International Journal of Refrigeration 23 (2000) 430±443 www.elsevier.com/locate/ijrefrig Analytical investigation of two dierent absorption modes: falling ®lm and bubble types Yong Tae Kang *, Atsushi Akisawa, Takao Kashiwagi Department of Mechanical Systems Engineering, Tokyo University of Agriculture and Technology, 2-24-16, Nakamachi, Koganei, Tokyo 184-8588, Japan Abstract The objectives of this paper are to analyze a combined heat and mass transfer for an ammonia±water absorption process, and to carry out the parametric analysis to evaluate the eects of important variables such as heat and mass transfer areas on the absorption rate for two dierent absorption modes Ð falling ®lm and bubble modes. A plate heat exchanger with an oset strip ®n (OSF) in the coolant side was used to design the falling ®lm and the bubble absorber. It was found that the local absorption rate of the bubble mode was always higher than that of the falling ®lm model leading to about 48.7% smaller size of the heat exchanger than the falling ®lm mode. For the falling ®lm absorption mode, mass transfer resistance was dominant in the liquid ¯ow while both heat and mass transfer resistances were considerable in the vapor ¯ow. For the bubble absorption mode, mass transfer resistance was dominant in the liquid ¯ow while heat transfer resistance was dominant in the vapor region. Heat transfer coecients had a more signi®cant eect on the heat exchanger size (absorption rate) in the falling ®lm mode than in the bubble mode, while mass transfer coecients had a more signi®cant eect in the bubble mode than in the falling ®lm mode. # 2000 Elsevier Science Ltd and IIR. All rights reserved. Keywords: Refrigerating system; Absorption system; Absorber; Falling ®lm; Bubble; Performance Comparaison de deux modes d'absorption: ®lm tombant et bulles: falling ®lm and bubble types ReÂsume Le auteurs avaient deux objectifs en eectuant cette eÂtude: l'analyse des transferts de chaleur et de masse pour le processus d'absorption ammoniac-eau, et l'analyse parameÂtrique a®n d'eÂvaluer les eets des variables importantes tels que les surfaces d'eÂchange de chaleur et de masse, sur la vitesse d'absorption pour les deux modes d'absorption Ð aÁ ®lm tombant et aÁ bulles. Un eÂchangeur aÁ plaques muni d'ailettes en ruban deÂcaleÂes (oset strip ®n) installeÂes du cote refroidissant a eÂte utilise pour la conception du ®lm tombant et de l'absorbeur aÁ bulle. Les reÂsultats montrent que l'absorption locale de l'absorbeur aÁ bulles est toujours plus eÂleveÂe que pour le ®lm tombantaÂ; ceci permet de reÂduire la taille de l'eÂchangeur de chaleur de 48,7% laÁ ouÁ la l'eÂchange avec bulles est utiliseÂ. Pour le mode absorption par ®lm tombant, la reÂsistance au transfert de masse dominait lors de l'eÂcoulement liquide, alors que les reÂsistances des transferts de chaleur et de masse eÂtaient toutes les deux eÂleveÂes dans le cas de l'eÂcoulement de vapeur. Pour le mode absorption aÁ bulles, la reÂsistance au transfert de masse dominait lors de l'eÂcoulement liquide, alors que la reÂsistance au transfert de chaleur dominait dans la reÂgion de l'eÂcoulement de vapeur. Lors de l'utilisation du mode absorption par ®lm tombant, les coecients de transfert de chaleur exercËaient un eet plus signi®catif sur la taille de l'eÂchangeur de chaleur (vitesse d'absorption) que le mode d'absorption aÁ bulles, alors que, lors de l'utilisation du mode absorption aÁ bulles, les coecients * Corresponding author. School of Mechanical Engineering, Kyung Hee University, South Korea. Tel.: +82-331-201-2990; fax: +82-331-202-8106. 0140-7007/00/$20.00 # 2000 Elsevier Science Ltd and IIR. All rights reserved. PII: S0140-7007(99)00075-4 Y. Tae Kang et al. / International Journal of Refrigeration 23 (2000) 430±443 431 de transfert de masse exercËaient un eet plus signi®catif que le mode d'absorption aÁ ®lm tombant. # 2000 Elsevier Science Ltd and IIR. All rights reserved. Mots cleÂs: SysteÁme frigori®que; SysteÁme aÁ absorption; Absorbeur; Film tombant; Bulle; Performance Nomenclature A ai ap as Cp cM Dcm dB do d1 F f g H h i j L LMTD : M N No Nu Pr Q Re Rw S Sc St T t U V x area (m2) interfacial area per unit volume (m2 m-3) projected area (m2) surface area (m2) molar heat capacity (J kmol-1 K-1) molar density, r/M, (kmol m-3) diameter of the bubble column (m) bubble diameter (m) ori®ce diameter (m) distance between two plates (m) mass transfer coecient (kmol m-2 s-1) friction factor gravitational acceleration (m s-1) enthalpy (J kmol-1) heat transfer coecient (W m-2 K-1) incremental number, 1,2,3 ... j factor, Nu Re-1 Pr-1/3) length (m) logarithmic mean temperature dierence (K) molar ¯ow rate (kmol s-1) molar ¯ux (kmol m-2 s-1) number of ori®ce Nusselt number Prandtl number heat transfer (W) Reynolds number wall resistance (m2 K W-1) volume ¯ux (m3 s-1) Schmidt number Stantan