Proceedings of IMECE2007ASME International Mechanical Engineering Congress &

ExpositionNovember 11-15, 2007, Seattle, USA

IMECE2007-43551

NUMERICAL SIMULATIONS OF DYNAMICS AND HEAT TRANSFER ASSOCIATEDWITH A SINGLE BUBBLE IN THE PRESENCE OF NONCONDENSABLES

Jinfeng Wu Vijay K. Dhir∗

Henry Samueli School of Engineering and Applied ScienceMechanical and Aerospace Engineering Department

University of CaliforniaLos Angeles, California 90095Email: vdhir@seas.ucla.edu

ABSTRACTUnder subcooled boiling conditions, the liquid may contain

dissolved noncondensabe gases. During phase change at thebubble-liquid interface, noncondensable gases will be injectedinto the bubble along with vapor. Due to heat transfer into sub-cooled liquid, vapor will condense in the upper regions of thebubble and the bubble interface is impermeable to noncondens-ables. As a result, noncondensabe gases will accumulate at thetop of bubbles. This existing gradient of noncondensable concen-tration inside bubble determines the saturation temperature gra-dient around the bubble surface. The nonuniform saturation tem-perature may cause a difference in surface tension which wouldgive rise to thermocapillary convection in the vicinity of the in-terface. So far, this description is merely a hypothesis. It is feltthat much inspection is in vital demand to clarify the uncertaintyas to the role of noncondensables throughout this process. Inthis study, air is taken as noncondensable gas, and the aim isto investigate the effects of noncondensable air on heat transferand bubble dynamics. The results from a numerical procedurecoupling level set function with moving mesh method show theevidence of effects of noncondensable air imposed on heat trans-fer and the induced flow pattern is presented as well.

∗Address all correspondence to this author.

NOMENCLATURECg concentration or mass fraction of aircp specific heat at constant pressureD diffusion coefficient−→g gravity vectorge earth normal gravityH step functionh grid spacing for the macro regionh f g latent heat of evaporationk thermal conductivityl0 characteristic lengthM molecular weight−→m mass flux vectorMa Marangoni numberp pressureq heat fluxR̄ universal gas constantr radial coordinateT temperaturet timet0 characteristic time∆T temperature difference−→u velocity vector, (u,v)−→u int interfacial velocity vectoru0 characteristic velocityx volume fraction

1 Copyright c© 2007 by ASME

Y height of computational domainy vertical coordinate

Greek symbolsα thermal diffusivityβT coefficient of thermal expansionδt thermal layer thicknessκ interfacial curvatureµ dynamic viscosityρ densityσ surface tensionφ level set functionϕ contact angle

Subscripts0 initial conditiong gasint interfacel liquidm mixture inside bubblere f reference statesat saturationsub subcoolingsup superheatv vaporw wall

INTRODUCTIONNucleate boiling is a liquid-vapor phase-change process as-

sociated with bubble formation. As it is a very efficient modeof heat transfer, the boiling process has attracted the attentionfrom many researchers in the last half century. Subcooled nucle-ate pool boiling exists when the bulk temperature in the liquidpool is less than the saturation temperature of the liquid at thegiven system pressure, and the temperature of the heating sur-face exceeds the nucleation temperature which is higher than thesaturation temperature. In reality under subcooled boiling condi-tions, a certain amount of noncondensable gases is in existenceinside the system. With increasing liquid bulk temperature, thesolubility of noncondensables in water usually keeps decreas-ing. When subcooled boiling occurs, the evaporation processwill carry noncondensable gases, which has not been compelledfrom the system, into bubbles with vapor, meanwhile the vaporwill condense in the upper regions of the bubble and the bubbleinterface is impermeable to noncondensables. As a result, thenoncondensables would accumulate at the top of bubbles. Thisgradient of noncondensable concentration inside bubble yields anonuniform saturation temperature to be present along the bub-ble interface. Furthermore, the different surface tension arising

from this temperature gradient may initiate thermocapillary con-vection. Studying the effects of thermocapillary convection un-der terrestrial situations is rather difficult, as the thermocapillaryforce may be over-shadowed by the gravity force. Therefore,studying a bubble growth when noncondensables are present isoften carried out under microgravity.

