Evaluation of antifreeze solutions for use inice builders

B. MORISSETTE and J.D. SHEPPARD

department ^r^^lEngineering^ MacdonaldCampus ofMcGill University, Ste-Anne deBellevue, QC, Canada H9X3V9. Received 30March 1993; accepted 8 September 1993.

Morisette, B. and Sheppard, J.D. 1993. Evaluation of antifreezesolutions for use in ice builders. Can. Agric. Eng. 35:261-267.Adding salt, glycol, or alcohol (antifreezes) to water reduces thefreezing point. Thefeasibility of combining in onedevice, thecharacteristics ofboth icebuilder andsecondary refrigerant chiller forthesupply of coolant at a temperature below 0°C is discussed. Therelative performance ofthree antifreeze solutions was tested using asmall icebuilder andtheresults arepresented. Propylene glycol gavethebestperformance, achieving a finalsolution temperature between-3.2 and -3.6°C with rates of freezing comparable to those obtainedwith water. Calculated heat transfer rates and ice accumulation timesare compared with the experimental data. Good agreement wasobtained by adjustment of the convective heat transfer coefficientand the thermal conductivity of the ice.

Key words: ice builder, refrigeration, chiller, antifreeze, modelling

L'addition de sel, de glycol ou d'alcool (antigels) a de l'eauabaisse le point de congelation. La faisabilite de combiner dans uneunite operationnelle, les caracteristiques d'une banque de glace etd'un refroidisseur a solution d'antigel (refrigerant secondaire) pourproduire un melange refrigerant a une temperature inferieure a 0°C,est discutee. L'utilisation d'une petite banque de glace a permis deverifier la performance relative des antigels et les resultats sontpresented dans ce rapport. Le propylene glycol donne les meilleursresultats; une solution finale ayant une temperature entre -3.2 et-3.6°C est obtenue, avec une vitesse deformation delaglace comparable a celle de l'eau. La quantite de chaleur transferee et le temps deformationde la glace ont ete evalues par calcul et sont compares avecles resultatsexperimentaux. Une bonne correlation a ete obtenue parajustement du coefficient de transfert de chaleur a la surface et de laconductivite thermique de la glace.

Mots cles: banque de glace, refrigeration, refroidisseur, antigel,modelisation.

INTRODUCTION

A tank in which the accumulation and storage of ice providethe cooling capacity for chilled water is called an ice builder.Ice builders can offer certain economic advantages whenrelatively large quantities of chilled water are required intermittently. If the ice builder is designed correctly, a uniformsupply ofwater at 1°C canbesupplied forpeak cooling loads,thus, reducing the required refrigeration capacity and permitting the building of a cold reserve during the off-peak periodwhen energy costs are often lower (Stubblefield 1979).

The ice builder type of water chiller consists of an insulated tank containing coils or plates submerged in water. Iceis formed on the surface of the coils or plates, which arerefrigerated by Freon , ammonia, or another refrigerantcirculating inside. Ice builder coils are generally made from

steel pipes of 25.4 mm or 31.8 mm diameter with a maximumice buildup of 64 mm in thickness. The water is kept constantly in motion around the surface of the ice, either bymechanical agitation or, more often, by air agitation. Therefrigerant temperature in the ice bank system is usuallymaintained between -6.7 and -18°C (MacCracken 1984).Temperature detectors or electrodes are used to control thethickness of the ice. Warmed water returns from the coolingload to the bottom of the tank, and the chilled water ispumped out from the top (ASHRAE 1982).

Chilled water is a good coolingmedium, but is limitedbythe minimum temperatureat which it can be supplied to theload, usually not lowerthan 1°C(Lindsay et al. 1974), limiting the final product temperature to about 4°C. However, forthe cooling of dairy products the secondary refrigerantshould be supplied to the product heat exchanger at -2°C,requiring the use of an antifreeze solution. The most commonantifreeze solutions used as secondary refrigerants are calcium chloride, ethylene glycol, and propylene glycol. Thepurpose of this project was to investigate the technical feasibility of combining in one device, the characteristics of bothan ice builder and a chiller for antifreeze solutions. Thiswould provide the inherent advantages of an ice builder, alarge reserve of cooling capacity for peak loads, with theadded ability to supply a secondary refrigerant at a temperature below 0°C (Stubblefield 1979; Gilbertson and Jandu1984).The technical feasibility of such a system will depend onthe effects of the antifreeze solution on the characteristics of theice and its rate of formation.

