A STUDY OF SCRAPED-SURFACE HEAT EXCHANGER IN ICE-MAKING APPLICATIONS Alexander C hi-To C hong A thesis submined in conformQ with the requirwients for the degree of Master of Applid Science Graduate Depamnent of Chernid Engineering and Applied Chemi. University of Toronto O Copyn'ght by Alexander Chi-To Chong 2001
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STUDY OF SCRAPED-SURFACE HEAT EXCHANGER ICE-MAKING …€¦ · 1.3 ûrganization 2.1 History 2.2 Ice Making Application 3.1 Heat Transfer in Scraped-Surface Heat Exchanger 3.2 Heat
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A STUDY OF SCRAPED-SURFACE HEAT EXCHANGER IN ICE-MAKING APPLICATIONS
Alexander C hi-To C hong
A thesis submined in conformQ with the requirwients for the degree of Master of Applid Science Graduate Depamnent of Chernid Engineering and Applied C h e m i .
University of Toronto
O Copyn'ght by Alexander Chi-To Chong 2001
NationaI Libiary Bibiiothéque nationale du Canada
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Master of Applied Science 700 1
Alexander Chi-To Chong
Graduate Department of Chemical Engineering and Applied Chemise University of Toronto
The performance of an industrial scnped-surtàce ice generator. supplied by
Sunwell Technologies Inc.. has been investigatcd both expenmentall> and numericaily.
The aluminium ice genentor consisted of multiple retiigerant passages sumiunding a
centrai scraped-surface channel. in which an ice-slurry was made from a brine solution.
A computer model was developed to simulate the steady-state operation. This
simulation model consisted of three sections: i) computational mesh generation. ii)
steady-aite parameters evaluation. and iii) radial temperature presentation.
Tests on the ice generator were performed within a broad range of operating
conditions. both with and without ice formation. and the data were compared with the
simulation results.
The model could predict the esperimental heat exchange rates and tefigerant
pressure drop data with standard deviations of =14?/0 and 110%. respectively. Since the
mode1 could give a reasonable prediction. the radiai temperature profiles were examineci
in detail to understand the degm of temperature variation on the scraped-sdace.
I wodd like to take this opportunity to thank for those who have helped me in the pmgress of this thesis. Especially,
Prof. Masahiro Kawaji as the thesis supervisor
Mr, Vladimir GoIdstein as the supporter of the current research
Dr. Ming-Jian Wang as the research supervisor
Mr. Roger Castonguary for assistance in the testing faciiities
Ms. Connie Zhang as my love
Abstract Acknowledgernents Table of Contents List of Figures List of Tables
** 11
iii iv vi ix
1 .1 Background 1.2 Objectives and Scope 1.3 ûrganization
2.1 History 2.2 Ice Making Application
3.1 Heat Transfer in Scraped-Surface Heat Exchanger 3.2 Heat Transfer in Forced Convective Boiling 3 -3 Pressure Drop in Two-Phase Flow 3.4 Properties of lce SIurry
4.1 Heat Exchanger Design 4.2 Experimental Apparatus 4.3 Test Procedure 4.4 Data Evaluation
5.1 Cross Section of Heat Exchanger 5.2 Process Simulation 5.3 Temperature Distribution (cross-section)
6.1 Results Experirnents Simulations
6 2 Discussions Cornparison of Experimental and Simulated Results Simulations Experimental Observations Final Remarks on the Simulation Mode1
7. CONCLUSIONS AND RECOMMENDATIONS 90
7.1 Conclusions 7 2 Recommendations
Nomenclature
References
Appendix A : Correlation and Experimentai Emrs
Appendix B : Computer codes
Appendix C : Experimental resuits
Appendix D : Simulation d t s
Figure
2.1
2.2
3.1
3.2
3.3
4.1
4.2
4.3
4- 4
4.5
4.6
4.7
4.8
4.9
5.1
5.2
5.3
5.4
5.5
5.6
5.7
6.1
6.2
6.3
6.4
Description
Illustration of a typical scraped-surface heat exchanger
Generai types of interfacial crystaI structures
Illustration of the ice generator
Parameter F in Chen's correlation
Parameter S in Chen's correlation
Scraped-surface heat exchanger (cross section and flow channels)
Photograph of the heat exchanger column tested
Photograph of the heat exchanger cross section
Photograph on the testing apparatus
Generai experimental test layout
Photograph of the rotor stiaft with scrapers
Measurements on test loop
Process of heat exchange rate detemiination
Temperature change dong heat exchanger
Structure of simulation mode1
Process of heat transfer rate evaiuation
Process of heat and mass bdance evaluation
Condition for correlating the ice M o n
Illustration of cooiing process h m brine to ice slurry
Heat exchanger with n axial elements
Process of pressure gradient evaluation
Variation of temperature ùi brine channel
Variation of ice fiadon in brine cbannel
Variation of salt concentration (liquid phase) in brhe channel
Variation of temperaîure in ceEgerant cchanels
Page
LIST OF FIGURES (cont'd)
Figure
6.5
6.6
6.7
6.8
6.9
6.10
6.1 1
6.12
6.13
6.14
6.15
6.16
6.17
6.18
6.19
6.20
6.21
6.22
6.23
6.24
6.25
6.26
6.27
6.28
6.31
Description
Variation of pressure in refigerant channels
Variation of vapour quality in refiigerant channels
Variation of heat transfer rate in each fluid channe1 (ice making mode)
Variation of heat transfer rate in each fluid channe[ (chilliig mode)
Wail temperature profiles (brine channel)
Wall temperature profiles (refiigerant channel a)
Wall temperature profiles (refrigerant channel b)
Wall temperature profiles (refiigerant channel c)
WalI temperature profiles (refiigerant channel (i)
WalI ternperature profiles (refngerant channel e)
Wall heat flux profiles (brine channel)
Wall heat flux profiles (refiigerant channel a)
Wall heat flux profiles (refiigerant channel 6)
Wail heat flux profiles (refiigerant channel c)
Wall heat flux profiles (refiigerant channel d)
Wail heat tlux profiles (refigerant channel e)
Cross sectionai temperature profile (element I )
Cross sectional temperature profile felement 4)
Cross sedona1 temperature profile (element II)
Cross sectional temperature profile (element 20)
Cornparison of brindice slurry exit ternperature
Cornparison of the predicted and measured exit ice fiaction
Comparison of refiigerant exit pressure
Comparison of refiigerant exit temperature
Cornparison of refiigerant exit vapour quaüty
Page
vii
LIST OF FIGURES (cont'd)
Figure Description
6.32 Cornparison of refigerant pressure drop
6.33 Comparison of heat exchange rate
6.34 Camparison of change in refrigerant pressure (resr run 19)
6.35 Effect of rotationai speed (vertical orientation)
6.36 Effect of rotationai speed (horizontai orientation)
Page
Table Description
5- 1 Process variables in simulation
6.1 Range of experimental parameters for simulation
6.2 Summary of experimental results for simulation
6.3 Range of overail heat transfer coefficient
6.4 Generai summary of simulation results
Page
INTRODUCTION
An ice-slurry can be used for air-conditioning of large and small buildings,
cooling h h fish aboard fishing vessels, and refngeration in supermarkas. among
others. For these applications, a large amount of ice crystds has to be not only produced
continuously, but aIso automatidiy removed. There are few industrial ice generator
desigus that are commercially avaiiable yet. One such ice generator is a scraped-surface
heat exchanger king developed by SunweIl Technologies, Inc. of Woodbridge, Ontario.
This heat exchanger is made of an extnided aluminium column, with multiple passages of
cefigerant surounding a central brine channel for ice making.
One of the major advantages of ice-slurry compared to conventional ice storage is
the ease of transportation where it wi be easily punped. In cornparhg with chilIed
water system, ice slurry has a higher themal storing unit and a steady kezing
temperature. Other advantage would be its liquidized f o n where it can cover completely
the surface of the materials king cooled, hence, providing a better cooiiig rate. tn
addition, an ice sliny machine operates more efficiently compared to the conventionai
ice machines since the scraped-surfke rnechanism provides higher rate of convection on
the heat trander surface.
The objectives of the present study were to experimentally detamine the
performance characteristics of Sunweli's scraped surface heat exchanger aizd to better
understand the heat transfer characteristics by deveioping a numerical simulation model.
capable of predicting the steady state operation under different inlet conditions of the
working fluids. Since multiple reûigerant channels surround the centrai cooling channel
(like a fînned heat exchanger), the wall temperatwr profiIe may not be uniform. A non-
uniform temperature distribution on the channel inner wall is ûelieved to be responsible
for ice crystal buildup and fieeang up of the scraper blades rotating inside the brine
channel. Thus, an understanding of the temperature distribution dong the heat uansfer
surfixes is an important objective in this study.
To this end, a set of cornputer codes were written to predict the boundary
temperature and heat flux profiles at different axial locations of the heat exchanger. In
addition to the boundary temperature and heat flux profiles prediction, the codes are able
to generate the cross-sectional temperature pmfües and the local conditions of the
working fluids (brindice sluny and refiigerant).
Testing on the scraped d a c e heat exchanger was conducted to obtain data that
could be used to veri@ the cornputer model. The heat exchanger was conaected to a
customized hot gas bypass refiigeration unit, Operathg skills were acquired to gain MI
control of the system, in order to achieve various operathg conditions for testing. The
heat exchanger was instrumenteci for data recording and cali'brations were performed on
the rneasuring instruments. A data acquisition system was set up to record the steady
state operating parameters during the tests. The binary solution used for ice m a h g was
sodium chloride solution. Tests were conducted within a broad range of operating
conditions. Seved test nins were chosen and cornparisons wete made between the
experimental and simulation results for vecïfïcation O t the cornputer mode!.
As a preview of the whole pmject. the organization of the current thesis is
presented in the following paragraphs.
h "Chapter 2: L i t e r m e Review ", the history of the scraped-surface heat
exchangers is presented. This summary is based on the pubiicaîions fiom the past to the
most recent. The descriptions of the scraped-surface heat exchangers used in the ice-
making industries are dso provided.
In "Chapcer 3: Theoretical Background". the heat -fer theories on both the
ice-slurry side and the codant side (refngerant) of the heat exchanger are summarized-
The concepts involveci in evaluating the thermal pmperties of ice slurry (a two-phase
solidAiquid mixhue), are a h ptesented,
In "Chaprer 4: Erperimenral Appuraîus and Procedure ", the consiruction of the
prototype heat exchanger and the experimental setup are described. The apparatus, the
working fluids, refiigerant loop, instnimenâation and testing procedure are summarized.
in "Cbpter 5: Simularion Mode!", the development of the simulation mode1
(cornputer code) is presented and expIained in detail.
