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Experimental correlation of combined heat and mass transfer for NH3–H2O falling film absorption
International Journal of Refrigeration 22 (1999) 250–262
Experimental correlation of combined heat and mass transfer for NH3 –H2O falling film absorption Yong Tae Kang*, Atsushi Akisawa, Takao Kashiwagi Department of Mechanical Systems Engineering, Tokyo University of Agriculture and Technology, 24-16 Nakamachi, 2-Chome, Koganei, Tokyo 184, Japan Received 7 July 1998; received in revised form 3 December 1998; accepted 7 December 1998
Abstract In this article, experimental analysis was performed for ammonia–water falling film absorption process in a plate heat exchanger with enhanced surfaces such as offset strip fin. This article examined the effects of liquid and vapor flow characteristics, inlet subcooling of the liquid flow and inlet concentration difference on heat and mass transfer performance. The inlet liquid concentration was selected as 5%, 10% and 15% of ammonia by mass while the inlet vapor concentration was varied from 64.7% to 79.7%. It was found that before absorption started, there was a rectification process at the top of the test section by the inlet subcooling effect. Water desorption phenomenon was found near the bottom of the test section. It was found that the lower inlet liquid temperature and the higher inlet vapor temperature, the higher Nusselt and Sherwood numbers are obtained. Nusselt and Sherwood number correlations were developed as functions of falling film Reynolds Re1, vapor Reynolds number Rev, inlet subcooling and inlet concentration difference with ^ 15% and ^ 20% error bands, respectively. 䉷 1999 Elsevier Science Ltd and IIR. All rights reserved. Keywords: Refrigerating system; Absorption system; Ammonia–water; Falling film absorption; Mass transfer; Heat transfer
Corre´lation expe´rimentale entre le transfert de chaleur et de masse pour de l’absorption au NH3 –H2O a` film tombant Resume´ Cet article de´crit une analyse expe´rimentale d’un processus d’absorption ammoniac–eau a` film tombant dans un e´changeur a` plaques muni de surfaces ame´liore´es telles des ailettes en ruban. On examine les effets des caracte´ristiques de l’e´coulement du liquide et de la vapeur, le sous-refroidissement a` l’arrive´e de l’e´coulement du liquide et la diffe´rence de concentration a` l’entre´e sur la performance du transfert de chaleur et de masse. Les concentrations en ammoniac (m/v) du liquide a` l’arrive´e se´lectionne´es e´taient de 5%, 10% et 15%, et les concentrations de la vapeur variaient entre 64,7% et 79,7%. Avant que le processus d’absorption de´marre, on a constate´ un processus de rectification (duˆ au sous-refroidissement a` l’entre´e) dans la partie supe´rieure de la section e´tudie´e. On a e´galement observe´ un phe´nome`ne de de´sorption d’eau vers la parte infe´rieure de la section e´tudie´e. Des nombres de Nusselt et de Sherwood augmentaient avec les baisses de tempe´rature du liquide a` l’entre´e infe´rieure et avec des augmentations de tempe´rature de la vapeur a` l’entre´e. Les corre´lations des nombres de Nusselt et de Sherwood ont e´te´ de´veloppe´es en fonction du nombre de Reynolds Re1 du film tombant, du nombre de Reynolds de la vapeur
* Corresponding author. Tel.: ⫹81 423 887282; fax: ⫹81 423 887076. E-mail address: [email protected] (Y.T. Kang) 0140-7007/99/$20.00 䉷 1999 Elsevier Science Ltd and IIR. All rights reserved. PII: S0140-700 7(98)00076-0
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Rev, le sous-refroidissement a` l’entre´e et le diffe´rence de concentration a` l’entre´e avec des marges d’erreur de ^ 15% et ^20% respectivement. 䉷 1999 Elsevier Science Ltd and IIR. All rights reserved. Mots cle´s: Syste`me frigorifique; Syste`me a` absorption; Ammoniac–eau; Film tombant; Transfert de masse; Transfert de chaleur
Nomenclature A area (m 2) Ac cross sectional area (m 2) Af,a fin area in absorption side (m 2) fin area in coolant side (m 2) Af,c Aw,c wall area in coolant side (m 2) wall area in absorption side (m 2) Aw,a G gravitational acceleration (ms ⫺2) H enthalpy (J/kg ⫺1) h heat transfer coefficient (W m ⫺2 K ⫺1) K overall mass transfer coefficient (ms ⫺1) k thermal conductivity (W m ⫺1 K ⫺1) m_ mass flow rate (kg s ⫺1) LMTD log mean temperature difference Nu Nusselt number P pressure (Pa) Pr Prandtl number Q heat transfer rate (J s ⫺1) Re Reynolds number Sh Sherwood number Sc Schmidt number T temperature (⬚C) U overall heat transfer coefficient (W m ⫺2 K ⫺1) x concentration Greek symbols G mass flow rate per perimeter (kg s ⫺1 m ⫺1) b diffusivitly (ms ⫺1) d wall thickness (m) g kinematic viscosity (m 2s ⫺1) hf fin efficiency m dynamic viscosity (kg m ⫺1s ⫺1) r density (kg m ⫺3) Super- and subscripts Abs absorption c coolant eff effective eq equilibrium fin fin hyd hydraulic i interface l liquid film lb bulk liquid li liquid at interface lm log mean OSF offset strip fin rec rectangular v vapor vb bulk vapor
vi w
vapor at interface wall
1. Introduction The use of binary and ternary mixtures as a working fluid was strongly recommended to improve the system performance not only in absorption cycles but also in combined cycles of power generation and absorption cycles. The internal heat exchange owing to the temperature glide of a binary mixture provides the fundamental basis for the absorption cycle such as Generator Absorber heat Exchange (GAX) cycle [1] and the combined cycle such as Kalina cycle [2]. Ammonia–water solution pair was widely used in absorption cycles because of its excellent thermal characteristics. It is also an attractive alternative to ozone-depleting chlorofluorocarbons (CFCs) and CO2-emitting hydrofluorocarbons (HFCs) used in conventional vapor compression systems. In both GAX and Kalina cycles, the absorber is one of the most critical components in the absorption systems from the viewpoint of size and performance. It is the largest component and has a complicated heat and mass transfer mechanism which influences the system performance significantly. Therefore, it is required to analyze the combined heat and mass transfer and to provide fundamental understandings of the heat and mass transfer mechanisms during the absorption process. Generally, the absorber has a falling film mode as a heat transfer mechanism. This heat transfer mode has a high heat transfer coefficient on the liquid film region and it is easily manufactured. Over the last ten years, ammonia–water falling film absorption has been extensively investigated both numerically and analytically [3–7]. However, a few papers have been found on the experimental analysis. Hoffmann and Ziegler [8] tested heat and mass transfer of aqueous ammonia in falling films on horizontal tube bundles. They did not provide the experimental results in the literature, but provided some experimental data in the presentation. The heat transfer coefficients ranged from 1.0 to 2.1 kW/m 2 K at the liquid concentration ranges between 20% and 53%. Rivera et al. [9] obtained experimental data on the heat transfer in forced convective boiling of ammonia–water mixture flowing upward in a vertical tube. The mean heat transfer coefficients ranged from 9.5 to 14.5 kW/m 2 K for ammonia concentration ranges between 38 and 48 wt.%. Morrison and Deans [10] reported that Marangoni effect generates significant disturbance in the liquid film for the condensation of ammonia–water mixture with a low
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Fig. 1. Schematic diagram of the experimental apparatus. Fig. 1. Sche´ma de l’appareil expe´rimental.
ammonia-concentration range of 0.23%–0.88%. These disturbances cause the heat transfer coefficient of the condensate film to increase by as much as 13%. The heat transfer coefficient of ammonia–water condensation on a horizontal tubes were ranged from 8.5 to 18.4 kW/m 2 K [10]. When the vapor temperature is higher than the liquid temperature in rectifier, condenser or absorber of ammonia–water systems, initially rectification occurs, and then absorption or condensation starts. The rectification process has a significant effect on the temperature and concentration profiles, and the heat exchanger size. Therefore, this article conducted both rectification and absorption experiments simultaneously. In analyzing the present experimental data, a control volume analysis was performed to develop Nusselt and Sherwood number correlations during the absorption process. Mass, concentration, energy and heat transfer equations were solved simultaneously for the control volume of the test section. Unlike the condensation process of a single component, the heat and mass transfer performance of a binary mixture condensation depends on the flow characteristics of not only the liquid flow but also
the vapor flow. Nusselt and Sherwood numbers were plotted as functions of vapor Reynolds number as well as the falling film Reynolds number to include the effect of the vapor flow characteristics on the absorption rate. In summary, this article conducts experimental analysis for ammonia–water falling film absorption process in a plate heat exchanger with offset strip fins (OSF) and rectangular plain fins. The objectives of this article is to analyze the combined heat and mass transfer during the ammonia– water absorption process, and to obtain heat and mass transfer coefficients (Nusselt and Sherwood numbers). This article examines the effects of the inlet subcooling of the liquid flow and the inlet concentration differences on the absorption rate. The experimental results from this article would provide fundamental understandings of the ammonia–water absorption process, and thus give an useful guideline in the design of ammonia–water absorption machines.
