Analyses of ice slurry formation using direct contact heat transfer

Applied Energy 86 (2009) 1170–1178

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Analyses of ice slurry formation using direct contact heat transfer M.N.A. Hawlader *, M.A. Wahed Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore

a r t i c l e

i n f o

Article history: Received 22 May 2008 Received in revised form 22 October 2008 Accepted 4 November 2008 Available online 27 December 2008 Keywords: Ice slurry Direct contact heat transfer Ice layer growth Mushy layer growth Droplet diameter Inlet temperature

a b s t r a c t In the present study, ice slurry is produced by direct contact heat transfer between water and a coolant, Fluroinert FC 84. An analytical model has been developed to predict the growth of ice around the injected supercooled coolant droplets, which involves phase change and heat transfer between layers. During the journey of the coolant droplets through the ice generator, detachment of ice layer formed on the droplets occurs. Equations have been development to describe the process of detachment. Experiments were performed to validate the model developed to predict the ice generation. Parametric studies were then carried out on ice growth rate for different variables, such as droplet diameters and initial liquid temperatures. Both droplet diameters and initial liquid temperatures play an important role in the ice formation around the supercooled liquid surface. Ice growth rate increases with the increase of the droplet diameter, while the growth rate decreases with the increase of the initial temperature of the liquid droplet. For an ice slurry system, it is found that the predicted values of ice slurry generation are in good agreement with the experimental findings. Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction In recent years, considerable attentions have been devoted to the development of an ice thermal energy storage system for district cooling purposes in order to save energy and reduce electrical cost, particularly during peak hours in summer [1]. It would be more appropriate to utilize the large latent heat of ice for more efficient cooling purposes rather than the sensible heat of chilled water, which requires larger flow rates and increased pumping power. In an ice storage system, using a heat exchanger for addition and withdrawal of cool energy, the freezing heat transfer performance decreases due to the buildup of ice layers on heat exchanger surfaces during storage of cool energy [2], as the heat transfer through this layer is purely due to diffusion and the thermal conductivity of ice is low. To resolve this problem, a novel thermal energy storage system with ice water slurry has been developed [3,4]. In this system, a direct contact heat transfer between two immiscible liquids has been utilized for ice formation, which provides better utilization of energy than previous systems. Developing a model to understand the physical phenomena of this ice formation would help to identify factors that affect the ice generation process and facilitate design of ice slurry cooling systems. An ice slurry system, which consists of fine ice crystals and liquid water, has a large thermal capacity due to its use of latent heat of fusion. Moreover, cooling capacity of slurry ice is about four to six times higher than that of conventional chilled water system [5]. * Corresponding author. Tel.: +65 6874 2218; fax: +65 6779 1459. E-mail address: [email protected] (M.N.A. Hawlader). 0306-2619/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2008.11.003

Several techniques for ice slurry formation by direct contact heat transfer have been developed recently. Kiatsiriroat et al. [6] conducted study on an ice thermal storage system using an injection of R12 refrigerant into the water to exchange heat directly. Kiatsiriorat et al. [7] also investigated the heat transfer characteristics of a direct contact cool energy storage system using R12 and R22. Refrigerant (R12 or R22) injected at temperature lower than 0 °C takes heat directly from the water in a storage tank and then gets evaporated. Matsumoto et al. [8] studied a new method of forming ice; a water–oil emulsion was cooled with stirring in a vessel and changed into ice–oil and water suspension. They found that ice–oil and water suspension (slush ice), which has a good fluidity, can be formed without adhering to the cooling surface. Chen et al. [9] investigated the nucleation probability of super cooled water inside cylindrical capsules. Song et al. [10] presented a simple model on direct contact heat transfer between two immiscible liquids in a countercurrent spray column. Mori et al. [11] proposed a method for manufacturing crystal ice from polymer gel, PCM (phase change material), where ice is generated in the water absorbing polymer gel by direct heat exchange. Another type of PCM, tetradecane particles, for ice production in a doubletube heat exchanger was proposed by Inaba and Morita [12]. They also proposed a new method for producing ice particles, composed of water and tetradecane, by injecting the tetradecane oil into a cold ethylene glycol water solution [13–15]. Wijeysundera et al. [16] studied the generation of ice slurry using direct contact heat transfer between water and injecting super cooled liquid Fluroinert (FC 84) and estimated the heat transfer co-efficient between liquid droplets and water. The objec-