number temperature (K) thickness (m) overall heat transfer coecient (W m-2 K-1) velocity (m s-1) molar concentration of ammonia (kmol kmol-1) 1. Introduction A compact heat exchanger incorporates a heat transfer surface and a heat transfer mode. The heat transfer surface must have a high area density (generally higher than 700 m2/m3) for a compact heat exchanger. The heat transfer mode must be developed to have a high overall heat transfer coecient, U, which will further z composition of ammonia in absorbing/desorbing vapor (kmol kmol-1) Greek symbols l absorption/desorption heat (J kmol-1) mass diusivity (m2 s-1) unit vector de®ned in Eq. (6) " gas hold-up f ®n eciency dynamic viscosity (Pa s) kinematic viscosity (m2 s-1) density (kg m-3) surface tension (N m-1) Subscripts a/d absorption/desorption B bubble bl large bubble bs small bubble c coolant CM column h heat i interface l liquid lb bulk liquid m mass OSF oset strip ®n o ori®ce senl sensible liquid senv sensible vapor t total trans transition v vapor vb bulk vapor w wall wi inner wall wo outer wall reduce the heat exchanger size. For heat transfer in a binary mixture such as ammonia±water absorption systems, the heat transfer mode should be carefully selected to reduce heat and mass transfer resistance which exist in both liquid and vapor regions. An absorption heat pump cycle using ammonia±water as a solution pair has been recommended for residential and small commercial heating and cooling systems [1]. The generator absorber 432 Y. Tae Kang et al. / International Journal of Refrigeration 23 (2000) 430±443 heat exchange (GAX) cycle using ammonia±water is the most suitable for residential heating and cooling with COP of 1.03 for cooling and 2.03 for heating. The ammonia±water solution pair is also an attractive alternative to ozone-depleting chloro¯uorocarbons (CFCs) used in conventional vapor compression heat pump systems. In the ammonia±water absorption heat pump systems, falling ®lm heat transfer and bubble type heat transfer have been recommended to enhance heat and mass transfer performances [2]. Thin falling ®lm heat transfer mode provides relatively high heat transfer coecients and is stable during operation. However, the falling ®lm heat transfer modes have wettability problems and need good liquid distributors at the inlet of the liquid ¯ow. Bubble type heat transfer provides not only high heat transfer coecients but also good wettability and mixing between the liquid and the vapor. However, bubble type heat transfer does require vapor distribution rather than liquid distribution. Generally, vapor distribution is easier to accomplish than liquid distribution. Fundamental characteristics of the bubble and the falling ®lm modes are compared in Table 1. This paper aims to compare the two dierent absorption modes in designing a plate heat exchanger as an absorber by considering combined heat and mass transfer. Over the last 10 years, many studies have extensively investigated the falling ®lm absorption process numerically and analytically in ammonia±water absorption systems [3±7]. However, most literature neglects the mass transfer resistance through the liquid ®lm by assuming very thin ®lm and well mixing. Furthermore, no literature has been found on the combined heat and mass transfer analysis considered in both liquid and vapor regions. This paper considers the combined heat and mass transfer in the liquid region as well as in the vapor region during the falling ®lm absorption process. Some literature has been found on heat and mass transfer analysis of the bubble absorber[2,8,9]. Ferreira et al. [8] developed a model for calculation of simultaneous heat and mass transfer processes in vertical tubular bubble absorbers for ammonia±water absorption systems. However, local values for important parameters such as temperature and concentration could not be obtained since only overall conditions were considered in the model. Herbine and Perez-Blanco [9] described a design model of the absorption process in an ammonia±water bubble absorber with a vertical tube. The authors obtained one dimensional temperature and concentration pro®les along the absorber length using empirical correlation for local overall heat and mass transfer coecients from literature. The mass transfer resistance inside the bubble was neglected in the design model. Recently, Kang et al. [2] developed a design model for a bubble absorber by using combined heat and mass transfer analysis. They consider the heat and mass transfer resistance not only in the liquid region but also inside the bubble by solving diusion and mass balance equations simultaneously. Various types of heat exchangers have been adopted to increase heat and mass transfer performance in absorption heat pump systems; tube in tube, tube in shell, and plate heat exchangers. In this paper, a plate heat exchanger is used in the absorber design for the fundamental comparisons of the bubble and the falling ®lm absorption modes because it provides high heat transfer coecients, good wettability, and liquid/vapor mixing compared with plain tubes. In summary, the objectives of this paper are to compare two dierent absorption modes in ammonia±water absorption heat pump systems, to develop design tools for the falling ®lm and the bubble absorbers, and ®nally to provide a criterion in designing heat exchanger components of the ammonia-water absorption systems. 