THEORETICAL MODEL OF ICE GROWTH

The heat transfer equation between the refrigerant inside thecoil and the liquid surrounding the coil was established forthe prediction of ice growth on pipes. The reduction in thefreezing temperature of the liquid due to the formation of iceadded further parameters to be considered compared to astandard ice builder using only water. As shown by Wubbenet al. (1987), the energy balance between the bath and itsenvironment is:

dE

dt '•• qenv + qm-rnr (Hg - Hf)

where:

dEldt = rate of energy transferred from bath,qenv = rate of heat transferred from environment,

(1)

CANADIAN AGRICULTURAL ENGINEERING Vol. 35, No. 4 October/November/December 1993 261

qm = rateof energy added to bath by mixing, andmr (Hg-Hf) =rate ofheat removed from bath byrefrigerant.

Since the rate of energy transferred from the bath is thesumof the changesin internalenergyof the bathcomponents,the left part of Eq. 1 can be replaced by:

dE

dt

dTc dTice'- mcCc —J- + mtceCice

dt dt

+ (m,L - mice) cldTL

dt

dmuuif-

dt(2)

The first three terms on the right side of Eq. 2 are the rateof heat loss from the coil, from the ice, and from the liquid asthe temperature of each decreases, while the last term is therate of energy released when the water freezes around thepipe. Since heat loss from the pipes represents only about0.2% of the energy transferred, it is ignored. However, thesecond and the third terms cannot be neglected (Wubben etal. 1987), because with the decrease of freezing temperaturethese two terms represent about 20% of the total energytransferred between initial and final conditions.

In Eq. 1, mr (Hg-Hf) can be established if the mass flowrate of refrigerant circulated is known. However, when arefrigerant flow meter is not available, this term can bereplaced by the equation of heat transfer through the pipe andice V- Geankoplis (1983) established that the rate of heattransfer by conduction and surface convection through amulti-layer cylinder in series can be defined by:

q =AT_ drivingforce1R^ resistance

(3)

where:

AT = Tt-Tr = temperature difference between liquid andrefrigerant, respectively, and

R - (r0-ri)lkAim = resistance through each cylinderfor conduction.

Aim is the log mean area for heat conduction through a cylinder and is given by:

Alm =Ai-A\

ln(A2/Ai)(4)

Factors for fouling on the inside and outside surfaces havenot been considered, as these surfaces will normally stayclean during operation. Contact resistance has not been considered at the interface between the coil and ice, therefore,both the outside surface of the coil and the inside surface of

the ice are at the same temperature (Geankoplis 1983). Thus,the overall heat transfer rate through a concentric pipe and icecylinder is:

q = -TL-Tr

1 | (r2-r\) | (n-n) ^ 1hiA\ fCcAclm kiceAicelm hoAl

(5)

Replacing mr (Hg-Hf) in Eq. 1 by q (Eq. 5), combining Eqs. 1and 2, and solving for dt gives:

262

_mice Cje dTice +(mL ~mice)CL dTL - Ujfdmjce ,^-q + qenv + qm

Equation 6 was solved byafinite integration method usingLotus 1-2-3™. A time interval was calculated for each 0.1mm increase in ice thickness, and by adding intervals the timerequired to reach a givenice thickness wasestimated.

The parameterTl is constant if pure water is used and Trwill be specified. Tice the mean ice temperature was estimated as the arithmetic mean of Tl and 7>. The adding ofantifreeze to water varies the parameter Tl and, therefore,must be considered. The liquid temperature Tl decreases asice is formed and this also lowers the freezing point of thewater as the antifreeze concentrates (Cant)- The relationshipbetween antifreeze concentration and water removal as the

result of ice formation is:

Cant —'mLCa

mL ~ mice Fant(7)

where Fant is a factor that takes into account the antifreezetrapped in the ice and is obtained from the experimental data.Therefore, the temperature Tl is now estimated by Eq. 8,where Stc is the slope of the freezing temperature curve, fromthe graph of specific gravity versus antifreeze concentrationand Ctecr obtained from published data, are shown inTable II.

