*2.1.1 Falling film phenomena*

Falling film can be either on vertical flat plate or horizontal tubes to maximize the heat transfer coefficient. Three main modes were shown when the liquid drop from any tube. It can take a shape of droplet, jet or sheet depending on the flow rate as shown in **Figure 7**. Combined modes usually took place. By increasing the flow rate, the mode changes to droplet-jet, jet, jet- sheet and finally sheet mode. Multimodes can be appeared at the same time for the same flow rate, depending on the number of tubes aligned vertically. More secription of the flow pattern for the falling film can be found in [24–27]. For the purpose of freezing for the CTS, several articles talked about the possibility of utilizing the advantages of high heat transfer coefficient to be used for freezing.

For the maximum falling film flow, the sheet mode took place. This mode is shown clearly in the upper two test tubes, the rest shows sheet-jet mode. Some of the falling film splashed from the down tubes. By reducing the flow rate, jet mode is achieved and it is observed clearly on the upper tubes and the rest is a jet-droplet mode. A small amount of the falling film splashed from the down tubes. With further decrease in the flow rate, a steady droplet mode all over the test tubes was noticed with no splash from the tubes.

#### **Figure 7.**

*Idealized innertubes falling film modes: (a) sheet mode, (b) mixed of sheet and jet, (c) jet mode, (d) droplet-jet mode, (e) droplet mode, (f) sheet mode [24].*

### **2.2 Ice formation characteristics**

The formation of ice begins usually where the inlet coolant exists due to the lowest temperature there. The regularity of ice depends on the types of stream that moves on the tubes. It is obvious that the formation of ice increases with time. However, the ice formation reduces heat transfer due to an increase in the insulation of ice (increased thickness of ice causes an increase in thermal resistance and consequently reduction of heat transfer through ice layer). It has been observed that as the ice accumulates on the test tubes, it takes longer time to remove it from the test tubes by the discharge cycle and relatively large quantity of ice is melted.

Ice accumulates circumferentially on the tube surfaces until the tube spacing is filled with ice which makes it harder in discharging process (**Figure 8**).

#### **2.3 Heat transfer analysis for freezing**

Heat transfer assessment on tubes bundle is based on detecting of temperature change, temperature of the liquid flowing through the tube bundle and temperature of outside liquid with simultaneous measuring of the current flow of liquids. This way, the real value of the heat transfer is determined at the tube bundle working under the set conditions. And subsequently, the corresponding heat transfer coefficient can be determined. Series arrangement has the advantage of high flow rate inside the tube and consequently high Reynolds number and high inside heat transfer coefficient. However, it difficult to be designed and maintain. In contrast, parallel arrangement is more convenient for industry, but reduces the inside heat transfer coefficient due to the inside flow is divided in to the all tubes and hence reducing the Reynolds number and so the inside heat transfer coefficient.

For the CTS, the heat transferred from the outside liquid to the entire coolant. The amount of heat transferred is determined from the temperature difference and the corresponding fluid flow rate. When solidification is taken place, the outside liquid loss sensible heat to reach the freezing point and then latent heat, to form ice. The rest of the outside liquid cools down while it is contacting the outside of the cold tubes.

The heat transfers from the outside liquid to the inside coolant via ice layer and the tube wall as shown in **Figure 9**. The thermal conductivity of the tube wall is usually very high comparing to the ice layer, so the tube resistance is usually ignored.

**Figure 8.** *Ice photo on the formed ice on the tube at time of (a) 50, (b) 198 minutes.*

*Solidification and Melting of Phase Change Material in Cold Thermal Storage Systems DOI: http://dx.doi.org/10.5772/intechopen.96674*

**Figure 9.** *Thermal resistance for ice accumulates on the tubes [28].*

The rate of heat transfer from the outside fluid to the coolant inside the tube can be calculated as:

$$\dot{Q}\_{ins} = \frac{(T\_{\infty,o} - T\_{ave,i})}{R\_o + R\_{ice} + R\_i} \tag{4}$$

