i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5 e1 0 2 8
Available online at www.sciencedirect.com
w w w . i i fi i r . o r g
journal homepage: www.elsevier.com/locate/ijrefrig
Proposal and validation of a model for the dynamic simulation of a solar-assisted single-stage LiBr/water absorption chiller G. Evola a, N. Le Pierre`s b,*, F. Boudehenn c, P. Papillon c a
LEPMI, CNRS UMR 5279, 50 avenue du lac Le´man, 73377 Le Bourget du Lac, France LOCIE, CNRS UMR 5271, Universite´ de Savoie, Polytech Annecy-Chambe´ry, 73376 Le Bourget du Lac, France c CEA LITEN, BP 332, 50 avenue du lac Le´man, 73377 Le Bourget du Lac, France b
article info
abstract
Article history:
In this paper, a general mathematical model for the dynamic simulation of a single-effect
Received 28 November 2011
LiBr/water absorption chiller is presented. The model is based on mass and energy
Received in revised form
balances applied to the internal components of the machine, and it accounts for the non-
21 September 2012
steady behaviour due to thermal and mass storage in the components. The validation of
Accepted 18 October 2012
the mathematical model is performed through experimental data collected on a commer-
Available online 1 November 2012
cial small-capacity water-cooled unit. Due to the peculiar technology adopted in the real chiller, a special effort was made to identify the appropriate values of the main physical
Keywords:
parameters. The validation of the model is based on the values of the water temperature at
Absorption chiller
the outlet of the machine, as no measurement inside the machine was possible; anyway,
Lithium bromide
a consistency analysis applied to the internal parameters is also presented. The agreement
Dynamic performance
between experimental and simulated results is very good, both on a daily and on a seasonal
Simulation
basis. ª 2012 Elsevier Ltd and IIR. All rights reserved.
Experimental results
Proposition et validation d’un mode`le pour la simulation dynamique d’un refroidisseur a` absorption au LiBr / eau solaire monoe´tage´ Mots cle´s : Refroidisseur a` absorption ; Bromure de lithium ; Performance dynamique ; Simulation ; Re´sultats expe´rimentaux
1.
Introduction
Dynamic simulation plays a very important role in the description of the real performance of an energy conversion system, especially during the activation stage or part-load
operation. Such a problem is extremely relevant for absorption chillers, where the high mass of the internal components and the accumulation of the fluids inside the vessels usually make the transient phase longer than in mechanical compression chillers.
* Corresponding author. Tel.: þ33 47 975 88 58; fax: þ33 47 975 81 44. E-mail address:
[email protected] (N. Le Pierre`s). 0140-7007/$ e see front matter ª 2012 Elsevier Ltd and IIR. All rights reserved. http://dx.doi.org/10.1016/j.ijrefrig.2012.10.013
1016
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5 e1 0 2 8
Nomenclature Variables A cp Cd D f F h H H I _ m M Nu p Pr Re Q_ s S t T U V V_ x z
surface (m2) specific heat capacity (J kg1 K1) discharge coefficient (e) diameter (m) specific backflow (e) fouling factor (m2 kW1) specific enthalpy (J kg1) height difference between two components (m) daily solar irradiation on the collector plane (kWh m2 day1) solar irradiance on the collector plane (W m2) mass flow rate (kg s1) mass (kg) Nusselt number (e) pressure (Pa) Prandtl number (e) Reynolds number (e) thermal power (W) thickness (m) pipe section (m2) time (s) temperature (K) heat transfer coefficient (W m2 K1) volume (m3) volumetric flow rate (m3 s1) concentration (e) level of the liquid inside a component (m)
Very interesting papers on this topic have been presented in scientific literature. Jeong et al. (1998) propose a dynamic model for the simulation of a steam-driven LiBr/water absorption heat pump that exploits low-grade waste heat. The model includes storage terms to take into account the thermal capacity of the container and the solution mass storage in the components, but no thermal inertia is attributed to the heat exchangers. Solution and vapour mass flow rates are not constant, as they are determined as a function of the pressure difference between the vessels. The simulation time step is automatically adjusted; the model has been verified, with good agreement, through operational data, but only by looking at the thermal power exchanged by the absorber and the condenser. Ko¨hlenbach and Ziegler (2008a, 2008b) paid a lot of attention to the dynamic behaviour, by accounting for heat and mass storage, as well as to the solution transport delay between generator and absorber e and the way back; on the contrary, their model is over-simplified as far as the description of the steady state is concerned: as an example, water and LiBr/water solution have constant property data, and a detailed enthalpy calculation for each state of the system is avoided. Hence, their model is able to describe very accurately the shape of the dynamic response to a change in the input conditions, but a low accuracy on the numerical values is obtained after verification with the experimental measurements on a commercial 10 kW single-stage absorption chiller.
