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Evaluation of mass absorption in LiBr flat-fan sheets
Applied Energy 86 (2009) 2574–2582
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Evaluation of mass absorption in LiBr flat-fan sheets E. Palacios a,*, M. Izquierdo b,d, J.D. Marcos c, R. Lizarte d a
Escuela Universitaria de Ingeniería Técnica Industrial, U.P.M., Ronda de Valencia 3, 28012 Madrid, Spain Instituto de Ciencias de la Construcción Eduardo Torroja, C.S.I.C., Serrano Galvache 4, 28033 Madrid, Spain Escuela Técnica Superior de Ingeniería Industrial, U.N.E.D., Juan del Rosal 12, 28040 Madrid, Spain d Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Madrid, Spain b c
a r t i c l e
i n f o
Article history: Received 2 September 2008 Received in revised form 3 April 2009 Accepted 16 April 2009 Available online 13 June 2009 Keywords: Adiabatic absorption Lithium bromide aqueous solution Air conditioning Flat-fan sheet
a b s t r a c t Experiments were conducted to determine the absorption rates of refrigerant vapour in an aqueous lithium bromide flat-fan sheet for use in absorption air-conditioning systems. The solution flow rates tested ranged from 0.023 to 0.054 kg/s (84–194 kg/h), with pressure losses in the injection nozzle of from 40 to 250 kPa. The effect of the mass flow rate on both solution residence time and the sheet deformation rate was also analyzed in absorption chambers of a pre-defined length, along with the effect of the sub-cooling temperature on the amount of vapour absorbed. The downstream evolution of approach to equilibrium factor F was quantified. The mass transfer coefficient values were found to be over 3 104 m/s. In absorption chambers 100 mm long, over 0.8 g/s l of vapour were absorbed per chamber absorption volume. Moreover, about 600 g of vapour were absorbed per kJ of solution flow work. Flat-fan sheet configurations were found to perform better than falling film and spray absorbers. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Absorption heat pumps, and particularly absorption machines, are presently seen as a possible, environmentally friendly alternative to conventional vapour compression chillers in small power applications. The size of the absorption machine, however, and especially the size of one of its key components, the absorber, will have to be scaled down to make this system commercially viable. The market has shown a preference for falling film absorbers, in which the sub-cooled solution that flows into the absorber slides along the outer surface of the tube bank inside the unit. At the same time, an external refrigerant fluid flows through the tube bank, collecting the absorption heat [1]. The general instability of the solution sheet generated [2], however, may reduce the vapour–solution interface area. The remedy for this drawback is to over-size the absorber. Moreover, falling film absorbers are unsuitable for viscous solutions such as aqueous LiBr because the thickness of the sheet formed hinders vapour absorption. Most of the approaches to compact absorber design seek to raise the vapour–solution interface area. Among the most effective in this regard are bubble absorbers [3–6]. According to numerical simulations performed by Keizer [7], with bubbles, absorber size could be reduced by half. Merrill and Perez-Blanco [8] and Merrill [9] acknowledged, however, that further experimental analysis is required. In any event, the high energy demands in bubbling a va-
* Corresponding author. Tel.: +34 913366874; fax: +34 913367676. E-mail address: [email protected] (E. Palacios). 0306-2619/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2009.04.033
pour through a liquid solution [10,11] seriously limit the efficiency of this system. This negative aspect is mainly the reason for which bubble absorber are not appropriate for water–LiBr systems. Spray absorbers increase the solution surface area by atomization, generating a population of small droplets [12,13]. Despite Mehta and Sharma’s [14] defence of the low cost of spray absorbers, however, like vapour bubbling, liquid atomization is energy-intensive. Nonetheless, spray absorbers are a type of adiabatic absorber, in which vapour absorption is achieved without releasing the absorption heat. Adiabatic absorbers are fitted with an external loop in which a compact heat exchanger removes the absorption heat from the solution in a multi-pass process. Hence, there is no need for any heat exchange surface inside the absorber, or, therefore, for any material surface. It is clear that, in this way, the poor wetting of the surface is prevented, which is what calls for oversizing in falling film absorbers. Another possible strategy for reducing absorber size is to increase interface efficiency by inducing mixing. Since convection mechanisms are known to be more efficient than diffusion in transport processes [15], Kang et al. [16,17] proposed generating Marangoni recirculation by adding specific surfactants to induce mixing in the liquid solution. Nevertheless, an effort has been done to get a fully understanding of the way these additives increase the rate of the transfer processes [18–20]. Conversely, Tsai and PerezBlanco [21] suggested the use of passive and active mechanisms for the same purpose. By contrast to active techniques, which involve more complex devices, the formation of inherently unstable, free liquid sheet seems to be a suitable mechanism for inducing mixing. In
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Nomenclature A cS D20 F hlv m h Labs _S m _v m p T V Vspr
vapour–solution interface area (mm2) solution-specific heat (J/kg °C) mean droplet diameter based on the surface area (lm) approach to equilibrium factor (–) vapour condensation plus dilution enthalpy (J/kg) mean mass transport coefficient (m/s) length of the test section in the absorption chamber (mm) injected solution mass flow rate (kg/h) mass flow rate of absorbed vapour (kg/h) absorption chamber pressure (kPa) temperature (°C) absorption chamber volume (l) volume of injected solution (mm3)
particular, flat-fan liquid sheets may be a good choice because of the ongoing generation of interface entailed. Flat-fan liquid sheet develops radially between thick edges as it develops. As a consequence, the liquid–gas interface area increases, forcing the liquid to move from the core of the sheet to its interface. The result can be a significant enhancement of the mass transfer rate. Sheet gets distorted and eventually disintegrates into droplets due to the amplification of natural disturbances. In this way, sheet disintegration also could contribute to the interface renewal and, consequently, to the mass transfer rate raise. Hence, conversely to spray configuration, in which the efficiency of the generated droplet declines when the droplets reach mechanical equilibrium [22,23], flat-fan liquid sheet configuration forces the liquid interface renewal at any time. Another appealing feature of flat-fan sheets is that they can be densely packed. Furthermore, since flat fan formation calls for only moderate amounts of energy, absorbers with low pressure losses can be used. An aqueous lithium bromide flat-fan sheet was chosen for the present study because it is characterized by lower energy demands than liquid atomization. The present study focused on scaling down chamber volume and reducing pressure loss across the absorption chamber. Variations in the amount of vapour absorbed were quantified over a range of solution flow rates. Absorption chamber size and the mechanical energy consumed in fan sheet development were likewise determined. The experimental setup designed for this purpose, the measuring principle applied and the results obtained are discussed in the following sections. 2. Experimental measurements 2.1. Experimental setup The experiments were conducted in a stainless steel chamber where the fan sheet developed, became unstable and broke up into droplets (see Fig. 1). The four sides of the chamber were glazed in order to allow optical access. The solution was injected into the chamber through a Spraying Systems Co. vee-jet type nozzle usable with absorption machines, to generate a fan sheet. A magnetically driven gear pump re-circulated the solution. The refrigerant vapour was fed into the absorber from a supply box through a handle-governed valve, which maintained chamber conditions at the pressure setting with a precision of ±0.05 kPa. The length of the test section in the chamber was defined to be the distance between the tip of the injector nozzle and a fixed point at a sufficient distance from the solution remaining on the floor of the chamber. The tube on which the injector nozzle was mounted
x
mass fraction of lithium bromide in the solution (%)
Greek symbols qS solution density (kg/m3) h sheet angle (°) Subscripts adiab mass equilibrium for the vapour adiabatic absorption process eq thermodynamic equilibrium i test section inlet o test section outlet
could be adjusted to vary the length of the test section by raising or lowering the nozzle. The apparatus was fitted with two absolute pressure transducers that measured the pressure upstream of the nozzle and inside the chamber. The temperature, density and flow rate of the circulating solution were recorded on a Coriolis-type meter. Two T-type calibrated thermocouples, positioned at the inlet manifold and the test section exit, recorded the temperature of the solution at the beginning and end of the vapour absorption process, respectively. The instrument specifications are summarized in Table 1. The sprayed solution was imaged with a single high-energy Argon spark flash lamp that back-illuminated the spray and a CCD digital camera. The images were subsequently analyzed to quantify the area of the vapour–solution interface. 2.2. Data collection Several trials were conducted. Before initiating each, the apparatus was filled with a known amount of solution, small enough to prevent the spray deposit accumulating on the floor of the chamber from rising to the level of the outlet thermocouple. The test section length, Labs, was set with the injector nozzle tube. Any atmospheric air existing in the chamber was evacuated with a vacuum pump prior to starting the trials. The refrigerant, in this case water vapour, was generated in the vapour supply box at temperatures of 10–45 °C by vapourizing liquid water with an electric heater. The vapour flowed into the absorption chamber through a handle-governed valve, which kept the absorption chamber pressure at the specified level. Once the working pressure was reached in the absorber, the solution was pumped into the apparatus at the pre-established _ S;i . The temperature of the solution rose during mass flow rate, m the trial due to the heat generated by vapour absorption, while the density declined as a result. The following parameters were recorded at 30-s intervals:
solution temperature at the inlet (Ti), mean solution temperature at the outlet (To), solution density prior to spraying (qS,i) and absorption chamber pressure (p).