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Nomenclature surface area of droplet, m2 specific heat, J kg1 K1 drag co-efficient drop diameter, m acceleration due to gravity, m s2 convective heat transfer co-efficient, W m2 K1 thermal conductivity, W m1 K1 thickness of ice layer, m latent heat, J kg1 depth, m mass, kg temperature, °C time, s velocity of liquid droplet, m s1

tive of the present study is to provide a better understanding of the physical phenomena of ice and mushy layers growth around a super cooled liquid droplet and investigate the effects of different parameters on the growth rate of these layers. To achieve the desired goal, a mathematical model has been developed and experiments were performed under different conditions to validate the model. 2. Analytical model: ice formation The model described in the following sections incorporates the physical phenomena of ice slurry formation process. The liquid coolant (much below 0 °C), having the properties of immiscibility and higher density than water, is injected into a body of water to produce ice slurry. A nozzle is used to deliver the coolant (in the form of droplets) to the surface of ice slurry generator. As it travels through the water, due to the temperature difference between the two fluids, the coolant droplets act as a heat sink and absorb heat from water. Once the water temperature reaches 0 °C, subsequent cooling leads to a phase change and ice is generated around the coolant droplets. During the journey of droplets through water, ice layer formed on the surface of droplets will be detached due to different forces acting on it and travel to the top of the tank leading to the formation of ice slurry. The initial cooling of water to 0 °C has been adequately dealt with by Wijeysundera et al. [16]. In this analysis, attention has been focused on the formation of ice layer, its growth and the detachment of layer from the surface of the droplets. 2.1. Conception of mushy layer For the analysis of the phase change energy storage system [17,18], the mushy layer concept has already been investigated. According to these analyses, mushy layer is the physical state between solid and liquid states in which the liquid fraction varies from zero to unity; in other words, this mushy layer can be portrayed as a pseudo porous media in which the porosity varies from unity to zero, as the layer solidifies. In the current analysis, the mushy layer concept has been introduced for the phase change process of liquid water into ice. Fig. 1 shows water temperature profile in ice slurry generator, when the coolant, FC 84, with initial Td = 10 °C and velocity, V = 0.15 m/s was passed through the tank. During the experiment, it was observed that the ice generation started when the water temperature was in the range of 0.5 °C to 1.5 °C. This layer is likely to be confined to laminar sub-layer, where the fluid movement is negligible. Once the first layer of ice was

Greek symbols d mushy layer thickness, m k time constant, s1 q density, kg m3 Subscripts d droplet m mushy layer i ice layer f ice/mushy layer interface w water

1.5

Water Temperature, C

A C CD D g h k l LF l m T t V

Ice generation

1 0.5 0 130 -0.5

150

170

190

210

230

250

-1 -1.5

Time, sec Fig. 1. Water temperature in the ice slurry generator.

