International Journal of Multiphase Flow 40 (2012) 56–67

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International Journal of Multiphase Flow

journal homepage: www.elsevier .com/locate / i jmulflow

Measurement of two-phase flow and heat transfer parameters usinginfrared thermometry

Tae Hoon Kim, Eric Kommer, Serguei Dessiatoun, Jungho Kim ⇑University of Maryland, Department of Mechanical Engineering, College Park, MD 20742, USA

a r t i c l e i n f o

Article history:Received 30 September 2011Received in revised form 28 November 2011Accepted 28 November 2011Available online 9 December 2011

Keywords:Infrared thermographyHeat transfer distributionTwo-phase flowsDroplet evaporation flow boilingLiquid film thickness

0301-9322/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.ijmultiphaseflow.2011.11.012

⇑ Corresponding author. Tel.: +1 301 405 5437.E-mail address: kimjh@umd.edu (J. Kim).

a b s t r a c t

A novel technique to measure heat transfer and liquid film thickness distributions over relatively largeareas for two-phase flow and heat transfer phenomena using infrared (IR) thermometry is described.IR thermometry is an established technology that can be used to measure temperatures when opticalaccess to the surface is available in the wavelengths of interest. In this work, a midwave IR camera(3.6–5.1 lm) is used to determine the temperature distribution within a multilayer consisting of a siliconsubstrate coated with a thin insulator. Since silicon is largely transparent to IR radiation, the temperatureof the inner and outer walls of the multilayer can be measured by coating selected areas with a thin, IRopaque film. If the fluid used is also partially transparent to IR, the flow can be visualized and the liquidfilm thickness can be measured. The theoretical basis for the technique is given along with a descriptionof the test apparatus and data reduction procedure. The technique is demonstrated by determining theheat transfer coefficient distributions produced by droplet evaporation and flow boiling heat transfer.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction evaporation in microchannels was proposed by Thome et al.

Definitive understanding of phase change heat transfer mecha-nisms remains elusive due its sensitivity to many variables, but alsodue to a lack of reliable local information that can enable models tobe tested. Although point measurements or area averaged measure-ments of variables such as local film thickness and heat transfer havebeen made, techniques whereby these quantities can be measuredover large areas are generally lacking. Point or average measure-ments may be appropriate at very low heat fluxes where insignifi-cant evaporation occurs and the flow regime does not change, butsuch measurements are insufficient for model validation.

Techniques that have been used in the past to measure localfilm thickness have utilized capacitance sensors, conductanceprobes, confocal microscopes, and other techniques such as reflec-tance (e.g., Coney, 1973, Klausner et al., 1990, Han and Shikazono,2009, and Shedd and Newell, 1998). The heat transfer has usuallybeen measured using thermocouples welded to the tube walls orby resistively heating the walls and measuring the average walltemperature. The authors are not aware of any techniques wherebyliquid film and heat transfer distributions in flow boiling are mea-sured over relatively large areas with high resolution. If the heattransfer distribution along the walls of a tube could be measured,it could be used to verify models of the heat transfer variations pre-dicted by models of slug flow, wavy annular flow, annular flowdryout, etc. For example, a three-zone model of elongated bubble

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(2004) and Dupont et al. (2004). The model assumes that heat istransferred to a liquid slug, an elongated bubble, and a vapor slug(Fig. 1). Heat transfer to the elongated bubble is thought to occurthrough the thin liquid film between the vapor and the wall. Thebubble frequency, liquid film thickness, and heat transfer to the li-quid and vapor slugs are obtained from correlations. The globallyaveraged heat flux was measured and used for model verification.Much stronger verification of the model can be made if measure-ments of the local heat flux were available to verify the heat trans-fer rates before, during, and after passage of the bubble.

In flow regime based models (e.g., Kattan et al., 1998a,b,c), thelocal flow boiling heat transfer coefficients are predicted basedon the tube perimeter fraction wetted by liquid. For example, fora horizontal stratified flow in a circular tube, the local heat transfercoefficient is given by

htp ¼rihdryhvapor þ rið2p� hdryÞhwet

2prið1Þ

where hwet is assumed to be composed of a nucleate boiling compo-nent and a convective component in a power law form:

hwet ¼ h3nb þ h3

c

� �1=3ð2Þ

For annular and intermittent flow, htp ¼ hwet . The local void frac-tion needed to evaluate liquid and vapor velocities is calculatedusing correlations (e.g., Rouhani and Axelsson, 1970). Again, verifi-cation of these models can benefit greatly from measurements ofthe local heat transfer distribution in the various regimes.

Fig. 1. Three-zone heat transfer model for evaporation in a microchannel from [1]. Lp is the total length of the triplet. Ll, Ldry and Lfilm are the length of the liquid slug, the dryzone and the liquid film trapped by the bubble, respectively. The internal radius and diameter of the tube are R and d while d0 and dmin are the thicknesses of the liquid filmtrapped between the elongated bubble and the channel wall at its formation and at dry out.

