experimental set up for wire

experiment, identical for cells A and B.

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carried out using a horizontal platinum wire of 0.2 mm diameter and 45 mm length, heated by Joule effect (d.c. current) which served as both a resistance heater and a resistance thermometer. The use of such a small test section is due to limitations in space, power and time imposed by flight experiments constraints: a little thermal inertia is required for the test sample in order to acquire a statistically meaningful number of data in a relatively short time.

The electric field was produced applying a d.c. high voltage (up to 7 kV) between the wire and a coaxial 8-rod cylindrical “squirrel cage”, of 60 mm diameter and 200 mm length. The highly non-uniform resulting electric field configuration (see Fig.4) is discussed in [27] and exhibited strong gradients in the proximity of the heating surface.

The bulk liquid temperature in each cell was calculated as the arithmetic mean of the values provided by four sensor (AD590-M) located in the cell. The wire temperature Tw was obtained through its electric resistance R, evaluated as the ratio of the voltage drop ΔV across the wire and the current I flowing in the wire, and a temperature-resistance calibration curve. The heat flux was obtained as the power (ΔV x I) divided by the wire lateral area.

Experimental results

The effect exerted by electrical and gravitational (equivalent) force fields on nucleate boiling on the vapour pattern close to the heater is shown in Fig.5.

Photos a, b, c refer to cell B, i.e. the one in the absence of electric field. In this case, the increase of bubble size due to the acceleration reduction is clearly detectable, passing from photo a to photo b. In this latter picture, the bubbles depart from the wire in any direction: as this behaviour persists with time it demonstrates the existence of both a low value of residual acceleration and a very small g-jitter.

Figure 4. Electric field distribution around the heated wire, for

an applied high voltage of 10 kV.

(a) Cell B (no field) q” = 130 kW/m2, NucleateBoiling at Earth Gravity.

(b) Cell B (no field) q” = 130 kW/m2, at g/g0 = 10-5,Close to CHF.

(c) Cell B (no field) q” = 210 kW/m2, at NormalGravity, Close to CHF.

(d) Cell A (7kV) q” = 510kW/m2, Earth Gravity Closeto CHF

(e) Cell A (7kV) q” = 510kW/m2, Low Gravity(g/g0 = 10-5), Close to CHF

Figure 5. Vapor patterns at different values of gravity and electric

field. Bubble size can be appreciated with reference to the length of the heating wire (45 mm).

- 5 -

The above two photos refer to the same heat flux that, for earth gravity, is located in the nucleate region of the boiling curve, while, in low gravity, corresponds to a condition very close to CHF. This same condition on earth corresponds to photo c, i.e. to a much higher heat flux and to a smaller average bubble size. Conversely the other two photos (d and e) refer to the presence of the electric field (cell A).

Both the photos are associated to a point on the boiling curve very close to the occurrence of CHF. Bubble size is enormously reduced and is practically the same regardless of the acceleration value. For this value of applied high voltage (7kV), the achievable critical heat flux is the same, as shown in the pictures’ labels. An identical behaviour of the vapour pattern (big bubbles in low gravity and significant bubble size reduction due to the electric field) can be observed in the whole nucleate boiling region. This is a further confirmation of previous observations by LOTHAR in parabolic flight (g/g0=10-2) [28] and is also in agreement with those done by other authors in low gravity without electric field and on earth with and without electric fields. The problem of how this vapour pattern modification reflects on the heat exchange is a

crucial one. The boiling curves obtained before and during the sounding

rocket flight are reported in Fig.6 (a) and (b). Fig.6a refers to cell B (photos a, b, c of Fig.5) and thus to the absence of electric field. The two curves (at normal g and in low gravity) almost coincide, apart for a little shift of the low gravity curve towards higher wall superheats in correspondence of the highest heat flux. On the contrary, the extension of the boiling curve is heavily influenced by gravity, in the sense that a reduction in the acceleration produces a decrease in the critical heat flux. A discussion on the influence of the electric field and gravity on CHF can be found in [29], [30]. The change in the vapour pattern shown in Fig.5 does not seem to exert any influence on nucleate boiling heat transfer, while it seems to be somehow correlated to the heat exchange in the region of the highest heat fluxes and to the achievable value of CHF. Figure 6b, referring to cell A (photos d and e of Fig.5), describes the same situation in the presence of the electric field. The large extension of the nucleate boiling regime caused by the application of the electric field is clearly visible and, in the present case, is the same independently of the gravity acceleration. At the same time, the two boiling curves are almost coincident, without the already discussed shift of the low gravity curve at the highest fluxes. The values of the applied voltage (0 and 7 kV) have been chosen in order to stress the phenomena as much as possible. They are somehow “extreme”, in the sense that the voltage of 7 kV, in the present case, is such that the electric forces are absolutely prevailing on the gravity ones. For intermediate values of electric fields this heat transfer degradation can be followed, at higher heat fluxes by an enhancement of the heat exchange due to the field. In other words, the two curves (with and without applied field), having different slopes can cross one another. What discussed above is in agreement with previous findings in parabolic flight, discussed in [28] for R113 and in [27] for FC-72.

