Analysis of the Heat Transfer Performance of Vapor-Condenser during Vacuum Cooling

Transcription

1 Analysis of the Heat Transfer Performance of Vapor-Condenser during Vacuum Cooling Gailian. Li, Tingxiang Jin *, and Chunxia Hu School of Mechanical & Electricity engineering, Zhengzhou Uniersity of Light Industry, 5 Dong Feng Road, Zhengzhou 452, Henan Proince, P.R. China Tel.: txjin@126.com Abstract. The heat transfer performance of apor-condenser has been studied under different temperature of cold trap and different thickness of the ost layer in this paper. The relationship between dimensionless number Nu and Kn is obtained. The results show that the capturing efficiency of cold trap increases with the decrease of the surface temperature of apor-condenser. The ost accumulated on the surface of apor-condenser can cause the oerall heat transfer coefficient decrease, which has a negatie effect on heat transfer of aporcondenser. Kn has an effect on the heat transfer of apor-condenser during acuum cooling. Keywords: Heat transfer performance; Vapor-condenser; Cold trap; Vacuum cooling. 1 Introduction Vacuum cooling is a rapid eaporatie cooling method. Vacuum cooling has been successfully used to cool egetables and flowers since the 195s [1]. In the recent years, for the safety of foods, a rapid cooling treatment after cooking process should be used to minimize the growth of suriing organisms. Compared with the conentional cooling methods, acuum cooling has many adantages. Therefore, many researches hae highlighted the applications of acuum cooling for the cooked meats [2-4]. In addition, heat and mass transfer characteristics during acuum cooling hae been inestigated. Predictie models can proide much aluable information for the cooling process of large cooked meat joints under broad experimental conditions within a short time. Wang and Sun hae deeloped a mathematical model for describing the acuum cooling process of the large cooked meat joints [5-7]. A acuum cooler is a machine to maintain the defined acuum pressure in a sealed chamber, where the boiling of the water in the cooked meats occurs to produce the cooling effect. Theoretically, only the speed of acuum pump is high enough to produce the defined acuum pressure in the acuum chamber. Howeer, at a low pressure, the olume ratio of steam and water is ery large. For example, when the pressure is 173 Pa, the corresponding saturation temperature is 8, the specific * Corresponding author. D. Li, Y. Liu, and Y. Chen (Eds.): CCTA 21, Part I, IFIP AICT 344, pp , 211. IFIP International Federation for Information Processing 211

2 Analysis of the Heat Transfer Performance of Vapor-Condenser during Vacuum Cooling 239 Nomenclature Q Cold load of apor-condenser,w R Gas constant for water apor, hs Sublimation heat of ice, T The Kelin temperature, K m Mass flux, kg s ; 3 Specific olume, ; P Pressure, Pa J mol J kg K Pr Nu Prandtl number; Nusselt number; Kn Knudsen number; Greeks Thickness, m m kg Density kg m 3 The ratio of specific heat; D Gas constant, J mol K Thermal conductiity, J m K s t Time, s ; Stefan s constant, 5.7 W m K ; A Area, m 2 Emissiity; d Diameter, m ; Mean ee path of ee molecular, m ; 2 Heat transfer coefficient W m K Subscripts h o, h i Enthalpy J kg Frost layer 1 C p Specific heat at constant pressure, J kg K Vapor t Time, s ; i Inlet; Ft Thermal accommodation factor; o Outlet; F Tangential momentum accommodation factor c Coolant; m 3 kg olume is If the entire apor is eacuated only through the acuum pump, the speed of acuum pump should be ery large, many acuum pumps are required in the acuum cooler, which is obiously unsuitable. In order to remoe the large amount of water apor and keep the cooling cycle within a reasonable length of time, the apor-condenser is used to economically and practically handle the large olume of water apor by condensing the apor back to water and then draining it through the drain ale. The acuum pump and the apor-condenser in the acuum cooling system are used to remoe the water apor eaporated om the cooked meats. Generally, the temperature of the apor-condenser is about 3 ~-5 during acuum cooling. The large temperature difference exits between the surface of apor-condenser and the water apor in the acuum chamber. Consequently, the water apor will become the ost at the surface of apor-condenser. The ost formation on the cold surface below acts not only as a thermal insulator between the surface and the water apor, but also significantly reduces the heat transfer performance of apor-condenser, which can result in the decrease of the capability of capturing water apor in the apor-condenser. In order to improe the capturing efficiency of the apor-condenser, the eaporation temperature of reigerant in the acuum cooler must be lowered. Howeer, the lower eaporation temperature will add the cost of acuum cooler and energy consumption. Therefore, it is ery important to inestigate the heat transfer performance of apor-condenser for designing and optimizing the acuum cooling system. The phase change heat transfer theory under acuum pressure is hardly studied. Hong and Leena [8] hae modeled the ost characteristics under atmosphere pressure. In the current study, the heat transfer performance of apor-condenser in the acuum cooler is inestigated. Moreoer, the factors of affecting the heat transfer performance of apor-condenser are also analyzed.