Greek letters a convective coefficient (W m2 K1) l thermal conductivity (W m1 K1) r density (kg m3) z pressure loss coefficient (-) Subscripts and superscripts a absorber abs absorbed av average value c condenser d dissipated des desorbed ext external ev evaporator g generator hx heat exchanger in inlet int internal l liquid max maximum value o outdoor out outlet s solution sh shell v vapour w water
The work also includes a sensitivity analysis to some internal parameters, which is not supported by experimental verification. The model developed by Shin et al. (2009) applies to highcapacity double effect absorption chillers. It has been verified against experimental data collected on a commercial direct-fired chiller of medium capacity during 370 min of operation, with an acquisition time step as high as 5 s. On the whole, the model proved to be quite reliable at steady operation; on the contrary, during the first 90 min, i.e. when the transient behaviour was particularly pronounced, differences up to 10 C were observed between simulated and experimental values of the temperatures inside generator and absorber. Furthermore, during the same period the error on the determination of the instantaneous capacity reached 20%. Other works have been recently presented by Gomri (2010) and Bakhtiari et al. (2011); both works are based on a simplified steady-state model of a single or multiple effect absorption chiller. In the first case, the model is used for evaluating the performance sensitivity to the main operating parameters, even under a second law perspective, but no validation is presented, whereas in the second work the model is validated through experimental data and used for the optimization of the chiller design. Myat et al. (2011) presented an effective dynamic model for the evaluation of temperature and concentration profiles in a single stage LiBr/water absorption chiller; their model also
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5 e1 0 2 8
includes some relations for the calculation of the heat transfer coefficients and finally leads to an entropy analysis of the chiller, but it is not validated through experimental results. The model described in the present paper has been conceived in the framework of a research project where a commercial solar-assisted single-stage absorption chiller is being monitored to verify its performance in the airconditioning of an office space. As a consequence, some specific features are needed: - the model must be suitable for the simulation of commercial units; - as the driving water flow is heated through solar energy, which is not steady, a dynamic model is necessary; - the aim of the model is not to get an extremely precise description of the transient response of the machine, but to describe with good accuracy the time profile of the chiller behaviour when subject to load variations in the time scale of a few minutes; - the model must determine the water outlet temperature and the thermal power at each section of the absorption chiller; - the model should also present good accuracy in the description of the average chiller performance (daily, weekly or even seasonal). For this reason, the validation of the dynamic model is not based on the application of a load perturbation starting from a steady state, but it is performed by means of real operating conditions, with a continuous change of all the external parameters over several days of operation. Section 2 describes the equations included in the mathematical model, as well as the hypotheses that justify such equations. Section 3 presents the calculation of the physical parameters to be adopted in the mathematical model to simulate the commercial single-stage absorption unit considered in this study. Section 4 comments on the experimental data and their comparison with the simulated results. Section 5 shows a consistency analysis that investigates into the capability of the model to correctly describe the internal behaviour of the machine and its response to a sudden change in the forcing conditions. Section 6 concerns the use of the proposed model to identify some improvements in the experimental solar-assisted cooling system.
2.
Description of the model
A single-stage LiBr/water absorption chiller is made up of a generator, an absorber, an evaporator and a condenser; the circulation of the solution is assured by a solution pump, and a solution heat exchanger is normally used to internally recover thermal energy (see Fig. 1). At the generator, a heat source is supplied, in order to desorb the refrigerant (water vapour) from the solution; the vapour moves towards the condenser, where it is condensed at a high pressure. The remaining solution, called strong as it is rich in LiBr, flows down via the heat exchanger to the absorber; here it is exposed to the vapour coming from the evaporator, that is absorbed in the solution at low pressure
1017
and temperature. The diluted solution is then conveyed to the generator by the solution pump. The cold production occurs at the evaporator. In order to simplify the formulation and the consequent implementation of the model, some assumptions are made: a temperature, pressure and LiBr concentration are homogenous inside each component (Myat et al., 2011); b the pressure inside the generator equals that in the condenser, and the same relation holds between absorber and evaporator; c the cooling water outlet temperature in the absorber corresponds to the cooling water inlet temperature at the condenser; d the fluid transport delay between two components is neglected; e each heat exchanger has a constant overall heat transfer coefficient, as already stated by Ko¨hlenbach and Ziegler (2008a) and Jeong et al. (1998); f the LiBr/water solution leaving the generator and the absorber is saturated (Ko¨hlenbach and Ziegler, 2008a); g the throttling valves between generator/absorber and condenser/evaporator are adiabatic; h the vapour produced in the evaporator is saturated, thus no superheating is allowed, as remarked by Shin et al. (2009) and Gomri (2010); i the volumetric flow rate of diluted solution conveyed by the solution pump from the absorber to the generator is assumed constant. Most of the above simplifying assumptions are quite reasonable (b, c, g, i) or well established in the literature on the topic (a, d, e, h). Only the assumption f might be questionable: Myat et al. (2011) underline that in a well-designed absorber the solution inside the component and at its outlet is normally slightly sub-cooled. However, when simulating commercial absorption units, it is not possible to access the inside of the machine, thus there is no way to verify through experimental measurements the accuracy of this last assumption.
2.1.
Generator and absorber
If looking at the scheme described in Fig. 1, the mass balance for the solution and the vapour in the generator can be respectively written as follows, by including the storage of both fluids in the vessel: _ s;out;g m _ v;des ¼ _ s;in;g m m
_ v;out;g ¼ _ v;des m m
dMv;g dt
dMs;g dt
(1)
(2)
The ideal gas law can be used for the vapour, Eq. (3). This position is allowed as the vapour pressure inside a singlestage LiBr/water absorption chiller is normally between 1 and 10 kPa, i.e. far lower than the critical pressure; in this conditions, the error made on the evaluation of the specific volume by using the ideal gas law is lower than 0.1%, whatever the vapour temperature, as remarked in (Cengel, 1997). In Eq. (3) the volume Vv occupied by the vapour is calculated by
1018
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5 e1 0 2 8
CONDENSER
m v,out,g
m v,in,c
GENERATOR
M v,c
M v,g
m s,in,g
m v,des
Q hx,c
m w,c
Q d,c
m w,g
ml
Q d,g Q hx,g M s,g
M l,c High pressure
m s,out,g
m l,out,c
Solution exch
Low pressure
m v,in,a
m v,out,e M v,e
m l,in,e
m ev
m s,in,a
m v,abs m w,e
Q d.e
Pump
M v,a
Q d,a
Q hx,e
Q hx,a
m w,a
M l,e
M s,a ABSORBER
EVAPORATOR
m s,out,a
Fig. 1 e Description of the main components inside the absorption machine (white arrows: vapour, black arrows: liquid).