formed, it would grow slowly depending on the cooling available at the interface. As time elapsed, the water temperature increased to 1 °C, which was below the freezing temperature of water. As found in the case of freezing and melting of phase change materials used for the purpose of energy storage [18], there exist a mushy layer region between the ice layer and the surrounding water at 0 °C, and the temperature of this mushy layer would vary between ice surface temperature and water temperature. As the temperature of this region is below the freezing point, it is assumed that ice nucleation may start from this region, rejecting the latent heat of fusion. Hence, the temperature of this region would increase, as shown in Fig. 1. This means that mushy layer is a mixture of very fine ice particles and water, and the temperature distribution across this layer would affect the ice generation around the coolant droplets. 2.2. Mathematical analyses In this section, a mathematical model is presented to predict the ice generation phenomena. The analytical procedure follows the heat transfer from the surrounding water through the mushy layer and the ice layer to the liquid droplet. Since the coolant droplet propagates through the water at 0 °C, the model also includes the analysis of the droplet propagation and the subsequent effect of the forces acting on the moving droplet in the water leading to the detachment of ice from the surface of the droplets. The analytical model, therefore, represents a more realistic approach to predict the ice layer growth around the coolant droplets and its detachment. Fig. 2a shows the physical phenomena of ice formation around a coolant droplet, when the surrounding water is at 0 °C. For analysis,

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a

Liquid droplet

b Water Mushy layer Ice Layer

y

Liquid droplet

Water dy

c

dqyi

Td

Ti

Tm

L

δ

T

y=0 Fig. 2. (a) Physical ice formation. (b) Schematic of liquid droplet ice–mushy–water layers. (c) Cross-section of ice–mushy–water layers.

a single liquid droplet is considered, as shown in Fig. 2b. Since, the droplet is very small, a small cross-section of the coolant droplet, Fig. 2c, is considered for applying the governing equations and relative boundary conditions for the analysis. In the present model, it is considered that the growth process of ice layer and mushy layer around the impinging coolant droplets occurs in two distinct stages: I. at the first stage, water comes in contact with the super cooled liquid droplets and freezes instantaneously; II. at the second stage, both ice and mushy layer develop simultaneously.

2.2.1. Initial ice layer formation At initial stage (t = 0), the supercooled liquid droplet is injected into the water maintained at bulk temperature of 0 °C or less. The moment the droplet comes in contact with water in the immediate neighbourhood of the droplet surface, the water molecules will attach to the surface. This thin layer of water molecules would experience predominated laminar shear stresses. Due to the latent heat of fusion, this laminar sub-layer of water molecules would change the phase into the ice layer, as shown in Fig. 3. Thickness of this initial ice layer can be derived from the laminar sub-layer equation [19]

L5

mw V

ð1Þ

where V* is the expression for velocity in terms of the properties of the water

V ¼

rffiffiffiffiffiffiffi

sw qw

ð1:aÞ

Water bulk Temperature, Tw =0˚C

t Td

Initial ice layer

Fig. 3. Schematic diagram of initial ice formation process during an infinitesimal duration.

Here, sw is the shear stress which is expressed as

sw ¼ 0:03325qw V 7=4 v w1=4 R1=4

ð1:bÞ

2.2.2. Development of ice and mushy layers Here, the diffusive heat transfer equations are described for the simultaneous growth of ice and mushy layers. In the ice layer region, the heat diffusion equation is

qi C i

oT i ¼ qy i  qyþdy i ot

where qy i and qyþdy i are incoming and outgoing heat of ice layer, respectively. After simplification, the equation reduces to

qi C i

  oT i o oT i ki ¼ oy ot oy

ð2Þ

where k, q, C are the thermal conductivity, density and specific heat, subscript i denotes ice layer.

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Under steady sate condition, subject to boundary conditions of Ti(0) = Td at y = 0, t > 0 and Ti(L) = Tf at y = L, t > 0, the solution of Eq. (2) becomes

T i ðy; tÞ ¼

  Tf  Td y þ Td L

ð3Þ d¼

During the ice formation, the heat conducted through the ice layer into the liquid droplet. Equating the energy balance

 dT d dT  md C d ¼ ki A  dy y¼0 dt

kt

ð4Þ 6ki qd C d D.

where Tdi = initial droplet temperature and constant, k ¼ Again, the interface temperature, Tf can be deduced from the Stefan condition [20], the change of the moving ice/mushy layers interfaces, L(t), is proportional to the heat flux across it