T.H. Kim et al. / International Journal of Multiphase Flow 40 (2012) 56–67 57

The objectives of this paper are to describe and demonstrate anIR thermometry based technique whereby the local heat transferproduced by two-phase flows can be measured with high spatialand temporal resolution. The application of the technique to themeasurement of liquid film thickness is also described. IR ther-mometry is an established technology that can be used to measuretemperatures when optical access to the surface is available in thewavelengths of interest, and has been used to measure heat trans-fer distributions during pool boiling heat transfer. Golobic et al.(2009) and Stephan and co-workers (e.g., Schweizer and Stephan,2009) used an IR camera to measure the heat transfer distributionunder single nucleating bubbles as they grew on a thin metal foils.Stephan has recently begun using a thicker CaF substrate in placeof the thin film in order to increase the heat capacity of the sub-strate (Fischer et al., 2011) so it is more representative of real sur-faces. Gerardi et al. (2010) used a high speed IR camera inconjunction with a video camera to measure bubble behavior onan ITO heated sapphire substrate. The IR camera measured thetemperature distribution at the ITO surface, while a video camerawas used to visualize the fluid behavior. Krebs et al. (2010), Shenet al. (2010) and Mani et al. (2012) used IR thermography to studyflow boiling in microchannels, droplet evaporation, and jetimpingement, respectively. In these studies, an IR camera was usedto view through a silicon substrate to visualize in great detail thetemperature distribution at the silicon/water interface. Sefianeet al. (2008) used IR thermography to visualize the spontaneouslyoccurring hydrothermal waves within evaporating methanol, etha-nol, and FC-72 droplets.

In the present work, a midwave IR camera (3.6–5.1 lm) is usedto measure the temperature variations within a multilayer consist-ing of a silicon substrate coated with a thin thermal insulator thatis partially transparent to IR. The insulator amplifies the tempera-ture variations and provides a strong signal for the IR camera. Sincesilicon is largely transparent to IR radiation, the temperature of theinner and outer walls of the multilayer can be measured by coatingselected areas with a thin IR opaque film. The fluid used (FC-72) isalso partially transparent to IR over a broad range of wavelengths,allowing the flow to be visualized and the film thickness to bemeasured. The theoretical basis for the technique, a descriptionof the test apparatus and data reduction procedure, and experi-mental validation are presented in the sections below.

2. Theoretical background

Consider the multilayer wall consisting of a silicon substrateonto which polyimide tape (polyimide layer + acrylic adhesive) is

attached as shown schematically on Fig. 2a. An opaque black paintthat is much thinner than the other layers is applied to the top ofthe polyimide tape. The black surface is exposed to a two-phaseflow. The polyimide tape is necessary to measure heat transfercoefficient distributions of the expected magnitude since the highthermal conductivity of the silicon substrate would simply smearout any temperature variations through substrate conduction,reducing both the magnitude of the temperature differences aswell as the spatial resolution.

To obtain the heat transfer coefficient at the fluid-wall interface,the temperature gradient within the polyimide tape is required. Ifthe time-varying temperatures of the black surface Ts1(t) and Ts2(t)are known, the instantaneous temperature profile within the mul-tilayer can be obtained through an unsteady heat conduction sim-ulation. If the polyimide tape is thin compared with the spatialresolution of the camera and the temperature gradient is much lar-ger in the x-direction than in the y- and z-directions, a 1-D heatconduction assumption can be used. The 3-D heat conductionequation must be used otherwise. Assuming 1-D heat conduction,the governing equations within the layers are given by

qsicp;si@T@t¼ ksir2T þ _qsi ð3aÞ

qAcp;A@T@t¼ kAr2T ð3bÞ

qPcp;P@T@t¼ kPr2T ð3cÞ

and the system is subject to the boundary conditions T = Ts1(y,z, t) atx = 0, T = Ts2(y,z, t) at x = LSi + LA + LP.

Consider now the calculation of the black surface temperatureTs1(t). This temperature is not directly available since the energymeasured by the IR camera consists of emission from the black sur-face, emission from each of the layers (which depends on the tem-perature profile within them), and reflection from thesurroundings. Since the optical properties of the polyimide andadhesive are similar, they are treated as a single layer in the radi-ation calculation as indicated in Fig. 2b. The total energy measuredby the camera (Ec) is the sum of the energies emitted by each layerwithin the spectral bandwidth of the IR camera (k1–k2):

Ec ¼ q1�cE1 þ eSi�cESi þ eT�cET þ ss�cEs ð4Þ

where E1 ¼ Fk1�k2rT41 is the blackbody radiation due to the sur-

roundings, ESi ¼R LSi

0 aSiFk1�k2r½TSiðxÞ�4 expð�aSixÞdx is the energyemitted by the silicon that reaches the Si-1 interface,

Fig. 2. Model descriptions. (a) System schematic for the conduction problem. (b) System schematic for the radiation problem.

1 For the condition used for the experimental verification described below, theitial transient was found to have completely decayed after 0.1 s.

58 T.H. Kim et al. / International Journal of Multiphase Flow 40 (2012) 56–67

ET ¼R LT

0 aT Fk1�k2r½TTðxÞ�4 expð�aT xÞdx is the energy emitted by thetape that reaches the T–Si interface, Es ¼ Fk1�k2rT4

s;1 is the blackbodyradiation of the black surface.

