Bubble spreading during the boiling crisis: modelling and experimenting in microgravity

0.35 MB·

by  Vadim Nikolayev

To be published in Microgravity Science and Technology
Presented at ELGRA Symposium at Santorini, Greece 21-23/09/2005
Bubble spreading during the boiling crisis: modelling and experimenting in
microgravity
V. Nikolayev,1,2,∗ D. Beysens,1,2 Y. Garrabos,3 C. Lecoutre,3 and D. Chatain1
1ESEME, Service des Basses Temp´eratures, DRFMC/DSM/CEA-Grenoble,
17 rue des Martyrs, 38054 Grenoble Cedex 9, France
2CEA-ESEME, ESPCI-PMMH, 10, rue Vauquelin, 75231 Paris Cedex 5, France
3CNRS-ESEME, Institut de Chimie de la Mati`ere Condens´ee de Bordeaux,
Universit´e de Bordeaux I, Avenue du Dr. Schweitzer, 33608 Pessac Cedex, France
6 (Dated: January 29, 2016)
1 Abstract
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Boiling is a very efficient way to transfer heat from a heater to the liquid carrier. We discuss the boiling crisis, a transition
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between two regimes of boiling: nucleate and film boiling. The boiling crisis results in a sharp decrease in the heat transfer
n rate, which can cause a major accident in industrial heat exchangers. In this communication, we present a physical model of
a
the boiling crisis based on the vapor recoil effect. Under the action of the vapor recoil the gas bubbles begin to spread over
J
theheaterthusforming agerm forthevaporfilm. Thevaporrecoil force notonlycauses itsspreading, it alsocreates astrong

8 adhesion to the heater that prevents the bubble departure, thus favoring the further spreading. Near the liquid-gas critical
2 point,thebubblegrowth isveryslowandallows thekineticsofthebubblespreadingtobeobserved. Sincethesurface tension

