- Email: [email protected]
mass transfer in LiBr–H2O solution flowing over a cooled horizontal tube
International Communications in Heat and Mass Transfer 32 (2005) 445 – 453 www.elsevier.com/locate/ichmt
Experimental study of film flow and heat/mass transfer in LiBr–H2O solution flowing over a cooled horizontal tubeB S.S. Seol*, S.Y. Lee Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Science Town, Daejeon 305-701, Republic of Korea
Abstract Heat and mass transfer characteristics of thin-film flow of LiBr–H2O solution over a single horizontal tube were examined experimentally and a useful set of the measured data were provided. Variables were the flow rate and temperature of the solution, absorber pressure, and the drainage pattern. The liquid film appeared wavy as the absorption rate became large; this could be achieved by decreasing the flow rate and the temperature of the solution and/or by increasing the absorber pressure. Absorption rate strongly depended on the absorber pressure when the solution flow rate was small, while on the solution temperature as the flow rate became large. The absorption performance was higher with the sheet-flow drainage for small flow rates; however, the reverse was true when the flow rate was increased. D 2004 Elsevier Ltd. All rights reserved. Keywords: Absorption; LiBr–H2O solution; Heat and mass transfer; Drainage patterns
1. Introduction The absorption refrigeration system is becoming more popular as one of the air-conditioning equipment since it is known to be the energy-saving and environment-friendly system. The efficiency of absorption refrigeration system depends strongly on the performance of the absorber, which is the most important component. However, due to the complexity of the heat and mass transfer behavior of the solution flow inside the absorber, the performance of the system is yet to be predicted accurately. B
Communicated by J.P. Hartnett and W.J. Minkowycz. * Corresponding author. Tel.: +82 42 869 3066; fax: +82 42 869 8207. E-mail address: [email protected] (S.S. Seol).
0735-1933/$ - see front matter D 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2004.07.007
446
S.S. Seol, S.Y. Lee / Int. Commun. Heat and Mass Tranf. 32 (2005) 445–453
To cover a large refrigerating capacity, the shell-and-tube type absorbers are widely adopted. The solution is sprayed at the top of the tube bank consisting of the horizontal cooling tubes and absorbs the water vapor as it flows down to the bottom of absorber. In order to predict the absorber performance, it is essential to understand the heat and mass transfer characteristics of the solution film flowing over a single horizontal tube. Many numerical models of heat and mass transfer in falling film absorption have been studied [1]. For a horizontal tube, the distributions of velocity, temperature, and concentration in the liquid film can be estimated through numerical analyses. Andberg et al. [2], Morioka and Kiyota [3], and Choudhury et al. [4] predicted the absorption efficiency with various numerical models. Also, for a system with multiple rows of tubes, Kirby and Perez-Blanco [5] performed a numerical study to predict the absorption efficiency. However, most of the numerical studies are based on the liquid film flowing over a single horizontal tube and the assumption of laminar flow with a flat interface of the liquid film, which seems rather ideal. In other words, there is few theoretical modeling and experimental data for the laminar-wavy regime, despite such a regime is prevailing in the range of the practical usage. Though there are experimental reports [6–9] on the absorption characteristics of horizontal tubes, most of them are on the overall absorption performance of the flows in tube-bundle assemblies, and the separate effect of each parameter cannot be deduced. It is also difficult to identify the flow pattern of liquid film, and the characteristics of heat and mass transfer. To evaluate the absorber performance precisely, therefore, it is essential to examine flow patterns associated with the heat and mass transfer characteristics of the flow over a single horizontal tube. In the present study, the separate effect of each parameter has been investigated for a single horizontal tube to provide quantitative data covering the ranges of practical operations.
2. Experimental apparatus and method Fig. 1 shows the details of the test chamber. Here, water vapor is the refrigerant and the LiBr–H2O solution is the absorbent. A concentrated solution was supplied through the nozzle array installed at the top of the test section. At the same time, the water vapor(steam) was supplied to the test section through a pair of tubes. Inside the test section, the concentrated solution discharged from the nozzle array flowed
Fig. 1. Test chamber.
S.S. Seol, S.Y. Lee / Int. Commun. Heat and Mass Tranf. 32 (2005) 445–453
447
Table 1 Range and uncertainty of parameters Parameter Qs X s,i Ts,i Tc,i pA
Range
Experimental error 6
6
3.3310 8.3310 60, 62 wt.% 32–50 8C 32–508C 0.53–1.33 kPa
3 1
ms
9
3 1
F6610 m s F0.1 wt.% F0.2 8C F0.2 8C F13.2 Pa
Uncertainty F1.13% F0.17% F0.05% F0.05% F1.43%
over a cooled horizontal tube(test tube) and absorbed the water vapor to be diluted as it flowed down. The outer and inner diameters of the cooled horizontal tube were 19.05 mm and 16.6 mm, respectively. Temperatures of the LiBr–H2O solution at the top (Ts,i) and the bottom (Ts,o) of the horizontal test tube and the chamber pressure(absorber pressure, p A) were measured. In measuring Ts,o, the temperatures at three different points along the bottom line were averaged. To evaluate the heat removal rate by the cooling water, inlet and outlet temperatures of the cooling water were measured. Ktype thermocouples were used to measure the temperature. The chamber was measured by using a Utype mercury vacuum manometer and an absolute barometer. When the water dissolved in the solution evaporates, instead of absorption, the absorber pressure was maintained to prescribed values by using an auxiliary cooler and a solution-spraying device that can continuously exhaust the water vapor from the test chamber. The experimental parameters and their ranges are listed in Table 1. The separate effects of each parameter on the absorption performance were carefully examined. Since the absorption rate of the refrigerant was not directly available, it was deduced from the solution temperatures at the top and the bottom of the tube. Fig. 2 shows the control volume of the liquid–film flow around the test tube to
Fig. 2. Absorption at liquid film flowing over a cooled horizontal tube.