3 24 G. Li, T. Jin, and C. Hu 2 Experimental Apparatus The laboratory-scale acuum cooler as shown in Fig. 1 was built by Shanghai Pudong Freezing Dryer Instruments Co. Ltd. (Shanghai, China). Vacuum cooler has four basic components: a acuum chamber, a acuum pump, a apor-condenser and a reigeration system. The apor-condenser is an eaporator in the reigeration system and a condenser capturing water apor eaporated om the cooked meats during acuum cooling. The cooling coil of apor-condenser is set up in a stainless cylindrical steel, which is enclosed with 3 mm thickness polyurethane foam to preent heat transfer. The stainless cylindrical steel with apor-condenser is defined as cold trap. The water apor is eaporated om the cooked meats during acuum cooling. The aporcondenser and acuum pump remoes the water apor and air to reduce the pressure in the acuum chamber. Because of the large temperature difference between the cold trap and the water apor, the large amount of water apor can enter into the cold trap. One part of water apor is condensed into water by liquefaction, and the other part of water apor become ost on the surface of apor-condenser by solidification. 1-bleeding ale; 2-weight sensor; 3-sample; 4-thermal couple; 5-pressure sensor; 6-acuum chamber; 7-electronic balance; 8-compute; 9-temperature controller; 1-coolant outlet; 11- coolant inlet; 12-cold trap; 13-acuum pump; 14-pressure controller; 15-I-718P module Fig. 1. Schematic diagram of the acuum cooler system A set of T-type copper-constantan thermocouples with an accuracy of ±.1 are used to record the temperature of the cold trap. The mass flux of coolant is measured through supersonic flowmeter (UFLO2P, USA). The acuum pressure is measured through the pressure transducer (CPCA-13Z) with an accuracy of ±.5 Pa, the range of pressure transducer is 1 Pa~1 Kpa. The mass of the sample and water are measured through the electric balance (JA122, made in China). Thermal conductiity of

4 Analysis of the Heat Transfer Performance of Vapor-Condenser during Vacuum Cooling 241 ost layer is measured by an unsteady state method using a line heat thermal conductiity probe, based on the design of Sweat as described by Scully [13, 14]. The thickness of ost layer is directly determined by a micrometer haing a.1mm resolution. 3 Theoretical Analysis of Heat Transfer in Cold Trap 3.1 The Formation Mechanism of the Frost on the Surface of Vapor-Condenser Fig. 2 shows the formation process of ost. The sensible heat is transferred om the water apor in the cold trap to the ost surface by the temperature difference driing Sensible heat transfer Latent heat transfer Frost surface Heat transfer by conduction Frost layer Phase change Water apor diffusion Vapor- condenser!!surface Fig. 2. The formation process of the ost Fig. 3. Ice crystal shape (1) Plate-like forms: (a) plate, (b) simple sectored plate, (c) dendritic sectored plate, (d) fern-like stellar dendrite; (2) Column-like forms: (e) needle crystal, (f) hollow column, or sheath-like crystal