Tl = Stc Cant + Cterc (8)

Average values for the specific heat of the antifreeze solutions (cl) were obtained from ASHRAE (1985) and from theHandbook of Air Conditioning System Design (Carrier Corp.1965).

MATERIALS AND METHODS

Apparatus

All experiments were performed using a small ice builder,shown diagrammatically in Fig. 1. As with standard icebuilders, the coil was made from schedule 40 steel pipe of25.4 mm nominal diameter. Four lengths of pipe were connected in series, two lengths placed 130 mm above thebottom of the tank and two lengths 100 mm below the top ofthe liquid. The elbows and ends of the pipes were locatedoutside the water bath to eliminate the need to account for end

effects and the geometry of the elbows. The piping outsidethe tank was insulated with 12.5 mm Armaflex M. The tankwas constructed of plywood lined with 51 mm of high densityStyrofoam insulation. The inside dimensions of the tank were451 mm x 1217 mm x and 555 mm (width x length x height),giving a working liquid volume of 236 L with a liquid levelof 430 mm. The tank was made water tight by covering theinside with PVC membrane roofing material and sealingaround the joints with thethermoplastic sealant PRO 2000T(Bulldog Grip).

The ice builder was connected to an existing Freon 12refrigeration system. Different configurations were tried inorder to obtain the most uniform possible ice growth on eachof the four pipes. The flooded evaporator system gave themost stable result. All the pipes were filled with refrigerant,

MORISSETTE and SHEPPARD

102 mm x 500 mm

drum accumulator

Fig. 1. Schematic diagram of the ice builder showing theinsulated box containing the solution and theevaporator pipes.

completely wetting the inside pipe surface. However, due tothe small height difference between the bottom pipe of theevaporator coil and the liquid accumulator return pipe, somegas accumulation occurred in the pipes. The liquid level inthe accumulator was controlled by a thermostatic expansionvalve with the bulb located on the accumulator outlet pipe.When the liquid level rose above a certain point, the gasflowing out of the evaporator pipes entrained fine droplets ofliquid refrigerant. This reduced the gas superheat, thus, closing the expansion valve. Similarly, a decrease in the liquidlevel decreased the amount of liquid entrainment, therebyincreasing the gas superheat and opening the expansionvalve.

The refrigerant temperature in the coil needed to be keptas constant as possible during the trials in order to establisha data set at a specific refrigerant temperature (Tr). This wasachieved by stabilizing the refrigerant pressure, with avariation of ± 1°C, with the help of an auxiliary evaporatorwarmed by forced air. The thermostatic expansion valve onthe auxiliary evaporator was used as a proportional pressurecontroller, by placing the bulb in ice to fix the thermostaticelement pressure. It was possible to adjust the operatingpressure by varying the spring strength, thereby obtaining thedesired refrigerant temperature. Some minor adjustment wasrequired during the trial to compensate for the error in theproportional controller with changing conditions. As the iceaccumulated in the ice builder, the heat transfer decreased,reducing the refrigerant pressure. To compensate for thiseffect, the rate of heat removal in the auxiliary evaporatorwas increased by opening the expansion valve, increasing therefrigerant flow and the operating pressure.

Mechanical agitation of the water or antifreeze solutionwith a recirculating pump has an advantage over air agitationsince the entrapment of air bubbles in the ice is largelyavoided. Pumped agitation was tried with a 6.2% by weightcalcium chloride solution. The solution was pumped out from

the top at one end of the ice builder and was returned by adistribution pipe located at the bottom. The pipe was perforated with sixholes of 6 mm diameter pointing upwards andspaced 200 mmapart.Flowrates of 10and 27 L/min(at 10.3kPa and 24.1 kPa) were tried but unequal ice growth wasobserved, principally underneath the pipe. A flow rate ofapproximately 50L/min (at69kPa) gave uniform icegrowthbut, at 10 mm ice thickness and a refrigerant temperature of-15°C, the energy added by the 0.75 kW pump (qm) was toogreatandno further ice buildupcouldbe achieved. Therefore,this method was abandoned in favour of a lowenergy agitation system using compressed air. Airwas distributed bya 13mm pipe located at the bottom of the bath, pierced by eight1.6 mm diameter holes placed in the lowerpart of the pipe,spaced 152 mm apart. The air pressure was regulated to 10.3kPa to give a flow rate of 0.953 L/s at 21°C. The heat addedby air mixing (qm) was estimated to be 26 W, while the heatgain from the environment (qenv) was measured to be 59 Waveraged over 11 hours and 40 minutes with an ambient roomtemperature of 27°C.

