Thermal Science & Engineering Vol.21 No.2 (2013)

A contribution to the basic understanding of nucleate boiling phenomena:
generic experiments and numerical simulationsPeter Stephan†‡, Axel Sielaff†, Sebastian Fischer†, Jochen Dietl† and Stefan Herbert†

Abstract
Since Nukiyama's pioneering experiment and findings in the 1930s many researchers have further investigated the boiling process and developed empirical or semi-empirical methods to predict the boilingheat transfer coefficient. However, several details of the local heat transport phenomena are still not fully
understood. The heat transfer from the heated wall to the bulk fluid is extremely complex and many aspects are involved: nucleation, dynamic wetting characteristics, surface tension and other fluid properties,
gravitation, bulk subcooling, etc…
Only in the recent years experimental methods reached spatial and temporal resolutions that allow
observing the boiling process on the scales of these individual aspects and local dynamic phenomena in
the two-phase boundary layer. Similarly, numerical methods reached a level of robustness and resolutionthat allows studying the influence of these aspects and phenomena in a computer simulation. This work
will give an overview on recent developments and modern experimental and numerical methods nucleateboiling heat transfer research, Results from combined generic experiments and numerical simulations arepresented. They give a deep insight into the local and transient transport phenomena in the two-phaseboundary layer.
Key Words: Nucleate boiling, Vapor bubble, Departure diameter, Conjugated heat transfer

further discussion of the Nukiyama Curve which de-

NOMENCLATUREc:thermal capacityk:thermal conductivityq:heat fluxT:temperaturex, ycartesian coordinatesα:
thermal diffusivity
ξ, η:
local coordinatesδ:
thicknessρ:densityτ:
time
subscripts
0
:
input
s
:
solid

scribes the relation between wall superheat T comparedto saturation temperature and the heat flux q in the different pool boiling regimes. This curve was presented in1934 by Shiro Nukiyama in his pioneering paper entitled“The Maximum and Minimum Values of the Heat Q
Transmitted from Metal to Boiling Water under Atmospheric Pressure”. Nukiyama (1934) found this characteristic relation in an experiment using an electrically heated metallic wire evaluating accurately temperature andheat flux. Nukiyama’s work became a guideline to heattransfer engineering for the design and control of boilers

INTRODUCTION

and/or steam generators. Important heat transfer statessuch as the onset of nucleate boiling (ONB), the critical

Boiling is an important phase change and heat trans-

heat flux (CHF), and the Leidenfrost temperature arefer method with a wide variety of technical applications.

related to characteristic changes in the slope of theProbably each and every undergraduate course on boiling

Nukiyama Curve.

heat transfer worldwide starts with a presentation andReceived: February 7, 2013, Editor : Katsunori Hanamura
Institute of Technical Thermodynamics, TU Darmstadt, Petersenstr. 17, D-64287 Darmstadt, Germany‡ Center of Smart Interfaces, TU Darmstadt, Petersenstr. 17, D-64287 Darmstadt, Germany†- 39 -© 2013 The Heat Transfer Society of Japan

Thermal Science & Engineering Vol.21 No.2 (2013)

Since Nukiyama’s work many researchers have stud-boiling heat transfer. He attributed these parameters ei-

ied boiling heat transfer experimentally, theoretically andther to the fluid (fluid properties, liquid-vapor phaselater also numerically. Their focus was mainly the inves-change characteristics, etc.), to the solid heater (thermo-

tigation of the nucleate boiling regime, i.e. the regime inphysical properties, roughness, etc.) or to the heater-fluid

between ONB and CHF, because this regime is the mostinterface (wettability, active site density, etc.). With thatimportant one in the majority of applications. As a result

it becomes very obvious that the heat transport process isquite a huge number of empirical correlations for theextremely complex. Thus, purely empirical research andheat transfer coefficient h=q/T were published formany specific cases. These correlations are the basis ofglobal measurements, i.e. time and space averaged tem-

today’s design methods, but typically they are only rea-ma’s pioneering work are still justified to characterize

sonably accurate for certain fluids in a limited range of

nucleate boiling heat transfer for new wall surfaces (e.g.

process parameters, because they do not entirely describe

microstructured surfaces) or new fluids (e.g. nanofluids).

the complex and dynamic two-phase transport phenom-

However, the tremendous progress in measurement tech-ena and their interaction. The reason for that is very sim-niques as well as in numerical methods and computerple and astonishing at the same time after almost hun-performance since about a decade or so today allows adred years of boiling research: the complex and dynamic

detailed investigation of the nucleate boiling process

two-phase transport phenomena and their interaction arewith high spatial and temporal resolution. This opens a

still not fully understood. However, it is generally ac-path towards a deeper basic understanding of the local

cepted in the scientific community that the following

transport phenomena and may lead to more physicallytransport phenomena play a role during vapor bubble

based prediction methods in future.

growth and detachment: Transient conduction from the superheated liquidboundary layer to the liquid-vapor interface
 Evaporation at the liquid-vapor interface in the superheated near wall region ‘Micro layer’ evaporation in the thin film region
near the moving contact line at the foot of the bubble
 Partial recondensation of vapor when the bubble
moves out of the superheated boundary layer incase of a subcooled bulk region
 Forced convection induced by the moving interface(flow of colder liquid from the bulk into the wakeof the rising bubble)
 Natural convection and buoyancy
 Marangoni convection due to temperature gradients Transient heat conduction in the solid wall underneath the bubble
 Diffusive mass transfer and Marangoni convection
due to concentration gradients in case of fluid mixtures
However, which of these transport phenomena dom-

perature and heat flux observations, similar to Nukiya-

In the following sections the authors present a seriesof very generic nucleate boiling experiments using highresolution measurement techniques and closely aligned
numerical simulations that include multiple characteristic
scales of the boiling process.
2. STATE OF THE ART REVIEW
2.1 Generic experiments
In the past two decades measurement techniques withhigh temporal and spatial resolution have become available. Ensuing this development, many researches involved in experimental investigations of nucleate boilingredirected their focus from global measurements of heattransfer to the more fundamental aspect of investigatingheat transfer at single bubbles. Today, it is broad consensus in the scientific community that in order to understand the physical process of nucleate boiling, one firstinate under which process conditions is partially still an

