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Fluid dynamics and heat transfer in cold water thawing
Journal of Food Engineering 78 (2007) 1221–1227 www.elsevier.com/locate/jfoodeng
Fluid dynamics and heat transfer in cold water thawing Michael Leung a
a,*
, Wing-Han Ching a, Dennis Y.C. Leung a, Gabriel C.K. Lam
b
Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong b Nature and Technologies (HK) Limited, Hong Kong Received 17 January 2005; received in revised form 23 July 2005; accepted 17 October 2005 Available online 15 March 2006
Abstract Cold water thawing method using running water is most popular when frozen food is required to thaw within a short period of time. Although cold water thawing has long been used commonly in food processing, catering, as well as household cooking, most users do not fully understand the thawing mechanisms and behaviors, leading to poor time control, excessive consumption of water, and unnecessary waste water discharge. In this investigation, numerical modeling and experimental validation were conducted to study the important fluid dynamics and heat transfer in cold water thawing. Computational fluid dynamics (CFD) modeling was employed to analyze the water flow and convective heat transfer on the food surface. Inside the food body, the heat transfer by conduction with a moving phase-change interface was determined by finite difference (FD) method. A parametric study revealed the effects of the flow rate and temperature of the water inlet on the thawing process performance. It was found that the water flow rate could be much less than what commonly used to obtain virtually the same thawing performance. Finally, proper equipment design, control, and operation were recommended to achieve high thawing rate and efficient use of water. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Cold water thawing; Moving phase-change interface; Computational fluid dynamics
1. Introduction Frozen food is normally stored at 18 °C for preservation. Thawing is necessary before any subsequent food processing or cooking. There are different frozen food thawing methods available, including cold water thawing (Chourot, Boillereaux, Havet, & Bail, 1997), refrigerator thawing (Anderson, Sun, Erdogdu, & Singh, 2004), microwave thawing (Basak & Ayappa, 2002; Zeng & Faghri, 1994), high-pressure thawing (Denys, Van Loey, & Hendrickx, 2000), among others. Cold water thawing method is favorable when a short thawing time is required. In this method, frozen food is immersed in a tank of cold water at a temperature above the melting point of the food. Heat transfer occurs due to
*
Corresponding author. Tel.: +852 2859 2628; fax: +852 2858 5415. E-mail addresses: [email protected], [email protected] (M. Leung). 0260-8774/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2005.10.042
the temperature difference between the food and the water. As illustrated in Fig. 1, the food surface gains heat from the surrounding water by convection and the heat is conducted into the body. A phase-change interface between frozen and thawed food materials will be first formed on the food surface when the surface temperature reaches the melting point. The interface will then move inwards as the food continues to gain heat. Eventually, the interface vanishes at the center as the thawing process finishes. The analysis of the thermal behaviors is classified as a moving phasechange interface heat transfer problem (Hsieh & Leung, 2001; Leung, 2001; Leung, Ching, Leung, & Lam, 2005). One can speed up the cold water thawing process by promoting force convection in the water tank to increase the convective heat transfer. Adding an electrical stirrer may effectively increase the force convection. Alternatively, force convection can be achieved by running water in an overflowing tank. This approach using simpler mechanical design without any electrical component is often more acceptable in the demanding commercial kitchen
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M. Leung et al. / Journal of Food Engineering 78 (2007) 1221–1227
be manipulated by changing the fluid flow field. The commercial CFD software FLUENT 6.1 was used to facilitate the analysis. A k–e turbulence model was selected as the rough surface of food behaved as a turbulence promoter. 3.1. Thermal stratification effect
Fig. 1. Cold water thawing mechanisms.
environment. Therefore, the emphasis of this study is on cold water thawing method using running water. It is generally true that the faster the running water flows, the faster the frozen food is thawed. However, no quantitative analysis is available to facilitate any thawing process control. The consequences are often poor thawing time control, excessive consumption of water, and unnecessary waste water discharge. 2. Methodology The main objectives of this study were to characterize the mechanisms of cold water thawing and, accordingly, to design an efficient thawing device. Numerical modeling was employed to simulate the fluid flow and heat transfer involved. A CFD model was constructed to determine the water flow and convective heat transfer. A steady-state CFD modeling was implemented to analyze the thermal stratification effect for preliminary design of cold water thawing device configuration. Subsequently, a FD model was set up to estimate the transient temperature variation inside the food body. Special formulation was incorporated in the FD model to take into account the latent heat absorption by the moving phase-change interface. Laboratory tests were conducted for validation of the numerical CFD and FD modeling. Finally, the numerical model was used to carry out a parametric study. Based on the findings, appropriate design and operating parameters were specified for cold water thawing applications in small to medium size restaurants.