Fk1�k2 is total emitted energy from a blackbody contained withthe wavelength interval k1–k2 and can be obtained from tables orby integrating the Plank distribution. The coefficients q1-c, eSi-c,eT-c, and ss-c account for the attenuation and reflection within themultilayer wall, and are given by

q1�c ¼ qSi�1 þð1� qSi�1Þ

2qapp;Si�Ts2Si

1� qSi�1qapp;Si�Ts2Si

ð5Þ

eSi�c ¼ð1� qSi�1Þð1þ qapp;Si�TsSiÞ

1� qSi�1qapp;Si�Ts2Si

ð6Þ

eT�c ¼ð1� qSi�1Þð1� qSi�TÞð1þ qT�ssTÞsSi

1� qSi�1qapp;Si�Ts2Si

� �1� qSi�TqT�ss2

T

� � ð7Þ

ss�c ¼ð1� qSi�1Þð1� qSi�TÞð1� qT�sÞsSisT

1� qSi�1qapp;Si�Ts2Si

� �1� qSi�TqT�ss2

T

� � ð8Þ

qapp;Si�T ¼ qSi�T þð1� qSi�TÞ

2qT�ss2T

1� qSi�TqT�ss2T

ð9Þ

The derivation of the above equations is given in the Appendix.The optical properties of the various layers along with the temper-ature of the surroundings (T1) are assumed to be known. The tem-perature distribution within the silicon [TSi(x)] and the tape [TT(x)]and the temperature of the black surface (Ts,1) are not known ini-tially, but can be obtained by solving the coupled conduction andradiation problems according to the following algorithm:

1. Assume an arbitrary temperature profile within the multi-layer at t = 0.

2. Compute ESi and ET from the temperature distribution anddetermine an updated Es and surface temperature Ts,1 fromEq. (4).

3. Solve the conduction equation using the updated Ts,1 toobtain a new temperature profile at t = Dt.

4. Repeat steps 2 and 3 for each successive time step.

The effect of the assumed initial temperature profile within themultilayer will decay after which the true temperature profile willbe known.1 The heat flux from the wall to the fluid can be obtainedfrom the derivative of the instantaneous temperature profile withinthe polyimide at the black surface according to q00 ¼ �kP

@T@x

��x¼0.

3. Experimental results

3.1. Radiant property determination

The above model requires knowledge of the reflectivity andabsorptivity of the materials used. These were determined experi-mentally using the two configurations shown in Fig. 3. The black-body consisted of a large cylindrical cavity at a controlledtemperature behind a small orifice as shown in Fig. 4. The emissiv-ity of this blackbody is estimated to be >0.999 using the relationprovided in Quinn (1967).

The apparent reflectivity was determined using the experimen-tal setup shown in Fig. 3a. The blackbody was positioned such thatemission from it reflected from either the front or back surface ofthe layer to be tested. The total energy reaching the IR camera con-sisted of the blackbody energy reflected from the layer, the self-

in

InsulationAluminum

Black paint

Film heaterThermocouple

50 mm

150 mm

10 mm

12 mm

12 mm

Fig. 4. Blackbody construction.

T.H. Kim et al. / International Journal of Multiphase Flow 40 (2012) 56–67 59

emission of the layer, and the transmission of energy from the sur-roundings through the layer:

Ec1 ¼ qapp;m—1 Fk1�k2rT4b

� �þ eapp;m—1 Fk1�k2rT4

m

� �þ sapp;m—1 Fk1�k2rT4

1

� �ð10Þ

The measurement was then repeated without the blackbody:

Ec2 ¼ qapp;m�1 Fk1�k2rT41

� �þ eapp;m�1 Fk1�k2rT4

m

� �þ sapp;m�1 Fk1�k2rT4

1

� �ð11Þ

Subtraction of Eq. (10) from Eq. (11) allowed the apparent reflectiv-ity to be determined since the temperature Tb and T1 are known.

The apparent transmissivity was determined using the setupshown in Fig. 3b. The total energy reaching the camera with andwithout the blackbody are given by

Ec3 ¼ qapp;m�1 Fk1�k2rT41

� �þ eapp;m�1 Fk1�k2rT4

m

� �þ sapp;m�1 Fk1�k2rT4

b

� �ð12Þ

Ec4 ¼ qapp;m�1 Fk1�k2rT41

� �þ eapp;m�1 Fk1�k2rT4

m

� �þ sapp;m�1 Fk1�k2rT4

1

� �ð13Þ

Subtracting one from the other allowed the apparent transmissivityto be determined. The apparent reflectivity and transmissivity for asingle layer m sandwiched by two identical layers n are given by

qapp;m�1 ¼ qm�1 þð1� qm�1Þ

2qm�1s2m

1� q2m�1s2

mð14Þ

sapp;m�1 ¼ð1� qm�1Þ

2sm

1� q2m�1s2

mð15Þ

(see Appendix for a derivation), from which qm-1 and sm can be ob-tained. The absorption coefficient can then be obtained from theBeer–Lambert law, sm, and the layer thickness.

The above technique was verified by measuring the reflectivityof a double side-polished silicon wafer (n = 3.43 at k = 3.7 lm) inair (n = 1.00). An analytical expression for the reflectivity at thesilicon–air interface is given by

qSi�air ¼nSi � nair

nSi þ nair

� �2

¼ 0:301 ð16Þ

This was in good agreement with the experimentally measured va-lue of qSi-air = 0.34.

The reflectivity of the tape was calculated using the indices ofrefraction of the polyimide (npolyimide = 1.7) and air to be

(a) (b

IR

Eb

Ec

T

Film, Tm

Blackbody

IR

Fig. 3. Schematic of experimental setup used to measure the reflectivity and transtransmissivity measurement.

qpolyimide�air ¼npolyimide � nair

npolyimide þ nair

� �2

¼ 0:07 ð17Þ

If the index of refraction of the acrylic adhesive was assumed tobe that of acrylic (nadhesive = 1.5), the reflection would beqadhesive-air = 0.04. The reflection between the polyimide and adhe-sive is very small qpolyimide-adhesive = 0.004. Since reflection withinthe tape is small and since the reflectivities of the polyimide andthe acrylic adhesive are similar, the tape was considered to behaveas a single optical layer with polyimide properties. The absorptioncoefficient of the tape was measured experimentally. A summaryof the optical properties of the silicon and polyimide tape are givenon Table 1. The absorption coefficient of the polyimide tape is seento be much larger than that of the silicon.