subtracting the volume of the solution from that of the entire vessel, see Eq. (4). Mv;g $Rv $Tg ¼ pg $Vv
(3)
Vv ¼ Vg Ms;g =rs;g
(4)
Furthermore, the mass balance on LiBr, see Eq. (5), and the energy balance on the solution, see Eq. (6), hold: _ s;in;g $xs;in;g m _ s;out;g $xs;out;g m
dxs;g dMs;g þ xs;g $ ¼ Ms;g $ dt dt
(5)
_ v;des $hv;des þ m _ s;out;g $hs;out;g m _ s;in;g $hs;in;g Q_ hx;g Q_ d;g ¼ m þ
d Mcp;g $Tg dt
(6)
In Eq. (6), the convective and radiative heat transfer between vapour and solution is neglected. The solution is assumed to be fully mixed at each simulation step; as a consequence the enthalpy and the salt concentration in the solution leaving the vessel correspond to those inside the vessel. Furthermore, according to Alefeld and Radermacher (1993) the temperature of the vapour desorbed in the generator corresponds to the saturation temperature associated with the diluted solution entering the component; as a consequence the vapour will be super-heated with respect to the solution contained inside the vessel. In addition, the model takes into account the thermal inertia of the shell; the shell is assumed at thermal equilibrium with the solution (Tsh ¼ Tg), thus its thermal capacity can be composed with that of the solution itself in Eq. (6), where M ¼ Msh þ Ms and cp is the average specific heat capacity (Shin et al., 2009), defined as:
cp;g ¼
Msh $cp;sh þ Ms $cp;s Msh þ Ms
(7)
The thermal power released into the environment can be assessed by introducing an overall thermal resistance Rg between the solution in the generator and the outdoor air: (8) Q_ d;g ¼ Tg To Rg Such a scheme can be extended to the absorber, just accounting for the different direction of the vapour flow, which enters the component and is absorbed in the solution. The thermodynamic state of the vapour entering the absorber corresponds to that of the vapour produced in the evaporator; its enthalpy is assessed as a function of temperature and pressure through the relations available in (Florides et al., 2003), that are derived by fitting the data presented in (Rogers and Mayhew, 1992). In the equations previously presented, the thermodynamic properties of the LiBr/water solution (enthalpy, density, specific heat, thermal conductivity, viscosity) are calculated through appropriate polynomial functions reported in (Florides et al., 2003).
2.2.
Condenser and evaporator
Fig. 1 also shows the scheme used to describe the condenser. In this component the liquid phase is condensed vapour instead of LiBr/water solution; as a consequence, the mass balance on the condensate and the vapour can be written as: _ l;out;c ¼ _l m m
dMl;c dt
(9)
_l¼ _ v;in;c m m
dMv;c dt
(10)
1019
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5 e1 0 2 8
In addition, Eqs. (3) and (4) can be rewritten, whereas the energy balance applied to the vapour yields: d _ l hl m _ v;in;c hv;in;c þ Mcp;c $Tc Q_ hx;c Q_ d;c ¼ m dt
(11)
Furthermore, the vapour and the condensate are saturated; the enthalpy of the inlet vapour is the same as for the vapour flowing out of the generator. As described before, the shell is assumed at thermal equilibrium with the working fluid, thus the specific heat capacity used in Eq. (11) is an average one (Shin et al., 2009). The equations can be easily extended to the evaporator by looking at the scheme in Fig. 1; as an example, the following energy balance holds: d _ ev $hev m _ l;in;e $hl;in;e þ Mcp;e $Te Q_ hx;e Q_ d;e ¼ m dt
(12)
Here, the enthalpy of the saturated vapour produced inside the evaporator is determined by means of the relations available in (Florides et al., 2003) and already used for the generator.
2.3.
dThx Q_ hx;w Q_ hx ¼ Mcp;hx $ dt 0
In order to evaluate the heat flux conveyed by the hot water to the solution inside the generator, a model of the internal heat exchanger is also required. According to this model, a uniform temperature Thx can be assigned to the metal core of the heat exchanger, whose thermal capacity is Mchx. A distinction can then be made between the heat flux released by the water and delivered to the surface of the exchanger, see Eq. (13), and that transferred from the exchanger to the solution, see Eq. (14). The latter depends on the internal (exchanger solution) heat transfer coefficient UAint, whereas the former can also be written as in Eq. (15), i.e. as a function of the external (water exchanger) heat transfer coefficient of the heat exchanger, UAext, and the mean logarithmic temperature. The difference between such fluxes represents the thermal energy stored on the body of the heat exchanger (see Eq. (16)). The heat transfer coefficients UAint and UAext can be easily assessed as shown in Eq. (17); in order to understand this definition, one must remember that each heat exchanger consists of a bank of cylindrical tubes, and that a uniform temperature Thx is attributed to the tube itself. The simplification introduced in Eq. (17) is justified by the very low thermal resistance associated with the conductive heat transfer through the tube thickness: due to the high thermal conductivity of copper (l ¼ 387 W m1 K1) and the reduced thickness (normally not higher than 1 mm), the contribution of this term on the overall thermal resistance would be lower than 1%, as shown by a preliminary analysis carried out by the authors.
overall thermal resistance
(17) In the above equations, the density and the specific heat of water are determined as a function of the inlet temperature, according to the relations reported by Florides et al. (2003). Thanks to the model of the heat exchanger, it is possible to predict the outlet water temperature and the heat flux released to the solution once the water mass flow and its inlet temperature are known, as well as the temperature of the solution inside the generator. The same approach can be easily extended to the heat exchanger inside the other components.
Other devices
As previously stated, the volumetric flow rate of the diluted solution conveyed by the solution pump is constant, and imposed as an input value. On the contrary, the strong solution flow rate from the generator to the absorber cannot be held constant, as it depends on the pressure and the height difference between the generator and the absorber. According to this scheme, the mass flow rate of the strong solution can be assessed as: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h iffi u u2$r $ pg pa þ r $g$ðH þ zÞ s;g t s;g _ s;out;g ¼ Cd $S$ (18) m z Here, the pressure losses in the solution heat exchanger and the corresponding piping are described through a resistance coefficient z. The level z of the solution inside the generator is continuously updated, as a function of the mass of solution actually contained inside the vessel; the vertical distance H between the bottom of the generator and the solution inlet of the absorber is also considered. The same expression is used to calculate the condensate mass flow rate from the condenser to the evaporator. In both cases, the pressure loss coefficient is not set constant, but it is assumed to change as a function of the fluid height inside the upper vessel. Such an assumption corresponds to the control logic which is often adopted in absorption chillers, where an increase in the resistance of the throttling valve is induced when the level of the liquid gets too low, in order to prevent the vessel from getting empty. In this work, the following formulation is proposed: z ¼ z0 $ðz0 =zÞ2
Q_ hx;w ¼ rw $V_ w $cp;w $ Tw;in Tw;out
(13)
Q_ hx ¼ UAint $ðThx Ts Þ
(14)
Tw;in Thx ðTw;out Thx Þ Q_ hx;w ¼ UAext $ Tw;in Thx ln ðTw;out Thx Þ
(15)
11
B C B 1 C Dhx =2 Dhx þshx ahx;ext $Ahx B C UAext ¼ Ahx $B þ $ln þFext C z B ahx;ext C lhx Dhx 1 þahx;ext $Fext @ |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}A
2.4.