2. System description Fig. 1 shows a fundamental GAX cycle used in ammonia±water absorption systems. The internal heat Table 1 Fundamental characteristics of the falling ®lm and bubble modes Tableau 1 CaracteÂristiques des modes d'absorption aÁ ®lm tombant ou aÁ bulles Heat transfer mode Falling ®lm mode Bubble modes Con®guration Interfacial area Heat transfer Area Mixing Wettability Liquid Distributor Vapor Distributor Flooding Heat and mass transfer Compactness Horizontal tube bundles vertical tubes Small ~ Interfacial Area Poor Critical Yes Liquid management No Yes for counter No for cocurrent Liquid and vapor Good Packed type plate HX Large Smaller than interfacial area Excellent Excellent No Yes/ori®ce vapor management Yes Liquid and vapor Excellent Y. Tae Kang et al. / International Journal of Refrigeration 23 (2000) 430±443 433 Fig. 1. System diagram of a fundamental GAX system using ammonia-water solution pair. Fig. 1. ScheÂma du systeÁme GAX utilisant le couple actif ammoniac-eau. exchange due to the temperature glide of a binary mixture provides the fundamental basis for the GAX cycle. In the GAX cycle, the temperature ranges partially overlap between the absorber and generator. The ``overlapped'' heat Ð this is the particular feature of the GAX cycle Ð is transferred from the absorber to the generator within the cycle leading to a higher COP. The GAX cycle consists of the following components Ð hydronically cooled absorber (HCA), solution cooled absorber (SCA), GAX absorber (GAXA), gas ®red desorber (GFD), solution heated desorber (SHD), GAX desorber (GAXD), recti®er, condenser, evaporator, precooler and air coils. In the GAX cycle, the absorber components play important roles to improve the cycle performance. Therefore, the bubble and falling ®lm absorbers would be designed and compared based on thermal conditions of the HCA in the GAX cycle. The HCA was selected as a sample calculation because it is a simple component (hydronic ¯uid in the coolant side). However, the present model can also be applied to design all absorbers and desorbers in ammonia±water systems by changing the hydronic ¯uid to solution liquid (SCA and SHD), ¯ue gas (GFD) and solution pair (GAXA and GAXD). Table 2 summarizes the thermal conditions used in the design of the HCA for a typical 3RT GAX system. Table 2 Thermal conditions of the HCA Tableau 2 Conditions thermiques de l'absorbeur refroidi par eau Liquid temperature (K) Vapor temperature (K) Coolant temperature (K) Liquid mass ¯ow rate (kmol/h) Vapor mass ¯ow rate (kmol/h) Coolant mass ¯ow rate (kg/h) Liquid concentration Vapor concentration System pressure (kPa) Inlet Outlet 347.6 285.3 319.5 3.91 2.42 1360.8 0.2795 0.9873 557.2 321.9 ~ 329.0 5.25 1.09 1360.8 0.4558 ~ Fig. 2 shows the schematic diagram of the plate heat exchangers with falling ®lm and bubble absorption modes. Ammonia±water liquid solution ¯ows down from the top inside of the plate heat exchanger while vapor solution ¯ows up counter to the liquid ¯ow. The hydronic ¯uid (ethylene glycol 35% aqueous solution) ¯ows up the counter to the liquid solution ¯ow. Therefore, there are two dierent counter current ¯ows : one is between the liquid and vapor solution ¯ows, and the other is between the liquid solution and the hydronic 434 Y. Tae Kang et al. / International Journal of Refrigeration 23 (2000) 430±443 Fig. 2. Schematic diagram of plate heat exchangers with falling ®lm and bubble absorption modes. Fig. 2. ScheÂma des eÂchangeurs aÁ plaques utiliseÂs pour les modes d'absorption aÁ ®lm tombant et aÁ bulles. Table 3 Geometric conditions of the plate heat exchanger Tableau 3 GeÂomeÂtrie de l'eÂchangeur aÁ plaque d1 (mm) d2 (mm) d3 (mm) tw (mm) do (mm) 6.223 7.643 12.723 0.71 2.54 Losf (mm) Hosf (mm) Sosf (mm) Tosf (mm) No 3.81 2.54 2.54 0.354 8 Fig. 3. Schematic diagram of the oset strip ®n. Fig. 3. ScheÂma des ailettes en rubans deÂcaleÂes. ¯uid (coolant). For the falling ®lm mode, a liquid distributor is required to provide a good wettability at the top of the heat exchanger. However, for the bubble modes, a vapor distributor (which has several ori®ces) is required to obtain a good mixing rate between liquid and vapor at the bottom of the heat exchanger. Oset strip ®ns (OSF) are inserted to enhance the heat transfer coecient in the