IMD

Hiroyuki Kumano a,*, Tetsuo Hirata a, Yosuke Hagiwara b, Fumito Tamura a
a Department of Mechanical Systems Engineering, Shinshu University, 4-17-1 Wakasato, Nagano 380-8553, Japan. b West Japan Railway Co., 2-4-24 Shibata, Kita-ku, Osaka 530-8341, Japan

Continued from RACA Journal August 2012

3: Results and discussion
3.1: Flow characteristics
The effect of storage time on the relationship between pressure drop and IPF is shown in figure 5. Figure 5 (a) and (b) shows the results in the case of laminar and turbulent flow, respectively. Under laminar flow conditions, the pressure drop increases with IPF. However, the increasing rate of pressure drop decreases with increase in storage time. Under turbulent flow conditions, the pressure drop is constant despite the variation of IPF and storage time.
In this study, the effect of storage on the ice slurry flow characteristics was investigated experimentally and the effects of Re and IPF were revealed simultaneously. Therefore, a coefficient of pipe friction was introduced to clarify their effect as well as our previous study (Kumano et al, 2010a).
Theoretical values of the coefficient of pipe friction were calculated from Re, and the comparison between experimental and theoretical values were carried out. Theoretical values of the coefficient of pipe friction can be calculated using equations (2) and (3) for laminar and turbulent flow, respectively.


Here, Re is given as the experimental parameter, and calculated from the kinematic viscosity of the ethanol solution in the ice slurry. The experimental results were compared with the coefficient of pipe friction of the ethanol solution to clarify the fundamental flow characteristics of the ice slurry.


The ratio of the coefficient of pipe friction obtained from the experiments to the theoretical values of the coefficient of pipe friction was introduced to reveal the flow characteristics of the ice slurry.The relationship between the ratio of coefficients of pipe friction and storage time is shown in figure 6. Figure 6 (a), (b) and (c) shows the results in the case of a 5, 10 and 15 % IPF, respectively, under laminar flow conditions. Moreover, the variation in average diameter of the ice particles is shown together in the figures. The ratio of coefficients of pipe friction is small in the case of a high Re, and the ratio of the coefficients of pipe friction decreases with increase in storage time in the region less than four hours for each IPF. The tendency is significant in the case of a high IPF. A possible reason for this observation is that the average diameter of the ice particles increases relatively compared with the tube diameter. In our previous study (Kumano et al, 2010a), when the tube diameter was varied from 4,3 to 10,2 mm, the same tendency was observed. On the other hand, the results for four and six hour of storage time are similar.


Therefore, the storage time was set at more than six hours to confirm the effects of long-term storage on the flow characteristics. Figure 7 shows the relationship between the ratio of coefficients of pipe friction and the storage time. The IPF was set at 15 %. It was found that the effect of storage times greater than six hour on the ratio of coefficients of pipe friction is insignificant.


Moreover, the ice slurry did not flow in the tube at more than 12 hour storage because of a blockage in the tube. For more than 6 hour storage, it seems that agglomeration of the ice particles occurs and the effect of the agglomeration becomes larger than the effect of the increase in average diameter of ice particles. As a result, the ratio of coefficients of pipe friction did not vary for long-term storage.


Figure eight shows the relationship between the ratio of coefficients of pipe friction and storage time under turbulent flow conditions with IPF set at 15 %. It was found that the ratio of the coefficients of pipe friction is one for each storage time despite the increase in average diameter of the ice particles.
Moreover, in the case of 5 and 10 % IPF, the tendency was similar. That is, the coefficient of pipe friction of the ice slurry corresponded to the coefficient of pipe friction of only the ethanol solution, and the effect of the storage on the flow characteristics of the ice slurry is insignificant for the turbulent flow condition.

Heat transfer characteristics
In this study, the melting heat transfer characteristics of the ice slurry were investigated experimentally. Then, the heat transfer coefficients were calculated from the temperature of the ice slurry and the inner surface temperature of the tube, using equation (1). The heat transfer coefficients were then calculated at the upper, middle and lower positions. However, it was found that the difference due to position is not significant.


Therefore, the effect of the buoyancy force on the ice particles can be neglected, and the heat transfer coefficients were calculated from the average values of the upper, middle and lower positions. Figure 9 shows the effects of storage time on the relationship between the heat transfer coefficient and IPF. Figure 9 (a) and (b) shows the results for laminar and turbulent flow. The position of measurement is 0,7 m from the beginning of the heating section. Under laminar flow conditions, the heat transfer coefficients increase with IPF for each storage time, and the increasing rate decreases with increase in storage time. On the other hand, under turbulent flow conditions, the heat transfer coefficient is almost constant despite the variation in IPF. In this study, Nusselt number, Nu, is introduced to clarify the effects of storage time appropriately, as well as our previous study (Kumano et al, 2010b). Moreover, Nu obtained from the experiments, Nuexp, is compared with its theoretical values and is defined as follows:


Here, the thermal conductivity of the ice slurry, k, is decided as the thermal conductivity of water at 273,15 K, because the thermal conductivity of the ethanol solution is not clear. The theoretical values of the Nu can be calculated using equations (5) and (6) for laminar and turbulent flows, respectively.