Heat exchangers
(16)
(19)
where z0 and z0 are nominal values. The use of such a condition is a real novelty if compared to other models available in the literature, such as those proposed by Ko¨hlenbach and Ziegler (2008a) or Shin et al. (2009), and it has relevantly improved the stability and the consistency of the model. As regards the solution heat exchanger between the generator and the absorber, no thermal inertia has been
1020
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5 e1 0 2 8
considered. Its heat transfer coefficient UAhx is assumed constant and assigned as an input; its efficiency can be easily assessed as a function of UAhx and the solution mass flow, through well-known relationships valid for counter-flow heat exchangers (Incropera et al., 2006).
3.
Definition of the parameters
The mathematical model presented so far refers to a general LiBr/water single effect absorption machine. In this work the model will be applied to a commercial water-cooled unit with a nominal cooling capacity of 4.5 kW, manufactured by Rotartica. This chiller is installed at INES (Institut National de l’Energie Solaire) near Chambe´ry (France), where it is used in the framework of a national research program aimed at assessing the performance of different solar-assisted refrigeration systems. Actually, the Rotartica chiller is a very particular one, as the absorption cycle is carried out into an hermetically welded spheroid container of approximately 500 mm diameter by 500 mm long, rotated at 400 rpm about a horizontal axis, as described in (Monne´ et al., 2011) and also in (Gilchrist et al., 2002) for a similar model. The rotation of the components improves the heat transfer coefficients and the efficiency of the cooling production, but an additional electricity consumption of around 400 W has to be accounted for to maintain the rotation. Furthermore, the solution pump is not electrically driven, as the pumping power is derived from rotation, by converting the kinetic energy at the outer radius of the vessel into pressure. Further information on the Rotartica chiller is reported by Izquierdo et al. (2008) and Garcia Cascales et al. (2011). In order to use the proposed model for the simulation of the Rotartica chiller, a special effort was devoted to the parameter identification. As a matter of fact, when dealing with commercial chillers the internal components are usually not accessible, thus the only way to determine their geometry is based on schemes of the chiller available on the technical sheets which is the approach followed in this work. In Table 1 the values of all the constant inlet parameters used in the model are reported. For the evaluation of the cumulated heat capacities, the materials are copper in the heat exchangers and iron in the vessel. The value of the discharge coefficient Cd is quite typical and commonly accepted in the case of circular sharp-edged orifices (Massey and Ward-Smith, 1998), whereas the thermal resistance R between each component and the outdoors was estimated roughly by knowing the geometry of the machine. Furthermore, in Eq. (17) the convective heat transfer coefficient aext between the water flow and the surface of the tubes in each component is assessed by using the correlations proposed by Gnielinski (1976): 2
f ¼ ð0:079$ ln ðReÞ 1:64Þ
¼
0:125$f $ðRe 1000Þ$Pr 0:5 1 þ 12:7$ 0:125f $ðPr2=3 1Þ
aext ¼
lw Dhx
(20a)
(20b)
(20c)
According to Gnielinsky, the Eqs. (20a) and (20b) can be applied for Re > 3000, thus they are more general than the well-known Dittus-Boelter correlation, valid for Re > 10000. The viscosity and the thermal conductivity of water, respectively required to determine the Reynolds number and to solve Eq. (20c), are determined as a function of the temperature through appropriate relations available in (Florides et al., 2003). In addition, the value of the fouling factor F for the internal and external surface of the tubes can be assumed as high as 0.09 m2 K kW1 (Howell et al., 2005). As concerns the convective heat transfer coefficient on the solution side in the absorber and the generator, some experimental values have been derived by Rivera and Xicale (2001). However, these values refer to a geometry that is quite different from that of the Rotartica chiller, where the heat exchangers rotate with the vessel at 550 rpm (58 rad s1). For this reason, in this work the heat transfer coefficients determined by Gilchrist et al. (2002) for the Interotex machine are adopted (aint ¼ 9000 W m2 K1), as the latter is very similar to the Rotartica machine. In addition, the heat transfer coefficient for both water boiling and condensation on a circular surface can be assessed through appropriate relations available in the literature (Incropera et al., 2006). It must be remembered that the thermodynamic properties of the LiBr/water mixture as well as those of liquid water and water vapour can be calculated as a function of the temperature and pressure, thus they normally vary with time. However, in the determination of the heat transfer coefficients a fixed average temperature was considered for each fluid, in order to get constant values and simplify the implementation of the model. Finally, the volumetric flow rate of the diluted solution conveyed from the absorber to the generator is kept constant and equal to 0.0185 l s1. The mass flow rate changes at each time step as a function of the solution density. No calibration was applied to optimise the values reported in Table 1.
4.
