8TH INTERNATIONAL SYMPOSIUM ON FLOW VISUALIZATION (1998)

212.1

Abstract

The aim of the presented study is to test thesimultaneous application of two acquisitionmethods, namely Particle Image Velocimetry& Thermometry combined with InfraredThermography in an experimentalinvestigation of natural convection. The first,based on liquid crystals tracers, allows fullfield temperature and flow analysis; thesecond is used to monitor Thermal BoundaryConditions at external non-isothermal wallsbounding the flow domain.

Experimental and numerical studies havebeen made for transient and steady naturalconvection in a differentially heated cube filledwith water. The analysis is carried out forpure convection of water in the vicinity of thefreezing region (cold wall temperature Tc=0oC), and for convection of wateraccompanied by freezing (Tc ≤ -10oC). Theopposite hot wall temperature is fixed at+10oC.

1. Introduction

Natural convection and phase change heattransfer such as melting and solidification areof interest in a wide range of technologies andpractical applications, e.g. crystal growth frommelts and solutions, heat transfer and fluid

flow in nuclear reactors, purification ofmaterials, latent heat energy storage for solar-heated housing and recently even in a solardynamic power system for use in Earth-orbiting spacecraft.

In recent years, several experimental andnumerical studies have been dedicated tonatural convection in freezing water,indicating the complexity of the problem [1].Its numerical modelling or experimentalanalysis is not an easy task. As a matter offact, existing numerical codes appear to fail inmodelling details of solidification. Thenumerical simulations performed by Banaszeket. al. [2], Kowalewski & Rebow [3], andmost recently by Giangi et al. [4] show severaldifferences in the front shape and front pattern.It seems that the numerical models needseveral improvements.

Among other model simplifications, apossible agent responsible for thediscrepancies can be inaccuracy in modellingof the Thermal Boundary Conditions (TBC) atthe “passive”, non-isothermal side walls.Previous investigation, performed by thesecond author and co-workers [5,6], haveshown that gentle natural convection can beextraordinarily sensitive to small changes inthe TBC at the side walls. It appeared that onlysmall variation of the TBCs change thedirection and structure of the three-dimensional spiralling motion in thedifferentially heated cavity. The flow structurecould be properly modelled only by applyingto the numerical code the temperature fieldsmeasured at the side walls [7].

Complex flow structures, their sensitivityto small variation of the flow parameters,initial and boundary conditions require theapplication of appropriate experimental

INFRARED AND LIQUID CRYSTAL THERMOGRAPHYIN NATURAL CONVECTION

Tomasz S. Wisniewski, Tomasz A. Kowalewski, Marek Rebow

Keywords: infrared thermography, liquid crystals thermography, natural convection

Author(s): Tomasz S. Wisniewski1, Tomasz A.Kowalewski 2 , Marek Rebow, Karolina Blogowska1 1

1Institute of Heat Engineering, Warsaw University ofTechnology, Nowowiejska 25, 00-665 Warsaw, Poland.

2Center of Mechanics, IPPT PAN Polish Academy ofSciences, Swietokrzyska 21, 00-049 Warsaw, Poland.

Tomasz S. Wisniewski, Tomasz A. Kowalewski, Marek Rebow

212.2

methods to validate the numerical results. Itrequires application of full field acquisitionmethods, which can give transient data for thevelocity and temperature fields of theinvestigated flow.

Particle Image Velocimetry &Thermometry (PIVT), described in detailelsewhere [8], appears to be a valuable methodfor monitoring two-dimensional velocity andtemperature fields within the flow. Themethod is based on the application ofThermochromic Liquid Crystals (TLC)suspended in a working fluid as seeding.Temperature and velocity maps so obtainedcan be compared directly with their numericalcounterparts.

The aforementioned discrepanciesbetween numerical and observed results forceus to verify Thermal Boundary Conditionsimposed on the “passive”, non-isothermal sidewalls of the cavity. To control heat fluxthrough these walls, measurement of bothinternal and external temperature fields atthese walls becomes necessary. Such apossibility is offered by combined applicationof Infrared and TLCs based Thermography.Temperature fields obtained by IRT at externalwalls, and internal temperature maps fromPIVT measurements enrich our description ofthe physical experiment allowing betterverification of numerical models.

To avoid geometrical complications anduncertainty of the thermophysical properties, asimple model of water freezing in adifferentially heated cavity is considered. Ourmain goal is to test the applicability of boththermographic techniques in verifying theTBCs for the investigated flow. Theexperimental results obtained are comparedwith numerical simulation performed using themodified 3-D finite difference codeFREEZE3D [9].