448
S.S. Seol, S.Y. Lee / Int. Commun. Heat and Mass Tranf. 32 (2005) 445–453
analyze the heat and mass balance. The balance relations and the equation of state for the flow of the LiBr–H2O solution are as follows. Wi þ WR ¼ Wo
ð1Þ
Xi Wi ¼ Xo Wo
ð2Þ
ii Wi þ iR WR ¼ io Wo þ qcWAo
ð3Þ
io ¼ io ðTo ; Xo Þ
ð4Þ
From Eqs. (1)–(4), four unknowns(X o, Wo, i o, and W R) can be obtained by the iteration method since all the other quantities are given. The property values of LiBr–H2O solution are taken from the numerical data by Patterson and Perez-Blanco [10]. The heat removal by the test tube can be estimated by measuring the temperature rise of the cooling water as follows. ð5Þ qcW ¼ Wc cp;c Tc;o Tc;i =Ao The heat transfer coefficient inside the test tube(h i) can be obtained by condensing the steam at the external surface of the test tube with the flow rate and the temperature of the cooling water being the same as the absorption test. The values of h i were 3200F50 Wm2K1 and 700F20 Wm2K1 with and without a heat-transfer augmentation device inside the tube, respectively.
3. Results and discussions 3.1. Behavior of film flow The heat and mass transfer characteristics are determined by the inlet conditions of the refrigerant and the solution to the absorber, and also by the shape of the solution film at the exterior of the cooled tube, dependent on the drainage pattern of upper tube [11]. Mostly the solution is introduced to the top portion of the upper tube through an array of nozzles, and flows down along the external surface. When the solution flow rate is small, dripping flow occurs at the bottom part of the tube due to the surface tension. As the solution flow rate increases, the liquid columns are formed at the bottom of the tube. If the flow rate is kept increasing, the drainage pattern converts to the sheet flow. Most of the previous numerical results were based on the assumption of the sheet-flow drainage. Hence, to provide the reference data satisfying this assumption, the sheet-flow drainage pattern was intentionally induced by placing a thin, vertical plate just below the test tube as shown in Fig. 2. Also, the measured results were compared with the case of the jet(liquid column)-flow drainage. Fig. 3 shows the variation of the flow pattern of the LiBr–H2O solution with and without absorption for the case of the sheet-flow drainage. For reference, the nozzle array and the horizontal tube in the absence of the liquid flow are shown in Fig. 3(a). When there is no vapor absorption, Fig. 3(b), the solution flowed down along the external surface with a flat interface. Once the vapor absorption began, the absorption rate became larger as the absorber pressure increased, and waves were formed at the film surface as shown in Fig. 3(c). Further increase of the absorber pressure caused a larger disturbance on the film flow; and often, as shown in Fig. 3(d), the liquid film was partly ruptured to form the dry spots
S.S. Seol, S.Y. Lee / Int. Commun. Heat and Mass Tranf. 32 (2005) 445–453
449
Fig. 3. Photographs of solution film flowing over a cooled horizontal tube ( Q s=3.33106 m3/s, Ts,i=32 8C, X s,i=62 wt.%, Tc,i=26 8C, h i=3200 Wm2K1, Sheet drainage). (a) Without solution; (b) Without absorption; (c) p A=1.07 kPa; (d) p A=1.33 kPa.
intermittently. It should be emphasized that the formation of the waves was not by the increase of the solution flow rate but by the active vapor absorption at the interface. Fig. 4(a) shows the change of the heat flux removed by the cooling water( qUc) with the solution inlet temperature for the sheet drainage. In the same figure, the operation region of the surface wave formation is shown. Waves are formed when the solution temperature is low and/or the absorber pressure is high. In the range without surface wave formation, the dependence of the heat removal rate on the solution inlet temperature appears almost linear; however, in the wave formation range, the trend largely deviates from the linearity and results in the higher rate of heat removal. The lines in Fig. 4(b) indicate the wave formation boundaries for different solution flow rates. Left-hand sides of the lines are the regions of the wave formation. The surface waves are more apt to occur with the smaller flow rate.
