A study of cooling rate of the supercooled water inside of cylindrical capsulesEtude sur la vitesse de refroidissement de l'eau surrefroidie à l'intérieur de capsules cylindriques

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Abstract

An experimental apparatus was developed to investigate the supercooling phenomenon of pure water inside cylindrical capsules used for cold storage process. The Phase Change Material (PCM) used was distilled water. The external coolant material was a water–alcohol mixture (50% vol.), controlled by a constant temperature bath (CTB) in four fixed values (−4 °C, −6 °C, −8 °C, and −10 °C). Temperatures varying with time were measured inside and outside the capsule. Cylindrical capsules with internal diameter of 30 mm, 45 mm, and 80 mm, with 1.5 mm wall thickness were made in aluminum, bronze or acrylic materials. The Cooling Rate (CR) was investigated for different positions on the internal wall of the capsule, for different external coolant temperatures (Tc), different capsules diameters and different materials. The results showed that the cooling rate is a strong function of the angular position on the internal wall, the coolant temperature, the capsule material, and the capsule's diameter.

Introduction

The thermal storage for refrigeration systems is an important concept for energy conservation programs. Water is widely used as a phase-change material (PCM) due to its advantages: high value in latent heat, stable chemical properties, low cost and easy acquisition, no environmental pollution concern, and compatibility with the materials used in cooling storage process. However, there are a few disadvantages in using water as PCM. The most serious problem found is the supercooling phenomenon occurring in water solidification during the thermal storage cooling process.

While the water is cooled in an enclosed container, generally, freezing does not occur at its freezing point, Tf (0 °C at atmospheric pressure). Instead, it is normally cooled below Tf before ice nucleation happens. Supercooled water refers to a state of metastable liquid even though the water temperature is below its freezing temperature. The metastable state will end when nucleation occurs and the thin plate-like crystal of dendritic ice grows inside the supercooled region of water. During the dendritic ice-growing process, latent heat is released from the dendritic ice and consumed by supercooled water. At the end of this growing process, the temperature of the water usually returns to its freezing point (Tf). If the metastable state exists and remains during the thermal storage process, thermal energy can only be stored in the form of a sensible heat. In this case, the storage capacity is strongly reduced. Because of this, it is very important to prevent the supercooling state occurrence and to acquire a precise knowledge from the water supercooling phenomenon during a thermal storage process.

During the freezing process of pure or multi-component materials, different situations can occur with or without solidification (Milón and Braga, 2004, Milón and Braga, 2005b). A description of several processes is presented for supercooling encapsulated water. In Fig. 1 (curve I), the “regular” freezing process, without supercooling, is observed. This typical curve, with stable phase change, normally happens inside capsules of high thermal conductive and low coolant temperatures. It is observed that the process begins with a PCM temperature Ti and immediately releases the liquid sensible heat (line a). After this, it changes the phase while releases the latent heat (line d). Finally, all the PCM becomes ice and starts to release the solid sensible heat (line e). In this process, supercooling does not happen. In the same Fig. 1 (curve II), the PCM is cooled, releasing a sensible heat (line a). As in the first case, it is possible to observe when the PCM reaches the density inversion temperature (Tdi); but, later, the internal temperature crosses the freezing point (Tf) without solidification. After this, it keeps lowering the temperature below Tf in metastable liquid state (line b). The metastable state will finish when the nucleation occurs (T = Tn) and thin-plaque-like crystals of dendritic ice grows in the supercooled region of water (line c). During the dendritic ice growth process, the latent heat is released from the dendritic ice and is absorbed by the surrounded supercooled water. At the end of this dendritic growth process, usually, the water temperature returns to its freezing point and, then, starts the regular phase change (line d). And so, at the end of the solidification process, sensible heat begins to be released (e). This type of curve appears commonly for different capsule materials with coolant temperatures relatively low. Curve III in Fig. 1 presents the permanent supercooling and non-freezing process. This phenomenon occurs when the metastable liquid state (b) remains for an undetermined time and the PCM only releases sensible heat. This curve is common in low thermal conductivity capsules with high coolant temperatures (near Tf). More details are shown in Milón and Braga, 2004, Milón and Braga, 2005b.

The Cooling Rate (CR) is an important parameter in the supercooling phenomenon and nucleation of the water inside capsules and needs special attention.

Several studies about Cooling Rate were realized (Okawa et al., 2001, Chen and Lee, 1998, Yoon et al., 2001, Lee et al., 1996, Debenedetti, 1996, Gilpin, 1977). In these papers the Cooling Rate is defined as:CR=i=1nCRin=i=1n(TIWiTIWi1)tan,orCR=SDDtwhere,

  • CR is the cooling rate in the internal wall, °C min−1;

  • TIWi is the internal wall temperature in i, °C;

  • TIWi1 is the internal wall temperature in i  1, °C;

  • ta is the time interval of acquisition data, min;

  • n is the number of measurements;

  • Dt is the total supercooling period, min, and

  • SD is the supercooling degree, °C.

In Fig. 2 it is shown the concept of CR, expressed by different authors (Chen and Lee, 1998, Gilpin, 1977).

The present article is based on some observations done in previous experiments made by Milón and Braga, 2004, Milón and Braga, 2005b, Milón and Braga, 2005a, where they observed that the concept of the cooling rate would have to be reviewed and reformulated, since they observed that the CR varies with the position where TIWi is measured. The objective of this article is to redefine the concept of the cooling rate related to different variables like, external coolant temperature, position of the temperature sensor on the internal wall of the capsule, diameter and material of the capsules.

Section snippets

Experimental apparatus

The experimental apparatus shown schematically in Fig. 3, consists of a test section (a), a cooling system (b), and a measurement and data acquisition system (c).

Experimental procedure

In the beginning of each test (Fig. 3), the CTB-IC imposes the initial temperature (Ti) to the PCM (25 °C for all the experiments). Simultaneously, the CTB imposes the temperature to the coolant (Tc) according to each experiment, circulating it through an external reservoir. Subsequently the CTB-IC stops circulating through the test section and the CTB starts to circulate the coolant, imposing quickly the temperature Tc (2 min approximately). The experiment ends with the beginning of phase change

Cooling process

Fig. 5 presents a typical curve of cooling water inside an aluminum capsule with 45 mm of internal diameter and external coolant temperature equal to −6 °C. It is possible to observe that the density inversion phenomenon strongly influences the temperature distribution along the time. At the beginning of the experiment, the thermocouples at the central region of the capsule (G, H and F) present higher temperatures than the ones on the wall. Due to the convection cells symmetry, it is possible to

Conclusions

As mentioned before, the CR value is determined with smaller uncertainty in A (central-inferior point of the wall cavity) and it is a function of the material thermal conductivity, external heat transfer characteristics and internal diameter of the capsule. In these experiments, the supercooling phenomenon was evaluated in horizontal cylindrical capsules, which were externally cooled by ascending vertical flow.

The smaller dispersion of the CR value, according to the position of the temperature

Acknowledgments

This paper was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico – CNPq of Brazil. The authors also wish to thank the agreement between Pontifical Catholic University of Rio de Janeiro, Brazil and San Pablo Catholic University, Peru for motivating this research.

References (10)

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