ð5Þ

To calculate L(t), solving the equation, Eq. (5) gives

dL u0 u1 ¼  dt L d þ khm

ð6Þ

km ðT w T f Þ f T d Þ where u0 ¼ ki ðT qi HFS ; u1 ¼ qi HFS . First term on the right hand side of Eq. (6) represents the heat conduction through the ice. This indicates that the ice growth rate decreases with the increase of the temperature of the liquid droplet and the increase of the ice layer thickness. The second term on the right hand side is proportional to u1 which incorporates the mushy layer. For mushy layer, the heat diffusion equation can be written as

qm C m

oT m ¼ ðqy m  qyþdy m Þ  qL ot

where qy m , qyþdy m and qL are incoming, outgoing heat and latent heat of mushy layer, respectively. Here, the concentration of ice nuclei would be comparatively lower than the ice–mushy layer interface region, where the presence of embryo [21] (cluster like water molecules) is relatively high. As these are very fine ice particles (nucleated ice), the latent heat contribution in the mushy layer is likely to be small and it is neglected in this analysis. However, it has been taken into account in the interface of ice–mushy layer region, as described in Eq. (5). Then, rearranging and simplifying the heat diffusion equation in the form as

oT m km o2 T m ¼ ot qm C m oy2

ð10Þ

To calculate the heat transfer co-efficient, Whitaker [22] proposed a co-relation for flow past a sphere in the form 1

T d ¼ T f þ ðT di  T f Þe L

  dL dT i  dT m  ¼ ki   km dt dy y¼L dy y¼L

km T m  T f  h Tw  Tm

2

Nu ¼ 2 þ ð0:4Re2 þ 0:06Re3 ÞPr0:4

where RHS is heat conducted through the ice layer and LHS is the change of liquid droplet energy. After simplifying and integrating, the liquid droplet profile can be deduced from the relation as

qi HFS

This represents a quasi-steady temperature profile of the mushy layer, whereby the mushy layer temperature profile varies with time since the growth of both ice layer, LðtÞ and mushy layer, dðtÞ are time dependent.To calculate d(t), solving Eq. (9) gives

where 3:5  Re  7:6  10

2.3. Detachment of ice layer When the coolant droplets were injected into the water column and it was observed that ice accumulated at the top of the ice slurry generating tank, as shown in Fig. 4. The ice generated around the downward moving coolant droplets is detached due to the resultant forces acting on the descending droplet and moved upwards due to the density differences. It is assumed that a spherical liquid droplet enters into the fluid medium (water) with a velocity V. Then, there are three distinct forces acting on the droplet. As shown in Fig. 5, the forces acting on the droplet are (i) Body force, FW (ii) Drag force, FD (iii) Buoyant force, FB. Then, applying Newton’s second law and considering the downward force be positive, Change of momentum = Body force – Buoyant force – Drag force

M

dV ¼ Mg  Mw g  0:5C D qw AV 2 dt

dV ¼ dt

  Mw 0:5C D qw ðpR2 ÞV 2 1 g M M

ð7Þ

(i) T m ðLÞ ¼ T f aty ¼ L, and (ii) at the mushy/water layer interface, y = L + d,

dT m j dy y¼Lþd

ð8Þ

gives

Tm ¼ Tf þ

ðT w  T f Þ ðy  LÞ ðd þ khm Þ

ð12Þ

where M = Mass of ice + Mass of liquid droplet = p6 ½fðD þ 2LÞ3  D3 g qi þ D3 qd  Mw = Mass of displacement water = p6 ðD þ 2LÞ3 qw where q; C D ; A are the density, drag co-efficient, area of the liquid sphere and the subscript i, d, w denote ice, coolant droplet and the fluid medium(water), respectively. For 1 < Re < 2  105 , the value of C D varies in the range of 0.4– 0.5 [23,24]. Here, the value of C D is considered to be 0.45. Rearranging Eq. (12), we get

The solution of equation under steady state conditions with the boundary conditions

hðT w  T m jy¼Lþd Þ ¼ km

ð11Þ

4

ð9Þ Fig. 4. Ice particles accumulated over ice slurry generator.