3.2. Uncertainty analysis

The experimental uncertainty in the calculated heat flux wasdetermined by perturbing each experimental parameter a smallamount one at a time and running the algorithm to find the sensi-tivity to the variables at varying heat fluxes. Many of the assumedphysical constants (e.g. thermal conductivity and thickness of sili-con) introduced errors that were several orders of magnitude smal-ler than the important sources of error and were therefore omitted.The parameters that resulted in the highest error along with theirvalues and assumed are tabulated in Table 2. The maximum totalerror, calculated as the RMS of each individual error, increases withheat flux and is summarized in Table 3 at various heat fluxes.

3.3. Validation and demonstration

3.3.1. Air coolingTo validate the experimental technique and algorithm, the

apparatus shown in Fig. 5 was used. A Si wafer was heated by athin film heater. Polyimide tape (30 lm total thickness) with a thinblack coating was deposited onto the top of the Si wafer to

)

EbEc

T

Film, Tm

Blackbody

missivty of a single layer. (a) Apparent reflectivity measurement. (b) Apparent

Table 1Optical properties of the silicon and polyimide tape.

Material Absorption coefficient (m�1)Silicon 52.6Polyimide tape 7110

Interface ReflectivitySi–air 0.34Polyimide–air 0.07Polyimide–Si 0.14

Table 3Summary of uncertainty analysis.

Heat flux (W/cm2) 2.0 4.0 6.0 8.0 10.0Max Error (W/cm2) 0.35 0.47 0.62 0.80 0.98

Fig. 5. Experimental setup for validation (not to scale).

Fig. 6. Comparison of the top temperature, Ts1(t), determined using the algorithmand the energy measured through the bottom EBot,c(t) (computed temperature) withthat measured directly using Etop(t) (actual temperature).

60 T.H. Kim et al. / International Journal of Multiphase Flow 40 (2012) 56–67

measure the top surface temperature Ts1(t). The black coating(6 lm thick) was produced by silk screening onto the polyimidetape Nazdar GV111 paint consisting of about 20% carbon black ina vinyl chloride/vinyl acetate copolymer after curing. The high car-bon black content ensured the coating was opaque, and its highthermal conductivity relative to the polyimide and thinness al-lowed its temperature to be assumed to be uniform.

The emissivity of the black surface was experimentally deter-mined. The polyimide tape with black coating was attached to aheated aluminum plate containing a thermocouple. The platewas heated to temperatures between 45–95 �C, and the energyemitted from the surface along with the energy reflected fromthe surroundings were measured using the IR camera. The total en-ergy measured by the IR camera is given by

Ec ¼ eFk1�k2rT4s þ ð1� eÞFk1�k2rT4

1 ð18Þ

from which the surface emissivity can be determined. The emissiv-ity of the black coating was measured to be 0.90.

A small piece of a polyimide tape with black coating was at-tached to the bottom of the wafer to measure the bottom surfacetemperature Ts2(t). Gold coated mirrors were used to simulta-neously measure the energy emitted from both the top [ETop(t)]and bottom [EBot,c(t),EBot,b(t)] surfaces. Since the black surfaceswere not transparent to IR, the black surface temperatures on thetop [Ts1(t)] and bottom [Ts2(t)] surfaces could be directly obtainedusing the energies [ETop(t),EBot,b(t)] using an IR camera (Electro-physics Silver 660 M). The black surface temperature on the topof the wafer Ts1(t) could also be calculated based on the algorithmusing EBot,c(t) and Ts2(t). To validate this calculation, the calculatedtop surface temperature was compared with the temperature ob-tained from ETop(t) as the top of the wafer was cooled using anair jet. Results are shown in Fig. 6. The air jet was turned on att = 5.7 s, resulting in a drop in the surface temperature. When theair jet was turned off at t = 10.9 s, the temperature recovered. Goodagreement within 0.5 �C was seen between the measured and com-puted values, demonstrating that the algorithm can be used toaccurately predict the true surface temperature.

3.3.2. Droplet evaporationTo further demonstrate the power of the technique, the appara-

tus shown in Fig. 5 was used to measure the wall heat flux during

Table 2Parameters with largest effect on uncertainty analysis.

Experimental constant Value UncertaintyEmissivity of the black coating 0.90 0.01Absorptivity of the polyimide tape 7110 (m�1) 500 (m�1)Polyimide thickness 15 lm 2 lmAdhesive thickness 15 lm 2 lmReflectivity of silicon–air interface 0.34 0.017Reflectivity of silicon-polyimide interface 0.14 0.007Thermal conductivity of polyimide 0.12 W/m-K 0.01 W/m-KThermal conductivity of adhesive 0.20 W/m-K 0.01 W/m-K

evaporation of a single droplet of PF-5060. The substrate washeated to 83 �C by attaching a thin film heater to the silicon wafer,after which a syringe was used to deposit a droplet onto the topsurface. The IR camera was used to measure the heat transfer tothe droplet from below the wafer. Fig. 7 shows temperature andheat flux contours as the droplet evaporates and illustrates howthe local temperature and heat transfer can be measured with highspatial and temporal resolution.2

The droplet reached its first maximum diameter approximately21 ms after impact, then contracted until 42 ms. During this pro-cess, high heat transfer between the droplet and the heated surfacewas observed inside the droplet with a maximum heat transfer of

2 A movie of the droplet evaporation process is available online at (mmc1.mpg).

Temperature (oC) Heat Flux (W/cm2) Temperature (oC) Heat Flux (W/cm2)

5 mmt = 0 ms t = 308 ms

t = 21 ms t = 317 ms

t = 42 ms t = 329 ms

t = 72 ms t = 336 ms

t = 145 ms t = 368 ms

t = 242 ms t = 399 ms

t = 273 ms t = 459 ms

Fig. 7. Temperature and heat flux contours for droplet evaporation.