The trial was concluded when qS,i fell below approximately 1.620 kg/l. The same procedure was followed in subsequent trials, varying the test section length and/or the solution flow rate at the inlet. The test conditions are given in Table 2.
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Fig. 1. (a) Experimental setup. (b) Elevation view and cross-section of the injector nozzle: A = 1.2, B = 3.4, D1 = 6.7, D = 3.6 and L = 10.1 (dimensions in mm).
Table 1 Instrument specifications. Instrument
Type
Range
Accuracy
Flow rate, density and temperature meter
Coriolis
Thermocouples Pressure sensor Pressure sensor
T Absolute pressure Absolute pressure
(0.19 < m < 600) Kg/h (0.3 < q < 5) Kg/l (180 < T < 150) °C 10–60 °C 0–2.5 bar 8.3–250 mbar
Mass flow rate: ±0.1% VM Density: ±4 g/1 Temperature: ±1 °C ±0.5 °C 0.5% span <0.1% span
Table 2 Test conditions. Chamber pressure, q (kPa) Inlet solution temperature Ti (°C) _ S;i (kg/h) Inlet solution flow rate. m Lithium bromide concentration, xi (%)
0.6–2.2 21–27 (q = 0.6) 38–50 (q = 2.2) 84–194 58–60
2.3. Measuring principle The objective was to obtain the mass flow rate of the vapour ab m and the approach _ v , the mean mass transfer coefficient h sorbed m to equilibrium factor F. m and F were calcu_ v, h The outlet values of the magnitudes m lated from the data recorded in each trial using the measuring principle described below:
Inlet sub-cooling temperature, Teqi Ti (°C) Drop pressure along the injector nozzle (kPa)
9–21 15–102
Test section length, Labs (mm) Flow velocity (m/s)
3.5–43 4.4–10.2
Assuming adiabatic absorption, the mass flow rate of the vapour _ v , can be determined by measuring the temperature absorbed, m rise observed in the injected solution as a result of the heat released during vapour absorption. Consequently, the energy balance _ v can be between the nozzle exit and the outlet thermocouple, m found from the expression:
_ S;i _v ¼m m
cS ðT o T i Þ hlv
ð1Þ
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where cS denotes the solution-specific heat and hlv is the variation in enthalpy generated as a result of vapour condensation and subsequent dilution. Any change in the internal energy of the water absorbed was assumed to be negligible and therefore disregarded. _ v was two orders This assumption was justified by the fact that m _ S;i , as discussed in Section 3 below. of magnitude lower than m _ v , the mean mass transfer coefficient in the test secKnowing m m , can be obtained from: tion, h
m A Dq S _v ¼h m
ð2Þ
where A is the area of the solution–vapour interface and DqS is the mean difference in solution density in the test section. For an absor_ v , given a conber able to handle a given mass flow rate of vapour, m stant DqS , minimizing the absorber size is tantamount to m A=V, where V is the volume occupied by the spray, maximizing h i.e., the volume of the absorption chamber. In Expression (2), area A is obtained by adding the interface of the liquid spray to the overall interface area of the droplets generated during disintegration. Both magnitudes were measured by analyzing the images of the back-illuminated spray. The parameter DqS , in turn, may be computed from (Kim et al. [24,25]):
DqS qS;i Dxlm
ð3Þ
where Dxlm is the mean difference in the mass fraction of LiBr found from the expression:
Dxlm ¼
D xi D xo ; lnðDxi =Dxo Þ
i:e:; Dxlm ¼ Dxi
Dxo = Dxi 1 lnðDxo =Dxi Þ
ð4Þ
where Dx is the local difference between the actual mass fraction of LiBr, x, and the mass fraction at equilibrium, xeq, at pressure p and local solution temperature T. The approach to equilibrium factor, F, in turn, can be found from:
F¼
x i xo xi xo;adiab
ð5Þ
_ LiBr =m _ S is the mass fraction of LiBr in the aqueous soluwhere x ¼ m tion. The subscripts i and o refer to the test section inlet and outlet, respectively. The subscript adiab refers to the thermodynamic equilibrium reached during adiabatic absorption. Note that the magni-
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tude xo;adiab depends on the inlet conditions only. It follows from Eq. (4) that the mass fraction of LiBr at the test section outlet, _ LiBr =m _ S;o , is xo ¼ m
xo ¼
xi 1 þ cS =hlv ðT o T i Þ
ð6Þ
where the mass fraction of LiBr at the absorber inlet can be found from the empirical qS,i and Ti values [26]. An F value of <1, i.e., where xo > xo,adiab, indicates that vapour absorption is underway. This process involves local imbalance: in other words, at any test section length, the temperature T of the solution is lower than the equilibrium temperature, Teq, as computed from the local values of p and x. The difference between these two temperatures, Teq T, is the sub-cooling temperature. 3. Results and discussion The following items contain a discussion of the effect of sheet development on the amount of refrigerant absorbed, as well as of absorption chamber volume and pressure loss. 3.1. Liquid spray configuration As shown in Fig. 2, the flat-fan liquid sheet produced by the fan nozzle used in the trials expanded as it descended along the x–y plane. This was due to the radial movement induced in the solution as it flowed through the convergent conduit, which was fitted with two lateral slots (see Fig. 1). The sheet thinned out as it expanded. Sheet thickness decreased as the distance from the virtual origin, located inside the nozzle, increased. This point was placed at the intersection of the two imaginary lines drawn along the initial trajectories of the primary rims, which define the liquid sheet angle h. Downstream of the exit, these rims retracted towards the sheet bulk, became unstable and disintegrated into droplets. Sheet recession is governed by the equilibrium between surface tension and inertia. Meanwhile, the sheet bulk, distorted by the surface tension action, eventually broke up as well [27–30]. With the downstream expansion of the liquid sheet, the interface area per volume of injected solution, A/Vspr, grew until the sheet disintegrated into droplets, after which A/Vspr declined, as
Fig. 2. Expanding liquid sheet produced by a flat-fan nozzle (solution flow rate: 152 kg/h, chamber pressure: 0.4 kPa), (a) front view, (b) side view.
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Fig. 4. (a) Absorption chamber volume per volume of solution injected versus length. (b) Pressure drop in the injector nozzle versus solution mass flow rate. Fig. 3. (a) Interface area per volume of injected solution versus time. (b) Liquid sheet angle and mean droplet diameter (based on the surface area, D20, of the droplet population generated by liquid sheet disintegration) versus solution mass flow rate.
Fig. 3a shows. The time lapsing from injection was calculated by dividing the distance to the injector tip by the flow velocity, defined to be the volumetric flow divided by the cross-sectional area of the injector at the exit. The latter magnitude was calculated using the equivalent diameter provided by the injector manufacturer. The initial variation in A/Vspr is indicative of the deformation rate of the solution in the sheet. Fluid deformation entails the renewal of the sheet surface. As a result, the refrigerant-poor core moves to interface enhancing vapour absorption. The values of A/Vspr per unit of time ranged from 1.5 to 6.5 (mm s)1 when the solution flow rate was raised from 92 to 232 kg/h. Nonetheless, after reaching a peak value, A/Vspr was observed to decline progressively as a result of rim retraction, particularly at the lower flow rates. Even though rim retraction caused A/Vspr to decline, it is reasonable to assume that, due to sheet bulk divergence, the deformation rate of the sheet did not decrease. The liquid surface was also intensely renewed as the sheet disintegrated into droplets, possibly enhancing vapour absorption. Fig. 3a shows that A/Vspr rose more steeply when the solution flow rate was higher. The experiments also showed that the time lapsing from injection to sheet disintegration was shortened at the higher solution flow rate. More specifically, disintegration time rose from approximately 16 to 33 ms when the solution flow rate was decreased from 232 kg/h to 122 kg/h. Given the length of time it took for the sheet to disintegrate, most of the vapour absorption would be expected to take place in the sheet, while the droplets would play a secondary role.