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FD

composed of the buoyant force, drag force and gravitational force. When these forces exceed the cohesion tension force, the ice layer would be detached from the liquid droplet and move upwards due to the buoyancy effect.

FB

3. Experimental studies

FW

Moving downwards Fig. 5. Forces on a descending liquid droplet in a fluid medium.

where, R is radius of the droplet. After rearrangement

dV ¼ P2 V 2 þ Q 2 dt or

dV þ P2 V 2 ¼ Q 2 dt

ð13Þ

where

P¼

p C D qw R2 2

!12

M

;

Q¼

  12 Mw 1 g M

The differential Eq. (13) can be solved by the technique of separation of variables, leading to the following solution, with the initial condition, V = Vi at t = 0.

VðtÞ ¼

  Q S1 P Sþ1

ð14Þ

i where S ¼ QQ þPV Expð2PQtÞ. PV i The necessary condition for the ice removal is given by

F T  ðF B  F G þ F D Þ 0

ð15Þ

where F T is the cohesion force between the liquid droplet and the ice layer. In the present analysis, it is assumed that the cohesion force between these two layers remain same, though the change of this force with the change of the temperature was negligibly small. As the coolant droplets are injected into the water, the ice layer grows around the liquid droplet and continues to grow as long as the surface tension of the droplet overcomes the resultant forces

Experiments were conducted to provide a better understanding of the mechanism of ice slurry formation and the results were compared with the predicted values. A schematic diagram of the experimental test-rig for the visualization of ice formation is shown in Fig. 6. The main components of the experimental test-rig are the test section, metallic balls, a cold bath, a high speed digital CCD camera and an adjustable camera stand. Visualization of ice generation around the liquid droplet surface was a difficult task due to the formation of large number of droplets when the coolant was delivered into the ice slurry generator. As a result, it was hard to track the phenomena of ice formation on a single droplet surface. For this reason in this present study, a metallic ball made of steel was used to simulate the ice formation phenomena on its surface, where both steel ball and liquid droplet of FC 84, have similar properties of higher density and immiscibility characteristics. The test section, made of transparent polyvinyl acrylic resin was filled with water and maintained the desired temperature using a cold bath. A built-in pump (max. flow rate 20 l/min) inside the cold bath added the sufficient pressure to the water to circulate between the cold bath and the test section. The metal ball suspended at the top of the section moved slowly towards the bottom of the test section. This ball was pre-cooled to sub-zero temperatures. As a result, when the super cooled metal ball propagated through the chilled water at 0 °C, ice was formed on the surface. The digital CCD camera together with the optical zoom system mounted on the adjustable stand tracked the ball to visualize the ice formation on the ball surface. The mean diameter of the spherical ball was 50 mm. The liquid droplets were, generally, smaller in size. The reasons of choosing larger shaped spherical ball were for clear visualization of the freezing phenomena of water as well as for measuring the thickness of ice layer. The physical properties of this spherical ball are indicated in Table 1. As observed from Fig. 7, ice generation on the ball surface was captured for different durations with higher optical zoom, 3.5. During this experiment, the thickness of the mushy layer could

Ice particle y=0.47m

Cold Bath Image Processing

Simulating ball Insulator Camera System Water Fig. 6. Schematic diagram of experimental apparatus.

M.N.A. Hawlader, M.A. Wahed / Applied Energy 86 (2009) 1170–1178 Table 1 Physical properties of the materials.

