measurement of falling film thickness around a horizontal tube using a laser measurement technique

Heat Transfer Engineering, 25(8):28–34, 2004Copyright C©© Taylor & Francis Inc.ISSN: 0145-7632 print / 1521-0537 onlineDOI: 10.1080/01457630490519899

Measurement of FallingFilm Thickness Arounda Horizontal Tube Usinga Laser MeasurementTechnique

D. GSTOEHL, J. F. ROQUES, P. CRISINEL, and J. R. THOMELaboratory of Heat and Mass Transfer, Swiss Federal Institute of Technology, Lausanne,Switzerland

A new optical method for the non-intrusive measurement of falling film thickness on the perimeter ofhorizontal tubes is described. The technique uses a high-speed digital video camera to capture theimages of the liquid interface that are illuminated by a laser sheet, with the contrast enhanced by afluorescent powder in the fluid. The results are compared to those predicted by the Nusselt fallingfilm theory, showing relatively good agreement around the upper perimeter of the tube but muchpoorer agreement on the lower perimeter. The corresponding effects on heat transfer have also beenestimated.

Falling film condensation and evaporation are impor-tant heat transfer processes in shell-side condensationand evaporation. In the laminar regime, convective heattransfer across the film is essentially a one-dimensionalheat conduction problem. In particular, Nusselt [1] hasstudied laminar film condensation on vertical and in-clined plates and on the perimeter of horizontal tubes,and he proposed a theory for film condensation heattransfer that has become a classic method presented intextbooks and handbooks. His method has also been ap-plied to condensation on a vertical array of horizontaltubes, assuming a continuous sheet flow from tube totube, which results in the classic tube row effect expres-

This research was sponsored by the EPFL/LTCM Falling Film ResearchClub together with a financial contribution by the EPFL. Club members areAxima AG; Dunham-Bush, Inc; UOP, Inc; Wieland Werke; and WolverineTube, Inc.

Address correspondence to Prof. John Richard Thome, Laboratory ofHeat and Mass Transfer (LTCM), Faculty of Engineering Sciences and Tech-niques (STI), Swiss Federal Institute of Technology (EPFL), CH 1015 Lau-sanne, Switzerland. E-mail: [email protected]

sion. For the liquid film thickness δ on an inclined plate,he developed the following expression:

δ =(

3µL�

ρL (ρL − ρG)g sin β

) 13

(1)

where β is the angle between the plate and the horizontaland � is the local flow rate on the plate. He used the sameexpression to describe condensation on a horizontal tubeby varying β around the perimeter, where � is the flowrate on one side of the tube and 2� is the total flowrate on the tube. With this definition, the film Reynoldsnumber

Re = 4�

µL(2)

is equivalent on the plate and on the tube.For a fully developed laminar film flow, heat is trans-

ferred across the film by one-dimensional heat con-duction, such that the local heat transfer coefficient isinversely proportional to the film thickness. Hence,

28

falling film heat transfer, whether for condensing, evap-orating, or subcooled films, is very sensitive to the ac-tual thickness of the film. Nusselt assumed momentumeffects on the falling film to be negligible; hence, thisraises the question as to whether or not this is valid forflow around a tube and also in regard to different spac-ings between the tubes in an array. Consequently, filmthickness is an important parameter in these processesand merits further study to determine the limitations ofthe Nusselt theory, which is the topic of our present in-terest. Furthermore, numerous numerical publicationshave appeared in the literature in the past few years onfalling films flows, typically not verified by any flowvisualization of the film’s interface or thickness.

The thickness of a liquid film flowing on a horizontaltube has been investigated experimentally by several au-thors using different techniques. Thomson [2] measuredthe water film thickness by means of a micrometer at theangular position of β = 90◦ from the top of the tube.His results were in good agreement with Nusselt’s the-ory over the range considered. Rogers and Goindi [3]used a similar technique with three dial point gaugesmounted at 45◦, 90◦, and 135◦ locations. An electriccircuit was used to indicate when the point just estab-lished contact with the water film. Their values wereabout 30% greater than theoretical values of Nusselt.

Another popular technique for film flows on verti-cal surfaces is use of parallel-wire conductance probes.Conductance probes relate the film thickness to the elec-trical resistance between two electrodes immersed in theliquid film ([4–6]). The disadvantage of this method isthe intrusion of the probes into the liquid film, whichmay perturb the film flow and raise the surface at theinsertion location due to surface tension effects.