Experimental verification
In order to check the reliability of the proposed model for the simulation of the Rotartica absorption machine, the authors used the experimental results collected during a test campaign carried out at INES in summer 2009, from May 27 to September 10. The results of the simulations were compared to the experimental data and the agreement between them was verified. The Rotartica absorption chiller installed at INES is powered by thermal energy produced in a solar field composed of 30-m2 flat plate solar collectors; a 400-l tank is used to store the hot water, and no backup is provided to drive the absorption machine when solar energy is not sufficient. The heat rejection is carried out by means of a water flow that is cooled down in a horizontal ground heat exchanger, made up of twenty-two polyethylene pipes divided into two layers, buried at a depth of 0.75 m and 1.1 m, respectively; the length of every pipe is around 100 m. The chilled water produced by the absorption chiller is stored in a 300-l tank and then used to feed three fan coils for the
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5 e1 0 2 8
1021
Table 1 e Constant inlet parameters for the Rotartica absorption machine. Parameter Cd Fint, Fext Hc Hg Mcp,a Mcp,c Mcp,e Mcp,g Mcp,hx,a Mcp,hx,c Mcp,hx,e Mcp,hx,g Ra Rc Re Rg Rv Sc Sg UAint,a UAint,c UAint,e UAint,g UAext,a UAext,c UAext,e UAext,g UAhx Va Vc Ve Vg z0,c z0,g z0,c z0,g
Unit
Value
Description
e m2 kW1 m m kJ K1 kJ K1 kJ K1 kJ K1 kJ K1 kJ K1 kJ K1 kJ K1 K W1 K W1 K W1 K W1 J kg1 K1 m2 m2 W K1 W K1 W K1 W K1 W K1 W K1 W K1 W K1 W K1 m3 m3 m3 m3 M M e e
0.61 0.09 103 0 0 58.5 33.0 38.0 58.5 4.94 3.04 2.66 2.66 4 4 4 4 455 2 105 2 104 13970 9720 6620 7290 4780 3320 2240 2890 42 0.024 0.014 0.024 0.024 0.2 0.2 1400 1400
Discharge coefficient Fouling factors Height between condenser bottom and evaporator inlet Height between generator bottom and absorber inlet Cumulated heat capacity of the absorber Cumulated heat capacity of the condenser Cumulated heat capacity of the evaporator Cumulated heat capacity of the generator Cumulated heat capacity of the absorber heat exchanger Cumulated heat capacity of the condenser heat exchanger Cumulated heat capacity of the evaporator heat exchanger Cumulated heat capacity of the generator heat exchanger Thermal resistance between absorber and outdoors Thermal resistance between condenser and outdoors Thermal resistance between evaporator and outdoors Thermal resistance between generator and outdoors Gas constant for water vapour Pipe section between condenser and evaporator Pipe section between generator and absorber Internal heat transfer coefficient of the absorber Internal heat transfer coefficient of the condenser Internal heat transfer coefficient of the evaporator Internal heat transfer coefficient of the generator External heat transfer coefficient of the absorber External heat transfer coefficient of the condenser External heat transfer coefficient of the evaporator External heat transfer coefficient of the generator Overall heat transfer coefficient of the solution exchanger Volume of the absorber Volume of the condenser Volume of the evaporator Volume of the generator Nominal height of the liquid inside the condenser Nominal height of the solution inside the generator Pressure loss coefficient (condenser/evaporator) Pressure loss coefficient (generator/absorber)
air conditioning of some office rooms. It is worth mentioning that the system was not designed for insuring standard comfort conditions in the offices (e.g. indoor temperature always below 26 C), but rather for refreshing the offices, so keeping the indoor temperature at 5e8 C below outdoor air. Hence, no control system has been implemented in the conditioned spaces: the system keeps working as long as sufficient thermal energy is available to drive the absorption machine. During the experimental campaign only the water temperatures at the inlet and at the outlet of the machine were measured, together with the water flow rates at each component. The temperatures were measured by means of Pt1000 temperature sensors calibrated together with the whole measurement chain (sensor, wire, acquisition system), with an absolute uncertainty of 0.15 C. The uncertainty in the measure of the volumetric flow rates was 2% according to the manufacturer of the flow meters. All the data were acquired every 120 s; it was not possible to reduce the acquisition time step, due to the need of storing the experimental data for long periods (up to 1 week) without saturating the memory of the acquisition system. No data were acquired inside the machine, such as pressure, temperature and LiBr concentration in each component,
because the interior of the machine was not accessible and no internal sensors had been installed by the manufacturers. For this reason, the agreement between simulated and experimental results was verified based on the outlet water temperatures and on the thermal power exchanged by the absorption chiller at each section. Figs. 2 and 3 report the behaviour of the absorption machine during two sunny days (14th of August and 8th of September). These days are representative of the greatest part of the experimental campaign: actually, during cloudy days the absorption machine did not normally switch on, because of the insufficient driving temperature provided by the solar plant. The main climatic data registered during both the aforementioned days and the whole experimental campaign are reported in Table 2. As shown in the graphs, at around 11:00, as soon as the water available at the generator inlet reaches 80 C, the absorption machine turns on (see Fig. 2); the cold production is almost immediate, as can be noticed from the profile of the inlet and outlet temperatures at the evaporator. The chiller produces cold water at mild temperatures, with a minimum value of 13.7 C on August the 14th and 18.1 C on September the 8th, respectively. The highest driving temperature is
1022
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5 e1 0 2 8
Inlet
b
Outlet
Inlet
Outlet
Temperature [°C]
Temperature [°C]
a
Time [h]
Time [h]
Fig. 2 e Experimental inlet and outlet temperature profiles for the absorption chiller (a: 14th of August, b: 8th of September).
around 90 C. On the heat rejection loop, the water inlet temperature keeps in the range 30e35 C on August the 14th and 37e42 C on September the 8th. The reason for the different performance during these 2 days is that during a short period of the experimental campaign (from the 25th of August to the 8th of September), a section of the ground heat exchanger was closed for experimental reasons. As expected, due to the lower surface available for heat rejection, the water temperature in the rejection loop raised in comparison with normal operation days, such as the 14th of August. This induced a reduction in the cooling capacity, hence an increase in the outlet temperature of the chilled water. The machine eventually stops when the driving temperature gets lower than 76 C, which occurs at around 17:40 on September the 8th. In addition, one can notice that the cooling power keeps almost constant between 11:30 and 15:30 (around 6 kW on August 14th and 4 kW on September 8th, see Fig. 3), but an important reduction occurs during the last hours of operation. Furthermore, the thermal COP, defined as the ratio of the cooling power produced at the evaporator to the thermal power required at the generator, is quite stable and sufficiently high (0.71e0.75 and 0.65e0.7 in the two representative days, respectively).