3

Density (kg m ) Specific heat (kJ kg1 K1) Thermal conductivity (W m1 K1)

Liquid, FC 84

Steel ball

1730 1.05 0.06

7840 0.47 59

1175

the coolant droplet. The physical properties associated with ice formation, caused by the vertically falling supercooled liquid droplets are given in Table 2. In the following analysis, two parameters are considered: the droplet diameter, D and the coolant droplet temperature, Td during injection. 4.1. Comparison of ice formations

not be measured. It would be very difficult to figure out this layer due to very thin section of very fine ice particles and water below 0 °C. However, in the experiment, very fine ice particles were observed which propagated around the growing ice layer. Measurement of the ice thicknesses from the captured photographs was the most important phenomena for the experimental results analyses. An image analyzing software (Windows OS), Image-Pro Plus 6.0, was used to acquire data and to analyze the images. To reduce the uncertainties of measurements, calibrated scale was used. Also, mean values were considered for each image analysis. 4. Results and discussion As stated earlier, ice formation on the supercooled liquid surface was captured with a digital camera, as shown in Fig. 7. These results were then analyzed to validate the mathematical model developed to predict the growth rate of ice generation around

As observed from Fig. 7, a series of photographs show the growth of ice generation around the supercooled surface for a period of time, where the surface temperature is at about 10 °C and the water temperature is at about 1 °C. At the initial stage, ice nucleates around the supercooled surface and form a very thin layer of ice and after that, there is a sharp growth of ice layer which continues for next few seconds. Finally, no noticeable change in the ice layer thickness. Experimentally measured ice growth rate is compared with the predicted results. In this context, instead of liquid droplet, the iron ball properties are considered while other phenomena remain same. Fig. 8 shows the comparative results of the ice formation between the prediction and the experimental observation. From this analysis, it is observed that the simulation results are in the range of the experimental values and the deviation of the simulating values from those of experimental is less than 3%. Based on these analyses, ice generation on the supercooled liquid (FC 84) droplet is predicted.

Fig. 7. Ice formation phenomena (D = 50 mm, Td = 10 °C, iron ball).

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Table 2 Parameter values used for Figs. 9–12. CD ki km

J kg1 K1 W m1 K1 W m1 K1 kg m3 kg m3 kg m3 J kg1 °C

1050 2.18 0.52 1730 917 1000 3.344  105 0

qd qi qm LF Tw

Ice layer thickness, mm

2.5

2 1.5

1 0.5

Theoretical Experimental

0 1

0

2

3

4

5

6

7

Time, sec Fig. 8. Comparison of the formation of ice layers.

This indicates that the relative effect of the ice growth rate decreases with the increase of the droplet diameters. With the increase of droplet diameter, ice layer thickness increases. But, ice acts as insulator, which will prevent the heat flow from the surroundings to the droplet with more ice thickness. This explains the relative decreasing of ice layer growth rate for increasing droplet size. According to the assumption, as stated in Eq. (7), mushy layer would develop around the ice layer. This layer consists of very fine ice particles and water with temperature between surrounding water and ice layer temperatures. The rate of mushy layer growth for different droplet diameters is shown in Fig. 10. It shows an increasing layer growth around ice. As observed from the Fig. 10, mushy layer growth rate is found significantly same as the ice layer growth rate at initial stage. Due to the higher ice generation rate during initial stage, more latent heat would be rejected in this mushy layer which may cause the higher growth rate of this layer as well. After this initial expansion, the mushy layer grows steadily at a constant rate. One of the possible reasons is the expansion characteristics of ice which pushes the mushy layer. Another possible reason is that ice layer may act as an insulating layer which may cause the reduction of heat flow from the surroundings to the droplets and this heat is trapped in the mushy layer region, existing between the ice layer and the surrounding water. 4.3. Effect of initial liquid temperature