In "Chaprer 6: Results and Discussions ", both the experimental and simdation
results are presented and c o m p d . The coUected data, experimental observations and
Page 4
the simulation results are discussed in detail. Furthemore, the aitemative research areas
are also discussed.
in "Chapter 7: Conclusions and Recommendations", the fmdings and the
suggestions based on bis research are summarized. Further research directions are
recommended for subsequent work.
Supporting materiais are coiiected in the "Appendices ", UicIudig the computer
code for the simulation model, the themai pmperties of the fluids used, and the Ml
record of both the experimental and simulated results,
2. LITERATURE REVIEW
Scraped-surface heat exchangers (SSHE) were fmt introduced to the industry for
use in applications involving viscous materiais. The scraping action dong the heat
transfer wall disturbs the formation of the boundary layer; moreover, it enhances the fluid
exchange rate between the boundary and the biilk. Hence, the heat transfer coefficient is
greatiy improved due to continuous surface renewal. in Fipire 2.1, a typicai type of
scrapers is shown.
Figure 2.1: Illustration of a typical scraped-surface heat exchanger
in later years, scraped-surface heat exchangers have been used fiquentiy in
crystallization processes due to their ability to remove crystais h m the h a t transfer
surface. Generaiiy, high super-cooiing of the fluid on the heat mns5n surface will result
in certain undesired crystai growth properties like deadritic structure, and scaiing
problems. The continuous movement of saapers can prevent the crystais h m growing
Page 6
- -
on the wall of the heat exchanger. in Figiire 2.2, the general types of crystal structures
formed during h e z h g are iiiustrated.
Figure 22: General types of interfacial crystal structures
In ment years, the scraped-surface heat exchangers have k e n used in the ice-
making indusûy, where a two-phase homogeneous solidAiquid mixture (icz slurry) is
directiy produced due to the continuous movement of scrapers.
In this section, the research history of sçraped-surface heat exchangers is
describeci.
Huggins (1931) was the first researcher who introduced the idea of scraped-
surface k a t exchangers. His study invo!ved processing of both viscous and non-viscous
materids. During his study, he found that the heat transfer coefficient was eipatly
enhanced with the use of scrapers instead of stirrers in viscous apptications.
Page 7
- -
Hodton (1944) used water as the heat traosfer medium and studied the effets of
flow rate and rotationai speed of the scraping action. Fmm bis tests, he suspected that the
heat transfer coefficient could be a hction of scraping frequency.
Kool (1958), Latinen (1958) and Hariott (1959), al1 came up with a theoretical
model for intemal heat transfer coefficient derivecl h m the penetration theory with
surface renewal. This model predicted well ttie experimental data h m Houlton (1944).
Frorn this model, neither the viscosity nor the axial velocity would influence the heat
m~s fe r coefficient. Hariott confinned that the penetration model could describe the low
viscosity application resuits adequately well.
Skelland (1958) studied the behaviour of a votator, which was a high-speed
scraped-surface heat exchanger. The scrapers he used were not spring-loaded but were
allowed to float with a stagnant liquid layer on the hait exchanger wall. He derived a
general correlation for the heat transfer coefficient using a dimensional analysis. The
exponents for the dimensionless groups were derived empirically fiom the experimental
data. However, this mode1 did not agree well with the data of Houlton (1944). Due to
the lack of agreement, Skelland (1962) later proposeci a more reiiable correlation, which
was in satisfactory
the next chapter.
Penny and
agreement with the penettation theory as d e s c r i i in more detail in
Be11 (1967) suggested that axial dispersion probabiy played an
imporiant role in the data of Skeliand because of the low axial flow rates used.
Tromrnelen (1971) studied flow patterns and heat ma4er properties in a scraped-
surface heat exchanger. He used a viscous medium in his experiments, and developed an
Page 8
empincai mode[ based on the p e n d o n theory. He suggested an empirical multiplier
that accounted for the axial dispersion, incomplete tempetanire equalization and mixing.
De Goede et ai. (1991) studied the heat transfer properties of a scraped-surface
heat exchanger in the turtiuient regime. in their experiments, a sufficiently short heat
exchanger was used where the axial distance was shorter than the diameter of the
exchanger. A CFD mode1 was developed using a commercial code, PHOENICS. for
predicting the development of a vortex between the scraper blades. They aiso developed
a theoretical model based on the approach pmposed by Trommelen (1971).
Bel et al. (1996) studied a scraped-surface heat exchanger for an ice-slurry
application. They accounted for the thermodynamic pmperties of ice slurry in the
development of their model, which was formulateci in terms of both the axial and
rotatiod ReynoIds numbers. The experimental resuIts showed that the influence of
rotational speed on the heat transfer coefficient was not direccly proportional. Moreover,
the influence of axial flow rates in 1amina.r region was ody on the ice production, where
the heat transfer coefficient was not significantIy affécted.
3. TrnORETICAL BACKGROUND
In the following sections, the heat transfer theones required in consmicting the
present simulation mode1 are summarized. The contents inckuded are, a) the evaluation
of convective heat transfer on the brine side for a scraped-surface heat exchger, b) the
evaluation of convective boiiing heat transfer on the freon side, c) the evaiuation of
pressure drop in a two-phase fieon flow (liquid/gas), and d) the evaiuation of the ice
slurry thermal pmperties.
Figure 3.1 : Illwmation of the ice gcnerator
3.1 ~ E A T TRANsm M SCRAPED-SURFACE HEAT EXCHANGER
To account for the enhanced heat transfer on the srraped-surface on the brine side,
previous researchers used two main approaches: ï) a theoretical approach or ui an
empirical approach, The theoretid or semi-theoretical approach involves the
peuetration theory with d a c e renewai. The empiricai approach involves dimensionai
analysis. These two approaches are discussed below.
Page 10
The theory of unsteady heat ûansfér to a semi-infinite solid is applied to the liquid
adjacent to the heat transfer sirrface before king scraped. The i i e interval that the
liquid stays on the surface will be the tirne between two scraping actions. The liquid
previously staying on the surface is removed totally and new liquid Erom the hulk wilI be
redeposited with each scraper pas. Combining the penetration and the sirrfàce renewal
theories, the theoretical equation for the Nusselt number, Nu, which is the dimension~ess
heat transfer coefficient, is given by,
where h, is the scraped-surface heat transfer coefficient, k is the fluid thermal
conductivity, B is the number of scrapers, hi is the rotational speed and D is the internai
diameter of the heat exchanger. The Peclet number. PeR, represents the product of the
Reynolds number and the Prandti number.
However, this theoretical equation oversimplifies the actual phenomena occurring
in the scraped-surface heat exchanger. In most cases, the liquid at the heat m s f e r
d a c e is not weil mixed with the bulk fluid, and in the case of viscous liquids, the fluid
h m the bulk can be partiy cdeposited behind the scraper blades. The hcat transfer
coefficient for viscous fiquids, therefore, is Iess than the prediction h m Eu. (3.1). in
addition, the heat transfer coefficient can also be idluenceci by other parameters such as
axiaI fluid velocity, the diameter and length of the exchanger.
Page I I
Skelland (1958) deveIoped the first empirical correlation, Eq. 13.3), using a
dirnensionaI anaiysis for a votator which is a srnail high-speed (axial fluid vekity) unit.
In his first correlation, he accounted for the liquid viscosity as well as the axial fluid
velociy and the geornetric parameters of the exchanger. However, considerition o f the
number of scrapers was neglected during his derivation of the following correlation.
where h, is the jacket heat transfer coefficient (inner shell), k is the fluid thermai
conductivity, D, is the diameter of scraper ( a h equal to inside dimeter of ihell). v is
the bulk average axiai fluid velocity, p is the ffuid dynamic viscosity, C, is the fiuid
specific heat capacity. IV is the number of scrapers and L is the axial length of the heat
exchanger.
SkeiIand et ai. (1962) then derived another empiricai equation. Eq. '3.4). again
using the dimensional analysis. In this correlation. he included the influence of the ff uid
viscosity in the empiricai constants. In addition to thc: viscosity effect, he &O included
the effect of the number of scrapers. He suggested two sets of empirical constants to
distinguish between viscous Iiquids and thin mobüe Iiquids, however, he did not specif) a
concrete relationship between the heat transfer coefficient and viscosity. ïhe correlation
is given by,
Page 12
where the Reynolds number, Re, is defined with the internai diameter, D,, of the heat
exchanger, Dr is the diameter of the rotor shafi and B is the number of scrapers.
From Skelland's suggestion, the constants a and b in Eq. (3.4) were Iound to be
0.014 and 0.96, respectively, for viscous liquida For thin mobile liquids. the constants
are O. 039 and 0.7.
Since cefigerant was used as the cooIant in the current research heat transfer in
forced convective boiling ne& to be reviewed. In the following, the theories adopted
for constructing the simulation mode1 are summarized.
Chen (1963) sumrnarized the experimental data obtained by other rexmchers for
convective boiling and compared their proposed correlations with al1 the experimental
data available at that time. However, the comlations he examineci could nct provide a
satisfactory result. Hence, he developed a new correlation that could satisfj a broad
range of forced convective boiling heat tramfer data for water and organk liqlid syterns.
His correlation. &en by Eq. (3.51, consisted of both the saturated nucleate boiling heat
transfer coefficient (hVCd and the two-phase forced convection contribution (h3.
h, =hW +hc (3.5)
He suggested that the forced convective contribution couid be represented by a
Dim-Boelter type equation. He also mggesteci tbat the liquid properties shoitid be used,
instead of two-phase mixture pmperties, in the heat transfer terms. in addition he
defineci a parameter. F, to account for the acceleration effect of liquid due to vapour shear
stress.
Page 13
Here, G is the total two-phase
diarneter, and subscripts f and
G(I - X)D, Re, =
Pf G - D,
Re, = - P m
m a s flux, x is the vapour quality, Dh is the hydraulic
p refer to single-phase liquid and two-pke mixnue,
respectively. The two-phase Reynolds number, Re,, is defined using the total m a s flux,
G, the hydrauiic diameter, Di, and the two-phase mixture viscosi~, pm.
Since the parameter, F. given by Eq. (3.9), was defined as a flow parameter. he
expected that it could be expresseci as a function of the Lockhart-Martinelli parameter,
X,, given by Eq. (3.10). The parameter. F. was experimentally determined and it was
presented graphicaily as iliustrated in Figure 3.2.