From field surveys and interviews in many catering kitchens, it was observed that the users commonly performed cold water thawing of frozen meat by letting the meat sink to the bottom of a water container constantly overflowed by running tap water on top. The setup became a thermally stratified container as ‘‘heat rises and cold sinks’’. As both water inlet and outlet were located on top, the flow momentum on the bottom was relatively weak to overcome the stratification. The stratification would cause poor convective heat transfer because the frozen meat would be mostly surrounded by water at a lower temperature. The problem could be mitigated by changing the position of the water inlet from the top to the bottom as illustrated in Fig. 2. The enhanced thawing performance due to the elimination of the adverse stratification could be determined by transient CFD analysis. However, the transient CFD computation would be extremely expensive and thus impractical. Instead, a steady-state CFD analysis was conducted to study the stratification effects of the two water inlet configurations shown in Fig. 2. The value of Ts equal to 5 °C was arbitrarily selected within the typical operating temperature range between 18 °C and 24 °C. Although the steady-state convective heat transfer coefficient, h, was obtained based on constant Ts, its value would be comparable to the h value in the actual transient thawing process with varying Ts. It was because h under force convection
3. Computational fluid dynamics (CFD) analysis In cold water thawing, the convective heat transfer on the food surface can be expressed by q ¼ hðT s T 1 Þ;
ð1Þ
where q, h, Ts, and T1 are heat flux, convective heat transfer coefficient, mean food surface temperature, and bulk water temperature, respectively. A thermal-fluid analysis was conducted to study how the thermal property, h, could
Fig. 2. CFD models for study of thermal stratification effect.
M. Leung et al. / Journal of Food Engineering 78 (2007) 1221–1227
should mostly depend on the water flow which was steady. The buoyancy effect caused by the varying Ts would be less important. The dimensions and operating conditions shown in Fig. 2 were specially set to provide an approximate representation of an average subset of a full-scale cold water thawing device. The water overflow was modeled by a radial outlet located on the perimeter on the top of the cylinder. The concentric 3-D physical domain was set up in an axisymmetric coordinate system for computation. The CFD results are depicted in Fig. 3. With the water inlet located on top, the large temperature variation with cold water staying on the bottom clearly revealed the thermal stratification developed in the flow field. As the lower part of the meat gained heat from the low-temperature water, the overall convective heat transfer was low. The magnitude of stratification became worst if the inlet flow rate decreased. Relocating the water inlet on the bottom could result in a better mixed condition. Hence, the convective heat transfer was enhanced. Quantitatively, Eq. (1) was employed to calculate the convective heat transfer coefficient, h. The bulk water temperature, T1, and the average heat flux, q, on the food surface were easily obtained by the commercial software adopted (FLUENT 6.1). The built-in program functions were used to compute the average temperature of the water bath for T1 and integrate the heat flux over the spherical boundary for q. The values of T1 and q were substituted into in Eq. (1) with Ts equal to 5 °C to calculate the convective heat transfer coefficient, h. It was found that locating the water inlet on the bottom yielded a significant 33% increase in the h value from 1034 W m2 K1 to 1376 W m2 K1. 3.2. Convective heat transfer Based on the above findings, a simple but effective design was generated as shown in Fig. 4. The device consisted of a plastic water tank (270 mm diameter; 350 mm
Fig. 3. Comparison between steady-state temperature fields resulting from water inlet on top and bottom.
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Fig. 4. Design of cold water thawing device.
tall) and a stainless steel rack, plus minor modification for a water inlet on the bottom. All the items needed were commonly available in restaurant kitchens. During the operation, the frozen food is fully immersed in water and spread evenly at an upper position for uniform thawing. The design was sized to process about 2 kg of frozen food simultaneously. The capacity was suitable for practical applications in small to medium size restaurants. In order to characterize the cold water thawing device for setting appropriate operating parameters, CFD analysis was carried out for the configuration shown in Fig. 4 to determine how the convective heat transfer coefficient, h, varied with the apparent speed of water flow, defined as the ratio of volumetric inlet water flow rate to cross-sectional area of the tank. The results are presented in Fig. 5. The h values were used in the modeling of heat transfer by conduction as described in the following section.
Fig. 5. Convective heat transfer coefficient versus apparent speed of water flow.