Compact absorber design seeks to reduce the volume of the vapour–solution interface. The absorption chamber volume, defined to be the volume of a single flat-fan sheet, was calculated assuming a chamber with a rectangular section 0.01 m wide. Fig. 4a shows the variation in absorption chamber length versus chamber volume per volume of injected solution, V/Vspr. Another important feature in absorber design is pressure loss. In the absorber configuration analyzed in this paper, the pressure loss was primarily the loss observed when the solution flowed across the injector nozzle. Fig. 4b shows the pressure drop in the injector nozzle versus solution mass flow rate. This data show that the pressure drop in the injector increased with the square of the mass flow rate, exhibiting a value of 25 kPa at a flow rate of 107 kg/h. While the sheet angle peaked within the solution flow rate interval studied, the pressure loss rate continued to grow with increasing flow rates. In the flat-fan nozzle tested in this study, the pressure drop climbed from 0.25 to 0.60 kPa per kg/h when the flow rate increased from 107 to 218 kg/h due to the rise in the turbulent energy generated in the nozzle. Nonetheless, pressure loss was clearly less intense in the flat-fan nozzle than in spray absorbers [13]. 3.2. Attainment of equilibrium absorption 3.2.1. Mean mass transfer coefficient One of the key parameters that governs the vapour transfer rate, m . As mentioned above, one _ v , is the mass transfer coefficient, h m possible way to quicken the slow absorption inherent in molecular diffusion is by stimulating convective mixing in the liquid. In this regard, the expansion-driven renewal of the sheet surface may enhance vapour absorption.
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m , versus absorption chamber length Fig. 5. (a) Mean mass transfer coefficient h (mass flow rate: sheet A: 188 kg/h; sheet B: 144 kg/h; sheet C: 100 kg/h; initial sub_ S versus absorption chamber length. _ v =m cooling temperature: 14 °C). (b) m
Fig. 5a shows the downstream evolution of the mass transfer m , for flat fan solution sheet produced at mass flow coefficient, h rates of 188, 144 and 100 kg/h (sheet A, B and C, respectively). m was observed to decline sharply in the first 60 mm Coefficient h (i.e., in approximately the first 6–12 ms after the solution was injected, depending on the flow rate in question) to about 3 104 m/s. This reduction was due to the solution flow regimen got laminar downstream due to the intense slimming of the sheet. The undulation in the sheet surface near the injector tip generated by the turbulent energy inside the nozzle would heighten flow mixing. These waves dampened as the sheet thinned out downstream, however. m values grew with the The data showed that while the initial h solution flow rate, very likely due to the higher deformation rate in
the sheet (see Fig. 3a), turbulent energy also increased, as shown by the intensification of the pressure drop in the injector (see Fig. 4b). m was one orWith values upward of 3 104 m/s in all cases, h der of magnitude larger than reported by other researchers for the isothermal falling film configuration (see Table 3). Moreover, in the m was five times higher than flat-fan sheet tested in this study, h found by Warnakulasuriya and Worek [13] for the spray configuration. This can be attributed to the effect of interface renewal, which plays only a minor role in falling film and spray configurations. _ v , is the Another determinant in the vapour absorption rate, m m is known, the effect area of the vapour–liquid interface, A. Once h of varying A may be evaluated. Fig. 5b shows the downstream evolution of the refrigerant vapour mass absorbed per mass of solution _ S , for sheets A, B and C. The value of m _ v =m _ S was ob_ v =m injected, m served to be higher in sheet A than sheet B at all test section m lengths, a finding consistent with the behaviour exhibited by h _ v =m _S and A, which increased with the solution flow rate. The m parameter was similar in sheets A and C, however, despite the difference in flow rate: the time lapsing from injection was, then, nearly 50% shorter in sheet A than sheet C. These results show that, m A in sheet C was offset at any position downstream, the lower h by the longer time lapsing after injection. These conditions were not observed in sheet B, however, inferring the existence of a certain range of solution flow rates that combine low residence time m A values. Solution flow in the absorption chamber with low h rates within this interval should be avoided because of their low _ S. _ v =m m _ S value, the absorption _ v =m It is concluded that, for a fixed m chamber length rises as the solution flow rate is increased due to the subsequent reduction in the solution residence time. Nevertheless, this tendency could change if the reduction in residence time that the solution flow rate rise involves is offset by the resulting inm A. crease in h Experiments shown that the flow rate of the vapour absorbed _ v =A is up to 0.0169 kg/s m2 in an absorption per interface area, m chamber 200 mm long, length required for absorption to nearly come to an end. This means that the heat transfer per fan sheet _ v =A found is about one orarea is about 42 kW/m2. Note that the m der of magnitude larger than that typical for conventional falling film design, which is 0.0027 kg/s m2. Experimental results shown in this paper have let design the flat-fan sheet absorber [34–36] of a low power absorption cooling machine prototype. The performance of this machine is being checked and it will be published in the next future. 3.2.2. Effect of the initial sub-cooling temperature The experimental results in Fig. 5b also show that the value of _ S at equilibrium in sheets A and C differed from the value _ v =m m _ S in_ v =m in sheet B. Fig. 6, in turn, shows that the peak value of m creased linearly with the sub-cooled temperature. This linear correlation concurred with findings reported by Arzoz et al. [33] for fluids with other morphologies. Therefore, sheets A and C reached _ S value because their initial sub-cooling _ v =m the same maximum m temperature was the same.
Table 3 m . Mass transfer coefficient, h m 105 (m/s) h
Absorber type
Reference
Methodology
Solution
Falling film absorber
Kim et al. [25] Miller and Perez-Blanco [31] Venegas [32] Warnakulasuriya and Worek [13]
Experimental
LiBr–H2O
Spray absorber a
Droplet mean diameter: 500 lm.
Theoretical
a
LiBr–H2O
0.5–0.7 1.9 2 6
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_ v =m _ S versus sub-cooling temperature at the injector exit Fig. 6. Equilibrium m ðT eq;i T i Þ. The analytical expression in the graph represents the linear model used to fit the data.
Fig. 7. Approach to equilibrium factor, F, versus length. The points on Figure represent the break-up length and the break-up time in milliseconds for each mass flow rate (mass flow rate: sheet A, 188 kg/h; sheet B, 144 kg/h; sheet C, 100 kg/h; sub-cooling temperature at the injection exit: 14 °C).
3.2.3. Approach to equilibrium factor Fig. 7 shows that the approach to equilibrium factor, F, increased monotonously downstream to a value of about 0.9 when it was very near equilibrium. F reached 0.9 in 20 ms at a flow rate of 100 kg/s (sheet C). It took twice that long, however, when the flow rate was raised to 188 kg/ h (sheet A). This finding has two consequences. On the one hand, the interface area per volume injected was larger in sheet A due m was higher to its larger flow rate (Fig. 3a). And on the other, h as well due to its larger deformation rate (Fig. 5a). With respect to the effect of sheet disintegration on the vapour absorption rate, no evidence was found of a change in F growth upon sheet disintegration, despite the renewal of liquid interface that sheet disintegration entails. When sheets A, B and C disintegrated at tres 17, 24 and 27 ms, respectively, absorption had nearly come to an end (F > 0.8), minimizing any possible effect of the new interface area. 3.3. Absorption chamber size and mechanical energy demands As mentioned above, the aim in compact absorber design is to m A per absorption chamber volume V. maximize the magnitude h Fig. 8a shows the downstream evolution of the vapour absorbed per volume of absorption chamber for a range of solution flows.
Fig. 8. (a) Vapour absorbed per absorption chamber volume versus absorption chamber length. (b) Vapour absorbed per solution flow work versus absorption chamber length (mass flow rate: sheet A, 188 kg/h; sheet B, 144 kg/h; sheet C, 100 kg/h; sub-cooling temperature at the injection exit: 14 °C).
According to these findings, cooling power declined steeply as the absorption chamber length increased, particularly in the first 100 mm or 20 ms, when the vapour absorbed per volume dropped to 0.8 g/s l. Nevertheless, the vapour absorbed per volume is about 0.3 g/s l at 200 mm, when absorption is nearly at an end. Hence, the heat transfer per absorber volume exceeds 743 W/l. Note that the average vapour absorbed per volume in the flat-fan sheet design is clearly larger than that found for low power conventional falling film chillers, which is about 0.068 g/s l. In view of all this results, it is stated that the flat-fan sheet configuration could reduce the absorption chamber size to at the very last end five times. The flow rate of the vapour absorbed per absorption chamber volume was also observed to be lower in sheet B, with a flow rate of 144 kg/h, than in sheets A and C, with rates of 188 and 100 kg/h, respectively. The impact of the solution flow rate on the absorption chamber volume depends on the combined effect of two parameters. On the one hand, a high flow rate entails a high sheet angle m , (Fig. 3b) and therefore a large chamber volume and a high h i.e., a high rate of absorbed vapour. On the other, at low flow rates the chamber volume is small and the rate of absorbed vapour low. Here also, the decisive factor is the residence time in the absorption chamber, which is high at low flow rates and low at high rates.