BOILING EXPERIMENTS ON PLATES

After having used wires to demonstrate the feasibility of EHD-enhanced boiling in microgravity, the interest was directed towards heaters of industrial relevance, namely flat plates. In particular a heating surface 20x20 mm was selected. Only Lee and Merte [31] and Ohta [4] had used before heaters of similar or larger size, but never at so high heat fluxes (up to 200 kW/m2). Precursory experiment in parabolic flight (see Fig.7a) demonstrated that generally, the heat transfer coefficient decreased in microgravity, except for a small band of values around 10 kW/m2, where a small increase in micro-g was encountered. In particular, a strong degradation in microgravity for heat flux greater than 30 kW/m2 was encountered. With an applied potential of 5 kV, the variation of heat transfer coefficient at high heat fluxes are less marked, see Fig.7b; in particular, far less degradation than in the former case can be noted at heat flux of 30 and 40 kW/m2. On this basis, with the sponsorship of ESA, a new apparatus, ARIEL, was designed for an orbital flight experiment.

ARIEL experimental apparatus

The ARIEL apparatus, shown in Fig.8, contained a 10 mm thick plate of zinc sulphide (ZnS) of 50 mm diameter, inserted in an aluminum container of about 1 liter volume. The entire facility had an overall mass of about 9.5 kg. The container was provided with a glass window and an illuminating system which allowed for the visualization in the visible range from

0 5 10 15 20 25ΔT

sat (K)

0

50

100

150

200

250

q" (k

W/m

2 )

micro-g

Curve 3

MASER8 FLIGHT 14/05/99(a) Cell B, V=0 kV

0 5 10 15 20 25ΔT

sat (K)

0

100

200

300

400

500

600

q" (k

W/m

2 )

normal g

micro-g

MASER8 FLIGHT 14/05/99(b) Cell A, V=7 kV

Figure 6. Boiling curves for FC-72 at normal and at reduced

gravity (g/g0=10-5). a) In the absence of electric field. b) In the presence of an applied high voltage of 7kV.

- 6 -

the lateral side. The active heating element consisted of a square layer of 20x20 mm, with a thickness of gold of 40 nm, deposited by sputtering over a ZnS substrate. The gold layer was transparent to visible light but not to IR radiation, while the ZnS was transparent in both radiation ranges. In this way, images of the boiling patterns in the visible range and of surface emission in the IR range could also be obtained from the lower side of the apparatus.

The gold layer was electrically heated by dc current, (up to

13 A) achieving heat fluxes up to 200 kW/m2. The voltage drop across the gold layer was monitored via two sense wires soldered at its sides. The heating element proved to be very adherent to ZnS and resistant throughout repeated series of tests; no significant degradation of the coating and of its electrical properties was observed. The upper side of the heater was facing a pool of FC-72. The fluid was thoroughly degassed before the filling of the apparatus, which was sealed. Also in this case a bellows, connected to the main vessel, was operated by pressurized nitrogen in the secondary side, in order to compensate for volume variation due to thermal dilatation and vapor production, and to keep the pressure constant at 100±3 kPa (corresponding to a saturation temperature of 56.6±0.8°C for FC-72). An external electrical heater and a plate heat exchanger allowed for the heat removal and the set up of the bulk fluid temperature, which was regulated within ±0.5 K before the start of each test. Other measurements included the pressure in the cell, by means of an extensimetric transducer, and the fluid bulk temperature, obtained as the average of the output of two AD-590M transducers placed inside the cell at 3 mm and 10 mm from the heater, respectively. A Pt-100 sensor, stuck on the external surface of the ZnS plate, monitored its temperature.

The average temperature of the heating surface, Tw, was evaluated by making use of a linear relationship between the heater electrical resistance and its temperature, where the coefficients R0 and α were determined via experimental calibration during the setup of the apparatus, and checked by means of a short standard test before each power step.