hydronic ¯uid side. Fig. 3 shows the schematic diagram of the OSF used in the present paper. Table 3 summarizes the geometric dimensions used in the plate heat exchanger for the HCA. 3. Analysis In thin falling ®lm mode, mass transfer resistance within the thin ®lm has been assumed to be negligible [5,10]. In this paper, however, combined heat and mass transfer is considered in the liquid region as well as in the vapor region during the absorption process. The bubble type mode has a dierent absorption process. In this mode, combined heat and mass transfer was also considered in both liquid and vapor regions since there is signi®cant mixing between the liquid and the vapor. Based on the fundamental assumptions summarized in Table 4, diusion, concentration, mass and energy bal- Y. Tae Kang et al. / International Journal of Refrigeration 23 (2000) 430±443 435 Table 4 Fundamental assumptions for analysis Tableau 4 HypotheÁses utiliseÂes dans l'analyse Falling ®lm mode Bubble mode a. The absorption process is steady±state, and the system pressure is constant. b. The liquid/vapor interface is in equilibrium state. c. The heat transfer surface is completely wet. d. The liquid ®lm is thin and well mixed. e. No ¯ooding occurs a. The absorption process is steady±state, and the system pressure is constant. b. All bubbles have the same size and velocity at each local position. c. Bubble coalescence and breakup are negligible. d. There is no direct heat transfer between the vapor and the hydronic ¯uid. Table 5 Information on bubble dynamics Tableau 5 Informations sur la dynamique des bulles Vv Vsh Gas hold-up "v Deckwer and Schumpe [11] Vtrans Vv ÿ Vtrans ifVv 5Vtrans Vbs Vbl if Vv 4Vtrans where 3 ÿ0:273 0:03 Vbs l l l 2:25 v g4l ÿ0:077 0:077 Vbl l Vbs l l Vv ÿ Vtrans 0:757 3 l l 2:4 v g4l and Vtrans ÿ0:61 0:5 0:11 0:5eÿ193v l Vbs Bubble diameter Bhavaraju et al. [12] For low vapor ¯ow rates S5St 0:32g1=2 dB g 6do 4=3 for ReB 51:0 108l g 6do 5=6 for ReB 51:0 g 6do g 1=3 For high vapor ¯ow rates S5St dB 0:21 3:23Reÿ0:1 o;l Fro;v do where Reo;l 4l S S2 and Fro;v 5 do g do l 2 0:5 3 2 0:1 1 gDcm l gDcm l "1:13 v 3Dcm 2l Interfacial area Akita and Yoshida[13] ai Slip velocity for counter ¯ow Vs Vv Vl "v 1 "v 436 Y. Tae Kang et al. / International Journal of Refrigeration 23 (2000) 430±443 ances are solved simultaneously for a given control volume. For the bubble mode, some information on gas dynamics such as gas hold-up, bubble diameter, interfacial area and slip velocity is required. This information is summarized in Table 5. Temperatures, concentrations, heat transfer coecients, and absorption rates are compared for the two dierent absorption modes. With these comparisons for given geometric conditions, this paper provides a criterion to evaluate which mode is better for absorbers or desorbers in ammonia±water absorption heat hump systems. 4. Control volume analysis The control volume analysis was carried out based on the incremental section as shown in Fig. 4. For both falling ®lm and bubble modes, the vapor moves up in the counter direction to the liquid ¯ow which enters from the top and leaves the heat exchanger to the bottom. The hydronic ¯uid ¯ows up counter to the liquid ¯ow inside the plate heat exchanger. ÿ NNH3 NH2 0 z ÿ xlb z ÿ xvi Fv ln F1 ln z ÿ xli z ÿ xvb where z is the molar composition of ammonia in the absorbing/desorbing vapor, which is given by z NNH NNH3 NH2 0 The total molar ¯ux absorbed or desorbed, NNH3+ NH2 0 , is expressed as the following equation by considering the diusion in the liquid and vapor regions [14]. 2 where F is the mass transfer coecient, and the molar ¯ux, N, is de®ned as positive for absorption and negative for desorption. The correlations for the mass transfer coecients used are summarized in Table 6 for the falling ®lm mode and in Table 7 for the bubble mode. Based on the control volume as shown in Fig. 4, concentration and mass balance equations are established as follows. 5.1. Concentration balance : : Mvb ixvb i Mvb i 1 vb : NNH3 NH2 0 zAm 3 and 5. Diusion 1 : : Mlb ixlb i Mlb i 1xlb i 1 ÿ lb NNH3 NH2 0 zAm 4 where Am is the mass transfer area between the liquid and the vapor. The mass transfer area is the same as the heat transfer area in the falling ®lm mode while it is dierent from the heat transfer area in the bubble mode. Table 6 Heat and mass transfer coecients used in the design of falling ®lm absorber Tableau 6 Coecients de transfert de chaleur et de masse utiliseÂs dans la conception de l'absorbeur aÁ ®lm tombant Heat transfer coecient Liquid region Chun and Seban [15] for falling ®lm ¯ow Vapor region Dittus and Boelter [16] for turbulent ¯ow Hydronic ¯uid region (Webb [17]) sOSF ÿ0:154 tOSF ÿ0:15 tOSF ÿ0:068 j 0:652Reÿ0:54 Dh hOSF lOSF sOSF " #0:1 0:51 tOSF 0:46 tOSF ÿ1:06 1:34 sOSF ÿ5 1 5:6310 ReDh hOSF lOSF sOSF where 4sOSF hOSF lOSF Dh 2 sOSF