For thermal resistance shown in Fig., then

$$\dot{Q}\_{o-i} = \frac{(T\_{\infty,\rho} - T\_{\text{ave},i})}{\frac{1}{h\_o 2\pi r\_{\text{var}}l} + ln} \tag{5}$$

### *2.3.1 Heat transfer coefficient inside the tube hi*

The inside heat transfer coefficient is given by:

$$h\_i = \text{Nu}K/D \tag{6}$$

#### **Where:**

In order to get *Nu, Re* must be calculated and is given by, R ¼ *ρumDh=μ*,where the velocity of the coolant at the test tube, *um* = *m*´ *<sup>c</sup>=ρAi* and, *m*´ *<sup>c</sup>* is mass flow rate of the coolant which enters to the test section.

For constant surface temperature condition, and laminar flow, Re ≤ 2300, Nusselt number is given by many researchers. One is given by Incropera, F.P. et al., as:

$$Nu = 1.86 \left[ \frac{RePr}{l/D} \right]^{1/3} + \left[ \frac{\mu}{\mu\_s} \right]^{0.14} \tag{7}$$

Where this equation can be applied for the following condition**:** *Ts* (surface temperature) = constant.

$$0.48 < \text{Pr} < 16,700.$$

$$0.0044 < (\mu/\mu\_s) < 9.75.$$

And for turbulent flow, where Re ≥ 10,000, Nusselt number can be calculated by

$$Nu = 0.023 \Re^{0.8} Pr^{0.3} \tag{8}$$

Where the ranges are.

$$0.7 \le \text{Pr} \le 160.$$

$$l/D \ge 10.$$

All properties except *μ<sup>s</sup>* should be evaluated at the average value of the inlet and outlet temperature, *Tave* ¼ ð Þ *Ti* þ *To =*2.

#### *2.3.2 Outside heat transfer coefficient*

[29, 30], developed correlations to approximate the heat transfer coefficient for the outside flow (falling film), As follows:

For high Re, (sheet mode):

$$Nu = 2.194 \Re\_f^{0.28} Pr^{0.14} Ar^{-0.2} \left(\frac{s}{d}\right)^{0.07} \tag{9}$$

For medium Re, (jet mode):

$$Nu = \mathbf{1.378} \mathbf{R}\_f^{0.42} Pr^{0.26} Ar^{-0.23} \left(\frac{s}{d}\right)^{0.08} \tag{10}$$

For low Re, (droplet mode):

$$Nu = 0.113 \Re\_f^{0.85} Pr^{0.85} Ar^{-0.27} \left(\frac{s}{d}\right)^{0.04} \tag{11}$$

The liquid properties were evaluated at film temperature *Tf*. Where.

*Nu* is modified Nusselt number *<sup>ν</sup>*<sup>2</sup> *g* <sup>1</sup>*=*<sup>3</sup> *h=k: Ref* is film Reynolds number 2*Γ=μ* Pr

 $Pr$  is Prandtl number  $C\_p\mu/k$  (1.20)

*Ar* Archimedes number based on tube diameter *d*<sup>3</sup> *g=ν*<sup>2</sup>

Eq. 4 estimate the instantaneous heat transfer ac certain time for specific ice radius. For the whole experiment run for specific time, we need to get the total heat absorbed from the outside fluid. The outside fluid is either at stationary state or moving across the tube. For the first case if the outside liquid at constant condition

$$\dot{Q}\_{s,l,\varepsilon} = \frac{m\_l}{t} \mathbf{C}\_{p,l} \left( T\_{li} - T\_{lf} \right) \tag{12}$$

Where *Tli* and *Tlf* are the initial and final temperature of the outside liquid respectively.

For the second case where the outside fluid is moving across the tubes, the sensible transfer heat rate is calculated by

$$
\dot{Q}\_{s,l,m} = \dot{m}\_l C\_{p,l} (T\_{li} - T\_{lo}) \tag{13}
$$

Where *Tli* and *Tlo* are inlet and exit temperature of the outside liquid.

Part of the outside liquid freezes on the outside tube. The freezing consumes latent heat which can be calculated as:

$$
\dot{Q}\_{\hat{fr}} = \frac{M\_{i\varepsilon}L}{frozenttime} \tag{14}
$$

Where L is the latent heat of fusion for the PCM.