The determination of the actual heat flux through the boiling surface is affected by the geometrical configuration of the heater. In fact, due to the relatively high conductivity of the ZnS substrate (k = 16.7 W/m K, similar to stainless steel), a significant fraction of the heating power may follow alternate paths, consisting of conduction throughout the ZnS plate and removal by natural convection from the sides of the plate; in microgravity, due to the lack of buoyancy, natural convection is replaced by transient conduction in the fluid, and this effect is negligible. A computer model of the heating plate has been set up to correct the heat flux value [32].

The electrostatic field was imposed by means of a grid of five stainless steel rods, 1 mm in diameter, laid parallel to heater, at a distance of 5 mm from it (from rod axis to plate). The grid was connected to a high voltage power supply, able to provide up to 10 kV dc. The electric field distribution in the unperturbed liquid close to the heating surface (see Fig.9) was nearly uniform, the gradients being due to the spacing among the rods: it had been completely uniform in the case of a solid plate facing the heater.

A preliminary analysis of part of the experimental data is reported in [32, 33]. The results reported herein are referred to a bulk temperature of 40 and 44°C (16.6 and 12.6 K of subcooling).

Experimental results

Terrestrial conditions The boiling curve in normal gravity, for a subcooling of

12.6 K, without electric field is reported in Fig.10. In the present geometrical configuration, in terrestrial conditions the electric field is rather ininfluential on the boiling performance, except for a slight delay of the onset of nucleate boiling. Critical heat flux was never reached in terrestrial gravity: the classical Zuber-Kutatelatze correlation, corrected with the Ivey-Morris correlation to account for subcooling [34], shows

Figure 8. Sketch of the ARIEL apparatus.

HV0

0.1

1

10

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

alph

a (k

W/m

²K)

HF 5 kW/m²HF 10 kW/m²HF 20 kW/m²HF 30kW/m²HF 40 kW/m²

1 g 1.8 g micro-g 1.8 g 1 g

(a)

HV5

0.1

1

10

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

alph

a (k

W/m

²K)

HF 5 kW/m²HF 10 kW/m²HF 20 kW/m²HF 30kW/m²HF 40 kW/m²

1 g 1.8 g micro-g 1.8 g 1 g

(b)

Figure 7. Heat transfer coefficient (alpha) vs. time in parabolic flight, for various values of the heat flux (HF) in the absence (a) or in

the presence (b) of electric field (5kV).

- 7 -

that it should be located around 210 kW/m2, i.e. above the maximum achievable heat rate.

The boiling flow patterns for a heat flux of 88 kW/m2 are reported in Fig.11: as they are steady, only one picture is included, from side and bottom, respectively.

Microgravity conditions The boiling curves in microgravity, for different values of

the applied electric potential, are shown in Fig.12. It can be noted that in microgravity the average wall superheat is anyway larger than in terrestrial conditions. Another very peculiar feature is the scatter of the wall superheat, present in the absence of electric field, or for low values of it. This periodic behavior induces also small pressure oscillations in the cell, which cannot be dampened by the regulation system. The oscillations of average surface temperature are well correlated with the flow patterns, as shown in Fig.13: in particular, this behavior is caused by the presence of a large mass of vapor, cyclically spreading and collapsing over the surface, and it can be noted that the departure of the vapor mass corresponds to a drastic quenching of the heated surface, followed by a progressive overheating corresponding to increasing coalescence of the nucleated bubbles over the surface. For the highest value of the electric potential, the amount of vapor is much reduced, and the scatter disappears. This can be observed in the plots reported in Fig.12. It can be seen also how the size of the coalesced mass of vapor gradually increases up to reach a size comparable with the heater, see Fig.14: it can be appreciated how even a low value of the

0 40 80 120ΔTsat , (K)

0

50

100

150

200

q",(k

W/m

2 )

Figure 10. Boiling curve in terrestrial gravity, for ΔTsub = 12.6 K, no

electric field.

0 40 80 120ΔTsat , (K)

0

50

100

150

200

q",(k

W/m

2 )

(a)

0 40 80 120ΔTsat , (K)

0

50

100

150

200

q",(k

W/m

2 )

(b)

0 40 80 120ΔTsat , (K)

0

50

100

150

200

q",(k

W/m

2 )

© Figure 12. Boiling curves in microgravity, ΔTsub = 12.6 K, for no EF

(a), HV= 1kV (b), HV = 10 kV (c).

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5x 10-3

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10-3

x, (m)

y, (m

)

FIGURE 9. Trend of the electric field in the unperturbed liquid

(isopotential lines and arrows indicating field intensity).

20 mm 20 mm

Figure 11. Boiling flow patterns in normal gravity (q”=88 kW/m2, no electric field)

- 8 -

applied potential is sufficient to drastically reduce the presence of uncondensed vapor, at least for low values of heat flux. For HV=10 kV, nearly the same boiling pattern as in terrestrial gravity (compare Figs.11 and 15) is got.