is very small in this regime, only microgravity conditions can preserve a convex bubbleshape. In theexperiments both in the
]
n Mir space station and in the magnetic levitation facility, we directly observed an increase of the apparent contact angle and
y spreading of thedryspot underthebubble. Numericalsimulations of thethermally controlled bubblegrowth show thisvapor
d recoil effect too thusconfirming our model of the boiling crisis.
-
u
l I. INTRODUCTION of the heater. The recent revival of the interest to the
f
. microgravityboilingingeneralandtoBCinparticularis
s
c relatedto the developmentof the engine [3]of the upper
si Duringthenucleateboiling,separategasbubblesform stage of Ariane 5 launcher that will need to be restarted
y at the heater surface. The liquid phase of the fluid is under microgravity conditions.
h
p thus in the direct contact with the heater and the heat The boiling can be very different since it is dependent
[ transferrateisverylarge. Thisfeatureexplainsthe high onmanyparameterslikesystempressure,presenceofthe
technological importance of boiling in the applications externally imposed fluid flow, temperature in the fluid
1 where the high rate cooling of the heater surface is re- bulk that can be at saturation or below, thermophysical
v
quired. Besides the nucleate boiling, another regime of propertiesofthefluidandtheheateretc. Inallcases,BC
3
7 boiling exists: film boiling. During the film boiling, the begins in a verythin fluid layer(adjacent to the heater),
6 heater is covered by a quasi-continuous gas film. This the thickness of which is small in comparison with the
7 film thermally insulates the heater from the liquid and bubble size. The phenomena at this scale “feel” only
0 the heat transfer rate is much smaller than in nucleate the averaged values of macroscopic flow variables and
1. boilingregime. Thetransitionfromnucleatetofilmboil- thus do not depend on details of the flow regime which
0 ing thus causes a sharp loss of the heat transfer and the should not thus change the BC mechanism. However
6 heater can melt down if the heating power is not con- the contributionof the microscalehydrodynamicmotion
1 trolled. This transition is called “Boiling Crisis” (BC), (thatcanchangeinmagnitudewiththesystempressure,
v: or “CHF phenomenon” since it occurs when the heat see below) to the BC triggering is still unclear.
i flux q from the heater attains a threshold value qCHF
X For the reasons of industrial importance, boiling is
called “Critical Heat Flux” (CHF) [1, 2]. In spite of the
r considerableamountofstudiesdevotedtothisimportant mostly studied at low pressures comparing to the crit-
a ical pressure p (the pressure of the gas-liquid critical
phenomenon,itsmechanismisnotwellunderstood. This c
point) of the fluid under study, e.g. for water or freonat
difficulty originatesfromthe violence ofthe fluid motion
atmospheric pressure. q is then large (of the order
duringtheconventionalboilingthatontheonehandcon- CHF
of several MW/m2 for water) and the boiling close to it
cealsthemechanismsofbubblegrowthfromdetailedob-
is indeed extremely violent. However, it is well known
servation, and on the other hand hugely complicates di-
[1] that q decreases at high pressures where BC can
rect numerical simulations. Most still unanswered ques- CHF
thus be observed at a smaller heat flux. In addition, the
tions concern close vicinity of the heating surface, down
thermal diffusivity is smaller in this regime, the bubble
tothescaleofthefootofabubblegrowingatthesurface
growthslowsdown,andtheopticaldistortionsdisappear
duetotheslownessofthefluidmotion. Fromthepointof
view of the modelling, this slowness permits to simplify
∗email: [email protected]: [phone] the problem by neglecting the hydrodynamic stresses at
fax: [phone] the bubble interface,the shape ofwhichcanthenbe cal-
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culated in the quasi-static approximation. A numerical simulation [10] of such a process requires
solvingofcoupledthermalconduction(bothinsolidand
liquid) and capillary problems. The capillary problem
II. FORCE OF VAPOR RECOIL AND BUBBLE includes a solution for the bubble shape in the quasi-
SPREADING staticapproximationinwhichthelocalbubblecurvature
K is defined by the modified Laplace equation Kσ =
Severalgroups[4–6]proposedthevaporrecoilinstabil- ∆p+P . The bubble shape can be determined from the
r
ity [7] as a reason for BC. Although they did not make functionK =K(l)(Fig.2). ∆pistheconstantdifference
clearwhyandhowthisinstabilitycaninducethespread- ofthe pressuresinthe bubble andin the restofthe fluid
ingofadryspot,theseauthorsshowthatthevaporrecoil and σ is the surface tension. P and then K vary along
r
can be an important factor. the interface and attain their maxima near the line of