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4. Heat transfer by conduction with moving phase-change interface In frozen food thawing, it is well recognized that the actual phase change does not occur at a single melting point, but rather over a temperature range (ASHRAE, 2002, Chap. 8; Miki & Hayakawa, 1996). This phenomenon can be explained by the fact that the concentration of undissolved solid in liquid water gradually decreases during the thawing process and thus the melting temperature increases correspondingly (Pham, 1987). Besides, the biological tissues are porous media in which the frozen microscopic pores are filled up with ice crystal. As a pore undergoes a melting process, the crystal–liquid equilibrium ruled by the Clausius–Clapeyron relationship contributes to the shift of the melting temperature (Coussy, 2005; Talamucci, 2003). The distribution of latent heat over the melting temperature range in frozen food thawing is a very complex issue depending on the composition of constituents and the pore size distribution in biological tissues. The phase change occurs over a temperature range below 0 °C but it is normally a narrow range within a few degrees centigrade (Anderson et al., 2004). For this reason, the phase-change behavior can be simplified to a single melting point model in the numerical analysis. Using the melting point of bulk water equal to 0 °C offers a conservative analysis to determine sufficient time taken for complete thawing. The food body temperature variation due to internal heat conduction was determined by FD method. The spherical body was discretized into 100 evenly-spaced nodes in the radial direction from the center to the surface. Conventional FD energy balance equations were formulated for the center node, internal nodes, and surface node. A negative generation term was added to each FD equation to take into account the latent heat absorption when the moving phase-change interface at the melting point traveled along the radial direction. The formulation of this generation term included the mean velocity of the moving interface between the time frames m and m + 1, vI ¼
rImþ1 rmI Dt
direction. As the phase-change interface was moving from the spherical surface towards the center, rImþ1 was smaller than rmI during the thawing process. The expression for GI shown in Eq. (3) was thus negative that represented a heat absorption for the food material changing phase from a frozen state to a thawed state. With the addition of Eq. (3) to conventional FD heat conduction formulas, the position of the phase-change interface at time frame m ðrmI Þ could be numerically found. Then, the speed of the moving interface at different time could be calculated by Eq. (2). One set of the modeling results simulating an experimental test is presented here to demonstrate the typical thawing behavior. A round piece of frozen pork initially at uniform 18 °C was suddenly immersed in the cold water thawing tank shown in Fig. 4. The material properties of the lean pork specimen and the operating conditions are given in Table 1. The numerical results in terms of time-dependent temperature profiles are plotted in Fig. 6. At the beginning, the specimen surface temperTable 1 Input values for illustrative modeling computation Pork specimen (lean) Density, q (kg m3) Thermal conductivity, k (W m1 K1) Heat capacity below melting point, CpjT<0 °C (J kg1 K1) Heat capacity above melting point, CpjT>0 °C (J kg1 K1) Latent heat, L (J kg1) Melting point (°C) Specimen diameter (mm) Initial temperature (°C)
1433a 0.69212b 2219b 3601b 241,904b 0 50 18
Cold water thawing operations Volumetric flow rate (L min1) Apparent speed of water flow (mm s1) Convective heat transfer coefficient, h (W m2 K1) Mean temperature of water inlet (°C)
0.5 0.15 819 20.4
a b
Obtained by measurements of the pork specimen. Refer to ASHRAE (2002, Chap. 8) for material properties of pork.
ð2Þ
and the amount of latent heat absorption, 8 3 3 4p > ðrmþ1 Þ ðrmI Þ qL 3 I > < AI vI qL ¼ ; for nth node Dt GI ¼ where T n drops below T L ; > > : 0; elsewhere, ð3Þ where rI was the radial coordinate of the moving phasechange interface; AI was the spherical shell area of the phase-change interface; interface area times the velocity, AIvI, was equal to the volumetric rate of phase change; q was the food density; L was the food latent heat; TL was the melting point; Dt was the time step; superscript m indicated the number of time frames; and subscript n indicated the nth node of the spatial domain discretized in the radial
Fig. 6. Numerical modeling results of cold water thawing of a round frozen pork of 50 mm diameter.
M. Leung et al. / Journal of Food Engineering 78 (2007) 1221–1227
Fig. 7. Movement of phase-change interface in terms of radial coordinate versus time.
ature, shown by the solid diamonds, quickly increased and approached the water temperature. On the other hand, the center temperature, shown by the empty squares, increased at a lower rate to about the melting point at 0 °C and stayed for an extended period as the inner body was undergoing phase transformation from a frozen state to a thawed state. Once the center temperature exceeded the melting point, the specimen was completely thawed. The thawing time period was 51 min long. Without any further absorption of latent heat, the subsequent center temperature increased rapidly. Eventually, the entire specimen body reached the equilibrium at the surrounding water temperature. These phenomena showed the considerable effect of the latent heat on the temperature field in a thawing process. The corresponding movement of the phase-change interface is shown in Fig. 7. The interface was initially formed on the surface after the specimen was immersed in the water flow for 0.03 min. The interface moved inwards and reached the center after 51 min when the specimen was completely thawed. 5. Empirical validation The numerical results presented in Section 4 were verified by experimental test results. In this experiment, lean pork was used for the specimen and the estimated mass composition data were 55.93% moisture, 27.8% protein, 8.32% fat, 0.3% carbohydrate, and 7.65% ash (ASHRAE, 2002, Chap. 8). The specimen was cut to a 50-mm sphere and weighed to determine its density. Two thermal couples were installed to measure the body temperature at the center and at a position 10 mm away from the center sideway. The initial condition was obtained by placing the specimen in a freezer to reach a uniform temperature of 18 °C. The specimen was then immersed in the cold water thawing tank shown in Fig. 4. The inlet water flow rate was regu-
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Fig. 8. Comparison between experimental measurements and numerical modeling results of cold water thawing of frozen pork.
