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Experimental evaluation of ammonia adiabatic absorption into ammonia–lithium nitrate solution using a fog jet nozzle
Applied Thermal Engineering 50 (2013) 781e790
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Experimental evaluation of ammonia adiabatic absorption into ammoniaelithium nitrate solution using a fog jet nozzle Alejandro Zacarías a, María Venegas b, *, Antonio Lecuona b, Rubén Ventas b a b
Academia de Térmicas/SEPI ESIME Azcapotzalco, Instituto Politécnico Nacional, Av. de las Granjas 682, Col. Santa Catarina, 02550 Distrito Federal, Mexico Departamento de Ingeniería Térmica y de Fluidos, Universidad Carlos III de Madrid, Avda. Universidad 30, 28911 Leganés, Madrid, Spain
h i g h l i g h t s < Adiabatic absorption of NH3 vapour into NH3eLiNO3 using fog jet nozzle created spray. < Pressure drop of the solution entering to the absorption chamber is evaluated. < Approach to adiabatic equilibrium factor (F) is between 0.82 and 0.93 at 205 mm height. < Experimental values of mass transfer coefficient and outlet subcooling are presented. < Correlations for F and Sherwood number are given.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 March 2012 Accepted 3 July 2012 Available online 16 July 2012
This paper presents the experimental assessment of the adiabatic absorption of ammonia vapour into an ammoniaelithium nitrate solution using a fog jet nozzle. The ammonia mass fraction was kept constant at 46.08% and the absorber pressure was varied in the range 355e411 kPa. The nozzle was located at the top of the absorption chamber, at a height of 205 mm measured from the bottom surface. The diluted solution flow rate was modified between 0.04 and 0.08 kg s1 and the solution inlet temperature in the range 25.9e30.2 C. The influence of these variables on the approach to adiabatic equilibrium factor, outlet subcooling, absorption ratio and mass transfer coefficient is analysed. The approach to adiabatic equilibrium factor for the conditions essayed is always between 0.82 and 0.93. Pressure drop of the solution entering the absorption chamber is also evaluated. Correlations for the approach to adiabatic equilibrium factor and the Sherwood number are given. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Ammoniaelithium nitrate solution Adiabatic absorption Fog jet nozzle Mass transfer Pressure drop
1. Introduction Mass transfer in the absorber is one of the main limiting factors for increasing performance and reducing size of absorption machines. Current technology use absorbers relying on laminar falling films, but other absorption methods have shown their potential for reducing both the heat and mass transfer area and, as a result, the absorber dimensions. One of these methods consists on dispersing the liquid solution in drops and/or free-flying sheets inside an adiabatic chamber, putting the solution in contact with the refrigerant vapour. This way, evacuating the absorption heat in the chamber is not possible. This method has received growing interest in the last years, demonstrated in the review presented in what follows. In this
* Corresponding author. Tel.: þ34 916248776; fax: þ34 916249430. E-mail address: [email protected] (M. Venegas). 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2012.07.006
configuration, the heat and mass transfer processes are separated in two devices: the single-phase solution subcooler and the adiabatic absorption chamber. The absorber is known as adiabatic because heat is not extracted from the solution at the same time the mass transfer occurs. The concentrated solution is cooled below the saturation temperature in the subcooler, allowing absorption to occur in the downstream adiabatic chamber, what increases the solution temperature. A conventional single-phase heat exchanger can be used for the subcooler, e.g. a commercial plate heat exchanger (PHE) in favour of cost and bulk. Other advantages of this method are a more compact absorber and avoidance of the wetting difficulties of the absorber tubes surface, problem that has been discussed by Jeong and Garimella [1], among others. The mass transfer to solution drops and sheets and the internal heat transfer are processes of complex modelling as the mass and energy conservation equations must be solved simultaneously, taking into account fluid motion at both sides of the interface. To date, analytical models to predict the simultaneous variation of the
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Nomenclature a
A b Cp do D Dh DI EQI f F Fo PHE G hm k Ka L* Le LI _ m MVD P PI PIC Pr QI QIC R Ra Re
constant of the linear relation X ¼ a,T þ b at a given equilibrium pressure in the Dühring diagram, function of pressure, concentration and temperature (K1) area (m2) constant specific heat at constant pressure (kJ kg1 K1) nozzle exit diameter (mm) liquid mass diffusivity (m2 s1) hydraulic diameter (m) density indicator energy and volumetric flow indicator Darcy friction factor. Generic function approach to equilibrium factor Fourier number, Fo ¼ a,s=R2 plate heat exchanger _ mass flux G ¼ m=A (kg m2 s1) mass transfer coefficient (mm s1) thermal conductivity (W m1 K1) Kutateladze number (Ka ¼ a$Dh/Cpcs) characteristic length of the adiabatic chamber (m) Lewis number (Le ¼ acs/Dcs)eq equivalent length (m) liquid level indicator mass flow rate (kg s1) mean volume diameter (mm) pressure (Pa) pressure indicator pressure control Prandtl number (Pr ¼ mcs $Cpcs =kcs ) volumetric flow rate indicator volumetric flow rate control droplet radius (m) absorption ratio (kgv kg1 ds ) _ cs =p$mcs 7do ) solution Reynolds number (Re ¼ 4m
concentration and temperature, considering size, velocity, internal circulation, flow pattern, etc. do not exist. If all these factors could be accurately considered, the characteristics of the heat and mass transfer in individual drops or sheets would correctly predict the global process that takes place in adiabatic absorbers of absorption refrigeration systems. To date, several studies analyse the simplified simultaneous heat and mass transfer in drops and sheets. Zacarías et al. [2] presented a revision of the works developed in relation to solution sheets. A review of the up to date efforts regarding absorption into solution drops is presented in the following: 1.1. Analytical studies Nakoryakov and Grigoreva [3] developed the first-known analytical model of the simultaneous heat and mass transfer in independent spherical drops. This model is valid for static droplets and does not consider the angular variation of the concentration and temperature inside the spherical droplet. The authors present an equation, valid to obtain the mass transfer coefficient, in terms of the Fourier (Fo), Lewis (Le) and Kutateladze (Ka) numbers. Fenton et al. [4] developed, and validated experimentally, an analytical model for the absorption of ammonia vapour by a water spray. The model predicted the vapour absorbed to within 15% deviation when the ratio of water to ammonia is greater than or equal to that specified in ASHRAE [5]. In this case ammonia vapour
Sc SD Sh T TI TIC u X WI
solution Schmidt number (Sc ¼ mcs =rcs Dcs ) standard deviation solution Sherwood number (Sh ¼ hm L* =Dcs ) temperature ( C) temperature indicator temperature control solution average velocity inside the pipe or accessory (m s1) refrigerant mass fraction (%) wattmeter
Greek symbols Dh specific absorption heat (kJ kg1) DP pressure drop (Pa) DT temperature difference, subcooling ( C) DX concentration difference (%) DXlm logarithmic mean concentration difference (%) DPI pressure drop indicator a liquid thermal diffusivity (m2 s1) m viscosity (Pa s) r density (kg m3) s surface tension (N m1) s time (s) Subscripts a absorber ad adiabatic cs concentrated solution ds diluted solution exp experimental eq equilibrium fric frictional i inlet o outlet v vapour
removal from air is under interest because of safety and environmental protection purposes. Thus, the ammonia is much diluted into water. For similar reasons, Huang [6] presented a model to calculate the removal efficiency of ammonia by a fine water spray. The author considers the effects of droplet pH, droplet diameter, ammonium concentration, ammonia concentration, and liquid-to-air ratio. The results showed that absorption increases as the droplet pH, ammonium concentration, or droplet diameter decrease and when the ammonia concentration or liquid-to-air ratio increase. The removal of ammonia from air is a more complex problem that the pure ammonia absorption as diffusion in the gaseous phase does not have to be taken into account in the later. 1.2. Numerical studies The main limitation of analytical models is given by the simplifications assumed during the solution of equations, which makes the models only valid for special cases. For this reason, and due to the lack of suitable experimental correlations in many occasions, several authors have solved more complex cases in a numerical way. Apparently the first reported numerical models include those of Morioka et al. [7] and Lu et al. [8]. In both cases, the absorption of water vapour by water-lithium bromide solution spherical droplets is analyzed when experiencing internal circulation, which is driven
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by external shear of the free-falling droplets. Morioka et al. [7] showed that the absorption ratio can be increased by the internal circulation, and also that this increment depends on the Reynolds number and the residence time. Lu et al. [8] showed the effect of the absorption heat released in the mass transfer process. Venegas et al. [9] modelled the simultaneous internal heat and mass transfer during absorption of ammonia vapour by ammoniaelithium nitrate solution drops. The low-pressure absorber of a double stage refrigeration system was considered in the model. Heat and mass transfer coefficients obtained using the spray absorption method were obtained. Calculated heat transfer coefficient was one order of magnitude higher than that experimentally obtained by Infante Ferreira [10] using the same solution in a vertical falling film absorber. In a later paper, Venegas et al. [11] performed a simulation considering ammoniaelithium nitrate droplets with diameters equal to 60 and 100 mm. Results showed that these small drops follow the Newman isothermal droplet model [12] for mass transfer. Droplets achieved the equilibrium state in times shorter than 1 s. In a following paper, Venegas et al. [13] using the same solution, divided the spray in three regions: liquid jet, deceleration of the drops and uniform motion. Results showed that the mass transferred is maximum (about 60% of the total) during the deceleration period of the drops. This period represented about 13.4% of the time required to reach the equilibrium state at the end of the absorption chamber. Elperin et al. [14] also simulated numerically the simultaneous heat and mass transfer of water vapour into isolated disperse spherical droplets of water-lithium bromide solution. The authors concluded that the resulting increase of the inter-phase temperature decreases the absorption driving potential, the mass flux and the equilibrium concentration. They obtained a good agreement with the experimental results reported by Paniev [15] and Burdukov et al. [16]. 1.3. Experimental studies Experimental studies on simultaneous heat and mass transfer are not as scarce as analytical or numerical studies. Paniev [15] developed the first known work related to solutions used in absorption refrigeration system. Paniev, and Burdukov et al. [16], used the water - lithium bromide solution. Their works intended to verify experimentally the equation obtained by Nakoryakov and Grigoreva [3]. Results obtained show a great discrepancy for Fourier numbers in the range Fo < 0.01 and Fo > 0.04. Ryan et al. [17] also performed several experiments using the same working fluid. The authors conclude that the simple model developed by Newman [12] is suitable for predicting the mass transfer to dispersed droplets in an adiabatic absorber. Some experimental works using other pairs have also been published. For example, Fenton et al. [4] analysed the absorption of ammonia by pure water droplets while Summerer et al. [18] and Flamensbeck et al. [19]studied the simultaneous heat and mass transfer between binary or ternary mixtures and water. More recently, Arzoz et al. [20] developed experiments using the water-lithium bromide solution and free falling droplets of about 4 mm diameter. Warnakulasuriya and Worek [21,22], using water as refrigerant and a lithium bromide-based absorbent called LZBÔ, made some experiments using droplets of 252e338 mm MVD. The authors show that mass transfer results, evaluated in terms of the Sherwood number, are up to 4 times higher than those obtained in conventional absorption systems. Wang et al. [23] performed a direct application of an adiabatic spray absorber, using the water-lithium bromide solution in an aircooled absorption refrigeration machine. Gutiérrez [24] and
783
Gutiérrez-Urueta et al. [25] developed experiments using also the H2O-LiBr solution and the dispersion of the liquid using free falling drops, like Arzoz et al. [20]. The authors concluded that this configuration allows obtaining lower absorption performance than the arrangement using a flat fan nozzle for the dispersion of the solution. In the last years, Zacarías [26] and Ventas [27] have used a fog jet nozzle to disperse the solution inside an adiabatic absorption chamber using the ammoniaelithium nitrate solution. Ventas et al. [28] recently presented the results of an experimental study modifying the ammonia mass fraction and the absorber pressure in the ranges 0.419 to 0.586 and 429e945 kPa, respectively. Ammoniaelithium nitrate is a promising alternative solution for refrigeration applications that conventionally use the ammoniaewater solution, e.g. Venegas et al. [29]. Different techniques for dispersing the solution in drops inside the adiabatic absorption chamber exist, depending on the nozzle used: hollow cone, fog jet, full cone, etc. In the present work, a commercial fog jet nozzle is used to evaluate experimentally the absorption process of ammonia by a lithium nitrate solution, as its form factor is potentially compact. The absorber pressures considered in this study are lower than those tested by Ventas et al. [28], what makes the present study relevant for sub-cero cooling. Here, the effect on the absorption of a variation of mass flow rate at the inlet of the absorber is included too. The present paper offers additional experimental evidence in order to better evaluate the mass transfer capacity and pressure drop of this adiabatic absorption configuration. Correlations here developed aim at the designer in the dimensioning of the absorption chamber. 2. Experimental setup In the present study the experimental facility is composed by a thermo-chemical compressor, i.e. the generator, single-pass absorber and heat recovery exchanger as main components (see Fig. 1). Auxiliary components are: the external water heater, the solution subcooler and the ammonia vapour cooler. A detailed description of the facility has been previously documented elsewhere, e.g. Zacarías et al. [2,30]. The refrigerant mass fraction was kept at X ¼ 46.08% along the experimentation, with a standard deviation of 0.057%. Table 1 shows the results of an uncertainty analysis for the measured variables used in the present study. Properties of ammonia were taken from Engineering Equation Solver software, EESÒ [31], which uses the fundamental equation of state developed by [32]. In the open literature, correlations to calculate the surface tension of the ammoniaelithium nitrate solution are not available, for this reason it was estimated performing a statistical fit of data available in Infante Ferreira [33], as a function of temperature and concentration. The correlation obtained is:
sðX;TÞ ¼ 4544:17þ36895:5X 92650:66X 2 þ76511:46X 3 28:64T þ1:02T 2 0:01T 3
(1)
The goodness of fit parameter for this correlation is R2 ¼ 96%. All other solution properties were calculated using correlations given by Libotean et al. [34,35] and Libotean [36]. 2.1. Adiabatic absorption chamber Fig. 2 shows a photograph of the adiabatic absorption chamber in the test rig. A detailed description of the geometrical characteristics of the absorption chamber can be found in Zacarías et al. [2]. The fog jet nozzle used in the present study is the model 3/4 -7G-SS 1, which is
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Fig. 1. Layout of the experimental setup.