Fig. 4. Effect of wave formation (X s,i=60 wt.%, Tc,i=32 8C, h i=3200 Wm2K1, Sheet drainage). (a) Cooling heat flux, Q s=3.33106 [m3s1]; (b) Region of wave formation.
450
S.S. Seol, S.Y. Lee / Int. Commun. Heat and Mass Tranf. 32 (2005) 445–453
Table 2 shows a selected set of the experimental data for the sheet drainage in the practical operation ranges of the absorption refrigeration systems. 3.2. Effect of sprayed solution temperature The heat and mass transfer performances of an absorber are determined by the inlet conditions of the water vapor(refrigerant) and the solution to the test chamber. Figs. 5 and 6 show the solution temperature at the test chamber outlet and absorption rate per unit surface area(W R/A o), respectively, for various inlet temperatures and flow rates of the solution with the jet-flow drainage. The lines in those figures are the curve-fitted results of the measured data using the least square method based on the quadratic function. As shown in Fig. 5, the outlet temperature of the solution increases almost linearly with the solution inlet temperature except for the cases of small solution flow rates with high absorber pressures. The data points in Fig. 6 are deduced from the tube outlet temperature and the flux of heat removal. The positive values indicate absorption of the water vapor while the negative values imply evaporation. For a given value of the cooling water temperature(Tc,i), the heat removal rate increases with the increase of the solution inlet temperature. However, when the saturation pressure of the solution corresponding to the temperature and concentration at the absorber inlet becomes higher than absorber pressure, evaporation takes place instead of absorption. Absorber performance is enhanced with the lower solution temperature. Table 2 Experimental data ( Q s=3.33106 m3/s, Q c=5.56106 m3/s, X s,i=60 wt.%, h i=3200 Wm2K1, sheet drainage) p A [kPa]
Tc,i [8C]
Tc,o [8C]
Ts,i [8C]
Ts,o [8C]
p A [kPa]
Tc,i [8C]
Tc,o [8C]
Ts,i [8C]
Ts,o [8C]
0.53 0.53 0.53 0.67 0.67 0.67 0.67 0.67 0.67 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.93 0.93 0.93 0.93 0.93 0.93 0.93
32.0 32.0 32.0 31.9 32.0 32.0 31.9 32.0 32.0 32.0 32.1 32.0 32.0 32.0 32.0 32.0 31.9 32.0 32.0 32.0 32.0 32.0 32.0 32.0
32.2 32.6 32.8 32.4 32.8 33.0 33.1 33.4 33.6 32.8 33.0 33.1 33.3 33.6 33.8 34.0 34.1 33.2 33.2 33.3 33.5 33.7 33.9 34.1
32.6 35.7 38.2 32.6 35.8 38.2 40.0 42.4 44.7 32.6 35.8 38.2 39.9 42.5 44.7 46.8 49.3 32.6 35.9 38.4 40.0 42.5 44.7 46.9
33.5 34.1 34.6 34.7 35.4 35.8 36.1 36.7 37.3 36.1 36.4 36.8 37.3 37.8 38.3 38.7 39.3 37.2 37.6 37.7 38.0 38.6 39.0 39.7
1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.20 1.20 1.20 1.20 1.20 1.20 1.20 1.20 1.33 1.33 1.33 1.33 1.33 1.33 1.33 1.33
32.0 32.1 32.0 32.0 32.1 32.1 32.0 32.0 32.0 32.0 32.0 32.0 32.1 32.0 32.0 32.0 32.0 32.1 32.0 32.0 32.1 32.1 32.1 31.9
33.6 33.6 33.5 33.6 33.9 34.1 34.2 34.4 33.9 33.8 33.8 33.8 34.0 34.1 34.3 34.5 34.2 34.2 34.0 34.0 34.2 34.3 34.5 34.5
32.5 35.8 38.5 40.1 42.5 44.7 47.0 49.2 32.5 35.8 38.4 40.0 42.5 44.7 47.0 49.4 32.6 35.7 38.5 40.1 42.4 44.7 47.1 49.5
38.7 38.6 38.8 39.1 39.4 39.9 40.2 41.2 39.8 39.8 39.7 39.8 40.0 40.4 41.0 42.0 40.9 41.0 40.6 40.7 40.7 41.0 41.6 42.6
S.S. Seol, S.Y. Lee / Int. Commun. Heat and Mass Tranf. 32 (2005) 445–453
451
Fig. 5. Variation of solution outlet temperature with solution inlet temperature (X s,i=60 wt.%, Tc,i=32 8C, h i=700 Wm2K1, Jet drainage). (a) Q s=3.33106 [m3s1]; (b) Q s=6.67106 [m3s1].