Experimental procedure

Trials were performed with water, calcium chloride, methanol and, propylene glycol solutions at -15°C and -10°C withair agitation, and for comparison, at -15°C without agitation.Each trial began by first cooling the liquid close to its freezing point while agitating with air to maintain a uniformtemperature. When the liquid temperature reached less than2°C above its freezing point, the trial was started. For eachtrial, the following measurements were made: solution temperature, solution specific gravity, outside diameter of icegrowth, refrigerant temperatures and pressures (liquid feed,liquid in evaporator coil, and gas outlet). These parameterswere recorded at 15 minute intervals for the first hour, at halfhour intervals for the next three hours and, thereafter, athourly intervals until the maximum ice growth was achieved.Due to the large surface area of the tank compared to itsvolume, the change in level was not accurate enough to beused in the determination of ice formed, as previously reported by Wubben et al. (1987). Therefore, a specially madecalliper was used to measure ice growth at the midpoint ofeach pipe. The ice thickness varied along the length of thepipes by as much as 5 mm. To account for this, the icediameter was measured at five locations on each pipe. Fromthese 20 readings, a factor was established relating the midpoint ice thickness to the mean. This factor, which variedbetween 1.005 and 1.025, was used in the calculation of themean values for ice thickness and ice volume. To account for

air bubbles and antifreeze solution trapped in the ice, the icedensity was then calculated by weighing the ice at the end ofeach trial.

RESULTS AND DISCUSSION

Ice characteristics

Table I compares the experimental results of initial and finalconditions for tap water and each antifreeze solution tested.Air trapped in the ice was detected for all four solutionstested, however, water produced clear ice. With air agitation,the air bubbles were about 5 mm in diameter and located in

the bottom part of the ice cylinder in a circular section of

CANADIAN AGRICULTURAL ENGINEERING Vol. 35, No. 4 October/November/December 1993 263

Table I Summary ofexperimental results1

Concentration (% by wt.) Temperature (°C) Ice density (kg/m )9

Freezing time (h) Heat trans, rate3 (W/m)

Solution

Initial -15° -15°A-10°A -15° -15°A-10°A -15° -15°A -10°A -15° -15°A -10°A -15° -15°A-10°A

Water

Calcium chloride

Methanol

Propylene glycol

6.2 7.7 8.5 7.5

4.3 5.5 5.6 5.2

12.8 13.7 14.6 13.4

0.2 0.0 0.0

_4.4 -4.4 -3.8

-4.0 -4.1 -3.7

-3.3 -3.6 -3.2

916 907 887

891 873 865

808 825 889

812 813 838

3.0 4.0 5.3

4.2 4.2 13.6

4.0 4.7 10.7

3.6 3.4 13.4

152 139 100

118 100 52

114 100 45

124 111 48

Notes:

1 -15° and-10° referto thetemperature of therefrigerant in thecoiland"A" means air agitation wasused.2 freezing times toreach 30mm ice thickness.3 heat transfer rate permeter ofpipe length with 30mm ice thickness (calculated with Eq. 5).

120°. Without agitation, the bubbles were smaller (about 1mm diameter) and were uniformly dispersed throughout theice. These bubbles likely came from gas that had been dissolved in the liquid, since air agitation was used tothoroughly mix the solution before the test was started.

Without agitation the ice was more symmetrically formedaround the pipe. However, in both cases variation in icethickness occurred, probably due to unequal distribution ofFreon in the pipe changing the heat transfer coefficient.With agitation, the variation in ice thickness was greater, dueto the unequal liquid movement at the surface of the ice.Greater liquid movement would cause the ice to be formedmore slowly because the liquid would be at a slightly highertemperature than the ice surface. With air agitation, as withpump agitation, it proved difficult to obtain uniform liquidmovement around the ice surface.