2. Experimental apparatus and procedures Fig. 1 shows the schematic diagram of the experimental
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Fig. 2. Schematic diagram and geometric details of the test section (all dimensions are in mm). Fig. 2. Sche´ma et ge´ome´trie de la section e´tudie´e (dimensions en mm).
apparatus for the falling film absorption test. The experimental setup consists of a liquid supply loop, a vapor supply loop, a liquid outlet loop, a vapor outlet loop, a coolant line and the test section. The liquid mass flow rate was controlled by a solution pump with an invertor and measured by a liquid mass flow meter before entering the test section. Mass flow meters were special order-made for ammonia– water solution which has an maximum error of ^ 0.03 g/s. The inlet liquid temperature was measured by a thermocouple (K-type) at the center of the tube at liquid inlet and outlet. All the thermocouples were calibrated before installation at three different points. The liquid concentration was initially measured by measuring and mixing pure ammonia and water and was also confirmed the density and the titration methods. Suppressed liquid (20% ammonia aqueous solution) was pumped from a solution tank to a generator where vapor is generated. The two phase flow entered a separator in equilibrium state. The vapor and the liquid were separated in a separator, in which the liquid flow
was visualized at the bottom of the separator. The vapor path to the test section was completely insulated so that wet vapor was assumed not to be generated owing to the heat loss. The temperature and the pressure in the separator were carefully measured by a thermocouple and a pressure gauge to calculate the vapor concentration. The pressure was measured by a special pressure gauge for ammonia– water system, which was near the atmospheric pressure. In the experimental setup, the vapor may flow either in the cocurrent or counter-current directions to the liquid flow, which flows down by the gravity force. The separator pressure was a little bit higher than the vapor inlet of the test section so that the vapor could be introduced to the test section continuously. During the current experiments, the saturated vapor and the suppressed liquid from the solution tank enter the test section from the top, so that the liquid and the vapor streams flow in the co-current direction. The strong solution (rich in ammonia) after the absorption process leaves the test section from the bottom, goes to
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Fig. 3. Schematic diagram of the rectangular fin and OSF. Fig. 3. Sche´ma de l’ailette rectangulaire et ailette en ruban.
the solution collection tank and a neutralization tank. The coolant (city water) enters the test section from the bottom, flows up in the counter-cross direction to the liquid solution flow. The inlet liquid concentration was selected as 5%, 10% and 15% of ammonia by mass for the current experiments while the inlet vapor concentration varied from 64.7%–79.7% which were calculated from equilibrium condition at a given temperature and pressure of the separator. The experimental data were taken for a certain period of steady state operation. The steady state was confirmed by the test section pressure variation. Initially, the pressure of the test section increased as the vapor was introduced. Finally, the system pressure was kept constant, which was the criterion for the steady state operation. Table 1 Geometric dimensions of the OSF and rectangular plain fins Tableau 1 Dimensions de l’ailette en ruban et des ailettes rectangulaires lisses
hfin (mm) tfin (mm) Lfin (mm) Sfin (mm) Fin pitch (mm)
Offset strip fin (absorption side)
Rectangular plain fin (coolant side)
4.88 0.20 3.18 1.75 1.95
3.00 0.20 95.0 2.97 3.18
Fig. 2 shows the schematic diagram and geometric dimensions of the test section. The test section has OSF between two plates in the absorption side, and rectangular plain fins between two plates in the coolant side. The OSF was used to enhance heat and mass transfer during the absorption process, and the plain fins were used to enhance the heat transfer coefficient in the coolant side. These fins were made of stainless steel. In the current test section, the liquid flows down on the wall and the OSF while the vapor flows down in the core region. The liquid and vapor flows mix together at the exit of each offset fin, and then separate again at the next offset fin-liquid on the wall and vapor in the core region. The flow pattern inside the test section was visualized through the sight glasses at the top and the bottom to confirm the falling film mode. A liquid distributor was installed at the top of the test section to obtain even liquid distribution which was also confirmed through the sight glasses. The coolant enters the test section from the right side of the bottom, and flows out to the left side of the top of the test section as shown in Fig. 2. A data acquisition system was used to record the inlet and outlet temperatures, concentrations, mass flow rates and the system pressure. Six thermocouples were used to measure the inlet and outlet temperatures of the liquid, vapor, and coolant around the test section. Fig. 3 shows the schematic diagrams of the OSF and the rectangular plain fins used in the experimental setup. The geometric dimensions of the enhanced fins are shown in Table 1. The experimental conditions are summarized in Table 2. During the experiments, the maximum measurement errors in temperature, liquid mass flow rate and liquid concentration were ^ 0.24⬚C and ^ 0.03 g/s, ^ 0.1%, respectively.
3. Data reduction Fig. 4 shows the control volume of the test section for data reduction process. In absorption side, temperature was measured at four different locations; the liquid inlet (T1) and outlet (T2), and the vapor inlet (T3) and outlet (T4). For the coolant side, temperature was measured at two different locations; the inlet (T5) and outlet (T6). Mass flow rate was measured at five different locations; the liquid inlet m_ 1 and outlet m_ 2 , the coolant inlet m_ 5 , the liquid before Table 2 Experimental ranges of inlet conditions Tableau 2 Eventail des conditions expe´rimentales a` l’entre´e Liquid flow rate (g/s) Vapor flow rate (g/s) Coolant flow rate (g/s) Liquid temperature (⬚C) Vapor temperature (⬚C) Liquid concentration (%) Vapor concentration (%)
4.0–10.15 0.62–0.90 98.83–121.25 17.0–37.2 54.5–66.5 5.0–15.0 64.7–79.7
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balances: m_ 1 ⫹ m_ 3 m_ 2 ⫹ m_ 4 ;
1
m_ 1 x1 ⫹ m_ 3 x3 m_ 2 x2 ⫹ m_ 4 x4 ;
2
Qc m_ 6 H6 ⫺ m_ 5 H5 Qc m_ 1 H1 ⫹ m_ 3 H3 ⫺ m_ 2 H2 ⫺ m_ 4 H4 :
3
4. Heat and mass transfer analysis The heat transferred to the coolant can be expressed in the following heat transfer equation: Qc UA × F × DTlm ;
4
where F is a correction factor in the calculation of DTlm for the cross-counter current flow, which ranged 0.9–1.0 depending upon the temperature conditions, and Fig. 4. Control volume of the test section. Fig. 4. Re´gulation du volume de la section e´tudie´e.
the generator m_ 10 , and the liquid outlet from the separator m_ 8 . The inlet vapor flow rate m_ 3 was calculated from m_ 8 and m_ 10 . The inlet vapor concentration (x3) was calculated based on equilibrium condition at (T3, P3) because the inlet vapor is in a saturated state. State equation by Ziegler and Trepp [11] was used in the calculation of ammonia–water properties. The liquid outlet concentration (x2), the vapor outlet mass flow rate m_ 4 and concentration (x4) were obtained from the following concentration, mass and energy
DTlm
T1 ⫺ T6 ⫺ T2 ⫺ T5 ; ln T1 ⫺ T6 = T2 ⫺ T5
1 1 dw 1 ⫹ ⫹ UA habs Aabs hc Ac k w Aw
5 6
and Aabs Aw;a ⫹ hf;a Af;a
and
Ac Aw;c ⫹ hf;c Af;c ; 7
where various areas in Eqs. (6) and (7) are defined in the section of the nomenclature. h f,a and h f,c are fin efficiencies in absorption and coolant side, respectively. The heat transfer area was measured before assembling the test section, and the uncertainty in the measurement of heat transfer area
Fig. 5. Liquid and vapor temperature profiles at the test section. Fig. 5. Tempe´ratures du liquide et de la vapeur dans la section e´tudie´e.