Figure 3 2 Parameter F m Chen's correlation
Page N
For the nucleate boiling contribution, Eq. (3.11), Chen used the nucleate pool
boiling correlation h m Forster and Zuber's (1955) analysis. in order to account for the
flow effect on the temperature gradients near the wall, which controls nucleation, he
incorporated a nucleation suppression factor, S, into the comlation where the factor
would approach unity at low flows and zero at high flows. Since the parameter. S,
represented the flow effect, it was expected to be a function of the two-phase Reynolds
number, Rep The parameter. S, was experimentally determined and presented
graphically as illustrateci in Figure 3.3. In Chen's comlation. the suppression factor. S.
wodd approach unity at low flows and zero at high flows.
0.79 O 45 0.49
h , = 0.00 122 kr PI ATwO 24 ApwO 75 (s) (3.11) 03. O H 0.24 1 b o s ~ , ik Pr
Figure 33: Parameter S in Chen's correlation
Evaiuation of the pressure drop in the refngerant channels is aiso important in the
current construction of the simulation model. in generai, the total pressure drop, Ap, can
be separated into three components, a) fnctionai, dpf, b) accelerationai, .&,, and c)
gravitationai, dp,, Lockhar-Martinelli (1949) mode1 w-as adopted since it provides
accurate pressure drop estimates in the low mass velocity range (G < 1360 kg/m2-K).
&=Q/ +Qa+Qr (3.13)
Lockhart and Marthelli (1949) correlateci the two-phase friction pressure drop.
dp/, using a two-phase friction multiplier, @'. as follows:
7
&r = Q p ' 9 3 1 - (3.1 4)
Ln this correlation, the two-phase fiction pressure drop is related to the single-
flow aioae in the channel. Altematively, it can a h be correlateci assuming the vapour
phase to be flowing alone.
For smooth tubes, the fanning fiiction factor, f, is caiculated using a Reynolds
number based on the iiquid phase flowing done.
f = 0.079 Re, -02s
Page 16
In the Lockhart-Martinelli comlation, the two-phase fiction multiplier, &, was
defined as a function of the Lockhart-Martinelli parameter, &. The fiction multiplier
comlation is given by,
where c is a constant. Four regimes are dehed based on the behaviour of the flow
(viscous or turbulent) when the respective phases are considered to pass alone through
the channet. Different values of c were recommended for, a) both phases in turbulent
flow (C = 201, b) liquid phase turbulent and vapour phase viscous (c = IC), c) liquid
phase viscous and vapour phase turbulent (c = IZ), and d) both phases viscous (c = 5).
Turbulent condition is achieved when the single-phase Reynolds number exceeds 100.
The accelerationai pressure drop, 4, is evaluated h m a momentum balance
between two points in the channel. Lockhart and Martinelli (1949) derived a correlation
based on a separated flow model, in which liquid and vapour phases are considered to
flow independentiy with their own velocity, in contrast with the hornogeneous rnodel. in
which both phases are a r e e d to flow at the same mean velocity. Using the separated
flow model, the accelerational pressure drop is given by:
where a is the void tiaction and x is the flow quaiity.
Page 2 7
Buttenvorth (1975) suggested a generaiized form, Eq. (3.19), for the void k t ion ,
which encompasses severai frequently used models, depending on the values of A and
exponents p, q and r.
The constants were found to be, A = 0.28, p = 0.64. q = O. 36, and r = 0.07 for the
Lockhart-MartineIli model.
The gravitational pressure &op, &y. (3.20). results from the hydrost~tic head of
the fluid. The change of void fraction due to the heat transfer effect is accowited for by
the integral. The negative sign denotes the pressure recovery, caused by a d o m tlow in
an inclined or verticd pipe.
in order to construct a simulation model or to operate the scraped-surface heat
exchanger described previously, the evaluation of ice slurry pmperties is critical. Bel et
ai. (1996) suggested the following rnethods for evaluating various properties. The
subscripts, îs, î and 1 will be used to cepresent ice sluny, ice, and liquid phase,
rqxcti.ely.
Page 18
Assurning an ice-slurry is an immiscible multiphase mixture, the mixture density
can be expressed as a hct ion of weight fraction and density as foiiows,
where the weight hction and density are denoted by Xand p, respectively.
Jeffrey (1973) suggested an equation for evduating the thermal conductivity of
two-phase solid/liquid mixture. His model is based on a randorn suspension ofspheres in
a liquid phase, and is given by,
ku =k , ( l+3a , f l+3p , , ' f l ' y ) (3.77)
where k and p represent the thennai conductivity and volume Fraction, respectively. The
parameters a, p, and yare evaluated with the following equations,
Bel et al. (1996) developed an enthalpy model for evaiuating the specific heat
capacity of an ice-slurry. This mode[ works only in ice durries produceci using binary
solutions, where the nonaystallizing component wouid be concentrated ir the liquid
phase wheneva ice fraction inmases. Based on the eutectic behaviour of the binary
Page 19
--
sdution, freezing temperature wili shifi as concentration changes in the liquid phase.
Therefore, the fieezing temperature wilI change as the mixture enthalpy changes while
the fluid is undergoing a phase change. The specific heat capacity is then evaluated as
follows,
where cp denotes the apparent specific heat capacity evaluated under constant pressure,
and h and T represent the ceference enthalpy and temperature of the mixture, respectively.
Thomas (1965) developed a relation for two-phase liquidlsolid mi.uture viscosity
in tems of the liquid phase viscosity. This relation assumed Newtonian suspensions of
uniform spheiiçal particles in fluid. Assuming the ice slurry to have the same
characteristics, the viscosity of ice slurry can then be expressed as follows,
p rn =p,(l+2.5pl +10.05~~~+0.00273exp(l6.6~~)) (3.2 7)
where p and p represent the dynarnic viscosity and the volume fraction, respectively.
4. EXPERIMENTAL APPARATUS AND PROCEDURE
The sçraped-dace heat exchanger under investigation was testai over a broad
range of conditions. Descriptions of the exchanger are provided in the next section and
the experimenîal techniques are presented in the rest of this chapter. ui order to
understand the operating parameters in greater detail, a set of cornputer codes was written
to simulate the heat exchange pmess. The development of this simulation model is
discwsed in the next Chapter.
The scraped-dace heat exchanger tested was provided by Sunwell
Tecbnotogies, Inc. This exchanger was made out of an duminum alloy, 6063-T6. and
was extrudeci with a specific cross sectional contiguration. Basicaily, the heat exchanger
consistai of muitiple channels on the outside boundaq for refiigerant circulahon and one
centrai channel for ice-slurry. The scrapers were mounted onto a rotating shaR which
was located at the center of the centrai chamel. ïüe cross section of the hex exchanger
is illustrated in Figure X I .
The exchanger was constructecl with a total of 20 channels for passing a cdd
retiigemt flow. These 20 channeis were made up of 4 ideaticaI circuits, and sach circuit
incIuded 5 chaanels with diiïkrent sbape con6gurations. The cold fluid wa spIit into
four streams and each stream passed h u g h the kat excbanger five times (five channels
wtth different shapes). The cold fluid p a s d b u g h the five channels in a specific
se~uence as indicated in Figure 4.1, with the Ietters h m a to e identwg the channeis.
The general testing procedure is surnmarized in this section. During each test, the
iüst requirement was to adjust the brine storage temperature by using the rz6igeration
system. Afier setting the temperature of the brine, the refiigerant passing Uito the
evaporator was shut off. The fIow rate of b ~ e passing tbrougb the evaporator was
adjusteci and the cefigerant was introduced back into the evaporator. Moreover, certain
adjustment was required to configure the refiigeration system with the desireci testing
Page 26
parameters. Refrigerant was once again shut off for clearing any ice lefi inside the
evaporator. This was done to make sure there were no ice crystalr Ieft on the heat
transfer surface that could not be removed by the scrapers. Refrigerant was -heu slowly
introduced at the previous flowrate, About one hou. was passed for the systecl to reach a
steady-state condition; however, Longer periods were required in some cases. The data
acquisition system was then initiateci to collect the required parameters for 15 minutes-
Diuing this tirne, three samples of ice slurry at the evaporator exit were collected. A
cidorimetric measurement was made on each sample to determine the ice fraction and the
overail heat transfer rate of the evaporator. h r s due to instnimentation during
experhents are sumrnarized in Appendix A.
For venfication of the simulation model, the overall heat exchange rate is one of
the main parameters of interest. The performance of the heat exchanger can be
characterized by the overail heat transfer coefficient. The procedures for evaluating both
the heat exchange rate and the overail heat transfer coefficient are presented in this
section.
The most important parameter to be detemhed is the heat exchange rdte between
the working fluids (brine and refiigerant) across the channels. This section concerns the
procedure for evaluating the heat exchange rate that involves ice making. The heat
exchange rate is evaluated h m the thermal capacity of products (ice slmksj on the hot
Page 2 7
side (scraped-surface channel) of the kat exchanger. In order to determine the heat
exchange rate, samples of ice slurries were coffected at the exit of the heat exchanger
during the tests.
Figure 4.8: Process of heat exchange rate determination
The procedure for determining the heat exchange rate is illustrated in Figure 4.8.
The ice slurry sample is mixed with a certain amount of warrn water until al1 the ice has
melted. The thermal capacity is then evaiuated by performing an energy balance on this
mixing process. An overall energy balance is given by,
Q, +Q, =Q,
where the energy content of warm water is.
Qw =m. - c P w - ( ~ * -T,)
and that of the fhai mixture,
b Qm = m. - c,, - (w, ) (4.3)
Here, Q represents the energy content, m reptesents the mas, cp represents -Sie specific
heat capacity, and T represents the temperature. The subscripts, is, w, m and ref represent
the ice slurry sample, the added water, the final mixture and the refemce point,
respectively, The Superscnpts, w and b, represent water and brine, respectively.
Page 28
The heat exchange rate, qh, is given by,
4h =4 -Qu/mu
where K, represents the rnass flow rate of brine in the sera@-surface channel.
Combining Eqs. (4.1) to (4.4, an expression for the heat exchange rate resdts as
given by Ey. (4.51. The heat exchange rate, qh, is then evaluated by assigning the brine
idet temperature as the reference temperature, TM
qh = ni, bme; km - 7-4 )- mwc,'k. - Lf 111 mm
The overall heat transfer coefficient, U,, is nonnaliy used to indicate the
perfomance of a heat exchanger in engineering practice. The development of' the overall
heat ûansfer coefficient for the current heat exchanger is presented in the remainder of
this section. The evaluation is based on the ice making operation of the heat exchanger.