lOSF hOSF lOSF tOSF bOSF tOSF sOSF Fig. 4. Control volume for an incremental section in the bubble absorption mode. Fig. 4. Volume de calcul pour une section increÂmentielle en mode absorption aÁ bulles. Mass transfer coecient Liquid region Heat and mass transfer analogy (Chilton and Colburn[18]) Vapor region Heat and mass transfer analogy (Chilton and Colburn[18]) Y. Tae Kang et al. / International Journal of Refrigeration 23 (2000) 430±443 Table 7 Heat and mass transfer coecients used in the design of bubble absorber Tableau 7 Coecients de transfert de chaleur et de masse utiliseÂs dans la conception de l'absorbeur aÁ bulles Heat transfer coecient 1 if it flows into the control volume at ith section ÿ1 if it flows out from the control volume ith section 6 5.2. Mass balance : : Mvb i Mvb i 1 vb NNH3 NH2 0 Am 7 and Liquid region (Deckwer [19]) ÿ0:25 l Vv dB ÿ0:25 V2v l Cpl ÿ:05 Stl 0:1 l gdB kl : : Mlb i Mlb i 1 ÿ lb NNH3 NH2 O Am 8 5.3. Energy balance where hl Stl l Cpl Vv The total energy transferred to the coolant is expressed as the following equation based on the control volume as shown in Fig. 4. h : i : Qc Mlb i 1Hlb i 1 ÿ Mlb iHlb i ÿlb h : i : Mvb i 1Hvb i 1 ÿ Mvb iHvb i ÿvb h : i : Mc i 1Hc i 1 ÿ Mc iHc i c Vapor region (Clift et al. [20]) 0 11=4 as Cpv Scv 2=3 B 48 2v C hv 1:4 @ v A ap cM Prv 2 dB l 2 3 l Hydronic ¯uid region (Webb [17]) sOSF ÿ0:154 tOSF ÿ0:15 tOSF ÿ0:068 j 0:652Reÿ0:54 Dh hOSF lOSF sOSF " #0:1 0:51 0:46 tOSF tOSF ÿ1:06 1:34 sOSF ÿ5 1 5:6310 ReDh hOSF lOSF sOSF 9 The sensible heat of vapor ¯ow is transferred from the vapor to the interface due to the combined heat and mass transfer, which is given by Kang et al. [22] as where 4sOSF hOSF lOSF Dh 2 sOSF lOSF hOSF lOSF tOSF bOSF tOSF sOSF Mass transfer coecient Liquid region Volumetric mass transfer coecient (Hikita et al. [21]) ÿ0:248 0:243 Fl ai cM Vv Vv l 1:76 4l g v l ÿ0:604 14:9f g t l l l 3 where f is equal to 1.0 for nonelectrolyte solutions Mass transfer coecient in liquid region (Akita and Yoshida [13]) 0:5 3 0:25 2 3=8 Fl c M d B Vl gdB gdB l 0:5 V2l l l Qsenv Co;vb hv Tvb ÿ Ti Am 1 ÿ eÿco;vb 10 NNH3 CPNH3 NH2 O CpH2 O hvb 11 where Co;vb The sensible heat of liquid ¯ow is also expressed as the following equation. Qsenl Vapor region (Clift et al. [20]) 0 11=4 Co;lb hl Ti ÿ Tlb Am 1 ÿ eÿCo;lb 12 The absorption/desorption heat transferred through the interfacial area, Qa/d is expressed as Fv cM ap 48 2v B C 1:4@ v A as 2 dB l 2 3 l Qa=d NNH3 NH2 O la=d Am In the bubble mode, the mass transfer area is given by Am ai Ac L 437 5 where ai and Ac are the speci®c interfacial area (m2/m3) and the cross-sectional area of the plate heat exchanger, respectively. In Eqs. (3) and (4), is a unit vector to take into account the ¯ow direction (co-current or countercurrent ¯ows), which is de®ned as follows; 13 where la=d is de®ned as la=d Hvb i ÿ Hlb i 14 Eq. (14) implies that the latent heat la=d , is the enthalpy dierence due to the phase change between the bulk vapor and the bulk liquid (not between the vapor and liquid at the interface). 438 Y. Tae Kang et al. / International Journal of Refrigeration 23 (2000) 430±443 5.4. Heat transfer equation Now, heat transferred to the coolant is given by Qc UAh LMTD 15 where UAh 1 1 1 Rw hl Ah hc Ao j Af 16 and LMTD Tlb i ÿ Tc i ÿ Tlb i 1 ÿ Tc i 1 " # Tlb i ÿ Tc i ln ÿ Tlb i 1 ÿ Tc i1 17 The correlations for the heat transfer coecients used in Eq. (16) are summarized in Table 6. de®ne each temperature and concentration clearly. Figs 6a and b shows the temperature pro®les for the falling ®lm and the bubble absorption modes, respectively. In both the falling ®lm and the bubble modes, the bulk liquid temperature, Tlb, is very close to the interface temperature, Ti, which is the equilibrium temperature at give concentration and pressure. For both absorption modes, this implies that the heat transfer resistance in the eective mass transfer region of the liquid ¯ow is negligible compared with the total heat transfer resistance from the bulk liquid ¯ow to the wall. In the falling ®lm mode, the bulk vapor temperature increases gradually with the increasing length of the heat exchanger, and is still lower than the coolant temperature at the outlet of the vapor ¯ow. In the bubble mode, the vapor temperature increases rapidly from the bottom of the heat exchanger, where 6. Results and discussion Temperature, concentration and total absorption rate pro®les were obtained as a function of the length of the heat exchanger by solving diusion, mass, concentration, energy and heat transfer equations simultaneously. Parametric analysis was performed to study the eects of heat and mass transfer areas, heat transfer coecients and mass transfer coecients on the absorption rate. The typical temperature and concentration pro®les for the counter-current absorption are shown in Fig. 5 to Fig. 5. Typical