T.H. Kim et al. / International Journal of Multiphase Flow 40 (2012) 56–67 61

about 23 W/cm2. After 42 ms, the droplet spread again and thediameter reached a second maximum at 242 ms. During this time,nucleate boiling within the droplet resulted in a higher heat trans-fer (about 10 W/cm2) at the center of the droplet than at the edges.After 242 ms and until the droplet evaporates, the droplet size de-creased due to evaporation at the rim of the droplet. Nucleate boil-ing ceased as the droplet thinned and ruptured. The highest heattransfer occurred at the receding three-phase contact line asexpected.

The above results are for PF-5060 evaporating on the blackpainted surface and may not be representative for evaporationon silicon. Due to the highly wetting nature of PF-5060, however,the effect of contact angle is not expected to be important. Surfaceeffects may be much larger when water is used, however.

3.3.3. Gravity effects on flow boilingThe technique was also used to measure flow boiling heat trans-

fer during the high gravity and low gravity conditions produced byan aircraft. A polished tube 6 mm ID � 8 mm OD � 120 mm longwas manufactured from a block of single crystal n-type silicon with>1 X-cm resistivity. Two current taps and two voltage taps consist-ing of a chromium adhesion layer and 2000 Å of aluminum weredeposited at the ends of the tube after they were doped to mini-mize contact resistance (<1 X), allowing the power dissipated bythe tube to be determined using a four-wire measurement. Thetube was heated using a power supply that could impose up to300 V across the tube, producing a nominal heat flux of up to4 W/cm2. Polyimide tape was attached to the inside of the tube,but only half of the tape had a black coating (Fig. 8). The mirror

IR Camera

Temperature Measurement

Flow Visualization

Silicon tube

Black coating

Gold mirrors

Fig. 8. Mirror setup to allow simultaneous flow visualization and measurement ofmultilayer temperatures. The green lines indicate the location of the black coatingon the inner and outer surfaces of the silicon tube. (For interpretation of thereferences to color in this figure legend, the reader is referred to the web version ofthis article.)

Fig. 9. Solid model of flow loop.

62 T.H. Kim et al. / International Journal of Multiphase Flow 40 (2012) 56–67

arrangement allowed simultaneous visualization of the flow alongwith measurement of the temperature distribution on the insideand outside of the tube.

A flow loop (Fig. 9) was constructed so FC-72 could be pumpedthrough the tube at known mass fluxes up to 200 kg/m2-s and inlettemperatures from room temperature to near saturated(Tsat = 57 �C for FC-72 at 1 atm). The primary loop included the sil-icon test section where wall temperature measurements weremade using the IR camera. The two-phase mixture exiting the testsection was condensed in a counterflow heat exchanger thenpumped through a flowmeter and preheater before entering thetest section again. An accumulator (expansion tank) was used tokeep the pressure within the loop at nominally 1 atm. The temper-ature of the FC-72 exiting the heat exchanger was controlled byoccasionally pumping cold water through the heat exchanger.

The variable gravity environment was produced by a Zero GCorporation 727 aircraft flying parabolic arcs as part of NASA’sFAST program in July, 2011. Approximately 20 s of 1.8 g pullupwas followed by 20 s of low-g (±0.01 g) and 20 s of 1.8 g pullout.Up to 40 parabolas were flown per flight and four flights weremade. The test section was oriented such that the liquid enteredthe tube in a vertical upward flow configuration—because the flowproduced is nominally axisymmetric, heat transfer data was re-duced only along the axis of the tube. This configuration alsoavoids refraction effects that can occur due to the curvature ofthe tube when viewing the tube off-axis.

The heat transfer coefficient distribution is shown on Fig. 10aas the fluid flows through the tube in a low-g environment at arelatively low mass flux of 44 kg/m2-s.3 Large variations are ob-served where liquid rewets the surface with peaks up to12,000 W/m2-K. Very low heat transfer is also observed on thetube, indicating dryout of the surface. Time averaged heat transfercoefficient distributions along the tube in high-g and low-g areshown on Fig. 10b. The effect of gravity is minimal in the first halfof the tube where the flow is dominated by bubbles dispersed in aliquid. The heat transfer deteriorates towards the tube exit, how-ever, as the flow transitions to a wavy annular type flow with peri-odic dryout. Additional data at various flow rates and inletenthalpies will be presented in future work.