Every fluid molecule evaporated from the liquid in- the triple contact liquid-gas-solid. Since curvature is the
terface causes a recoil force analogous to that created first derivative of the angle formed by the tangent to
by the gas emitted by a rocket engine. It pushes the the bubble interface and the horizon, the large K means
interface towards the liquid side in the normal direc- thatthis anglevariesstronglynearthe contactline. The
tion. This force appears because the fluid necessarily apparent contact angle θ measured at some distance
ap
expands while transforming from liquid to gas phase. from the contact line can thus deviate strongly from its
Obviously,the strongerthe evaporationrateη (massper actual value θ imposed at the contact line, see Fig. 2.
eq
timeandinterfacearea),thelargerthevaporrecoilforce.
The vapor recoil force per unit interface area reads [7]
P = η2(ρ−1−ρ−1), where ρ (ρ ) signifies liquid (gas) (cid:8)
r V L L V
density. (cid:8)(cid:10) (cid:9)(cid:14)(cid:15)(cid:3)(cid:14)(cid:16)
(cid:1)(cid:0)(cid:2)(cid:4)(cid:5)
(cid:11)(cid:17)(cid:18)(cid:19)(cid:20)
(cid:7)(cid:3)(cid:7)(cid:7)(cid:9)(cid:6)
(cid:11)(cid:12)(cid:13)
(cid:22)
(cid:21)(cid:10) (cid:21)(cid:10)
vapor
recoil
force bubble FIG. 2: Apparent (θap) and actual (θeq) contact angles. The
l solid circle indicates the contact line, the zero point for the
r
curvilinear coordinate l measured along the bubble contour.
Thearrowsshowthedirectionsofthevaporrecoilforceinthe
heater
vicinity of the contact line and its vertical component that
creates an additional adhesion of the bubbleto the heater.
The time of residence of a vapor bubble on the heater
FIG. 1: Sketch illustrating the vapor recoil effect. The am-
isanimportantparametersincethebubblemightsimply
plitude and direction of the vapor recoil force are shown by
arrows. Thethicknesslr ofthebeltonthebubblesurface, in departfromtheheaterbeforehavingtimetospread. The
whichthevaporrecoilforceisimportant,isexaggeratedwith determination of the residence time requires the forces
respect to thebubblesize. acting on the bubble to be analyzed. Such an analysis
[11]showsthatthe vaporrecoilcreatesanadditionalad-
Let us now consider a growing vapor bubble attached hesionthatpreventsthe bubble departureassoonasthe
to the heater surface (Fig. 1). While the temperature bubble spreading begins, i.e. when the vapor recoil be-
of the vapor-liquidinterface is constant and equal to the comes important. This adhesion force can be obtained
saturationtemperature for the givensystem pressurefor by integrating the vertical component Pv of P~ (Fig. 2)
r r
the pure fluid (see the discussion in [2, 8, 9] and refer- over the bubble interface.
encestherein), astrongtemperaturegradientformsnear The thermal problem is extremely delicate since most
the heating surface. The liquid is overheated in a ther- of heat transfer occurs at a scale l much smaller than
r
mal boundary layer, and the heat flux q at the bubble the bubble size. Extremely fine meshing is thus needed
L
surface is thus elevated in a “belt” of the bubble surface toobtainthecorrectvaluesofthefluxesnearthecontact
adjacentto the bubble foot. As a matter offact, mostof line. Another difficulty appears since the position of one
theevaporationintothevaporbubbleisproducedinthis of the solution domain boundaries, that is of the bubble
belt, whose thickness l is much smaller than the bubble interface, is not known in advance and depends (trough
r
radius. Since η ≈q /H, where H is the latent heat, the P ) on the solution of the thermal problem itself. The
L r
vapor recoil near the contact line is much larger than at solution of the full problem thus needs to be found by
the other part of the bubble surface. Consequently, the time-consuming iterations.
bubble should deform as if the triple contact line were The simulated bubble growth is presented in Fig. 3.
pulled apart from the bubble center as shown in Fig. 1. It can be seen that the dry spot is initially very small
Therefore, under the action of the vapor recoil the dry andremainssoduringthe initialgrowthstage. Atabout
spot under the vapor bubble should spread so that the 180 ms the dry spot begins to grow suddenly, i.e. the
bubble will cover the heater surface. bubble spreads. Such a spreading represents the begin-
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50ms 150ms 200ms Another particularity of the near-criticalsystems con-
sists in the symmetry of the co-existence curve (temper-
aturedependence ofρ andρ ) withrespecttothe crit-
L V
icaldensity ρ : (ρ +ρ )/2=ρ . When the averagecell
c L V c
density is equal to ρ , the gas volume remains constant
dry spot c
and equal to one half of the cell volume throughout the
300ms 450ms 500ms
heating. The gas mass howeverincreases (and the liquid
massdecreases)duringtheheatingbecauseofthedensity
change. This makes the optical observations even more
convenient.