Under laminar flow conditions, it was found that a thermal boundary layer develops rapidly and the heat transfer coefficient becomes constant. Therefore, the theoretical Nu under constant heat flux was used as the theoretical value. Under turbulent flow conditions, the Colburn equation was used. Moreover, the ratios of Nu obtained from the experiments to the theoretical values of Nu were used to clarify the heat transfer characteristics of the ice slurry. Figure 10 shows the relationship between ratio of Nu and storage time in the case of a 5, 10 and 15 % IPF, respectively, and under laminar flow conditions. The variation in average diameter of the ice particles is shown together. From the figures, it was found that the ratio of Nu decreases with increase in storage time for each IPF.


However, the differences caused by the variation of Re are small compared with the coefficients of pipe friction. Here, the storage time was set at more than 6 hours to confirm the long-term storage effects. Figure 11 shows the relationship between the ratio of Nu and storage time for a 15 % IPF. It was found that the effect of storage time for more than six hours is not remarkable. For less than six hours storage, Nu decreases with increase in storage time. It seems that the increase in average diameter of ice particles caused the decrease in Nu. Here, the relationship between the thickness of the thermal boundary layer and the average ice particle diameter is considered. The thickness of the thermal boundary layer can be calculated approximately from Nu and the characteristic length.

Table 2 shows the variation in thickness of the thermal boundary layer and the average diameter of the ice particles in the region for less than six hours storage. It was found that the thickness of the thermal boundary layer and the average diameter are on the same level and increase with storage time. For more than six hours of storage, Nu is constant despite the increase in average diameter of the ice particles, and the tendency is similar to the coefficients of pipe friction. In this region, agglomeration between the ice particles occurs, and it seems that the agglomeration causes this result. However, a detailed mechanism is not clear and should be considered in future work. Figure 12 shows the relationship between the ratio of Nu and storage time under turbulent flow conditions with IPF set at 15 %. The ratios of Nu decrease slightly with increase in storage time. However, it was found that they are almost one for each storage time, and the tendency is similar to the coefficient of pipe friction. As a result, the effect of storage on flow and heat transfer characteristics for the turbulent flow condition is not significant.

Conclusion
In this study, the effect of storage on the flow and heat transfer characteristics of an ice slurry was investigated experimentally. Variations of the size and shape of the ice particles in the ice slurry during the storage were observed, and pressure drop and heat transfer coefficients were measured by varying Re, storage time and IPF. Under laminar flow conditions, it was found that the ratios of the coefficients of pipe friction and Nu decrease with storage times less than six hours. On the other hand, for more than six hours storage, these values are constant, despite the increase in average diameter of the ice particles. Under turbulent flow conditions, the ratios of coefficients of pipe friction and Nu are almost constant, and the effect of storage on the flow and heat transfer characteristics for the turbulent flow condition is not significant.

References
Ayel, V, Lottin, O, Peerhossaini, H, 2003. Rheology, flow behaviour and heat transfer of ice slurries: a review of the state of the art. Int J Refrigeration 26, 95e107.
Bellas, J, Chaer, I, Tassou, SA, 2002. Heat transfer and pressure drop of ice slurries in plate heat exchangers. Appl Therm Eng 22, 721e732.
Doetsch, C, 2001. Pressure drop and flow pattern of ice slurries. In: Proc of the Third Workshop on Ice Slurries of the IIR. pp 53e59.
Egolf, PW, Kauffeld, M, 2005. From physical properties of ice slurries to industrial ice slurry applications. Int J Refrigeration 28, 4e12.
Guilpart, A, Fournaison, L, Ben Lakhdar, MA, Flick, D, Lallemand, A, 1999. Experimental study and calculation method of transport characteristics of ice slurries. In: Proc Of the First IIR Workshop on Ice Slurries. pp 74e82.
Kitanovski, A, Poredos, A, 2002. Concentration distribution and viscosity of ice-slurry in heterogeneous flow. Int J Refrigeration 25, 827e835.
Knodel, BD, France, DM, Choi, US, Wambsganns, MW, 2000. Heat transfer and pressure drop in ice-water slurries. Appl Therm Eng 20, 671e685.
Kumano, H, Hirata, T, Shirakawa, M, Shouji, R, Hagiwara, Y, 2010a. Flow characteristics of ice slurry in narrow tubes. Int J Refrigeration 33, 1513e1522.
Kumano, H, Hirata, T, Shouji, R, Shirakawa, M, 2010b Experimental study on heat transfer characteristics of ice slurry. Int J Refrigeration 33, 1540e1549.
Lee, DW, Yoon, ES, Joo, MC, Sharma, A, 2006. Heat transfer characteristics of the ice slurry at melting process. Int J Refrigeration 29, 451e455.
Niezgoda-Zelasko, B, Zalewski, W, 2006. Momentum transfer of ice slurry flow in tubes, experimental investigations. Int J Refrigeration 29, 418e428.
Pronk, P, Hansen, TM, Infante Ferreira, CA, Witkamp, GJ, 2005. Time-dependent behaviour of different ice slurries during storage. Int J Refrigeration 28, 27e36.
Saito, A, 2002. Recent advances in research on cold thermal energy storage. Int J Refrigeration 25, 177e189.