*Solidification and Melting of Phase Change Material in Cold Thermal Storage Systems DOI: http://dx.doi.org/10.5772/intechopen.96674*

The formed ice is now cooled to a temperature below the freezing temperature which is consider as sensible heat and is given by

$$\dot{Q}\_{s,s} = \mathbf{M}\_{ice} \mathbf{C}\_{p,ice} \left( T\_f - T\_c \right) / \text{time} \tag{15}$$

Hence the total heat transfer through the ice layer can be computed as:

$$
\dot{Q}\_{O-i} = \dot{Q}\_{s,l} + \dot{Q}\_{\hat{r}} + \dot{Q}\_{s,r} \tag{16}
$$

The total heat transfer absorbed by the coolant can be given by:

$$
\dot{Q}\_{c,act} = \dot{m}\_c \mathbf{C}\_{pc} (T\_{co} - T\_{ci}) \tag{17}
$$

where the coolant flow rate *m*´ *<sup>c</sup>* (kg/s), and *Tci*∧*Tco* are its inlet and outlet temperature.

The average rate of heat transfer from the test tubes to the coolant at a specific time, *Q*´ *<sup>c</sup>*,*ave* is calculated by the following equation:

$$
\dot{\mathbf{Q}}\_{c,ave} = \left[ \int\_{t=0}^{t=n} \dot{\mathbf{Q}}\_c \, dt \right] / time \tag{18}
$$

where:

t: is the interval time in minutes

n: is the indicated time

This integration can be obtained by the trapezoidal rule of integration:

$$\int\_{a}^{b} f(\mathbf{x})d\mathbf{x} = \frac{b-a}{2n} \left[ f(\mathbf{x}\_{0}) + \mathfrak{Y}(\mathbf{x}\_{1}) + \mathfrak{Y}(\mathbf{x}\_{2}) + \dots + \mathfrak{Y}(\mathbf{x}\_{n-1}) + f(\mathbf{x}\_{n}) \right] \tag{19}$$

By substituting the *h*<sup>i</sup> and *h*<sup>o</sup> in Eq. 10 to get the overall heat transfer coefficient and then substitute in Eq. 9 to get the calculated rate of heat transfer from the test tubes to the coolant at a specific ice thickness, *Q*´ *<sup>c</sup>*,*cal* which needs to be compared with the total heat transfer to the coolant *Q*´ *<sup>c</sup>*,*act* which was given from Eq. 6.

The experimental overall heat transfer coefficient, *h*ov is determined using the equation

$$h\_{ov} = \frac{\not{Q}\_{\rho - i}}{A\_{icc} \Delta T\_{lm}} \tag{20}$$

where, *Aice* is the heat transfer area and Δ*Tlm* is the logarithmic temperature difference between the working fluid flows. The ice layer affects the heat transfer coefficient since the thermal conductivity of the ice is low and as its thickness increases the thermal resistance increases which lead to lower heat transfer coefficient.

#### **2.4 Affecting parameters on freezing**

Ice freezing quantity is affected by the outside flow rate (mode of the falling film) and its temperature, as well as by coolant flow rate and coolant temperature (**Table 3**).

#### *2.4.1 Effects of the falling film behavior on ice accumulation*

In the beginning of the freezing process high heat transfer coefficient was shown which reaches to 1000 W/m<sup>2</sup> .K, which shows the influence of the failing film.


#### **Table 3.**

*Effects of different parameters on the performance of cold thermal storage.*

**Figure 10.**

*The effect of ice accumulation with time on the rate of freezing.*

However, by the further accumulation of ice, the heat transfer coefficient drops as of the effect of low thermal conductivity of ice. To get the best advantages of the falling film an optimum design must be applied to have quick charging and discharging operations so, more ice can be formed in short time and then collect it at the bottom of the reservoir. The falling film quantity must be adequate and the flow rate must handle the drag force of the tubes.