Q_ j ¼ rw $V_ j $cp;w $ðTout Tin Þj
(21)
Here, the density r of water is calculated as a function of the inlet temperature (Florides et al., 2003). The water flow rates measured on the real system are: Hot water flow rate at the generator: V_ w;g ¼ 0:82 [m3 h1] Cold water flow rate at the evaporator: V_ w;e ¼ 1:34 [m3 h1] Cooling water flow rate at the condenser: V_ w;c ¼ 2:20 [m3 h1] Furthermore, the control logic of the absorption machine were implemented, according to which the machine switches on when the driving temperature gets higher than 80 C, and it turns off below 76 C.
Fig. 3 e Experimental energy performance of the absorption chiller (a: 14th of August, b: 8th of September).
COP [-]
Thermal power [kW]
b
COP [-]
Thermal power [kW]
a
Here again, the better performance of the machine in the first day, where the cooling power is almost 30% higher than the machine nominal capacity, can be justified by the more favourable operating conditions (lower temperature on the heat rejection side). Afterwards, the same representative days discussed above were used to run the simulations, by using the water inlet temperature profiles shown in Fig. 2 as an input to the mathematical model, as well as the experimental values of the water flow rate. The model provides as output the values of the water outlet temperatures and the thermal powers, calculated as:
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5 e1 0 2 8
Table 2 e Main climatic data for the experimental campaign.
14th of August 8th of September Whole period (27/05e10/09)
Tav ext [ C]
Tmax ext [ C]
Imax [W m2]
H [kWh m2 day1]
23.4 18.0 21.8
33.5 28.6 40.6
827.3 813.2 1053.0
6.36 5.93 5.42
The system of equations is solved on the simulation tool SimSpark by using a NewtoneRaphson procedure with forward finite difference approximation; the simulation is performed with a time step as long as 5 s. The discrepancy between experimental and simulated results is shown in Figs. 4 and 5. In the first diagram, it is possible to see the profile of the difference between simulated and measured outlet temperatures during the chosen days. As regards the evaporator outlet temperature (see Fig. 4), this discrepancy keeps always very low (between 0.2 C and 0.2 C). The precision of the model is also good for the generator and the condenser outlet temperatures, as the discrepancy with the experimental results never exceeds 0.4 C. Furthermore, the percentage error on the evaluation of the thermal and cooling power is moderate, as shown in Fig. 5. Here, each point in the graphs allows the comparison between an experimental acquisition and its corresponding simulated value (there is one point every 120 s of machine operation). The deviation between experimental value and simulated result is measured by the distance from the diagonal line, where a perfect match between the two values holds. One can remark that the absolute deviation is always lower than 10% for all the components, but during the greatest part of the operation time it is even lower than 5%. The error at the evaporator (Fig. 5a) and the generator (Fig. 5b) tends to be higher at low capacity, whereas it is almost negligible at high capacity. The average error seems to be higher at the heat rejection section (Fig. 5c). Because of such discrepancies, an error on the evaluation of the thermal COP is expected, which keeps however always lower than 5% (Fig. 5d). Apart from verifying the capability of the model to describe the dynamic performance of the absorption machine, it is also important to test its reliability on a long time basis. To this aim,
after calculating the profile of the thermal power exchanged at each component, one can integrate over time in order to obtain the overall thermal energy during a certain time interval. Table 3 reports the results of this procedure performed both over the representative days previously described and over the whole test campaign (107 days). The results are very encouraging, as the absolute error on the cumulated daily and seasonal cold production is lower than 0.3%; the error on the average thermal COP is also very low. The highest discrepancy e around 5% e between experimental and simulated data occurs on the heat rejection side (condenser þ absorber). If looking more in detail, one can notice that the sum of the simulated values of the overall thermal energy provided at the generator and evaporator does not correspond to that rejected by the machine, as one would expect, but the latter is around 1e2% lower than the former. As a matter of fact, the process is not adiabatic, and the thermal energy stored in the generator is partially dissipated to the environment. On the contrary, when looking at the experimental data, the thermal energy rejected by the machine is always higher than the sum of that measured at generator and evaporator, and the difference can even reach 5%. This discrepancy might be attributed to the heat produced by the electric motor placed inside the machine to maintain the rotation. The results in Table 3 show that the proposed model not only can be used to follow with a good approximation the daily dynamic behaviour of the Rotartica absorption machine, but also to evaluate its overall performance over a long period. In any case, due to the amplitude of the acquisition time step used in the experimental test rig (120 s), nothing can be said about the precision of the model for transient phenomena whose duration is shorter than that.
5.
Consistency analysis
As shown before, the verification of the agreement between simulated and experimental data was carried out through the temperatures measured at the outlet of the absorption machine, due to the impossibility to make measurements inside the chiller. Nonetheless, the model is able to reproduce the profile of pressure, temperature and LiBr concentration inside the components, as well as the vapour and solution
b
Error [°C]
Error [°C]
a
1023
Time [h]
Time [h]
Fig. 4 e Discrepancy between simulated and experimental outlet temperatures (a: 14th of August, b: 8th of September).
1024
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5 e1 0 2 8
a
b
c
d
Fig. 5 e Comparison between simulated and experimental energy performance (both days). Solid line: 10% error; dotted line: 5% error.
mass flow rates. The values of these parameters are shown in Fig. 6 for the first day used in the previous analysis (14th of August). The parameter f represented in Fig. 6c is known as specific backflow, and is defined as the ratio of the diluted solution e which is rich in refrigerant e to the vapour produced in the evaporator (Eicker, 2003):
f¼
_ s;out;a xg m ¼ mev xg xa
(22)
It must be underlined that the diluted solution mass flow rate pumped from the absorber to the generator is not constant (see Fig. 6c), even though the volumetric flow rate was set constant, due to the variation in the solution density.