Several previous experiments, e.g. [31], [35] showed that in microgravity bubbles keep on detaching from the surface, but are hardly removed far away from it, due to the lack of buoyancy. The boiling pattern in microgravity thus consists of a large bubble, of approximately the same size of the heater, originated by coalescence and residing few millimeters apart of the heater surface, engulfing the bubbles originated from the heater. On one hand, the action of this big bubble removes the vapor from the surface, on the other hand its behavior becomes more and more erratic with increasing size. The images taken through the surface and shown herein (Fig.13) support the idea that this big bubble cyclically spreads over the surface and collapses, causing temperature oscillations. Eventually, the bubble keeps staying steadily in contact with the heater, causing its dryout and consequent heat transfer degradation.

From the analysis of the images, it is actually difficult to discern whether the surface underneath the large vapor mass is actually wetted or less: according to the reported values of temperature, at least periodic contacts of the liquid with the surface should occur, otherwise the surface overheating should rise to higher values, as demonstrated by ground experiments carried out on a breadboard equipped with the same heater at higher heat rates [36]. It appears reasonable to infer that the extent of liquid-wall contacts is progressively reduced, thus causing a gradual heat transfer degradation rather than a sudden crisis.

The presence of a boiling transition in microgravity is quite evident in Fig.12. Its occurrence is not as sudden as a critical heat flux transition in normal gravity, and the values of wall overheat after the transition are quite low compared with the usual film boiling ones in terrestrial gravity. Actually, a change in slope, rather than a jump in wall superheat, is observable in Fig.12; a discontinuity is present only for the highest applied voltage, 10 kV (Fig.12c). The effect of electric field in deferring the crisis to highest heat flux can be appreciated. For low or no electric field, the change of slope is associated with the disappearing of wall temperature oscillations, which means that the large bubble is not periodically hovered and the surface is no more quenched by the incoming liquid. This is illustrated in Figs.16-17. For the applied potential of 10 kV, on the contrary, the jump is determined by the sudden disruption of the nucleate flow pattern, as reported in Fig.18, and the transition is quite similar to the “terrestrial” one. In both cases, the oscillatory behavior is absent after the transition.

The heat transfer coefficient (referred to the wall superheat, as usual in boiling) is plotted in Fig.19, for terrestrial and microgravity data, and for different values of electric field. As the electrical field is nearly ineffective on ground, for terrestrial data only the series at 0 kV is reported. It may be noted that the application of an electric field above 5 kV increases the heat transfer coefficient over the terrestrial value for low heat flux, and delays the boiling transition.

In the same figure, the data are compared with the VDI Heat Atlas correlation (VDI, 1993)

39

40

41

42

43

44

45

46

47

48

49

1003298 1003299 1003300 1003301 1003302 1003303 1003304 1003305t [s]

ΔTs

at [

K]

Figure 13. Association between boiling patterns and surface temperature trend, q”= 88 kW/m2, no electric field.

HV = 0 kV HV = 1 kV HV = 10 kV

20 mm 20 mm 20 mm

q”= 63 kW/m2

q”= 88 kW/m2

q”= 100 kW/m2

q”= 138 kW/m2

q”= 163 kW/m2

Figure 14. Side views of boiling (at maximum void fraction) for different values of heat flux and electric field: HV = 0 kV (left), HV =

1 kV (center), HV = 10 kV (right).

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0.3

,

" where 0.9 0.3"

m

nb

nb ref ref crit

h q pm h q p

⎛ ⎞ ⎛ ⎞= = −⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠

(9)

where hnb,ref is a reference value, experimentally determined for the heat flux q″ref. (100 kW/m2 in the present case) A very good agreement is obtained with the coefficient m given by the correlation (m = 0.774) for terrestrial conditions, and the fit is also acceptable at intermediate heat fluxes for micro-g data. 20 mm 20 mm

Figure 15. Boiling flow patterns in reduced gravity

(q”=88 kW/m2, HV = 10 kV)

20 mm 20 mm

q”= 100 kW/m2

20 mm 20 mm

q”= 150 kW/m2

Figure 16. Bottom views of boiling flow pattern before and after transition, at minimum (left) and maximum (right) void fraction, for

no electric field

20 mm 20 mm

q”= 113 kW/m2

20 mm 20 mm

q”= 163 kW/m2

Figure 17. Bottom views of boiling flow pattern before and after transition, at minimum (left) and maximum (right) void fraction, for

HV = 1 kV

20 mm 20 mm

q”= 163 kW/m2 q”= 188 kW/m2

Figure 18. Bottom views of boiling flow pattern before and after transition, for HV = 10 kV

80 120 160 200q", (kW/m2)

1000

2000

3000

4000

5000

h sat, (

W/m

2 K)

HV = 0 kV, micro-gVDI corr., micro-gHV = 1 kV, micro-gHV = 5 kV, micro-gHV = 10 kV, micro-gHV = 0 kV, terr. gVDI corr., terr. g

Figure 19. Heat transfer coefficient in terrestrial and microgravity conditions, for ΔTsub = 16.6 K. Values for different applied electric

fields are plotted for microgravity data.