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was ^ 0.14%. The fin efficiencies of the center and side fins on absorption side were about 50% and 25%, respectively, depending on the fin geometry and thermal conditions. By combining Eqs. (4)–(6), the heat transfer coefficient in the absorption side, habs, is given by the following equation: habs
1 : Aabs FDTlm =Qc ⫺ dw =kw Aw ⫺ 1=hc Ac
8
In Eq. (8), the heat transfer coefficient in the coolant side, hc was calculated using the correlation by Kays and London [12] for the plain rectangular fins, which has ^ 5.0% of uncertainty. Finally, Nusselt number for the falling film absorption heat transfer is defined as follows: !1=3 h n2l Nuabs abs : 10 kl g The Nusselt type film thickness was used as the characteristic length because the gravity is the driving force for the falling film movement. As for the mass transfer, the absorption rate is expressed in the following equations by using the overall mass transfer coefficients, K1. Dm_ abs Kl rl Aabs Dxlm;l ; where Dxlm;l
11
"
# xeq T3 ⫺ xl T1 ⫺ xeq T4 ⫺ xl T2 l l ÿ : 12 ln ÿ eq xl T3 ⫺ xl T1 = xeq l T4 ⫺ xl T2
By using the overall mass transfer coefficient, Sherwood number for the falling film absorption is defined as follows: !1=3 Kl n2l Shl : 13 bl g The uncertainties in the calculation of Nuabs consist of two major components: uncertainty in U and uncertainty in the derivation of Nu from U and hi. Heat loss was not included in the error analysis because all the test loop and test section were completely insulated. According to the overall heat transfer equation, the sensitivity equation for U can be expressed as:
12U 12Q ⫹ 12A ⫹ 12LMTD :
14
For the subject experimental data, the uncertainties in Q, A and LMTD were 4.8%, 0.14% and 2.0%, respectively. Therefore, the uncertainty in U was estimated to be ^5.20%. A simplified version of the relationship between uncertainties in the overall resistance and the components is as follows: R tot 2 R c 2 12R abs 1R tot ⫹ 1R c ; 15 R abs R abs where R is the resistance to heat transfer, and subscripts tot, abs and c refer to the overall, absorption side, and coolant side, respectively. For a sample data point with Re1 25.51, The ratio of R(abs) to R(c) was 1.60, respectively. This
means R(tot)/R(abs) is 2.60/1.60 ( 1.625). Substituting this into the earlier equation
12R abs 2:6412R tot ⫹
1 2 1 : 2:56 R c
16
Knowing that the uncertainties from the overall and coolant side are 5.20% and 5.0% respectively, the uncertainty in the absorption side Nuabs was estimated as ^ 9.01% for the considered experimental data. The uncertainties in the calculation of Sh consist of three major components: uncertainties in Dm_ abs , Aabs, and Dxlm,l. Therefore, the sensitivity equation for Sh1 could be expressed as
12Sh 12Dm_ abs ⫹ 12A ⫹ 12Dxlm;l :
17
For the subject experimental data, the uncertainties in Dm_ abs , Aabs and Dxlm,l were 6.0%, 0.14% and 2.3%, respectively. Therefore, the uncertainly in Sh1 was estimated to be ^ 6.42%. The uncertainly in Dxlm,l ranged ^ 0.8%–3.9% depending on the concentration differences for all experimental data. In calculation of Nu and Sh for all experimental data, the uncertainties ranged 5.4%–12.5%, and 4.6%–8.7%, respectively.
5. Results and discussion In this article, heat and mass transfer coefficients were measured by experiments for co-current absorption processes in a plate heat exchanger which has OSF between two plates. When the vapor in contact with the liquid film is in motion, a gas shear force may be exerted on the liquid film at the interface. In the case of low liquid velocity and high vapor velocity, disturbances resulting from the gas shear originate at the interface. In the present experiments, the ratio of vapor to liquid mass flow rates ranged 0.14– 0.23, therefore the gas shear was reasonably assumed to be negligible. Nusselt and Sherwood numbers were obtained for ammonia–water absorption process using a spread sheet program which was made based on the data reduction analysis. Fig. 5 shows the liquid and vapor temperatures at the top and the bottom of the test section for different inlet liquid concentrations with different inlet subcooling. The temperature difference between the vapor and liquid varied with the local position and it became 0⬚C or below 0⬚C near the bottom of the test section. These conditions are general in absorber component of ammonia–water systems. The actual temperature profiles of the liquid and the vapor may not be linear. However, the temperatures were linearly plotted using only the top and the bottom locations for simple explanation. During the current experiments, the liquid temperature increased as the liquid film flowed down along the surface because eof the absorption heat release near the interface and the sensible heat transfer from the vapor to the liquid flow. The sensible liquid and vapor heat transfer ranged 5.4%–23.0% and 1.5%–38.0% of the
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Fig. 6. Representative temperature and concentration profiles for rectification and absorption processes. Fig. 6. Tempe´ratures et concentrations pendant les processus de rectification et d’absorption.
total heat transferred to the coolant, respectively. Therefore, the sensible heat transfer had somewhat effect on the total heat transfer. The temperature variation of liquid and vapor flows ranged 10⬚C–20⬚C and 5⬚C–10⬚C, respectively. The temperature variation depended on the inlet subcooling and the ratio of the sensible heat to the latent heat transfer. At the top, the liquid flow was in subcooled state at a low temperature, T1 while the vapor flow was in equilibrium state at a high temperature, T3 so that there was a rectification process according to the representative temperature and concentration profiles as shown in Fig. 6. Initially, at the top of the test section, the bulk vapor concentration, xvb was lower than the equilibrium vapor concentration at the interface, xvi. As the rectification occurred, the bulk vapor concentration increased and the corresponding bulk vapor temperature decreased sharply owing to the water rectification from the vapor [13]. After the rectification process, the bulk vapor concentration became higher than the equilibrium vapor concentration, thereafter the absorption started. Near the bottom of the test section, water desorption was found by checking ammonia balance of liquid and vapor flows. Physically, this means that ammonia vapor is absorbed into the liquid flow while water liquid evaporated into the vapor flow. This phenomenon was also described by Keizer [14], Kang and Christensen [5] and Herbine and PerezBlanco [15] by considering combined heat and mass transfer during ammonia–water absorption process. Fig. 7 shows the effect of the inlet subcooling of the liquid flow on the heat and mass transfer coefficients. As can be
seen in Fig. 7, the heat and mass transfer coefficients increased as the inlet subcooling increased for a given liquid mass flow rate and inlet concentration difference. It was found that the inlet subcooling has more significant effect on heat transfer than mass transfer for a given liquid mass flow rate and inlet concentration difference. The heat and mass transfer coefficients ranged 500–2100 W/m 2 K and 1.0–55 × 10– 5 m/s, respectively, depending on the inlet thermal conditions for all the current experiments. The inlet subcooling of the liquid ranged 22.5⬚C–40.0⬚C for all the current experiments. Fig. 8 shows the effect of inlet concentration difference on the heat and mass transfer coefficients. The inlet concentration difference ranged 60.0%–75.0% during the experiments. It was found that the heat transfer coefficient decreases while the mass transfer coefficient increases with increasing the inlet concentration difference for given liquid mass flow rate and inlet subcooling of the liquid flow. The different trends of heat and mass transfer coefficients are discussed in detail in Section 7 by considering the combined heat and mass transfer analysis. Fig. 9 shows the effects of falling film Reynolds number Re1 on Nusselt and Sherwood numbers. The Sherwood number, Sh1 was obtained by the definition of overall mass transfer coefficient K1 as shown in Eq. (13). As can be seen in Fig. 9, Nusselt and Sherwood numbers increased with increasing the falling film Reynolds number. In the current experiments of ammonia–water mixture, Nusselt number and Sherwood number ranged 0.04–0.16 and
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Fig. 7. The affect of inlet subcooling on heat and mass transfer coefficients. Fig. 7. Effet du sous-refroidissement a` l’entre´e sur les coefficients de transfert de chaleur et de masse.
0.4–2.0, respectively, depending on the inlet thermal conditions. The Nusselt number was much lower than 1.0 for the falling film heat transfer mode because the characteristic length in Eq. (10) is defined differently from the forced convection case in which Nusselt number is generally larger than 1.0. The Nusselt number was lower than the Sherwood number because Lewis number, Le ( a 1/b 1) ranged from 9.0 to 27.0 for the current experimental conditions. This implies that the effective thickness of thermal boundary layer is thicker than that of the diffusion boundary layer,
which was confirmed by visualization work of the ammonia–water absorption using holographic interferometer by Kang et al. [16]. Fig. 10 shows the effects of vapor Reynolds number Rev on Nusselt and Sherwood numbers. The heat and mass transfer performance of a binary mixture condensation such as ammonia–water absorption depends on the flow characteristics of not only the liquid flow but also the vapor flow [17]. It was suggested that the vapor flow rate be maximized to increase heat and mass transfer
Fig. 8. The effect of inlet concentration difference, x3 –x1 on habs and K1. Fig. 8. Effet de la diffe´rence de concentration a` l’entre´e, x3 –x1 sur habs et K1.
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Fig. 9. The effect of Re1 on Nuabs and Sh1. Fig. 9. Effet de Re1 sur Nuabs et Sh1.
performance in ammonia–water absorption process. From the current experiments, both Nusselt and Sherwood numbers were found to be increased as the Reynolds number of the vapor flow increased for the given liquid mass flow rate, inlet subcooling and the inlet concentration difference. The sensible heat of the vapor flow is transferred from the vapor to the liquid region during the rectification process while it is from the liquid to the vapor region during the absorption process by the temperature profile as shown in Fig. 6. As Rev increased, both heat and mass transfer increases in the vapor region. Kang et al. [18] fond that the mass transfer resistance is dominant rather than the
heat transfer resistance in the vapor region for the falling film absorption mode (without rectification process) by solving the diffusion, concentration, mass, and energy equations in the vapor region simultaneously.