2. Formulation of the Problem

An experimental study has been made oftransient and steady convection in adifferentially heated cube-shaped enclosurewith inner dimension equal to 38 mm (Fig. 1).Distilled water is used as a working fluid. Twoopposite vertical walls are assumed isothermal.One of them is held at a temperature Tc = 0oC,

that is the freezing point of the liquid Tr, in thecase of natural convection without phasechange or below the freezing point = 10oC.The other four walls, made of 6 mm lowthermal conductivity material (Plexiglas) allowthe entry of heat from the external air. Tc =−10oC when ice growth is also analysed. Theopposite vertical wall is held at a temperatureTh.

Fig. 1. The cubical box with differentially heated walls.

To make the heat transfer through theside walls well defined, a constant flux of airgenerated by a low speed fan was directed atthe cavity. The temperature of the air stream isText = 23.8°C.

Heat transfer from the gas environmentthrough the Plexiglas walls is relatively lowand its effect on the internal flow can beconsidered to be small. However, in theexperiment the air temperature is well abovethe internal fluid temperature, and at least inthe near wall regions this may apparentlymodify the flow.

The initial fluid temperature is equal to To

= Th = +10°C. A zero initial velocity flow fieldis assumed. The convection starts when at timet=0 the cold wall temperature is suddenlydecreased to 0oC in the convection or −10oC inthe freezing experiments.

Three basic dimensionless parametersdefining the freezing problem driven by bothconduction and free convection are theRayleigh number (Ra), the Prandtl number(Pr) and the Stefan number (Ste), given as

Ra =g THβ

αν∆ 3

, Pr =να and S te =

c T

L

p

f

∆,

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Infrared and liquid crystal thermography in natural convection

where ∆T = Th - Tr is the differencebetween the temperatures of the hot wall Th

and the phase interface Tr. In the abovedefinitions g, H, α, β, ν, cp,, Lf, denote,respectively, the gravitational acceleration, thecavity height, the thermal diffusivity, thecoefficient of thermal expansion, the kinematicviscosity, the specific heat and the latent heatof fusion.

Due to the temperature dependent fluidproperties, especially the strongly non-linearvariation of water density, the non-dimensional description of the problembecomes only formal. For such a description,the physical properties of the fluid are takenfor the arbitrary selected reference temperatureTr=0oC. The corresponding non-dimensionalvalues calculated for temperature difference∆T=10oC and 38 mm cavity are:Ra=1.503.106, Pr=13.3, Ste=0.125.

3. Test apparatus and experimentalprocedure

The experimental set-up is sketched inFig. 2. The cubic convection box has twoisothermal walls made of a black anodisedmetal. Their constant temperature ismaintained by anti-freeze coolant flowingthrough the attached antechamber. Thetemperature of the cooling and heating liquidsare controlled by two thermostats. Seedingwith thermochromic liquid crystals is used,

allowing instantaneous measurement of thevelocity and temperature to be made.

For the flow visualization the cavity isilluminated with a 2 mm thick sheet of whitelight from a specially constructed halogenlamp. The colour images of TLCs flowseeding are observed in the perpendiculardirection by a 3CCD RGB camera (Sony XC-003). The 24-bit images of 768x564 pixelsresolution are acquired using a 32-bit framegrabber (ITI).

The infrared images of the front side wallare acquired with a low wavelength infraredscanner Agema 900, and used to evaluate thetemperature field at the external surface of thewall. The IR Images of the cavity were takenfrom 110 mm distance. Due to the spaceconstraints, in the present configuration it isimpossible to obtain images from the RGB andthe IR camera simultaneously. Hence, acomputer controlled system of three steppingmotors is used to move the cavity and the RGBcamera. It allows the acquisition of flowimages of two different vertical cross-sections(near the front wall and at the centre of thecavity), and two infrared images of the frontwall. The images are taken fully automaticallywithin 10 seconds. The relatively longrelaxation time of the flow allows us to assumethat all images are taken at the same instance.