An illustration of the changes in temperatures (brine and refngerant) aionp !he
heat exchanger is presented in Figure 4.9. As illutrated the k t transfer pmcess can k
separateci into two regions: i) Region I. the chilling process and ii) Region II. the ice
making ptocess.
Page 29
Figure 4.9: Temperature variation along heat exchanger
In order to perform the analysis of the overall heat transfer coefficient. the
following assumptions had to be made,
0 The super-cwling effect of brine during the transition fiom chilling to ice making
process was neglected.
The boiling temperature of reîiigerant. T, was assumed constant and the average
saturation temperature between the refngerant channel iniet and outiet was used.
0 The ûwing temperature of brine in Region II was assumed constant at the average
temperature in the ice-making region.
Remon Ir Chilling
The heat transfer rate in the chilling region. q,, is given by,
- b qc = mb - c,, - ATc (4- 61
qc =U, - A , .AT, (4.71
where Eb is the mas flow rate of brine. c i is the specific heat capacity of brine, ATc is
the change in brine temperature h m inlet to initial m g , Uc is the overall heat
trarlsfer coefficient in the chilling region. A, is the hait transfer area (scraped-dace) in
Page 30
the chiIlhg region and ATLu is the log-mean temperature difference. The log-mean
temperature difference is defined as follows,
ATLu = (AT AT, ' ) /~ (A~; /AT;) (4 8)
where AT, and ATh' are the temperature ciifferences between the brine and the refkigerant
at the inlet and initial freezing, respectively.
Page 31
Region II: Ice MaRng
The heat transfer rate in the ice making region, qi, is given by,
4, ' 4 , -4, (4- 9)
4, =ut -4 *ATrn (4.1 O)
where q, is the measured total heat transfer rate, U, is the overall heat transfer coefficient
in the ice-making region and A, is the heat transfer area (scraped-dace) in the ice-
making region. The temperature diEerence in the ice making region, AT,, is defmed as
follows,
um = 0.5 - (AT; + AT;) (4. I I )
where dTfiO is the temperature difference between the working fluids at the exit of the
scraped-surface chanael.
Overall Heat Tramfer Coefficient
The overall heat transfer coefficient. Un, is defhed by averiighg the performance
in both the chilling and the ice making regions. The coefficients. Il, and II, in Eqs. (4. ))
and (4.1 O), are used to define the average overall heat transfer coefficient. II,, üs follows.
s = u ~ A & ~ -0 +I/A,)-' +a - (I+ A J ) (4.12)
where A, is the total heat transfer a r a (scraped-surface) and A, is the area ratio between
chilling and ice making regions. The a m ratio is given by Eq- (4.13).
4 = Ac14 = ( q h , )-(a /AT,\, )
SIMULATION MODEL
A set of computer codes for the simulation model was developed consisting of
three individual programs: a) to generate a mesh for the evaiuation of the temperature
profile at each cross-section of the heat exchanger, b) to simulate the steady-state
condition based on the tluid conditions at the iniet, and c) to present the caiculated two-
dimensional temperature profiles graphically. The Listings of computer codes can be
found in ..lppendi.r B.
In order to calculate the heat transfer rate between the working fluids. the
temperature distribution in the heat exchanger cross section must be evaluated. A finite
mesh was then required to perform the calculation of the temperature distrïmtion over
the heat exchanger cross section as shown in Figure. 4. I .
A computer program was written to generate the cross sectional mes11 for use in
the simulation model. This geometric mesh was formed with square mesh in the interna1
portion of the heat exchanger and triangdar mesh on the boundary. The purpose of using
triangular elements on the bounda~~ was to inmase the smoothness around the cwature
driring the transformation of the actuai figure into the h i t e ciifference mesh.
The pmgram accepteci the size of mesh as input and generated the mesh with
diffierent resolutions in some output fües, which stored the information required durhg
the e x e d o n of the simulation program. in addition, mesh with different resolution
could be easiiy chosen during the simulation.
Page 32
5.2 PROCESS SIMULATION
A finite ciifference approach was employed in the simulation model. The heat
exchanger was divided axiaily Uito a finite number of segments. Each segment consisted
of the same axial length and the same cross section.
in order to evaiuate the steady-state operating condition, an iterative approach was
used. Three tasks were perfomed at each stage of iteration: a) heat transfer rate
evaiuation, b) heat and m a s balance evaim'on, and c) pressure drop evaiuation, The
flow chart for the simulation model is ilIustrated ia Figirre 5.1, and the process vaiables
are listed in Tuble 5.1.
Table 5.1 : Process variables in simulation rine ne channel i tb Temperature of f l u i d i XS s a l t concen t r a t ion of l i q u i d 1 XI ice f r a c t i o n l ~ e f r i g e r a n t channels
tc Temperature 1 PZ Pressure x, vapour q u a l i t y
l ~ e a t t r a n s f e r r a t e s 1 gb b r i n e channel I
1 q Ref r ige ran t channels
The main pirrpose of this step was to evaluate the heat exchange rate between the
fluids (brine and refiigerant) in each axial ekment in addition to the heat transfer rate,
the temperature profiles and the boundary heat flux profiles were aiso of in~erest. The
general structure of this subroutine is üIustrated in Figure 5.2, and the variables wd are
as foiiows. The descriptions of the variables are summarized in Tuble 5. I above.
input variables: 4 X* ph xr
Output Vanables: qb q,
Page 33
+ To simulate the steady natc proces of the scraped- surface heat exchanger
End of Simulation u
Pqamtion Stage
+ Operating condition of procrss and q u i & parameters for simulation
+ Predetennination of ammon constants used during ituation
+ Prrparation of initial values for simulation
Tempcrature and heat flux diim%ution gencraticm Rocedurcs for evaluating h e intcnncdiate h a t transfcr rates at each axial elcmcnts
Evnluation of fluid condition at each node in b i h brine and refrigmt channels
Evaluation of pressure drop in i t M g m t channrls Cdculation of fluid pmperties at cach nodc in refrigerant channeis
Check if al1 pnmss variabia have canvqeû
Output staec + Output of pmcess condition 4 Output of t empaam and heat !lux ditniution
Tamination of scraped-surface heat exchanger simulation
I Figure 5.1 : Structure of simulation mode1
Page 31
Temwrature Profile
The convection heat d e r coefficients wae calculated before the evaluation of
the temperature profiie. The averaged fluid properties beâween the inlet and the exit of the
axial segment were used to evaluate the heat ûansîkr coefficients. The thermal properties
of ice s l q were evaluated using the methods descni in section 3-3.k "Propclrties of
Ice Sltmy''. The ernpirical correlation, Eq, (3.9, devetoped by Skelland et al. (1962) was
used to calculate the heat transfer coefficient h the sçraped-surface channel.
The heat transfer coefficient in the refiigerant channels was evaiiiated using
Chen's correlation, Eq. (3.9. for flow boiling heat transfer under two-ghase flow
conditions. To account for the heat transfer coefficient of superheated cefigerant vapour.
the DittusBoelter correlation, Eq. (3. 1)' was used.
Nu, = 0.023 Ftedo8 Rn (5.1)
The constant n was equaI to O. J or 0.3, for heating or cooling of fluid, respectively.
The Gauss-Seidel iterative rnethod was appiied to the evaiuation of the
temperature distribution. However, the nucleate boiling portion of the mode1 included
the terni ( A T ~ ~ ~ ~ ~ A ~ ~ ~ ' * ) ' ) . Therefore, the nucleate boiling tenn rnw be rekshed to a
new vahe at each iterative sep.
Heat Flux Profile (boundmJ and Heat T r d e r Rote
The boundary heat flux pro6ies were evaiuated using the convective heat d e r
coefficient, h, and the temperature diffefence between the heat M e r surface, T,di, and
the buik fluid temperature, Tfid, as fouows.
Evaluate the heat iransfcr rates at each axial elemcnt of the scraped-dkce kat exchanger
Evaluation of the heat transfer nues in axial element N
Hau T m f a coemc1enr l
1 Evaluanon I
6T-6 i .R
i
Evalutacion of the heat transfer cocfticient for convedon (both brine and refngerant channels)
Convergence criteria in 2-D temprranuc profile iteration
Evaluation of steady state 2-D temperarure profile Usage of Guass-Seidel i t d v c appmach Nuclme boiling suppression in r r f i g m t channels
Chcck ifdl the nodal temperatures converge
Hcat Fiux Profiles and H a t Transfm Rate Calcularion
EvaIuation ofthe boundary heat fluxes in both brine and ntkigemt channcis
The heat gain or loss by cach Buid channcl will bc tte summation OC the imundary heat fluxes
Check if the hcat transfer baween the channcls is balanccd If ihc heat transfer is not b a l a n d the convergence cntrria for temperature profile rvaluation will be rcàuced by a fmr R
- - - --
End of each axiaI element evaluation
Tammab'on of the hem transfer rate evaluation
Figure 5 2 : Process of heat transfer tate evaluation
Page 36
The heat transfer rate in Watts h m each channel surface was equal to the
summation of the heat fluxes h m aü axial nodes,
where i represents the node location dong the channel wall, and A, is the heat transfer
area associated with the node i.
Heat and mass balances for each fluid in each axial segment were perforrned
accordmg to the procedure summarized in Figwe 53 . The variables us& were as
follows:
Input variables: th pn 46. q r
Output variables: x, x, x,
Brine Side
As brine was partially crystdized, a unifonn distribution of salt concentration
was assumed in the resuiting liquid. By performing heat and mass balances on the brine
side, the ice hction distribution was calculated as a function of the heat transfer rate and
the initial salinity of brine. A general relation between the salinity and the ice hction is
given by,
where x,' is the initiai salinity, x," is the fiml saünity (liquici phase), and x,O is the ice
weight fi;iction.
Page 37
P e d m mars balances for the fuu'te segrnais of each channe1 (bine and rciiigaant), ming the htal tmnsfer rate
Mass balance for an axial clmenr N of brire
Evaluate l e exit condition for the auid elanoit h m the heat and mass b a i a m
End o f ihe axial elmient N calculation
EvaIuation for the Refngcmt Channeli
Evalumion fbr axial elment N in channel C Shc scqwntial ordcr dqxnds on the flow direction
Evduation of the a i t vapour quality h m f ie h a t and mass baiancc
End of calculation for ihc a d elemcnt N frofess in chamiel C
I i
I
EvaIuarion of the quality chanse via ttic bend wnnecting channcl C and chanacl C + I
C = 5?