4.2. Effect of droplet diameter In this experiment, effect of the droplet diameters on ice and mushy layers growth over a period of time were analyzed for the same initial conditions: droplet temperature, Td = 10 °C and flow rate V = 0.15 m/s. Fig. 9 shows the growth of ice layers up to the residence time for various droplet diameters: 4 mm, 7 mm and 10 mm. It showed that the ice layer thickness increases with the increase of droplet diameters. The initial growth rate of ice layer is very rapid for the first 0.5 second irrespective of the droplet diameters, after that there are differences in the degree of growth rate for different diameters. In case of 4 mm droplet, this growth rate is about 0.12 mm/s while 0.17 mm/s for 10 mm droplet; the ice growth rate around the liquid droplets increases with the increase of the droplet diameters. Initially, heat from the surroundings is conducted to the droplet surfaces, independent of droplet volume. For this reason, irrespective of droplet diameters, ice growth rate is similar for a while. Then, heat conduction to the liquid droplets as heat sinks depends on the droplets volumes. This may explain the reason for increasing both ice thickness and growth rate with respect to droplet diameters.

In this section, the effects of ice layer and mushy layer growth for liquid droplets injecting at different temperatures from 10 °C to 30 °C are shown. Liquid droplet diameter, D = 10 mm and injecting velocity, V = 0.15 m/s are kept constant for all those cases. As observed from Fig. 11, growth rate of ice around the droplet surface injecting at lower temperature is faster. Growth rate is maximum 0.60 mm/s for droplet initial temperature 30 °C while minimum 0.17 mm/s for 10 °C. This result suggests that more ice grows with the decrease of injecting temperature which is analogous to the Eqs. (6)–(11) stating that the ice growth rate increases with decreasing the temperature of the liquid droplet. It is also observed Fig. 11 that more ice generates with a faster growth rate if the initial liquid droplet temperature is lowered. From the result, it is found that the ice thickness is as high as 3.9 mm when the liquid temperature is at 30 °C. As a result, in an ice generator, more ice with faster rate can be accomplished by lowering the liquid temperature. However, a lot of cooling energy is required to decrease the liquid temperature to such a level, which may not be economically viable. As shown in Fig. 12, the mushy layer is very thin, in micrometer range, as compared to the thickness of the ice layer, which is millimeter range. Also, it is observed that there is a proportional rela-

1.8

1.4

mushy layer, mm

Ice layer, mm

1.6

1.2 1 0.8 0.6 Dd =10mm

0.4

Dd = 7 mm

0.2

Dd = 4 mm

0 0

1

2

3

4

5

6

7

8

Time, sec Fig. 9. Ice layer growth for different drop diameter, Dd.

9

10

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

Dd =10 mm Dd = 7 mm Dd = 4 mm

0

1

2

3

4

5

6

7

8

Time, sec Fig. 10. Mushy layer growth for different drop diameter, Dd.

9

10

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4.5

4

4

3.5 3

Ice mass, kg

Ice layer, mm

3.5 3 2.5 2 1.5 1

Td =-30 ºC

2

Exp. 1

1.5

Exp. 2

1

Exp. 3 Exp. 4

0.5

Td = -20 ºC

0.5

2.5

Estimated

0

Td = -10 ºC

2

0 0

1

2

3

4

5

6

7

8

9

4

6

8

10

12

Coolant flow rate, lit/min

10

Time, sec Fig. 13. Ice formation of the ice slurry system (mass of water = 10 kg, nozzle diameter = 6 mm, duration of ice formation = 30 min).

Fig. 11. Ice layer growth for different drop temperature, Td.

parative results illustrate that the model for ice formation can be utilized for the analysis of heat transfer between two immiscible liquids.