In some studies attentions were directed toward the influ-ences of gravity level, thermocapillary convection and noncon-densable concentration on this heat transfer process. From thepool boiling experiments conducted in 1980s and 1990s undermicrogravity conditions with saturated and subcooled liquids,Straub [13] observed that under subcooled boiling a convectionforms jet streams above the head of the bubbles, this flow doesnot actually contribute to the overall heat transfer itself and thisflow is absent in saturated liquid. Those observation led theauthor a hypothesis: under subcooled boiling, noncondensablegases are carried along with the evaporating vapor into a bubble,at the portion of the interface exposed to subcooled liquid onlyvapor condense. As a result, noncondensable gases accumulateat the top portion of the bubble and reduce the partial pressureof vapor, therefore lower the saturation temperature. In this way,noncondensable gases can act as a source of thermocapillary flowin subcooled boiling. Marek and Straub [6] proposed that ther-mocapillary convection could enhance heat transfer. The authorclaimed Nu with thermocapillary convection can be as much as3.5 times Nu without thermocapillary in the case of flow arounda sessile and pending half-spherical bubble for Ma = 104. Bya combined analytical and numerical approach the authors as-sumed a non-deformable, spherical bubble interface, and con-cluded that heat transfer can be increased dramatically if thebulk gas concentration exceeds a certain value, also the bubblebecomes less sensitive to the accumulation of noncondensableswith increasing subcooling. Henry et al. [2] performed experi-ments with 99.3% pure n-perfluorohexane under reduced gravityof 10−2ge. The authors claimed in the case of gas-saturated boil-ing the formed bubble is predominately a gas bubble and causesdry-out over a larger portion of the heater surface and lowersdown the heat transfer from the wall. The authors believed thecause of the thermocapillary motion remains unclear, instead ofdissolved gas suggested by Straub [13].

From the above-mentioned literature, some contradictionsare still in existence and many questions remain unanswered.Since Straub proposed his hypothesis, some researchers have ap-plied this theory to explain the observation in their own experi-ments. Unfortunately no current instruments are available to de-tect the small amount of noncondensables in the system duringexperiments and verify its feasiblities. Meanwhile, numericalsimulation may provide a tool to complement experiments andaid in interpreting the physics. In literature related to numericalstudies, many assumptions were made, such as: hemisphericalbubble shape, stationary bubble, artificial temperature gradientor adiabatic interfacial conditions. The conclusions base on these

2 Copyright c© 2007 by ASME

assumptions were not able to capture the physics accurately be-hind the scenes. In this study, air is taken as noncondensablegases and a numerical procedure which is capable to redistributemesh and sustain the highly dense node concentration around theinterface as the bubble grows, extends a model proposed by Sonet al. [10] and also relaxes many assumptions is undertaken tosimulate this complex phenomenon and study the effects of non-condensable air throughout this process.

NUMERICAL FORMULATIONTo analyze the growth of a single bubble in subcooled nu-

cleate boiling, we extend the numerical model originally devel-oped by Son et al. [10]. In that model, the computational domainis divided into two parts: a micro region and a macro region.The micro region is a thin film that lies underneath the bubblewhereas the macro region consists of the bubble and the liquidsurrounding the bubble. Numerical simulations of fluid flow andheat transfer are carried out for a time-dependent system in bothmicro and macro regions. The computed shapes of the interfacein the micro region and the macro region are matched at the outeredge of the micro-layer for a given contact angle. In the numeri-cal analysis, a level-set function is solved to represent the macroregion.

The assumptions in this study are the following: the processis two-dimensional and axisymmetric; the flows are laminar; thewall temperature remains constant; water at atmospheric pres-sure is used as the test fluid, the properties associated with wa-ter not effected by dissolved air; the thermodynamic propertiesof the individual phases are assumed to be insensitive to smallchanges in temperature and pressure except for surface tension.