-
End of the ticat and mass batance evaluation for the nFriguant chmcis
i
Figure 53: Rocess of heat and mass b c e evaIuation
Page 38
A correlation required for ice fiaction, xi", was developed using the process shown
in Figue 5-4, by dividing the coohg process into two individual portions: a) chilling of
brine and b) phase change of water, as shown in Figure 5-5. The balances are $ven by,
(5 7)
where q is the total heat ttansfm rate- q b is the heat ûansfèr rate to brine, q, is the heat
transfer rate to produce ice, mb is the total m a s flow rate, x,O is the 6nai ice weight
hction, c, is the specific heat of brine, TB0 is the final freezing point, h, is the enthalpy of
water, and Ho is the final enthalpy of ice.
/ 1 s: in liquid p h u I
Figure 5.4: Condition for correlating the ice fraction
1 !
Figure 55: UIustration of coolhg process h m brine to ice slurry
Page 39
Substitution of Eqs. (5.6) and (5.7) into (5.5) yields,
y mb =(~-x,o).c, -(T/ - o " c ) + ~ ~ ~ . ( I ~ . -HJ
So, h m Eqs. (5.4) and (5.8),
The generai form of the ice fraction correlation was derived as follows,
A=A,,-(X;P+B~-X;+K,, (3. 11)
K = A, -x,' (5.12)
w h m the coefficients Ah Bo, Ko and Ar in Eqs. (5.1 1) and (5.12) were determineci t'rom a
regression analysis of various ice hction daci.
in evaluating the exit fluid condition at an axial segment f as show in Figiire 5.6.
the summation of the term (q /mb) is required (fiom elernent 1 tofi. This terni represents
the heat transfer rate to a unit mas of fluid passing through the segment. Two
contributions are predetennined as given by Eqs. (5.13) and (5. Id) for evaiuating the exit
ice ûaction. The first one is the heat ûansfer rate required for cooling the fluid d o m to
bC. The second one is the heat transfer rate required for cooling the fluid down to the
initial fieezing point.
Figure 5.6: Heat exchanger with n axial elements
Page JO
where Tb1 is the iniet brine temperature.
rtie terrn ( y ) was used to check if any ice was produced. The sub-cooling eff'ct of mb /P
brine before fieezing was assurned to be negligible.
The term, (q/mb)i, in Eq. (5.15) was wasd in combination with the ice fraction
correlation for calcuiating the exit ice hction. For the case of no ice generation. a
simple heat balance was perfonned to cdcdate the change in brine temperature.
Refiineranr Side
A general heat balance, Eq. (j.16), was performed based on the change in thermal
properties of the refrigerant between the idet and the outlet of an axial segment.
(5.161
where hf is the liquid enthalpy, hJg is the latent heat of vapobtion, x, is the vapour
quality, q is the heat transfer rate and Er is the m a s flow rate. The superscripts i and O
represent inlet and outlet. respectiveIy. The enthalpies were calculated b d on the
saturated conditions of the fluid.
Page 41
533.2 Pressure Gradient Evduation
The pressure drop calcuiation procedure is summarhed in Figure 5.7. The
pressures and temperatures of the refrigmt at each node were evaluated. Each axial
element was M e r divided into a certain number of segments for pressure gradient
integration, using the following parameters.
input variables: qn Xr
Output variables: r, p,
The comlations and models for evduating the two-phase pressure gradients have
been described in section 3.3: "Pressure h o p in Two-Phme Flow ". in ihe case of
superheated vapour, the Fanning equation, Eq. ( > . I - ) , was used for calculating the
fictional pressure gradient.
Micro-fins were fabricated in the refîigerant channels for heat transfer
enhancement. The effects of the micro-fins on the hydradic diameter and heat transfer
coefficient were taken into account durùig the construction of the simulation model. A
correction factor was used to modify the evaiuated heat ûansfèr coefficients and the
hydrauiic diameter. The correction factor.&, used was the ratio of the heat trrinsfer areas
with and without micro-6ns. The e f k t of the micro-fins altered the hydrauiic diameter
due to the increase in the wetted perimeter, P,. However, the change in the cross
sectional area could be negiected
Page 42
End of the Iih damnt & w o n
Figure 5.7: Rocess of pressu~e gradient evduatioa
Page 33
Due to iasufficient information avaiiable on the heat transfer enhancement effect
of the micro-tins, the folIowing assumption was made in constnicting the computer
model. It was assumed that the heat transfer enhancement was maidy caused by the
in& internd surface am; hence, the heat tramfer enhancement factor IW defined
to yield the enhanced heat transfer rate,
q=h.f,.A-AT (5- 19)
where A represents the surface rn without accounting for the micro-fins and ( h f i
represents the enhanced heat transfer coefficient.
53 TEMPERATURE DISTRIBUTION (CROSS-SECTION)
A computer code was written to plot the predicted two-dimensional temperature
profile at each mss section of the heat exchanger. Some of the output files from the
geometry program and the simulation prograrn were used as the input to this graphical
output program. The resuits h m this prograrn would dispIay the temperatun: variations
througholrt the whoIe cross-sectionai plane of the heat exc hanger in more detai 1.
6. RESULTS AND DISCUSSIONS
Several experimental test runs were chosen to verify the simulation mdel. These
test ruus and the simulation resuits are presented in the next section, "Results". in
addition to the recorded experimental data, observations made during experiments are
also presented. A cornparison of the resulting steady-state conditions. fiom the
experimenîs and the SimuIations, is discussed in the Iater section, "Discussions ". This
section also discusses the difûcuities confiontecl during the experiments and the
simulation mode1 deveIopment.
The exphenta1 d t s h m test runs conducted to verio the shulütion mode1
and the correspondhg computer simuiation resuits are presented in this sectioc
The heat exchaager in the current research was operated over a broad range of
conditions. Aithough an enormous amount of test data has been o b t a only several
experimentd resuits replesenting the typical operating conditions of the heat exchanger
can be presented here.
Experiments on the scraped-dace heat exchanger were conducted and the data
fiom a total of 65 test nms were tecocded using the data acquisition system. Due to the
extensive simulation time reqilired, ten test nms out of 65 were chosen to verify the
computer simulation modef. Table 6. I presents the ranges of the operating parameters
Page 45
for the test runs. Within these ten test m, two were conducted without producing any
ice, in order to check the applicability of the simulation mode1 to both chilling as well as
ice-making modes.
Table 6.1: Range of experimental parameters
&??rig.Wt si&
aIrz t l a r r r e Lpb 0-15 0.059 met Taper*ure
. C -2.7 -7.7
ut P r e s s u r e k ~ a 450.8 379.1
ut V p m r alauty - 0.20 0.12
mlT COmIIIOIO
Briae side kit T ~ e r n t u r e c O. 7 -3.5 kit Ice fmuion - 0.21 O. 0
h*tguunt s2de
kit T q - t u r e 'C -7.1 -U. 9 hit P T e s ~ e k& 330.1 328.6 kit Vapeur PCILLxty - 0.86 0.38
The operating parameters for each of the chosen test runs are summarized in
Table 6.2. They are divided into two categories, "Inlet Condition" and "Ourlet
Condition ".
Table 6.2: Summary of experimental results for sirnulalion
l ü U T C OUIITI OH
*An. SU. Hi18 I l o r r a c e ka/. *.@IV a . 1 6 1 a . 1 9 6 @ . A 3 1 a .A96 0 . T t 3 @ . I I 3 @ . A t 9 O . l t 9 0 . 1 1 9
In l r t T a p . r a t u r e * c 0 . a * O .O O a @ 1 . 3 0 C S @ 9 . 9 0 l a . O0 0 . 8 1 a . 7 1 @ . 7 1
In l r t S a l i n i t y D . O40 1. ( 4 8 e . 048 a . *Sb a #6@ D . a b @ a .OS@ O . 028 0 . 0 3 8 O . a 3 0
-LI C O l i l T l Q
& k g sldr ExLo T r * p r r + t u r r 'E - 3 . S @ -1 . D O - 3 . a @ - 3 . 1 0 - 3 . 0 ) O , a9 e . 7 ) -;.OS e l .O7 -t . O 1
E x i t I r e t r a c t i o n - 0 . 1 1 O.#& O . @ J O . 1 4 a . A4 1 . 0 ) 0 . 0 6 O .11 O . 1 3 O .11 - E M ~ S t i q e r r s u r r 'r - 1 . 3 8 - 9 . 0 @ - Y ? a 4 a -11 SI - a . $ * - 8 , sa - 7 0 9 -1 . 1 9 - 7 . 1 1
L u i s Pre i r u r r Ma 3 1 6 . 1 > ? a . S $ 6 8 b f l e . 0 l t b . 6 3 7 4 . 3 3 7 3 . 6 3 8 0 . 4 3 e b . 1 3 9 e . l
E n i r Vapour O u a l i t y O . ) @ 0 . 4 1 0 . S l O 6 1 I ?7 1. 41 O . O 0 . 1 4 O . 6 1 e . 6 k
Page 17
The "Inlet Condition" of the workùig fluids (brine and refiigerant) and the
rotationai speed of the rotor shaft (scraping speed) were used as inputs to the simulation
program. The "Ourler Condition " indicates the exiting siatus of the working fluids and
the heat exchange rate. These parameters were used in verifjhg the accuracy of the
simulation model.
The resdts f?om the typical test mw are a h presented as the overall k a t -fer
coefficient in Tuble 6.3. In evaluathg the coefficients for the two test nins in the chitling
mode, certain modifications were made to Eq. (4.12). The area ratio, A, was assigned to
be infinity in the case of no ice making and the term. ATh', in defining the log mean
temperature difference was taken as the temperature gradient at the exit of the heat
exchanger (scraped-surface channe!). Within the range of typical operating conditions,
the o v d I heat transfer coefficient was found to be 3.4 kw/rn2-OC (*lS%). The relation
betweea the other parameters and the overail kat transfer coefficient is Firrther discussed
later in the section, "Diswsion ".
Table 63: Range of overall h a t transfer coefficient
m r a l l k a t Trarwf cr Cacf f icient
in conducting the experiments, some results could be obtained only as qualitative
observations due to the difficulties in qwntifyuig the operation, One of the observations
made was the sound generated by the scraping action on the heat transfer sirrface during
the crystallization proces. As Iow sdt concentration hine was & during the ice-
making operation, a distinctive sound is produced by the mechanism of scnpùig. The
sound started mostly during the transition h m the c h i h g process to the ice-making
process. The chiliiig process represents the operating period where there is CO ice king
forrned. During the transition period, the fluid first undergoes a super-cooling period
where the temperature falls below the k z h g point. This sound started imediately
&er the super-cwling period and just at the beginniDg of the crystallization period.