3.3.4. Liquid film thicknessWe close this paper with a discussion on how the technique can

be used to measure liquid film thickness in a tube. Consider thecase where a liquid film flows along the inside walls of a round

3 A movie of flow boiling in low-g is available online at (mmc2.mp4).

tube as can occur during annular flow (Fig. 11). The tube and liquidare in thermal equilibrium at temperature Ts, and placed in a largeenclosure at temperature T1. The IR camera looks through the tubeat a black surface at Thot. The energy measured by the IR camera Ec

consists of energy from the surroundings that are reflected fromthe front, the emission from the tube and liquid, and the energyemitted from Thot that is transmitted through the tube and liquid.It can be shown thatEc ¼ q1f�cEb;1 þ ½ð1� smÞemf�c þ ð1� slÞelf�c þ ð1� slÞelr�c

þ ð1� smÞemr�c�Eb;S þ shot;r�cEb;hot ð19Þwhere

Eb;1 ¼ rT41; Eb;S ¼ rT4

S ; Eb;hot ¼ rT4hot

sl ¼ expð�alLlÞ; sm ¼ expð�amLmÞ

q1f�c ¼ q1—m þð1� q1—mÞ

2qapp;4s2m

1� q1—mqapp;4s2m

emf�c ¼ð1� q1—mÞð1þ qapp;4smÞ

1� q1—mqapp;4s2m

elf�c ¼ð1� q1—mÞsm

1� q1—mqapp;4s2m�ð1� ql�mÞð1þ qapp;3slÞ

1� ql�mqapp;3s2l

elr�c ¼ð1� q1—mÞsm

1� q1—mqapp;4s2m� ð1� ql�mÞsl

1� ql�mqapp;3s2l

� ð1� ql�vÞ1� ql�vqapp;2

�ð1� ql�vÞð1þ qapp;1slÞ

1� ql�vqapp;1s2l

emr�c ¼ð1� q1—mÞsm

1� q1—mqapp;4s2m� ð1� ql�mÞsl

1� ql�mqapp;3s2l

� ð1� ql�vÞ1� ql�vqapp;2

� ð1� ql�vÞð1� ql�mÞð1þ q1—msmÞsl

1� ql�vqapp;1s2l

� �1� ql�mq1—ms2

m

� �

shot;r�c ¼ð1� q1—mÞsm

1� q1—mqapp;4s2m� ð1� ql�mÞsl

1� ql�mqapp;3s2l

� ð1� ql�vÞ1� ql�vqapp;2

� ð1� ql�vÞð1� ql�mÞð1� q1—mÞslsm

1� ql�vqapp;1s2l

� �1� ql�mq1—ms2

m

� �

qapp;1 ¼ ql�m þð1� ql�mÞ

2q1—ms2m

1� ql�mq1—ms2m

0 50 100 150 200 250 300 350 400 450 500 550 6000

1000

2000

3000

4000

5000

6000

Pixel

Avg.

Hea

t Tra

nsfe

r AVG h (High-g) = 3041 (W/m2K)AVG h (Low-g) = 1891 (W/m2K)

High-g (0-20s)Low-g (25-40s)

Coe

ffici

ent (

W/m

2 K)

(a)

(b)

Fig. 10. Flow boiling heat transfer during vertical upward flow at a mass flux of 44 kg/m2-s and fluid inlet temperature of 55 �C. The heat flux applied to the tube is nominally4 W/cm2. (a) Heat transfer coefficient distribution at a representative time in a low-g environment. (b) Time averaged heat transfer distribution in high-g (1.8 g) and low-genvironments.

Fig. 11. Schematic of axisymmetric liquid layer flowing on the inside of a tube (medium m).

T.H. Kim et al. / International Journal of Multiphase Flow 40 (2012) 56–67 63

qapp;2 ¼ ql�v þð1� ql�vÞ

2qapp;1s2l

1� ql�vqapp;1s2l

qapp;3 ¼ ql�v þð1� ql�vÞ

2qapp;2

1� ql�vqapp;2

qapp;4 ¼ ql�m þð1� ql�mÞ

2qapp;3s2l

1� ql�mqapp;3s2l

All parameters in Eq. (19) can be measured with the exception of sl,from which the liquid film thickness Ll can be determined. If heattransfer occurs across the liquid film, the temperature variationwithin the liquid needs to be accounted for.

The range of film thicknesses that can be measured dependsprimarily on the absorption coefficient of the fluid. A plot of theeffective transmissivity of a liquid film flowing within a silicontube (Fig. 11) with 1 mm thick walls as the liquid film thicknessis varied is shown in Fig. 12. The effective transmissivity is onlyabout 0.33 even when no liquid flows in the tube due to reflectionat the silicon interfaces. As the liquid film thickness increases, theeffective transmissivity decreases and the system becomes effec-tively opaque at large thicknesses. If it is assumed that the trans-missivity can be accurately measured between 20% and 80% ofthese limits (horizontal dashed lines in Fig. 12), the range of liquidfilm thickness that can be measured can be found. For example, itis expected that only thin water films (�4–40 lm) can be mea-sured due to its high absorption coefficient while FC-72 films canbe measured over a much broader range (�150–1000 lm).

64 T.H. Kim et al. / International Journal of Multiphase Flow 40 (2012) 56–67

4. Closing remarks

A new technique for the measurement of high resolution heattransfer distributions due to two phase flow phenomena basedon IR thermometry has been described. The technique was demon-strated on droplet evaporation and flow boiling in low-g environ-ments. The equations needed to calculate the thickness of anisothermal liquid film in round tubes were derived and estimateswere made of liquid film thicknesses that can be measured.

Acknowledgements

This work was sponsored by NASA through Grant NNX09A-K39A. The grant monitor was Mr. John McQuillen. The flights onthe Zero G Corporation aircraft were made possible through theNASA FAST program.

Appendix A

A.1. Beer–Lambert law

Consider radiation of intensity I0 (W/m2) striking a layer ofthickness L. The intensity of the radiation (I) exiting the other sideis given by I = I0exp(�aL) where a (m�1) is the absorption coeffi-cient and represents the ability of the layer to attenuate the incom-ing radiation. The transmissivity of a layer due to absorption alonecan be expressed as s = exp(�aL).