based on a diverging layout of seven solid cone injectors. This configuration has also been used by Ventas et al. [28]. Fig. 3 shows a photograph of the nozzle. The height selected to locate its tip was 205 mm measured from the bottom of the chamber. A photograph of the atomization pattern obtained using the fog jet nozzle, corresponding to a pressure drop of 200 kPa, can be found in Ventas et al. [28]. 3. Data reduction
the concentration that the solution ideally reaches in an adiabatic process is required, while in the second one the solution temperature at the outlet of the ideal adiabatic process is necessary. Approach to adiabatic equilibrium factor:
F ¼
3.1. Mass transfer analysis The mass transfer analysis performed in the present paper is based on the evaluation of different parameters, already described in detail in Zacarías et al. [2]. A classification of these parameters is done in the following.
Xds Xcs Xeq; ad Xcs
Outlet subcooling:
DTo ¼ Teq;ad Tds
3.1.1. Parameters requiring adiabatic absorption equilibrium data Two parameters that take into account in their definition the adiabatic absorption process are described below. In the first one,
Table 1 Results of the uncertainty analysis for measured variables. Variable
Type
Range
Uncertainty
T of the solution at the absorber inlet T of the solution at the absorber outlet T of the vapour at the absorber inlet P at the absorber inlet
Thermoresistance PT100 Thermoresistance PT100 Thermoresistance PT100 Absolute pressure transducer Absolute pressure transducer Coriolis flow meter Coriolis flow meter Coriolis flow meter
10e60 C
0.40 C
10e60 C
0.58 C
10e60 C
0.51 C
0e1 MPa
1 kPa
0e1 MPa
1 kPa
0e0.3 kg/s 0e10,000 kg/m3 0e0.1 kg/s
0.03% f.s. 0.03% f.s. 0.05% f.s.
Pa _ ds m rds. _v m
(2)
Fig. 2. Photograph of the adiabatic absorption chamber.
(3)
A. Zacarías et al. / Applied Thermal Engineering 50 (2013) 781e790
785
DX1 ¼ Xeq;i Xcs
(8)
DX2 ¼ Xeq;o Xds
(9)
In these equations, the saturation concentrations Xeq,i and Xeq,o are calculated using the absorber pressure and the local solution temperatures. Variables used in the definitions of the parameters described previously are determined using mass rate balances in the absorber _ cs , Xcs): (m
_ cs ¼ m _ ds m _v m Xcs ¼
(10)
_ ds m _v Xds $m _ cs m
(11)
or correlations (Xds), as described in Zacarías et al. [2]. The diluted _ v , the _ ds , the vapour mass flow rate m solution mass flow rate m density rds and the temperature Tds were experimentally measured. 3.2. Pressure drop Fig. 3. Fog jet nozzle from Spraying systems CoTM.
3.1.2. Parameters non requiring adiabatic absorption equilibrium data Three other parameters are used in the present paper to assess the mass transfer. They can also be used in the characterisation of diabatic absorbers. Absorption ratio:
Ra ¼
_v m _ ds m
(4)
Pressure drop of the solution in the injection nozzle is determined by subtracting losses to the measured pressure drop:
DPa ¼ DPexp DPfric
DPexp is the pressure drop measured as the difference between the inlet pipe Pcs and the absorption chamber Pa. Gravitational pressure gradient was not considered given the small vertical distance between both pressure transducers. Frictional pressure loss inside the pipes including connections, DPfric , is determined adding contributions in the form:
DPfric Mass transfer coefficient:
hm
Gv ¼ rds $DXlm
(5)
Absorption mass flux:
Gv ¼
_v m Aa
DX1 DX2 DX1 ln DX2
(7)
! (13)
These elements must be included because the pressure transducer located in the inlet pipe is distant from the absorber inlet. Darcy friction factor for pipes is obtained from Incropera and DeWitt [37]: 1=4
Zacarías et al. [2] offer a discussion about the different ways the reference area Aa has been defined in the literature. In the present study, Aa was defined as the area of the cone containing all the drops generated, in this case equal to 0.198 m2. The height was equal to 205 mm and the diameter was proportional to the value given by the injector manufacturer at 1 m height (1.5 m). This definition of the mass transfer area indicates the envelope of the volume occupied and allows comparing the mass transfer coefficient with other spray configurations. Besides this, it avoids imprecision associated with drops diameters, a variable changing along experimentation with pressure difference, ammonia mass fraction and temperature. In the present study, the mean logarithmic concentration difference DXlm has been defined as:
DXlm ¼
r$u2 $Leq 1 ¼ f Dh 2
f ¼ 0:316,ReDh (6)
(12)
for ReDh 2 104
(14)
Here, the Reynolds number ReDh is based on the pipe diameterDh. 4. Results and discussion 4.1. Absorption 10 experiments were recorded using the fog jet nozzle. The aperture of the vapour expansion valve upstream of the nozzle was kept constant, allowing pressure variations inside the absorption chamber. The pressure obtained varied between 355 and 411 kPa, corresponding to subzero cooling. Two variables were controlled: the inlet solution subcooling, DTi ¼ Teq;i Tcs (the inlet solution temperature was varied between 25.9 and 30.2 C) and the diluted solution mass flow rate (0.04e0.08 kg s1). The effect of these controlled variables on the parameters defined previously to characterise the mass transfer: absorption mass flux, approach to adiabatic equilibrium factor, outlet subcooling, absorption ratio and mass transfer coefficient, is shown in the following. The increase of the inlet solution subcooling leads to a higher capacity for vapour absorption, resulting in higher refrigerant mass fraction changes inside the adiabatic chamber for a fixed solution
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0.003
2.5
Outlet subcooling, Teq,ad -Tds [ºC]
Vapour flow rate, mv [kg/s]
m cs = 0.04 [kg/s ]
0.002
0.001 m cs = 0.04 [kg/s ] m cs = 0.05 [kg/s ] m cs = 0.08 [kg/s ]
0 12
15
18 21 Inlet subcooling, Teq,i -Tcs [ºC]
2
m cs = 0.08 [kg/s ]
1.5 1 0.5 0 -0.5 -1 500
24
Fig. 4. Vapour mass flow rate as a function of the inlet subcooling for three different inlet solution mass flow rates.
mass flow rate. Consequently, higher inlet subcooling produced higher vapour mass flow rates. As the whole facility is working under steady state conditions, and the absorber is the limiting component to increase capacity, the amount of refrigerant vapour separated in the generator increases. The resultant vapour mass flow rate was between 0.8 and 2.2 g s1 Fig. 4 allows observing the experimental relation obtained between vapour mass flow rate and inlet solution subcooling. On the other hand, if the inlet subcooling is unchanged, the increase of the solution mass flow rate also implied a higher vapour mass flow rate, as observed in Fig. 4. More quantity of subcooled solution surface is available to absorb refrigerant vapour as a consequence of a higher atomization and flow rate, overcoming the shorter residence time effect of faster moving droplets. The net result is an increase of the vapour mass flow rate. The absorption mass flux obtained is between 0.004 and 0.010 kg m2 s1. The variation of this parameter is similar to that obtained for the vapour flow rate, because, as defined in Eq. (6), it only depends on the vapour mass flow rate and the absorber area, with the latter being constant. This parameter has been used elsewhere to assess the mass transfer, see for example Vallès et al. [39], Yoon et al. [40], Cerezo et al. [41], Palacios et al. [42], among others.
m cs = 0.05 [kg/s ]
1000
1500
2000
2500
Solution Reynolds number, Recs [ ] Fig. 6. Relation between outlet subcooling and solution Reynolds number, for three values of the solution mass flow rate. The uncertainties of the outlet subcooling are shown.