A layer of ice is thought to have fiozen onto the heat tramfer surfacc but could
not be fully removed by the scrapers. This is probably the cause of the distinctive sound
king heard. This suggestion is proven by observing the flow at the exit of the brine flow
channel after shutting d o m the refrigeration system. Layers of ice were collected at the
exit of the brine flow channel. and the shape of the ice conformed to the curvature of the
scraped-surface. The formation of an ice layer is not desirable h m an operaton point of
view since it would likely decrease the k a t transfer rate because of low thermal
conductivity of ice (2.21 W/mK) and Iead to an unstable operating condition. Besides
decreasing the heat d e r rate, ice iayer formation causes lowering of refngerant
bailhg temperature and damages to scrapers. In some cases, the distinctive sound might
not be easily detected when the frozen ice is unifonnly b d t up on the iaternal wall. The
uniformity of the ice layer cteates a generally smooth surface where the scrapers are
skating on top of the ice layer.
Simulations were perfomed in accordance with the experimental conditions of
the chosen test runs descri'bed in the previous section. The d t i n g outputs h m the
Page 49
-
computer simulation for each of the test nins can be subdivided into four categories;
generai resuiîs, axiai distribution, boundary profles and cross sectional profiles. Each
category of the simulation results is M e r explainai below.
The general d i s of aü the simulations performed are f i presented. These
resuits are later compared with the experimental d t s in order to veriSf the feasibility of
the computer simulation model. Due to an enormous amount of simulation results
obtained, "test run mcmber 19" is used to illustrate the remaining categmies of the
results. This simulation represents a typical o p t i o n of the heat exchanger during ice
making. The simulations of other test nins are presented in Appendix D, "Simularion
Results ".
6.12.1 Summary of Ceneral ResuIts
The general resuits obtained fiom the computer simulation are the exit conditions
of the working fluids and the heat exchange rate as summarized in Table 6.4. In
veriwg the feasibility of the simulation mode[, these parameters were compared with
the d t s of the experimentd test ctms shown earüer in Table 6.2.
The information on the mesh useci in the simulation is fûst presented Ùi Tuble 6.4.
The "mesh site" indicates the dimension of the me& used for the evaluation of cross
sectional temperature distriiutions. The "no. of Gaial elemenrs " represents the number of
segments that the heat excbanger is divided ZuCialIy. Tite "aial element size" under
Process Inform~ltion shows the axiai length of each element axiaily.
(8 ) hafnb+a buttoo* - aar; rajruira ar#
(-1 Aov1rfib aitano - (rd) a r n r t i ~ d nit- - (a) isnarirdriba .rbtmo -
r r ~ r d p; ig
1-) rsyor.i# rrg aet?no - (-1 IhfUt l* i 381'mo - ( a ) i snn lhhaa ailmo -
Jut *a
: ( W u ) p i id* fiuoflr(â41 - ioatoqey
: (rlbq) aav:atp r r w - : (-1 hattrnb ailuf . : (rd] a~nerasd ailu! - : (1) i f m r s d w a ~ 4 p f i
W.. 6 1.) ~II:
: ( r p q ) bWlWt$ * r w - : (-1 Aafuttrr aituf - : (3) irnarridwa ailut -
aul:u ~01%-
Page 51
in Tuble 6.4, there are 8 parameters in the input condition and they are divided
into 3 sections: brine, refngerant and agitator. The brine section indudes the inlet
temperature, d i t y and mass flow rate. Most of the test nins were perfonned with the
b h e inlet temperature of (close to) O°C in the ice-making mode. Runs 20 and 2 1 were
performed with a higher temperature (-IPC) for testing in the chilling mode. The
refngerant section includes the inlet temperature, pressure, vapour quality and mass tlow
rate. The agitator section has oniy one parameter that is the rotational speed of the rotor
shaft holding the scrapers. Based on these input parameters, the simulation mode1
predicted the output conditions which will be compared with the experimentd results in
the later sections. On the brine side, the output condition includes the temperature,
salinity and ice fraction. The output temperature wiH be associated with the salinity
(freezing temperature). The salinity represents the salt concentration in the liquid phase
and increases if water freezes and turns into ice. n e salinity is then directly related to
the change in ice tiaction. On the refigerant side, the output condition ilcludes the
temperature, pressure and vapour quality. The heat iransfer rate will be the rnost
important result used in comparing the predictions with the expenmental resuirs.
6.1.2.2 Axial Distribution
The "Axial Distribution " results contain the axid vananations in the properties of
the working fluids (brine and reûigerant) dong the flow channels. in addition to the
working fluid properties, the heat transfer rate to each fluid channel at each cross section
dong the heat exchanger was also obtained. The redts h m the simdation of "test nm
Page 52
number 19" are presented below as an illustration. The parameters are plotted against a
dimensionless distance h m the brine inlet.
The conditions of the working f i d s are shown in F i p e s 6.1 through 6.k in Figure
6.1, the brine temperature faUs iiaeariy in the chilling region (nonnalized axia! distance <
02) and then remains relatively constant thereafter (nod ized axial distance :* 03) at the
freePng temperature. ïhe iœ W o n Figure 6.2) and salt concentration /Figure 6.3)
increase Linearly in the ice-mahg region (nomalized axial distance > 03). In Figure 6.4.
the legend trI-û5 represents the tempaature in the refrigerant channets, where h n n e l 1 is
equal to channel a (presented earlier in Figure 4 I ) , 2 to b and so on. The m w s indiate the
flow direction of the refiigefant. The saturation temperature (Figure 6.4) and pressure
(Fipire 6.5) MI linearly in each individual chamel. The figures show a larger reduction rate
in the beginning channel, then smaüer at the end This is relateci to the size of the channels
and it WU be discussed in later sections. ûn the orher hand, the vapow q d t y variation
(Figrue 6.61 shows a greater reduction rate at the last channe1 cornpareci to the first channel.
The heat d e r rate in each refigerant channel is plotted in Fip-2 6. ' dong
with that for the brine channel. Once the fluids enter the ice-rnaking region, the heat
transfer rates are predicted to remah neady constant. in contrast, a plot of the heat
m f e r rates for "test run d e r 20" (chilling mode) is provided in F i g m 6.8 as a
counterpart to the "test run number 19 ", shows continuously varying heat tmsfer mes
thughout the heat exchanger. in Figtrres f i 7 and 6.8. qb and qr represent the heat
transfer rates for the brine channe1 and the refiigerant channels, respectively, where the
numbers after qr represents the refngerant channel numkr.
Page 53
O. O 0 . 2 0-4 0.6 0.8 1. O
N o r e r l i t s d Axial Distance
Figure 6.1 : Variation of temperature in brine channel
Figure 62: Variation of ice fraction in brine channel
Page 54
Figure 63: Variation of salt concentration (liquid phase) in brine channel
Figure 6.4: Variation of temperature in refngerant channels
Page 55
Figure 6.5: Variation of pressure in refrigerant channeb
Figure 6.6: Variation of vapour quaiity in refngerant channels
Page 56
Figure 6.7: Variation of heat transfer rate in each fluid channel (ice making)
Figure 6.8: Variation of heat W e r rate in each fi uid channel (chilling)
6.123 Bounda y Profdes
Both the temperature and the heat flux distributions calculateci for each axial
segment of each fluid channel are plotted against the angle around the heat transfer
d a c e of the fluid channel. The boundary temperature distribution plots are presented in
Figures 6.9 through 6.11, while the boundary heat flux distribution plots are presented in
Figures 6.15 through 6.20. The nomenclature and the orientation of the channels c m be
found in the previous section (Figure 4. II. The distriiution plots for the brine channel
cover ody one quadrant of the cross section since al1 four quadrants have the same shape.
The zero-degree Sine corresponds to the line, as illustrated in Figure 4.1, besides the
rej?igeranr channel a; and the distribution is plotted against the angie in the an&
clockwise direction. For each refiigerant channel. the zero-degree angle is the point
closest to the brine channel with a plus sign corresponding the anti-clockwise direction.
Boundary profiles at different axial locations are plotted on the same p p h to
illumate the variation of profiles dong the heat exchanger. These results are taken h m
the simulation results of "test run number 19". For the wall temperature distribution
plots, for both the brine and refrigerant channels, the top contour is the profite at the
segment closest to the brine inlet. For the heat flux profiles, the sarne trend as the wall
tempemm plots exists where the top contour is the profile closest to the brine idet for
the refngerant charnels, however, the bottom contour of the heat flux plot for the brine
channel is the profile at the segment closest to the brine idet.
Page 58
Figure 6.9: Wall temperature profiles (brine channel)
r i p . r i e a n (üatraqmramt C h u n d #l lut h m u ï u M . a l : U 9 T e m t Run m i œ d i t d m a t h 20 mami d t 8 .sd rih PO1
-*xi-i
--cd-:
rxl-l nx? -4
- axL-i -,,.xi-a -a:-:
-ui-i
ml-+ 4x1-ici
ml-:
axi-1-
a ? - i . ai-:.
ml-i!
ul-Li.
-Ml-1-
- -1-11,
axl-i'' d - 2 1 i
~ - - - -
- i eo - 5 -oa -4s s 6: 90 135 IOC
Figure 6.10: Wall temperature profiles (refngenuit channe1 a)
Page 59
Figure 6.1 1 : Wall temperature profiles (refiïgerant channel 6)
Figure 6.12: Wal t temperature profiIes (refngerant channel c)
Page 60
Figure 6.13: Wall temperature profiles (refigerant channel d)
Figure 6.14: WdI temperature promes (refngcmt channel e)
in Figure. 6.33. a trend of decreasing overall heat d e r coefficient with the
rotational speed is shown for the vertical orientation of the heat exchanger. This senes
was conducted under the same operating conditions; i.e. the same refngerant flow-rate
and the same brine flow-rate. In contrast a peak was found in the horizontal orientation
test series as shown in Figure 6.34. Thus. an increase in rotationai speed does not always
benefit the overall performance of a scraped-surface heat exchanger in ice-making
applications. as previously reported by Bel et al. ( 1996).
However. the expenments performed in the present work are insuficient ro
iIlustrate the general effect of the rotational speed. since the experimentai conditions
covered were quite limited. In addition. one of the dificulties in showing the effect of
the rotational speed is the operating condition of the working fluids. Any changes in the
heat transfer rate will affect the fluid condition such that the effect of the rotationai speed
cannot be obsewed clearly. Hence. further investigations shodd be performed
specifically to smdy the effect of rotationai speed on the scraped-surface heat transfer for
ice crystallization.