Tsat Tsat+30° Tsat+60°
(cid:31)
FIG.3: Vaporbubblespreadingundertheinfluenceofvapor
recoilsimulatedforwaterat10MPa. Thecolorindicatesthe
N=0.01 N=0.5 N=1.0
localtemperaturewithrespecttothesaturationtemperature (cid:25)(cid:26)(cid:27)(cid:28)(cid:27)(cid:29) (cid:25)(cid:26)(cid:27)(cid:28)(cid:30) (cid:25)(cid:26)(cid:29)
Tsat =311◦C; q=0.1 MW/m2.

(cid:24) (cid:23)
ning of formation of the gas film characteristic for BC.
The apparent contact angle grows sharply while θ is
eq
maintained to be zero throughout the simulation. Zero
FIG. 4: Snapshots of the vapor bubble (V) growing in near
value was chosen because the wetting case is most com- critical liquid (L), both experimental (a) and calculated (b)
mon. Theeffectisevenstrongerforlargercontactangles for the given valuesof thevapor recoil strength N. The zero
wherethedryspotexistsfromtheverybeginning. Fig.3 valueoftheactual contact angle isimposed while theappar-
also shows the formationof a hot spot at the heater sur- ent contact angle attains a large value.
face in the middle of the dry area. This temperature
rise illustrates the alreadydiscussedblocking of the heat
Two series of experiments were carriedout up to now.
transfer by vapor.
Thefirst[8]usedSF fluidonboardoftheMirspacesta-
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tion in the ALICE-2 apparatus designed by the French
CNES agency. The choice of SF is made for practical
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III. EXPERIMENTS IN REDUCED GRAVITY reasons: the critical point of this fluid is T = 45.6◦C,
c
p =38 bar and requires much less severe conditions for
c
◦
To overcome the experimental difficulties encountered theexperimentthanforexamplewater(374 C,220bar).
during the observationsof BC atlow pressures,we carry Some of the results of this experiment are presented in
out our experiments at very high pressures,in the vicin- Fig.4a. Thesequentialphotosofthegrowingvaporbub-
ity of the critical point. We take advantage of the so- ble are takenthroughthe transparentbases of the cylin-
called “critical slowing down” observed near the critical drical cell, the lateral copper walls of which are being
point. In fact, due to the smallness of the thermal diffu- heated. Spreadingof the dry spot under the bubble sim-
sivity,thegrowingprocessofasinglevaporbubble could ilar to that in Fig. 3 can be seen.
be observed during tens of minutes thus allowing for a The bubble shapes calculated for different values of
very detailed analysis. The CHF value is also vanishing the vapor recoil strength N = R Pr(l)dl/σ (where the
at the critical point [1] so that BC can be examined at integration is performed along the bubble contour) are
a small heat flux q that does not necessarily induce a presented for comparison in Fig. 4b. Only the capillary
strong fluid motion which might hinder the optical ob- problem was solved using θ = 0 as a boundary condi-
eq
servations. However, near-critical bubble growth exper- tion. The P (l) expression used was that of [12].
r
iments have an important drawback. Since the surface However, the cells in ALICE-2 were not suitable to
tension becomes very low near the critical point, gravity control the heat supply or to measure it. It did not per-
completely flattens the liquid interface. Weightlessness mit to change the bubble position with respect to the
conditions are thus necessary to preserve the usual con- cell either. These limitations have been overcome in the
vex bubble shape. experimental H setup that makes use of the magnetic
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In our already performed experiments, the cells are levitation facility [13, 14] at CEA-Grenoble. A cylindri-
closed and only pure fluid is present in them so that its cal cell of 8 mm diameter and 5 mm height is filled with
totalmassandvolumeremainsconstant. Unlikethecon- H at critical density. The sapphire transparentbases of
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ventional boiling experiments, the gas bubble is not nu- the cell are good heat conductors in the cryogenic tem-
cleated but exists already before the cell heating begins. perature range (T = 33K for H ). The lateral cell wall
c 2
The bubble growth is then observed. is made of stainless steel which is on the contrary the
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thermalinsulator. The fluid is heatedby one of the win- bubblesurfaceposition(includingthecontactline)needs
dowswhilethetemperatureoftheotherismaintainedby to be determined rigorously, without employing any hy-
the temperature regulation system which permits us to potheses on the interface shape like “liquid microlayer”
measure the heat flux removed from the cell. The earth hypothesis used conventionally [15] to describe the con-
gravity is compensated by magnetic forces within 2% in tact line heat transfer.
the cell volume. The position of the cell with respect
to the magnetic field is chosen so that the residual force
positions the bubble against the heating window. The !! " #
growthofthe dryspotcanthusbe directlyobservedand
is illustrated in Fig. 5. Small vapor bubbles grow and
depart from the heater under the action of the residual
magnetic forces. The bubble spreading begins however
for the unique (largest) vapor bubble. One can see that FIG.5: Gasspreadingat32K(wellbeyondthecriticalregion)
thesamemechanismofthedryspotspreadingworksalso asvisualizedthroughthetransparentheaterinmagneticlevi-
relatively far from the critical point. Indeed, the experi- tationexperiment. (a)Beginningofthedryspotgrowth. (b)
ments were performed for up to 3% deviation from p . Bubble partially spread. (c) Complete drying of the heater.
c
Nucleated small bubbles (boiling) are visible in (a-b). The
volumeof thelarge bubbleremains nearly constant through-
out the evolution.
IV. CONCLUSIONS
Theexperimentsarealsoneededtobecarriedon. The
This paper deals with the vapor recoil model which
drop spreading will be studied quantitatively, both un-
describes the triggering of the boiling crisis. The results
der magnetic levitation and in microgravity on board of
of both simulations and experiments in low gravity con-
the International Space Station in the CNES DECLIC
firm this model. However, further studies are necessary.
apparatus.
The simulations of the bubble departure under the in-
Acknowledgments
fluence of gravityor/andexternally imposed flow should
beperformedtodetermineq ,theheatfluxnecessary
CHF
to trigger the boiling crisis. This is a complex problem ThisworkwaspartiallysupportedbyCNES.Wethank
because oftwo reasons. First, the heat transfersingular- alloftheALICEteamandeveryoneinvolvedintotheMir
ity at the contact line needs to be resolved. Second, the missions.
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