Fig. 5 shows the approach to adiabatic equilibrium factor F for three different inlet solution mass flow rates as a function of the solution Reynolds number. Results indicate the increase of F when Recs increases. As this figure shows, high values of F have been obtained. Values of F obtained in the present study are in the same range of those obtained by Ventas et al. [28] using the same solution and fog jet nozzle, but are about 3.7% higher than those obtained by Zacarías et al. [2] (between 0.81 and 0.89) using this solution and a flat fan nozzle in an adiabatic absorber. A high value of this parameter is important to minimize the recirculation ratio of the solution through the solution subcooler (see Ventas et al. [38]), and thus minimising the pump work and the size of accessories. Additionally, the use of F to evaluate the mass transfer is important because it does not depend on arbitrary parameters like the reference area Aa used in the mass transfer coefficient. The identification of this area is especially difficult and expensive in atomization processes where sprays or sheets are generated. Fig. 6 represents the outlet subcooling DTo. a function of the solution Reynolds number Recs. As it can be observed, outlet subcooling is small and decreases when the Reynolds number increases. It could be motivated by the smaller diameters of the resulting droplets, inducing higher inter-phase surface per unit of
1
0.9
Ra= mv /mds [kg v /kg s]
Approach to equilibrium factor, F [ ]
0.04
0.8
0.7
m cs = 0.04 [kg/s] m cs = 0.05 [kg/s]
0.6
m cs = 0.08 [kg/s]
0.03
0.02
m cs = 0.04 [kg/s] m cs = 0.05 [kg/s] m cs = 0.08 [kg/s]
0.5 700
1000
1300
1600
1900
2200
Solution Reynolds number, Recs [ ] Fig. 5. Approach to adiabatic equilibrium factor as a function of the solution Reynolds number, for three inlet solution mass flow rates. The uncertainties of the adiabatic approach to equilibrium factor are shown.
0.01 10
15
20
25
Inlet subcooling, Teq,i -Tcs [ºC] Fig. 7. Relation between absorption ratio and inlet subcooling. The uncertainties of the absorption ratio are shown.
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300 m cs = 0.04 [kg/s]
0.6
2.033
ΔPa=43720.5·mcs
m cs = 0.05 [kg/s] m cs = 0.08 [kg/s]
ΔPa [kPa]
Mass transfer coefficient, h m [mm/s]
0.8
787
0.4
200
100 0.2
0 700
1000
1300
1600
1900
2200
0 0
0.02
Solution Reynolds number, Recs [ ]
0.04
0.06
0.08
0.1
Inlet solution flow rate, mcs [kg/s]
Fig. 8. Mass transfer coefficient as a function of the solution Reynolds number, for three inlet solution mass flow rates. The uncertainties of the mass transfer coefficient are shown.
solution volume, higher droplets instabilities and consequently higher mass transfer rates. The high values of the metrological uncertainties show that outlet subcooling is not an accurate variable to evaluate the performance of the adiabatic absorber, as it is shown in the Fig. 6 error bars. In spite of this trouble, the outlet subcoolings found in this paper are smaller than those reported by Summerer et al. [18] using binary and ternary hydroxide mixtures (NaOH, KOH and CsOH) and water as refrigerant. These authors used fog jet, full jet and spiral nozzles. In that research paper, when the atomizer was located 200 mm above the liquid surface, the smallest outlet subcooling reported was 1.9 C. The better results here obtained can be attributed to differences in the inlet subcooling (in the present study it was varied between 15.1 C and 20.9 C), in the thermal and transport properties between the working solutions and between droplets sizes generated in each case. The much lower vapour density for water-based solutions reduces the liquid surface instabilities and reduces the residence time because of the lower aerodynamic drag. Fig. 7 shows the absorption ratio Ra as a function of the inlet subcooling. As it can be expected, absorption is helped by subcooling. When the inlet solution temperature decreases, solution separates from its corresponding equilibrium state at the given absorption pressure, raising the ammonia mass flux to the solution. The linear correlation obtained between Ra and DTi . incides with findings reported by Zacarías et al. [2] and Arzoz et al. [20]. Values of Ra obtained in the present study are in the same range of those obtained by Ventas et al. [28] using the same solution and fog jet nozzle.
Fig. 9. Pressure drop of the solution in the injection nozzle as a function of its flow rate.
Fig. 8 presents the relation between the mass transfer coefficient hm and Recs. Both variables are linearly related, showing the benefits on absorption of a Recs increase. Table 2 shows a comparison between values of hm obtained in different studies. It can be observed that adiabatic absorbers allow obtaining high mass transfer coefficients, but not necessarily higher than the values obtained using diabatic absorbers. Results given now regarding the mass transfer coefficient are about half of the values presented in Zacarías et al. [2] using a flat fan nozzle. Values obtained in the present paper are of the same range of those obtained in Venegas et al. [13] in a theoretical study. However, conclusions derived from this comparison are not straightforward because different surfaces areas have been used in each case. Zacarías et al. [2] use the area of two isosceles triangles representing both faces of the flat fan sheet, while Venegas et al. [13] employ the surface area of the uniformly sized spray droplets, considered as spheres. The rest of surface areas used can be consulted in the works cited in Table 2. Besides that, solution concentration and pressure are also different in these studies. 4.2. Pressure drop Fig. 9 shows the pressure drop of the solution in the nozzle located at the inlet of the absorption chamber as a function of the solution mass flow rate. The equation resulting from a power fit between both variables is offered. These pressure losses are not a limiting factor in ammonia absorption machines because of the relatively high pressure difference available, Venegas et al. [13].
Table 2 Comparison between mass transfer coefficients hm reported in the literature. Reference
Absorber type
Configuration
Method
Solution
hm 105 (m s1)
Vallès et al. [39] Yoon et al. [40] Cerezo et al. [41] Kim et al. [43] Soto and Pinazo [44] Lee et al. [45] Zacarías et al. [2] Venegas et al. [13] Arzoz et al. [20] Palacios et al. [42] Palacios et al. [46] This work
Diabatic in PHE Diabatic Diabatic Diabatic Diabatic Diabatic Adiabatic Adiabatic Adiabatic Adiabatic Adiabatic Adiabatic
Spray (full cone) Falling film (helical) Bubble Slug flow Falling film (horizontal) Falling film (horizontal) Spray (flat fan) Spray (full cone) Falling film Spray (conical) Spray (flat fan) Spray (fog jet)
Experimental Experimental Experimental Experimental Experimental Experimental Experimental Numerical Experimental Experimental Experimental Experimental
Organic mixtures H2OeLiBr NH3eH2O NH3eH2O H2OeLiBr NH3eH2O NH3eLiNO3 NH3eLiNO3 H2OeLiBr H2OeLiBr H2OeLiBr NH3eLiNO3
1e2.5 2e4 100e200 8e56 0.2e4.2 0.6e3.3 34e101 8.1e86 1e15 75e200 25e210 17e47
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A. Zacarías et al. / Applied Thermal Engineering 50 (2013) 781e790 Table 3 Results of the uncertainty analysis for the calculated variables with a confidence level of 95%.
1
Correlated F [ ]
+2%
0.9 -2%
Variable
Average
Maximum
Absorption ratio, Ra Inlet subcooling, DTi Outlet subcooling, DTo Approach to adiabatic equilibrium factor, F Absorption mass flux, Gv Mass transfer coefficient, hm Pressure drop in the injection nozzle, DPa.
3.8% 0.94 C 0.87 C 5.7% 3.8% 36.8% 1.3%
6.2% 0.95 C 0.88 C 7.5% 6.2% 56.6% 2.2%
0.8
In the Sherwood number: 0.7 0.7
0.8
0.9
1
Experimental F [ ]
hm $L* Dcs
4.3. Mass transfer correlations Zacarías [26] and Ventas et al. [38] showed that the approach to adiabatic equilibrium factor has a large influence on the results of a numerically modelled thermo-chemical compressor. Warnakulasuriya and Worek [21] obtained an experimental correlation for F as a function of the Sherwood number Sh. They used the highly viscous fluid LZBÔ supplied by the company TraneÔ. Zacarías et al. [2] obtained correlations for F and Sh, using the ammoniaelithium nitrate solution and a flat fan nozzle in an adiabatic absorber. These are the only experimental correlations available in the open literature, as far as the authors’ knowledge. With the aim of obtaining correlations of F and Sh, in the present study the procedure described in Zacarías et al. [2] is followed. The best correlation for F obtained, with the goodness of fit parameter R2 ¼ 88.7%, is:
!0:791 Pa 1:018 DTi F ¼ Pcs Teq;ad 8 884:2< Re < 1979 ; 55:4< Pr < 63 cs cs < with : DTi Pa : 0:598 < < 0:859; 0:367< < 0:482 Pcs Teq;ad
Sh ¼ 0:729$Re1:308 Sc0:966 cs cs with : 884:2< Recs < 1979; 15; 061 < Sccs < 19; 642
(15)
Correlated Sh*10-8 [ ]
+10%
1.2
-10%
0.8
0.4 0.4
0.8
1.2
1.6
Experimental Sh*10-8 [ ] Fig. 11. Correlated vs. experimental Sh.
(17)
The solution temperature at the inlet of the absorption chamber has been used to calculate all properties in Eqs. (15)e(17). These equations can be of profit for the simulation and design of adiabatic absorbers using fog jet nozzles and the ammoniaelithium nitrate solution in the operating conditions defined by the ranges of the dimensionless groups, typical for a single effect chiller. Figs. 10 and 11 show a comparison between experimental and predicted values of the approach to adiabatic equilibrium factor F and Sherwood number Sh using Eqs. (15) and (17) respectively. All of the predicted data differ less than 2% and 10% respectively from the experimental data, indicating that the correlations are good. An uncertainty analysis was developed as in Taylor and Kuyatt [47]. Uncertainty propagation was performed using the software Engineering Equation Solver, EESÔ, which offers a calculation tool
2
1.6
(16)
L* is the characteristic length, equal to 0.205 m, here defined as the height of the absorption spray. In the present study, the following correlation was obtained with R2 ¼ 97.5%:
Fig. 10. Correlated vs. experimental F.
3:98,107 $Re0:657 Pr2:343 cs cs
Sh ¼
Fig. 12. Sensitivity of mass transfer parameters to measured variables.
A. Zacarías et al. / Applied Thermal Engineering 50 (2013) 781e790
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Correlations for the approach to adiabatic equilibrium factor and Sherwood number have been obtained. They can be used to predict the performance of adiabatic absorbers. Acknowledgements The financial support of this study by the Spanish Ministry of Education and Science research grant ENE2005-08255-C02-02, ENE2009-11097 and Project CCG07-UC3M/ENE-3411, by the Local Government of Madrid and UC3M, is greatly appreciated. A. Zacarías also acknowledges the financial support given by National Board of Science and Technology and the Instituto Politécnico Nacional of Mexico. The authors want to acknowledge the help of Mr. Manuel Santos, Mr. Carlos Cobos and Mr. Ciro Vereda in the laboratory work. References
Fig. 13. Measured variables along time. Standard deviation (SD) is shown in the units of each variable.
based on this background. Table 3 offers results of the average and maximum uncertainties obtained for main variables calculated in the present study. The maximum uncertainty was obtained for the mass transfer coefficient, with an average value of 36.8%. A sensitivity study also has been performed. Fig. 12 shows the contribution of each measured variable to the total uncertainty of the mass transfer parameter evaluated (the contribution is shown in percentage inside each rectangle). Four of the measured variables are not represented in the figure because their contribution is lower than 0.6%. As can be observed, vapour mass flow rate has the highest influence on the absorption ratio Ra and the absorption mass flux Gv uncertainties. Density and temperature of the diluted solution determine the uncertainty of the mass transfer coefficient hm and of the outlet subcooling DTo. .he solution temperature at the absorber inlet only influences the approach to adiabatic equilibrium factor F uncertainty. Values shown in the graph were obtained as averages of all experiments. The experimental data were recorded every 8 s during a period of time of 600 s, in order to obtain every experimental point. Oscillations of measured variables during this period were very small. Fig. 13 shows the time evolution of variables represented in Fig. 12, for one point. The standard deviation around a constant value is very small, demonstrating that the experiments can be considered as steady state. 5. Conclusions The following conclusions have been achieved from the analysis of the mass transfer process inside the adiabatic absorption chamber: Inlet solution subcooling has a comprehensible positive effect over the vapour mass flow rate and the absorption ratio. The approach to adiabatic equilibrium factors are higher than those previously reported by the authors using a flat fan nozzle. The high values obtained indicate that fog jet nozzles may improve absorption in adiabatic absorbers, even for low absorption pressures. Solution pressure drops required at the nozzle of the absorption chamber are compatible with ammonia absorption systems because of the relatively high pressure difference available, allowing mass flow control by throttling.