6. Experimental correlations In this article, Nusselt and Sherwood numbers were correlated as functions of Re1 and Rev to evaluate the effects of the vapor and liquid flow characteristics on the absorption
Fig. 10. The effect of Rev on Nuabs and Sh1. Fig. 10. Effet de Rev sur Nuabs et Sh1.
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Fig. 11. Nusselt number correlation. Fig. 11. Corre´lation du nombre de Nusselt.
rate as follows:
vapor Reynolds numbers, and thermal conditions are within the valid ranges, however, the correlations can be used in the calculation of Nuabs and Sh1 for plate heat exchangers with OSF which are widely used in ammonia–water absorption heat pump systems.
Nuabs 0:8530 ×10⫺3 ·Rel 1:5180 Rev 0:1759
DTsub;i T1
1:8790
Dx31 x1
⫺0:5756 18
and
7. Parametric analysis
Sh1 0:6996
This article analyses the effects of liquid mass flow rate, vapor mass flow rate, liquid and vapor temperatures, and liquid and vapor concentrations on heat and mass transfer performance. From the current experimental results, the effects of each inlet thermal condition on Nusselt and Sherwood numbers are summarized in Table 3. In Table 3, " represents “increased” or “became higher”, and # represents “decreased” or “became lower”. The results from this parametric analysis are valid for the falling film absorption of
× 10⫺7 ·Rel 0:8874 Rev 1:265
DTsub;i T1
0:8844
Dx31 x1
0:5304
;
19 where Rel
4Gl ml
and
Gl
m_ l : perimeter
20
In Eqs. (18) and (19), Rev was calculated based on the hydraulic diameter in the vapor flow, dhyd,v ( 4Ac/ perimeter). All experimental data for Nuabs and Sh1 were plotted in Figs. 11 and 12 with ^ 15% and ^ 20% error bonds, respectively. The Reynolds numbers of liquid and vapor flow were ranged 6.78–25.51 and 26921–40913 in the above experimental correlation, respectively. All the thermal conditions are summarized in Table 2. The present Nuabs and Sh1 correlations cannot be generally used for ammonia water falling film absorption process. As long as the liquid and
Table 3 Summary of parametric effects on Nuabs and Sh1 from the experimental results Tableau 3 Re´sume´ des effets parame´triques sur Nuabs et Sh1 a` partir des re´sultats expe´rimentaux Parameter
Nuabs
Sh1
Inlet liquid temperature, T1 " Inlet vapor temperature T3 " Inlet liquid concentration x1 #
# " #
# " "
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Fig. 12. Sherwood number correlation. Fig. 12. Corre´lation du nombre de Sherwood.
ammonia–water mixture with rectification process at the inlet conditions as shown in Fig. 6. 7.1. Liquid and vapor mass flow rates It was found that both heat and mass transfer coefficients increased with increasing liquid and vapor mass flow rates. As can be seen in the experimental correlations, Nusselt number is more significantly affected by falling film Reynolds number than Reynolds number of vapor flow while Sherwood number is more significantly affected by Reynolds number of vapor flow than falling film Reynolds number. Therefore, even though there exists combined heat and mass transfer effects from both liquid and vapor mass flow rates, it is recommended that liquid mass flow rate be increased to primarily enhance heat transfer performance, and vapor flow rate can be increased to primarily enhance mass transfer performance. 7.2. Inlet liquid and vapor temperatures It was found from the experiments that Nusselt and Sherwood number increased as the inlet liquid temperature, T1 decreased for a given inlet vapor temperature, T3. This can be explained from the viewpoints of heat transfer and combined heat and mass transfer as follows: As T1 decreases, the sensible heat from the vapor to the liquid increases, leading to a higher Nusselt number (heat transfer). As T1 decreases, the corresponding equilibrium temperature, Ti decreases so that a vapor equilibrium concentration xvi becomes higher, which results in a larger rectification
amount leading to higher Nusselt and Sherwood numbers (combined heat and mass transfer). As T3 increases for a given T1, the sensible heat from the vapor to the liquid also increases (heat transfer). As T3 increases, the corresponding bulk vapor concentration, xvb decreases leading to a larger rectification amount (combined heat and mass transfer). Therefore, it could be concluded that the lower T1 and the higher T3, the higher Nusselt and Sherwood numbers are obtained.
7.3. Inlet liquid concentration It was found from the experiments that as the inlet liquid concentration, x1 decreased for a given inlet vapor concentration, x3, Sherwood number increased while Nusselt number decreased. This can be explained from the viewpoints of mass transfer and combined heat and mass transfer as follows: As x1 decreases, the potential concentration difference, xeq 1 T3 ⫺ x1 increases leading to a higher Sherwood number (mass transfer). As x1 decreases, the corresponding equilibrium concentration xvi decreases, which results in a lower rectification amount leading to a lower Nusselt and Sherwood numbers (combined heat and mass transfer). This opposite trends from the mass transfer and the combined heat and mass transfer could be explained as follows. The absorption process after the rectification process has more significant effect on Sherwood number than the rectification at the top on Sherwood number, noting that the absorption rate increases as x1 decreases. This
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was why Sherwood number increased with decreasing x1 from the current experiments. 8. Conclusions The present experimental results were obtained under the condition that the inlet vapor temperature was higher than the inlet liquid temperature. Therefore, the present experimental correlations should be used under the inlet subcooling condition. The following conclusions were drawn from the present experimental studies: (1) It was found that there was a rectification process at the top of the test section by the inlet subcooling effect. After the rectification process near the top, absorption starts when the bulk vapor concentration becomes higher than the equilibrium vapor concentration at the interface. Near the bottom of the test section, water desorption occurred to meet the mass balance of ammonia. (2) The heat and mass transfer coefficients increased as the inlet subcooling increased for given liquid mass flow rate and inlet concentration difference. It was found that the inlet subcooling has more significant effect on heat transfer than mass transfer. The heat transfer coefficient decreases while the mass transfer coefficient increases with increasing the inlet concentration difference for given liquid mass flow rate and inlet subcooling of the liquid flow. (3) It was found that Nusselt number is more significantly affected by falling film Reynolds number than Reynolds number of vapor flow while Sherwood number is more significantly affected by Reynolds number of vapor flow than falling film Reynolds number. (4) The lower T1 and the higher T3, the higher Nusselt and Sherwood numbers are obtained. (5) It was found that the Sherwood number increased while Nusselt number decreased as x1 decreased. (6) The following Nusselt and Sherwood number correlations were developed with ^ 15% and ^ 20% error bands, respectively. Nuabs 0:8530 × 10⫺3 ·Rel 1:5180 Rev 0:1759
DTsub;i T1
1:8790
Dx31 x1
⫺0:5756
and Sh1 0:6996 × 10⫺7 ·Rel 0:8874 Rev 1:265
DTsub;i T1
0:8844
Dx31 x1
0:5304
:
Acknowledgements This work was partially funded by Japan Science and Technology Corporation (JST). The authors would like to thank Mr. Y. Fujita in Tokyo University of Agriculture and Technology for his assistance during the experiments.