lated at 0.5 L min1, equivalent to an apparent speed of 0.15 mm s1. The temperature measurements are plotted with the numerical modeling results in Fig. 8. A reasonable agreement was obtained. The discrepancy was probably due to the fact that the input thermal properties used in the modeling slightly deviated from the actual values. For instance, the frozen pork did not actually melt at a single melting point of 0 °C, but rather over a temperature range from 3 to 0 °C. For this reason, the middle segments of the measured temperature profiles near the melting point exhibited a minor slope, rather than a flat line as generated by the numerical model. Nevertheless, the assumption of constant properties yielded reasonable numerical prediction. The numerical modeling and experimental validation were also conducted for thawing of frozen chicken. Similar agreement was obtained. 6. Parametric study After the numerical model using CFD and FD methods was validated by experimental data, the model was used to perform a parametric study to search for control and operating parameters for proper use of cold water thawing. 6.1. Effect of water flow rate Firstly, the primary interest was to obtain the relationship between the thawing time and the water flow rate. For the same input values presented in Table 1 except the mean water inlet temperature changed to the yearly average of 24 °C in Hong Kong, the numerical modeling outputs are plotted in Fig. 9. As expected, an increase in the speed of water flow would increase the convective heat transfer coefficient and, thus, reduce the thawing time
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Fig. 10. Thawing time versus water inlet temperature in cold water thawing of frozen pork.
6.2. Effect of water inlet temperature
Fig. 9. Thawing time versus water flow rate in cold water thawing of frozen pork sized to different diameters: (a) 125 mm, (b) 50 mm, and (c) 25 mm.
period. However, up to certain apparent speed of water flow, i.e. 0.15 mm s1, an increase in the speed caused an insignificant reduction in the thawing time. For instance, as shown in Fig. 9b for thawing of a 50-mm pork specimen, an increase in the flow speed by 100% from 0.15 mm s1 (0.5 L min1) to 0.29 mm s1 (1 L min1) would shorten the thawing time by only 0.3 min, a 0.8% reduction. The reason was that at a high speed of water flow, the thermal resistance of the convective heat transfer mode was reduced to a magnitude much lower than that of the conductive heat transfer mode. In other words, conduction became the ‘‘bottle neck’’ in the overall heat transfer of the thawing process. Therefore, further enhancement in the convective heat transfer did not contribute significantly to the thawing performance. In consideration of the environmental and economical use of water, it is recommended that cold water thawing should be operating at a water flow of 0.15 mm s1 to achieve a nearly shortest thawing time period. For the cold water thawing device shown in Fig. 4, the equivalent volumetric flow rate is 0.5 L min1. In comparison with the typical flow rate about 5 L min1 that is commonly observed in restaurant kitchens, the estimated saving in water consumption is 90% and so are the cost savings in water consumption and waste water discharge.
The water inlet temperature is another parameter that affects the performance of cold water thawing significantly. An increase in water inlet temperature can increase both convective and conductive heat transfer modes. The numerical modeling results generated by different water inlet temperatures are presented in Fig. 10. The figure implies that the time taken for a complete cold water thawing process using tap water in the winter can be twice as much as that in the summer, depending on the local climatic conditions. One may make use of the information presented in Fig. 10 to determine the effect of using warm thawing water on the thawing rate. 7. Conclusions In this study, the fluid flow and heat transfer involved in cold water thawing were analyzed by numerical modeling using CFD and FD methods. The numerical results agreed reasonably well with the experimental measurements. Using the numerical model as a design tool, a simple cold water thawing device was designed to reduce the thermal stratification and, thus, improve the thawing efficiency. The recommended apparent speed of water flow was 0.15 mm s1 resulting in nearly the shortest thawing time. Any higher flow rate would only cause a marginal reduction in the thawing time because the conductive thermal resistance, rather than the convective thermal resistance, became the dominating factor in the overall heat transfer. One may implement the recommendations or refer to the numerical and experimental results presented in paper to improve the performance of cold water thawing method. Acknowledgments The work described in this paper was fully supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No.
M. Leung et al. / Journal of Food Engineering 78 (2007) 1221–1227
HKU 1008/01E) and a grant from the Environment and Conservation Fund (Project 20/2002). References Anderson, B. A., Sun, S., Erdogdu, F., & Singh, R. P. (2004). Thawing and freezing of selected meat products in household refrigerators. International Journal of Refrigeration, 27, 63–72. ASHRAE (2002). 2002 ASHRAE handbook—refrigeration (SI). Basak, T., & Ayappa, K. G. . (2002). Role of length scales on microwave thawing dynamics in 2D cylinders. International Journal of Heat and Mass Transfer, 45, 4543–4559. Chourot, J.-M., Boillereaux, L., Havet, M., & Bail, A. L. (1997). Numerical modeling of high pressure thawing: application to water thawing. Journal of Food Engineering, 34, 63–75. Coussy, O. (2005). Poromechanics of freezing materials. Journal of the Mechanics and Physics of Solids, 53, 1689–1718. Denys, S., Van Loey, A. M., & Hendrickx, M. E. (2000). Modeling conductive heat transfer during high-pressure thawing processes: determination of latent heat as a function of pressure. Biotechnology Progress, 16, 447–455.