5 242 G. Li, T. Jin, and C. Hu force between the water apor and the ost surface. Some of the transferred moisture deposits on the ost layer, causing the ost layer to grow. The remainder diffuses into the ost layer. The heat of sublimation caused by the phase change of the added ost layer is transferred through the ost layer. The latent heat and sensible heat transferred om the water apor are then transferred through the ost layer by conduction. The water apor diffusing into the ost layer changes phase within the ost layer. The ost density increases as a result of this process. The ost layer is a porous medium composed of ice crystal and air. The ice crystal has different shapes during the formation of the ost layer. Ice crystal shapes are classified into main forms: plate-like forms and column-like forms. The microscopic structure of ice crystal is shown as in Fig. 3 [9]. During the formation of the ost, the mass flux through water apor diffusing into the ost layer can be calculated by the Clapeyron-Clausius equation. The expression is as follows [1]: m& = h s + λ RT D 2 ( Q ice ρ f r ) 1+ ρice ρ.5 [ ] r h f s P ( ice ) 1 ρice Where Q is the reigeration load of apor-condenser; [11]: h s is the sublimation heat of ice; R is the gas constant; T is the surface temperature of the ost layer; and ice are respectiely specific olume of water apor and ice; ρ and ρ ice are respectiely density of ost layer and ice; f r P is the partial pressure of water apor; D is the diffusiity of water apor; λ is the thermal conductiity of the ost layer, the expression is as follows λ ρ ρ ρ f r = (2) The density of ost can change during the formation of ost. as: dρ f m& f r d dρ r r f = dt 2r 4 dt dr r (1) can be expressed (3)

6 Analysis of the Heat Transfer Performance of Vapor-Condenser during Vacuum Cooling Heat Transfer in Cold Trap The temperature of cold trap is about 3 ~ 6. The water apor eaporated om the cooked meats will become the ost at the surface of apor-condenser in the cold trap. The ost layer at the surface of apor-condenser gets thicker and thicker with the increment of time. The ost layer is a porous structure composed of ice crystal and air pores. Moreoer, the porous structure contains a low thermal conductiity, which reduces the thermal conductiity of the ost layer. Finally, the ost layer results in a significant heat transfer resistance om the water apor to the surface of apor-condenser in the cold trap. The relationship between the heat flux and the thickness of the ost layer can be expressed: Where ΔT q = λ f (4) r δ λ is the thermal conductiity of the ost layer; δ is the thickness of the ost layer. Heat transfer coefficient, k is an important index to ealuate the heat transfer performance. Heat transfer coefficient of cold trap is measured by the qusai-stable method in this experiment. The total heat transfer coefficient is expressed as follows: k Q = A ΔT m Where A is the total area of heat transfer; the logarithmic temperature difference, Δ T m, can be expressed as: ΔT m Ti To = Ti Te ln To Te Where T e is the eaporation temperature. On the other hand, the total heat transfer coefficient is also theoretically determined by: 1 k = 1 α + δ λ + 1 α Where α is the heat transfer coefficient of apor in cold trap; α c the heat transfer coefficient of coolant in coil of apor-condenser; d 1 and d 2 are respectiely inner and outer diameters. The reigeration load of apor-condenser, Q, in Eq. (1) and Eq. (5) can be calculated by the enthalpy difference of reigerant between inlet and outlet. c d 1 d 2 (5) (6) (7)

7 244 G. Li, T. Jin, and C. Hu Q = m& ( h h ) c o i (8) Where m& c is the mass flux of reigerant; h o, h i is respectiely the enthalpy of reigerant in outlet and inlet. Q is also calculated through heat transfer of gas in cold trap. The expression can be gien by: Q ( ) ( ) Tml T 4 4 α A T T + εa T T + m& f C pf dt + C p dt + h r r s (9) T Tml = σ Where C pf, r C p is the specific heat of the ost and water apor; T is the gas T is the sublimation temperature. temperature in cold trap; ml The acuum pump and apor-condenser can cause the reduction of pressure in cold trap. When the gases in cold trap are at low pressure, the slip flow occurs. The relatie importance of effects due to the rarefaction of a gas in cold trap can be indicated by Knudsen number ( Kn ), a ration of the magnitude of the mean ee molecular path ( λ ) in the gas to the characteristic dimension ( L ) in the flow field. When the slip flow occurs in the cold trap, the gas adjacent to the surface no longer reaches the elocity or temperature of the surface. The gas at the surface of the ost has a tangential elocity and it slips along the surface. The temperature of the gas at the surface of the ost is finitely different om the surface temperature of the ost layer, and there is a jump in temperature between the surface of the ost layer and the adjacent gas. The energy and momentum equations in cylindrical coordinates can be written as [12]: T u x = λ 1 ρc r p T r r r P 1 u = r x r r r (1) μ (11) The slip elocity as a function of the elocity gradient near the wall of cold trap can be expressed as: F 2 u ur= r = λ (12) F r r= r The temperature jump in slip flow at the wall of cold trap can be written as: T T w Ft 2 2γ λ T = F γ + 1 Pr r t r= r (13)