E. Palacios et al. / Applied Energy 86 (2009) 2574–2582
As a result, the vapour absorbed per absorption chamber volume was found to be lowest at medium flow rates. A comparison of flat-fan liquid sheet configuration flow velocities to the velocity reported for the spray configuration studied by [13] showed flow to be five times slower in the former, meaning that residence time was five times longer assuming absorption chambers of the same length and similar solution flow rates. On the other hand, in a 200 mm-length absorption chamber, the interface area to absorber volume ratio, A/V, is 33 103 m1 for the flatfan liquid sheet system and 3.6 103 m1 for the spray configuration. Hence, A/V is about one order of magnitude larger for the flatm was found to be fan sheet than for the spray mode. Additionally, h five times larger for the flat-fan sheet configuration as it was abovementioned. All these features are a clear indication that chamber volume can be reduced with the fan configuration. Another important feature in absorber design is pressure loss in the solution or the mechanical energy consumed. The pressure loss in the absorption chamber was primarily the loss generated as the solution flowed across the injector nozzle. As Fig. 8b shows, the vapour absorbed per solution flow work was over 750 g/kJ at a mass flow rate of 100 kg/h in a 200-mm absorption chamber and substantially lower at flow rates of 144 and of 188 kg/h. This can be attributed to the fact that the pressure loss in the injector nozzle increased fast with the solution flow rate (Fig. 4b). Since the flow rate of the vapour absorbed increased only slightly with the solution flow rate (Fig. 5b), however, low flow rates should be used when reducing the mechanical energy consumed by the absorber is a concern. This is another advantage to flat-fan sheet absorption against spray absorption: the mechanic energy involved in the former is clearly lower than that in the latter. The overall conclusion reached, therefore, is that the lower end of the range of solution flow rates studied here is preferred for compact absorber design, because they combine a comparatively small energy demand with a reasonably high rate of vapour absorbed per absorption chamber volume.
4. Conclusions The present study addresses adiabatic absorption in a flat-fan sheet. Experiments were conducted with an aqueous lithium bromide sheet in a low pressure water vapour atmosphere. The findings showed that sheet expansion enhanced mass transfer. Higher mass absorption coefficients were therefore reached at higher solution flow rates, as a result of more intense deformation of the vapour–solution interface. The mass transfer coefficients obtained were upward of 3 104 m/s, i.e., one full order of magnitude higher than found for falling film absorbers. The experiments also showed that absorption took place primarily in the liquid sheet prior to disintegration and that the contribution of the droplets forming subsequently was therefore secondary. Another relevant finding was that, regardless of absorption _ S values were recorded for inter_ v =m chamber length, the lowest m mediate solution flow rates due to their shorter residence times m A values compared to lower and higher flow rates, and lower h respectively. The average vapour absorbed per volume found for a 200 mmlength flat-fan sheet absorber was upward of 0.3 g/s l. In light of the high mass transfer coefficient values and small volumes found in this study for flat-fan sheets, conventional falling film absorption chambers could be scaled down at least end five times if absorbers were designed to this configuration. Indeed, vapour absorbed per chamber volume values upward of 0.8 kg/s l were obtained for chamber lengths of under 100 mm.
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High levels of absorbed vapour per solution flow work are another beneficial feature of this type of configuration, particularly at the lowest flow rate: values of over 750 g/kJ at a mass flow rate of 100 kg/h were obtained in a chamber with a length of 200 mm. Relevant parameters of the absorber design, namely residence m , A/V and mechanic energy consumption, were found to time, h be more favourably valued in flat-fan sheet absorbers as compared to spray absorbers. Flat-fan sheet configurations were found to exhibit higher absorption performance than both falling film and spray absorbers Acknowledgements This study was funded by Spanish Ministry of Science and Technology Project DPI-2002-02439 and Spanish Ministry of Education and Science Project ENE-2005-08255-CO2-01. These contributions are gratefully acknowledged. References [1] Killion JD, Garimella S. A critical review of models of coupled heat and mass transfer in falling-film absorption. Int J Refrig 2001;24:755–97. [2] Martín L. Investigación sobre transferencia de calor y masa en absorbedores de máquinas de absorción. PhD thesis. Universidad del País Vasco;1993. [3] Herbine GS, Perez-Blanco H. Model of an ammonia–water bubble absorber. ASHRAE Trans 1995;101:1324–32. [4] Kang YT, Hashiwaki T, Christensen RN. Ammonia–water bubble absorber with a plate heat exchanger. ASHRAE Trans 1998;104:956–66. [5] Kang YT, Akisawa A, Kashiwagi T. Analytical investigation of two different absorption modes: falling film and bubble types. Int J Refrig 2000;23:430–43. [6] Kang YT, Nagano T, Kashiwagi T. Visualization of bubble behavior and bubble diameter correlation for NH3–H2O bubble absorption. Int J Refrig 2002;25:127–35. [7] Keizer C. Absorption refrigeration machines. PhD thesis, Delft University of Technology, Delft, Holland; 1982. [8] Merrill T, Perez-Blanco H. Combined heat and mass transfer during bubble absorption in binary solutions. Int J Heat Mass Transfer 1997;40:589–603. [9] Merrill T. Thermally controlled bubble collapse in binary solutions. Int J Heat Mass Transfer 2000;43:3287–98. [10] Charpentier JC. A review of the data on mass transfer parameters in most of gas–liquid reactors. In: Proceedings of two-phase flows and heat transfer. NATO Advanced Study Institute; 1976. p. 869–910. [11] Garimella S. Miniaturized heat and mass transfer technology for absorption heat pumps. ISHPC’99. In: Proceedings of the international sorption heat pump conference. Munich, Germany; 1999. p. 661–70. [12] Ryan WA. Water absorption in an adiabatic spray of aqueous lithium bromide solution. In: International absorption heat pump conference. ASME, vol. 31; 1994; p. 155–62. [13] Warnakulasuriya FSK, Worekx WM. Drop formation of swirl-jet nozzles with high viscous solution in vacuum-new absorbent in spray absorption refrigeration. Int J Heat Mass Transfer 2008;51:3362–8. [14] Mehta KC, Sharma MM. Mass transfer in spray columns. British Chem Eng 1970;15:1440–4. [15] Yang R, Jou T-M. Non-absorbable gas effect on the wavy film absorption process. Int J Heat Mass Transfer 1998;41:3657–68. [16] Kang YT, Akisawa A, Kashiwagi T. Visualization and model development of Marangoni convection in NH3–H2O system. Int J Refrig 1999;22:640–9. [17] Kang YT, Iizuka K, Akisawa A, Kashiwagi T. Experiments on heat transfer additives in NH3–H2O solution. ISHPC’99. In: Proceedings of the international sorption heat pump conference. Munich, Germany; 1999. p. 291–6. [18] Yuand Z, Herold KE. Surface tension of pure water and aqueous lithium bromide with 2-ethyl-hexanol. Appl Therm Eng 2001;21:881–97. [19] Kulankara S, Herold KE. Surface tension of aqueous lithium bromide with heat/ mass transfer enhancement additives: the effect of additive vapour transport. Int J Refrig 2002;25:383–9. [20] Koenig MS, Grossman G, Gommed K. The role of surfactant absorption rate in heat and mass transfer enhancement in absorption heat pumps. Int J Refrig 2003;26:129–39. [21] Tsai B-B, Perez-Blanco H. Limits of mass transfer enhancement in lithium bromide–water absorbers by active techniques. Int J Heat Mass Transfer 1998;41:2409–16. [22] Morioka I, Kiyota M, Ousaka A, Kobayashi T. Analysis of steam absorption by a subcooled droplet of aqueous solution of LiBr. JSME Int J, Series II 1992;35(3):458–64. [23] Amokrane H, Caussade B. Gas absorption into a moving spheroidal water drop. J Atmos Sci 1998;56:1808–29. [24] Kim JK, Bernan NS, Chau DSC, Wood BD. Absorption of water vapour into falling films of aqueous lithium bromide. Int J Refrig 1995;18:486–95. [25] Kim JK, Bernan NS, Wood BD. The interfacial turbulence in falling films absorption: effects of additives. Int J Refrig 1996;18:486–95.
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[26] Uemura T, Hasaba S. Tech Repr Kansai Univ 1964;6:31–55. [27] Hagerty WW, Shea JF. A study of the stability of plane fluid sheets. J Appl Mech 1955;22:509–14. [28] Taylor GI. The dynamics of thin sheets of fluid. II Waves on fluid sheets. III Disintegration of fluid sheets. Proc Roy Soc Lond Ser 1959;A 253: 296–321. [29] Mehring C, Sirignano WA. Nonlinear capillarity wave distortion and disintegration of thin planar liquid sheets. J Fluid Mech 1999;388:69–113. [30] Lin SP. Breakup of liquid sheets and jets. Cambridge University Press; 2003. [31] Miller WA, Perez-Blanco H. Vertical-tube aqueous LiBr falling film absorption using advanced surfaces. In: International absorption heat pump conference. ASME; 1994.