has to gain deeper understanding of the phenomena in-open question. Moreover, the heterogeneous bubble nu-

volved in single bubble heat transfer. Apart from gaining

cleation process is even less understood and an a priori

insight into phenomena, single bubble experiments addi-

prediction of the active nucleation site density is stilltionally can be used to develop and validate numericalimpossible. In a rather recent review paper, published inmodels for single bubble heat transfer. Such numericala special issue on boiling heat transfer, Manglik (2006)

models allow determining phenomena on geometric andlisted the numerous influencing parameters on nucleate

temporal scales that are still not accessible through ex-- 40 -© 2013 The Heat Transfer Society of Japan

Thermal Science & Engineering Vol.21 No.2 (2013)

periments, but might have a major impact onto the pro-ameter and frequency as well as the heat flux and waiting

cess.

time between bubble detachment and subsequent bubble

The group around Dhir conducted experiments on the

nucleation were evaluated for different cavity depths.

influence of wall superheat and liquid subcooling on

Using a similar setup measurements with multiple artifi-

bubble growth rates and liftoff behavior. Qiu et al. (2002)

cial cavities and interacting neighboring bubbles werecarried out experiments on the growth and departure dy-

performed (Hutter et al., 2012).

namics of single water vapor bubbles growing on an arti-

Kim et al. (2002) carried out experimental investiga-

ficial nucleation site on a heated and polished silicontions of pool boiling phenomena using silicon micro-

wafer. They found that the wall superheat has – if any –heater arrays consisting of small rectangular platinum

only a small effect on the equivalent bubble departure

resistance heaters. Two different quadratic microheater

diameter, while increasing liquid subcooling seems toarrays were employed: one with 7 mm side length andresult in a slight decrease of the bubble departure diame-

one with 2.7 mm side length. Each microheater arrayter. However, it was found that the bubble growth time

consisted of 10 by 10 single microheater elements, thus,

decreases significantly with increasing wall superheat

the microheater size was 0.7 mm or 0.27 mm, respec-

and increases with increasing liquid subcooling. Of

tively. Through a feedback loop, each element of thecourse, bubble departure radius and frequency depends

array could be run either in constant heat flux or constanton gravitational buoyancy forces. Recently Dhir et al.

temperature mode, allowing measurement of the other(2012) carried out nucleate boiling experiments on thequantity. It should be noted that while the mean heat flux

International Space Station (ISS) under very good mi-or temperature across each microheater element was kept

crogravity conditions with gravity levels between

constant or measured, the local distributions across each-7-7

6 x 10 gE and 1.2 x 10 gE (gE being the earth gravita-

microheater remained unknown. Using these heater ar-

tional acceleration). It was observed that for low wallrays in microgravity experiments during parabolic flights

superheats lateral bubble mergers led to one big single

Raj and Kim (2010a) found a characteristic thresholdbubble attached to the heater surface acting as a heat sinkvalue: the ratio of the lateral heater size to the fluid ca-

through vapor recondensation at the bubble cap. At

pillary length LH / LC. Pool boiling heat transfer below LH

higher wall superheats however, the big bubble detached/ LC ≈ 2.1 was found to be heater size dependent, whereas

from the wall and merged with smaller bubbles generat-

above this threshold value no influence of the lateral

ed on the heater surface sucking them away from theheater size could be determined by Raj and Kim (2010a)

wall. This shows the importance of bubble coalescenceand Raj et al. (2010b). Delgoshaei and Kim (2010) ana-

on the overall heat transfer, at least in the absence oflyzed the transient heat flux from single microheater el-buoyancy.

ements of the array and calculated an equivalent bubble

Siedel et al. (2008) used a 40 µm thin circular copper

departure diameter: The calculation was based on theplate with a diameter of 18 mm which is soldered to aassumption that all heat from the heater elements below

copper cylinder heated by a cartridge heater. The boilingthe bubble is transferred through contact line and/or mi-surface was polished and an artificial cavity placed in thecrolayer evaporation into latent heat of the vapor. Thiscenter. The single bubble growth dynamics were ob-

equivalent bubble diameter was compared to the physicalserved using a high speed camera. For high wall super-

bubble diameter taken from bubble images. A physicalheats an oscillation of the bubble was detected. It wasdiameter larger than the equivalent one was attributed tofound that the bubble growth time depends on wall su-

additional evaporative heat transfer from the superheatedperheat, whereas the detachment volume is independent,

liquid. They found that long bubble growth times andwhich is in accordance with the findings of Qiu et al.

short waiting times between two successive bubble(2002).

growth periods promoted the contribution from wall heat

Hutter et al. (2010) used a silicon wafer with inte-transfer, while ebullition cycles with short waiting times

grated micro-sensors and single etched artificial cavities

are dominated by evaporation from the superheated liq-

(40 to 100µm in depth, 10µm in width). The bubble di-uid layer.