To avoid contact with the liquid film, non-intrusivemethods have been developed. For instance, Dukler andBergelin [7] used a capacitance method to measure theliquid film thickness on a vertical plate. An electricalcondenser was made by placing a small plate in frontof the vertical plate. The electrical capacitance of thiselectrical condenser is a function of the liquid film thick-ness on the vertical plate, and hence the method can becalibrated to make such measurements.

More recently, optical methods have become morewidely used. Zhang et al. [8] measured the liquid filmthickness on a vertical tube. They used the images froma video camera to measure the average thickness, whilea laser and a photo diode were used to measure the tran-sient amplitude of waves. Desevaux et al. [9] presentedan interface measurement technique for a liquid filmflowing inside small grooves by laser-induced fluores-cence. The advantage of this method is a high resolutionin the detection of the liquid–gas interface. Also, Sheddand Newell [10] have used a light diode source and its

reflection to measure pointwise film flow thickness inannular two-phase flows.

In this article, the film thickness of a liquid flowingaround the outside of a horizontal plain tube is measuredusing laser-induced fluorescence. A high-speed digitalvideo camera is used to record the locus of the inter-face, which also provides a high temporal and spatialresolution.

DESCRIPTION OF TEST FACILITY

A schematic of the test facility is shown in Figure 1.It is composed of three main parts:

• Fluid circuit. The fluid starts out in the tank that servesas a reservoir for the whole circuit and then passesthrough a centrifugal pump and a filter. The flow rateis measured with one of two rotameters, which arenecessary to cover the desired ranges of mass flowand viscosity. The liquid temperature in the tank ismaintained constant by a small heat exchanger coil atthe bottom, which is regulated with a fluid from anautomatic controlled temperature bath.

• Tranquilization chamber. Its function is to provide auniform flow distribution along the top tube and fromthe top tube onto the second tube. It is 300 × 260 ×10 mm (inside Height × Width × Depth), with theflow entering at the top through two holes and leavingat the bottom through a flat plate with 1 mm diameterholes spaced 2 mm apart center-to-center. The lengthof this distribution system is 200 mm.

• Test section. It is comprised of three horizontal tubesin a vertical array on which the liquid flows. The tubesare conventional 19.05 mm-diameter plain coppertubes whose surfaces are carefully cleaned. They areheld at one end, and the distance between them is fixedwith specially manufactured spacers. Care is taken to

Figure 1 A diagram of the test setup.

heat transfer engineering vol. 25 no. 8 2004 29

obtain a precise alignment of the horizontal tubes intoa vertical array. The liquid film thickness is measuredon the second tube with a technique described in thefollowing section.

FILM MEASUREMENT TECHNIQUEAND TEST CONDITIONS

Flow visualization is realized using laser-induced flu-orescence and laser tomography techniques. The liquidfilm on the tube, is illuminated by a laser sheet in theradial direction along the horizontal axis of the tube, asillustrated in Figure 2. When the light impinges on theliquid, the free surface becomes visible. A digital high-speed camera is used to observe the illuminated sectionin a direction perpendicular to the laser sheet. The laserand the camera are mounted on a support that can bepivoted around the center of the tube.

The laser sheet is generated by an arrangement oflenses that is connected to the light source by an opticalfiber. The light source is a continuous laser emitting agreen ray with a wavelength of 532 nm. Rhodamine isadded to the test liquid for its fluorescent properties ata concentration of 0.15 g per liter. The fluorescent lightemitted by the liquid is viewed through a filter placed infront of the camera which eliminates reflections of thelaser light. The camera is equipped with a high magni-fication objective; thus, the field of view is about 3.3 ×3.1 mm. The images from the camera have a resolutionof 512 × 480 pixels. Figure 3 (left photo) illustrates theresulting image of the film interface along the axis ofthe tube. At every angular position around the tube, 60images are taken at a speed of 125 frames per second.Figure 3 (right photo) shows an image of the dry tubeobtained at each angular location, which is used as thereference to determine the film thickness. Each pixelhas a resolution of 6.4 µm (3300 µm/512 pixels) whilethe interface detection is very good because of the sharpcontrast, resulting in an error of about 20 µm in the filmthickness.

For visualization in the lower part of the tube (β >

90◦), the position of the laser sheet and camera are in-

Figure 2 A diagram of the film thickness measurement setup.