1

mushy layer, mm

0.9 0.8

5. Conclusion

0.7 0.6 0.5 0.4 0.3 0.2

Td =-30 ºC

0.1

Td = -20 ºC

0

Td = -10 ºC

0

1

2

3

4

5

6

7

8

9

10

Time, sec Fig. 12. Mushy layer growth for different drop temperature, Td.

tionship between mushy layer growth rate and the liquid droplet temperature. With decreasing the inlet temperature from 10 °C to 30 °C, the mushy layer growth rate increases to about 44% whereas ice growth rate increased by about 71%. This may indicate that the change of the mushy layer thickness is not significant compare to the ice layer thickness when the liquid droplet temperature is lowered considerably. Also, from both Figs. 11 and 12, it is observed that the residence time and duration of ice generation are reduced as the liquid droplet temperatures are lowered. As the temperature of the liquid droplet decreases, more ice is generated at the droplet surface which may increases the drag force as well as the buoyant force of the downward moving droplet. This may affect the total force balance and ice is detached earlier from the droplet surface. 4.4. Ice formation From the above model, ice formation is estimated for the ice slurry system from an equation described by Wijeysundera et al. [16]. Fig. 13 shows the comparative values of ice mass obtained from analyses and experiments. It shows that, for both cases, the amount of ice formation increases with the increase of the coolant flow rate from 4 l/min to 10 l/min in the ice slurry system. It is also observed that the estimated values of ice formation are higher than the experimental results. In the model, it is assumed that ice forms uniformly around the droplet surface, while in practice ice may not be formed consistently due to the drag force and the buoyancy force acted on the descending liquid droplet. Furthermore, some droplets may coalesce to each other which could affect the ice formation on the droplet surface. However, the com-

In an attempt to develop a novel ice slurry generator for district cooling purposes, experiments and analyses has been performed to provide a better understanding of ice formation, growth and detachment from the droplets producing ice slurry. A mathematical model has been developed to analyze the growth of ice on coolant droplets, where the concept of a mushy layer has also been introduced. In order to validate the results, a series of experiments were conducted and the results were compared with the predicted values. The growth of ice layer obtained from the experiments shows good agreement with analyses. Once the simulation program is validated, a parametric study has been conducted to study the influence of droplet diameter and temperature. An increase of droplet diameter leads to an increase in ice growth rate. Similarly, as the initial temperature of the droplet is decreased, an increase in the growth rate is observed. Comparative analyses between the estimated and the experimental results reveal that the model can describe the ice and mushy layers growth, and also the production of ice slurry. This model, therefore, gives a better insight and provides useful information to understand the physical phenomena of ice slurry formation by direct contact of two immiscible liquids. This would facilitate the development of improved design and operational guidelines for the implementations of ice slurry cooling system. References [1] Grumman DJ, Butkus AS. The ice storage option. ASHRAE J 1998;1:29–33. [2] Braddy TW. Achieving energy conservation with ice-based thermal storage. ASHRAE Transfer 1994;100:1735–45. [3] Morikawa H, Miyawaki M, Fujimoto T, Aizawa J. Studies on Application of dynamic ice for district cooling (Part 1. Slurry ice transport system). In: Proceedings of JSME conference, Japan, 1993. p. 930–63. [4] Snoek CW. Ice-slurry based district cooling systems. In: Proceeding of European institute of environmental energy district cooling workshop, Herming, Denmark, 1994. p. 1–12. [5] Ure Z, Mashrae M. Slurry ice based cooling systems. In: Proceedings of IIR 20th international conference, Sydney, Australia, 1999 [paper no. 3]. [6] Kiatsiriroat T, Sirplubpla P, Nuntaphan A. Performance analysis of refrigeration cycle using a direct contact evaporator. Int J Energy Res 1998;22:1179–90. [7] Kiatsiriroat T, Vithayasai S, Vorayos N, Nuntaphan A, Vorayos N. Heat Transfer prediction for direct contact ice thermal energy storage. Energy Convers Manage 2003;44:497–508. [8] Matsumoto K, Okada M, Kawagoe T, Kang C. Ice storage system with water–oil mixture formation of suspension with high IPF. Int J Refrig 2003;23:336–44. [9] Chen SL, Wang PP, Lee TS. An experimental investigation of nucleation probability of supercooled water inside cylindrical capsules. Exp Therm Fluid Sci 1999;18:299–306.

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