8 Analysis of the Heat Transfer Performance of Vapor-Condenser during Vacuum Cooling 245 Where λ is mean ee path of water apor; F is the tangential momentum accommodation factor; F is the thermal accommodation factor; γ is the ratio of specific t heat; Pr is the Prandtl number; r is the radius of cold trap. The Nusselt number can be gien om Eq. (1) and (11): 48 Nu = 2 36Kn 6Kn 2 Ft Kn 1+ 6Kn F 4 Result and Discussion t 2 λ 1 γ + 1 Pr r 4.1 The Influence of the Frost Layer on Heat Transfer in Cold Trap γ (14) Fig. 4 shows the experimental data for the thermal conductiity of the ost. The time ranges, for which the data were taken, are gien on Fig. 4. When the experimental temperature of cold trap is 45, the aerage thermal conductiity of the ost layer 1 1 during acuum cooling is.172w m K. It can be also found om Fig. 4 that the thermal conductiity of the ost layer increases with the increment of time. This is because the density and the thickness of the ost layer depend on the temperature of the ost and the time. The lower temperature, the more water apor in cold trap becomes the ost on the surface of apor-condenser and diffuses into the ost layer, which can increase the density and the thickness of the ost layer. The relationship between the thermal conductiity of the ost layer and the density of the ost layer has been shown in Eq. (2). Fig. 4. Thermal conductiity of the ost layer

9 246 G. Li, T. Jin, and C. Hu Fig. 5 shows the heat transfer coefficient in different thickness of the ost layer. When the thickness of the ost layer is 1 mm, the heat transfer coefficient is about W m K. The heat transfer coefficient is 3.3 W m K at 5 mm thickness of the ost layer. Which means that the heat transfer resistance increases when the ost layer gets thick. The results show that the experimental data match with Eq. (7). Fig. 5. The influence of thickness of the ost layer on the heat transfer coefficient 4.2 The Influence of Temperature of Cold Trap on the Capturing Efficiency The capturing efficiency of cold trap can be defined as follows: M = M pw tw 1% η (15) Where M pw is the total captured practical amount of the ost by solidify and water by condensation in cold trap; M tw is the captured theoretical amount of the ost by solidify and water by condensation in cold trap. Fig. 6 shows the capturing efficiency of cold trap in different temperature of cold trap. It can be found that the lower temperature of cold trap is, the higher the capturing efficiency of cold trap is. When the temperature of cold trap is about -55,the capturing efficiency of cold trap is aboe 9%. Howeer, if the temperature of cold trap decreases to -4, the capturing efficiency of cold trap is about 2%. Therefore, the temperature of cold trap should be ery low so that the cold trap can capture more water apor. On the other hand, if the temperature of cold trap is too low, some water apors become the ost on the surface of apor-condenser and on the wall of cold

10 Analysis of the Heat Transfer Performance of Vapor-Condenser during Vacuum Cooling 247 trap, the thick ost layer has the low thermal conductiity. Which increases the heat transfer resistance between the surface of apor-condenser and the water apor. With the increment of thickness and density of the ost layer, the heat transfer resistance between the surface of apor-condenser and the water apor increases, the temperature of cold trap become high so that the capturing efficiency of cold trap gets more and more low. Fig. 6. The influence of temperature of cold trap on the capture efficiency Fig. 7. The relationship between Nu and Kn