temperature and concentration pro®les for the counter-current absorption process. Fig. 5. Pro®ls de tempeÂrature et de concentration typiques pour le processus d'absorption aÁ contre-courant. Fig. 6. (a) Temperature pro®les for the falling ®lm absorbtion mode; (b) Temperature pro®les for the bubble absorption mode. Fig. 6 (a) Pro®ls de tempeÂrature pour le mode absorption aÁ ®lm tombant; (b) Pro®ls de tempeÂrature pour le mode d'absorption aÁ bulles. Y. Tae Kang et al. / International Journal of Refrigeration 23 (2000) 430±443 the inlet of the vapor ¯ow is, and approaches to the interface temperature. This implies that the heat transfer resistance in the vapor region is considerable for both falling ®lm and the bubble modes. In the bubble mode, the vapor temperature starts to be higher than the coolant temperature when it is about 4 cm from the length of the heat exchanger (from the bottom). The temperature pro®le of the bulk vapor ¯ow is completely dierent between the falling ®lm and the bubble absorption modes. This dierence is due to the following combined heat and mass transfer characteristics of two dierent absorption modes. First, the liquid and vapor are mixed well with each other in the bubble mode while they are completely separated in the falling ®lm mode. Therefore, the heat transfer resistance within the vapor ¯ow is more signi®cant in the falling ®lm mode than in the bubble mode. Second, the pro®le of the bulk vapor temperature depends on the characteristic of the bubble dynamics. Fig. 7 shows the pro®les of bubble diameter, gas hold-up, heat and mass transfer areas during the bubble absorption process. The bubble size and gas hold-up decrease with the increasing length of the absorber, and have similar decreasing trends. This is reasonable because the mass ¯ow rate of the vapor decreases along the length due to the absorption process resulting in a decreasing bubble size. The same explanation can be applied to the trend of the gas hold-up. Theses pro®les change rapidly up to the length of about 6.0 cm, thereafter the pro®les change gradually along the length. These pro®les are mainly aected by the combined heat and mass transfer characteristics such as mass transfer direction. During the bubble absorption process, the heat transfer area is constant while the mass transfer area is varied with the length of the heat exchanger, which is in¯uenced by the bubble dynamics such as bubble diameter and the gas hold-up. In the 439 current bubble absorption process, the mass transfer area was always larger than the heat transfer area. This is one of the main reasons for having a smaller size of the heat exchanger for the bubble mode rather than the falling ®lm mode. In the falling ®lm mode, both heat and mass transfer areas are constant through the entire length of the heat exchanger. The design results are summarized in Table 8. As can be seen in Table 8, the bubble absorption mode has about 48.7% smaller size of the heat exchanger than the falling ®lm mode. Fig. 8a and b show the molar concentration pro®les for the falling ®lm and the bubble absorption modes, respectively. The molar composition of the absorbing vapor, z, is determined by solving the diusion and the mass balance equations simultaneously. For the counter-current absorption process, it was found that the composition of the absorbing vapor should be larger than xvb, i. e. xvb<z. Kang et al. [7] generated a general map of the molar composition of absorbing/desorbing vapor for every component in ammonia±water absorption heat pump systems. In the current falling ®lm absorption process, the molar composition, z, was always less than 1.0 through the entire length. However, the molar composition was found to be larger than 1.0 up to the 10.0 cm from the bottom in the bubble mode. Thereafter, it was less than 1.0, which means that both ammonia and water components are absorbed in the same direction from the vapor into the liquid region. When z became larger than 1.0, ammonia was absorbed into the liquid region while water was desorbed into the vapor region; opposite direction of mass transfer between ammonia and water components. Herbine and Perez-Blanco [9] also found the initial water desorption phenomenon during a cocurrent ammonia±water absorption process. It was found from Fig. 8a that the bulk liquid concentration was somewhat lower than the interface concentration while the bulk liquid temperature is very close to the interface temperature. This implies, in the falling ®lm mode, that the liquid ¯ow is in a subcooled state due to the mass transfer resistance within the eective mass transfer region of the liquid ¯ow. It was found from Fig. 8b that the bulk vapor concentration was almost equal to the equilibrium concentration while Table 8 Design results of the falling ®lm and bubble absorbers Tableau 8 CriteÁres retenus