The interface separating the two phases is advanced at therate of the interficial velocity −→u int and is captured by solving thefollowing equation for the level set function φ,

∂φ∂t = −−→u int ·∇φ, (1)

−→u int = −→u +mρ

. (2)

A reinitialization equation is solved until steady state to en-sure that |∇φ| = 1,

∂φ∂t = sign(φo)(1−|∇φ|). (3)

Next, we present the governing equations of continuity, mo-

mentum, energy and species conservation for the macro region,

∂ρ∂t +∇ · (ρ−→u ) = 0, (4)

ρ(∂−→u∂t +−→u ·∇−→u ) = −∇p+ρ−→g −ρβT (T −Tsat)

−→g−σκ∇H +(−→τ ·∇σ)−→τ ∇H+∇ ·µ∇−→u +∇ ·µ∇−→u T (5)

ρcpl(∂T∂t +−→u ·∇T ) = ∇ · k∇T for H > 0,

T = Tsat(pv) = Tsat,xg=0

+xgR̄T 2

sat,xg=0

Mh f gfor H = 0 (6)

ρ(∂Cg∂t +−→u ·∇Cg) = ∇ ·ρD∇Cg for H < 0 (7)

The fifth term of right hand side of momentum equation accountsfor the surface tension variation along the interface, which hasappeared in Murata and Mochizuki [7] and James and Lowen-grub [3]. The vapor in the bubble was assumed to remain at thesaturation temperature. As such, the energy equation in the va-por is not numerically solved, however, the saturation tempera-ture variation caused by the partial pressure of vapor is taken intoaccount by applying Clausius-Clapeyon equation. Additionally,σ is taken as a function of temperature (Lay and Dhir [5]), givenas:

σ = σre f [1−1.22

Tcritical(T −Tre f )] (8)

In the above equations, some relations are defined as fol-lows,

H = 1 i f φ ≥+1.5h,

= 0 i f φ ≤−1.5h, (9)= 0.5+φ/(3h)+ sin[2πφ/(3h)]/(2π), otherwise

ρ = ρm +(ρl −ρm)H= ρv +ρg +(ρl −ρv −ρg)H (10)

µ−1 = µ−1v +(µ−1

l −µ−1v )H (11)

k−1 = k−1l H (12)

where ρm and ρ are the density of the mixture inside bubble andthe fluid density respectively. ρm can be determined as the fol-lowing procedure: molar fraction xg is easily gained from the

3 Copyright c© 2007 by ASME

concentration Cg in the form of mass fraction from the previoustime, then Tsat is computed by solving Eq. (6). Next, a formula ofvapor density as a function of Tsat from Wagner et al. [14] is ap-plied to obtain ρv, and hence ρm is known based on the definitionof Cg. µ is the fluid shear viscosity and k is the thermal conduc-tivity. The value of the level set is used to derive the propertiesin the thin region around the interface. This prevents numericalinstability arising from discontinuity in the properties. Also, Eq.(12) is consistent with the assumption that the vapor temperatureremains almost constant at Tsat .

The governing equations are non-dimensionalized using thecharacteristic length, time and velocity scales, l0, t0 and u0, re-spectively.

l0 =

√

σg(ρl −ρv)

, (13)

u0 =√

gl0 =

[

σg(ρl −ρv)

]1/4, (14)

t0 =l0u0

=

[

σg3(ρl −ρv)

]1/4. (15)

The temperature is non-dimensionalized such that the walltemperature is 1 and the subcooled liquid temperature is 0. Theconcentration is non-dimensionalized by Cgl in subcooled boil-ing cases.

The boundary conditions for the governing equations are,At the wall (y = 0),

u = 0, v = 0,∂φ∂y =−cosϕ, T = Tw,

∂Cg∂y = 0. (16)

At the top of computational domain (y = Y ),

∂u∂y = 0,

∂v∂y = 0,

∂φ∂y = 0, T = Tl Cg = Cgl . (17)

At the planes of symmetry (r = 0,R),

u = 0,∂v∂r = 0,

∂φ∂r = 0,

∂T∂r = 0,

∂Cg∂r = 0. (18)

Table 1. Concentration of Air Inside Liquid

Subcooling 0◦C 1◦C 5◦C 7.5◦C

Cgl 0 5.31E −7 2.486E−6 3.583E −6

At the bubble interface,

ρmD∇Cg = −Cg k∇Th f g

, for Condensation (19)

ρmD∇Cg = −Cg−Cgl1−Cgl

k∇Th f g

, for Evap. (20)

Initially, the fluid velocity is set to be zero. The tempera-ture profile is taken to be linear in the natural convection thermalboundary layer, and its thickness, δT , is given by Kays and Craw-ford [4]:

δT = 7.14(νlαl/gβT ∆T )1/3. (21)

To determine Cgl , the thermodynamic equilibrium state atthe top of computational domain is assumed. The partial pressureof vapor is the saturation pressure corresponding to the tempera-ture of subcooled liquid. Therefore, the molar fraction of vaporand air are straight forward to obtain. Henry number is appliedto divide the molar fraction of air in vapor side to get the molarconcentration of air in liquid side which is converted into massfraction: Cgl . Cgl is assumed a constant for a fixed subcoolingtemperature, this may deviate from the reality, but it makes senseon a physical base.