References [1] Altenkirch E, Tenckhoff B. Absorptionakaeltemaschine zur kontinuerlichen Erzeugung von Kaelte und Waerme oder acuh von Arbeit, German Patent No. 278, 076, 1914. [2] Kalina AI. Combined cycle system with novel bottoming cycle. ASME Journal of Engineering for Gas Turbine and Power 1984;106:737–742. [3] Perez-Blanco H. A model of an ammonia–water falling film absorber. ASHRAE Transaction, Part 1 1988;94(94):467– 483. [4] Arman B, Panchal CB. Absorption analysis of ammonia in an aqueous solution, Proceedings of 28th IECEC, Paper No 93462, vol. 1, 1993, pp.873–878. [5] Kang YT, Christensen RN. Development of a counter-current model for a vertical fluted tube GAX absorber. Proceedings of the International Absorption Heat Pump Conference, ASME, AES-31, vol. 7, 1994:16. [6] Lu DC, Lee CC. Investigation of condensation heat transfer of nonazeotropic refrigerant mixtures in a horizontal tube. Proceedings of 10th International Heat Transfer Conference, Brighton, UK, vol. 3, 1994:353–358. [7] Kang YT, Chen W, Christensen RN. A generalized design model by combined heat and mass transfer analysis in NH3 – H2O absorption heat pump systems. ASHRAE Transaction 1997;103(1):444–453. [8] Hoffmann L, Ziegler F. Experimental investigation of heat and mass transfer with aqueous ammonia. Proceedings of the International Absorption Heat Pump Conference, Montreal, Canada, vol. 1, 1996:383–392. [9] Rivera W, Best R, Velez V. Experimental heat transfer coefficients in two phase flow for the ammonia-water and ammonialithium nitrate mixtures. Proceedings of the International Absorption Heat-Pump Conference, Montreal, Canada, vol. 1, 1996:327–334. [10] Morrison JNA, Deans J. Augmentation of steam condensation heat transfer by addition of ammonia. International Journal of Heat and Mass Transfer 1997;40(4):765–772. [11] Ziegler B, Trepp Ch. Equation of state of ammonia–water mixtures. International Journal of Refrigeration 1984;7(2):101–106. [12] Kays WM, London AL. Compact heat exchanger Ch. 10. 3. New York: McGraw-Hill, 1984. [13] Kang YT, Chen W, Christensen RN. Design of ammonia– water condenser with a fluted tube. ASHRAE Transaction 1996;102(2):587–595. [14] Keizer C. Absorption refrigeration machines. Ph.D. Dissertation, Technische Hogeschool Delft, Netherlands, 1982:88. [15] Herbine GS, Perez-Blanco H. Model of an ammonia–water bubble absorber. ASHRAE Transactions 1995;101(1):1324– 1330. [16] Kang YT, Akisawa A, Kashiwagi T. Visualization of Marangoni convection in ammonia–water solution using holographic interferometer. Submitted for publication, 1998. [17] Kang YT, Stout R, Christensen RN. Experimental investigation on flooding in a fluted tube with and without a twisted insert. Journal of Enhanced Heat Transfer 1997;4(2):111–129. [18] Kang YT, Akisawa A, Kashiwagi T. Analytical investigation of two different absorption modes: falling film and bubble types. International Journal of Refrigeration, 1999, in press.
Experimental correlation of combined heat and mass transfer for NH3 –H2O falling film absorption Yong Tae Kang*, Atsushi Akisawa, Takao Kashiwagi Department of Mechanical Systems Engineering, Tokyo University of Agriculture and Technology, 24-16 Nakamachi, 2-Chome, Koganei, Tokyo 184, Japan Received 7 July 1998; received in revised form 3 December 1998; accepted 7 December 1998
Abstract In this article, experimental analysis was performed for ammonia–water falling film absorption process in a plate heat exchanger with enhanced surfaces such as offset strip fin. This article examined the effects of liquid and vapor flow characteristics, inlet subcooling of the liquid flow and inlet concentration difference on heat and mass transfer performance. The inlet liquid concentration was selected as 5%, 10% and 15% of ammonia by mass while the inlet vapor concentration was varied from 64.7% to 79.7%. It was found that before absorption started, there was a rectification process at the top of the test section by the inlet subcooling effect. Water desorption phenomenon was found near the bottom of the test section. It was found that the lower inlet liquid temperature and the higher inlet vapor temperature, the higher Nusselt and Sherwood numbers are obtained. Nusselt and Sherwood number correlations were developed as functions of falling film Reynolds Re1, vapor Reynolds number Rev, inlet subcooling and inlet concentration difference with ^ 15% and ^ 20% error bands, respectively. 䉷 1999 Elsevier Science Ltd and IIR. All rights reserved. Keywords: Refrigerating system; Absorption system; Ammonia–water; Falling film absorption; Mass transfer; Heat transfer
Corre´lation expe´rimentale entre le transfert de chaleur et de masse pour de l’absorption au NH3 –H2O a` film tombant Resume´ Cet article de´crit une analyse expe´rimentale d’un processus d’absorption ammoniac–eau a` film tombant dans un e´changeur a` plaques muni de surfaces ame´liore´es telles des ailettes en ruban. On examine les effets des caracte´ristiques de l’e´coulement du liquide et de la vapeur, le sous-refroidissement a` l’arrive´e de l’e´coulement du liquide et la diffe´rence de concentration a` l’entre´e sur la performance du transfert de chaleur et de masse. Les concentrations en ammoniac (m/v) du liquide a` l’arrive´e se´lectionne´es e´taient de 5%, 10% et 15%, et les concentrations de la vapeur variaient entre 64,7% et 79,7%. Avant que le processus d’absorption de´marre, on a constate´ un processus de rectification (duˆ au sous-refroidissement a` l’entre´e) dans la partie supe´rieure de la section e´tudie´e. On a e´galement observe´ un phe´nome`ne de de´sorption d’eau vers la parte infe´rieure de la section e´tudie´e. Des nombres de Nusselt et de Sherwood augmentaient avec les baisses de tempe´rature du liquide a` l’entre´e infe´rieure et avec des augmentations de tempe´rature de la vapeur a` l’entre´e. Les corre´lations des nombres de Nusselt et de Sherwood ont e´te´ de´veloppe´es en fonction du nombre de Reynolds Re1 du film tombant, du nombre de Reynolds de la vapeur
* Corresponding author. Tel.: ⫹81 423 887282; fax: ⫹81 423 887076. E-mail address: [email protected] (Y.T. Kang) 0140-7007/99/$20.00 䉷 1999 Elsevier Science Ltd and IIR. All rights reserved. PII: S0140-700 7(98)00076-0
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251
Rev, le sous-refroidissement a` l’entre´e et le diffe´rence de concentration a` l’entre´e avec des marges d’erreur de ^ 15% et ^20% respectivement. 䉷 1999 Elsevier Science Ltd and IIR. All rights reserved. Mots cle´s: Syste`me frigorifique; Syste`me a` absorption; Ammoniac–eau; Film tombant; Transfert de masse; Transfert de chaleur
Nomenclature A area (m 2) Ac cross sectional area (m 2) Af,a fin area in absorption side (m 2) fin area in coolant side (m 2) Af,c Aw,c wall area in coolant side (m 2) wall area in absorption side (m 2) Aw,a G gravitational acceleration (ms ⫺2) H enthalpy (J/kg ⫺1) h heat transfer coefficient (W m ⫺2 K ⫺1) K overall mass transfer coefficient (ms ⫺1) k thermal conductivity (W m ⫺1 K ⫺1) m_ mass flow rate (kg s ⫺1) LMTD log mean temperature difference Nu Nusselt number P pressure (Pa) Pr Prandtl number Q heat transfer rate (J s ⫺1) Re Reynolds number Sh Sherwood number Sc Schmidt number T temperature (⬚C) U overall heat transfer coefficient (W m ⫺2 K ⫺1) x concentration Greek symbols G mass flow rate per perimeter (kg s ⫺1 m ⫺1) b diffusivitly (ms ⫺1) d wall thickness (m) g kinematic viscosity (m 2s ⫺1) hf fin efficiency m dynamic viscosity (kg m ⫺1s ⫺1) r density (kg m ⫺3) Super- and subscripts Abs absorption c coolant eff effective eq equilibrium fin fin hyd hydraulic i interface l liquid film lb bulk liquid li liquid at interface lm log mean OSF offset strip fin rec rectangular v vapor vb bulk vapor
vi w
vapor at interface wall
1. Introduction The use of binary and ternary mixtures as a working fluid was strongly recommended to improve the system performance not only in absorption cycles but also in combined cycles of power generation and absorption cycles. The internal heat exchange owing to the temperature glide of a binary mixture provides the fundamental basis for the absorption cycle such as Generator Absorber heat Exchange (GAX) cycle [1] and the combined cycle such as Kalina cycle [2]. Ammonia–water solution pair was widely used in absorption cycles because of its excellent thermal characteristics. It is also an attractive alternative to ozone-depleting chlorofluorocarbons (CFCs) and CO2-emitting hydrofluorocarbons (HFCs) used in conventional vapor compression systems. In both GAX and Kalina cycles, the absorber is one of the most critical components in the absorption systems from the viewpoint of size and performance. It is the largest component and has a complicated heat and mass transfer mechanism which influences the system performance significantly. Therefore, it is required to analyze the combined heat and mass transfer and to provide fundamental understandings of the heat and mass transfer mechanisms during the absorption process. Generally, the absorber has a falling film mode as a heat transfer mechanism. This heat transfer mode has a high heat transfer coefficient on the liquid film region and it is easily manufactured. Over the last ten years, ammonia–water falling film absorption has been extensively investigated both numerically and analytically [3–7]. However, a few papers have been found on the experimental analysis. Hoffmann and Ziegler [8] tested heat and mass transfer of aqueous ammonia in falling films on horizontal tube bundles. They did not provide the experimental results in the literature, but provided some experimental data in the presentation. The heat transfer coefficients ranged from 1.0 to 2.1 kW/m 2 K at the liquid concentration ranges between 20% and 53%. Rivera et al. [9] obtained experimental data on the heat transfer in forced convective boiling of ammonia–water mixture flowing upward in a vertical tube. The mean heat transfer coefficients ranged from 9.5 to 14.5 kW/m 2 K for ammonia concentration ranges between 38 and 48 wt.%. Morrison and Deans [10] reported that Marangoni effect generates significant disturbance in the liquid film for the condensation of ammonia–water mixture with a low
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Fig. 1. Schematic diagram of the experimental apparatus. Fig. 1. Sche´ma de l’appareil expe´rimental.