Table 3 e Experimental and simulated values for daily and seasonal energy performance. Generator [kWh] Daily performance (14th of August) Experimental 46.8 Simulated 47.1 Error þ0.6% Daily performance (8th of September) Experimental 34.7 Simulated 34.0 Error 2.0% Full test campaign (27/05e10/09) Experimental 3278 Simulated 3251 Error 0.8%
Evaporator [kWh]
Gener þ Evap [kWh]
Heat rejection [kWh]
Thermal COP [e]
34.7 34.6 0.1%
81.5 81.7 e
85.0 80.9 4.8%
0.741 0.735 0.7%
23.4 23.4 þ0.0%
58.1 57.4 e
58.7 56.2 4.2%
0.674 0.688 þ2.0%
5849 5559 4.9%
0.718 0.727 þ1.2%
2354 2362 þ0.3%
5632 5613 e
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5 e1 0 2 8
This density is highly influenced by the LiBr concentration, according to the relation proposed in (Florides et al., 2003). In order to check the internal consistency of the mathematical model, a further test was carried out (see also Ko¨hlenbach and Ziegler, 2008b). A new simulation was run by adopting constant cooling and chilled water inlet temperatures 30 C and 18 C, respectively e and a step change from 80 C to 90 C e to the driving temperature. In this case the simulation time step was set at 1 s. The duration of the simulation is 2000 s; the temperature step occurs at 1000 s after the beginning, as a certain delay is needed to wait for the system to reach steady operation in the initial operating conditions. Such an analysis is also helpful to investigate into mass and thermal storage effects. As shown in Fig. 7, the temperature step is followed by a steep increase of the thermal power released to the solution in the generator (see graph g), hence by an increase of the mass flow of vapour desorbed (see graph e). As a consequence of the higher vapour production rate, the LiBr concentration of the diluted solution inside the generator starts growing (see graph d). A more important vapour flow rate is then conveyed to the condenser but actually, due to the storage effects, the increase of the condensation rate follows in a slower fashion (see the curve m_l in graph e). Therefore, the condenser pressure rises, which is also communicated to the generator (see graph d); as saturation holds in the condenser, such a pressure increase also induces a temperature rise (see graph b). Fig. 7g also shows that the thermal power delivered to the generator tends to decrease after the initial step; such an effect is due to the growing temperature of the solution (see graph a), and then to the reduced heat transfer potential. It is interesting to underline that, despite the reduced thermal power, the vapour production keeps rising (see graph e): as a matter of fact, at higher pressure and temperature the energy needed to release an unit mass of vapour is lower. Again from Fig. 7e, one can notice that during the transient stage, the evaporation rate at the evaporator keeps higher than the liquid production rate at the condenser; this implies a fall in the evaporator absorber pressure (see graph d) and a consequent reduction in the evaporator temperature (see graph c). Furthermore, due to the time lag between vapour production in the generator and in the evaporator, a higher generator thermal power is not immediately followed by an equivalent rise in cooling production (see graph g, time 1000), thus the thermal COP initially shows a sudden decrease. However, such a fall is progressively recovered as long as the cooling power grows and the thermal power decreases. As far as the solution mass flow is concerned, the strong solution conveyed from the generator to the absorber initially decreases (see graph f), as a consequence of the higher vapour production. However, as far as the temperature and the LiBr concentration at generator rise, the density of the strong solution gets higher, and this implies, at around 1040 s, an inversion in the curve representing the strong solution rate (see graph f). In the absorber, temperature and LiBr concentration also rise (see graphs b and d), due to the same tendency previously identified at the generator. The simulated behaviour of the absorption chiller after a step of 10 K in the driving temperature is then coherent with what would be expected from thermodynamics. Such a test also showed that, due to thermal and mass storage effects,
1025
a
b
c
Fig. 6 e Simulated values for the main internal parameters (14th of August). (a): Pressure and LiBr concentration, (b): temperature, (c): mass flow rates.
a transient period of at least 400 s is needed by the chiller to reach new steady-state operation.
6. Use of the simulations for the system improvement The model presented and validated in the previous sections is useful to simulate the performance of the Rotartica chiller when integrated into a solar-assisted air-conditioning system,
1026
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5 e1 0 2 8
b
°
°
a
d
°
c
e
f
g
Fig. 7 e Simulated response of the absorption chiller to a step variation in the driving temperature.
as it is able to describe with good accuracy the dynamic response of the chiller both to load variations and to a continuous change in the driving temperature. In a solarassisted system, the latter are strictly connected with the
environmental conditions, especially if no back-up is available, as occurs in the plant considered in this study. In order to show the usefulness of the model in a practical case, several simulations were carried out to investigate into
1027
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5 e1 0 2 8
Fig. 8 e Experimental values of the climatic data for the period considered in the simulations (from the 11th to the 17th of August).
the effect of the size of the storage tanks on the chiller performance e measured by its cold production and its thermal COP e when the chiller is used in a solar-assisted air-conditioning system like the one installed at INES and described in Section 4. This system contains two storage tanks: - the hot storage tank (400 l) is used to collect the hot water produced by the solar section, and provides the hot water flow that drives the absorption unit; - the cold storage tank (300 l) is used to store the chilled water produced by the absorption unit, and provides cold water to feed the fan-coil units. More details concerning the layout of the system, the models used to simulate the other components (solar collectors, storage tanks) and the reliability of such models can be found in (Evola et al., 2010). A first series of simulations was performed by varying the size of the hot storage tank (from 200 to 1000 l) and keeping the volume of the cold storage tank at the real value. Then, in a second series of simulations, the volume of the hot storage tank was kept constant (400 l) and the cold storage tank was varied between 200 and 600 l. In all the simulations an insulating layer made up of 40 mm of polystyrene is applied to the storage tanks. The simulations were run over one week (from the 11th to the 17th of August) by using, as input values for the model, the
climatic data registered during the experimental campaign. The corresponding profiles of the outdoor temperature and of the solar irradiance on the surface of the collectors are reported in Fig. 8 The results of such parametric analysis are shown in Table 4. In order to justify them, it is useful to remind that the absorption unit starts working when the driving temperature reaches 80 C, and eventually stops when the latter gets lower than 76 C. As a rule, the higher the volume of the hot storage is, the longer it takes for the hot water to reach the minimum driving temperature needed to run the absorption unit: as a consequence, the unit starts working late in the morning. However, a higher storage volume also allows a slower thermal discharge, thus the daily operation has a duration that does not change noticeably as a function of the hot storage volume. On the whole, higher storage volume means lower average temperatures, which induces for the Rotartica absorption unit a slight decrease in the cold production but also a slight increase in the average thermal COP. On the other hand, a variation in the volume of the cold storage tank does not affect the driving conditions, thus the chiller activation time stays the same. However, in this case, higher storage volume means higher average temperatures for the chilled water, which improves the average thermal COP of the absorption unit and reduces the overall cold production.