[1] S. Jeong, S. Garimella, Falling-film and droplet mode heat and mass transfer in a horizontal tube LiBr/water absorber, Int. J. Heat Mass Transf. 45 (2002) 1445e1458. [2] A. Zacarías, M. Venegas, R. Ventas, A. Lecuona, Experimental assessment of ammonia adiabatic absorption into ammonia-lithium nitrate solution using a flat fan nozzle, Appl. Therm. Eng. 31 (2011) 3569e3579. [3] V.E. Nakoryakov, N.I. Grigoreva, Combined heat and mass transfer during absorption in droplets and films, J. Eng. Phys. 32 (1977) 243e247. [4] D.L. Fenton, A.F. Noeth, R.L. Gorton, Absorption of ammonia into water, ASHRAE Trans. 97 (1991) 204e213. [5] Safety Code for Mechanical Refrigeration, ASHRAE, Atlanta, USA, 1989, ANSI/ ASHRAE Standard 15-1989. [6] C.H. Huang, Theoretical model of absorption of ammonia by fine water spray, Environ. Eng. Sci. 22 (2005) 535e541. [7] I. Morioka, M. Kiyota, A. Ousaka, T. Kobayashi, Analysis of steam absorption by a subcooled droplet of aqueous solution of LiBr, JSME Int. J. 35 (Series II) (1992) 458e464. [8] H.H. Lu, T. Ch. Wu, Y.M. Yang, J.R. Maa, Transient heat and mass transfer in a drop experiencing absorption with internal circulation, Int. Commun. Heat Mass Transf. 25 (1998) 1115e1126. [9] M. Venegas, D. Arzoz, P. Rodríguez, M. Izquierdo, Heat and mass transfer in LiNO3-NH3 spray absorption system, Int. Commun. Heat Mass Transf. 30 (2003) 805e815. [10] C.A. Infante Ferreira, Operating Characteristics of NH3-LiNO3 and NH3-NaSCN Absorption Refrigeration Machines, 19th International Congress of Refrigeration, vol. IIIa, The Hague, the Netherlands, 1995, pp. 321e328. [11] M. Venegas, M. Izquierdo, P. Rodríguez, A. Lecuona, Heat and mass transfer during absorption of ammonia vapour by LiNO3eNH3 solution droplets, Int. J. Heat Mass Transf. 47 (2004) 2653e2667. [12] A. Newman, The drying of porous solids: diffusion and surface emission equations, Trans. A.I.Ch.E 27 (1931) 203e220. [13] M. Venegas, P. Rodríguez, A. Lecuona, M. Izquierdo, Spray absorbers in absorption systems using lithium nitrateeammonia solution, Int. J. Refrig. 28 (2005) 554e564. [14] T. Elperin, A. Fominykha, Z. Orenbakh, Coupled heat and mass transfer during nonisothermal absorption by falling droplet with internal circulation, Int. J. Refrig. 30 (2007) 274e281. [15] G.A. Paniev, Absorption heat and mass transfer on droplets in a polydispersed spray, Heat Transfer-Soviet Res. 15 (1983) 62e72. [16] A.P. Burdukov, A.R. Dorokhov, G.A. Paniev, Combined heat and mass transfer in absorption on droplets, Soviet J. Appl. Phys. 3 (1989) 39e45. [17] W.A. Ryan, F. Ruiz, J. Wurm, Model development and verification of spray absorption for gas driven cooling systems, in: Proceedings of International Gas Research Conference, Cannes, France, 1995, pp. 1483e1493. [18] F. Summerer, F. Ziegler, P. Riesch, G. Alefeld, Hydroxide absorption heat pumps with spray absorber, ASHRAE Technical Data Bull. 12 (1996) 50e57. [19] M. Flamensbeck, F. Summerer, P. Riesch, F. Ziegler, G. Alefeld, A cost effective absorption chiller with plate heat exchangers using water and hydroxides, Appl. Therm. Eng. 18 (1998) 413e425. [20] D. Arzoz, P. Rodríguez, M. Izquierdo, Experimental study on the adiabatic absorption of water vapor into LiBr-H2O Solutions, Appl. Therm. Eng. 25 (2005) 797e811. [21] F.S.K. Warnakulasuriya, W.M. Worek, Adiabatic water absorption properties of an aqueous absorbent at very low pressures in a spray absorber, Int. J. Heat Mass Transf. 49 (2006) 1592e1602. [22] F.S.K. Warnakulasuriya, W.M. Worek, Drop formation of swirl-jet nozzles with high viscous solution in vacuum-new absorbent in spray absorption refrigeration, Int. J. Heat Mass Transf. 51 (2008) 3362e3368. [23] L. Wang, G.M. Chen, Q. Wang, M. Zhong, Thermodynamic performance analysis of gas-fired air-cooled adiabatic absorption refrigeration system, Appl. Therm. Eng. 27 (2007) 1642e1652.
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A. Zacarías et al. / Applied Thermal Engineering 50 (2013) 781e790
[24] G. Gutiérrez, Thermo-fluid Dynamic Evaluation of Components in Adiabatic Absorption Systems, Ph.D. Thesis, Universidad Carlos III de Madrid, Madrid, Spain, 2009. [25] G. Gutiérrez-Urueta, P. Rodríguez, M. Venegas, F. Ziegler, M.C. RodríguezHidalgo, Experimental performances of a LiBr-water absorption facility equipped with adiabatic absorber, Int. J. Refrig. 34 (2011) 1749e1759. [26] A. Zacarías, Mass and Heat Transfer in Adiabatic Absorbers with Application to the Ammoniaelithium Nitrate Solution, Ph.D. Thesis, Universidad Carlos III de Madrid, Madrid, Spain, 2009 (in Spanish). [27] R. Ventas, Study of Absorption Machines with the Ammoniaelithium Nitrate Solution: Hybrid Cycles Boosted with Mechanical Compression, Ph.D. Thesis, Universidad Carlos III de Madrid, Madrid, Spain, 2010 (in Spanish). [28] R. Ventas, C. Vereda, A. Lecuona, M. Venegas, M.C. Rodríguez-Hidalgo, Effect of the NH3-LiNO3 concentration and pressure in a fog-jet spray adiabatic absorber, Appl. Therm. Eng. 37 (2012) 430e437. [29] M. Venegas, M. Izquierdo, M. de Vega, A. Lecuona, Thermodynamic study of multistage absorption cycles using low-temperature heat, Int. J. Energy Res. 26 (2002) 775e791. [30] A. Zacarías, R. Ventas, M. Venegas, A. Lecuona, Boiling heat transfer and pressure drop of ammonia-lithium nitrate solution in a plate generator, Int. J. Heat Mass Transf. 53 (2010) 4768e4779. [31] S.A. Klein, Engineering Equation Solver, Academic Professional, 2011, V8.944-3D. [32] R. Tillner-Roth, F. Harms-Watzenberg, H.D. Baehr, A new fundamental equation for ammonia, DKV-Tagungsbericht 20 (1993) 167e181 (in German). [33] C.A. Infante Ferreira, Vertical tubular absorbers for ammonia-salt absorption refrigeration, Ph.D. Thesis, Delft Technical University, Delft, Holland, 1985. [34] S. Libotean, D. Salavera, M. Vallés, X. Esteve, A. Coronas, Vapor-liquid equilibrium of ammoniaþlithium nitrateþwater and ammoniaþlithium nitrate solutions from (293.15 to 353.15) K, J. Chem. Eng. Data 52 (2007) 1050e1055. [35] S. Libotean, A. Martín, D. Salavera, M. Vallés, X. Esteve, A. Coronas, Densities, viscosities and heat capacities of ammonia-lithium nitrate and ammonialithium nitrate-water solutions between (293.15 and 353.15) K, J. Chem. Eng. Data 53 (2008) 2383e2388.
[36] S.N. Libotean, Thermophysical characterization of the ternary mixture ammonia/lithium nitrate/water for absorption refrigeration applications, Ph.D. Thesis, Universitat Rovira I Virgili, Tarragona, Spain, 2008 (in Spanish). [37] F.P. Incropera, D.P. De-Witt, Heat Transfer Fundamentals, fourth ed., Pearson Prentice Hall, Naucalpan de Juárez, Mexico, 1999 (in Spanish). [38] R. Ventas, A. Lecuona, M. Legrand, M.C. Rodriguez, On the recirculation of ammonia-lithium nitrate solution in adiabatic absorbers for chillers, App. Therm. Eng. 30 (2010) 2770e2777. [39] M. Vallès, M. Bourouis, D. Boer, A. Coronas, Absorption of organic fluid mixtures in plate heat exchanger, Int. J. Therm. Sci. 42 (2003) 85e94. [40] J.-I. Yoon, O.-K. Kwon, Ch.-G. Moon, H.-S. Lee, P. Bansal, Heat and mass transfer characteristics of a helical absorber using LiBr and LiBr þ LiI þ LiNO3 þ LiCl solutions, Int. J. Heat Mass Transf. 48 (2005) 2102e2109. [41] J. Cerezo, M. Bourouis, M. Vallès, A. Coronas, R. Best, Experimental study of an ammoniaewater bubble absorber using a plate heat exchanger for absorption refrigeration machines, Appl. Therm. Eng. 29 (2009) 1005e1011. [42] E. Palacios, M. Izquierdo, R. Lizarte, J.D. Marcos, lithium bromide absorption machines: pressure drop and mass transfer in solutions conical sheets, Energy Conv. Manag. 50 (2009) 1802e1809. [43] H.Y. Kim, B.B. Saha, S. Koyama, Development of a slug flow absorber working with ammoniaewater mixture: part IIddata reduction model for local heat and mass transfer characterization, Int. J. Refrig. 26 (2003) 698e706. [44] V.M. Soto, J.M. Pinazo, Validation of a model for the absorption process of H2O(vap) by a LiBr(aq) in a horizontal tube bundle, using a multi-factorial analysis, Int. J. Heat Mass Transf. 46 (2003) 3299e3312. [45] S. Lee, L. Kumar Bohra, S. Garimella, A. Krishna Nagavarapu, Measurement of absorption rates in horizontal-tube falling-film ammonia-water absorbers, Int. J. Refrig. 35 (2012) 613e632. [46] M. Palacios, J.D. Izquierdo, R. Marcos, Lizarte, Evaluation of mass absorption in LiBr flat-fan sheets, Appl. Energy 86 (2009) 2574e2582. [47] B.N. Taylor, C.E. Kuyatt, Guidelines for evaluating and Expressing the uncertainty of NIST Measurement results, National Institute of standards and Technolog, NIST Technical Note 1297 (1994).