- 41 -© 2013 The Heat Transfer Society of Japan

Thermal Science & Engineering Vol.21 No.2 (2013)

Auracher and Buchholz (2005) developed a heater

3D oscillatory thermocapillary convection was charac-with implemented constantan/copper microthermocou-

terized based on a critical bubble radius and a criticalples. For local measurements of the surface temperaturetemperature gradient. Barthès et al (2006) studied heata 6 by 6 grid of thermocouples with an individual diam-transfer to single vapor bubbles and Marangoni convec-

eter of 38 µm and a spacing of 0.2 mm in between wastion patterns in degassed and non-degassed fluid using

used. The thermocouple connection was only 3.6 µm

shadowgraphy and a heat flux meter to measure theunderneath a gold coated boiling surface. To calculate

time-resolved average heat flux from a downward facing

the local heat flux from the transient local temperature

heater wall to the fluid. In the non-degassed case con-measurements a 3D inverse heat transfer method was

vection instabilities were observed. They were attributed

developed and used in cooperation with Marquardt’s

to thermocapillary convection.

group (Heng et al., 2008, 2010, 2011). The measure-

The group of Di Marco conducted experiments underments indicated that a substantial amount of heat is re-normal gravity (earth) and microgravity with the main

moved from the heater in the contact line region. Addi-

focus on the evaluation of the forces acting on a growing

tional measurements using microoptical probes andvapor bubble and the effect of an electrical field on thegold/constantan microthermocouples with a diameter offorce balance. It was shown that an electrical field can

only 12.7 µm in the 2-phase fluid were conducted byresult in an additional force for bubble detachment, andAuracher and Buchholz (2005). The microoptical probes

thus has a potential to replace the gravitational force

were fabricated of an etched glass fiber. Due to the dif-during boiling heat transfer in space applications. Di

ferent refraction indexes of liquid and vapor, a phase

Marco and Grassi (2002) reported an increase of criticaldetection at the tip could be performed. Because of theirheat flux CHF with electrical field intensity (represented

small dimensions the influence of the probes onto theby the applied voltage) under microgravity. With highboiling process was assumed to be small. The small

voltages applied (Uelec. Field ≈ 10 kV), CHF under micro-

thermal mass of the tiny microthermocouple enabled

gravity was comparable to CHF under normal gravity

measurements at a much higher measurement frequen-

without electrical field. These measurements were car-cies than applying commercial thermocouples. Void frac-ried out using horizontal platinum wires of different di-tion and the temperature fluctuations near the surface

ameters ranging from 0.2 to 0.6 mm, which served aswere measured.

both, resistance heater and resistance thermometer, so

Tadrist et al. analyzed heat transfer to single bubbles

only global results and no results for single bubbles

with special emphasis to the contribution of Marangoni

could be obtained. Di Marco et al. (2003) carried outor thermocapillary convection. By injecting air bubbles

experiments with single nitrogen bubbles injected intofrom an orifice onto a downward facing heater wall at

FC-72 and subjected to electrical fields of varying inten-

different Marangoni numbers Arlabosse et al. (2000)

sity under normal gravity and microgravity conditions.

found that the ratio of heat transferred from the wall withDi Marco et al. (2012a) presented a force balance in-a bubble to heat transferred without a bubble increased

cluding the electrical field force, buoyancy, internal bub-with rising Marangoni number. In this study the heat flux

ble pressure and surface tension forces. It was found thatwas measured using a heat flux meter, thus time andthe presence of an electric field does not only exert aspace averaged values were recorded. The flow profile

force onto the bubble, but also influences the bubble

around the bubbles was characterized applying particle

shape, changing the other terms of the force balance. For

image velocimetry (PIV). It was found that the maxi-

an upward facing surface configuration Di Marcomum Reynolds number of the induced flow scales line-(2012b) reported an elongation of the generated nitrogenarly with increasing Marangoni number for constantbubbles through the electric field, leading to an increase

Bond and Prandtl numbers. Reynard et al. (2001, 2005)of the internal bubble overpressure.

studied 3D oscillatory thermocapillary convection pat-Starting in the early 1990s Kenning et al. used ther-terns around an air bubble injected close to a heated wall.

mo-chromic liquid crystal (TLC) thermography to inves-

Within the experiments a threshold value for the onset oftigate pool boiling processes. As the color of the liquid- 42 -© 2013 The Heat Transfer Society of Japan

Thermal Science & Engineering Vol.21 No.2 (2013)

crystals changes with temperature local temperaturethermal capacity. In a similar setup Golobic and Gjerkes

measurements could be performed. Due to the extremely(2001) heated the foil not electrically but with laser radi-small size of the crystals the spatial resolution mainly

ation from underneath. Heating different locations of thedepends on the resolution of the camera. Kenning andfoil allowed activating multiple bubble nucleation sites

Yan (1996) used a 0.13 mm thick stainless steel plate as

and investigating interactions between them.

boiling surface which was heated electrically. The plate

Geradi et al. (2009, 2010) used IR thermography to

was coated with unencapsulated liquid crystals on theobserve the temperature distribution on the surface of anbackside. The colors of the TLC layer and the bubble

Indium Tin Oxid (ITO) coated sapphire glass. This al-

dynamics were recorded with 200fps using a high speed

lowed for the simultaneous observation of the bubble

camera. The local temperature field was derived from thefrom underneath with a high speed black and white cam-

local color field and used to calculate the local surface

era.

heat flux by means of the following two dimensional

Buongiorno (2011a, 2011b) measured the thickness ofenergy balance for the wall material:

the liquid layer underneath a growing bubble applying an

Using

this

IR-transparent

heaterKim

andinterferometry technique. The interference fringe pattern  2T  2T    s cs T .
q  q0  k s s  x 2 y 2 is caused by passage of the light through the thin film
and can be observed through the transparent heater. The(1)film thickness was calculated by evaluating the interfer-

Herein, q is the surface heat flux, q0 the input heat flux,

ence wavelength. Using the same technique a DEtection

δs the wall thickness, and ks, ρs and cs the thermal con-of Phase by Infrared Thermometry (DEPIcT) was done.

ductivity, density and specific heat of the solid heater

Duan et al. (2012) performed PIV measurement during

material, respectively. Kenning pointed out that the local

nucleate boiling to visualize the velocity distribution

heat removal by growing bubbles induces a transientaround bubbles. It was found that the velocity on top of

temperature variation of the heating surface. Using thethe bubble is generally higher than at its bottom.

same measurement technique Kenning et al. (2001, 2009)

Sodtke et al. (2006a, 2006b) measured the local wall

also performed experiments with sliding bubbles along atemperature below growing vapor bubbles under normal

tilted plate. He reported differences in wall temperaturegravity and under microgravity conditions. They em-

profiles below the bubbles on horizontal and verticalployed a 10 µm thin stainless steel foil as resistanceheaters.