The densities of ice produced from the tap water werelower than those expected: that is 887 to 916 kg/m insteadof the expected 921 kg/m . This was due to the air bubblestrapped in the ice and, as expected, the ice densities werehigher in the tests without agitation, with the exception ofmethanol. Increasing the refrigerant temperature to -10°Calso had an effect on ice density; with water and calciumchloride the densities were lower, while for methanol andpropylene glycol densities were greater. However, these results are questionable because, except for the tap water, thetests were stopped before the maximum ice accumulation andminimum temperature had been reached.

When antifreeze was added to the water, the ice was notclear but was white, resembling hard snow. The ice structureappeared as if layers of snow were pressed on each other. Aswith the tap water, air was trapped in the ice below the pipe.However, the air was not trapped in bubbles, but in holes, 1to 3 mm in diameter, starting on the pipe surface and radiating to the outside of the ice cylinder. In some locations therewere open channels up to 10 mm wide (at maximum icegrowth) at the pipe bottom. Particularly common in the softeror lower density ice, these channels ranged in length from afew tens of millimetres to the entire length of the pipe. Theice was soft and was not firmly attached to the surface of thepipe, in contrast to the ice produced from pure water. Theonly exception to this was the calcium chloride solution withno air agitation, where a hammer and a scraper were required

264

to break the ice. This ice also had the highest density, 891 kg/m .The temperatures of the solutions at the conclusion of the

tests were 1.2 to 1.9°C higher than anticipated. This wasbecause the final concentrations of antifreeze solutions were

lower than expected, caused by the presence of antifreeze inthe ice, 1.2% for calcium chloride and 2.0% for methanol.Propylene glycol proved to be the exception as the finalantifreeze content of the ice was measured to be 0.0%. How

ever, the small density difference between water andpropylene glycol and the small variation at low concentrations may have rendered the reading inaccurate.

Heat transfer and rate of ice growth

The results obtained with the three antifreeze solutions and

the plain tap water under the three different test conditionsare presented in Table I. In comparison to tap water, thepresence of an antifreeze reduced the rate of heat transfer andresulted in a correspondingly slower rate of ice growth. Thiscan be explained by the substantially smaller temperaturedifference between refrigerant and antifreeze solution and thedecrease in density and thermal conductivity of the ice. Of thethree antifreeze solutions, the propylene glycol solution gavethe highest heat transfer rate, 124 W/m of pipe length with arefrigerant temperature of -15°C and without air agitation.This rate is about 18% slower than with tap water, mainlyfrom the smaller temperature difference. Thus, when therefrigerant temperature was increased to -10°C, the rate ofheat transfer was reduced further to only about 50% of thatattained in the plain water.

In Figs. 2 to 5, the results from the heat transfer simulations are shown as solid, dotted or dashed lines overlappingthe actual data points for either the tap water or the propyleneglycol solution. Values for the parameters used in the calculations are shown in Table II. In each case the best curve fit

was obtained by varying the two unknown parameters: theconvective heat transfer coefficient (h0) and the thermal conductivity of the ice (kice)- Neale et al. (1981) reported aconvective heat transfer coefficient of 700 W«m" •°C" for asimilar system using water. In the tests reported here, the rateof heat transfer was dominated by conduction through the icelayer and was insensitive to h0, except early in the tests whenthe ice thickness was minimal. Figure 6 illustrates the effectsof varying kice while freezing the propylene glycol solution

MORISSETTE and SHEPPARD

24 -,

20

-•— with agitation at Tr of -15 °C•A-- with agitation at Tr of -10 °C

-*— withoutagitationat Tr of -15 °C

30 40 50

Ice thickness (mm)60 70

Fig. 2. The time required to achieve ice growth on theevaporator pipes in plain water under threedifferent operating conditions.