ValidationTo validate this moving mesh method coupled with level set

function, we studied a case of bubbles rising in a quiescent liquidand compared the results to those given by Ryskin and Leal [8]and Son [11]. A phase-change problem with an analytical solu-tion was described in Son [12] and is used to test the capabilityof our method to include heat transfer. The numerical resultsfor those two cases are reported in Wu et al. [15]. In addition,the comparison between numerical simulations and experimentaldata will be addressed in another paper which is in preparation.This validation process lends support to latter numerical resultsin the next section.

RESULTS AND DISCUSSIONSIn this section, the numerical results including saturated and

subcooled boiling, pure water as well as systems containing dis-

4 Copyright c© 2007 by ASME

0

0.5

1

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2

2.5

3

3.5

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Equi

vale

nt d

iam

eter

[mm

]

Time [s]

Subcooling=0oC, Cg,l=0

Subcooling=1oC, Cg,l=5.31E-7

Subcooling=5oC, Cg,l=2.486E-6

Subcooling=7.5oC, Cg,l=3.583E-6

Cg,0 = 0.0Cg,0 = 0.2Cg,0 = 0.4

Figure 1. Growth rate under conditions of wall superheat = 8◦C, contactangle = 54◦, pressure = 1.013×105Pa, g/ge = 1

solved air as test fluid under various gravity levels are presented.The saturated cases are regarded as a reference state by compar-ison to which the effects of subcooling and concentration of aircould be manifested clearly. All the numerical results are takenfrom the computation of the first cycle.

EARTH NORMAL GRAVITY, g/ge = 1 Numerical sim-ulations of single bubble dynamics during saturated and sub-cooled nucleate boiling for a wall superheat of 8◦C, contact angleof 54◦ and system pressure of 1.013×105Pa are performed withdifferent initial mass fraction of air inside bubble (i.e. Cg,0 = 0,0.2 and 0.4). The initial mass fraction of air inside bubble isreasonably made for the recognition of the fact that the bubbleembryo starts with trapped air from wall imperfection in real-ity. For saturated boiling, zero concentration of air is assumedin liquid side. The growth rate of the bubble is adopted as theprimary means of comparing the effects of different parameters.The actual volume of the bubble is first computed, thereafter it isconverted into an equivalent diameter of a sphere.

Figure 1 shows the growth rate of the bubble with four dif-ferent initial mass fraction of air inside bubble and varying sub-cooling of 0◦C, 1◦C ,5◦C and 7.5◦C respectively. The higherconcentration of air inside bubble would lower saturation tem-perature, as a result, the departure diameter becomes larger andthe growth period is shortened. For instance, initial Cg,0 = 0.2and 0.4 would decrease saturation temperature by 3.83◦C and8.34◦C respectively. For subcooling of 1◦C, the bubble detachesfrom the wall at a size which is smaller than its maximum size.This bubble shrinkage near the point of departure is caused bythe negative total heat transfer to the bubble, i.e., condensationheat transfer is larger than the sum of evaporation heat trans-fer around the bubble and from the microlayer, as described inSingh [9]. For subcooling of 5◦C and 7.5◦C, in all cases, the

-0.2

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0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Heat

Tra

nsfe

r Thr

ough

Inte

rface

[w]

Time [s]

∆Tsub = 0oC∆Tsub = 1oC∆Tsub = 5oC

∆Tsub = 7.5oC

Figure 2. Heat transfer rate through interface for Cg,0 = 0, Cg,l = 0,under conditions of wall superheat = 8◦C, contact angle = 54◦, pressure= 1.013×105Pa, g/ge = 1

bubble grows to a maximum size and then begins to shrink. Thisshrinkage is due to the large condensation heat transfer that oc-curs at the upper portion of the bubble. As a result, the bubblenever achieves the bubble departure size. Eventually a balanceis reached in evaporation and condensation rate, and the bubbleremains attached to the heating surface. Figure 2 reveals the totalheat transfer through bubble interface for four different subcool-ing. The positive initial higher heat transfer rate accounts for therapid bubble growth at their early stage. As a bubble approachesto its departure, heat transfer drops to and below zero for sub-cooling of 0◦C and 1◦C respectively. For subcooling of 5◦C and7.5◦C, heat transfer around zero after 0.1s is in accord with thevery small change in bubble size.