heater. On the backside of the foil a thin TLC layer was

Theofanous et al. (2002) used Infrared (IR) thermog-

applied to record the color field with a high speed cam-raphy to measure the wall temperature field during boil-

era. Using an in-situ calibration method the RGB color

ing on top of a transparent 130 µm borosilicate glass

values could be mapped accurately to the 2D temperaturecoated with a titanium layer of 140 to 1000 nm thick-field. Figure 1 shows a typical temperature distribution

ness.

near the bubble foot along the contact line area under

Golobic et al. (2009, 2012) used an electrically heat-normal gravity and microgravity conditions. A compari-ed thin metal foils together with IR thermography toson of the measured temperature drop near the bubble

measure the 2D temperature field underneath the foil.

foot to the temperature drop predicted numerically fromThe small heat capacity of the heater and the absence ofa model by Stephan and Hammer (1994) yielded goodthe liquid crystal layer compared to Kenning’s earlier

qualitative agreement. The measurement technique wasstudies led to a smaller temperature difference between

later adapted and expanded by Wagner et al. (2007,

the temperature measurement plane and heater/fluid in-2008) and Schweizer and Stephan (2009). They replaced

terface. For evaluation of the local heat flux a 2D energy

the TLC temperature measurement technique by IRbalance (see equation (1)) was used. Golobic also men-thermography and included a method for local heat flux

tioned a potential disadvantage of the thin foil heater:

calculation. This heat flux calculation is based on a 2D

boiling heat transfer on such thin foil heaters might beenergy balance for each pixel of the temperature field,

deteriorated compared to massive heaters with higher

approximating the partial derivatives through a finite- 43 -© 2013 The Heat Transfer Society of Japan

Thermal Science & Engineering Vol.21 No.2 (2013)

differences scheme. This technique relies on the assump-

saturation temperature at the contact line due to the ac-tion that the temperature difference across the foil can be

cumulation of the less volatile component tends to de-neglected due to the very small thickness of the foil

crease the local superheat.

(Schweizer, 2009). Wagner et al. (2007) used a micro-thermocouple (MTC) to measure the transient temperature in a single vapor bubble as well as the tempera-

2.2 Numerical simulations
Due to the small length and time scales involved inture in the liquid in the wake of the bubble. A character-boiling processes the possibilities to gain insight by

istic result is shown in Fig. 2. They found that, as soon as

measurements are still limited. Numerical simulations

the MTC penetrates the bubble, the measured tempera-

theoretically do not have limitations in resolving time

ture drops from the superheated liquid temperature toand space, and therefore are a promising method to study

saturation temperature or little above inside the vapor

the local transport phenomena in boiling systems. How-

bubble. In the liquid phase in the wake of the bubble theever, to perform accurate simulations appropriate models

temperature slowly rises towards the initial superheat

for the complex physics involved have to be developed.

before the bubble was penetrated.
Schweizer and Stephan (2009) reported a heat flux
peak at the bubble foot related to enhanced contact line
heat transfer using FC-72 as a working fluid. It was reported that during a bubble coalescence a liquid drop
remained in the center of the coalesced bubble. Mukherjee and Dhir (2004) who used water as working fluid did
not report such droplet generation during bubble mergers.
A possible explanation for this discrepancy might be thevery different surface tensions of the working fluids.
Wagner and Stephan (2008) used the same heat flux
determination technique to study the effect of binary
mixtures onto single bubble heat transfer. Their hypothe-

Fig. 1 Color play of TLCs and local temperature drop below

sis was that the well-known heat transfer degradation of

the 3-phase contact line of a growing bubble under low

binary mixtures compared the pure components is related

gravity (left) and normal gravity (right) (Sodtke et al.

to local concentration gradient near the moving contact

2006b)

line. Indeed there study indicates that the local rise in

Fig. 2: Temperature measurement with microthermocouple (MTC) in the near wall 2-phase boundary layer (1: above
growing bubble, 2-4: inside the bubble, 5: in the wake of the rising bubble); Fluid: HFE-7100 at 500 mbar (Tsat=
40°C±0.5K)- 44 -© 2013 The Heat Transfer Society of Japan

Thermal Science & Engineering Vol.21 No.2 (2013)

duction in the liquid film but accounting for the interfacial heat resistance and the effect of disjoining pressure
and curvature on the liquid-vapor equilibrium.
In the beginning of numerical research on pool boiling, quasi-stationary simulations of the heat transferclose to a bubble attached to a heated wall were investigated by Stephan and Hammer (1994). In their simulations the liquid-vapor interface was represented by aboundary of the grid. The heat conduction within theheater is also accounted for. Bubble growth and deparFig. 3 Definition of the micro region from Kunkelmann
and Stephan (2010a)

ture processes were not included directly, but the heattransfer for bubbles of different size attached to the heater could be calculated separately. Convective heat trans-

Besides the modeling of heat transfer within the solid

fer and energy storage in the liquid were neglected. Thisand fluid phase and the representation of phase change

approach was extended from pure fluids to binary mix-

an appropriate handling of contact line heat transfer is antures by Kern and Stephan (2003). To extend the model

important part of boiling heat transfer modeling. As theto transient effects, Fuchs et al. (2006) added an arbitrary

film thickness of the liquid meniscus underneath a bub-

Lagrangian-Eulerian (ALE) kinematic description toble attached to the wall tends to zero at the contact line,

account for bubble growth and detachment. The liquid

the heat transfer resistance gets very small in the contact

vapor-interface was moved according to the actual evap-line area. This results in a very high heat flux in thisoration rate assuming a spherical bubble shape. Convec-

so-called micro region. Despite of the small dimensions

tive heat transfer and energy storage in the liquid wereof the micro region a considerable part of the overall heatincluded. To allow the results for heat transfer to be in-transfer can occur near the contact line. Kunkelmann anddependent of the initial conditions chosen, several suc-

Stephan (2010a) found about 20% of the total heat to be

cessive bubble cycles were calculated with a predefinedtransferred in the micro region. Fuchs et al. (2006) evenwaiting time between bubble detachment and nucleation.

reported a value of 32%.