3.3. Effect of absorber pressure The temperature and the refrigerant concentration at the free surface(the interface between the water vapor and the solution) increase as the absorber pressure is increased. Accordingly, the solution outlet temperature and the absorption rate increase altogether(Figs. 5 and 6). As shown in Fig. 5, the solution temperature tends to be higher at the outlet than at the inlet as the absorber pressure is raised. This means that the rate of heat absorption becomes greater than the rate of heat removal by the cooling water. Dependence of the solution outlet temperature and the heat removal rate on the absorber pressure appears large for the smaller flow rate. However, with the increase of the solution flow rate, those become less sensitive to the absorber pressure but strongly depend on the inlet solution temperature. Thus, the increasing trend of the solution outlet temperature is getting close to the diagonal lines of Fig. 5. Also the effect of the absorber pressure is more dominant with the lower temperature at the solution inlet and the waves are more likely to occur at the film surface, as evidenced in Fig. 4(a).
Fig. 6. Variation of absorption rate with solution inlet temperature (X s,i=60 wt.%, Tc,i=32 8C, h i=700 Wm2K1, Jet drainage).
452
S.S. Seol, S.Y. Lee / Int. Commun. Heat and Mass Tranf. 32 (2005) 445–453
Fig. 7. Variation of absorption rate with solution inlet temperature (X s,i=60 wt.%, Tc,i=32 8C, h i=700 Wm2K1, lines: Jet drainage, symbols: Sheet drainage). (a) Q s=3.33106 [m3s1]; (b) Q s=6.67106 [m3s1].
3.4. Effect of drainage pattern Fig. 7 shows the change of the absorption rate with the solution inlet temperature for different drainage patterns. In the figure, the lines and the symbols indicate the cases of jet-flow and the sheetflow drainage, respectively. Note that the lines are the same ones already plotted in Fig. 6. For low solution flow rates, a thick film at the bottom part of the horizontal tube forms jets intermittently, either spacewise or timewise. However, the solution at the bottom of the tube flows down immediately along the plate when the vertical plate is installed beneath the test tube. This stabilizes the solution film and covers the entire tube surface with a uniform thickness. Accordingly, the film becomes thinner, and the heat and mass transfer resistance across the liquid film decreases. Therefore, the absorption performance with the sheet-flow drainage appears higher compared to the case with the jetflow drainage, as shown in Fig. 7(a). However, when the solution flow rate becomes high, the locations of jet formation at the bottom of the tube move along the axial direction rather irregularly with increase in number, which enhances mixing effect; thus the absorption performance increases. Hence, the absorption performance becomes higher with the jet-flow drainage than with the sheet-flow drainage at the high flow rate condition as evidenced by Fig. 7(b).
4. Conclusions In this study, the film flow and the heat/mass transfer characteristics of LiBr–H2O solution flowing over a cooled horizontal test tube were investigated experimentally. The conclusions were made as follows. (1) For low solution temperature and high absorber pressure, absorption performance increases due to the wave formation at the free surface of the solution film. The wave formation occurs in wider ranges of the solution inlet temperature and the absorber pressure as the solution flow rate decreases.
S.S. Seol, S.Y. Lee / Int. Commun. Heat and Mass Tranf. 32 (2005) 445–453
453
(2) The solution outlet temperature is largely affected by the absorber pressure when the solution flow rate is small, but by the solution inlet temperature for the high flow rate condition. (3) The absorption performance with the sheet-flow drainage appears larger than that with the jet-flow drainage when the solution flow rate is small. However, the reverse is true for the high solution flow rate. Nomenclature A Area (m2) Specific heat (J kg1K1) cp h Heat transfer coefficient (Wm2K1) i Specific enthalpy (J kg1) P Pressure (kPa) Q Volumetric flow rate (m3s1) qU Heat flux (Wm2) T Temperature (8C) W Mass flow rate (kg s1) X Concentration of LiBr–H2O solution (wt.%) Subscripts A Absorber c Cooling water i Inside, inlet o Outside, outlet R Refrigerant s LiBr–H2O solution Acknowledgement This work was supported by Korea Advanced Institute Science and Technology (KAIST) and also by the Brain Korea 21 Project. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
J.D. Killion, S. Garimella, Int. J. Refrig. 24 (2001) 755. J.W. Andberg, G.C. Vliet, ASHRAE Trans. 93 (1987) 2454. I. Morioka, M. Kiyota, JSME Int. J., Ser. 2 34 (2) (1991) 183. S. Choudhury, D. Hisajima, T. Ohuchi, A. Nishiguchi, T. Fukushima, S. Sakaguchi, ASHRAE Trans. 99 (2) (1993) 81. M.J. Kirby, H. Perez-Blanco, Heat Pump Refrig. Syst. Des. 32 (1994) 1. G.C. Vliet, F.B. Cosenza, Proc. Absorption Heat Pump Conference (1991) 53. T. Nomura, N. Nishimura, S. Wei, S. Yamaguchi. Int. Absorption Heat Pump Conf. 31 (1993) 203. V.M.S. Frances, J.M.P. Ojer, Int. J. Heat Mass Transfer 46 (2003) 3299. J.K. Kim, C.W. Park, Y.T. Kang, Int. J. Refrig. 26 (2003) 575. M.R. Patterson, H. Perez-Blanco, ASHRAE Trans. 94 (1989) 2059. X. Hu, A.M. Jacobi, Exp. Therm. Fluid Sci. 16 (1998) 322.