(0cco 200

cdCD

I100-

-•— with agitation at Tr of -15 °C•A— with agitation at Tr of -10 °C

- «• - - without agitation at Tr of -15 °C

40 50

Ice thickness (mm)60

n

70

Fig. 3. The rate of heat transfer between the refrigerantand plain water in the ice builder under threedifferent operating conditions.

with a refrigerant temperature of -15°C and using air agitation. Due to the presence of gas bubbles all ice conductivitieswere found to be lower than the value established for ice

formed in pure water, 2.5 W»m" •°C" (Perry and Chilton1973).

The overall heat transfer rates were higher with no agitation under all conditions tested. The reduction in the

convective heat transfer coefficient was more than offset byan increase in the thermal conductivity of the ice, because ofless air entrapment and higher ice density. The exception tothis phenomenon was encountered with the methanol solution. Here the pattern of air entrapment was different andagitation increased the density of ice, although the thermalconductivity was still lower than with no agitation.

24

20

500

400 -'

E

B 300

COc

a>x

200 -

100

-•— with agitation at Tr of -15 °C••A— with agitationat Tr of -10 °C"O - - withoutagitationat Tr of -15 °C

20 30 40 50

Ice thickness (mm)

Fig. 4. The time required to achieve ice growth on theevaporator pipes in a solution of 12.8% (w/w)propylene glycol under three different

operating conditions.

•— with agitation at Tr of -15 °C

*•— with agitation at Tr of -10 °C

» - - without agitation at Tr of -15 °C

30 40 50

Ice thickness (mm)

Fig. 5. The rate of heat transfer between the refrigerantand the propylene glycol solutionin the icebuilder under three different operatingconditions.

CONCLUSIONS

It has been shown to be technically feasible to combine an icebuilder with a chiller to provide a cooling medium between-3 and -4°C. However, the problemof low ice density and adecrease in thermal conductivity is exacerbated in the presence of an antifreeze solution. A low energy method ofagitation, other than with air bubbles, should be investigated.In addition, the rate of heat transfer and ice growth is reducedas the freezing point is lowered due to the smaller temperature difference between the refrigerant and the bath. Thesefactors could probably be overcome by using longer evaporation pipes, thinner ice and lower refrigerant temperatures,but at an increased cost. Of the antifreezes tested, propyleneglycol appears to be the best choice for this application

CANADIAN AGRICULTURAL ENGINEERING Vol. 35, No. 4 October/November/December 1993

70

265

Table II. Parameters used for solvingheat transfer simulations

Products

Tr

<°Q

qenv+qm

(W)

Specificheat,

(J-kgVcCL

X)Fant Stc

(°C/%)"Ctetc

(°C)

ho

(W*m"2*°C"kice

l) (W^m-VCT1)

Water -15 A1-10 A1-15

85

85

59

4184

4184

4184

--

;600

600

400

1.8

1.9

2.0

Calcium

chloride

-15 A1-10 A1-15

85

85

59

3770

3770

3770

0.70

0.70

0.68

-0.632-0.632-0.632

0.9420.9420.942

700

700

500

1.6

1.4

2.0

Methanol -15 A1-10 A1-15

85

85

59

4310

4310

4310

0.75

0.75

0.75

-0.833-0.833-0.833

0.5830.5830.583

700

700

600

1.6

1.5

1.8

Propyleneglycol

-15 A1-10 A1-15

85

85

59

4510

4510

4510

0.41

0.41

0.41

-0.354-0.354-0.354

1.5041.5041.504

600

600

500

1.8

1.3

2.1

Cc\ =Cice ~

500 Mcg^C12000 J^kg'VC"1 at0°C

kc5 =k- 5Kice —

45.3 W*m~Vc_12.25W2«m«°C"1

L

mc

4.868 m

16 kg

p5 =

h06 =

3.4 x 105 J/kg921 kg/m31136W«m'Vc700 W^m'Vc1

l

mice 0 to 77.4 kgr\

ri

n

0.0134 m

0.0168 m

0.0168 to 0.076 m

Notes:1 ~>„*;~„~, A

from Dow Chemical Company (1990).' from Carrier Corporation (1965).[from ASHRAE (1985).1from Perry and Chilton (1973).' from Nealeetal. (1981).