Contents lists available at SciVerse ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Experimental evaluation of ammonia adiabatic absorption into ammoniaelithium nitrate solution using a fog jet nozzle Alejandro Zacarías a, María Venegas b, *, Antonio Lecuona b, Rubén Ventas b a b
Academia de Térmicas/SEPI ESIME Azcapotzalco, Instituto Politécnico Nacional, Av. de las Granjas 682, Col. Santa Catarina, 02550 Distrito Federal, Mexico Departamento de Ingeniería Térmica y de Fluidos, Universidad Carlos III de Madrid, Avda. Universidad 30, 28911 Leganés, Madrid, Spain
h i g h l i g h t s < Adiabatic absorption of NH3 vapour into NH3eLiNO3 using fog jet nozzle created spray. < Pressure drop of the solution entering to the absorption chamber is evaluated. < Approach to adiabatic equilibrium factor (F) is between 0.82 and 0.93 at 205 mm height. < Experimental values of mass transfer coefficient and outlet subcooling are presented. < Correlations for F and Sherwood number are given.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 March 2012 Accepted 3 July 2012 Available online 16 July 2012
This paper presents the experimental assessment of the adiabatic absorption of ammonia vapour into an ammoniaelithium nitrate solution using a fog jet nozzle. The ammonia mass fraction was kept constant at 46.08% and the absorber pressure was varied in the range 355e411 kPa. The nozzle was located at the top of the absorption chamber, at a height of 205 mm measured from the bottom surface. The diluted solution flow rate was modified between 0.04 and 0.08 kg s1 and the solution inlet temperature in the range 25.9e30.2 C. The influence of these variables on the approach to adiabatic equilibrium factor, outlet subcooling, absorption ratio and mass transfer coefficient is analysed. The approach to adiabatic equilibrium factor for the conditions essayed is always between 0.82 and 0.93. Pressure drop of the solution entering the absorption chamber is also evaluated. Correlations for the approach to adiabatic equilibrium factor and the Sherwood number are given. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Ammoniaelithium nitrate solution Adiabatic absorption Fog jet nozzle Mass transfer Pressure drop
1. Introduction Mass transfer in the absorber is one of the main limiting factors for increasing performance and reducing size of absorption machines. Current technology use absorbers relying on laminar falling films, but other absorption methods have shown their potential for reducing both the heat and mass transfer area and, as a result, the absorber dimensions. One of these methods consists on dispersing the liquid solution in drops and/or free-flying sheets inside an adiabatic chamber, putting the solution in contact with the refrigerant vapour. This way, evacuating the absorption heat in the chamber is not possible. This method has received growing interest in the last years, demonstrated in the review presented in what follows. In this
* Corresponding author. Tel.: þ34 916248776; fax: þ34 916249430. E-mail address: [email protected] (M. Venegas). 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2012.07.006
configuration, the heat and mass transfer processes are separated in two devices: the single-phase solution subcooler and the adiabatic absorption chamber. The absorber is known as adiabatic because heat is not extracted from the solution at the same time the mass transfer occurs. The concentrated solution is cooled below the saturation temperature in the subcooler, allowing absorption to occur in the downstream adiabatic chamber, what increases the solution temperature. A conventional single-phase heat exchanger can be used for the subcooler, e.g. a commercial plate heat exchanger (PHE) in favour of cost and bulk. Other advantages of this method are a more compact absorber and avoidance of the wetting difficulties of the absorber tubes surface, problem that has been discussed by Jeong and Garimella [1], among others. The mass transfer to solution drops and sheets and the internal heat transfer are processes of complex modelling as the mass and energy conservation equations must be solved simultaneously, taking into account fluid motion at both sides of the interface. To date, analytical models to predict the simultaneous variation of the
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Nomenclature a
A b Cp do D Dh DI EQI f F Fo PHE G hm k Ka L* Le LI _ m MVD P PI PIC Pr QI QIC R Ra Re
constant of the linear relation X ¼ a,T þ b at a given equilibrium pressure in the Dühring diagram, function of pressure, concentration and temperature (K1) area (m2) constant specific heat at constant pressure (kJ kg1 K1) nozzle exit diameter (mm) liquid mass diffusivity (m2 s1) hydraulic diameter (m) density indicator energy and volumetric flow indicator Darcy friction factor. Generic function approach to equilibrium factor Fourier number, Fo ¼ a,s=R2 plate heat exchanger _ mass flux G ¼ m=A (kg m2 s1) mass transfer coefficient (mm s1) thermal conductivity (W m1 K1) Kutateladze number (Ka ¼ a$Dh/Cpcs) characteristic length of the adiabatic chamber (m) Lewis number (Le ¼ acs/Dcs)eq equivalent length (m) liquid level indicator mass flow rate (kg s1) mean volume diameter (mm) pressure (Pa) pressure indicator pressure control Prandtl number (Pr ¼ mcs $Cpcs =kcs ) volumetric flow rate indicator volumetric flow rate control droplet radius (m) absorption ratio (kgv kg1 ds ) _ cs =p$mcs 7do ) solution Reynolds number (Re ¼ 4m
concentration and temperature, considering size, velocity, internal circulation, flow pattern, etc. do not exist. If all these factors could be accurately considered, the characteristics of the heat and mass transfer in individual drops or sheets would correctly predict the global process that takes place in adiabatic absorbers of absorption refrigeration systems. To date, several studies analyse the simplified simultaneous heat and mass transfer in drops and sheets. Zacarías et al. [2] presented a revision of the works developed in relation to solution sheets. A review of the up to date efforts regarding absorption into solution drops is presented in the following: 1.1. Analytical studies Nakoryakov and Grigoreva [3] developed the first-known analytical model of the simultaneous heat and mass transfer in independent spherical drops. This model is valid for static droplets and does not consider the angular variation of the concentration and temperature inside the spherical droplet. The authors present an equation, valid to obtain the mass transfer coefficient, in terms of the Fourier (Fo), Lewis (Le) and Kutateladze (Ka) numbers. Fenton et al. [4] developed, and validated experimentally, an analytical model for the absorption of ammonia vapour by a water spray. The model predicted the vapour absorbed to within 15% deviation when the ratio of water to ammonia is greater than or equal to that specified in ASHRAE [5]. In this case ammonia vapour
Sc SD Sh T TI TIC u X WI
solution Schmidt number (Sc ¼ mcs =rcs Dcs ) standard deviation solution Sherwood number (Sh ¼ hm L* =Dcs ) temperature ( C) temperature indicator temperature control solution average velocity inside the pipe or accessory (m s1) refrigerant mass fraction (%) wattmeter
Greek symbols Dh specific absorption heat (kJ kg1) DP pressure drop (Pa) DT temperature difference, subcooling ( C) DX concentration difference (%) DXlm logarithmic mean concentration difference (%) DPI pressure drop indicator a liquid thermal diffusivity (m2 s1) m viscosity (Pa s) r density (kg m3) s surface tension (N m1) s time (s) Subscripts a absorber ad adiabatic cs concentrated solution ds diluted solution exp experimental eq equilibrium fric frictional i inlet o outlet v vapour
removal from air is under interest because of safety and environmental protection purposes. Thus, the ammonia is much diluted into water. For similar reasons, Huang [6] presented a model to calculate the removal efficiency of ammonia by a fine water spray. The author considers the effects of droplet pH, droplet diameter, ammonium concentration, ammonia concentration, and liquid-to-air ratio. The results showed that absorption increases as the droplet pH, ammonium concentration, or droplet diameter decrease and when the ammonia concentration or liquid-to-air ratio increase. The removal of ammonia from air is a more complex problem that the pure ammonia absorption as diffusion in the gaseous phase does not have to be taken into account in the later. 1.2. Numerical studies The main limitation of analytical models is given by the simplifications assumed during the solution of equations, which makes the models only valid for special cases. For this reason, and due to the lack of suitable experimental correlations in many occasions, several authors have solved more complex cases in a numerical way. Apparently the first reported numerical models include those of Morioka et al. [7] and Lu et al. [8]. In both cases, the absorption of water vapour by water-lithium bromide solution spherical droplets is analyzed when experiencing internal circulation, which is driven
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by external shear of the free-falling droplets. Morioka et al. [7] showed that the absorption ratio can be increased by the internal circulation, and also that this increment depends on the Reynolds number and the residence time. Lu et al. [8] showed the effect of the absorption heat released in the mass transfer process. Venegas et al. [9] modelled the simultaneous internal heat and mass transfer during absorption of ammonia vapour by ammoniaelithium nitrate solution drops. The low-pressure absorber of a double stage refrigeration system was considered in the model. Heat and mass transfer coefficients obtained using the spray absorption method were obtained. Calculated heat transfer coefficient was one order of magnitude higher than that experimentally obtained by Infante Ferreira [10] using the same solution in a vertical falling film absorber. In a later paper, Venegas et al. [11] performed a simulation considering ammoniaelithium nitrate droplets with diameters equal to 60 and 100 mm. Results showed that these small drops follow the Newman isothermal droplet model [12] for mass transfer. Droplets achieved the equilibrium state in times shorter than 1 s. In a following paper, Venegas et al. [13] using the same solution, divided the spray in three regions: liquid jet, deceleration of the drops and uniform motion. Results showed that the mass transferred is maximum (about 60% of the total) during the deceleration period of the drops. This period represented about 13.4% of the time required to reach the equilibrium state at the end of the absorption chamber. Elperin et al. [14] also simulated numerically the simultaneous heat and mass transfer of water vapour into isolated disperse spherical droplets of water-lithium bromide solution. The authors concluded that the resulting increase of the inter-phase temperature decreases the absorption driving potential, the mass flux and the equilibrium concentration. They obtained a good agreement with the experimental results reported by Paniev [15] and Burdukov et al. [16]. 1.3. Experimental studies Experimental studies on simultaneous heat and mass transfer are not as scarce as analytical or numerical studies. Paniev [15] developed the first known work related to solutions used in absorption refrigeration system. Paniev, and Burdukov et al. [16], used the water - lithium bromide solution. Their works intended to verify experimentally the equation obtained by Nakoryakov and Grigoreva [3]. Results obtained show a great discrepancy for Fourier numbers in the range Fo < 0.01 and Fo > 0.04. Ryan et al. [17] also performed several experiments using the same working fluid. The authors conclude that the simple model developed by Newman [12] is suitable for predicting the mass transfer to dispersed droplets in an adiabatic absorber. Some experimental works using other pairs have also been published. For example, Fenton et al. [4] analysed the absorption of ammonia by pure water droplets while Summerer et al. [18] and Flamensbeck et al. [19]studied the simultaneous heat and mass transfer between binary or ternary mixtures and water. More recently, Arzoz et al. [20] developed experiments using the water-lithium bromide solution and free falling droplets of about 4 mm diameter. Warnakulasuriya and Worek [21,22], using water as refrigerant and a lithium bromide-based absorbent called LZBÔ, made some experiments using droplets of 252e338 mm MVD. The authors show that mass transfer results, evaluated in terms of the Sherwood number, are up to 4 times higher than those obtained in conventional absorption systems. Wang et al. [23] performed a direct application of an adiabatic spray absorber, using the water-lithium bromide solution in an aircooled absorption refrigeration machine. Gutiérrez [24] and
783
Gutiérrez-Urueta et al. [25] developed experiments using also the H2O-LiBr solution and the dispersion of the liquid using free falling drops, like Arzoz et al. [20]. The authors concluded that this configuration allows obtaining lower absorption performance than the arrangement using a flat fan nozzle for the dispersion of the solution. In the last years, Zacarías [26] and Ventas [27] have used a fog jet nozzle to disperse the solution inside an adiabatic absorption chamber using the ammoniaelithium nitrate solution. Ventas et al. [28] recently presented the results of an experimental study modifying the ammonia mass fraction and the absorber pressure in the ranges 0.419 to 0.586 and 429e945 kPa, respectively. Ammoniaelithium nitrate is a promising alternative solution for refrigeration applications that conventionally use the ammoniaewater solution, e.g. Venegas et al. [29]. Different techniques for dispersing the solution in drops inside the adiabatic absorption chamber exist, depending on the nozzle used: hollow cone, fog jet, full cone, etc. In the present work, a commercial fog jet nozzle is used to evaluate experimentally the absorption process of ammonia by a lithium nitrate solution, as its form factor is potentially compact. The absorber pressures considered in this study are lower than those tested by Ventas et al. [28], what makes the present study relevant for sub-cero cooling. Here, the effect on the absorption of a variation of mass flow rate at the inlet of the absorber is included too. The present paper offers additional experimental evidence in order to better evaluate the mass transfer capacity and pressure drop of this adiabatic absorption configuration. Correlations here developed aim at the designer in the dimensioning of the absorption chamber. 2. Experimental setup In the present study the experimental facility is composed by a thermo-chemical compressor, i.e. the generator, single-pass absorber and heat recovery exchanger as main components (see Fig. 1). Auxiliary components are: the external water heater, the solution subcooler and the ammonia vapour cooler. A detailed description of the facility has been previously documented elsewhere, e.g. Zacarías et al. [2,30]. The refrigerant mass fraction was kept at X ¼ 46.08% along the experimentation, with a standard deviation of 0.057%. Table 1 shows the results of an uncertainty analysis for the measured variables used in the present study. Properties of ammonia were taken from Engineering Equation Solver software, EESÒ [31], which uses the fundamental equation of state developed by [32]. In the open literature, correlations to calculate the surface tension of the ammoniaelithium nitrate solution are not available, for this reason it was estimated performing a statistical fit of data available in Infante Ferreira [33], as a function of temperature and concentration. The correlation obtained is:
sðX;TÞ ¼ 4544:17þ36895:5X 92650:66X 2 þ76511:46X 3 28:64T þ1:02T 2 0:01T 3
(1)
The goodness of fit parameter for this correlation is R2 ¼ 96%. All other solution properties were calculated using correlations given by Libotean et al. [34,35] and Libotean [36]. 2.1. Adiabatic absorption chamber Fig. 2 shows a photograph of the adiabatic absorption chamber in the test rig. A detailed description of the geometrical characteristics of the absorption chamber can be found in Zacarías et al. [2]. The fog jet nozzle used in the present study is the model 3/4 -7G-SS 1, which is
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Fig. 1. Layout of the experimental setup.