pour la conception des absorbeurs aÁ ®lm tombant et aÁ bulles. Fig. 7. Bubble diameter, gas hold-up, heat and mass transfer area pro®les for the bubble absorption mode. Fig. 7. DiameÁtres des bulles, reÂtention de gaz et zones de transfert de chaleur et de masse pour le mode d'absorption aÁ bulles. Mode Falling ®lm Bubble Length (cm) Width (cm) NCM Depth (cm) 72.40 12.7 4 4.33 37.14 12.7 4 4.33 440 Y. Tae Kang et al. / International Journal of Refrigeration 23 (2000) 430±443 the bulk liquid concentration was somewhat lower than the equilibrium concentration. This implies that in the bubble mode mass transfer resistance is dominant in the liquid region rather than in the vapor region. The bulk liquid is in a subcooled state (xlb<xli) due to the considerable mass transfer resistance within the eective mass transfer region in the bubble absorber. By comparing Figs. 6a and 8a, for the falling ®lm absorption mode, it should be concluded that the mass transfer resistance is dominant within the eective mass transfer region in the liquid ¯ow while both heat and mass transfer resistances are considerable in the vapor ¯ow. From Figs. 6b and 8b, for the bubble absorption mode, it should be concluded that heat transfer resistance is dominant in the vapor region while the mass transfer resistance is domi- Fig. 8. (a) Molar concentration pro®les for the falling ®lm absorbtion mode; (b) molar concentration pro®les for the bubble absorption mode. Fig. 8. (a) Concentrations molaires pour le mode absorption aÁ ®lm tombant; (b) Concentrations molaires pour le mode absorption aÁ bulles. nant within the eective mass transfer region in the liquid ¯ow. These are unique outputs from this paper. Fig. 9 shows the heat transfer coecient pro®les for the falling ®lm and bubble absorption modes. The overall heat transfer coecient, U, which is de®ned in Eq. (16), was calculated from hl and hc in both absorption modes. In the falling ®lm mode, the heat transfer coecient in the coolant ¯ow was slightly smaller than that in the liquid ¯ow. In the bubble absorption mode, however, the heat transfer coecient in the coolant ¯ow was a dominant factor in determining the overall heat transfer coecient. The heat transfer coecient in the vapor ¯ow was much larger in the bubble mode than that in the falling ®lm mode. This is one of the main reasons to have a smaller size heat exchanger in the bubble mode rather than in the falling ®lm mode. The parametric analysis was performed to evaluate the eect of each heat transfer coecient on the heat exchanger size in the next section. Fig. 10 shows the pro®les of total absorption rate for the falling ®lm and the bubble modes. The local absorption rate (gradient of the pro®le) increases gradually in the falling ®lm mode, which can be explained by the temperature and the concentration pro®les as shown in Figs. 6a and 8a. For the bubble mode, however, the local absorption rate is the highest near the vapor inlet, decreases suddenly at the length of 5.0 cm, and increases again gradually along the length. The local absorption rate of the bubble mode is always higher than that of the falling ®lm mode. This is mainly due to the larger mass transfer area, a better mixing between the liquid and the vapor and the higher heat transfer coecients from the bubble mode than those from the falling ®lm mode. Fig. 9. Heat transfer coecients during the absorption processes. Fig. 9. Coecients de transfert de chaleur lors des processus d'absorption. Y. Tae Kang et al. / International Journal of Refrigeration 23 (2000) 430±443 7. Parametric analysis This paper performed parametric analysis to investigate the eects of important variables such as heat and mass transfer areas, heat transfer coecients and mass transfer coecients on the absorption rate (heat exchanger size). Fig. 11 shows the eect of heat and mass transfer areas on the size of the heat exchanger for both falling ®lm and bubble modes. The horizontal axis represents a modi®ed factor, MF, which is a multiplying factor of the original values of the heat and mass transfer areas. To investigate the eect of the mass transfer 441 area on the size of the heat exchanger, the mass transfer area was changed by varying MF from 0.5 to 1.5 while all the other conditions were kept constant (MF=1.0). For the falling ®lm mode, the heat and mass transfer areas were varied at the same time because they are exactly the same in practical heat exchangers. For the bubble mode, however, the mass transfer area was varied for a given heat transfer area because they can be changed separately in practical cases. This is why the eect of heat and mass transfer eect from the falling ®lm mode is more signi®cant than that of mass transfer area and that of heat transfer area from the bubble absorption mode. During the bubble absorption process, the eect of mass transfer area was found