Experimental study of film flow and heat/mass transfer in LiBr–H2O solution flowing over a cooled horizontal tubeB S.S. Seol*, S.Y. Lee Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Science Town, Daejeon 305-701, Republic of Korea
Abstract Heat and mass transfer characteristics of thin-film flow of LiBr–H2O solution over a single horizontal tube were examined experimentally and a useful set of the measured data were provided. Variables were the flow rate and temperature of the solution, absorber pressure, and the drainage pattern. The liquid film appeared wavy as the absorption rate became large; this could be achieved by decreasing the flow rate and the temperature of the solution and/or by increasing the absorber pressure. Absorption rate strongly depended on the absorber pressure when the solution flow rate was small, while on the solution temperature as the flow rate became large. The absorption performance was higher with the sheet-flow drainage for small flow rates; however, the reverse was true when the flow rate was increased. D 2004 Elsevier Ltd. All rights reserved. Keywords: Absorption; LiBr–H2O solution; Heat and mass transfer; Drainage patterns
1. Introduction The absorption refrigeration system is becoming more popular as one of the air-conditioning equipment since it is known to be the energy-saving and environment-friendly system. The efficiency of absorption refrigeration system depends strongly on the performance of the absorber, which is the most important component. However, due to the complexity of the heat and mass transfer behavior of the solution flow inside the absorber, the performance of the system is yet to be predicted accurately. B
Communicated by J.P. Hartnett and W.J. Minkowycz. * Corresponding author. Tel.: +82 42 869 3066; fax: +82 42 869 8207. E-mail address: [email protected] (S.S. Seol).
0735-1933/$ - see front matter D 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2004.07.007
446
S.S. Seol, S.Y. Lee / Int. Commun. Heat and Mass Tranf. 32 (2005) 445–453
To cover a large refrigerating capacity, the shell-and-tube type absorbers are widely adopted. The solution is sprayed at the top of the tube bank consisting of the horizontal cooling tubes and absorbs the water vapor as it flows down to the bottom of absorber. In order to predict the absorber performance, it is essential to understand the heat and mass transfer characteristics of the solution film flowing over a single horizontal tube. Many numerical models of heat and mass transfer in falling film absorption have been studied [1]. For a horizontal tube, the distributions of velocity, temperature, and concentration in the liquid film can be estimated through numerical analyses. Andberg et al. [2], Morioka and Kiyota [3], and Choudhury et al. [4] predicted the absorption efficiency with various numerical models. Also, for a system with multiple rows of tubes, Kirby and Perez-Blanco [5] performed a numerical study to predict the absorption efficiency. However, most of the numerical studies are based on the liquid film flowing over a single horizontal tube and the assumption of laminar flow with a flat interface of the liquid film, which seems rather ideal. In other words, there is few theoretical modeling and experimental data for the laminar-wavy regime, despite such a regime is prevailing in the range of the practical usage. Though there are experimental reports [6–9] on the absorption characteristics of horizontal tubes, most of them are on the overall absorption performance of the flows in tube-bundle assemblies, and the separate effect of each parameter cannot be deduced. It is also difficult to identify the flow pattern of liquid film, and the characteristics of heat and mass transfer. To evaluate the absorber performance precisely, therefore, it is essential to examine flow patterns associated with the heat and mass transfer characteristics of the flow over a single horizontal tube. In the present study, the separate effect of each parameter has been investigated for a single horizontal tube to provide quantitative data covering the ranges of practical operations.
2. Experimental apparatus and method Fig. 1 shows the details of the test chamber. Here, water vapor is the refrigerant and the LiBr–H2O solution is the absorbent. A concentrated solution was supplied through the nozzle array installed at the top of the test section. At the same time, the water vapor(steam) was supplied to the test section through a pair of tubes. Inside the test section, the concentrated solution discharged from the nozzle array flowed
Fig. 1. Test chamber.
S.S. Seol, S.Y. Lee / Int. Commun. Heat and Mass Tranf. 32 (2005) 445–453
447
Table 1 Range and uncertainty of parameters Parameter Qs X s,i Ts,i Tc,i pA
Range
Experimental error 6
6
3.3310 8.3310 60, 62 wt.% 32–50 8C 32–508C 0.53–1.33 kPa
3 1
ms
9
3 1
F6610 m s F0.1 wt.% F0.2 8C F0.2 8C F13.2 Pa
Uncertainty F1.13% F0.17% F0.05% F0.05% F1.43%
over a cooled horizontal tube(test tube) and absorbed the water vapor to be diluted as it flowed down. The outer and inner diameters of the cooled horizontal tube were 19.05 mm and 16.6 mm, respectively. Temperatures of the LiBr–H2O solution at the top (Ts,i) and the bottom (Ts,o) of the horizontal test tube and the chamber pressure(absorber pressure, p A) were measured. In measuring Ts,o, the temperatures at three different points along the bottom line were averaged. To evaluate the heat removal rate by the cooling water, inlet and outlet temperatures of the cooling water were measured. Ktype thermocouples were used to measure the temperature. The chamber was measured by using a Utype mercury vacuum manometer and an absolute barometer. When the water dissolved in the solution evaporates, instead of absorption, the absorber pressure was maintained to prescribed values by using an auxiliary cooler and a solution-spraying device that can continuously exhaust the water vapor from the test chamber. The experimental parameters and their ranges are listed in Table 1. The separate effects of each parameter on the absorption performance were carefully examined. Since the absorption rate of the refrigerant was not directly available, it was deduced from the solution temperatures at the top and the bottom of the tube. Fig. 2 shows the control volume of the liquid–film flow around the test tube to
Fig. 2. Absorption at liquid film flowing over a cooled horizontal tube.