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Hsieh, C. K., & Leung, M. (2001). Phase change in a cylinder and a cylindrical shell heated with an axisymmetric front moving in the axial direction. ASME Journal of Heat Transfer, 123, 476–484. Leung, M. (2001). Phase-change heat transfer in laser transformation hardening by moving Gaussian rectangular heat source. Journal of Physics D: Applied Physics, 34, 3434–3441. Leung, M., Ching, W. H., Leung, D. Y. C., & Lam, G. C. K. (2005). Theoretical study of heat transfer with moving phase-change interface in thawing of frozen food. Journal of Physics D: Applied Physics, 38, 477–482. Miki, H., & Hayakawa, K. (1996). An empirical equation for estimating food enthalpy in a freezing temperature range. Lebensmittel-Wissenschaft und-Technologie, 29, 659–663. Pham, Q. T. (1987). Calculation of bound water in frozen food. Journal of Food Science, 52, 210–212. Talamucci, F. (2003). Freezing processes in porous media: formation of ice lenses, swelling of the soil. Mathematical and Computer Modeling, 37, 595–602. Zeng, X., & Faghri, A. (1994). Experimental and numerical study of microwave thawing heat transfer for food materials. ASME Journal of Heat Transfer, 116, 446–455.
Fluid dynamics and heat transfer in cold water thawing Michael Leung a
a,*
, Wing-Han Ching a, Dennis Y.C. Leung a, Gabriel C.K. Lam
b
Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong b Nature and Technologies (HK) Limited, Hong Kong Received 17 January 2005; received in revised form 23 July 2005; accepted 17 October 2005 Available online 15 March 2006
Abstract Cold water thawing method using running water is most popular when frozen food is required to thaw within a short period of time. Although cold water thawing has long been used commonly in food processing, catering, as well as household cooking, most users do not fully understand the thawing mechanisms and behaviors, leading to poor time control, excessive consumption of water, and unnecessary waste water discharge. In this investigation, numerical modeling and experimental validation were conducted to study the important fluid dynamics and heat transfer in cold water thawing. Computational fluid dynamics (CFD) modeling was employed to analyze the water flow and convective heat transfer on the food surface. Inside the food body, the heat transfer by conduction with a moving phase-change interface was determined by finite difference (FD) method. A parametric study revealed the effects of the flow rate and temperature of the water inlet on the thawing process performance. It was found that the water flow rate could be much less than what commonly used to obtain virtually the same thawing performance. Finally, proper equipment design, control, and operation were recommended to achieve high thawing rate and efficient use of water. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Cold water thawing; Moving phase-change interface; Computational fluid dynamics
1. Introduction Frozen food is normally stored at 18 °C for preservation. Thawing is necessary before any subsequent food processing or cooking. There are different frozen food thawing methods available, including cold water thawing (Chourot, Boillereaux, Havet, & Bail, 1997), refrigerator thawing (Anderson, Sun, Erdogdu, & Singh, 2004), microwave thawing (Basak & Ayappa, 2002; Zeng & Faghri, 1994), high-pressure thawing (Denys, Van Loey, & Hendrickx, 2000), among others. Cold water thawing method is favorable when a short thawing time is required. In this method, frozen food is immersed in a tank of cold water at a temperature above the melting point of the food. Heat transfer occurs due to
*
Corresponding author. Tel.: +852 2859 2628; fax: +852 2858 5415. E-mail addresses: [email protected], [email protected] (M. Leung). 0260-8774/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2005.10.042
the temperature difference between the food and the water. As illustrated in Fig. 1, the food surface gains heat from the surrounding water by convection and the heat is conducted into the body. A phase-change interface between frozen and thawed food materials will be first formed on the food surface when the surface temperature reaches the melting point. The interface will then move inwards as the food continues to gain heat. Eventually, the interface vanishes at the center as the thawing process finishes. The analysis of the thermal behaviors is classified as a moving phasechange interface heat transfer problem (Hsieh & Leung, 2001; Leung, 2001; Leung, Ching, Leung, & Lam, 2005). One can speed up the cold water thawing process by promoting force convection in the water tank to increase the convective heat transfer. Adding an electrical stirrer may effectively increase the force convection. Alternatively, force convection can be achieved by running water in an overflowing tank. This approach using simpler mechanical design without any electrical component is often more acceptable in the demanding commercial kitchen
1222
M. Leung et al. / Journal of Food Engineering 78 (2007) 1221–1227
be manipulated by changing the fluid flow field. The commercial CFD software FLUENT 6.1 was used to facilitate the analysis. A k–e turbulence model was selected as the rough surface of food behaved as a turbulence promoter. 3.1. Thermal stratification effect
Fig. 1. Cold water thawing mechanisms.