266

20 30 40

Ice thickness (mm)

Fig.6. The effect of ice conductivity, kiCe, on the rate ofheat transfer and time for ice growth in the12.8% (w/w) propylene glycol solution with arefrigerant temperature of -15°C with agitation.

because of the relatively fast rate of ice growth. However,calcium chloride resulted in the highest ice density and lowest solution temperatures. The ice formed in the methanolsolution was peculiar as the density was highest with thehigher refrigerant temperature, -10°C. In the antifreeze solutions, the ice was easily loosened from the steel coolingsurface. In a system where there is a need to remove the icefrom the cooling surface, this could be a major advantage.The theoretical equations (Eqs. 5 and 6), describing the rateof heat transfer and time required, can be used to predict theperformanceof an ice builder. Correlation with experimentaldata was most sensitive to the thermal conductivity of the ice.

REFERENCES

ASHRAE. 1982. ASHRAE Handbook - 1982 Applications.American Society of Heating, Refrigerating and AirConditioning Engineers Inc., Atlanta, GA.

ASHRAE. 1985. ASHRAE Handbook -1985 Fundamentals.American Society of Heating, Refrigerating and AirConditioning Engineers Inc., Atlanta, GA.

MORISSETTE and SHEPPARD

Carrier Corporation. 1965. Handbook ofAir ConditioningSystem Design. Toronto, ON: McGraw-Hill Book Co.

Dow Chemical Company. 1990. Engineering and OperatingGuide for DOWFROST and DOWFROST HD. DowChemical Company, Midland, MI.

Geankoplis, C.J. 1983. Transport Processes and UnitOperations, 2nd ed. Boston,MA: Allyn and BaconInc.

Gilbertson, T.A. andR.S. Jandu. 1984. 24-Story office towerair-conditioning system employing ice storage - A casehistory. ASHRAE Transactions, AT-84-07,4:387-398.

Lindsay, R.T., M.A. Neale and H.J.M. Messer. 1974. Theperformance of an ice bank cooling system for use invegetable storage. Acta-Horticulturae 38(2):421-442.

Neale, M.A., R.T. Lindsay and H.J.M. Messer. 1981. Anexperimental cold store for vegetables. Journal ofAgriculturalEngineering Research 26(6):529-540.

MacCracken, CD. 1984. Design considerations for modularglycol ice storage systems. ASHRAE Transactions,AT-84-07, 3:374-386.

Perry, R.H. and C.H. Chilton. 1973. Chemical Engineer'sHandbook, 5th ed. New York, NY: McGraw-Hill BookCompany.

Stubblefield, R.R. 1979. Energy efficiency through icestorage. Heating/Piping/Air Conditioning,December:43-47.

Wubben E.A., H.N. Shapiro and R.M. Nelson. 1987.Production and storage of ice for cooling buildings.Journal ofSolar Energy Engineering 111:338-344.

NOMENCLATURE

A = area (m )

Aim = log mean area ofcylinder (m2)E = energy (J)

c = specific heat (J»kg"J •°C"!)Cant = antifreeze concentration (% by weight)Ctejc- constant for calculation of Tl (see Stc) (°C)Fant - factor for antifreeze trapped in ice (obtained from

experimental data)

h =convective heat transfer coefficient (W^irf^C1)Hg = enthalpy of vapour leavingevaporator (J/kg)Hf = enthalpy of liquid enteringevaporator (J/kg)k = thermal conductivity (W^m^C1)L = length of pipe (m)m = mass (kg)

mr = mass flow rate of refrigerant (kg/s)q = heat transfer rate (W)

qenv - heat transfer rate from environment (W)qm - rate of heat added by mixing (W)r ~ radius of cylinder (m)

R = resistance for heat conduction and convection

(°C/W)Stc = slope of freezing temperature curve from graph of

specific gravity vs antifreeze concentration, fora small range at low concentration (°C/%)

t = time (s)

= temperature (°C)= latent heat of freezing for water (J/kg)

3x

T

Uif

p = density of ice(kg/m3)

Subscripts

c = coil (pipe)0 = outside

r = refrigerant1 = inside of pipe wall3 = outside of ice cylinder

i = inside or initial

L = liquid in the tankw = water

2 = outside of pipe wall

CANADIAN AGRICULTURAL ENGINEERING Vol. 35, No. 4 October/November/December 1993 267