to be more signi®cant than that of the heat transfer area. Fig. 10. Total absorption rate pro®les for the falling ®lm and bubble modes. Fig. 10. Taux d'absorption totale pour les modes aÁ ®lm tombant et aÁ bulles. Fig. 11. The eects of heat andmass transfer areas on the heat exchanger size. Fig. 11. Eets des zones de transfert de chaleur et de masse sur la taille de l'eÂchangeur de chaleur. Fig. 12. (a) The eects of heat transfer coecients on the heat exchanger size in falling ®lm mode; (b) the eects of heat transfer coecients on the heat exchanger ize in bubble mode. Fig. 12. (a) Eets des coecients de transfert de chaleur sur la taille de l'eÂchangeur de chaleur pour le mode aÁ ®lm tombant; (b) Eets des coecients de transfert de chaleur sur la taille de l'eÂchangeur de chaleur pour le mode aÁ bulles. 442 Y. Tae Kang et al. / International Journal of Refrigeration 23 (2000) 430±443 8. Conclusions In this paper, two dierent absorption modes with a binary mixture (ammonia±water) were analyzed and compared. Parametric analysis was carried out to investigate the eects of heat and mass transfer areas, heat transfer coecients and mass transfer coecients on the heat exchanger size. The following conclusions were drawn from the present paper. Fig. 13. The eects of mass transfer coecients on the heat exchanger size during the absorption processes. Fig. 13. Eets des coecients de transfert de masse sur la taille de l'eÂchangeur de chaleur lors des processus d'absorption. Fig. 12a and b shows the eects of the heat transfer coecients in liquid (hl), vapor (hv) and coolant (hc) regions on the heat exchanger size for the falling ®lm and the bubble modes, respectively. In the falling ®lm mode as shown in Fig. 12a, the heat transfer coecient in the coolant ¯ow has the most signi®cant eect on the heat exchanger size and hl has the second, which has a slightly smaller eect than hc. The heat transfer coecient in the vapor ¯ow has the smallest eect on the heat exchanger size, but has a considerable eect. In the bubble mode as shown in Fig. 12b, the heat transfer coecient, hc has also the most signi®cant eect on the absorber size, hv has the second, and hl has the third. By comparison of Fig. 12a and b, it could be concluded that the heat transfer coecients have a more signi®cant eect on the heat exchanger size in the falling ®lm mode than in the bubble mode. Fig. 13 shows the eects of the mass transfer coecients in the liquid (Fl) and the vapor (Fv) regions on the heat exchanger size for both the falling ®lm and the bubble modes. As can be seen in Fig. 13, mass transfer coecients have more signi®cant eect on the heat exchanger size in the bubble mode than in the falling ®lm mode. For the falling ®lm mode, Fl has a more signi®cant eect on the heat exchanger size than Fv for MF ranges larger than 1.0. For the bubble absorption mode, the mass transfer coecient in the liquid region has a more signi®cant eect on the heat exchanger size than that in the vapor region. Therefore, it can summarized that the heat transfer coecient has a more signi®cant eect on the heat exchanger size in the falling ®lm mode than in the bubble mode, while the mass transfer coecient has a more signi®cant eect in the bubble mode than in the falling ®lm mode. 1. The local absorption rate of the bubble mode is always higher than that of the falling ®lm mode due to the larger mass transfer area, a better mixing and the higher heat transfer coecients from the bubble mode. The bubble absorption mode has about 48.7% smaller size of heat exchanger than the falling ®lm mode. 2. The temperature pro®le of the bulk vapor ¯ow is completely dierent between the falling ®lm and the bubble absorption modes. This dierence is due to the combined heat and mass transfer characteristics from two dierent absorption modes and the characteristics of the bubble dynamics form the bubble mode. 3. For the falling ®lm absorption mode, mass transfer resistance is dominant in the liquid ¯ow while both heat and mass transfer resistances are considerable in the vapor ¯ow. For the bubble absorption mode, mass transfer resistance is dominant in the liquid ¯ow while heat transfer resistance is dominant in the vapor region. These are unique outputs from this paper. 4. In the falling ®lm mode, hc has the most signi®cant eect on the heat exchanger size andhl has the second, and hv has the smallest eect on the heat exchanger size. In the bubble mode, the heat transfer coecient, hc has the most signi®cant eect on the absorber size, hv has the second, and hl has the third. 5. Heat transfer coecients have a more signi®cant eect on the heat exchanger size (absorption rate) in the falling ®lm mode than in the bubble mode, while mass transfer coecients have a more signi®cant eect in the bubble mode than in the falling ®lm mode. 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