A significant variation of the heat stored in the wall with

The present models for contact line heat transfer bytime was found. A different model using ALE mesh mo-

Stephan and Busse (1992) and Lay and Dhir (1995) aretion was developed by Welch (1998). He assumed abased on the concept of Potash and Wayner (1972). As

pinned contact line during the bubble growth and did notillustrated in Fig. 3, on a microscopic scale there is nouse a specific model for the contact line heat transfer.

actual contact line, but the liquid meniscus turns into an

Bai and Fujita (2000) as well employed the ALE

adsorbed film of liquid molecules sticking to the wall

method to simulate bubble growth. They assumed an

because of attractive intermolecular forces. The transi-

isothermal wall and made use of the model for evapora-tion region between the adsorbed film and the macrotion in the micro-region introduced by Stephan andregion is referred to as the micro or interline region. The

Hammer (1994). The influence of subcooling and re-typical length scale of this region is less than 1 µm.

duced gravity on flow dynamics and heat transfer were

Therefore this region is not directly included into boilingstudied and a variation in bubble growth rate and shape

simulations but a subscale model is derived which can be

could be observed.

used in the macroscopic simulation.

Big progress in performing transient simulations was

The conservation equations for mass and momentum

made by the development of Eulerian representations ofin the liquid film are simplified using the lubrication

the interface on a fixed grid, which allows more drastic

approximation. The intermolecular forces are capturedchanges in the interface topology than the moving meshby using the disjoining-pressure concept. The energy

approach does. One of these methods is the Volume ofequation is solved assuming one-dimensional heat con-Fluid (VoF) method developed by Hirt and Nichols- 45 -© 2013 The Heat Transfer Society of Japan

Thermal Science & Engineering Vol.21 No.2 (2013)(1981) which became applicable through the handling ofsation at the bubble tip and evaporation at the bubble

surface tension effects proposed by Brackbill et al.

foot compensate. Aktinol and Dhir (2012) extended the(1992). In addition, the level-set method by Osher andmodel to account for the transient heat conduction within

Sethian (1988) or front tracking methods using markers

the heater. The waiting time was no longer prescribed,

by Harlow and Welch (1965) were used. The latter one

but nucleation was tied on a certain wall superheat at thewas used by Esmaeeli and Tryggvason (2004), but theirposition of the nucleation site. The authors found thesimulations were limited to the case of film boiling. Fur-wall thickness and material to influence the waiting time

thermore, a gridless method has been proposed by Yoonsignificantly.

et al. (2001) for nucleate boiling simulation.

A computational model for the simulation of nucleate

Important contributions using the level-set methodboiling utilizing the VoF method was developed bywere done by the group of Dhir. Son et al. (1999) used a

Kunkelmann and Stephan (2009, 2010a, 2010b). Theylevel-set formulation to calculate the effect of the static

accounted for the coupled heat transfer between the fluid

contact angle and the wall superheat on bubble dynamics.

and a thin steel foil used as heater and included a model

They accounted for the contact line heat transfer but as-

for the contact line heat transfer. The static contact angle

sumed an isothermal wall. The waiting time between two

and the waiting time were prescribed according to ex-

successive bubbles was prescribed. Good agreement of

periments. Similar to Fuchs et al. (2006) and Son et al.

their numerical and experimental data was shown. This

(1999) multiple successive bubble cycles were calculated

model was further used to study the effect of liquid sub-to obtain results independent of the initial conditions.

cooling (Dhir, 2001, Wu et al., 2007) and the presence ofGood agreement of numerical and experimental results

contaminants (Bai and Dhir, 2001). Moreover, Son et al.

was achieved (Kunkelmann and Stephan, 2010a). A sig-

(2002) investigated the occurrence of vertical bubble

nificant temperature minimum at the heater surface at themergers between two successive bubbles. Lateral bubble

position of the contact line could be observed. Further-mergers were analyzed by Mukherjee and Dhir (2004).

more, a strong dependency of the near contact line heat

Mukherjee and Kandlikar (2007) used the same model totransfer on the direction of motion of the bubble foot was

study the effect of a dynamic contact angle on bubble

found. In particular, the highest local heat flux was

dynamics. They found mainly the advancing contact an-reached during the bubble detachment, i.e. in an advanc-gle to have influence on the growth rate. Wu and Dhiring contact line situation. This behavior has been con-(2010) further investigated the effect of liquid subcoolingfirmed through combined experiments and simulations

on the bubble growth. In particular, for low gravity con-by Kunkelmann et al. (2012) for various configurations

ditions they found steady state bubbles at which conden-in which moving contact lines appear.

Fig. 4 Schematic of the thermal capacitive IR-transparent heater design- 46 -© 2013 The Heat Transfer Society of Japan

Thermal Science & Engineering Vol.21 No.2 (2013)

3. COMBINED GENERIC EXPERIMENTS AND

about 400 nm, so the temperature measured by IR ther-

SIMULATIONS AT THE AUTHORS’ INSTITUTE

mography on the backside of the chromium based emissivity layer is only ~800 nm away from the heater fluid

3.1 Experimental method and measurement tech-interface. Because of their small thickness compared toniqueSingle bubble experiments and simulations help to

the CaF2 substrate thickness of 2 mm, the thermal re-enhance our understanding of bubble growth and heattion can be neglected. To control the position of bubble

transfer. On realistic boiling surfaces bubble interaction

formation on the heater, the heaters were equipped withwill occur which might result in a change of the heatan artificial nucleation site. In both assemblies, the one

transfer characteristics. Consequently, single bubble ex-with the thin foil heater and the one with the CaF2 based

periments and simulations can only be a first step to-heater, the general measurement method is the same (seewards a more comprehensive understanding of boilingFig. 4). The temperature distribution close to the sol-heat transfer. Recently, boiling experiments at twin cavi-

id-fluid interface is measured using a high speed infraredties have been conducted at the author’s institute to study