A.2. Emission from translucent materials

Translucent materials simultaneously generate and absorb radi-ation. Radiation generated within the layer must travel through thematerial before it reaches the surface, during which it is attenuatedin accordance with the Beer–Lambert law. Part of the radiationreaching the surface is emitted and the remainder can be reflectedback into the layer where it can be re-absorbed and re-reflected.The effective radiant properties of translucent materials is derivedbelow. It is assumed that the values all optical properties are inde-pendent of temperature.

Consider first the radiation emitted by a differential layer ofthickness dx with an emission coefficient e (m�1) and an absorptioncoefficient a (m�1) as shown in Fig. A1. The emission coefficientcharacterizes how black the layer is. The radiation flux emittedfrom the differential thickness dx in the x direction is given by

Liquid Film Thickness (µm)

Eff

ecti

ve T

rans

mis

sivi

ty

Fig. 12. Range of liquid film thicknesses that can accurately be measured on asilicon tube.

er[T(x)]4 dx. Because the differential element is thin, all of thisradiation leaves the differential volume. The radiation that is notabsorbed by the material that strikes the surface of the film atx = 0 is given by er[T(x)]4exp[�ax]dx. The total radiation energygenerated by the layer that strikes x = 0 can then be obtained byintegration:

E ¼Z L

0er½TðxÞ�4 exp½�ax�dx ðA:1Þ

For the special case where the temperature in the layer is uni-form, Eq. (A.1) reduces to

E ¼ earT4½1� expð�aLÞ� ðA:2Þ

In the limit of infinitely thick films, Eq. (A.2) indicates that theenergy flux is

EL!1 ¼earT4 ðA:3Þ

Since very thick films act like a blackbody radiating energy at T,the layer will emit radiation according to EL?1 = rT4, indicatingthat the relation between emission and absorption coefficients ise = a.

Consider next reflection at the surfaces. As mentioned above,part of the radiation reaching the surface of a layer can bereflected at the surface or transmitted through the surface multi-ple times as shown in Fig. A2 where medium m is sandwichedbetween two other media 1 and n. The energy emitted by thelayer that reaches the 1–m interface is given by Em and can becalculated from Eq. (A.1). The fraction of this energy that escapesfrom this surface is ð1� q1—mÞEm while the energy reflected backinto m is q1—mEm. The reflected energy that is not absorbedwithin m before arriving at the m-n interface is given byexpð�amLmÞq1—mEm ¼ smq1—mEm. This radiation is reflected againat the m–n interface, absorbed within m, and arrives at the 1–minterface. The second contribution to the energy that escapes the1–m interface is thus

ð1� q1�mÞq1�mqm�ns2mEm ðA:4Þ

This process of reflection occurs again with the result that thethird contribution is

ð1� q1�mÞq21�mq2

m—ns4mEm ðA:5Þ

The energy escaping through the 1–m interface is therefore

x

dx

L

,

Fig. A1. Radiation emitted within a translucent layer.

T.H. Kim et al. / International Journal of Multiphase Flow 40 (2012) 56–67 65

ð1� q1—mÞEm þ ð1� q1—mÞq1—mqm—ns2mEm þ ð1

� q1—mÞq21—mq2

m—ns4mEm þ � � �

¼ ð1� q1—mÞEm

X1n¼0

q1—mqm—ns2m

� �n ðA:6Þ

Thus far, only the radiation emitted toward the 1–m interfacehas been considered. Radiation is also emitted toward the m–ninterface and part of this energy escapes through the 1–m inter-face. By applying the same processes as shown in Fig. A2b, the en-ergy leaving the left surface can be expressed as.

ð1� q1—mÞqm—nsmEm þ ð1� q1—mÞq2m—nq1—ms3

mEm þ ð1� q1—mÞq3

m—nq21—ms5

mEm þ � � �

¼ ð1� q1—mÞqm—nsmEm

X1n¼0

q1—mqm—ns2m

� �n ðA:7Þ

The total emission from the 1–m interface (Em-1) is the sum-mation of Eqs. (A.6) and (A.7):

Em—1 ¼ ð1� q1—mÞð1þ qm—nsmÞEm

X1n¼0

q1—mqm—ns2m

� �n ðA:8Þ

Since q1—m, qm—n, and sm are always less than unity, the infiniteseries may be written in analytical form as

Em—1 ¼ð1� q1—mÞð1þ qm—nsmÞ

1� q1—mqm—ns2m

Em ðA:9Þ

Similarly, the energy emitted by m that escapes from the m–ninterface (Em–n) is given by

Em—n ¼ð1� qm—nÞð1þ q1—msmÞ

1� q1—mqm—ns2m

Em ðA:10Þ

A.3. Apparent reflectivity and apparent transmissivity of a single layer

Let us first consider the reflection of incoming radiation E1 froma single layer as shown in Fig. A3a. Part of the incoming energy isreflected from the 1–m interface. The remainder is attenuated bymedium m, and part of this is reflected from the m–n interface backtowards the 1–m interface. Using a similar line of reasoning asabove to account the infinite number of reflections, the total

Fig. A2. Emission from medium m through the1–m interface. q1–m = reflectivity betweeand sm = transmissivity of medium m. (a) Energy emitted by m towards the1–m interfacthat leaves the 1–m interface.

energy reflected from m is the sum of the energies leaving the1–m interface shown in Fig. A3a:

E1—m ¼ q1—mE1 þ ð1� q1—mÞ2qm—ns2

mE1 þ ð1

� q1—mÞ2q1—mq2

m—ns4mE1 þ ð1

� q1—mÞ2q21—mq3

m—ns6mE1 þ � � �

¼ E1½q1—m þ ð1� q1—mÞ2qm—ns2

m

�X1n¼0

ðq1—mqm—ns2mÞ

n�

¼ E1 q1—m þð1� q1—mÞ

2qm—ns2m

1� q1—mqm—ns2m

" #ðA:11Þ

The apparent reflectivity is therefore given by

qapp;1—m ¼ q1—m þð1� q1—mÞ

2qm—ns2m

1� q1—mqm—ns2m

ðA:12Þ

The apparent transmissivity of medium m to E1 is found in asimilar manner by summing the energies leaving the m–n interfacein Fig. A3b:

sapp;1—m ¼ð1� q1—mÞð1� qm—nÞsm

1� q1—mqm—ns2m

ðA:13Þ

The apparent transmissivity is seen to be independent of thedirection of the incoming radiation.

The apparent absorptivity of m can also be determined from asimilar accounting of energy absorbed within m to be

aapp;1—m ¼ð1� q1—mÞð1þ qm—nsmÞð1� smÞ

1� qm—nq1—ms2m

ðA:14Þ

We leave it as an exercise to the reader to verify thataapp;1—m þ qapp;1—m þ sapp;1—m ¼ 1. These apparent properties arethe same as those presented by McMahon (1950) if q1—m ¼ qm—n

and the temperature distribution in medium m is uniform.

n medium1 and medium m, qm–n = reflectivity between medium m and medium n,e that leaves the1–m interface. (b) Energy emitted by m towards the m–n interface

Fig. A3. Energy reflected and transmitted from medium m. (a) Apparent reflectivity. (b) Apparent transmissivity.

IR

, 1.0T =

m m n

, 0S s =

Medium m Medium n

Surface s

Ambient

cE

Fig. A4. Schematic diagram for two-layer materials.

66 T.H. Kim et al. / International Journal of Multiphase Flow 40 (2012) 56–67

A.4. Energy emission by two-layer materials including reflection fromambient

Consider now the case shown in Fig. A4. The energy striking anIR camera is composed of four components: the energy emitted byan opaque surface s, emission from the two media (m and n), andby reflection from the surroundings.

For the special case where es = 1, we need to consider each ofthe four energy components below:

A.4.1. Energy from surroundingsThe energy from the surroundings (E1 ¼ rT4

1) is reflected fromsurfaces 1–m and m–n is given by qapp;1—mE1. The energy trans-mitted through m is partly attenuated in n and the remainder iscompletely absorbed by surface s. No reflection occurs at surfaces, simplifying the analysis.

A.4.2. Energy emitted by mThe energy emitted by m leaving the interface 1–m is

given by

Em ¼Z Lm

0amr½TmðxÞ�4 expð�amxÞdx ðA:15Þ

The energy emitted by m that leaves interface m–n is again ab-sorbed either by n or s and does not reach the camera.

A.4.3. Energy emitted by nThe energy emitted by n that reaches interface m–n is

given by

En ¼Z Ln

0anr½TnðxÞ�4 expð�anxÞdx ðA:16Þ

The energy that is transmitted through m and reaches the IRcamera is given by sapp;1—mEn.

A.4.4. Energy emitted by sThe energy emitted from s (Es ¼ rT4

s ) that reaches interfacem–n is snEs ¼ expð�anLnÞEs. The portion transmitted through mthat strikes the camera is sapp;1—msnEs.

The total energy striking the camera is the sum of these fourcomponents and is given by

Ec ¼ q1—m þð1� q1—mÞ

2qm—ns2m

1� q1—mqm—ns2m

" #E1

þ ð1� q1—mÞð1þ qm—nsmÞ1� q1—mqm—ns2

m

Em

þ ð1� q1—mÞð1� qm—nÞsm

1� q1—mqm—ns2m

En

þ ð1� q1—mÞð1� qm—nÞsmsn

1� q1—mqm—ns2m

Es ðA:17Þ

If the surface s is not black (es < 1) but still opaque, reflectionsfrom this surface must be accounted for and the problem becomemore complex since an infinite number of reflections occur withintwo materials. For the sake of brevity, only the final results are gi-ven below. The energy striking the camera accounting for infinitereflections from surface s is given by

Ec ¼ q1—cE1 þ em�cEm þ en�cEn þ ss�cEs ðA:18Þ

where

q1—c ¼ q1—m þð1� q1—mÞ

2qapp;m—ns2m

1� q1—mqapp;m—ns2m

em�c ¼ð1� q1—mÞð1þ qapp;m—nsmÞ

1� q1—mqapp;m—ns2m

T.H. Kim et al. / International Journal of Multiphase Flow 40 (2012) 56–67 67

en�c ¼ð1� q1—mÞð1� qm—nÞð1þ qn�ssnÞ

1� q1—mqapp;m—ns2m

� �1� qm—nqn�ss2

n

� �

ss�c ¼ð1� q1—mÞð1� qm—nÞð1� qn�sÞsmsn

1� q1—mqapp;m—ns2m

� �1� qm—nqn�ss2

n

� �and

qapp;m—n ¼ qm—n þð1� qm—nÞ

2qn�ss2n

1� qm—nqn�ss2n:

Appendix B. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.ijmultiphaseflow.2011.11.012.

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