ammonia-concentration range of 0.23%–0.88%. These disturbances cause the heat transfer coefficient of the condensate film to increase by as much as 13%. The heat transfer coefficient of ammonia–water condensation on a horizontal tubes were ranged from 8.5 to 18.4 kW/m 2 K [10]. When the vapor temperature is higher than the liquid temperature in rectifier, condenser or absorber of ammonia–water systems, initially rectification occurs, and then absorption or condensation starts. The rectification process has a significant effect on the temperature and concentration profiles, and the heat exchanger size. Therefore, this article conducted both rectification and absorption experiments simultaneously. In analyzing the present experimental data, a control volume analysis was performed to develop Nusselt and Sherwood number correlations during the absorption process. Mass, concentration, energy and heat transfer equations were solved simultaneously for the control volume of the test section. Unlike the condensation process of a single component, the heat and mass transfer performance of a binary mixture condensation depends on the flow characteristics of not only the liquid flow but also
the vapor flow. Nusselt and Sherwood numbers were plotted as functions of vapor Reynolds number as well as the falling film Reynolds number to include the effect of the vapor flow characteristics on the absorption rate. In summary, this article conducts experimental analysis for ammonia–water falling film absorption process in a plate heat exchanger with offset strip fins (OSF) and rectangular plain fins. The objectives of this article is to analyze the combined heat and mass transfer during the ammonia– water absorption process, and to obtain heat and mass transfer coefficients (Nusselt and Sherwood numbers). This article examines the effects of the inlet subcooling of the liquid flow and the inlet concentration differences on the absorption rate. The experimental results from this article would provide fundamental understandings of the ammonia–water absorption process, and thus give an useful guideline in the design of ammonia–water absorption machines.
2. Experimental apparatus and procedures Fig. 1 shows the schematic diagram of the experimental
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253
Fig. 2. Schematic diagram and geometric details of the test section (all dimensions are in mm). Fig. 2. Sche´ma et ge´ome´trie de la section e´tudie´e (dimensions en mm).
apparatus for the falling film absorption test. The experimental setup consists of a liquid supply loop, a vapor supply loop, a liquid outlet loop, a vapor outlet loop, a coolant line and the test section. The liquid mass flow rate was controlled by a solution pump with an invertor and measured by a liquid mass flow meter before entering the test section. Mass flow meters were special order-made for ammonia– water solution which has an maximum error of ^ 0.03 g/s. The inlet liquid temperature was measured by a thermocouple (K-type) at the center of the tube at liquid inlet and outlet. All the thermocouples were calibrated before installation at three different points. The liquid concentration was initially measured by measuring and mixing pure ammonia and water and was also confirmed the density and the titration methods. Suppressed liquid (20% ammonia aqueous solution) was pumped from a solution tank to a generator where vapor is generated. The two phase flow entered a separator in equilibrium state. The vapor and the liquid were separated in a separator, in which the liquid flow
was visualized at the bottom of the separator. The vapor path to the test section was completely insulated so that wet vapor was assumed not to be generated owing to the heat loss. The temperature and the pressure in the separator were carefully measured by a thermocouple and a pressure gauge to calculate the vapor concentration. The pressure was measured by a special pressure gauge for ammonia– water system, which was near the atmospheric pressure. In the experimental setup, the vapor may flow either in the cocurrent or counter-current directions to the liquid flow, which flows down by the gravity force. The separator pressure was a little bit higher than the vapor inlet of the test section so that the vapor could be introduced to the test section continuously. During the current experiments, the saturated vapor and the suppressed liquid from the solution tank enter the test section from the top, so that the liquid and the vapor streams flow in the co-current direction. The strong solution (rich in ammonia) after the absorption process leaves the test section from the bottom, goes to
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Fig. 3. Schematic diagram of the rectangular fin and OSF. Fig. 3. Sche´ma de l’ailette rectangulaire et ailette en ruban.
the solution collection tank and a neutralization tank. The coolant (city water) enters the test section from the bottom, flows up in the counter-cross direction to the liquid solution flow. The inlet liquid concentration was selected as 5%, 10% and 15% of ammonia by mass for the current experiments while the inlet vapor concentration varied from 64.7%–79.7% which were calculated from equilibrium condition at a given temperature and pressure of the separator. The experimental data were taken for a certain period of steady state operation. The steady state was confirmed by the test section pressure variation. Initially, the pressure of the test section increased as the vapor was introduced. Finally, the system pressure was kept constant, which was the criterion for the steady state operation. Table 1 Geometric dimensions of the OSF and rectangular plain fins Tableau 1 Dimensions de l’ailette en ruban et des ailettes rectangulaires lisses
hfin (mm) tfin (mm) Lfin (mm) Sfin (mm) Fin pitch (mm)
Offset strip fin (absorption side)
Rectangular plain fin (coolant side)
4.88 0.20 3.18 1.75 1.95
3.00 0.20 95.0 2.97 3.18
Fig. 2 shows the schematic diagram and geometric dimensions of the test section. The test section has OSF between two plates in the absorption side, and rectangular plain fins between two plates in the coolant side. The OSF was used to enhance heat and mass transfer during the absorption process, and the plain fins were used to enhance the heat transfer coefficient in the coolant side. These fins were made of stainless steel. In the current test section, the liquid flows down on the wall and the OSF while the vapor flows down in the core region. The liquid and vapor flows mix together at the exit of each offset fin, and then separate again at the next offset fin-liquid on the wall and vapor in the core region. The flow pattern inside the test section was visualized through the sight glasses at the top and the bottom to confirm the falling film mode. A liquid distributor was installed at the top of the test section to obtain even liquid distribution which was also confirmed through the sight glasses. The coolant enters the test section from the right side of the bottom, and flows out to the left side of the top of the test section as shown in Fig. 2. A data acquisition system was used to record the inlet and outlet temperatures, concentrations, mass flow rates and the system pressure. Six thermocouples were used to measure the inlet and outlet temperatures of the liquid, vapor, and coolant around the test section. Fig. 3 shows the schematic diagrams of the OSF and the rectangular plain fins used in the experimental setup. The geometric dimensions of the enhanced fins are shown in Table 1. The experimental conditions are summarized in Table 2. During the experiments, the maximum measurement errors in temperature, liquid mass flow rate and liquid concentration were ^ 0.24⬚C and ^ 0.03 g/s, ^ 0.1%, respectively.
3. Data reduction Fig. 4 shows the control volume of the test section for data reduction process. In absorption side, temperature was measured at four different locations; the liquid inlet (T1) and outlet (T2), and the vapor inlet (T3) and outlet (T4). For the coolant side, temperature was measured at two different locations; the inlet (T5) and outlet (T6). Mass flow rate was measured at five different locations; the liquid inlet m_ 1 and outlet m_ 2 , the coolant inlet m_ 5 , the liquid before Table 2 Experimental ranges of inlet conditions Tableau 2 Eventail des conditions expe´rimentales a` l’entre´e Liquid flow rate (g/s) Vapor flow rate (g/s) Coolant flow rate (g/s) Liquid temperature (⬚C) Vapor temperature (⬚C) Liquid concentration (%) Vapor concentration (%)
4.0–10.15 0.62–0.90 98.83–121.25 17.0–37.2 54.5–66.5 5.0–15.0 64.7–79.7
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balances: m_ 1 ⫹ m_ 3 m_ 2 ⫹ m_ 4 ;
1
m_ 1 x1 ⫹ m_ 3 x3 m_ 2 x2 ⫹ m_ 4 x4 ;
2
Qc m_ 6 H6 ⫺ m_ 5 H5 Qc m_ 1 H1 ⫹ m_ 3 H3 ⫺ m_ 2 H2 ⫺ m_ 4 H4 :
3
4. Heat and mass transfer analysis The heat transferred to the coolant can be expressed in the following heat transfer equation: Qc UA × F × DTlm ;
4
where F is a correction factor in the calculation of DTlm for the cross-counter current flow, which ranged 0.9–1.0 depending upon the temperature conditions, and Fig. 4. Control volume of the test section. Fig. 4. Re´gulation du volume de la section e´tudie´e.
the generator m_ 10 , and the liquid outlet from the separator m_ 8 . The inlet vapor flow rate m_ 3 was calculated from m_ 8 and m_ 10 . The inlet vapor concentration (x3) was calculated based on equilibrium condition at (T3, P3) because the inlet vapor is in a saturated state. State equation by Ziegler and Trepp [11] was used in the calculation of ammonia–water properties. The liquid outlet concentration (x2), the vapor outlet mass flow rate m_ 4 and concentration (x4) were obtained from the following concentration, mass and energy
DTlm
T1 ⫺ T6 ⫺ T2 ⫺ T5 ; ln T1 ⫺ T6 = T2 ⫺ T5
1 1 dw 1 ⫹ ⫹ UA habs Aabs hc Ac k w Aw
5 6
and Aabs Aw;a ⫹ hf;a Af;a
and
Ac Aw;c ⫹ hf;c Af;c ; 7
where various areas in Eqs. (6) and (7) are defined in the section of the nomenclature. h f,a and h f,c are fin efficiencies in absorption and coolant side, respectively. The heat transfer area was measured before assembling the test section, and the uncertainty in the measurement of heat transfer area
Fig. 5. Liquid and vapor temperature profiles at the test section. Fig. 5. Tempe´ratures du liquide et de la vapeur dans la section e´tudie´e.