Figures 3 and 4 demonstrate the calculated flow field andtemperature profile for two different subcooling during bubblegrowth process. Since no obvious difference takes place betweencases of various contents of air in the system for the same sub-cooling, only one set of data is presented. From the numericalsimulation, it can be seen that the growing bubble pushes out theliquid. The location where the vapor-liquid interface contacts thewall is observed to move outward and then inward as the bub-ble grows and departs. The highest heat transfer rate occurs atthe base of the bubble. The nonuniform velocity inside bubbleresults in a noticeable vortex. The isotherm that terminates atthe bubble interface represents the saturation temperature. It dis-tinguishes the area where evaporation takes place from the areawhere condensation occurs. We can observe that the conden-sation area dominates the evaporation area during most of thegrowth period. For 5◦C subcooling, Vapor flowing upward fromthe base condenses over most of the interface. The liquid that hasjust condensed around the interface flows downward toward thewall and thins down the thermal layer near the base of the bubble.This in turn leads to saddle points in the isotherms. The isotherm

5 Copyright c© 2007 by ASME

t = 0.076 ms t = 10.0 ms

0

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1

1.5

2

-1 -0.5 0 0.5 1 0

0.5

1

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2

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t = 26.0 ms t = 41.2 ms

0

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1

1.5

2

-1 -0.5 0 0.5 1 0

0.5

1

1.5

2

-1 -0.5 0 0.5 1

t = 56.4 ms t = 71.6 ms

0

0.5

1

1.5

2

-1 -0.5 0 0.5 1 0

0.5

1

1.5

2

-1 -0.5 0 0.5 1

Figure 3. Flow field, temperature profile and concentration distributionunder conditions of wall superheat = 8◦C, liquid subcooling = 1◦C, con-tact angle = 54◦, pressure = 1.013× 105Pa, g/ge = 1, Cg,0 = 0.4,Cg,l = 5.31E −7.

distribution is quite different from the case for low subcooling asshown in Figures 3. The neighboring contours from concentra-tion distribution represent a difference of one tenth between themaximum and minimum values. The highest concentration of airoccurs at the top of the bubble and the concentration of air keepsdecreasing downward. At the bottom of bubble where the high-est heat transfer occurs, the influx composed of the lowest massfraction of air throughout the system will dilute concentrationthere.

t = 0.0002 s t = 0.013 s

0

0.5

1

1.5

2

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0.5

1

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2

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t = 0.133 s t = 0.253 s

0

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1

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-1 -0.5 0 0.5 1 0

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1

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-1 -0.5 0 0.5 1

t = 0.333 s t = 0.400 s

0

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-1 -0.5 0 0.5 1 0

0.5

1

1.5

2

-1 -0.5 0 0.5 1

Figure 4. Temperature distribution, velocity field and concentration pro-file for initial mass fraction of air = 0.4 under conditions of wall super-heat = 8◦C, liquid subcooling = 5◦C, contact angle = 54◦, pressure =1.013×105Pa, g/ge = 1, Cg,0 = 0.4, Cg,l = 2.486E−6.

MICROGRAVITY, g/ge = 0.01 This section presents theresults for the cases where the gravity levels are 1% of earth nor-mal gravity. Under these conditions, not only is the size of thebubble an order of magnitude larger, but also the time periods aremuch longer.