[32] Venegas M. Transferencia de Masa y Calor en gotas en procesos de absorción con nitrato de litio-amoniaco: Nuevas tecnologías, PhD thesis, Universidad Carlos III de Madrid; 2001. p. 129. [33] Arzoz D, Rodríguez P, Izquierdo M. Experimental study on the adiabatic absorption of water vapor into LiBr–H2O solutions. Appl Therm Eng 2005;25:797–811. [34] Izquierdo M. Máquina de Absorción de Bromuro de Litio-Agua de simple efecto, Patent number P200801738. [35] Izquierdo M, Martín E. Máquina de Absorción de Bromuro de Litio-Agua de doble efecto, Patent number P200803461. [36] Izquierdo M, Palacios E. Conjunto evaporador-absorbedor adiabático de lámina plana, Patent number P200900691.
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Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Evaluation of mass absorption in LiBr flat-fan sheets E. Palacios a,*, M. Izquierdo b,d, J.D. Marcos c, R. Lizarte d a
Escuela Universitaria de Ingeniería Técnica Industrial, U.P.M., Ronda de Valencia 3, 28012 Madrid, Spain Instituto de Ciencias de la Construcción Eduardo Torroja, C.S.I.C., Serrano Galvache 4, 28033 Madrid, Spain Escuela Técnica Superior de Ingeniería Industrial, U.N.E.D., Juan del Rosal 12, 28040 Madrid, Spain d Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Madrid, Spain b c
a r t i c l e
i n f o
Article history: Received 2 September 2008 Received in revised form 3 April 2009 Accepted 16 April 2009 Available online 13 June 2009 Keywords: Adiabatic absorption Lithium bromide aqueous solution Air conditioning Flat-fan sheet
a b s t r a c t Experiments were conducted to determine the absorption rates of refrigerant vapour in an aqueous lithium bromide flat-fan sheet for use in absorption air-conditioning systems. The solution flow rates tested ranged from 0.023 to 0.054 kg/s (84–194 kg/h), with pressure losses in the injection nozzle of from 40 to 250 kPa. The effect of the mass flow rate on both solution residence time and the sheet deformation rate was also analyzed in absorption chambers of a pre-defined length, along with the effect of the sub-cooling temperature on the amount of vapour absorbed. The downstream evolution of approach to equilibrium factor F was quantified. The mass transfer coefficient values were found to be over 3 104 m/s. In absorption chambers 100 mm long, over 0.8 g/s l of vapour were absorbed per chamber absorption volume. Moreover, about 600 g of vapour were absorbed per kJ of solution flow work. Flat-fan sheet configurations were found to perform better than falling film and spray absorbers. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Absorption heat pumps, and particularly absorption machines, are presently seen as a possible, environmentally friendly alternative to conventional vapour compression chillers in small power applications. The size of the absorption machine, however, and especially the size of one of its key components, the absorber, will have to be scaled down to make this system commercially viable. The market has shown a preference for falling film absorbers, in which the sub-cooled solution that flows into the absorber slides along the outer surface of the tube bank inside the unit. At the same time, an external refrigerant fluid flows through the tube bank, collecting the absorption heat [1]. The general instability of the solution sheet generated [2], however, may reduce the vapour–solution interface area. The remedy for this drawback is to over-size the absorber. Moreover, falling film absorbers are unsuitable for viscous solutions such as aqueous LiBr because the thickness of the sheet formed hinders vapour absorption. Most of the approaches to compact absorber design seek to raise the vapour–solution interface area. Among the most effective in this regard are bubble absorbers [3–6]. According to numerical simulations performed by Keizer [7], with bubbles, absorber size could be reduced by half. Merrill and Perez-Blanco [8] and Merrill [9] acknowledged, however, that further experimental analysis is required. In any event, the high energy demands in bubbling a va-
* Corresponding author. Tel.: +34 913366874; fax: +34 913367676. E-mail address: [email protected] (E. Palacios). 0306-2619/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2009.04.033
pour through a liquid solution [10,11] seriously limit the efficiency of this system. This negative aspect is mainly the reason for which bubble absorber are not appropriate for water–LiBr systems. Spray absorbers increase the solution surface area by atomization, generating a population of small droplets [12,13]. Despite Mehta and Sharma’s [14] defence of the low cost of spray absorbers, however, like vapour bubbling, liquid atomization is energy-intensive. Nonetheless, spray absorbers are a type of adiabatic absorber, in which vapour absorption is achieved without releasing the absorption heat. Adiabatic absorbers are fitted with an external loop in which a compact heat exchanger removes the absorption heat from the solution in a multi-pass process. Hence, there is no need for any heat exchange surface inside the absorber, or, therefore, for any material surface. It is clear that, in this way, the poor wetting of the surface is prevented, which is what calls for oversizing in falling film absorbers. Another possible strategy for reducing absorber size is to increase interface efficiency by inducing mixing. Since convection mechanisms are known to be more efficient than diffusion in transport processes [15], Kang et al. [16,17] proposed generating Marangoni recirculation by adding specific surfactants to induce mixing in the liquid solution. Nevertheless, an effort has been done to get a fully understanding of the way these additives increase the rate of the transfer processes [18–20]. Conversely, Tsai and PerezBlanco [21] suggested the use of passive and active mechanisms for the same purpose. By contrast to active techniques, which involve more complex devices, the formation of inherently unstable, free liquid sheet seems to be a suitable mechanism for inducing mixing. In
E. Palacios et al. / Applied Energy 86 (2009) 2574–2582
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Nomenclature A cS D20 F hlv m h Labs _S m _v m p T V Vspr
vapour–solution interface area (mm2) solution-specific heat (J/kg °C) mean droplet diameter based on the surface area (lm) approach to equilibrium factor (–) vapour condensation plus dilution enthalpy (J/kg) mean mass transport coefficient (m/s) length of the test section in the absorption chamber (mm) injected solution mass flow rate (kg/h) mass flow rate of absorbed vapour (kg/h) absorption chamber pressure (kPa) temperature (°C) absorption chamber volume (l) volume of injected solution (mm3)
particular, flat-fan liquid sheets may be a good choice because of the ongoing generation of interface entailed. Flat-fan liquid sheet develops radially between thick edges as it develops. As a consequence, the liquid–gas interface area increases, forcing the liquid to move from the core of the sheet to its interface. The result can be a significant enhancement of the mass transfer rate. Sheet gets distorted and eventually disintegrates into droplets due to the amplification of natural disturbances. In this way, sheet disintegration also could contribute to the interface renewal and, consequently, to the mass transfer rate raise. Hence, conversely to spray configuration, in which the efficiency of the generated droplet declines when the droplets reach mechanical equilibrium [22,23], flat-fan liquid sheet configuration forces the liquid interface renewal at any time. Another appealing feature of flat-fan sheets is that they can be densely packed. Furthermore, since flat fan formation calls for only moderate amounts of energy, absorbers with low pressure losses can be used. An aqueous lithium bromide flat-fan sheet was chosen for the present study because it is characterized by lower energy demands than liquid atomization. The present study focused on scaling down chamber volume and reducing pressure loss across the absorption chamber. Variations in the amount of vapour absorbed were quantified over a range of solution flow rates. Absorption chamber size and the mechanical energy consumed in fan sheet development were likewise determined. The experimental setup designed for this purpose, the measuring principle applied and the results obtained are discussed in the following sections. 2. Experimental measurements 2.1. Experimental setup The experiments were conducted in a stainless steel chamber where the fan sheet developed, became unstable and broke up into droplets (see Fig. 1). The four sides of the chamber were glazed in order to allow optical access. The solution was injected into the chamber through a Spraying Systems Co. vee-jet type nozzle usable with absorption machines, to generate a fan sheet. A magnetically driven gear pump re-circulated the solution. The refrigerant vapour was fed into the absorber from a supply box through a handle-governed valve, which maintained chamber conditions at the pressure setting with a precision of ±0.05 kPa. The length of the test section in the chamber was defined to be the distance between the tip of the injector nozzle and a fixed point at a sufficient distance from the solution remaining on the floor of the chamber. The tube on which the injector nozzle was mounted
x
mass fraction of lithium bromide in the solution (%)
Greek symbols qS solution density (kg/m3) h sheet angle (°) Subscripts adiab mass equilibrium for the vapour adiabatic absorption process eq thermodynamic equilibrium i test section inlet o test section outlet
could be adjusted to vary the length of the test section by raising or lowering the nozzle. The apparatus was fitted with two absolute pressure transducers that measured the pressure upstream of the nozzle and inside the chamber. The temperature, density and flow rate of the circulating solution were recorded on a Coriolis-type meter. Two T-type calibrated thermocouples, positioned at the inlet manifold and the test section exit, recorded the temperature of the solution at the beginning and end of the vapour absorption process, respectively. The instrument specifications are summarized in Table 1. The sprayed solution was imaged with a single high-energy Argon spark flash lamp that back-illuminated the spray and a CCD digital camera. The images were subsequently analyzed to quantify the area of the vapour–solution interface. 2.2. Data collection Several trials were conducted. Before initiating each, the apparatus was filled with a known amount of solution, small enough to prevent the spray deposit accumulating on the floor of the chamber from rising to the level of the outlet thermocouple. The test section length, Labs, was set with the injector nozzle tube. Any atmospheric air existing in the chamber was evacuated with a vacuum pump prior to starting the trials. The refrigerant, in this case water vapour, was generated in the vapour supply box at temperatures of 10–45 °C by vapourizing liquid water with an electric heater. The vapour flowed into the absorption chamber through a handle-governed valve, which kept the absorption chamber pressure at the specified level. Once the working pressure was reached in the absorber, the solution was pumped into the apparatus at the pre-established _ S;i . The temperature of the solution rose during mass flow rate, m the trial due to the heat generated by vapour absorption, while the density declined as a result. The following parameters were recorded at 30-s intervals:
solution temperature at the inlet (Ti), mean solution temperature at the outlet (To), solution density prior to spraying (qS,i) and absorption chamber pressure (p).