IR camera. In case of the sputtered CaF2 heater ab-

the conditions under which bubble merging can occur

sorbtion and emission within the heater substrate can be

and the implications for the local heat transfer. The ex-neglected as the transmissivity of the heater substrate isperiments were accompanied by numerical simulations,99.9 % for a thickness of 2 mm. Thus, the thermal radia-

to identify important parameters and bubble dynamics

tion detected by the IR camera originates from the back-with high temporal and spatial resolution.

side of the black layer. The electron count fields whichsistance and the heat storage of the two-layer composi-

Results presented in section 3.3 were gained on two

are the output of the detector chip of the IR camera aredifferent heater assemblies. A thin foil heater, close to the

mapped to the respective temperature through a pix-

design used by Kenning and Golobic, was used to inves-

el-wise in-situ calibration. To record the bubble shape,

tigate the effect of bubble coalescence. The foil surface

bubble movement and interaction, the IR camera is syn-was equipped with two artificial cavities at distances ofchronized with a high-speed black and white camera that

300 µm and 500 µm. To investigate the effect of the lim-

observes the fluid above the heater surface from the side.

ited heat storage capability of the thin foil heaters and

For the thin foil heater, the local heat flux was calcu-

their low thermal capacity compared to technical heaters,

lated from the temperature fields using equation (1) witha new thermal capacitive heater design has been devel-a finite differences approximation of the derivatives.

oped, which allows the measurement of the heater sur-

While numerical evaluation has shown that the assump-

face temperature (Fischer et al., 2012a). In Fig. 4 ation of negligible temperature gradients across the heater

schematic sketch of the heater design and the measure-thickness for the thin foil heater is justified, this assump-ment technique is shown. An IR transparent calcium flu-tion cannot hold true for the thermal capacitive IR trans-

oride (CaF2) substrate is coated by Physical Vapor Depo-

parent CaF2 heater. To determine the heat flux in thissition (PVD). The coating process itself is divided into

case, a transient 3D energy balance for the heater sub-two phases. The first phase provides a chromium based

strate must be used:layer for better emissivity on the CaF2 substrate, which isnecessary to enhance the quality of the IR thermographymeasurement technique. As the thermal diffusivity of thet  s t 


(2)

2

CaF2 substrate (αCaF ≈ 3.6e−6 m /s) is very close to thatof stainless steel (αSteel ≈ 3.8e−6 m2/s), the thermal

Herein αs is the thermal diffusivity of the IR trans-

transport in the heater substrate is very close to that inparent substrate. The entire substrate block is discretized

technical heaters. The second layer is a pure chromium

into finite volumes and equation (2) is solved on this gridlayer, which is deposited on top of the chromium basedusing the CFD-code OpenFOAM®. The preconditioned

layer, and which is used as electrical heating layer

temperature fields are patched into the calculation as athrough Joule heating. The thickness of each layer istransient boundary condition on top of the discretized- 47 -© 2013 The Heat Transfer Society of Japan

Thermal Science & Engineering Vol.21 No.2 (2013)

substrate. All other boundaries are considered to be adi-tive heater were also conducted in a low gravity envi-

is fixed for the solid region.
 The evaporative mass flux is calculated by the gradient based method described by Kunkelmann andStephan (2010a). With this method, the temperature
gradient close to the liquid-vapor interface is used
to calculate the mass flux within each time step.
The interface is assumed to be at saturation temperature at all times. An enthalpy sink in the temperature equation accordingly accounts for the heat ofevaporation. The volume sources for the continuity
equation are smeared by the method of Hardt andWondra (2008) to prevent instabilities caused bylarge local volume sources. The following steps are
performed to calculate the phase change: Calculation of the evaporative mass flux at the phaseboundary Calculation of the energy source terms caused byevaporation for the energy equation
 Solving a diffusion equation for the evaporative
mass flux Setting of mass sinks in the liquid region and mass
sources in the vapor region
 Rescaling of mass sinks and sources, such that massconservation is fulfilled
As mentioned, the thin film area in the vicinity of theronment during a parabolic flight. Due to the increased

contact line can play an important role in boiling pro-bubble growth period and bubble departure diameter

cesses and additional physics have to be considered. To

under low gravity, the spatial and temporal resolution of

capture the processes in this region, a subgrid scale mod-a bubble growth and detachment process is increased

el was implemented, which consists of a fourth ordercompared to measurements under normal gravity.

differential equation developed by Stephan and Busseabatic. As initial condition the substrate is assumed to be
at a uniform temperature corresponding to the mean
temperature of the first temperature field of a sequence.
To ensure the stability of the calculation, the temperaturefields are linearly interpolated in between the acquired
frames, so more time steps can be performed. From thiscalculation one obtains the transient local heat flux distribution between the CaF2 substrate and the chromium
based emissivity layer, which has the same temporal andspatial resolution as the temperature field. By superposition of this heat flux field with the electrically generated
heat flux within the pure chromium heating layer, theheat flux distribution at the heater-fluid interface is calculated. A discussion of the measurement accuracy andthe subsequent uncertainty of further derived quantities
using this method is presented by Fischer et al. (2012b).
With both heaters PF-5060 was used as working fluid.
The single bubble investigations on the thermal capaci-(1992). As the calculation of a solution at each time step
3.2 Numerical Method
Currently, numerical simulations are based on thewithin the flow solver would be too time consuming, thework of Kunkelmann and Stephan (2009). A standard

Matlab® for several parameters. The results can be fitted

2-phase finite volume solver from the open source CFD

by a series of root functions which are used in Open-

Software OpenFOAM® was extended to allow the sim-

FOAM®. The heat transferred within the contact line

ulation of conjugate boiling heat transfer.

region is added directly to the calculation of the evapora-calculations are performed with the software package