Figure 5 shows the growth rate of the bubble with two dif-ferent initial mass fraction of air inside bubble and two differentliquid temperature under conditions of wall superheat of 8◦C,contact angle of 54◦ and system pressure of 1.013×105Pa. Thetrends of bubble growth are similar to cases of earth normal grav-

6 Copyright c© 2007 by ASME

0

5

10

15

20

25

30

0 2 4 6 8 10 12

Equi

vale

nt d

iam

eter

[mm

]

Time [s]

Subcooling=0oC, Cg,l=0

Subcooling=5oC, Cg,l=2.486E-6

Cg,0 = 0.0Cg,0 = 0.2

Figure 5. Growth rate under conditions of wall superheat = 8◦C, contactangle = 54◦, pressure = 1.013×105Pa, g/ge = 0.01

-1

0

1

2

3

4

5

6

0 2 4 6 8 10 12

Heat

Tra

nsfe

r [w]

Time [s]

subcooling = 0oCsubcooling = 5oC

Figure 6. Heat transfer rate through interface for Cg,0 = 0, Cg,l = 0,under conditions of wall superheat = 8◦C, contact angle = 54◦, pressure= 1.013×105Pa, g/ge = 0.01

ity. The liquid with 5◦C subcooling shrinks the bubble to approx-imately an half in size from a saturated bubble. After maintain-ing a quasi-steady state under subcooled boiling conditions, thebubble with the presence of air inside the system remains at adiameter of 12.1mm, while it maintains a size of 10.9mm withthe absence of air. At the same time, these effect brought by airare not pronounced in saturated boiling. Figure 6 demonstratesthe total heat transfer rate across the interface for subcooling of0◦C and 5◦C. This plot indicates that the subcooling affects theheat transfer rate under microgravity much more substantial thanit does under earth normal gravity if Figure 2 is also in consider-ation, since the much more larger interfacial area is involved.

Figure 7 displays the calculated flow field and tempera-ture profile during bubble growth process under saturated boilingconditions. By comparison to its counterpart under earth normalgravity, a vortex in liquid side is in more violent and distorted

t = 0.005 s t = 0.58 s

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t = 1.69 s t = 2.80 s

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t = 3.92 s t = 5.08 s

0

0.5

1

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2

-1 -0.5 0 0.5 1 0

0.5

1

1.5

2

-1 -0.5 0 0.5 1

Figure 7. Flow field, temperature profile and concentration distributionunder conditions of wall superheat = 8◦C, liquid subcooling = 0◦C, con-tact angle = 54◦, pressure = 1.013×105Pa, g/ge = 0.01.

pattern. In Figures 8 and 9, the isotherms represent dimension-less temperature of 0.01 (i.e. 95.13◦C), 0.1, 0.2, 0.3, 0.3846 (i.e.100◦C), 0.5, till 0.9. An interesting observation of a protrudingprofile of 95.13◦C is made above the head of bubble in Figure 9.The differences between Figure 8 and 9 lay in two aspects, satu-ration temperature and surface tension. An extra numerical studyconsidering only saturation temperature variation and uniformsurface tension is conducted to determine which factor is respon-sible for this flow pattern in Figure 9. In that study, the growthrate, flow field and temperature distribution resemble what is de-picted in Figure 8. This leads us to conclude that thermocapillary

7 Copyright c© 2007 by ASME

t = 0.003 s t = 0.97 s

0

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t = 3.50 s t = 6.03 s

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t = 8.55 s t = 11.08 s

0

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-1 -0.5 0 0.5 1 0

0.5

1

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2

-1 -0.5 0 0.5 1

Figure 8. Temperature distribution and velocity field under conditions ofwall superheat = 8◦C, liquid subcooling = 5◦C, contact angle = 54◦, pres-sure = 1.013×105Pa, g/ge = 0.01, Cg,0 = 0.0, Cg,l = 0.

flow at the early stage of bubble growth drives the fluid flowingfrom the bubble base toward its top in the vicinity of the inter-face, enlarges the evaporation interfacial area and yields a largerbubble. It is also interesting to notice that this temperature distri-bution bears much similarity to experimental presentation in Abeand Iwasali [1], although different test fluids are applied in theirstudy.