Figure 3 Images of liquid film interface (left) and of dry tube(right). The difference between them gives the local film thicknessalong the interface.

verse. Due to geometrical restrictions, the visualizationcould only be performed between β = 22◦ and 62◦ onthe upper part of the tube and between β = 112◦ and152◦ on the lower part of the tube.

The numerical images are treated by an image pro-cessing software developed specifically for this purposein order to extract the interface of the liquid film. Thesame procedure is applied to the image of the dry tube toobtain the location of the surface of the tube. The liquidfilm thickness is the distance between these two con-tours. The film thickness is then obtained by averagingthe mean thickness of the liquid film obtained in sixtysuccessive images.

Several tests were performed to estimate the reli-ability of the measurement technique. The maximumobserved difference between two measurements underidentical conditions was ±0.05 mm, which correspondsto ±10% of a mean thickness of 0.5 mm, while the av-erage error was estimated to be ±7%.

Test Conditions

The intertube spacings of the measurements were3.2 mm, 6.4 mm, 9.5 mm, and 19.4 mm. To obtain awide range of Reynolds number, three different liquidswere used: water, reagent grade ethylene glycol, and awater–glycol mixture (50%–50% by mass). With eachfluid, three flow rates were chosen and tested to putthe intertube flowmode in the sheet mode, which is as-sumed in applying the Nusselt theory [1] to vertical rowsof horizontal tubes. All test conditions were below theReynolds number for transition to turbulent flow (typ-ically cited to be 1600–1800). For each test condition(one spacing and one flow rate), the film thickness wasmeasured at nine angular positions on the top part of thetube and nine positions on the bottom. The angular stepwas 5◦.

EXPERIMENTAL RESULTS AND DISCUSSION

Figure 4 illustrates the variation of the liquid filmthickness as a function of time at the angular position

30 heat transfer engineering vol. 25 no. 8 2004

Figure 4 Fluctuations in film thickness versus time.

β = 47◦ from the top of the tube for a tube spacing ofs = 6.4 mm. The plotted values are averaged values ofthe longitudinal profile of the film thickness from everypicture. The fluctuations in film thickness increase withan increasing Reynolds number. The same behavior canbe observed in Figure 5, which shows the deviation ofthe measured film thickness with time as a function ofthe Reynolds number for two angular positions. Thesefluctuations or ripples on the interface of the falling filmare relatively small (<12%) with respect to the filmthickness.

According to Butterworth [11], the film Reynoldsnumber for the onset of interfacial waves on a verticalplate is at about a film Reynolds number of 30. Thisvalue has been added in Figure 5 as a dotted verticalline. It can be seen that the measurements for glycolare near the threshold for the onset of waves, and themeasurements for water and water–glycol mixture areexpected to be in the wavy region. Also, in Figure 4, thewaves become of notable height only above Re = 30.

Figure 5 Fluctuations in film thickness versus the Reynoldsnumber.

Figure 6 Film thickness versus angle at Re = 30.

Some measurements of the film thickness are pre-sented in Figures 6–11. They show the measured filmthickness as a function of the angular position β. Eachgraph represents one fluid at one flow rate (one Renumber). The film thicknesses measured for all thetube spacings are shown. On the top part of the tube,the variation in film thickness with increasing inter-tube spacing is evident at the lower Reynolds num-bers, suggesting that momentum of the falling film tendsto decrease its thickness. However, at high Reynoldsnumbers, the thickness for s = 3.2 mm falls sharplycompared to the others, for which there is no readyexplanation. In general, over the top perimeter of thetube, the deviation from Nusselt theory increases withincreasing film Reynolds number.

The global trend of the measurements is compared tothe Nusselt model in the above figures (solid lines). Hismodel predicts a minimum in film thickness at β = 90◦and then an increase as the tangential component ofgravity decreases. While reasonably good agreement




is found on the top half of the tube at low Re values,this is not so on the lower half. Apparently the reasonfor this is that the momentum acquired by the film atβ = 90◦ is not lost by the fluid when β > 90◦, an effectthat is not covered by the Nusselt theory, which assumesnegligible momentum effects on the flow. Based on thefilm thickness data, it makes sense to use the Nusselttheory as is for the top half of the tube and to assumethe thickness remains unchanged at its value at β = 90◦for the lower half as a simple modification to the model(ignoring the large deviations at s = 3.2 mm). Thus, inthe upper part of the tube (0◦ < β < 90◦), the thicknessis predicted by Nusselt’s model (Eq. 1), while the filmthickness is constant in the lower part of the tube (90◦ <

β < 180◦), the value of which corresponds to the valuefrom Nusselt’s theory at β = 90◦ (dashed line).