environment. Therefore, the emphasis of this study is on cold water thawing method using running water. It is generally true that the faster the running water flows, the faster the frozen food is thawed. However, no quantitative analysis is available to facilitate any thawing process control. The consequences are often poor thawing time control, excessive consumption of water, and unnecessary waste water discharge. 2. Methodology The main objectives of this study were to characterize the mechanisms of cold water thawing and, accordingly, to design an efficient thawing device. Numerical modeling was employed to simulate the fluid flow and heat transfer involved. A CFD model was constructed to determine the water flow and convective heat transfer. A steady-state CFD modeling was implemented to analyze the thermal stratification effect for preliminary design of cold water thawing device configuration. Subsequently, a FD model was set up to estimate the transient temperature variation inside the food body. Special formulation was incorporated in the FD model to take into account the latent heat absorption by the moving phase-change interface. Laboratory tests were conducted for validation of the numerical CFD and FD modeling. Finally, the numerical model was used to carry out a parametric study. Based on the findings, appropriate design and operating parameters were specified for cold water thawing applications in small to medium size restaurants.
From field surveys and interviews in many catering kitchens, it was observed that the users commonly performed cold water thawing of frozen meat by letting the meat sink to the bottom of a water container constantly overflowed by running tap water on top. The setup became a thermally stratified container as ‘‘heat rises and cold sinks’’. As both water inlet and outlet were located on top, the flow momentum on the bottom was relatively weak to overcome the stratification. The stratification would cause poor convective heat transfer because the frozen meat would be mostly surrounded by water at a lower temperature. The problem could be mitigated by changing the position of the water inlet from the top to the bottom as illustrated in Fig. 2. The enhanced thawing performance due to the elimination of the adverse stratification could be determined by transient CFD analysis. However, the transient CFD computation would be extremely expensive and thus impractical. Instead, a steady-state CFD analysis was conducted to study the stratification effects of the two water inlet configurations shown in Fig. 2. The value of Ts equal to 5 °C was arbitrarily selected within the typical operating temperature range between 18 °C and 24 °C. Although the steady-state convective heat transfer coefficient, h, was obtained based on constant Ts, its value would be comparable to the h value in the actual transient thawing process with varying Ts. It was because h under force convection
3. Computational fluid dynamics (CFD) analysis In cold water thawing, the convective heat transfer on the food surface can be expressed by q ¼ hðT s T 1 Þ;
ð1Þ
where q, h, Ts, and T1 are heat flux, convective heat transfer coefficient, mean food surface temperature, and bulk water temperature, respectively. A thermal-fluid analysis was conducted to study how the thermal property, h, could
Fig. 2. CFD models for study of thermal stratification effect.
M. Leung et al. / Journal of Food Engineering 78 (2007) 1221–1227
should mostly depend on the water flow which was steady. The buoyancy effect caused by the varying Ts would be less important. The dimensions and operating conditions shown in Fig. 2 were specially set to provide an approximate representation of an average subset of a full-scale cold water thawing device. The water overflow was modeled by a radial outlet located on the perimeter on the top of the cylinder. The concentric 3-D physical domain was set up in an axisymmetric coordinate system for computation. The CFD results are depicted in Fig. 3. With the water inlet located on top, the large temperature variation with cold water staying on the bottom clearly revealed the thermal stratification developed in the flow field. As the lower part of the meat gained heat from the low-temperature water, the overall convective heat transfer was low. The magnitude of stratification became worst if the inlet flow rate decreased. Relocating the water inlet on the bottom could result in a better mixed condition. Hence, the convective heat transfer was enhanced. Quantitatively, Eq. (1) was employed to calculate the convective heat transfer coefficient, h. The bulk water temperature, T1, and the average heat flux, q, on the food surface were easily obtained by the commercial software adopted (FLUENT 6.1). The built-in program functions were used to compute the average temperature of the water bath for T1 and integrate the heat flux over the spherical boundary for q. The values of T1 and q were substituted into in Eq. (1) with Ts equal to 5 °C to calculate the convective heat transfer coefficient, h. It was found that locating the water inlet on the bottom yielded a significant 33% increase in the h value from 1034 W m2 K1 to 1376 W m2 K1. 3.2. Convective heat transfer Based on the above findings, a simple but effective design was generated as shown in Fig. 4. The device consisted of a plastic water tank (270 mm diameter; 350 mm
Fig. 3. Comparison between steady-state temperature fields resulting from water inlet on top and bottom.
1223
Fig. 4. Design of cold water thawing device.
tall) and a stainless steel rack, plus minor modification for a water inlet on the bottom. All the items needed were commonly available in restaurant kitchens. During the operation, the frozen food is fully immersed in water and spread evenly at an upper position for uniform thawing. The design was sized to process about 2 kg of frozen food simultaneously. The capacity was suitable for practical applications in small to medium size restaurants. In order to characterize the cold water thawing device for setting appropriate operating parameters, CFD analysis was carried out for the configuration shown in Fig. 4 to determine how the convective heat transfer coefficient, h, varied with the apparent speed of water flow, defined as the ratio of volumetric inlet water flow rate to cross-sectional area of the tank. The results are presented in Fig. 5. The h values were used in the modeling of heat transfer by conduction as described in the following section.