The trial was concluded when qS,i fell below approximately 1.620 kg/l. The same procedure was followed in subsequent trials, varying the test section length and/or the solution flow rate at the inlet. The test conditions are given in Table 2.
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Fig. 1. (a) Experimental setup. (b) Elevation view and cross-section of the injector nozzle: A = 1.2, B = 3.4, D1 = 6.7, D = 3.6 and L = 10.1 (dimensions in mm).
Table 1 Instrument specifications. Instrument
Type
Range
Accuracy
Flow rate, density and temperature meter
Coriolis
Thermocouples Pressure sensor Pressure sensor
T Absolute pressure Absolute pressure
(0.19 < m < 600) Kg/h (0.3 < q < 5) Kg/l (180 < T < 150) °C 10–60 °C 0–2.5 bar 8.3–250 mbar
Mass flow rate: ±0.1% VM Density: ±4 g/1 Temperature: ±1 °C ±0.5 °C 0.5% span <0.1% span
Table 2 Test conditions. Chamber pressure, q (kPa) Inlet solution temperature Ti (°C) _ S;i (kg/h) Inlet solution flow rate. m Lithium bromide concentration, xi (%)
0.6–2.2 21–27 (q = 0.6) 38–50 (q = 2.2) 84–194 58–60
2.3. Measuring principle The objective was to obtain the mass flow rate of the vapour ab m and the approach _ v , the mean mass transfer coefficient h sorbed m to equilibrium factor F. m and F were calcu_ v, h The outlet values of the magnitudes m lated from the data recorded in each trial using the measuring principle described below:
Inlet sub-cooling temperature, Teqi Ti (°C) Drop pressure along the injector nozzle (kPa)
9–21 15–102
Test section length, Labs (mm) Flow velocity (m/s)
3.5–43 4.4–10.2
Assuming adiabatic absorption, the mass flow rate of the vapour _ v , can be determined by measuring the temperature absorbed, m rise observed in the injected solution as a result of the heat released during vapour absorption. Consequently, the energy balance _ v can be between the nozzle exit and the outlet thermocouple, m found from the expression:
_ S;i _v ¼m m
cS ðT o T i Þ hlv
ð1Þ
E. Palacios et al. / Applied Energy 86 (2009) 2574–2582
where cS denotes the solution-specific heat and hlv is the variation in enthalpy generated as a result of vapour condensation and subsequent dilution. Any change in the internal energy of the water absorbed was assumed to be negligible and therefore disregarded. _ v was two orders This assumption was justified by the fact that m _ S;i , as discussed in Section 3 below. of magnitude lower than m _ v , the mean mass transfer coefficient in the test secKnowing m m , can be obtained from: tion, h
m A Dq S _v ¼h m
ð2Þ
where A is the area of the solution–vapour interface and DqS is the mean difference in solution density in the test section. For an absor_ v , given a conber able to handle a given mass flow rate of vapour, m stant DqS , minimizing the absorber size is tantamount to m A=V, where V is the volume occupied by the spray, maximizing h i.e., the volume of the absorption chamber. In Expression (2), area A is obtained by adding the interface of the liquid spray to the overall interface area of the droplets generated during disintegration. Both magnitudes were measured by analyzing the images of the back-illuminated spray. The parameter DqS , in turn, may be computed from (Kim et al. [24,25]):
DqS qS;i Dxlm
ð3Þ
where Dxlm is the mean difference in the mass fraction of LiBr found from the expression:
Dxlm ¼
D xi D xo ; lnðDxi =Dxo Þ
i:e:; Dxlm ¼ Dxi
Dxo = Dxi 1 lnðDxo =Dxi Þ
ð4Þ
where Dx is the local difference between the actual mass fraction of LiBr, x, and the mass fraction at equilibrium, xeq, at pressure p and local solution temperature T. The approach to equilibrium factor, F, in turn, can be found from:
F¼
x i xo xi xo;adiab
ð5Þ
_ LiBr =m _ S is the mass fraction of LiBr in the aqueous soluwhere x ¼ m tion. The subscripts i and o refer to the test section inlet and outlet, respectively. The subscript adiab refers to the thermodynamic equilibrium reached during adiabatic absorption. Note that the magni-
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tude xo;adiab depends on the inlet conditions only. It follows from Eq. (4) that the mass fraction of LiBr at the test section outlet, _ LiBr =m _ S;o , is xo ¼ m
xo ¼
xi 1 þ cS =hlv ðT o T i Þ
ð6Þ
where the mass fraction of LiBr at the absorber inlet can be found from the empirical qS,i and Ti values [26]. An F value of <1, i.e., where xo > xo,adiab, indicates that vapour absorption is underway. This process involves local imbalance: in other words, at any test section length, the temperature T of the solution is lower than the equilibrium temperature, Teq, as computed from the local values of p and x. The difference between these two temperatures, Teq T, is the sub-cooling temperature. 3. Results and discussion The following items contain a discussion of the effect of sheet development on the amount of refrigerant absorbed, as well as of absorption chamber volume and pressure loss. 3.1. Liquid spray configuration As shown in Fig. 2, the flat-fan liquid sheet produced by the fan nozzle used in the trials expanded as it descended along the x–y plane. This was due to the radial movement induced in the solution as it flowed through the convergent conduit, which was fitted with two lateral slots (see Fig. 1). The sheet thinned out as it expanded. Sheet thickness decreased as the distance from the virtual origin, located inside the nozzle, increased. This point was placed at the intersection of the two imaginary lines drawn along the initial trajectories of the primary rims, which define the liquid sheet angle h. Downstream of the exit, these rims retracted towards the sheet bulk, became unstable and disintegrated into droplets. Sheet recession is governed by the equilibrium between surface tension and inertia. Meanwhile, the sheet bulk, distorted by the surface tension action, eventually broke up as well [27–30]. With the downstream expansion of the liquid sheet, the interface area per volume of injected solution, A/Vspr, grew until the sheet disintegrated into droplets, after which A/Vspr declined, as
Fig. 2. Expanding liquid sheet produced by a flat-fan nozzle (solution flow rate: 152 kg/h, chamber pressure: 0.4 kPa), (a) front view, (b) side view.
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Fig. 4. (a) Absorption chamber volume per volume of solution injected versus length. (b) Pressure drop in the injector nozzle versus solution mass flow rate. Fig. 3. (a) Interface area per volume of injected solution versus time. (b) Liquid sheet angle and mean droplet diameter (based on the surface area, D20, of the droplet population generated by liquid sheet disintegration) versus solution mass flow rate.
Fig. 3a shows. The time lapsing from injection was calculated by dividing the distance to the injector tip by the flow velocity, defined to be the volumetric flow divided by the cross-sectional area of the injector at the exit. The latter magnitude was calculated using the equivalent diameter provided by the injector manufacturer. The initial variation in A/Vspr is indicative of the deformation rate of the solution in the sheet. Fluid deformation entails the renewal of the sheet surface. As a result, the refrigerant-poor core moves to interface enhancing vapour absorption. The values of A/Vspr per unit of time ranged from 1.5 to 6.5 (mm s)1 when the solution flow rate was raised from 92 to 232 kg/h. Nonetheless, after reaching a peak value, A/Vspr was observed to decline progressively as a result of rim retraction, particularly at the lower flow rates. Even though rim retraction caused A/Vspr to decline, it is reasonable to assume that, due to sheet bulk divergence, the deformation rate of the sheet did not decrease. The liquid surface was also intensely renewed as the sheet disintegrated into droplets, possibly enhancing vapour absorption. Fig. 3a shows that A/Vspr rose more steeply when the solution flow rate was higher. The experiments also showed that the time lapsing from injection to sheet disintegration was shortened at the higher solution flow rate. More specifically, disintegration time rose from approximately 16 to 33 ms when the solution flow rate was decreased from 232 kg/h to 122 kg/h. Given the length of time it took for the sheet to disintegrate, most of the vapour absorption would be expected to take place in the sheet, while the droplets would play a secondary role.