448
S.S. Seol, S.Y. Lee / Int. Commun. Heat and Mass Tranf. 32 (2005) 445–453
analyze the heat and mass balance. The balance relations and the equation of state for the flow of the LiBr–H2O solution are as follows. Wi þ WR ¼ Wo
ð1Þ
Xi Wi ¼ Xo Wo
ð2Þ
ii Wi þ iR WR ¼ io Wo þ qcWAo
ð3Þ
io ¼ io ðTo ; Xo Þ
ð4Þ
From Eqs. (1)–(4), four unknowns(X o, Wo, i o, and W R) can be obtained by the iteration method since all the other quantities are given. The property values of LiBr–H2O solution are taken from the numerical data by Patterson and Perez-Blanco [10]. The heat removal by the test tube can be estimated by measuring the temperature rise of the cooling water as follows. ð5Þ qcW ¼ Wc cp;c Tc;o Tc;i =Ao The heat transfer coefficient inside the test tube(h i) can be obtained by condensing the steam at the external surface of the test tube with the flow rate and the temperature of the cooling water being the same as the absorption test. The values of h i were 3200F50 Wm2K1 and 700F20 Wm2K1 with and without a heat-transfer augmentation device inside the tube, respectively.
3. Results and discussions 3.1. Behavior of film flow The heat and mass transfer characteristics are determined by the inlet conditions of the refrigerant and the solution to the absorber, and also by the shape of the solution film at the exterior of the cooled tube, dependent on the drainage pattern of upper tube [11]. Mostly the solution is introduced to the top portion of the upper tube through an array of nozzles, and flows down along the external surface. When the solution flow rate is small, dripping flow occurs at the bottom part of the tube due to the surface tension. As the solution flow rate increases, the liquid columns are formed at the bottom of the tube. If the flow rate is kept increasing, the drainage pattern converts to the sheet flow. Most of the previous numerical results were based on the assumption of the sheet-flow drainage. Hence, to provide the reference data satisfying this assumption, the sheet-flow drainage pattern was intentionally induced by placing a thin, vertical plate just below the test tube as shown in Fig. 2. Also, the measured results were compared with the case of the jet(liquid column)-flow drainage. Fig. 3 shows the variation of the flow pattern of the LiBr–H2O solution with and without absorption for the case of the sheet-flow drainage. For reference, the nozzle array and the horizontal tube in the absence of the liquid flow are shown in Fig. 3(a). When there is no vapor absorption, Fig. 3(b), the solution flowed down along the external surface with a flat interface. Once the vapor absorption began, the absorption rate became larger as the absorber pressure increased, and waves were formed at the film surface as shown in Fig. 3(c). Further increase of the absorber pressure caused a larger disturbance on the film flow; and often, as shown in Fig. 3(d), the liquid film was partly ruptured to form the dry spots
S.S. Seol, S.Y. Lee / Int. Commun. Heat and Mass Tranf. 32 (2005) 445–453
449
Fig. 3. Photographs of solution film flowing over a cooled horizontal tube ( Q s=3.33106 m3/s, Ts,i=32 8C, X s,i=62 wt.%, Tc,i=26 8C, h i=3200 Wm2K1, Sheet drainage). (a) Without solution; (b) Without absorption; (c) p A=1.07 kPa; (d) p A=1.33 kPa.
intermittently. It should be emphasized that the formation of the waves was not by the increase of the solution flow rate but by the active vapor absorption at the interface. Fig. 4(a) shows the change of the heat flux removed by the cooling water( qUc) with the solution inlet temperature for the sheet drainage. In the same figure, the operation region of the surface wave formation is shown. Waves are formed when the solution temperature is low and/or the absorber pressure is high. In the range without surface wave formation, the dependence of the heat removal rate on the solution inlet temperature appears almost linear; however, in the wave formation range, the trend largely deviates from the linearity and results in the higher rate of heat removal. The lines in Fig. 4(b) indicate the wave formation boundaries for different solution flow rates. Left-hand sides of the lines are the regions of the wave formation. The surface waves are more apt to occur with the smaller flow rate.
Fig. 4. Effect of wave formation (X s,i=60 wt.%, Tc,i=32 8C, h i=3200 Wm2K1, Sheet drainage). (a) Cooling heat flux, Q s=3.33106 [m3s1]; (b) Region of wave formation.