Fig. 5. Convective heat transfer coefficient versus apparent speed of water flow.
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4. Heat transfer by conduction with moving phase-change interface In frozen food thawing, it is well recognized that the actual phase change does not occur at a single melting point, but rather over a temperature range (ASHRAE, 2002, Chap. 8; Miki & Hayakawa, 1996). This phenomenon can be explained by the fact that the concentration of undissolved solid in liquid water gradually decreases during the thawing process and thus the melting temperature increases correspondingly (Pham, 1987). Besides, the biological tissues are porous media in which the frozen microscopic pores are filled up with ice crystal. As a pore undergoes a melting process, the crystal–liquid equilibrium ruled by the Clausius–Clapeyron relationship contributes to the shift of the melting temperature (Coussy, 2005; Talamucci, 2003). The distribution of latent heat over the melting temperature range in frozen food thawing is a very complex issue depending on the composition of constituents and the pore size distribution in biological tissues. The phase change occurs over a temperature range below 0 °C but it is normally a narrow range within a few degrees centigrade (Anderson et al., 2004). For this reason, the phase-change behavior can be simplified to a single melting point model in the numerical analysis. Using the melting point of bulk water equal to 0 °C offers a conservative analysis to determine sufficient time taken for complete thawing. The food body temperature variation due to internal heat conduction was determined by FD method. The spherical body was discretized into 100 evenly-spaced nodes in the radial direction from the center to the surface. Conventional FD energy balance equations were formulated for the center node, internal nodes, and surface node. A negative generation term was added to each FD equation to take into account the latent heat absorption when the moving phase-change interface at the melting point traveled along the radial direction. The formulation of this generation term included the mean velocity of the moving interface between the time frames m and m + 1, vI ¼
rImþ1 rmI Dt
direction. As the phase-change interface was moving from the spherical surface towards the center, rImþ1 was smaller than rmI during the thawing process. The expression for GI shown in Eq. (3) was thus negative that represented a heat absorption for the food material changing phase from a frozen state to a thawed state. With the addition of Eq. (3) to conventional FD heat conduction formulas, the position of the phase-change interface at time frame m ðrmI Þ could be numerically found. Then, the speed of the moving interface at different time could be calculated by Eq. (2). One set of the modeling results simulating an experimental test is presented here to demonstrate the typical thawing behavior. A round piece of frozen pork initially at uniform 18 °C was suddenly immersed in the cold water thawing tank shown in Fig. 4. The material properties of the lean pork specimen and the operating conditions are given in Table 1. The numerical results in terms of time-dependent temperature profiles are plotted in Fig. 6. At the beginning, the specimen surface temperTable 1 Input values for illustrative modeling computation Pork specimen (lean) Density, q (kg m3) Thermal conductivity, k (W m1 K1) Heat capacity below melting point, CpjT<0 °C (J kg1 K1) Heat capacity above melting point, CpjT>0 °C (J kg1 K1) Latent heat, L (J kg1) Melting point (°C) Specimen diameter (mm) Initial temperature (°C)
1433a 0.69212b 2219b 3601b 241,904b 0 50 18
Cold water thawing operations Volumetric flow rate (L min1) Apparent speed of water flow (mm s1) Convective heat transfer coefficient, h (W m2 K1) Mean temperature of water inlet (°C)
0.5 0.15 819 20.4
a b
Obtained by measurements of the pork specimen. Refer to ASHRAE (2002, Chap. 8) for material properties of pork.
ð2Þ
and the amount of latent heat absorption, 8 3 3 4p > ðrmþ1 Þ ðrmI Þ qL 3 I > < AI vI qL ¼ ; for nth node Dt GI ¼ where T n drops below T L ; > > : 0; elsewhere, ð3Þ where rI was the radial coordinate of the moving phasechange interface; AI was the spherical shell area of the phase-change interface; interface area times the velocity, AIvI, was equal to the volumetric rate of phase change; q was the food density; L was the food latent heat; TL was the melting point; Dt was the time step; superscript m indicated the number of time frames; and subscript n indicated the nth node of the spatial domain discretized in the radial
Fig. 6. Numerical modeling results of cold water thawing of a round frozen pork of 50 mm diameter.