Compact absorber design seeks to reduce the volume of the vapour–solution interface. The absorption chamber volume, defined to be the volume of a single flat-fan sheet, was calculated assuming a chamber with a rectangular section 0.01 m wide. Fig. 4a shows the variation in absorption chamber length versus chamber volume per volume of injected solution, V/Vspr. Another important feature in absorber design is pressure loss. In the absorber configuration analyzed in this paper, the pressure loss was primarily the loss observed when the solution flowed across the injector nozzle. Fig. 4b shows the pressure drop in the injector nozzle versus solution mass flow rate. This data show that the pressure drop in the injector increased with the square of the mass flow rate, exhibiting a value of 25 kPa at a flow rate of 107 kg/h. While the sheet angle peaked within the solution flow rate interval studied, the pressure loss rate continued to grow with increasing flow rates. In the flat-fan nozzle tested in this study, the pressure drop climbed from 0.25 to 0.60 kPa per kg/h when the flow rate increased from 107 to 218 kg/h due to the rise in the turbulent energy generated in the nozzle. Nonetheless, pressure loss was clearly less intense in the flat-fan nozzle than in spray absorbers [13]. 3.2. Attainment of equilibrium absorption 3.2.1. Mean mass transfer coefficient One of the key parameters that governs the vapour transfer rate, m . As mentioned above, one _ v , is the mass transfer coefficient, h m possible way to quicken the slow absorption inherent in molecular diffusion is by stimulating convective mixing in the liquid. In this regard, the expansion-driven renewal of the sheet surface may enhance vapour absorption.
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m , versus absorption chamber length Fig. 5. (a) Mean mass transfer coefficient h (mass flow rate: sheet A: 188 kg/h; sheet B: 144 kg/h; sheet C: 100 kg/h; initial sub_ S versus absorption chamber length. _ v =m cooling temperature: 14 °C). (b) m
Fig. 5a shows the downstream evolution of the mass transfer m , for flat fan solution sheet produced at mass flow coefficient, h rates of 188, 144 and 100 kg/h (sheet A, B and C, respectively). m was observed to decline sharply in the first 60 mm Coefficient h (i.e., in approximately the first 6–12 ms after the solution was injected, depending on the flow rate in question) to about 3 104 m/s. This reduction was due to the solution flow regimen got laminar downstream due to the intense slimming of the sheet. The undulation in the sheet surface near the injector tip generated by the turbulent energy inside the nozzle would heighten flow mixing. These waves dampened as the sheet thinned out downstream, however. m values grew with the The data showed that while the initial h solution flow rate, very likely due to the higher deformation rate in
the sheet (see Fig. 3a), turbulent energy also increased, as shown by the intensification of the pressure drop in the injector (see Fig. 4b). m was one orWith values upward of 3 104 m/s in all cases, h der of magnitude larger than reported by other researchers for the isothermal falling film configuration (see Table 3). Moreover, in the m was five times higher than flat-fan sheet tested in this study, h found by Warnakulasuriya and Worek [13] for the spray configuration. This can be attributed to the effect of interface renewal, which plays only a minor role in falling film and spray configurations. _ v , is the Another determinant in the vapour absorption rate, m m is known, the effect area of the vapour–liquid interface, A. Once h of varying A may be evaluated. Fig. 5b shows the downstream evolution of the refrigerant vapour mass absorbed per mass of solution _ S , for sheets A, B and C. The value of m _ v =m _ S was ob_ v =m injected, m served to be higher in sheet A than sheet B at all test section m lengths, a finding consistent with the behaviour exhibited by h _ v =m _S and A, which increased with the solution flow rate. The m parameter was similar in sheets A and C, however, despite the difference in flow rate: the time lapsing from injection was, then, nearly 50% shorter in sheet A than sheet C. These results show that, m A in sheet C was offset at any position downstream, the lower h by the longer time lapsing after injection. These conditions were not observed in sheet B, however, inferring the existence of a certain range of solution flow rates that combine low residence time m A values. Solution flow in the absorption chamber with low h rates within this interval should be avoided because of their low _ S. _ v =m m _ S value, the absorption _ v =m It is concluded that, for a fixed m chamber length rises as the solution flow rate is increased due to the subsequent reduction in the solution residence time. Nevertheless, this tendency could change if the reduction in residence time that the solution flow rate rise involves is offset by the resulting inm A. crease in h Experiments shown that the flow rate of the vapour absorbed _ v =A is up to 0.0169 kg/s m2 in an absorption per interface area, m chamber 200 mm long, length required for absorption to nearly come to an end. This means that the heat transfer per fan sheet _ v =A found is about one orarea is about 42 kW/m2. Note that the m der of magnitude larger than that typical for conventional falling film design, which is 0.0027 kg/s m2. Experimental results shown in this paper have let design the flat-fan sheet absorber [34–36] of a low power absorption cooling machine prototype. The performance of this machine is being checked and it will be published in the next future. 3.2.2. Effect of the initial sub-cooling temperature The experimental results in Fig. 5b also show that the value of _ S at equilibrium in sheets A and C differed from the value _ v =m m _ S in_ v =m in sheet B. Fig. 6, in turn, shows that the peak value of m creased linearly with the sub-cooled temperature. This linear correlation concurred with findings reported by Arzoz et al. [33] for fluids with other morphologies. Therefore, sheets A and C reached _ S value because their initial sub-cooling _ v =m the same maximum m temperature was the same.
Table 3 m . Mass transfer coefficient, h m 105 (m/s) h
Absorber type
Reference
Methodology
Solution
Falling film absorber
Kim et al. [25] Miller and Perez-Blanco [31] Venegas [32] Warnakulasuriya and Worek [13]
Experimental
LiBr–H2O
Spray absorber a
Droplet mean diameter: 500 lm.
Theoretical
a
LiBr–H2O
0.5–0.7 1.9 2 6
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_ v =m _ S versus sub-cooling temperature at the injector exit Fig. 6. Equilibrium m ðT eq;i T i Þ. The analytical expression in the graph represents the linear model used to fit the data.
Fig. 7. Approach to equilibrium factor, F, versus length. The points on Figure represent the break-up length and the break-up time in milliseconds for each mass flow rate (mass flow rate: sheet A, 188 kg/h; sheet B, 144 kg/h; sheet C, 100 kg/h; sub-cooling temperature at the injection exit: 14 °C).
3.2.3. Approach to equilibrium factor Fig. 7 shows that the approach to equilibrium factor, F, increased monotonously downstream to a value of about 0.9 when it was very near equilibrium. F reached 0.9 in 20 ms at a flow rate of 100 kg/s (sheet C). It took twice that long, however, when the flow rate was raised to 188 kg/ h (sheet A). This finding has two consequences. On the one hand, the interface area per volume injected was larger in sheet A due m was higher to its larger flow rate (Fig. 3a). And on the other, h as well due to its larger deformation rate (Fig. 5a). With respect to the effect of sheet disintegration on the vapour absorption rate, no evidence was found of a change in F growth upon sheet disintegration, despite the renewal of liquid interface that sheet disintegration entails. When sheets A, B and C disintegrated at tres 17, 24 and 27 ms, respectively, absorption had nearly come to an end (F > 0.8), minimizing any possible effect of the new interface area. 3.3. Absorption chamber size and mechanical energy demands As mentioned above, the aim in compact absorber design is to m A per absorption chamber volume V. maximize the magnitude h Fig. 8a shows the downstream evolution of the vapour absorbed per volume of absorption chamber for a range of solution flows.
Fig. 8. (a) Vapour absorbed per absorption chamber volume versus absorption chamber length. (b) Vapour absorbed per solution flow work versus absorption chamber length (mass flow rate: sheet A, 188 kg/h; sheet B, 144 kg/h; sheet C, 100 kg/h; sub-cooling temperature at the injection exit: 14 °C).