In the fluid domain the incompressible Navier-Stokes

tion mass flux. For the conjugate problem, the heat

equations are solved with the PISO algorithm. In Open-transfer at the contact line can be added to the heat flux

FOAM®, the interface is tracked with the Vol-boundary of the solid region.

ume-of-Fluid method (refer to Hirt and Nichols (1981))

In OpenFOAM® the VoF method is used to track theand interface compression is applied to prevent the nu-

movement of the phase boundary, which results in an

merical diffusion of the interface. In the solid domaininterface that is smeared over several cells. In order to beheat conduction is calculated and - depending on theable to accurately calculate the temperature gradient for

problem definition - a volumetric heat source or temper-

the evaporation model, a contour based reconstruction ofature gradient at the bottom is applied. The solid and thethe interface was implemented by Kunkelmann andfluid region are coupled by looping over the temperature

Stephan (2010b). The value of the VoF variable is inter-equations and adjusting the boundary conditions in thepolated from the cell centers to the points and assuming asolid and the fluid region. At the wall boundary, thelinear gradient, the points where the VoF variable attains

temperature is fixed for the fluid region and the heat flux

the value 0.5 can be calculated on the edges. With this- 48 -© 2013 The Heat Transfer Society of Japan

Thermal Science & Engineering Vol.21 No.2 (2013)

the interface normal and interface area can be determinedcurrents by one magnitude. Reducing the spurious cur-for each cell. The reconstructed interface can further-rents is an important issue as they increase the heatmore be used to calculate the curvature of the interface,transfer to the interface and therefore lead to an inaccu-

leading to a reduction in the velocities of the spurious

rate quantitative calculation of the evaporation rate.

Fig. 5 High speed image, temperature distribution and heat flux below a vapor bubble growing on a CaF2 heater during
expansion of the bubble foot (upper row) and during contraction of the bubble foot (lower row) under lunar
gravity (0.16 gE)

Fig. 6Integrated heat flux at the 3-phase contact line of a single bubble,
left: Experimental results (Schweizer, 2010), right: Numerical results (Kunkelmann, 2012)

The model allows full 3D simulations of boiling,- 49 -

evaporation and condensation processes. On hexahedral© 2013 The Heat Transfer Society of Japan

Thermal Science & Engineering Vol.21 No.2 (2013)

cells OpenFOAM® offers dynamic mesh refinementfrom the heater-fluid interface (depending on the thick-options which can be employed to highly resolve theness of the foil) the measurement plane of the CaF2 heat-interface region without a massive increase in the overall

er is only ~800 nm away from the interface. Therefore

number of cells. Furthermore, the model is fully paral-

the temperature signal on the thin foil heater is blurredlelized to benefit from the capabilities of today’s multi-

through lateral thermal conduction across the foil thick-core workstations and clusters.

ness, while there is only very small blurring across the

The different parts of the model were validated ex-

two sputtered layers of the CaF2 heater. The initial stages

tensively as described by Kunkelmann (2011). The per-of bubble growth are accompanied by high contact line

formance of the full model was demonstrated by Kun-

velocities, removing energy from the substrate fasterkelmann and Stephan (2010a) by simulating nucleate

than it can be re-supplied through thermal conduction.

boiling at a single nucleation site and comparing the re-This results in an apparently global temperature drop
below the growing bubble as seen in the upper row ofsults with experimental data of Wagner (2007).
Nucleation cannot be depicted with the numericalFig. 5. As the bubble foot reaches its maximum radius,

model. Therefore an initial bubble nucleus has to be set

the contact line velocity is slowed down and the temper-

with the same frequency, as it is observed in the experi-

ature drop below the bubble is compensated by thermal

ments. By simulating several cycles, the thermal bound-

conduction within the solid. At the 3-phase contact line

ary layer develops and consequently results are not de-however, energy is still constantly removed by contact

pending on initial conditions. Bubble diameter andline evaporation, resulting in a very narrow temperature

growth time were found to be within 20% of the experi-

drop close to the contact line (see Fig. 5, lower row). For

mental results. The temperature drop of the wall in thethe low receding contact line velocity during the contrac-

vicinity of the three phase contact line was 1.5 K for both,tion of the bubble foot, this temperature minimum close

experiments and simulations.

to the contact line stays localized until bubble departure.
The local heat flux peak at the 3-phase contact line is

3.3 Results
In Fig. 5 a typical result from measurements carriedeven higher in this case than in case of the expandingout on the IR transparent heater element as described inexperimental investigation carried out on thin foil heaters

section 3.1 is shown for an expanding bubble foot (re-by Schweizer (2010), even though distinctive differencesceding contact line, Fig. 5, upper row) and a contracting

in the thermal response of the solid were found. The re-bubble foot (advancing contact line, Fig. 5, lower row).

sults obtained by Schweizer (2010) are in very good

As it has been observed for foil heaters, the distinct heatagreement to numerical calculations by Kunkelmann

flux peak in close proximity of the 3-phase contact line is(2011). In Fig. 6 a comparison of experimental and nu-

also visible for this heater configuration. When compar-

merical results for the integrated heat flux at the contact

ing these results to those obtained by Schweizer andline of single bubbles is shown. Numerical simulations

Stephan (2009), one can notice that the temperature dropof moving 3-phase contact lines by Kunkelmann et al.

in the heater substrate caused by the bubble is one order(2012) indicate that the reason for higher heat flux dur-of magnitude lower. This difference is caused by theing the advancing contact line situation is that cold liquidmuch higher thermal capacity of the CaF2 heater com-

is sucked to the heater surface through the motion of thepared to the thin foil heater used by Schweizer andliquid vapor interface; see Fig. 7. As can be seen in theStephan (2009). However, the location of the tempera-