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CONCLUSIONS

The influence of gravity and electric field on nucleate pool boiling is described in the paper. In a first instance, experiments on a wire immersed in FC-72 were performed to demonstrate the feasibility of the technique in GABRIEL facility. In this case, a strongly non-uniform electric field, taking advantage of the cylindrical geometry, was adopted. In a second time, the attention was focused on a flat surface, of greater practical interest, and in this case only a nearly uniform electric field could be applied (ARIEL facility). The main conclusion that can be drawn from this study are shortly summarized as follows.

Gravitational and electric forces heavily affect the vapor pattern close to the heater. A reduction in gravity determines an increase in bubble size, while the application of an electric field lowers their size and increases bubble detachment frequency. In the absence of electric fields, the reduction of gravity causes only minor changes (almost negligible in wire geometry) in the nucleate boiling heat transfer coefficient, but dramatically reduces the extension of the nucleate boiling region, owing to a reduction of the critical heat flux.

The observation and comparison of the boiling patterns showed that void fraction in microgravity was increased with respect to terrestrial conditions. Bubble coalescence was eased, due to their low escaping velocity, and consequently the re-condensation of the vapor in the bulk subcooled fluid was impaired due to the reduced surface-volume ratio of the bubbles. On a plane surface, though nucleate boiling still took place in micro-g, its performance was partially degraded, and an oscillatory behavior of the surface temperature occurred due to the periodical growing and hovering of a large vapor mass above it.

In other terms, improving vapor removal away of the heater and avoiding bubble coalescence seem to be the major problems in microgravity, while bubble detachment takes equally place. In any case, long term steady state nucleate boiling seems to be possible in microgravity, especially in subcooled conditions.

The addition of an appropriate electric field widens the nucleate boiling region (increase of CHF) and the heat transfer coefficient becomes almost insensitive to gravity. These effects are more marked on wires than on plates, where, due to the different field geometry, a higher voltage is needed to attain the same effect, and demonstrate the progressive dominance of electric forces over buoyancy.

In particular, the main effects of electric field application are: • Reduction of overall void fraction, even at low values of

imposed voltage, due to reduction of bubble coalescence; • increase of boiling heat transfer coefficient on plates, at

higher values of applied voltage; • increase of critical heat flux.

The importance of these effects may vary depending on various factors, including geometry, subcooling and fluid nature. At the highest value of the applied electric field, bubbles were easily removed from the surface, and a boiling performance quite similar to terrestrial one, and in some instances even better, was restored.

ACKNOWLEDGEMENTS

The use the electric field in microgravity boiling is originally conceived by Prof. Walter Grassi, who introduced the author in the research environment, and namely in the microgravity field; his contribution and his support is gratefully acknowledged.

This work was funded by ESA under MAP AO-099-045 contract.

NOMENCLATURE

E, E electric field intensity (V/m) F, F force (N) g gravity acceleration (m/s2) h heat transfer coefficient (W/m2 K) HV applied high voltage (V) I electric current (A) n normal unit vector k thermal conductivity (W/m K) K surface curvature (1/m) p pressure (Pa) q” wall heat flux (W/m2 K) R heater electric resistance (Ω) Ro heater electric resistance at ref. temperature(Ω) S surface (m2) T temperature (°C) T0 reference temperature (°C) Tbulk fluid bulk temperature (°C) Tsat saturation temperature (°C) Tw wall temperature (°C) T Maxwell’s stress tensor (Pa) t time (s) V voltage (m3) v velocity (m/s) ΔTsat wall superheat, Tw-Tsat (K) ΔTsub fluid subcooling, Tsat-Tbulk (K) ε0 vacuum dielectric permittivity (F/m) εr relative dielectric permittivity ρ density (kg/m3) ρF free electric charge density (C/m3) σ surface tension (N/m) σe electrical conductivity (S/m) Suffixes D detachment DEP dielecrophoretic e electric g gas f liquid ref reference nb nucleate boiling

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