These two models (original and modified) are evalu-ated in Figures 12 and 13, respectively, comparing themeasured thickness versus that calculated by the modelfor all the tested spacings and Reynolds number. Two



dash lines are added to fix the domain of ±30% error.The film thicknesses are segregated by fluid as indicated.

In Figure 14, the models are compared statistically.For every measurement, the relative error is calculatedby:

εi = δmodel − δexp

δexp(3)

For one absolute value of the relative error, the mea-surements that give a relative error smaller than thechosen value are counted. The result is plotted relativeto the total number of measurements. Figures 12–14 arebased on a total of 633 thickness measurements.

CONSEQUENCES ON HEAT TRANSFER

Using the Nusselt theory (Eq. 1) for the film thick-ness, the following expression for the mean heat transfercoefficient can be found for laminar film condensation



Figure 12 Comparison of measured film thickness with that pre-dicted by the Nusselt model.

on a single tube:

α = C

(ρL (ρL − ρG)gλ3

LhLG

µL (Tsat − Twall)D

) 14

(4)

where his theoretical leading constant is C = 0.729.Performing a similar analysis using the film thicknessdescribed by the modified Nusselt model above gives aleading constant of C = 0.762. This means an augmen-tation of just 5% of the global heat transfer coefficientresults from the smaller-than-expected film thickness onthe lower part of the tube. This shows that the Nusselt

Figure 13 Comparison of measured film thickness with that pre-dicted by the modified Nusselt model.

Figure 14 Distribution of the relative error for the Nusselt modeland the modified Nusselt model.

theory for film flow is a good starting point not onlyfor laminar film condensation, but also for laminar filmevaporation as long as the intertube flow mode is sheetflow. Instead, for the droplet and column flow modes,significant three-dimensional effects are visible in ourvideos, which may be investigated in a future study.

With regard to falling film evaporation with nucleateboiling in the film, the thinner films on the lower half ofthe tube will tend to suppress nucleation and facilitatethe formation of dry patches, both of which would besignificantly detrimental to heat transfer.

Ignoring the results for s = 3.2 mm, which is smallerthan the tube spacing typically found in heat exchangers,the film thickness on the top of the tube tends to decreasewith increased tube spacing, which is logical becauseof the added momentum of the falling liquid. Hence,the falling film condensation heat transfer coefficientwill tend to increase with increasing s. With respect totube row effect on laminar film condensation on a tubebundle, the value of s can thus be expected to affectNusselt’s tube row effect expression by as much as25–30%.

CONCLUSIONS

A new optical method based on laser-induced flu-orescence and image processing of high-speed digitalvideos has been developed for measuring falling filmthicknesses on the outside of a horizontal tube. Thesenon-intrusive measurements are accurate to about ±7%and ±10% (mean and maximum errors, respectively) ofthe film thickness and also provide the variation in thethickness with time and axial position from image pro-cessing of the video sequences. Thus, compared to othermethods, this new technique does not interfere with the


flow and yields local film thicknesses as a function oftime and position along the segment of the film illumi-nated by the laser sheet. In particular, the present mea-surements show that while the classic Nusselt fallingfilm theory gives a reasonable prediction of film thick-ness on the top of the tube, it tends to significantly over-estimate values on the lower perimeter.

NOMENCLATURE

D tube diameter, mg acceleration due to gravity (9.81), m/s2

hLG latent heat, J/kgRe film Reynolds number, 4�/µs intertube spacing, mT temperature, K

Greek Symbols

α heat transfer coefficient, W/m2Kβ angular position on a horizontal tube measured

from the top or angle between a plate and thehorizontal, ◦

� film mass flow rate on one side per unit length ofcylinder, kg/ms

δ film thickness, mλ thermal conductivity, W/mKµ dynamic viscosity, Ns/m2

ρ density, kg/m3

Subscripts

G gasL liquidsat saturated condition

REFERENCES

[1] Nusselt, W., Die Oberflachenkondensation des Wasser-dampfes, Zeitschr. Ver. Deut. Ing., vol. 60, pp. 541–546, 569–575, 1916.