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was ^ 0.14%. The fin efficiencies of the center and side fins on absorption side were about 50% and 25%, respectively, depending on the fin geometry and thermal conditions. By combining Eqs. (4)–(6), the heat transfer coefficient in the absorption side, habs, is given by the following equation: habs
1 : Aabs FDTlm =Qc ⫺ dw =kw Aw ⫺ 1=hc Ac
8
In Eq. (8), the heat transfer coefficient in the coolant side, hc was calculated using the correlation by Kays and London [12] for the plain rectangular fins, which has ^ 5.0% of uncertainty. Finally, Nusselt number for the falling film absorption heat transfer is defined as follows: !1=3 h n2l Nuabs abs : 10 kl g The Nusselt type film thickness was used as the characteristic length because the gravity is the driving force for the falling film movement. As for the mass transfer, the absorption rate is expressed in the following equations by using the overall mass transfer coefficients, K1. Dm_ abs Kl rl Aabs Dxlm;l ; where Dxlm;l
11
"
# xeq T3 ⫺ xl T1 ⫺ xeq T4 ⫺ xl T2 l l ÿ : 12 ln ÿ eq xl T3 ⫺ xl T1 = xeq l T4 ⫺ xl T2
By using the overall mass transfer coefficient, Sherwood number for the falling film absorption is defined as follows: !1=3 Kl n2l Shl : 13 bl g The uncertainties in the calculation of Nuabs consist of two major components: uncertainty in U and uncertainty in the derivation of Nu from U and hi. Heat loss was not included in the error analysis because all the test loop and test section were completely insulated. According to the overall heat transfer equation, the sensitivity equation for U can be expressed as:
12U 12Q ⫹ 12A ⫹ 12LMTD :
14
For the subject experimental data, the uncertainties in Q, A and LMTD were 4.8%, 0.14% and 2.0%, respectively. Therefore, the uncertainty in U was estimated to be ^5.20%. A simplified version of the relationship between uncertainties in the overall resistance and the components is as follows: R tot 2 R c 2 12R abs 1R tot ⫹ 1R c ; 15 R abs R abs where R is the resistance to heat transfer, and subscripts tot, abs and c refer to the overall, absorption side, and coolant side, respectively. For a sample data point with Re1 25.51, The ratio of R(abs) to R(c) was 1.60, respectively. This
means R(tot)/R(abs) is 2.60/1.60 ( 1.625). Substituting this into the earlier equation
12R abs 2:6412R tot ⫹
1 2 1 : 2:56 R c
16
Knowing that the uncertainties from the overall and coolant side are 5.20% and 5.0% respectively, the uncertainty in the absorption side Nuabs was estimated as ^ 9.01% for the considered experimental data. The uncertainties in the calculation of Sh consist of three major components: uncertainties in Dm_ abs , Aabs, and Dxlm,l. Therefore, the sensitivity equation for Sh1 could be expressed as
12Sh 12Dm_ abs ⫹ 12A ⫹ 12Dxlm;l :
17
For the subject experimental data, the uncertainties in Dm_ abs , Aabs and Dxlm,l were 6.0%, 0.14% and 2.3%, respectively. Therefore, the uncertainly in Sh1 was estimated to be ^ 6.42%. The uncertainly in Dxlm,l ranged ^ 0.8%–3.9% depending on the concentration differences for all experimental data. In calculation of Nu and Sh for all experimental data, the uncertainties ranged 5.4%–12.5%, and 4.6%–8.7%, respectively.
5. Results and discussion In this article, heat and mass transfer coefficients were measured by experiments for co-current absorption processes in a plate heat exchanger which has OSF between two plates. When the vapor in contact with the liquid film is in motion, a gas shear force may be exerted on the liquid film at the interface. In the case of low liquid velocity and high vapor velocity, disturbances resulting from the gas shear originate at the interface. In the present experiments, the ratio of vapor to liquid mass flow rates ranged 0.14– 0.23, therefore the gas shear was reasonably assumed to be negligible. Nusselt and Sherwood numbers were obtained for ammonia–water absorption process using a spread sheet program which was made based on the data reduction analysis. Fig. 5 shows the liquid and vapor temperatures at the top and the bottom of the test section for different inlet liquid concentrations with different inlet subcooling. The temperature difference between the vapor and liquid varied with the local position and it became 0⬚C or below 0⬚C near the bottom of the test section. These conditions are general in absorber component of ammonia–water systems. The actual temperature profiles of the liquid and the vapor may not be linear. However, the temperatures were linearly plotted using only the top and the bottom locations for simple explanation. During the current experiments, the liquid temperature increased as the liquid film flowed down along the surface because eof the absorption heat release near the interface and the sensible heat transfer from the vapor to the liquid flow. The sensible liquid and vapor heat transfer ranged 5.4%–23.0% and 1.5%–38.0% of the
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Fig. 6. Representative temperature and concentration profiles for rectification and absorption processes. Fig. 6. Tempe´ratures et concentrations pendant les processus de rectification et d’absorption.
total heat transferred to the coolant, respectively. Therefore, the sensible heat transfer had somewhat effect on the total heat transfer. The temperature variation of liquid and vapor flows ranged 10⬚C–20⬚C and 5⬚C–10⬚C, respectively. The temperature variation depended on the inlet subcooling and the ratio of the sensible heat to the latent heat transfer. At the top, the liquid flow was in subcooled state at a low temperature, T1 while the vapor flow was in equilibrium state at a high temperature, T3 so that there was a rectification process according to the representative temperature and concentration profiles as shown in Fig. 6. Initially, at the top of the test section, the bulk vapor concentration, xvb was lower than the equilibrium vapor concentration at the interface, xvi. As the rectification occurred, the bulk vapor concentration increased and the corresponding bulk vapor temperature decreased sharply owing to the water rectification from the vapor [13]. After the rectification process, the bulk vapor concentration became higher than the equilibrium vapor concentration, thereafter the absorption started. Near the bottom of the test section, water desorption was found by checking ammonia balance of liquid and vapor flows. Physically, this means that ammonia vapor is absorbed into the liquid flow while water liquid evaporated into the vapor flow. This phenomenon was also described by Keizer [14], Kang and Christensen [5] and Herbine and PerezBlanco [15] by considering combined heat and mass transfer during ammonia–water absorption process. Fig. 7 shows the effect of the inlet subcooling of the liquid flow on the heat and mass transfer coefficients. As can be
seen in Fig. 7, the heat and mass transfer coefficients increased as the inlet subcooling increased for a given liquid mass flow rate and inlet concentration difference. It was found that the inlet subcooling has more significant effect on heat transfer than mass transfer for a given liquid mass flow rate and inlet concentration difference. The heat and mass transfer coefficients ranged 500–2100 W/m 2 K and 1.0–55 × 10– 5 m/s, respectively, depending on the inlet thermal conditions for all the current experiments. The inlet subcooling of the liquid ranged 22.5⬚C–40.0⬚C for all the current experiments. Fig. 8 shows the effect of inlet concentration difference on the heat and mass transfer coefficients. The inlet concentration difference ranged 60.0%–75.0% during the experiments. It was found that the heat transfer coefficient decreases while the mass transfer coefficient increases with increasing the inlet concentration difference for given liquid mass flow rate and inlet subcooling of the liquid flow. The different trends of heat and mass transfer coefficients are discussed in detail in Section 7 by considering the combined heat and mass transfer analysis. Fig. 9 shows the effects of falling film Reynolds number Re1 on Nusselt and Sherwood numbers. The Sherwood number, Sh1 was obtained by the definition of overall mass transfer coefficient K1 as shown in Eq. (13). As can be seen in Fig. 9, Nusselt and Sherwood numbers increased with increasing the falling film Reynolds number. In the current experiments of ammonia–water mixture, Nusselt number and Sherwood number ranged 0.04–0.16 and
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Fig. 7. The affect of inlet subcooling on heat and mass transfer coefficients. Fig. 7. Effet du sous-refroidissement a` l’entre´e sur les coefficients de transfert de chaleur et de masse.