450
S.S. Seol, S.Y. Lee / Int. Commun. Heat and Mass Tranf. 32 (2005) 445–453
Table 2 shows a selected set of the experimental data for the sheet drainage in the practical operation ranges of the absorption refrigeration systems. 3.2. Effect of sprayed solution temperature The heat and mass transfer performances of an absorber are determined by the inlet conditions of the water vapor(refrigerant) and the solution to the test chamber. Figs. 5 and 6 show the solution temperature at the test chamber outlet and absorption rate per unit surface area(W R/A o), respectively, for various inlet temperatures and flow rates of the solution with the jet-flow drainage. The lines in those figures are the curve-fitted results of the measured data using the least square method based on the quadratic function. As shown in Fig. 5, the outlet temperature of the solution increases almost linearly with the solution inlet temperature except for the cases of small solution flow rates with high absorber pressures. The data points in Fig. 6 are deduced from the tube outlet temperature and the flux of heat removal. The positive values indicate absorption of the water vapor while the negative values imply evaporation. For a given value of the cooling water temperature(Tc,i), the heat removal rate increases with the increase of the solution inlet temperature. However, when the saturation pressure of the solution corresponding to the temperature and concentration at the absorber inlet becomes higher than absorber pressure, evaporation takes place instead of absorption. Absorber performance is enhanced with the lower solution temperature. Table 2 Experimental data ( Q s=3.33106 m3/s, Q c=5.56106 m3/s, X s,i=60 wt.%, h i=3200 Wm2K1, sheet drainage) p A [kPa]
Tc,i [8C]
Tc,o [8C]
Ts,i [8C]
Ts,o [8C]
p A [kPa]
Tc,i [8C]
Tc,o [8C]
Ts,i [8C]
Ts,o [8C]
0.53 0.53 0.53 0.67 0.67 0.67 0.67 0.67 0.67 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.93 0.93 0.93 0.93 0.93 0.93 0.93
32.0 32.0 32.0 31.9 32.0 32.0 31.9 32.0 32.0 32.0 32.1 32.0 32.0 32.0 32.0 32.0 31.9 32.0 32.0 32.0 32.0 32.0 32.0 32.0
32.2 32.6 32.8 32.4 32.8 33.0 33.1 33.4 33.6 32.8 33.0 33.1 33.3 33.6 33.8 34.0 34.1 33.2 33.2 33.3 33.5 33.7 33.9 34.1
32.6 35.7 38.2 32.6 35.8 38.2 40.0 42.4 44.7 32.6 35.8 38.2 39.9 42.5 44.7 46.8 49.3 32.6 35.9 38.4 40.0 42.5 44.7 46.9
33.5 34.1 34.6 34.7 35.4 35.8 36.1 36.7 37.3 36.1 36.4 36.8 37.3 37.8 38.3 38.7 39.3 37.2 37.6 37.7 38.0 38.6 39.0 39.7
1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.20 1.20 1.20 1.20 1.20 1.20 1.20 1.20 1.33 1.33 1.33 1.33 1.33 1.33 1.33 1.33
32.0 32.1 32.0 32.0 32.1 32.1 32.0 32.0 32.0 32.0 32.0 32.0 32.1 32.0 32.0 32.0 32.0 32.1 32.0 32.0 32.1 32.1 32.1 31.9
33.6 33.6 33.5 33.6 33.9 34.1 34.2 34.4 33.9 33.8 33.8 33.8 34.0 34.1 34.3 34.5 34.2 34.2 34.0 34.0 34.2 34.3 34.5 34.5
32.5 35.8 38.5 40.1 42.5 44.7 47.0 49.2 32.5 35.8 38.4 40.0 42.5 44.7 47.0 49.4 32.6 35.7 38.5 40.1 42.4 44.7 47.1 49.5
38.7 38.6 38.8 39.1 39.4 39.9 40.2 41.2 39.8 39.8 39.7 39.8 40.0 40.4 41.0 42.0 40.9 41.0 40.6 40.7 40.7 41.0 41.6 42.6
S.S. Seol, S.Y. Lee / Int. Commun. Heat and Mass Tranf. 32 (2005) 445–453
451
Fig. 5. Variation of solution outlet temperature with solution inlet temperature (X s,i=60 wt.%, Tc,i=32 8C, h i=700 Wm2K1, Jet drainage). (a) Q s=3.33106 [m3s1]; (b) Q s=6.67106 [m3s1].