633.2 Scraped-Surface Heat Exchanger in Ice-Making
Two major dificulties have been found so far with the binary solution (sodium
chloride solution) during the operation of the ice generator. Both were found to be
cIosely related to the heat transfer and the crystallization processes at the scraped-surface
channel wall. One of the problems was described previously in Secrion 5-2.1.2, where a
hardened ice-layer. which couid not be scraped off. built up on the heat mander surface.
Page 85
-
Another issue was an inmashg drag force that was exerted to the scrapers during the
ice-making pmcess. These points are discussed in more detail below.
Hmdened ice-laver created on the scraped-strrfuce
During the experiments under certain operathg conditions, a hardentd ice layer
was found on the scraped surface of the heat exchanger. The ice Iayer adhering to the
surface could not be removed by the scrapers. It could be removed only when the
refiigeration system was shut down to reduce the adhesive force between the ice and
the surface. The presence of the fiozen ice layer on the heat transfer surface was
determined by observing the exiting flow; the flakes of ice were found to have the
sarne curvature as the d a c e . During the experiments, this ice freezing effect dso
created a distinctive sound. distinctly different h m the mechanicd vibra-ion. Other
than shuning off the refiigeration systern, there was no apparent method to resolve
this problem afler the h z e n ice layer had forrned. A possible future solution wodd
be to invent a sensor that could indicate formation of a fiozen ice layer hy detecting
the sound.
During the experiments (including the operation of other scraped-surface heat
exchanger units), it was found that the fiozen ice layer f o m more aisiiy as the
concentration of the brine is reduced. in addition, each specific design of scmped-
surface heat exchanger would be susceptible to ice-layer build-up rit different
minimum brine concentrations. The formation of the h z e n ice layer was found
mostly during the period h m chiiling to ice crystallizhg modcs at which
the distinctive sound could be heard h m the transition region inside the heaî
exchanger.
Page 86
Some techniques could, however, be used to prevent the h e z h g effect. During
operation, the chilling to ice-making transition region could be spread h u g h the
heat transfer area by increasing the flow rate and the severity of the effect couid be
reduced. A batch type operation in which the heat exchanger was comected to a
closed loop with a fixeci amount of brhe was used in the present experiment; hence,
the brine could be concentrated in a fast manner exceediig the minimum required
operating concentration. In this case, the hzen ice layer would slowly be scraped off
h m the heat transfer surface. There were more operathg methods to deal with the
fiozen ice effect; however, they were al1 based on the idea of increasing the bine
concentration. Prevention or resotution of this situation wouid require another
investigation.
Increused dran force exerred ont0 the scrawrs
Another operating problem with the scraped-surface heat exchangers in ice-
making applications is the increasing drag on the scrapers. This increased h g force
necessitated the usage of a higher power drive motor.
During the experiments, it was found that the pwer required to drive the scraping
rotor increased whenever the heat exchanger was in ice-making operation. Ln
addition, the power was increasing as the operating ice fiaction increased. However,
the power dropped to the same IeveI as in the c W g operation whenever the
refrigeration systern was shut down, This suggested the ice fraction was the main
factor causing the i n d operating power.
As the ice fraction increased, ice crystais codd no longer be easily repositioned
h m the near-Wall region into the core region of the brine flow channel, and the
entire near-Wall region wouid be occupied by an icehrine mixture. As a result,
surface renewai would become inefficient and the rate of heat removal wouid be
reduced tremendously due to a reduced temperature gradient (because of saturated
state during m g ) . Hence, most of the hait was probably removed from the outer
region where a higher density icehrine mixture and greater adhesion (or viscosity)
would exist. One of ttie evidences supporthg this scenario was findine a highly
dense icelbrine hollow cylinder inside the heat exchanger, after opening up the heat
exchanger following a long period of ice-making operation,
From above, the heat capacity distribution is an important factor for the
performance of a scraped-surface heat exchanger. However. a limited degree or
mixing would be a characteristic of ice slurry. At certain ice Fractions. ice slurry cm
become rigid enough (capable of holding liquid) that mixing would be difficult to
achieve.
The comrnon factor involved in both phenomena is the adhesion of ice onto the heat
transfer surface caused by continuous cooling. Formation of a hardened ice layer on the
surface occurs dmost instantaneously during the transition from a chilling to an ice
making mode. in contrast, the increasing drag force occurs in a slower manner where it
is caused by continuous build up of an ice crystai population dong the hcat transfer
surface. Hence, bey can be considered as situations where insufficient thermal
distribution occm between the bulk and boundary regions in accordance with specific
heat transfer rate. However, the crystaiiiition characteristics of binary solutions at
different concentrations are aiso a significant factor in the phenomena d e s c n i . Further
indepth research should be made to confhm this.
Page 88
6.233 Overail Heat Transfer Coefficients
A major benefit of a method capable of evaluating the overall heat trader
coefficient is for characterization of the generaI performance of the heat exchmgers with
a minimal number of parameters. A more general comparison can then be made after
data reduction (i.e. temperature difference). A complete set of overall heat transfer
coefficients obtained in the present work cm be found in Appendir C-2. These heat
transfer coefficient data will be highly beneficial for later cornparisons witii other ice-
making heat exchangers.
62.4 FINAL REMARKS ON THE SIMULATION MODEL
During the development of the simutation model, there existed certain dificutties.
One of the difficuities was to find suitable heat transfer correlations that couId be
incorporated into computer codes. Since the simulation model was constmcted using a
finite ciifference technique for calcuIating the heat conduction rate across the channel
walls, a well defined boiling heat transfer coefficient correlation (that could account for
the effect of wall temperature) for the coolant was needed. On the refiigerant side,
Chen's correlation that accounted for both nucleate boiling and forced convection
vaporization was suitable for the present purpose. The contributions of later mearchers
to the development of correlations for nucleate boiiiig suppression and forced convection
vaporization made it easy to incorporate Chen's correlation into a computer algorithm.
Another difficulty was in estimahg the two-phase pressure dmp for the
refiigerant flow. The Martinelii-Nelson correlation was chosen due to its applicability
Page 89
- - -
over a ~ i d e range of vapour quaiity, while other correlations were specifically targeted
for a certain vapour quality range and flow regimes.
On the brine side, Skelland's (1962) correlation for scraped-dace heat transfer
coefficient was used due to a lack of alternative correlations for ice making applications.
The Skelland's correlation had been used in practice and suggested by the industry for the
scraped-surface heat exchanger. Since the correlation was developed mainly for a single-
phase process, ice slurry was assumed to be homogeneous.
Due to insufficient data to account for the effect of micro fins on heat transfer in
refrigerant channels, the enhancement effect was estimated using the increase in heat
transfer area in the pressure drop calculation, the increased pressure drop was predicted
based on a slightiy increased wetted perimeter.
Finally, the effect of pressure variation in the brine channel was neglected due to
the sIow flow in the experimental apparatus. The pressure effect would not lx enough to
have a signifiant effect on the saturation characteristics, such as the freezing point.
7. CONCLUSIONS AND RECOMMEMDATIONS
In the present work, the heat transfer characteristics of a scraped surface heat
exchanger for ice-sluny generation was investigated both experimentally and
numericaiiy. The main focus was on the operation of the scraped surface heat exchanger
in ice making with a binary solution af sadiun chtoride (salt) and m e r .
A set of cornputer pmgrams was written in Fortran 90 to simulate the operating
conditions of the heat exchanger. Past literature in the fields of scraped surface heat
excbanger and two-phase flow were reviewed for constructing the simulation model,
During the model development, certain assumptiotts were made in order to simplifj the
simulation model. The rnodel consisted of k e main parts; generatioa of the geometric
mesh, evaiuation of the steady state conditions, and graphical display of the cross
sectional temperature profiles.
The evaluation of the steady state conditions in the ice-slurry and refiigerant
channels was the main part of the m d d since it involveci many computationi steps and
generated most of the results. An iterative approach was used in the simulation model,
where the iteration consisted of three procedures; the evduation of heat exchange rate,
the heat and m a s balances, and the evaluation of two-phase ptessure drop in refigerant
channels.
Physicai testing of the scraped d a c e heat exchanger was conducted over a broad
range of operating conditions. The expmhental d t s were then used to ver@ the
Page 9 1
predictions of the simulation modei. Tests were conducted in both ice-making and
c h i h g modes to enlarge the verifjing range of data, The most important parameters for
cornparisons between the expeximentai and simulation teSul& were the heat exchange rate
and the pressure drop in refiigerant channeb. The heat exchauge rate was found to be
more sensitive to the temperature differeace between the refngerant and ice-slurry,
compared to the heat hausfer coefficient. This is due to the relatively constant nature of
the heat transfer coefficient compared to the fluid tempera-. Pressure drap in the
refiigerant channels was also important for the heat exchange rate evaiuation because the
saturation temperature depends on the IocaI pressure.
Cornparisons of the measured and predicted heat exchange rate and pressure drop
showed mean deviations of 4 . 3 % and -8.2%, and standard deviatious of *14% and
&IO%, respectively. Therefore, the simulation mode1 developed was found to be capable
of reasonably predicting the performance of the scraped surface heat exchanger tested in
the current work. in addition, the consideration of micro-fius in the model was
acceptable, even though it was a simple appmach. Fdermore, the simulation model
can be used in the future for improving the existing ice generator design and the
development of new ice generator designs.
Mixing of ice-sluny and brine between the buik region and the wail d a c e in a
scraped d a c e kat exchanger is still poorly tmderstwd. The thermal
penetration may be low due to the saturateci properties (kezing point) of ice and
tiquid in a binary solution. Further resewch shouid be performed on this topic,
Page 92
- -
since the eahanced mixing is one of the most importaut factors in increased heat
d e r rates for ice makiug appiicatiom.
The process of ice formation on the scraped surface is not well understood and
needs to be fully investigated. if the ice crystah forming on the surface cannot be
scraped off easily, then the efficiency of heat exchanger would be significantly
reduced. Other pmblems associated with high ice fraction processing include
increased drag force on the scraper blades. Understanding how the ice crystals
fom on the wall in b h u y solutions with a Iow concentration of the secondary
component can be an interesthg field of research.