3.1 Particle Image Velocimetry &Thermometry

Fig. 2. A schematic view of the experimental set-up. PC (1) with the acquisition card controlling camera (2),halogen lamp (3) and three stepping motors (5) using driver (6). Temperature in the cavity (4) controlled by two

thermostates (7). Mirror (8) used to direct light sheet. IR camera (9) and IR controller (10)

Tomasz S. Wisniewski, Tomasz A. Kowalewski, Marek Rebow

212.4

As mentioned previously ThermochromicLiquid Crystal tracers dispersed in water havebeen applied to measure both temperature andvelocity flow fields. The mean diameter ofunencapsulated TLC droplets sphere is about50um. Their density being close to that ofwater and relative intense light scatteringpredispose the TLCs suspension as usefultracers for the flow visualization.

Digital Particle Image Velocimetry isused to obtain the velocity vector field fromthe flow images. For this purpose, the colourimages of TLC tracers are transformed toB&W intensity images. After applying specialfiltering techniques [10] bright images of thetracers, well suited to DPIV, are obtained.

For simultaneous measurement of thetwo-dimensional temperature field, the DigitalParticle Image Thermometry (DPIT) is used. Itis based on computer-aided evaluation of thedigital RGB flow images. To evaluatetemperature the generally applied [6,11] HSI(Hue, Saturation, Intensity) conversion of RGBimages is used. Temperature is determined byrelating the hue to a previously obtainedtemperature calibration curve [12].

The colour play interval of TLC used wasselected to cover a temperature range fromabout 2oC to 5oC. Due to the strong non-linearity of the hue-temperature relation, theaccuracy of the measured temperature dependson the hue value, and varies from about 3% to10% of the full colour play range.

TLCs are widely used for surfacethermography [13,14], however theirapplication for measuring temperature ofexternal walls of the cavity appeared non-practicable. Covering the side walls with aTLC layer or a special TLC sheet wouldstrongly reduce the optical access, anddiminish or totally eliminate the possibility ofresolving internal temperature and velocityfields. Hence, the Infrared Thermographyappears to be the only usable full fieldmeasuring technique at the moment.

3.2 Infrared ThermographyInfrared thermography is a well

established measurement technique for two-dimensional thermal maps. It has beensuccessfully employed to measure convective

heat fluxes in both steady and transienttechniques [15].

The system used in our experimentalstudies consists of a low wavelength AgemaThermovision 900 LW infrared scanner. Ituses a Mercury Cadmium Telluride (MCD)detector with liquid nitrogen cooling. Thespectral band covered is from 8 to 12 µm, withsome residual response outside this range. Thisspectral response results in low noise levelmeasurements at room temperature. Nominalsensitivity of the scanner is equal to 0.08°C at30°C. Our careful correction procedure, usingthermocouples and precise surface temperaturemeasurements allowed us to reach accuracyequal to 0.3°C.

The scanner image resolution is 200elements by 136 lines. Each image is digitisedin a frame of 272 x 136 pixels at 12 bit.Application software (Erika) allows selectionof useful dynamic range of images andconverts them to 8-bit TIFF images. Thesoftware allows adjustment of temperaturerange, choice of colour palette and preliminaryimage analysis.

The scanner used with a 20° x 10° lensand a close-up lens has a resolution of 0.23mrad. To improve the spatial resolution ofimages, the analysed field is acquired in twosteps. The first IR image covers the lower halfof the investigated side wall, the second imagethe upper half. The computer controlledsystem of stepping motors moving the cavity,allows us to minimize the interval betweenboth images to about 2s. Specially developedpost-processing software is used to merge bothhalf images to one full image of the wall witha resulting resolution of 272 x 272 pixels.

Due to continuity of the observed thermalfield, IR images of the cavity show a relativelysmooth transition of grey levels. This createspotential difficulty or inaccuracy inrecognizing the geometry of the analysedobject. To simplify post-processing of images(and their merging), small metal markers(visible in reproduced figures below) areattached at four sides of the wall. The markersare insulated from the wall, hence well visibledue to their different temperature. Comparingthe IR and RGB images of the front wall, the

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Infrared and liquid crystal thermography in natural convection

exact geometry of the cavity could be wellidentified.

4. Numerical Model

The obtained empirical results are furtherused to verify the performance and accuracy ofthe Finite Difference model developed tosimulate natural convection with solidification.A modified version of the three-dimensionalnumerical code FREEZE3D (Yeoh 1993) hasbeen used. The governing equations of aNewtonian fluid are those from the physicalconservation laws of mass, momentum andenergy. The main fluid properties, viscosity,thermal conductivity, specific heat and densityare given functions of temperature. However,the density variation is applied in thebuoyancy term only. The thermal properties ofice were assumed constant. The thermalconductivity, heat capacity and density of thePlexiglas used for the side walls weremeasured [7].