CONCLUSIONSA numerical procedure coupling the level set function with

the moving mesh method has been employed to simulate nucle-ate boiling with different mass of air inside the system, varioussubcooling and varying gravity level.

t = 0.003 s t = 0.97 s

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t = 3.50 s t = 6.03 s

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t = 8.55 s t = 11.08 s

0

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2

-1 -0.5 0 0.5 1 0

0.5

1

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2

-1 -0.5 0 0.5 1

Figure 9. Temperature distribution and velocity field under conditions ofwall superheat = 8◦C, liquid subcooling = 5◦C, contact angle = 54◦, pres-sure = 1.013×105Pa, g/ge = 0.01, Cg,0 = 0.2, Cg,l = 2.486E−6

The effects of noncondensables and subcooling on the bub-ble behaviors are more pronounced under microgravity than theydo under earth normal gravity conditions.

The effects of noncondensables on saturated cases are in-significant by comparison to subcooled cases. The higher contentof air inside the system increases the bubble size and shortens thegrowth period.

The thermocapillary force plays a more important role inflow pattern under microgravity conditions than it does undernormal gravity level. Some interesting flow patterns are reportedin current study.

Under microgravity, the flow becomes more violent and con-vection dominant, as a result, temperature distribution is moredistorted and dramatic.

8 Copyright c© 2007 by ASME

ACKNOWLEDGMENTThis work received support from NASA under Microgravity

Fluid Physics Program.

REFERENCES1. Abe, Y., Iwasaki, A., Observation of vapor bubble of

non-azeotropic binary mixture in microgravity with a two-wavelength interferometer, Proceedings of 5th ASME/JSMEJoint Thermal Engineering Conference, AJTE99-6418, SanDiego, California, 1999.

2. Henry, C. D., Kim, J., McQuillen, J., Dissolved gas ef-fects on thermocapillary convection during boiling in re-duced gravity environments, Heat Mass Transfer, vol. 42,pp919-928, 2006.

3. James, A. J., Lowengrub, J., A surfactant-conservingvolume-of-fluid method for interfacial flows with insolublesurfactant, J. of Computational Physics, vol. 201, pp685-722, 2004.

4. Kays, W. M., Crawford, M. E., Convective Heat and MassTransfer, p328, McGraw-Hill, New York, 1980.

5. Lay, J. H., Dhir, V. K., Shape of a Vapor Stem During Nu-cleate Boiling of Saturated Liquids, ASME Journal of HeatTransfer, vol. 117, pp394-401, 1995.

6. Marek, R., Straub, J., The origin of thermocapillary convec-tion in subcooled nucleate pool boiling, Int. J. Heat MassTransfer, vol. 44, pp619-632, 2001.

7. Murata, A., Mochizuki, S., Motion of droplets by theMarangoni force on a wall with a Temperature gradient,Heat Transfer-Asian Research, vol. 33, pp81-93, 2004.

8. Ryskin, G., Leal, L. G., Numerical Solution of Free-Boundary Problems in Fluid Mechanics, Part I, J. FluidMech., vol. 148, pp1-17, 1984.

9. Singh, S., Effect of Gravity and Liquid Subcooling on Bub-ble Dynamics, Master’s thesis, MAE Dept., UCLA, 1999.

10. Son, G., Dhir, V. K., and Ramanujapu, N., Dynamics andHeat Transfer Associated with a Single Bubble During Nu-cleate Boiling on a Horizontal Surface, Journal of HeatTransfer, vol. 121, pp. 623-631, 1999.

11. Son, G., Efficient Implementation of a Coupled Level-Setand Volume-of-Fluid Method for Three-Dimensional In-compressible Two-Phase Flows, Numerical Heat Transfer,Part B, vol. 43, pp549-565, 2003.

12. Son, G., A Numerical Method for Bubble Motion with PhaseChange, Numerical Heat Transfer, Part B, vol. 39, pp509-523, 2001.

13. Straub, J., Origin and Effect of Thermocapillary Convectionin Subcooled Boiling. Observation and Conclusions fromExperiments Performed at Microgravity, Ann. N.Y. Acad.Sci., vol. 974, pp348-363, 2002.

14. Wagner, W., Pruβ, A., The IAPWS Formulation 1995 for theThermodynamic Properties of Ordinary Water Substance for

General and Scientific Use, J. Phys. Chem. Ref. Data, vol.31, No. 2, pp387-535, 2002.

15. Wu, J., Dhir, V. K., and Qian, J., Numerical Simulation ofSubcooled Nucleate Boiling by Coupling Level-set Methodwith Moving Mesh Method, Numerical Heat Transfer, PartB, vol. 51, pp535-563, 2007.

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