based on a diverging layout of seven solid cone injectors. This configuration has also been used by Ventas et al. [28]. Fig. 3 shows a photograph of the nozzle. The height selected to locate its tip was 205 mm measured from the bottom of the chamber. A photograph of the atomization pattern obtained using the fog jet nozzle, corresponding to a pressure drop of 200 kPa, can be found in Ventas et al. [28]. 3. Data reduction
the concentration that the solution ideally reaches in an adiabatic process is required, while in the second one the solution temperature at the outlet of the ideal adiabatic process is necessary. Approach to adiabatic equilibrium factor:
F ¼
3.1. Mass transfer analysis The mass transfer analysis performed in the present paper is based on the evaluation of different parameters, already described in detail in Zacarías et al. [2]. A classification of these parameters is done in the following.
Xds Xcs Xeq; ad Xcs
Outlet subcooling:
DTo ¼ Teq;ad Tds
3.1.1. Parameters requiring adiabatic absorption equilibrium data Two parameters that take into account in their definition the adiabatic absorption process are described below. In the first one,
Table 1 Results of the uncertainty analysis for measured variables. Variable
Type
Range
Uncertainty
T of the solution at the absorber inlet T of the solution at the absorber outlet T of the vapour at the absorber inlet P at the absorber inlet
Thermoresistance PT100 Thermoresistance PT100 Thermoresistance PT100 Absolute pressure transducer Absolute pressure transducer Coriolis flow meter Coriolis flow meter Coriolis flow meter
10e60 C
0.40 C
10e60 C
0.58 C
10e60 C
0.51 C
0e1 MPa
1 kPa
0e1 MPa
1 kPa
0e0.3 kg/s 0e10,000 kg/m3 0e0.1 kg/s
0.03% f.s. 0.03% f.s. 0.05% f.s.
Pa _ ds m rds. _v m
(2)
Fig. 2. Photograph of the adiabatic absorption chamber.
(3)
A. Zacarías et al. / Applied Thermal Engineering 50 (2013) 781e790
785
DX1 ¼ Xeq;i Xcs
(8)
DX2 ¼ Xeq;o Xds
(9)
In these equations, the saturation concentrations Xeq,i and Xeq,o are calculated using the absorber pressure and the local solution temperatures. Variables used in the definitions of the parameters described previously are determined using mass rate balances in the absorber _ cs , Xcs): (m
_ cs ¼ m _ ds m _v m Xcs ¼
(10)
_ ds m _v Xds $m _ cs m
(11)
or correlations (Xds), as described in Zacarías et al. [2]. The diluted _ v , the _ ds , the vapour mass flow rate m solution mass flow rate m density rds and the temperature Tds were experimentally measured. 3.2. Pressure drop Fig. 3. Fog jet nozzle from Spraying systems CoTM.
3.1.2. Parameters non requiring adiabatic absorption equilibrium data Three other parameters are used in the present paper to assess the mass transfer. They can also be used in the characterisation of diabatic absorbers. Absorption ratio:
Ra ¼
_v m _ ds m
(4)
Pressure drop of the solution in the injection nozzle is determined by subtracting losses to the measured pressure drop:
DPa ¼ DPexp DPfric
DPexp is the pressure drop measured as the difference between the inlet pipe Pcs and the absorption chamber Pa. Gravitational pressure gradient was not considered given the small vertical distance between both pressure transducers. Frictional pressure loss inside the pipes including connections, DPfric , is determined adding contributions in the form:
DPfric Mass transfer coefficient:
hm
Gv ¼ rds $DXlm
(5)
Absorption mass flux:
Gv ¼
_v m Aa
DX1 DX2 DX1 ln DX2
(7)
! (13)
These elements must be included because the pressure transducer located in the inlet pipe is distant from the absorber inlet. Darcy friction factor for pipes is obtained from Incropera and DeWitt [37]: 1=4
Zacarías et al. [2] offer a discussion about the different ways the reference area Aa has been defined in the literature. In the present study, Aa was defined as the area of the cone containing all the drops generated, in this case equal to 0.198 m2. The height was equal to 205 mm and the diameter was proportional to the value given by the injector manufacturer at 1 m height (1.5 m). This definition of the mass transfer area indicates the envelope of the volume occupied and allows comparing the mass transfer coefficient with other spray configurations. Besides this, it avoids imprecision associated with drops diameters, a variable changing along experimentation with pressure difference, ammonia mass fraction and temperature. In the present study, the mean logarithmic concentration difference DXlm has been defined as:
DXlm ¼
r$u2 $Leq 1 ¼ f Dh 2
f ¼ 0:316,ReDh (6)
(12)
for ReDh 2 104
(14)
Here, the Reynolds number ReDh is based on the pipe diameterDh. 4. Results and discussion 4.1. Absorption 10 experiments were recorded using the fog jet nozzle. The aperture of the vapour expansion valve upstream of the nozzle was kept constant, allowing pressure variations inside the absorption chamber. The pressure obtained varied between 355 and 411 kPa, corresponding to subzero cooling. Two variables were controlled: the inlet solution subcooling, DTi ¼ Teq;i Tcs (the inlet solution temperature was varied between 25.9 and 30.2 C) and the diluted solution mass flow rate (0.04e0.08 kg s1). The effect of these controlled variables on the parameters defined previously to characterise the mass transfer: absorption mass flux, approach to adiabatic equilibrium factor, outlet subcooling, absorption ratio and mass transfer coefficient, is shown in the following. The increase of the inlet solution subcooling leads to a higher capacity for vapour absorption, resulting in higher refrigerant mass fraction changes inside the adiabatic chamber for a fixed solution
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A. Zacarías et al. / Applied Thermal Engineering 50 (2013) 781e790
0.003
2.5
Outlet subcooling, Teq,ad -Tds [ºC]
Vapour flow rate, mv [kg/s]
m cs = 0.04 [kg/s ]
0.002
0.001 m cs = 0.04 [kg/s ] m cs = 0.05 [kg/s ] m cs = 0.08 [kg/s ]
0 12
15
18 21 Inlet subcooling, Teq,i -Tcs [ºC]
2
m cs = 0.08 [kg/s ]
1.5 1 0.5 0 -0.5 -1 500
24
Fig. 4. Vapour mass flow rate as a function of the inlet subcooling for three different inlet solution mass flow rates.
mass flow rate. Consequently, higher inlet subcooling produced higher vapour mass flow rates. As the whole facility is working under steady state conditions, and the absorber is the limiting component to increase capacity, the amount of refrigerant vapour separated in the generator increases. The resultant vapour mass flow rate was between 0.8 and 2.2 g s1 Fig. 4 allows observing the experimental relation obtained between vapour mass flow rate and inlet solution subcooling. On the other hand, if the inlet subcooling is unchanged, the increase of the solution mass flow rate also implied a higher vapour mass flow rate, as observed in Fig. 4. More quantity of subcooled solution surface is available to absorb refrigerant vapour as a consequence of a higher atomization and flow rate, overcoming the shorter residence time effect of faster moving droplets. The net result is an increase of the vapour mass flow rate. The absorption mass flux obtained is between 0.004 and 0.010 kg m2 s1. The variation of this parameter is similar to that obtained for the vapour flow rate, because, as defined in Eq. (6), it only depends on the vapour mass flow rate and the absorber area, with the latter being constant. This parameter has been used elsewhere to assess the mass transfer, see for example Vallès et al. [39], Yoon et al. [40], Cerezo et al. [41], Palacios et al. [42], among others.
m cs = 0.05 [kg/s ]
1000
1500
2000
2500
Solution Reynolds number, Recs [ ] Fig. 6. Relation between outlet subcooling and solution Reynolds number, for three values of the solution mass flow rate. The uncertainties of the outlet subcooling are shown.