For the fluid domain the vorticity-vectorpotential formulation is used in the code. Theindependent variables are vorticity and thevector potential, whereas the pressure iseliminated and the continuity equation isautomatically satisfied.

The governing equations are solvedseparately for the fluid and solid domain usinga curvilinear co-ordinate system filling thephysical domain. As the physical domainchanges shape, the interface boundary grid isgenerated at each time step. The boundaryfitted grid is smoothed using the elliptic gridgeneration method. In solving the timedependent partial differential equations, anAlternating Direction Implicit (ADI) methodwhich marches in time is employed. Thevector-potential equation is solved using asuccessive over-relaxation (SOR) method ateach time step. A second order centraldifference approximation for spatialderivatives and a forward differenceapproximation in time are used.

When simulating experimentalconditions, the main problem which arises isthe proper definition of the thermal boundaryconditions. Two opposite walls are isothermal.Four other walls are made of 6mm Plexiglas.To approach as close as possible physical

conditions, the code was modified byimplementing the side walls into thecomputational domain. A separate energyequation is solved for the heat transfer fromthe external air through the four side walls.

Solutions are obtained using 31x31x41mesh points. 213 mesh points are used for thefluid domain, 5 additional mesh points at eachside for the Plexiglas walls, and 21x21x10mesh points for the ice domain. To test themesh dependence selected cases werecalculated increasing the number of grid pointsto 313 for the fluid domain. To start thefreezing calculations the initial grid for thesolid phase must exist. Hence, it was assumedthat at the first instant the cold wall is alreadycovered with an ice layer of non-dimensionalheight 0.02.

5. Results

5.1 Natural ConvectionAt the beginning, our interest was directed to

understanding the transient behaviour ofnatural convection of water in the vicinity ofthe freezing point. The experiments start byabruptly dropping the cold wall temperature to0oC. The effects of density inversion and ofthe thermal boundary conditions at non-isothermal walls on the flow structures arestudied to compare and eventually improve thenumerical code.

A typical flow structure exhibits twocirculation regions, where the water densitydecreases with temperature (upper) and anabnormal density variation (lower). It wasfound that the calculated flow pattern dependsstrongly on the modelling of the thermalboundary conditions at the side walls. Neitherisothermal nor constant heat flux models aresufficiently accurate to obtain the observedflow structures. The IR measured distributionof temperature at the external surface of theside wall (Fig. 3) indicates non-uniformity ofthe heat flux, which may be the possiblereason for observed discrepancies. Byresolving temperature differences recordedacross the wall, additional hints about thethermophysical properties of the Plexiglaswalls as well as about assumed air/wall heattransfer coefficient will be obtained.

Tomasz S. Wisniewski, Tomasz A. Kowalewski, Marek Rebow

212.6

a

1 m m/s

b

Fig. 3. IR thermographic image with two isothermallines green 6 oC and yellow 14 oC (a) of external surface

of the side wall and velocity field (b) at the verticalcentre plane z=0.5 for free convection of water at 2400 safter start of cooling; Tc=0 oC, Th=10oC, Text=23.8oC.

Freezing of WaterThe pure water freezing experiments

show, as already mentioned, two main flowcirculation regions. In the first, driven by„normal convection” and located in the upperpart of the cavity, there is a clockwisecirculation. It transports the hot liquid up tothe top wall and back along the isotherm of thedensity extreme. Interaction of the hot liquidwith the freezing front causes its melting anddepletion of the freezing plane. The secondflow circulation region, due to „abnormalconvection”, is located in the lower part of thecavity. There, a counter-clockwise circulationtransports the cold liquid up along the adjacentice surface and back to the bottom along theisotherm of the density extreme. This cold

water circulation only moderately modifies theheat balance at the interface. The convectiveheat transfer between both upper and lowerregions seems to be limited mainly to theupper right corner of the cavity. There, alongthe colliding cold and warm fluid layers, theheat is transferred from the hot wall to thelower parts of the cavity. The shape of thefreezing front reproduces this interaction,almost doubling the ice growth rate at thebottom (comp. Fig. 5).

a b

1 81 61 41 21 086420

-2-4-6-8-1 0

oCw a ll

w a ll

w a l l

w a l l

c d

Fig. 4. Freezing of water. IR thermographic images withtwo isothermal lines green 0 oC and yellow 6 oC (a) and

(b) and numerical solution of temperature distributionon the vertical side wall (c) and (d) at 500s (a) and (c)

and 3600 s (b) and (d) after start of cooling; Tc=-10 oC,Th=10 oC, Text=23.8oC.