11 248 G. Li, T. Jin, and C. Hu 4.3 The Influence of Vacuum Pressure on Heat Transfer in Cold Trap It is assumed that the gas in cold trap is diatomic. The ratio of specific heat of diatomic (γ ) is 1.4. The relationship between Nu and Kn can be gien in Eq. (14). Fig. 7 gies the ariation between Nu and Kn in the different thermal accommodation factor. Kn is correlated with the acuum pressure. It can be found that Nu decreases when the acuum pressure in cold trap decreases. This is because conection heat can reduce at low acuum pressure. Nu at the high thermal accommodation factor (1.) is higher than that at the low thermal accommodation factor (.8). The ariation of Nu is opposite to the ariation of Kn. 5 Conclusion The heat transfer performance of apor-condenser has been studied in different temperature of cold trap and different thickness of the ost layer in this paper. The lower the temperature of cold trap is, the more water apor is captured. At the same time, because of the low temperature in cold trap, water apor become ost at the surface of apor-condenser and on the wall of cold trap. The ost layer is a porous medium composed of ice crystal and air. The low thermal conductiity of the ost layer has a negatie effect on heat transfer of apor-condenser. When the accumulated ost at the surface of apor-condenser becomes thick, the capturing efficiency of cold trap will decrease. In addition, the relationship between dimensionless number Nu and Kn is obtained, the ariation of Nu is opposite to the ariation of Kn. Acknowledgements Funding for this research was proided by Henan Proincial Department of Education (P. R. China). References 1. Briley, G.C.: Vacuum cooling of egetables and flowers. Ashrae Journal 46(4), (24) 2. McDonald, K., Sun, D.-W., Kenny, T.: The effect of injection leel on the quality of a rapid acuum cooled cooked beef product. Journal of Food Engineering 47, (21) 3. Burfoot, D., Self, K.P., Hudson, W.R., Wilkins, T.J., James, S.J.: Effect of cooking and cooling method on the processing times, mass losses and bacterial condition of large meat joints. International Journal of Food Science and Technology 25, (199) 4. Desmond, E.M., Kenny, T.A., Ward, P., Sun, D.-W.: Effect of rapid and conentional cooling methods on the quality of cooked ham joints. Meat Science 56, (2) 5. Wang, L., Sun, D.-W.: Modelling acuum cooling process of cooked meat part 1: analysis of acuum cooling system. International Journal of Reigeration 25, (22)

12 Analysis of the Heat Transfer Performance of Vapor-Condenser during Vacuum Cooling Wang, L., Sun, D.-W.: Modelling acuum cooling process of cooked meat part 2: mass and heat transfer of cooked meat under acuum pressure. International Journal of Reigeration 25, (22) 7. Wang, L., Sun, D.-W.: Effect of operating conditions of a acuum cooler on cooling performance for large cooked meat joints. Journal of Food Engineering 61, (24) 8. Chen, H., Thomas, L., Besant, R.W.: Modeling ost characteristics on heat exchanger fins: Parts I, Numerical Model. ASHRAE Transactions, (2) 9. Na, B., Webb, R.L.: New model for ost growth rate. International Journal of Heat and Mass Transfer 47, (24) 1. Kondepudi, S.N., O Neal, D.L.: Performance of finned tube heat exchangers under osting conditions. International Journal of Reigeration 16(3), (1993) 11. Yonko, J.D., Sepsy, C.F.: An inestigation of the thermal conductiity of ost while forming on a flat horizontal plate. ASHRAE Trans. 73(2), (1967) 12. Barron, R.F., Wang, X.M., Ameel, T.A., et al.: The graetz problem extended to slip - flow. Int. J. Heat Mass Transfer 4(8), (1997) 13. Sweat, V.E.: Thermal properties of foods. In: Rao, M.A., Rizi, S.H. (eds.) Engineering Properties of Foods, pp Marcel Dekker, New York (1986) 14. Scully, M.M.: The influence of compositional changes in beef burgers and mashed potatoes on their temperatures following microwae heating and their thermal and dielectric properties. MSc Thesis, Uniersity College Dublin, Ireland (1998)