#### *2.4.2 Falling film backsplash*

While the falling film falls over the tubes vertically, some quantity leaves the falling film stream and falls outside the stream and drops to the bottom of the reservoir without further collision with the rest of the tubes. This phenomenon is *Solidification and Melting of Phase Change Material in Cold Thermal Storage Systems DOI: http://dx.doi.org/10.5772/intechopen.96674*

**Figure 11.** *Comparison of the formed ice for different coolant flow rate.*

**Figure 12.** *Comparison of the formed for different falling film flow rate.*

**Figure 13.** *Effect of variation of cooling temperature on freezing, [17].*

#### **Figure 14.**

*Comparison of the formed ice between series and parallel arrangements for m*´ *<sup>c</sup> =0.162 kg/s & m*´ *<sup>l</sup> =0.025 kg/s.*

**Figure 15.** *Comparing of ice quantity for tube with fin and finless tube, [17].*

#### **Figure 16.**

*Comparison of the experimental overall heat transfer coefficient between series and parallel arrangements for m*´ *<sup>c</sup> = 0.162 kg/s & m*´ *<sup>l</sup> =0.025 kg/s.*

*Solidification and Melting of Phase Change Material in Cold Thermal Storage Systems DOI: http://dx.doi.org/10.5772/intechopen.96674*

**Figure 17.** *Backsplash as shown in [31].*

called "backsplash". The result is shown in **Figure 17** was created by Jiri Pospisil, et al. The backsplash increases with increasing of tube spacing and can reach up to 70% of the total flow falls over the test section for tube spacing of 35 mm. The backsplash also increases with increasing of the falling film flow rate but with only small percentage.

## **3. Discharging of ice and reusing it**

In CTS systems the ice can be stored either on the tubes or in the isolated reservoir. For the ice on the tube system, the discharge system can be either inside the tube or outside the tubes. For the collected ice in an isolated reservoir, the ice must first be released from the tubes and then passing the warm water through the accumulated ice. **Table 4** provide previous effort for the discharging system to achieve the maximum capacity out of the CTS system.


#### **Table 4.**

*Summary of the works that have been done by several researchers to study the melting phenomena.*

### **3.1 Heat transfer analysis of discharging**

The absorbed heat required to release ice consists of the following heats: sensible heat of sub-cooled ice, latent heat of melted ice and sensible heat of melted water. Thus, the experimental ice melting be expressed as

$$Qexim = Q\text{ }smice + Q\text{ }Lmice + Q\text{ }sw\text{ }\tag{21}$$

where

$$Qsmice = M\_{mic}C\_{p,mic} \ (Ts - T\_0) / \tau\_{mic} \tag{22}$$

and

$$QL\_{mic} = \mathbf{M}\_{mic} L\_{mic} / \tau\_{mic} \tag{23}$$

and

$$Q\text{\\$}w = \text{M}\_{\text{mic}} \text{C}\_{p,w} (T\_w - T\_0 \ ) / \tau\_{\text{mic}} \tag{24}$$

This heat is added by the heating solution *Qhav* which is expressed as

$$Q\_{hav} = \frac{\int\_{t=0}^{t=n} \text{Qhdt}}{\text{time}} \tag{25}$$

where

t is the time interval, n is the indicated time, and

$$Q\_h = \dot{m}\_h \ C\_{p,h} (T\_{hi} - T\_{ho}) \tag{26}$$

The overall heat transfer coefficient *Uexim* of the experimental ice releasing is expressed as follows:

$$U\_{exim} = Q \operatorname{exim} / [A\_{ice} \ (\bar{T}\_h - T\_0)] \tag{27}$$

The fluid properties of water and ice are listed in **Table 5**.

#### **3.2 Characteristics of ice releasing**

The discharge cycle can melt the ice from inside to outside or from outside to inside depending on the flow of the warm brine that flow to the chiller. For the first case, the ice begins to melt from the inner surface of the formed ice toward the outer surface forming liquid between the tube surface and the ice layer. The ice layer is then decreases to the point that, it falls and collected at the bottom of the


**Table 5.** *Fluids properties.* *Solidification and Melting of Phase Change Material in Cold Thermal Storage Systems DOI: http://dx.doi.org/10.5772/intechopen.96674*

#### **Figure 18.** *Schematic for (a) ice formation and (b) ice releasing.*

reservoir. **Figure 18** displays a schematic diagram for ice formation and releasing. For the second case where the warm water falls on the outside of the ice layers, the ice layer has more time to tick to the tube. In charging cycle, it is mandatory not allowing the ice layer between tubes to stick together, otherwise it will take much more time to get released.