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Fig. 7. Movement of phase-change interface in terms of radial coordinate versus time.
ature, shown by the solid diamonds, quickly increased and approached the water temperature. On the other hand, the center temperature, shown by the empty squares, increased at a lower rate to about the melting point at 0 °C and stayed for an extended period as the inner body was undergoing phase transformation from a frozen state to a thawed state. Once the center temperature exceeded the melting point, the specimen was completely thawed. The thawing time period was 51 min long. Without any further absorption of latent heat, the subsequent center temperature increased rapidly. Eventually, the entire specimen body reached the equilibrium at the surrounding water temperature. These phenomena showed the considerable effect of the latent heat on the temperature field in a thawing process. The corresponding movement of the phase-change interface is shown in Fig. 7. The interface was initially formed on the surface after the specimen was immersed in the water flow for 0.03 min. The interface moved inwards and reached the center after 51 min when the specimen was completely thawed. 5. Empirical validation The numerical results presented in Section 4 were verified by experimental test results. In this experiment, lean pork was used for the specimen and the estimated mass composition data were 55.93% moisture, 27.8% protein, 8.32% fat, 0.3% carbohydrate, and 7.65% ash (ASHRAE, 2002, Chap. 8). The specimen was cut to a 50-mm sphere and weighed to determine its density. Two thermal couples were installed to measure the body temperature at the center and at a position 10 mm away from the center sideway. The initial condition was obtained by placing the specimen in a freezer to reach a uniform temperature of 18 °C. The specimen was then immersed in the cold water thawing tank shown in Fig. 4. The inlet water flow rate was regu-
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Fig. 8. Comparison between experimental measurements and numerical modeling results of cold water thawing of frozen pork.
lated at 0.5 L min1, equivalent to an apparent speed of 0.15 mm s1. The temperature measurements are plotted with the numerical modeling results in Fig. 8. A reasonable agreement was obtained. The discrepancy was probably due to the fact that the input thermal properties used in the modeling slightly deviated from the actual values. For instance, the frozen pork did not actually melt at a single melting point of 0 °C, but rather over a temperature range from 3 to 0 °C. For this reason, the middle segments of the measured temperature profiles near the melting point exhibited a minor slope, rather than a flat line as generated by the numerical model. Nevertheless, the assumption of constant properties yielded reasonable numerical prediction. The numerical modeling and experimental validation were also conducted for thawing of frozen chicken. Similar agreement was obtained. 6. Parametric study After the numerical model using CFD and FD methods was validated by experimental data, the model was used to perform a parametric study to search for control and operating parameters for proper use of cold water thawing. 6.1. Effect of water flow rate Firstly, the primary interest was to obtain the relationship between the thawing time and the water flow rate. For the same input values presented in Table 1 except the mean water inlet temperature changed to the yearly average of 24 °C in Hong Kong, the numerical modeling outputs are plotted in Fig. 9. As expected, an increase in the speed of water flow would increase the convective heat transfer coefficient and, thus, reduce the thawing time
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Fig. 10. Thawing time versus water inlet temperature in cold water thawing of frozen pork.
6.2. Effect of water inlet temperature
Fig. 9. Thawing time versus water flow rate in cold water thawing of frozen pork sized to different diameters: (a) 125 mm, (b) 50 mm, and (c) 25 mm.
period. However, up to certain apparent speed of water flow, i.e. 0.15 mm s1, an increase in the speed caused an insignificant reduction in the thawing time. For instance, as shown in Fig. 9b for thawing of a 50-mm pork specimen, an increase in the flow speed by 100% from 0.15 mm s1 (0.5 L min1) to 0.29 mm s1 (1 L min1) would shorten the thawing time by only 0.3 min, a 0.8% reduction. The reason was that at a high speed of water flow, the thermal resistance of the convective heat transfer mode was reduced to a magnitude much lower than that of the conductive heat transfer mode. In other words, conduction became the ‘‘bottle neck’’ in the overall heat transfer of the thawing process. Therefore, further enhancement in the convective heat transfer did not contribute significantly to the thawing performance. In consideration of the environmental and economical use of water, it is recommended that cold water thawing should be operating at a water flow of 0.15 mm s1 to achieve a nearly shortest thawing time period. For the cold water thawing device shown in Fig. 4, the equivalent volumetric flow rate is 0.5 L min1. In comparison with the typical flow rate about 5 L min1 that is commonly observed in restaurant kitchens, the estimated saving in water consumption is 90% and so are the cost savings in water consumption and waste water discharge.
The water inlet temperature is another parameter that affects the performance of cold water thawing significantly. An increase in water inlet temperature can increase both convective and conductive heat transfer modes. The numerical modeling results generated by different water inlet temperatures are presented in Fig. 10. The figure implies that the time taken for a complete cold water thawing process using tap water in the winter can be twice as much as that in the summer, depending on the local climatic conditions. One may make use of the information presented in Fig. 10 to determine the effect of using warm thawing water on the thawing rate. 7. Conclusions In this study, the fluid flow and heat transfer involved in cold water thawing were analyzed by numerical modeling using CFD and FD methods. The numerical results agreed reasonably well with the experimental measurements. Using the numerical model as a design tool, a simple cold water thawing device was designed to reduce the thermal stratification and, thus, improve the thawing efficiency. The recommended apparent speed of water flow was 0.15 mm s1 resulting in nearly the shortest thawing time. Any higher flow rate would only cause a marginal reduction in the thawing time because the conductive thermal resistance, rather than the convective thermal resistance, became the dominating factor in the overall heat transfer. One may implement the recommendations or refer to the numerical and experimental results presented in paper to improve the performance of cold water thawing method. Acknowledgments The work described in this paper was fully supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No.
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