Fig. 5 shows the approach to adiabatic equilibrium factor F for three different inlet solution mass flow rates as a function of the solution Reynolds number. Results indicate the increase of F when Recs increases. As this figure shows, high values of F have been obtained. Values of F obtained in the present study are in the same range of those obtained by Ventas et al. [28] using the same solution and fog jet nozzle, but are about 3.7% higher than those obtained by Zacarías et al. [2] (between 0.81 and 0.89) using this solution and a flat fan nozzle in an adiabatic absorber. A high value of this parameter is important to minimize the recirculation ratio of the solution through the solution subcooler (see Ventas et al. [38]), and thus minimising the pump work and the size of accessories. Additionally, the use of F to evaluate the mass transfer is important because it does not depend on arbitrary parameters like the reference area Aa used in the mass transfer coefficient. The identification of this area is especially difficult and expensive in atomization processes where sprays or sheets are generated. Fig. 6 represents the outlet subcooling DTo. a function of the solution Reynolds number Recs. As it can be observed, outlet subcooling is small and decreases when the Reynolds number increases. It could be motivated by the smaller diameters of the resulting droplets, inducing higher inter-phase surface per unit of
1
0.9
Ra= mv /mds [kg v /kg s]
Approach to equilibrium factor, F [ ]
0.04
0.8
0.7
m cs = 0.04 [kg/s] m cs = 0.05 [kg/s]
0.6
m cs = 0.08 [kg/s]
0.03
0.02
m cs = 0.04 [kg/s] m cs = 0.05 [kg/s] m cs = 0.08 [kg/s]
0.5 700
1000
1300
1600
1900
2200
Solution Reynolds number, Recs [ ] Fig. 5. Approach to adiabatic equilibrium factor as a function of the solution Reynolds number, for three inlet solution mass flow rates. The uncertainties of the adiabatic approach to equilibrium factor are shown.
0.01 10
15
20
25
Inlet subcooling, Teq,i -Tcs [ºC] Fig. 7. Relation between absorption ratio and inlet subcooling. The uncertainties of the absorption ratio are shown.
A. Zacarías et al. / Applied Thermal Engineering 50 (2013) 781e790
300 m cs = 0.04 [kg/s]
0.6
2.033
ΔPa=43720.5·mcs
m cs = 0.05 [kg/s] m cs = 0.08 [kg/s]
ΔPa [kPa]
Mass transfer coefficient, h m [mm/s]
0.8
787
0.4
200
100 0.2
0 700
1000
1300
1600
1900
2200
0 0
0.02
Solution Reynolds number, Recs [ ]
0.04
0.06
0.08
0.1
Inlet solution flow rate, mcs [kg/s]
Fig. 8. Mass transfer coefficient as a function of the solution Reynolds number, for three inlet solution mass flow rates. The uncertainties of the mass transfer coefficient are shown.
solution volume, higher droplets instabilities and consequently higher mass transfer rates. The high values of the metrological uncertainties show that outlet subcooling is not an accurate variable to evaluate the performance of the adiabatic absorber, as it is shown in the Fig. 6 error bars. In spite of this trouble, the outlet subcoolings found in this paper are smaller than those reported by Summerer et al. [18] using binary and ternary hydroxide mixtures (NaOH, KOH and CsOH) and water as refrigerant. These authors used fog jet, full jet and spiral nozzles. In that research paper, when the atomizer was located 200 mm above the liquid surface, the smallest outlet subcooling reported was 1.9 C. The better results here obtained can be attributed to differences in the inlet subcooling (in the present study it was varied between 15.1 C and 20.9 C), in the thermal and transport properties between the working solutions and between droplets sizes generated in each case. The much lower vapour density for water-based solutions reduces the liquid surface instabilities and reduces the residence time because of the lower aerodynamic drag. Fig. 7 shows the absorption ratio Ra as a function of the inlet subcooling. As it can be expected, absorption is helped by subcooling. When the inlet solution temperature decreases, solution separates from its corresponding equilibrium state at the given absorption pressure, raising the ammonia mass flux to the solution. The linear correlation obtained between Ra and DTi . incides with findings reported by Zacarías et al. [2] and Arzoz et al. [20]. Values of Ra obtained in the present study are in the same range of those obtained by Ventas et al. [28] using the same solution and fog jet nozzle.
Fig. 9. Pressure drop of the solution in the injection nozzle as a function of its flow rate.
Fig. 8 presents the relation between the mass transfer coefficient hm and Recs. Both variables are linearly related, showing the benefits on absorption of a Recs increase. Table 2 shows a comparison between values of hm obtained in different studies. It can be observed that adiabatic absorbers allow obtaining high mass transfer coefficients, but not necessarily higher than the values obtained using diabatic absorbers. Results given now regarding the mass transfer coefficient are about half of the values presented in Zacarías et al. [2] using a flat fan nozzle. Values obtained in the present paper are of the same range of those obtained in Venegas et al. [13] in a theoretical study. However, conclusions derived from this comparison are not straightforward because different surfaces areas have been used in each case. Zacarías et al. [2] use the area of two isosceles triangles representing both faces of the flat fan sheet, while Venegas et al. [13] employ the surface area of the uniformly sized spray droplets, considered as spheres. The rest of surface areas used can be consulted in the works cited in Table 2. Besides that, solution concentration and pressure are also different in these studies. 4.2. Pressure drop Fig. 9 shows the pressure drop of the solution in the nozzle located at the inlet of the absorption chamber as a function of the solution mass flow rate. The equation resulting from a power fit between both variables is offered. These pressure losses are not a limiting factor in ammonia absorption machines because of the relatively high pressure difference available, Venegas et al. [13].
Table 2 Comparison between mass transfer coefficients hm reported in the literature. Reference
Absorber type
Configuration
Method
Solution
hm 105 (m s1)
Vallès et al. [39] Yoon et al. [40] Cerezo et al. [41] Kim et al. [43] Soto and Pinazo [44] Lee et al. [45] Zacarías et al. [2] Venegas et al. [13] Arzoz et al. [20] Palacios et al. [42] Palacios et al. [46] This work
Diabatic in PHE Diabatic Diabatic Diabatic Diabatic Diabatic Adiabatic Adiabatic Adiabatic Adiabatic Adiabatic Adiabatic
Spray (full cone) Falling film (helical) Bubble Slug flow Falling film (horizontal) Falling film (horizontal) Spray (flat fan) Spray (full cone) Falling film Spray (conical) Spray (flat fan) Spray (fog jet)
Experimental Experimental Experimental Experimental Experimental Experimental Experimental Numerical Experimental Experimental Experimental Experimental
Organic mixtures H2OeLiBr NH3eH2O NH3eH2O H2OeLiBr NH3eH2O NH3eLiNO3 NH3eLiNO3 H2OeLiBr H2OeLiBr H2OeLiBr NH3eLiNO3
1e2.5 2e4 100e200 8e56 0.2e4.2 0.6e3.3 34e101 8.1e86 1e15 75e200 25e210 17e47
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A. Zacarías et al. / Applied Thermal Engineering 50 (2013) 781e790 Table 3 Results of the uncertainty analysis for the calculated variables with a confidence level of 95%.
1
Correlated F [ ]
+2%
0.9 -2%
Variable
Average
Maximum
Absorption ratio, Ra Inlet subcooling, DTi Outlet subcooling, DTo Approach to adiabatic equilibrium factor, F Absorption mass flux, Gv Mass transfer coefficient, hm Pressure drop in the injection nozzle, DPa.
3.8% 0.94 C 0.87 C 5.7% 3.8% 36.8% 1.3%
6.2% 0.95 C 0.88 C 7.5% 6.2% 56.6% 2.2%
0.8
In the Sherwood number: 0.7 0.7
0.8
0.9
1
Experimental F [ ]
hm $L* Dcs
4.3. Mass transfer correlations Zacarías [26] and Ventas et al. [38] showed that the approach to adiabatic equilibrium factor has a large influence on the results of a numerically modelled thermo-chemical compressor. Warnakulasuriya and Worek [21] obtained an experimental correlation for F as a function of the Sherwood number Sh. They used the highly viscous fluid LZBÔ supplied by the company TraneÔ. Zacarías et al. [2] obtained correlations for F and Sh, using the ammoniaelithium nitrate solution and a flat fan nozzle in an adiabatic absorber. These are the only experimental correlations available in the open literature, as far as the authors’ knowledge. With the aim of obtaining correlations of F and Sh, in the present study the procedure described in Zacarías et al. [2] is followed. The best correlation for F obtained, with the goodness of fit parameter R2 ¼ 88.7%, is:
!0:791 Pa 1:018 DTi F ¼ Pcs Teq;ad 8 884:2< Re < 1979 ; 55:4< Pr < 63 cs cs < with : DTi Pa : 0:598 < < 0:859; 0:367< < 0:482 Pcs Teq;ad
Sh ¼ 0:729$Re1:308 Sc0:966 cs cs with : 884:2< Recs < 1979; 15; 061 < Sccs < 19; 642
(15)
Correlated Sh*10-8 [ ]
+10%
1.2
-10%
0.8
0.4 0.4
0.8
1.2
1.6
Experimental Sh*10-8 [ ] Fig. 11. Correlated vs. experimental Sh.
(17)
The solution temperature at the inlet of the absorption chamber has been used to calculate all properties in Eqs. (15)e(17). These equations can be of profit for the simulation and design of adiabatic absorbers using fog jet nozzles and the ammoniaelithium nitrate solution in the operating conditions defined by the ranges of the dimensionless groups, typical for a single effect chiller. Figs. 10 and 11 show a comparison between experimental and predicted values of the approach to adiabatic equilibrium factor F and Sherwood number Sh using Eqs. (15) and (17) respectively. All of the predicted data differ less than 2% and 10% respectively from the experimental data, indicating that the correlations are good. An uncertainty analysis was developed as in Taylor and Kuyatt [47]. Uncertainty propagation was performed using the software Engineering Equation Solver, EESÔ, which offers a calculation tool
2
1.6
(16)
L* is the characteristic length, equal to 0.205 m, here defined as the height of the absorption spray. In the present study, the following correlation was obtained with R2 ¼ 97.5%:
Fig. 10. Correlated vs. experimental F.
3:98,107 $Re0:657 Pr2:343 cs cs
Sh ¼
Fig. 12. Sensitivity of mass transfer parameters to measured variables.
A. Zacarías et al. / Applied Thermal Engineering 50 (2013) 781e790
789
Correlations for the approach to adiabatic equilibrium factor and Sherwood number have been obtained. They can be used to predict the performance of adiabatic absorbers. Acknowledgements The financial support of this study by the Spanish Ministry of Education and Science research grant ENE2005-08255-C02-02, ENE2009-11097 and Project CCG07-UC3M/ENE-3411, by the Local Government of Madrid and UC3M, is greatly appreciated. A. Zacarías also acknowledges the financial support given by National Board of Science and Technology and the Instituto Politécnico Nacional of Mexico. The authors want to acknowledge the help of Mr. Manuel Santos, Mr. Carlos Cobos and Mr. Ciro Vereda in the laboratory work. References
Fig. 13. Measured variables along time. Standard deviation (SD) is shown in the units of each variable.
based on this background. Table 3 offers results of the average and maximum uncertainties obtained for main variables calculated in the present study. The maximum uncertainty was obtained for the mass transfer coefficient, with an average value of 36.8%. A sensitivity study also has been performed. Fig. 12 shows the contribution of each measured variable to the total uncertainty of the mass transfer parameter evaluated (the contribution is shown in percentage inside each rectangle). Four of the measured variables are not represented in the figure because their contribution is lower than 0.6%. As can be observed, vapour mass flow rate has the highest influence on the absorption ratio Ra and the absorption mass flux Gv uncertainties. Density and temperature of the diluted solution determine the uncertainty of the mass transfer coefficient hm and of the outlet subcooling DTo. .he solution temperature at the absorber inlet only influences the approach to adiabatic equilibrium factor F uncertainty. Values shown in the graph were obtained as averages of all experiments. The experimental data were recorded every 8 s during a period of time of 600 s, in order to obtain every experimental point. Oscillations of measured variables during this period were very small. Fig. 13 shows the time evolution of variables represented in Fig. 12, for one point. The standard deviation around a constant value is very small, demonstrating that the experiments can be considered as steady state. 5. Conclusions The following conclusions have been achieved from the analysis of the mass transfer process inside the adiabatic absorption chamber: Inlet solution subcooling has a comprehensible positive effect over the vapour mass flow rate and the absorption ratio. The approach to adiabatic equilibrium factors are higher than those previously reported by the authors using a flat fan nozzle. The high values obtained indicate that fog jet nozzles may improve absorption in adiabatic absorbers, even for low absorption pressures. Solution pressure drops required at the nozzle of the absorption chamber are compatible with ammonia absorption systems because of the relatively high pressure difference available, allowing mass flow control by throttling.