### *3.2.1 Released ice percentage*

During discharge process, some ice is melted and others falls to the bottom of the reservoir. **Figure 19** shows the percentage of the released solid ice for various average ice thicknesses for an experiment done by [40]. The temperature of the internal solution (the brine) is also affected the melting process as shown in the

**Figure 19.** *Effect of heating solution temperature on released ice percentage.*

**Figure 20.**

*Charging and the discharging rate for a 10 kW CTS system, was applied in the Institute for Thermodynamics and Thermal Engineering (ITW) of the University of Stuttgart [2].*

Figure which shows a small effect on the percentage of ice releasing. Koller et al. [2] studied charging and discharging for CTS and found that the discharging is about 70% benefit of the charging system as shown in **Figure 20**.

#### **3.3 Heat transfer coefficient for ice releasing**

The experimental overall heat transfer coefficient depends on heat transfer from the heated solutions to the solid ice which consists of sensible heat for sub-cooled ice, latent heat of melted ice and sensible heat of melted water. The ice surface area and the temperature difference between the heating fluids and melting point affects the experimental overall heat transfer coefficient *Uexim.* **Figure 21** shows the variation of the experimental overall heat transfer coefficient *Uexim* for solid ice releasing

**Figure 21.** *Effect of ice thickness on Uov.*

**Figure 22.** *Effect of ice thickness on the time of ice formation and ice releasing.*

*Solidification and Melting of Phase Change Material in Cold Thermal Storage Systems DOI: http://dx.doi.org/10.5772/intechopen.96674*

with ice thickness for the experiment done by [40]. As the ice thickness decreases as melting is taken place, *Uexim* is increasing to reach its maximum value of 350 W/m2 K when the ice thickness decreases to 4 mm. Usually the releasing of ice time is shorter than the freezing time, which may varies from 1/2 to ¼ depending on the ice thickness and the warming solution used for discharging (**Figure 22**).

## **4. Enhancing both charging and discharging for cold thermal storage**

#### **4.1 Utilize thin film**

Grooved tubes can be used which increases the heat transfer surface area and hence enhancing the heat transfer coefficient. The grove can also create a thin film which enhance the heat transfer as mention by [41]. Utilizing such techniques can reaches a heat flux of 1.400 MW/m<sup>2</sup> as shown in **Figure 23**.

#### *4.1.1 Using extended surface on the tube*

The cheat transfer can be enhanced on the cold tube by having extended surface. This will help not only in enhancing the heat transfer, but in also discharging the ice out of the tube, in cases when requires many on and off cycles to collect ice.

### *4.1.2 Using suitable PCMs*

PCMs have features of higher melting points than ice and reasonable latent heat of fusion which allow them to require less energy during charging cycle. The economic wise play an important role in utilizing such materials in PCMs

#### *4.1.2.1 Cost effectives of energy storage*

Thermo-economic optimization of an CTS system should be carried out, which considers the environmental aspects, and cost effective. The cost includes the capital and operational costs as well as the penalty cost due to CO2 emission. The pay back periods will be a major influence to convince investors to utilize the CTS. Electric Power Research Institute in USA have put a methodology for energy storage Valuation, shown in **Figure 24**. The methodology consists of four steps. It starts

**Figure 23.** *Thin film evaporation scenario.*

**Figure 24.**

by defining the expected direct benefits of the CTS and the technical requirements. It then required to simulate the unite cold effectiveness. It then need to define the indirect impact such as the environmental impact. The last step is to study the business issue, whether can this utilization of CTS convert into a cash or not. Lot of works were conducted for the feasibility study of utilizing the CTSs like [1, 42].