Sym bol Description Unit
Constant for comlation
Constant for Butterwonh (1975) void W o n
H a t -fer area in chilhg region
H a t uansfa arca in icc rnaillng region
Ha! uansfa arca of the heat achanga
Heat transfa arca ratio bctwcen chilling and ice making regions
Nodal heat transfct ana
Coefficient of icc fiaaion correlation Coefficient in the function for the coefficient of the ice fraction comlation Coefficient in the function for the constant of the icc fraction comlation
Constant for comlation
Coefficient in the hc t ion for the coefficient of the icc fraction comlation
FIuid spccific hcat capacity
Liquid spccific heat capacity
Constant for two-phase fiction multiplia correlation
S ~ e d nuclcatc boiling hcat transfcr coefficient
Twephase fomd convmivt h m transfa cocfficimt
R c f m a enthalpy of mixture
Convcctivc heu transfer coefficient
Enthalpy of water
Final aithalpy of icc
tnla liquid cnthaipy of rcûigerant
Inla latent hcat of vaporization
Outlet liquid cnthalpy of rc&igaant
Ouikt latent heat of vaporîzation
Latent hcat capacity (liquidlvapour)
muid themial conductivity
Liquid thamai conductivity
l a slurry thermal conductivity
Liquid thamai conductivity
I a aicrmai conductivity
Constant of i a naction correlation
Constant in the function for the d c i a i t of the icc W o n comlation
-
Axial laigh of hcat exchanger ni
Dinancc travclai m
Mass of wami watcr t Mas of mixturr t
Symbol Description
Brine mass flow rate
Inncr wal1 N w l t numba
Rotor mtational spccd
Nusscit number for cimlar channel
Randtl number
Saturatcd p m r c diffacna baxd on saturatcd and wall mpaanires
Total pressure drop
Friction pressure drop
Amlemtion pressure drop
Gravitation pressure drop
Singîc phase prssurr drop
Constant for Buncrworth (1975) void M o n
Wdted pcrirneter
Pccla number of internai wall
Constant for Buiiawonh (1975) void fraction
hcrgy conlent of ice slurry
Enagy contcnt of warm watcr
Encrgy conimt of mixture
H m exchange mc of heat achangcr
Hcat archange ratc in chiliiig region
Hcat atchangc rate in i a making
Hcat exchange rate for the hcat exchanger
Heat flux on the scrapcd wîkœ
Heat transfér rate
Noda1 hcat flux on the saapcd suriàcc
Hcst transfa rate to brine
Hcat tran-Ffér rate to produa iœ
Hcettransaratcatscgmntf
Symbol Description
Reynolds nurnbcr (ddincd with D,)
Two-phase Reynolds numba
Liquid Reynolds numba
Constant for Bunerworth (1WZ) void fracrion
Reynolds numbcr for circular channcl
Nucleatc boilig suppression factor
Diffcrence bctwccn sammcd and wall tanpaanuc
Temp«anirr of mixture
Change in brine tempaaturc h m inla to initial frrtPng
Log mcan tcmpcnuurr diffaencc
T cmpemhuc diffemce bawmi i c t slurry and rrfrigcrant at inla of hcat exchanger Tmpcraturc diffacnu bctwcen ice s l ~ z and rcîiigerant at mitial h z h g
Tempemue diffctcncc krwm i u slurry and rckigcraat at exit of hcat orchanger
Temperanirc of the fluid
Fmzing tempetanue at the exit of hcat exchanger
Tcmpaanire diaaicc bctwmi wall nrrfacc and ilow
Ovaall heat transfcr cocfficicnt in chilling rcgîon
Ovcmll hcat Dansfa coefîicicnt
Avuagc o v d l heat mander coefficient
Bulk avaagc axial fluid velocity
Vclocity in the Channel
Salinity in the Iiquid phase at thc ait of heat ucdiangcr
1ce haion at the ait of htat atchanga
Page 96
Unit Eq-
Page 97
Symbol Description Unit Eq-
x," Outlet vapour quality oinfngsant
4 Initial salinity of he brinc bcing cooled
xr' Inlet vapour quaiity of nûigaant
Panunetci for k, evaluation
Void CiPaion
PmkmCtn for k,, evaluation
Parameter for k,, evaluation
Icc volume fiaction
Two-phase Ection multiplia
Icc s l m y dynamic viscoaty
Liquid dynmic viscosity
Vapour dynamic viscosity
Huid dyiiamic viscosity
Liquid dynamic viscosity
Constant 3.14159 ... Angle h m vatical position
Icc slurry dcnsity
Icc dcnsity
Liquid dcnsity
Liquid dcnsity
Vapour dcnsity
Fiuid daisity
Vapour dcns-ty
Liquid dmsity
Liquid surface tension
Alexiades, V., et al., Mathematical Modelmg of Melting anà Freering Processes. USA:
Hemisphere hblishing Corporation, 1993.
Bel, O, et al., "Thermal Study of an Ice Sluny used as Refngerant in a Cwling Loop," in
Wen, M.Y., et al, "Evaporative Heat Tmsfer and Enhancement Performance of RibRoughened
Tube Annuli with Refrigerant 1 14," Int. J . Heur Mass Transfir, 37,3, 1994, pp. 425436.
CORRELATION AND EXPElUMENTAL ERROR
The properties of the working materials, bine solution (sodium chloridc solution),
refingerant (fieon 22) and ice are fomulated into functiom. These hctions were used in
the construction of the simulation model. The correlation of the properties is cummarized
in Appendix A- 1.
The hction of exit ice hction was used in the heat and mas balance of brine durhg
the iterative process of the simdation model. This function simplifies the computationd
process of the simulation; heuce, reducing the executing t h e of the program. This
hction is presented in Appendir A-2.
ï he experimental errors due to instrumentation are surnmarized in Appendix A-3.
A-1.1: Propenies of Sodium Chloride Solution
A- 1.2: Properties of F m n Z!
A- 1 3: Properties of Ice
A-2.1 : Function of Exit [ce Fraction
A-3.1 : Experimental E m r
AI. I
AI.2
Al.4
A L I
A3.1
The fimction is vaiid for the range of sait concentration fmm O to lûwt??. Fonns of
fiuiction are as foiiows:
y=l-(l+m)-b (A. 1)
where the pmperty, y, is a function of the salt concentration, x. The salt concentration is
dehed as the weight fraction of salt in soIution. The form of function in eq. A. I is used
for evaluating the fireePng point and the remaining pmperties will follow the fom of
function in eq. A.2. The coefficients to be used with the functions are listed in table A. 1
and the legend for prophes is provideci in table A.2.
Table A. 1: List of coefficients for function of promes (hne solution)
Prouedes Unit Cocficicnts
Table A 2 Legend for pmpecties (bine solution)
T,j, - the mitial ûeezing point
c, - the specific heat apacity
p -thedensity
p -thedynamicviscosity
k - the thermal conductivity
Saturated Pro~erties
The hct ion is valid for the range of saturated temperature fiom -M°C to 18OC. Forms
of fiuiction are as follows:
y =y , +m+bx2 +cx3 64.3)
where the property, y, is a function of the satrrrated temperature, x, except the function of
the saturated temperature. The saturateci temperature is correlated as a fiuiction of the
saturated pressure. Ail properties are correlated in the fùnction form as eq. A.3, except
the fiuiction for (Wdp)) , in the form as eq. A.#. And (Wdp)), is a fiuiction of the
saturated pressure. The coefficients for the function are listed in table A.3 und A.I. A
Iegend of symbols is provided in table A.5.
Table A.3: List of coefficients for function of properties (saturated iU2)
Propcrtia Unit Coeficienfs
Table A.4: Coefficients for hction of (dv Ji+),
Table AS: Legend for pmperties
- the santrated temperature
- the saniniteci pressure
- the liquid density
- the gas specific volume
-the liquid enthalpy
- the gas enthaipy
- the liquid specific heat capacity
- the gas çpecific heat capacity
- the liquid viscosity
- the gas viscosity
- the liquid thermal coaductivity
- the gas thermal conductivity
- the latent heat of capcity
- the surtace tension
SaturatedPtoDerties
The fùnction is vaiid in the range of 239 to 515kpa and -18 to I8OC. Form of function is
as follows:
y = y , + ~ P + ~ T + c P T + ~ P ' +eT2 (A. 5)
where P is the pressure in Pa and T is the temperature in OC. A list of coeEcients for
each of the superheated properties is provided in table A.6.
Table A.6: List of coefficients for function of properties (supeheated R22)
m~ertY ûensity Enthalpy Specific Heat
Unit k g h 3 J/kg J/kg/K
The properties of ice stated in the following are transformeci as fiuictions of the
temperature, T. The density of ice can be evaiuated h m eq. A.6. The thermal
conductivity of ice can be evaiuated h m eq. A.7, which it has been zupplied by
AIexiades and Solomon. The enthaipy of ice is correlateci in eq. A.8 using the data h m
the ASHRAE handbook. The tùnction of the enthaipy is valid within the range of -10 to
0°C.
p=917-(l+173-10' - T ) (A- 6)
k = 224 + 5.975 - lo5 (273 + T ) ' . ' ~ (A- 7)
h = 2.0769. T - 333.43 (A-@
In the previous section ''4.3.2.2 Hcat and Mus Balance Calculation, Brine Side ", the
consideration of exit ice fiaction evaluation was discussed. A function of exit ice f'ractioa
was formed to ease the computational work during the simdating process. The relation
between the initial salt concentration, the exit ice hction and the heat d e r rate is
shown in table A. 7.
Table A.7: Relation for the formation of exit ice fractian function
Based on the data calculated in table A.7, the exit ice fraction cm be correlated as a
function of initial salt concentration and heat d e r rate. The bct ion is stated as
follows:
where X: is the exit ice M o n , q is the heat transfer rate and m is the mass flowrate of
brine. The hc t ion was used to predict the exit ice fiaction with an inlet bine
temperature of O°C. The constants Kr and Kz in eq. A.9 are defined as func5ons of the
initial salt concentration of brine, and they are correlated as follows:
K, = A -(x,' )l + B -(x,')+C (A. IO)
K2 = D -(x,') (A. 11)
where x,' is the initial salt concentration of brine. The constants A, B, C and D were
evduated to be -8.6836, -l.6721,2.9999 and 4.6366, respectively.
Description Emr
Temperature 0.5 deg.C
Pressure 1 psi
THE COMPUTER CODES
The computer codes, written in Fortran 90 language, are provided in this appendix.
These cornputers were used to sunulate the steady-state operation of the scraped-muface
heat exchanger in study. Three sets of computer codes are presented:
a Geomeüic model, the codes for constnrcting the fmite elemental mesh of the heat
exc hanger cross-section.
O Simulation rnodel, the codes for evduating the steady-state operatine conditions
of the heat exchanger.
O Distribution model, the codes for displayhg the cross-sectional temperature
profiles in graphical forms.
The detailed usage and construction of the computer codes have been provided in
Chapter 5: '"Simzdation Model". A table of contents of this appendix is supplieci in the
following:
5 1: Geomewic Model
B-2: Simulation Model
B-3: Dimiution Model
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