3.3. Effect of absorber pressure The temperature and the refrigerant concentration at the free surface(the interface between the water vapor and the solution) increase as the absorber pressure is increased. Accordingly, the solution outlet temperature and the absorption rate increase altogether(Figs. 5 and 6). As shown in Fig. 5, the solution temperature tends to be higher at the outlet than at the inlet as the absorber pressure is raised. This means that the rate of heat absorption becomes greater than the rate of heat removal by the cooling water. Dependence of the solution outlet temperature and the heat removal rate on the absorber pressure appears large for the smaller flow rate. However, with the increase of the solution flow rate, those become less sensitive to the absorber pressure but strongly depend on the inlet solution temperature. Thus, the increasing trend of the solution outlet temperature is getting close to the diagonal lines of Fig. 5. Also the effect of the absorber pressure is more dominant with the lower temperature at the solution inlet and the waves are more likely to occur at the film surface, as evidenced in Fig. 4(a).
Fig. 6. Variation of absorption rate with solution inlet temperature (X s,i=60 wt.%, Tc,i=32 8C, h i=700 Wm2K1, Jet drainage).
452
S.S. Seol, S.Y. Lee / Int. Commun. Heat and Mass Tranf. 32 (2005) 445–453
Fig. 7. Variation of absorption rate with solution inlet temperature (X s,i=60 wt.%, Tc,i=32 8C, h i=700 Wm2K1, lines: Jet drainage, symbols: Sheet drainage). (a) Q s=3.33106 [m3s1]; (b) Q s=6.67106 [m3s1].
3.4. Effect of drainage pattern Fig. 7 shows the change of the absorption rate with the solution inlet temperature for different drainage patterns. In the figure, the lines and the symbols indicate the cases of jet-flow and the sheetflow drainage, respectively. Note that the lines are the same ones already plotted in Fig. 6. For low solution flow rates, a thick film at the bottom part of the horizontal tube forms jets intermittently, either spacewise or timewise. However, the solution at the bottom of the tube flows down immediately along the plate when the vertical plate is installed beneath the test tube. This stabilizes the solution film and covers the entire tube surface with a uniform thickness. Accordingly, the film becomes thinner, and the heat and mass transfer resistance across the liquid film decreases. Therefore, the absorption performance with the sheet-flow drainage appears higher compared to the case with the jetflow drainage, as shown in Fig. 7(a). However, when the solution flow rate becomes high, the locations of jet formation at the bottom of the tube move along the axial direction rather irregularly with increase in number, which enhances mixing effect; thus the absorption performance increases. Hence, the absorption performance becomes higher with the jet-flow drainage than with the sheet-flow drainage at the high flow rate condition as evidenced by Fig. 7(b).
4. Conclusions In this study, the film flow and the heat/mass transfer characteristics of LiBr–H2O solution flowing over a cooled horizontal test tube were investigated experimentally. The conclusions were made as follows. (1) For low solution temperature and high absorber pressure, absorption performance increases due to the wave formation at the free surface of the solution film. The wave formation occurs in wider ranges of the solution inlet temperature and the absorber pressure as the solution flow rate decreases.
S.S. Seol, S.Y. Lee / Int. Commun. Heat and Mass Tranf. 32 (2005) 445–453
453
(2) The solution outlet temperature is largely affected by the absorber pressure when the solution flow rate is small, but by the solution inlet temperature for the high flow rate condition. (3) The absorption performance with the sheet-flow drainage appears larger than that with the jet-flow drainage when the solution flow rate is small. However, the reverse is true for the high solution flow rate. Nomenclature A Area (m2) Specific heat (J kg1K1) cp h Heat transfer coefficient (Wm2K1) i Specific enthalpy (J kg1) P Pressure (kPa) Q Volumetric flow rate (m3s1) qU Heat flux (Wm2) T Temperature (8C) W Mass flow rate (kg s1) X Concentration of LiBr–H2O solution (wt.%) Subscripts A Absorber c Cooling water i Inside, inlet o Outside, outlet R Refrigerant s LiBr–H2O solution Acknowledgement This work was supported by Korea Advanced Institute Science and Technology (KAIST) and also by the Brain Korea 21 Project. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
J.D. Killion, S. Garimella, Int. J. Refrig. 24 (2001) 755. J.W. Andberg, G.C. Vliet, ASHRAE Trans. 93 (1987) 2454. I. Morioka, M. Kiyota, JSME Int. J., Ser. 2 34 (2) (1991) 183. S. Choudhury, D. Hisajima, T. Ohuchi, A. Nishiguchi, T. Fukushima, S. Sakaguchi, ASHRAE Trans. 99 (2) (1993) 81. M.J. Kirby, H. Perez-Blanco, Heat Pump Refrig. Syst. Des. 32 (1994) 1. G.C. Vliet, F.B. Cosenza, Proc. Absorption Heat Pump Conference (1991) 53. T. Nomura, N. Nishimura, S. Wei, S. Yamaguchi. Int. Absorption Heat Pump Conf. 31 (1993) 203. V.M.S. Frances, J.M.P. Ojer, Int. J. Heat Mass Transfer 46 (2003) 3299. J.K. Kim, C.W. Park, Y.T. Kang, Int. J. Refrig. 26 (2003) 575. M.R. Patterson, H. Perez-Blanco, ASHRAE Trans. 94 (1989) 2059. X. Hu, A.M. Jacobi, Exp. Therm. Fluid Sci. 16 (1998) 322.