0.4–2.0, respectively, depending on the inlet thermal conditions. The Nusselt number was much lower than 1.0 for the falling film heat transfer mode because the characteristic length in Eq. (10) is defined differently from the forced convection case in which Nusselt number is generally larger than 1.0. The Nusselt number was lower than the Sherwood number because Lewis number, Le ( a 1/b 1) ranged from 9.0 to 27.0 for the current experimental conditions. This implies that the effective thickness of thermal boundary layer is thicker than that of the diffusion boundary layer,
which was confirmed by visualization work of the ammonia–water absorption using holographic interferometer by Kang et al. [16]. Fig. 10 shows the effects of vapor Reynolds number Rev on Nusselt and Sherwood numbers. The heat and mass transfer performance of a binary mixture condensation such as ammonia–water absorption depends on the flow characteristics of not only the liquid flow but also the vapor flow [17]. It was suggested that the vapor flow rate be maximized to increase heat and mass transfer
Fig. 8. The effect of inlet concentration difference, x3 –x1 on habs and K1. Fig. 8. Effet de la diffe´rence de concentration a` l’entre´e, x3 –x1 sur habs et K1.
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259
Fig. 9. The effect of Re1 on Nuabs and Sh1. Fig. 9. Effet de Re1 sur Nuabs et Sh1.
performance in ammonia–water absorption process. From the current experiments, both Nusselt and Sherwood numbers were found to be increased as the Reynolds number of the vapor flow increased for the given liquid mass flow rate, inlet subcooling and the inlet concentration difference. The sensible heat of the vapor flow is transferred from the vapor to the liquid region during the rectification process while it is from the liquid to the vapor region during the absorption process by the temperature profile as shown in Fig. 6. As Rev increased, both heat and mass transfer increases in the vapor region. Kang et al. [18] fond that the mass transfer resistance is dominant rather than the
heat transfer resistance in the vapor region for the falling film absorption mode (without rectification process) by solving the diffusion, concentration, mass, and energy equations in the vapor region simultaneously.
6. Experimental correlations In this article, Nusselt and Sherwood numbers were correlated as functions of Re1 and Rev to evaluate the effects of the vapor and liquid flow characteristics on the absorption
Fig. 10. The effect of Rev on Nuabs and Sh1. Fig. 10. Effet de Rev sur Nuabs et Sh1.
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Fig. 11. Nusselt number correlation. Fig. 11. Corre´lation du nombre de Nusselt.
rate as follows:
vapor Reynolds numbers, and thermal conditions are within the valid ranges, however, the correlations can be used in the calculation of Nuabs and Sh1 for plate heat exchangers with OSF which are widely used in ammonia–water absorption heat pump systems.
Nuabs 0:8530 ×10⫺3 ·Rel 1:5180 Rev 0:1759
DTsub;i T1
1:8790
Dx31 x1
⫺0:5756 18
and
7. Parametric analysis
Sh1 0:6996
This article analyses the effects of liquid mass flow rate, vapor mass flow rate, liquid and vapor temperatures, and liquid and vapor concentrations on heat and mass transfer performance. From the current experimental results, the effects of each inlet thermal condition on Nusselt and Sherwood numbers are summarized in Table 3. In Table 3, " represents “increased” or “became higher”, and # represents “decreased” or “became lower”. The results from this parametric analysis are valid for the falling film absorption of
× 10⫺7 ·Rel 0:8874 Rev 1:265
DTsub;i T1
0:8844
Dx31 x1
0:5304
;
19 where Rel
4Gl ml
and
Gl
m_ l : perimeter
20
In Eqs. (18) and (19), Rev was calculated based on the hydraulic diameter in the vapor flow, dhyd,v ( 4Ac/ perimeter). All experimental data for Nuabs and Sh1 were plotted in Figs. 11 and 12 with ^ 15% and ^ 20% error bonds, respectively. The Reynolds numbers of liquid and vapor flow were ranged 6.78–25.51 and 26921–40913 in the above experimental correlation, respectively. All the thermal conditions are summarized in Table 2. The present Nuabs and Sh1 correlations cannot be generally used for ammonia water falling film absorption process. As long as the liquid and
Table 3 Summary of parametric effects on Nuabs and Sh1 from the experimental results Tableau 3 Re´sume´ des effets parame´triques sur Nuabs et Sh1 a` partir des re´sultats expe´rimentaux Parameter
Nuabs
Sh1
Inlet liquid temperature, T1 " Inlet vapor temperature T3 " Inlet liquid concentration x1 #
# " #
# " "
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261
Fig. 12. Sherwood number correlation. Fig. 12. Corre´lation du nombre de Sherwood.
ammonia–water mixture with rectification process at the inlet conditions as shown in Fig. 6. 7.1. Liquid and vapor mass flow rates It was found that both heat and mass transfer coefficients increased with increasing liquid and vapor mass flow rates. As can be seen in the experimental correlations, Nusselt number is more significantly affected by falling film Reynolds number than Reynolds number of vapor flow while Sherwood number is more significantly affected by Reynolds number of vapor flow than falling film Reynolds number. Therefore, even though there exists combined heat and mass transfer effects from both liquid and vapor mass flow rates, it is recommended that liquid mass flow rate be increased to primarily enhance heat transfer performance, and vapor flow rate can be increased to primarily enhance mass transfer performance. 7.2. Inlet liquid and vapor temperatures It was found from the experiments that Nusselt and Sherwood number increased as the inlet liquid temperature, T1 decreased for a given inlet vapor temperature, T3. This can be explained from the viewpoints of heat transfer and combined heat and mass transfer as follows: As T1 decreases, the sensible heat from the vapor to the liquid increases, leading to a higher Nusselt number (heat transfer). As T1 decreases, the corresponding equilibrium temperature, Ti decreases so that a vapor equilibrium concentration xvi becomes higher, which results in a larger rectification
amount leading to higher Nusselt and Sherwood numbers (combined heat and mass transfer). As T3 increases for a given T1, the sensible heat from the vapor to the liquid also increases (heat transfer). As T3 increases, the corresponding bulk vapor concentration, xvb decreases leading to a larger rectification amount (combined heat and mass transfer). Therefore, it could be concluded that the lower T1 and the higher T3, the higher Nusselt and Sherwood numbers are obtained.
7.3. Inlet liquid concentration It was found from the experiments that as the inlet liquid concentration, x1 decreased for a given inlet vapor concentration, x3, Sherwood number increased while Nusselt number decreased. This can be explained from the viewpoints of mass transfer and combined heat and mass transfer as follows: As x1 decreases, the potential concentration difference, xeq 1 T3 ⫺ x1 increases leading to a higher Sherwood number (mass transfer). As x1 decreases, the corresponding equilibrium concentration xvi decreases, which results in a lower rectification amount leading to a lower Nusselt and Sherwood numbers (combined heat and mass transfer). This opposite trends from the mass transfer and the combined heat and mass transfer could be explained as follows. The absorption process after the rectification process has more significant effect on Sherwood number than the rectification at the top on Sherwood number, noting that the absorption rate increases as x1 decreases. This
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was why Sherwood number increased with decreasing x1 from the current experiments. 8. Conclusions The present experimental results were obtained under the condition that the inlet vapor temperature was higher than the inlet liquid temperature. Therefore, the present experimental correlations should be used under the inlet subcooling condition. The following conclusions were drawn from the present experimental studies: (1) It was found that there was a rectification process at the top of the test section by the inlet subcooling effect. After the rectification process near the top, absorption starts when the bulk vapor concentration becomes higher than the equilibrium vapor concentration at the interface. Near the bottom of the test section, water desorption occurred to meet the mass balance of ammonia. (2) The heat and mass transfer coefficients increased as the inlet subcooling increased for given liquid mass flow rate and inlet concentration difference. It was found that the inlet subcooling has more significant effect on heat transfer than mass transfer. The heat transfer coefficient decreases while the mass transfer coefficient increases with increasing the inlet concentration difference for given liquid mass flow rate and inlet subcooling of the liquid flow. (3) It was found that Nusselt number is more significantly affected by falling film Reynolds number than Reynolds number of vapor flow while Sherwood number is more significantly affected by Reynolds number of vapor flow than falling film Reynolds number. (4) The lower T1 and the higher T3, the higher Nusselt and Sherwood numbers are obtained. (5) It was found that the Sherwood number increased while Nusselt number decreased as x1 decreased. (6) The following Nusselt and Sherwood number correlations were developed with ^ 15% and ^ 20% error bands, respectively. Nuabs 0:8530 × 10⫺3 ·Rel 1:5180 Rev 0:1759
DTsub;i T1
1:8790
Dx31 x1
⫺0:5756
and Sh1 0:6996 × 10⫺7 ·Rel 0:8874 Rev 1:265
DTsub;i T1
0:8844
Dx31 x1
0:5304
:
Acknowledgements This work was partially funded by Japan Science and Technology Corporation (JST). The authors would like to thank Mr. Y. Fujita in Tokyo University of Agriculture and Technology for his assistance during the experiments.
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