Fig. the highest temperature gradient occur either close

ture drop detected by the IR camera is much moreto the wall-liquid interface (advancing contact line dur-bounded by steep temperature gradients on the CaF2

ing detaching bubble phase) or close to the liquid-vapor

heater. This is caused by the differences in the measure-interface (receding contact line during growing bubble

ment plane. While the location of the temperature meas-

phase). Furthermore, the dry wall below the bubble heats

urement on the thin foil heater is 10 µm or 20 µm away

up und thus the temperature differences between wall

- 50 -

bubble foot. This result is in agreement with previous© 2013 The Heat Transfer Society of Japan

Thermal Science & Engineering Vol.21 No.2 (2013)

Fig. 7 Temperature field (colored curves, distance: 1 K) and streamlines of relative velocity (black curves) in close
vicinity of the 3-phase contact line during bubble growth (4 ms after nucleation) and detachment (10 ms after
nucleation) (Kunkelmann, 2011)
and saturated liquid are higher for the advancing contact

merical simulations.

line than for the receding one. A real heater element usu-

A comparison of the heat flux obtained from numeri-

ally has a rather high thermal capacity. This experimentcal simulations and from experiments is shown in Fig. 9.

proves that in such a case the transient heat transfer

From the numerical results it could be withdrawn thatwithin the solid material cannot be neglected, as it has aafter the bubble merger a capillary wave at the liq-

strong effect onto the local temperature and heat flux

uid-vapor interface propagates from the merging plane

distribution during the early stages of a bubble cycle.

along the bubble surface. The fast movement of the liq-

From the experiments with two artificial cavities it

uid-vapor interface and the 3-phase contact line follow-

was possible to show that for a given distance of the cav-

ing the merging process leads to a local enhancement ofities, an optimal pressure exists to maximize the proba-

the heat flux. This local heat flux enhancement can bebility of bubble merging to occur. In Fig. 8 the optimal

observed in Fig. 9 at the right and the left hand side ofpressure for two different cavity spacings is shown. If

the bubble at 4 ms and 6 ms after the merging event.

pressure is much lower or much higher than the optimalpressure bubble coalescence rarely occurs. At low pressures the nucleation site that is activated first creates afast growing bubble that covers immediately the second
nucleation site. Thus, only a single large bubble is observed. At high pressures bubble departure diameters aremuch smaller, consequently, two bubbles are generated
and growing next to each other without coalescence.
Therefore the optimal pressure for coalescence rises withdecreasing cavity distance.
During experiments with the thin foil heater at pressures below 600 mbar a residual liquid droplet was observed within the large bubble that was generated during
the merging process of the two small bubbles. The for-

Fig. 8Frequency of horizontal bubble coalescencemation of this droplet could be reproduced within nu-- 51 -© 2013 The Heat Transfer Society of Japan

Thermal Science & Engineering Vol.21 No.2 (2013)

Fig. 9 Comparison of experimental (top) und numerical (bottom) heat flux profile during coalescence

Heat sink

EnergyvapourConvective
heat transfer
to vapour atadsorbed
layer

Evaporation/condensation at
bubble hull
Periodicheatstorage inliquidboundary
layer

Evapo‐
rationnear
contact
line

Energyliquid

Mara‐
ngoni
conv‐
ectionConvec‐tive heattransfer
to bulk
liquidConductive heat transfer toliquid thermal boundary layer
Transient heat conduction and periodic local heat storage
in the wall
Heat source

Fig. 10

Heat paths from heater (heat source) to bulk fluid (heat sink) during a single bubble cycle of the nucleateboiling processsimulations the following conclusions on local transport
4. CONCLUSIONS ON LOCAL TRANSPORT

phenomena can be drawn. The related heat paths from

PHENOMENA: LEARNING OUTCOME

heat source (heater) to heat sink (bulk fluid) are sche-

Heat transfer and evaporation at a single bubble subsystem seems to represent nucleate boiling phenomenaquite well up to about 40 to 50% of the critical heat flux.
Above this heat flux bubble interactions and flow dynamics become more important. On the basis of numerous previous studies and the recently performed combined generic single bubble experiments and numerical- 52 -

matically shown in Fig. 10.
 Local transient effects in heat conduction in thewall underneath the bubble are quite pronounced.
Therefore, numerical models assuming constant andhomogeneous wall temperature do not depict animportant effect. During the bubble growth and departure phase the wall is locally cooled down. A
minimum temperature is observed underneath themoving contact line with large local temperature
gradients. During the bubble rise phase and waiting© 2013 The Heat Transfer Society of Japan

Thermal Science & Engineering Vol.21 No.2 (2013)












period the wall next to the nucleation site is reheated again.
The near contact line region evaporation accounts
for up to approx. 30% of the overall evaporation
rate during a complete bubble cycle. During the
growth phase with increasing bubble base radius(receding contact line) the local heat flux maximum
is less pronounced than during the bubble departurephase with decreasing base radius (advancing contact line).
Convective heat transfer from the wall to the liquidboundary layer next to the bubble accounts for atleast approx. 70% of the overall heat rejection fromthe wall.
Direct convective heat transfer from the wall to thevapor at the dry patch (adsorbed thin film) underneath the bubble contributes only very little to theoverall heat transfer.
The evaporation rate decreases dramatically during
the bubble rise phase. Recondensation might occur
depending on the subcooling of the bulk liquid.
The liquid boundary layer is cooled down during
the bubble growth and departure phase due tostrong evaporation. During the departure and the initial rise phase cold liquid flows from the bulk area
into the wake of the bubble. Later the liquid boundary layer next to the nucleation site locally heats up
again until nucleation occurs again.
Maragoni convection due to temperature gradientcan be neglected for pure fluids. Opposed to that,
Marangoni convection due to composition gradientin mixtures might be relevant.

Further studies, both, generic experiments as well as
numerical simulations, are needed. Attention should bedirected towards the phenomena during bubble mergers
to expand the knowledge of heat transfer phenomena
described in this paper towards higher heat flux regimes.
Understanding heterogeneous nucleation is still a totally
open issue, and predictions of active nucleation site densities are therefore impossible. Much work is needed
here.

of the award.
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ACKNOWLEDGMENT
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