The temperature distribution at the sidewalls is shown in Fig. 4. Comparing calculatedand IR measured fields we may recognise themain features, the characteristic “belly” of theisotherms close to the cold wall. The heat fluxthrough the top and bottom walls increases thetemperature in adjacent fluid layers. This inturn modifies the overall circulation pattern,shifting the position of the ice front back to thecold wall (Fig. 5). However, the numericalsimulation seems to overestimate this effect.Observed and calculated ice fronts aredifferent. Hence, also the temperature andvelocity fields are only qualitatively similar.

212.7

Infrared and liquid crystal thermography in natural convection

a b

ICE

1 mm/s

c dw a ll

w a ll

0

wall

wall

e f

Fig. 5. Freezing of water. TLC tracers (a) and (b),velocity filed (c) and (d) and numerical solution (e) and(f) at the vertical centre plane z=0.5 at 500s (a), (c) and(e) and at 3600 s (b), (d) and (f) after start of cooling.

Direct implementation of the IRmeasured thermal maps of the externalsurfaces to the code may clear out doubtsabout proper modelling of the TBC. However,there are other possible agents, responsible forthe difficulties encountered in modellingfreezing of water. Further studies are necessaryto verify the assumptions made and to considerin the modelling the following effects:• Fluid supercooling, these effect is observed

experimentally and may be of primaryimportance. Hence, numerical modellingof the nucleation delay time seemsnecessary.

• Thermal boundary layer at the interface.

• The colliding boundary layer, appearingdue to the density anomaly of water at thecavity diagonal boundary layer betweenhot (clockwise) circulation and cold (anti-clockwise) circulation.

• Imperfections in the solidus structure, non-homogeneity and layering.

• Non-ideal thermal contact between thesolidus and the box cooled surfaces.

• Verification of the availablethermophysical data. Effect of theirinaccuracy on the numerical result.

6. Final remarks The infrared technique allowed themeasurement of temperature with an accuracybetter then 0.3oC. The accuracy of temperaturemeasurements obtained with the help of liquidcrystal tracers varies from 0.2 oC to 0.6 oC,depending on the colour play range. It wasfound that the temperature fields measured atexternal surfaces of the side walls as well asthose of the top/bottom walls are far from beinguniform. The observed temperature patternreflects that visualised inside the cavity withhelp of liquid crystal tracers. The heat transferthrough the walls estimated from bothmeasurements is compared with theassumptions made in the numerical simulations.The detailed comparative analysis of numericalresults and experimental findings appears to bea unique alternative allowing the understandingof the limitations of the numerical model andgiving indications concerning its improvement.

Acknowledgements

The authors are indebted to G. Yeoh, G.de Vahl Davis and E. Leonardi (UNSW) fortheir computer code FREEZE3D.

This work was supported by KBN (TheState Committee for Scientific Research),Grant No 3T09C00212.

References

[1] Yeoh GH, Behnia M, de Vahl Davis G, Leonardi E.A numerical study of three-dimensional naturalconvection during freezing of water. Int. J. Num.Meth. Eng., Vol. 30, pp. 899-914, 1990.

[2] Banaszek, J., Rebow, M., Kowalewski T.A. 1997,Fixed grid finite element analysis of solidification,

Tomasz S. Wisniewski, Tomasz A. Kowalewski, Marek Rebow

212.8

Proc. of Advances in Computational Heat TransferCHT’97, Cesme, Begell House , pp.471-478, 1998.

[3] Kowalewski TA, Rebow M. Freezing of water inthe differentially heated cubic cavity. Int. J. CFD(submitted).

[4] Giangi M., Stella F., Kowalewski TA. Numericalsimulation of natural convection during iceformation. IV Congresso Nazionale SIMAI’98,Giardini Naxos (Messina), 1998.

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Movies:

1. Freezing of water. Temperature distributionon the vertical side wall measured using IRTduring 7000 s period. Tc=-10oC, Th=10oC,Text=23.8oC. (comp. Fig. 4)

2. Freezing of water. Numerical solution at thevertical centre plane z=0.5 during 3600 s. Tc =-10oC, Th=10oC, Text=23.8oC (comp. Fig. 5)