[2] Thomson, A. K. G., Heat Transmission in Film-Type Coolers,Journal of the Society of Chemical Industry, Japan, Supple-mental Bind., vol. 40, pp. 380T–384T, 1937.

[3] Rogers, J. T., and Goindi, S. S., Experimental Laminar FallingFilm Heat Transfer Coefficients on Large Diameter HorizontalTubes, Can. J. Chem. Eng., vol. 67, pp. 560–568, 1989.

[4] Coney, M. W. E., The Theory and Application of ConductanceProbes for the Measurement of Liquid Film Thickness in Two-Phase Flow, J. Phy. E, vol. 6, pp. 903–910, 1973.

[5] Brown, R. C., Andreussi, P., and Zanelli, S., The Use of WireProbes for Measurement of Liquid Film Thickness in AnnularGas–Liquid Flows, Can. J. Chem. Eng., vol. 56, pp. 754–757,1978.

[6] Koskie, J. E., Mudawar, I., and Tiederman, W. G., Parallel-Wire Probes for Measurement of Thick Liquid Films, Int. J.Multphase Flow, vol. 15, no. 4, pp. 521–530, 1989.

[7] Dukler, A. E., and Bergelin, O. P., Characteristics of Flow inFalling Liquid Films, Chem. Engineering Progress, vol. 48,no. 11, pp. 557–563, 1952.

[8] Zhang, J. T., Wang, B. X., and Peng, X. F., Falling LiquidFin Thickness Measurement by an Optical-Electronic Method,Review of Scientifique Instruments, vol. 71, no. 4, pp. 1883–1886, 2000.

[9] Desevaux, P., Homescu, D., Panday, P. K., and Prenel, J. P.,Interface Measurement Technique for Liquid Film FlowingInside Small Grooves by Laser Induced Fluorescence, AppliedThermal Engineering, vol. 22, pp. 521–534, 2002.

[10] Shedd, T. A., and Newell, T. A., Automated Optical LiquidFilm Thickness Measurement Method, Review of Scientific In-struments, vol. 69, no. 12, pp. 4205–4213, 1998.

[11] Butterworth, D., Film Condensation of Pure Vapor, Hemi-sphere Handbook of Heat Exchanger Design, Chapter 2.6.2,Hemisphere, New York, 1990.

Daniel Gstoehl is a Ph.D. student in the Labora-tory of Heat and Mass Transfer at the Swiss Fed-eral Institute of Technology in Lausanne (EPFL),Switzerland. He received his diploma at the SwissFederal Institute of Technology in Zurich (ETH)in 2000 in mechanical engineering. His researchis on falling film flow visualization and fallingfilm condensation heat transfer with plain and en-hanced tubes.

Jean-Francois Roques is a Ph.D. student inthe Laboratory of Heat and Mass Transfer atthe Swiss Federal Institute of Technology inLausanne (EPFL), Switzerland. He received hisdiploma at the EPFL in 1999 in mechanical engi-neering. His research is on falling film flow modetransitions, development of flow maps for predict-ing these transitions, and falling film evaporationheat transfer, all with plain and enhanced tubes.

Patrice Crisinel is an analyst in the Market RiskDepartment of UBS Warburg, Zurich, Switzer-land. He graduated from the Swiss Federal In-stitute of Technology Lausanne (EPFL), Switzer-land, in 2001 as a mechanical engineer. He workedactively during his diploma thesis on the presentresearch.

John R. Thome has been a professor of Heatand Mass Transfer at the Swiss Federal Instituteof Technology in Lausanne (EPFL), Switzerland,since 1998. His primary interests of research aretwo-phase flow and heat transfer. He received hisPh.D. at Oxford University, England, in 1978,and was formerly a professor at Michigan StateUniversity. From 1984 to 1998, he set up hisown international engineering consulting com-pany. He is the author of several books, includ-

ing Enhanced Boiling Heat Transfer (1990) and Convective Boiling andCondensation (1994) and has a new book entitled Wolverine EngineeringDatabook III that is available free at http://www.wlv.com/products. He re-ceived the ASME Heat Transfer Division’s Best Paper Award in 1998 for athree-part paper on flow boiling heat transfer published in the Journal of HeatTransfer. He has published over 40 journal papers since joining the EPFL.


measurement of falling film thickness around a horizontal tube using a laser measurement technique

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