[1] S. Jeong, S. Garimella, Falling-film and droplet mode heat and mass transfer in a horizontal tube LiBr/water absorber, Int. J. Heat Mass Transf. 45 (2002) 1445e1458. [2] A. Zacarías, M. Venegas, R. Ventas, A. Lecuona, Experimental assessment of ammonia adiabatic absorption into ammonia-lithium nitrate solution using a flat fan nozzle, Appl. Therm. Eng. 31 (2011) 3569e3579. [3] V.E. Nakoryakov, N.I. Grigoreva, Combined heat and mass transfer during absorption in droplets and films, J. Eng. Phys. 32 (1977) 243e247. [4] D.L. Fenton, A.F. Noeth, R.L. Gorton, Absorption of ammonia into water, ASHRAE Trans. 97 (1991) 204e213. [5] Safety Code for Mechanical Refrigeration, ASHRAE, Atlanta, USA, 1989, ANSI/ ASHRAE Standard 15-1989. [6] C.H. Huang, Theoretical model of absorption of ammonia by fine water spray, Environ. Eng. Sci. 22 (2005) 535e541. [7] I. Morioka, M. Kiyota, A. Ousaka, T. Kobayashi, Analysis of steam absorption by a subcooled droplet of aqueous solution of LiBr, JSME Int. J. 35 (Series II) (1992) 458e464. [8] H.H. Lu, T. Ch. Wu, Y.M. Yang, J.R. Maa, Transient heat and mass transfer in a drop experiencing absorption with internal circulation, Int. Commun. Heat Mass Transf. 25 (1998) 1115e1126. [9] M. Venegas, D. Arzoz, P. Rodríguez, M. Izquierdo, Heat and mass transfer in LiNO3-NH3 spray absorption system, Int. Commun. Heat Mass Transf. 30 (2003) 805e815. [10] C.A. Infante Ferreira, Operating Characteristics of NH3-LiNO3 and NH3-NaSCN Absorption Refrigeration Machines, 19th International Congress of Refrigeration, vol. IIIa, The Hague, the Netherlands, 1995, pp. 321e328. [11] M. Venegas, M. Izquierdo, P. Rodríguez, A. Lecuona, Heat and mass transfer during absorption of ammonia vapour by LiNO3eNH3 solution droplets, Int. J. Heat Mass Transf. 47 (2004) 2653e2667. [12] A. Newman, The drying of porous solids: diffusion and surface emission equations, Trans. A.I.Ch.E 27 (1931) 203e220. [13] M. Venegas, P. Rodríguez, A. Lecuona, M. Izquierdo, Spray absorbers in absorption systems using lithium nitrateeammonia solution, Int. J. Refrig. 28 (2005) 554e564. [14] T. Elperin, A. Fominykha, Z. Orenbakh, Coupled heat and mass transfer during nonisothermal absorption by falling droplet with internal circulation, Int. J. Refrig. 30 (2007) 274e281. [15] G.A. Paniev, Absorption heat and mass transfer on droplets in a polydispersed spray, Heat Transfer-Soviet Res. 15 (1983) 62e72. [16] A.P. Burdukov, A.R. Dorokhov, G.A. Paniev, Combined heat and mass transfer in absorption on droplets, Soviet J. Appl. Phys. 3 (1989) 39e45. [17] W.A. Ryan, F. Ruiz, J. Wurm, Model development and verification of spray absorption for gas driven cooling systems, in: Proceedings of International Gas Research Conference, Cannes, France, 1995, pp. 1483e1493. [18] F. Summerer, F. Ziegler, P. Riesch, G. Alefeld, Hydroxide absorption heat pumps with spray absorber, ASHRAE Technical Data Bull. 12 (1996) 50e57. [19] M. Flamensbeck, F. Summerer, P. Riesch, F. Ziegler, G. Alefeld, A cost effective absorption chiller with plate heat exchangers using water and hydroxides, Appl. Therm. Eng. 18 (1998) 413e425. [20] D. Arzoz, P. Rodríguez, M. Izquierdo, Experimental study on the adiabatic absorption of water vapor into LiBr-H2O Solutions, Appl. Therm. Eng. 25 (2005) 797e811. [21] F.S.K. Warnakulasuriya, W.M. Worek, Adiabatic water absorption properties of an aqueous absorbent at very low pressures in a spray absorber, Int. J. Heat Mass Transf. 49 (2006) 1592e1602. [22] F.S.K. Warnakulasuriya, W.M. Worek, Drop formation of swirl-jet nozzles with high viscous solution in vacuum-new absorbent in spray absorption refrigeration, Int. J. Heat Mass Transf. 51 (2008) 3362e3368. [23] L. Wang, G.M. Chen, Q. Wang, M. Zhong, Thermodynamic performance analysis of gas-fired air-cooled adiabatic absorption refrigeration system, Appl. Therm. Eng. 27 (2007) 1642e1652.
790
A. Zacarías et al. / Applied Thermal Engineering 50 (2013) 781e790
[24] G. Gutiérrez, Thermo-fluid Dynamic Evaluation of Components in Adiabatic Absorption Systems, Ph.D. Thesis, Universidad Carlos III de Madrid, Madrid, Spain, 2009. [25] G. Gutiérrez-Urueta, P. Rodríguez, M. Venegas, F. Ziegler, M.C. RodríguezHidalgo, Experimental performances of a LiBr-water absorption facility equipped with adiabatic absorber, Int. J. Refrig. 34 (2011) 1749e1759. [26] A. Zacarías, Mass and Heat Transfer in Adiabatic Absorbers with Application to the Ammoniaelithium Nitrate Solution, Ph.D. Thesis, Universidad Carlos III de Madrid, Madrid, Spain, 2009 (in Spanish). [27] R. Ventas, Study of Absorption Machines with the Ammoniaelithium Nitrate Solution: Hybrid Cycles Boosted with Mechanical Compression, Ph.D. Thesis, Universidad Carlos III de Madrid, Madrid, Spain, 2010 (in Spanish). [28] R. Ventas, C. Vereda, A. Lecuona, M. Venegas, M.C. Rodríguez-Hidalgo, Effect of the NH3-LiNO3 concentration and pressure in a fog-jet spray adiabatic absorber, Appl. Therm. Eng. 37 (2012) 430e437. [29] M. Venegas, M. Izquierdo, M. de Vega, A. Lecuona, Thermodynamic study of multistage absorption cycles using low-temperature heat, Int. J. Energy Res. 26 (2002) 775e791. [30] A. Zacarías, R. Ventas, M. Venegas, A. Lecuona, Boiling heat transfer and pressure drop of ammonia-lithium nitrate solution in a plate generator, Int. J. Heat Mass Transf. 53 (2010) 4768e4779. [31] S.A. Klein, Engineering Equation Solver, Academic Professional, 2011, V8.944-3D. [32] R. Tillner-Roth, F. Harms-Watzenberg, H.D. Baehr, A new fundamental equation for ammonia, DKV-Tagungsbericht 20 (1993) 167e181 (in German). [33] C.A. Infante Ferreira, Vertical tubular absorbers for ammonia-salt absorption refrigeration, Ph.D. Thesis, Delft Technical University, Delft, Holland, 1985. [34] S. Libotean, D. Salavera, M. Vallés, X. Esteve, A. Coronas, Vapor-liquid equilibrium of ammoniaþlithium nitrateþwater and ammoniaþlithium nitrate solutions from (293.15 to 353.15) K, J. Chem. Eng. Data 52 (2007) 1050e1055. [35] S. Libotean, A. Martín, D. Salavera, M. Vallés, X. Esteve, A. Coronas, Densities, viscosities and heat capacities of ammonia-lithium nitrate and ammonialithium nitrate-water solutions between (293.15 and 353.15) K, J. Chem. Eng. Data 53 (2008) 2383e2388.
[36] S.N. Libotean, Thermophysical characterization of the ternary mixture ammonia/lithium nitrate/water for absorption refrigeration applications, Ph.D. Thesis, Universitat Rovira I Virgili, Tarragona, Spain, 2008 (in Spanish). [37] F.P. Incropera, D.P. De-Witt, Heat Transfer Fundamentals, fourth ed., Pearson Prentice Hall, Naucalpan de Juárez, Mexico, 1999 (in Spanish). [38] R. Ventas, A. Lecuona, M. Legrand, M.C. Rodriguez, On the recirculation of ammonia-lithium nitrate solution in adiabatic absorbers for chillers, App. Therm. Eng. 30 (2010) 2770e2777. [39] M. Vallès, M. Bourouis, D. Boer, A. Coronas, Absorption of organic fluid mixtures in plate heat exchanger, Int. J. Therm. Sci. 42 (2003) 85e94. [40] J.-I. Yoon, O.-K. Kwon, Ch.-G. Moon, H.-S. Lee, P. Bansal, Heat and mass transfer characteristics of a helical absorber using LiBr and LiBr þ LiI þ LiNO3 þ LiCl solutions, Int. J. Heat Mass Transf. 48 (2005) 2102e2109. [41] J. Cerezo, M. Bourouis, M. Vallès, A. Coronas, R. Best, Experimental study of an ammoniaewater bubble absorber using a plate heat exchanger for absorption refrigeration machines, Appl. Therm. Eng. 29 (2009) 1005e1011. [42] E. Palacios, M. Izquierdo, R. Lizarte, J.D. Marcos, lithium bromide absorption machines: pressure drop and mass transfer in solutions conical sheets, Energy Conv. Manag. 50 (2009) 1802e1809. [43] H.Y. Kim, B.B. Saha, S. Koyama, Development of a slug flow absorber working with ammoniaewater mixture: part IIddata reduction model for local heat and mass transfer characterization, Int. J. Refrig. 26 (2003) 698e706. [44] V.M. Soto, J.M. Pinazo, Validation of a model for the absorption process of H2O(vap) by a LiBr(aq) in a horizontal tube bundle, using a multi-factorial analysis, Int. J. Heat Mass Transf. 46 (2003) 3299e3312. [45] S. Lee, L. Kumar Bohra, S. Garimella, A. Krishna Nagavarapu, Measurement of absorption rates in horizontal-tube falling-film ammonia-water absorbers, Int. J. Refrig. 35 (2012) 613e632. [46] M. Palacios, J.D. Izquierdo, R. Marcos, Lizarte, Evaluation of mass absorption in LiBr flat-fan sheets, Appl. Energy 86 (2009) 2574e2582. [47] B.N. Taylor, C.E. Kuyatt, Guidelines for evaluating and Expressing the uncertainty of NIST Measurement results, National Institute of standards and Technolog, NIST Technical Note 1297 (1994).