According to these findings, cooling power declined steeply as the absorption chamber length increased, particularly in the first 100 mm or 20 ms, when the vapour absorbed per volume dropped to 0.8 g/s l. Nevertheless, the vapour absorbed per volume is about 0.3 g/s l at 200 mm, when absorption is nearly at an end. Hence, the heat transfer per absorber volume exceeds 743 W/l. Note that the average vapour absorbed per volume in the flat-fan sheet design is clearly larger than that found for low power conventional falling film chillers, which is about 0.068 g/s l. In view of all this results, it is stated that the flat-fan sheet configuration could reduce the absorption chamber size to at the very last end five times. The flow rate of the vapour absorbed per absorption chamber volume was also observed to be lower in sheet B, with a flow rate of 144 kg/h, than in sheets A and C, with rates of 188 and 100 kg/h, respectively. The impact of the solution flow rate on the absorption chamber volume depends on the combined effect of two parameters. On the one hand, a high flow rate entails a high sheet angle m , (Fig. 3b) and therefore a large chamber volume and a high h i.e., a high rate of absorbed vapour. On the other, at low flow rates the chamber volume is small and the rate of absorbed vapour low. Here also, the decisive factor is the residence time in the absorption chamber, which is high at low flow rates and low at high rates.
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As a result, the vapour absorbed per absorption chamber volume was found to be lowest at medium flow rates. A comparison of flat-fan liquid sheet configuration flow velocities to the velocity reported for the spray configuration studied by [13] showed flow to be five times slower in the former, meaning that residence time was five times longer assuming absorption chambers of the same length and similar solution flow rates. On the other hand, in a 200 mm-length absorption chamber, the interface area to absorber volume ratio, A/V, is 33 103 m1 for the flatfan liquid sheet system and 3.6 103 m1 for the spray configuration. Hence, A/V is about one order of magnitude larger for the flatm was found to be fan sheet than for the spray mode. Additionally, h five times larger for the flat-fan sheet configuration as it was abovementioned. All these features are a clear indication that chamber volume can be reduced with the fan configuration. Another important feature in absorber design is pressure loss in the solution or the mechanical energy consumed. The pressure loss in the absorption chamber was primarily the loss generated as the solution flowed across the injector nozzle. As Fig. 8b shows, the vapour absorbed per solution flow work was over 750 g/kJ at a mass flow rate of 100 kg/h in a 200-mm absorption chamber and substantially lower at flow rates of 144 and of 188 kg/h. This can be attributed to the fact that the pressure loss in the injector nozzle increased fast with the solution flow rate (Fig. 4b). Since the flow rate of the vapour absorbed increased only slightly with the solution flow rate (Fig. 5b), however, low flow rates should be used when reducing the mechanical energy consumed by the absorber is a concern. This is another advantage to flat-fan sheet absorption against spray absorption: the mechanic energy involved in the former is clearly lower than that in the latter. The overall conclusion reached, therefore, is that the lower end of the range of solution flow rates studied here is preferred for compact absorber design, because they combine a comparatively small energy demand with a reasonably high rate of vapour absorbed per absorption chamber volume.
4. Conclusions The present study addresses adiabatic absorption in a flat-fan sheet. Experiments were conducted with an aqueous lithium bromide sheet in a low pressure water vapour atmosphere. The findings showed that sheet expansion enhanced mass transfer. Higher mass absorption coefficients were therefore reached at higher solution flow rates, as a result of more intense deformation of the vapour–solution interface. The mass transfer coefficients obtained were upward of 3 104 m/s, i.e., one full order of magnitude higher than found for falling film absorbers. The experiments also showed that absorption took place primarily in the liquid sheet prior to disintegration and that the contribution of the droplets forming subsequently was therefore secondary. Another relevant finding was that, regardless of absorption _ S values were recorded for inter_ v =m chamber length, the lowest m mediate solution flow rates due to their shorter residence times m A values compared to lower and higher flow rates, and lower h respectively. The average vapour absorbed per volume found for a 200 mmlength flat-fan sheet absorber was upward of 0.3 g/s l. In light of the high mass transfer coefficient values and small volumes found in this study for flat-fan sheets, conventional falling film absorption chambers could be scaled down at least end five times if absorbers were designed to this configuration. Indeed, vapour absorbed per chamber volume values upward of 0.8 kg/s l were obtained for chamber lengths of under 100 mm.
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High levels of absorbed vapour per solution flow work are another beneficial feature of this type of configuration, particularly at the lowest flow rate: values of over 750 g/kJ at a mass flow rate of 100 kg/h were obtained in a chamber with a length of 200 mm. Relevant parameters of the absorber design, namely residence m , A/V and mechanic energy consumption, were found to time, h be more favourably valued in flat-fan sheet absorbers as compared to spray absorbers. Flat-fan sheet configurations were found to exhibit higher absorption performance than both falling film and spray absorbers Acknowledgements This study was funded by Spanish Ministry of Science and Technology Project DPI-2002-02439 and Spanish Ministry of Education and Science Project ENE-2005-08255-CO2-01. These contributions are gratefully acknowledged. References [1] Killion JD, Garimella S. A critical review of models of coupled heat and mass transfer in falling-film absorption. Int J Refrig 2001;24:755–97. [2] Martín L. Investigación sobre transferencia de calor y masa en absorbedores de máquinas de absorción. PhD thesis. Universidad del País Vasco;1993. [3] Herbine GS, Perez-Blanco H. Model of an ammonia–water bubble absorber. ASHRAE Trans 1995;101:1324–32. [4] Kang YT, Hashiwaki T, Christensen RN. Ammonia–water bubble absorber with a plate heat exchanger. ASHRAE Trans 1998;104:956–66. [5] Kang YT, Akisawa A, Kashiwagi T. Analytical investigation of two different absorption modes: falling film and bubble types. Int J Refrig 2000;23:430–43. [6] Kang YT, Nagano T, Kashiwagi T. Visualization of bubble behavior and bubble diameter correlation for NH3–H2O bubble absorption. Int J Refrig 2002;25:127–35. [7] Keizer C. Absorption refrigeration machines. PhD thesis, Delft University of Technology, Delft, Holland; 1982. [8] Merrill T, Perez-Blanco H. Combined heat and mass transfer during bubble absorption in binary solutions. Int J Heat Mass Transfer 1997;40:589–603. [9] Merrill T. Thermally controlled bubble collapse in binary solutions. Int J Heat Mass Transfer 2000;43:3287–98. [10] Charpentier JC. A review of the data on mass transfer parameters in most of gas–liquid reactors. In: Proceedings of two-phase flows and heat transfer. NATO Advanced Study Institute; 1976. p. 869–910. [11] Garimella S. Miniaturized heat and mass transfer technology for absorption heat pumps. ISHPC’99. In: Proceedings of the international sorption heat pump conference. Munich, Germany; 1999. p. 661–70. [12] Ryan WA. Water absorption in an adiabatic spray of aqueous lithium bromide solution. In: International absorption heat pump conference. ASME, vol. 31; 1994; p. 155–62. [13] Warnakulasuriya FSK, Worekx WM. Drop formation of swirl-jet nozzles with high viscous solution in vacuum-new absorbent in spray absorption refrigeration. Int J Heat Mass Transfer 2008;51:3362–8. [14] Mehta KC, Sharma MM. Mass transfer in spray columns. British Chem Eng 1970;15:1440–4. [15] Yang R, Jou T-M. Non-absorbable gas effect on the wavy film absorption process. Int J Heat Mass Transfer 1998;41:3657–68. [16] Kang YT, Akisawa A, Kashiwagi T. Visualization and model development of Marangoni convection in NH3–H2O system. Int J Refrig 1999;22:640–9. [17] Kang YT, Iizuka K, Akisawa A, Kashiwagi T. Experiments on heat transfer additives in NH3–H2O solution. ISHPC’99. In: Proceedings of the international sorption heat pump conference. Munich, Germany; 1999. p. 291–6. [18] Yuand Z, Herold KE. Surface tension of pure water and aqueous lithium bromide with 2-ethyl-hexanol. Appl Therm Eng 2001;21:881–97. [19] Kulankara S, Herold KE. Surface tension of aqueous lithium bromide with heat/ mass transfer enhancement additives: the effect of additive vapour transport. Int J Refrig 2002;25:383–9. [20] Koenig MS, Grossman G, Gommed K. The role of surfactant absorption rate in heat and mass transfer enhancement in absorption heat pumps. Int J Refrig 2003;26:129–39. [21] Tsai B-B, Perez-Blanco H. Limits of mass transfer enhancement in lithium bromide–water absorbers by active techniques. Int J Heat Mass Transfer 1998;41:2409–16. [22] Morioka I, Kiyota M, Ousaka A, Kobayashi T. Analysis of steam absorption by a subcooled droplet of aqueous solution of LiBr. JSME Int J, Series II 1992;35(3):458–64. [23] Amokrane H, Caussade B. Gas absorption into a moving spheroidal water drop. J Atmos Sci 1998;56:1808–29. [24] Kim JK, Bernan NS, Chau DSC, Wood BD. Absorption of water vapour into falling films of aqueous lithium bromide. Int J Refrig 1995;18:486–95. [25] Kim JK, Bernan NS, Wood BD. The interfacial turbulence in falling films absorption: effects of additives. Int J Refrig 1996;18:486–95.
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