7.
Conclusions
In this paper, a dynamic model for the simulation of a commercial single-effect LiBr/water absorption chiller has been described. The structure of the model makes it suitable for a general use, but in this context it has been applied to the absorption unit distributed by Rotartica, which is different from common LiBr absorption chillers as the thermal cycle is performed inside a rotating vessel. After defining the values of the parameters which best describe the geometry of the Rotartica chiller, the reliability of the model has been verified by comparing the simulated results to those collected in an experimental installation. The comparison was based on the values of the outlet water temperature and on the thermal power exchanged at each section, as no internal parameters
Table 4 e Influence of the storage volume (up: hot storage e bottom: cold storage) on the performance of the absorption chiller. Storage volume (hot water) Chiller activation time Average daily cold production Average daily thermal COP COP variation Storage volume (cold water) Chiller activation time Average daily cold production Average thermal COP COP variation
[l]
200
400
600
800
1000
from to [kWh/day] []
10:10 17:00 39.2 0.705 1.0%
10:50 17:30 39.0 0.712 d
11:20 18:00 38.9 0.718 þ0.8%
11:50 18:20 38.8 0.724 þ1.6%
12:20 18:50 38.7 0.728 þ2.3%
[l] from to [kWh/day] []
200 10:50 17:30 38.6 0.708 0.6%
300 10:50 17:30 39.0 0.712 d
400 10:50 17:30 39.2 0.716 þ0.5%
500 10:50 17:30 39.4 0.719 þ1.0%
600 10:50 17:30 39.6 0.722 þ1.4%
1028
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5 e1 0 2 8
(pressure, salt concentration, temperature) could be measured inside the machine. The model shows a good agreement with the experimental data: the transient performance during two typical operation days is simulated with a satisfying accuracy, since the deviation between the instantaneous simulated and experimental values of cooling power and COP never exceeds 5%. The paper also verifies the capability of the model to describe the system performance on a long time basis: the results are very encouraging, as the error on the overall test campaign is around 1%. A fundamental condition to obtain such a high reliability is the good estimation of the chiller design parameters, based on the availability of design data and schemes provided by the manufacturers. In the paper, these results were obtained without any tuning or calibration of the input parameters. In addition, a consistency analysis was also performed to investigate the response of the model to a 10 K temperature step applied to the driving temperature. According to this test, the behaviour of the chiller is perfectly consistent with thermodynamics; the time needed to reach steady-state operation after the temperature step is around 8 min. Finally, an example of practical application of the model is presented, where simulations are used to investigate into the influence of the storage volume on the chiller performance, in the specific case of the solar-assisted air-conditioning system installed at INES (Institut National de l’Energie Solaire, France) for the air-conditioning of some offices. The simulations allowed to understand that increasing the volume of the hot storage is beneficial in order to improve the average thermal COP, even though a slight reduction in the cold production and a shift in the operating time must be accounted for. The dynamic model presented in this paper is then a reliable tool to evaluate the long-term behaviour of a single-effect LiBr/water absorption chiller, but also to follow its daily operational profile with good precision. Its use is suggested to study the interaction of the absorption unit with the other components of a solar-assisted cooling plant, with the aim of optimizing both the layout of the system and the control logic of the chiller.
Acknowledgements The experimental installation has been financed in the framework of the European project SOLERA (FP6), coordinated by Fraunhofer ISE. The study of its performance has been conducted in the framework of the research project ORASOL ANR 06-PBAT-009-01.
references
Alefeld, G., Radermacher, R., 1993. Heat Conversion Systems. CRC, USA.
Bakhtiari, B., Fradette, L., Legros, R., Paris, J., 2011. A model for analysis and design of H2OeLiBr absorption heat pumps. Energy Convers. Manage. 52, 1439e1448. Cengel, Y., 1997. Introduction to Thermodynamics and Heat Transfer. Mc Graw Hill, USA. Eicker, U., 2003. Solar Technologies for Buildings. John Wiley & Sons, USA. Evola, G., Le Pierre´s, N., Boudehenn, F., Papillon, P., 2010. Description and validation of a dynamic tool for the modeling of a solar-assisted absorption cooling machine. In: Proceedings of EUROSUN International Conference, Graz. Florides, G.A., Kalogirou, S.A., Tassou, S.A., Wrobel, L.C., 2003. Design and construction of a LiBrewater absorption machine. Energy Convers. Manage. 44, 2483e2508. Garcia Cascales, J.R., Vera Garcia, F., Cano Izquierdo, J.M., Delgado Marin, J.P., Martinez Sanchez, R., 2011. Modeling an absorption system assisted by solar energy. Appl. Therm. Eng. 31, 112e118. Gilchrist, K., Lorton, R., Green, J.R., 2002. Process intensification applied to an aqueous LiBr rotating absorption chiller with dry heat rejection. Appl. Therm. Eng. 22, 847e854. Gnielinski, V., 1976. New equations for heat and mass transfer in turbulent pipe and channel flow. Int. J. Chem. Eng. 16, 359e367. Gomri, R., 2010. Investigation of the potential of application of single effect and multiple effect absorption cooling systems. Energy Convers. Manage. 51, 1629e1636. Howell, R.H., Sauer, J.H., Coad, J.W., 2005. Principles of Heating, Ventilation and Air Conditioning. American Society of Heating, Refrigeration and Air Conditioning Engineers. Incropera, F., De Witt, D., Bergman, T., 2006. Introduction to Heat Transfer. John Wiley & Sons, USA. Izquierdo, M., Lizarte, R., Marcos, J.D., Gutie´rrez, G., 2008. Air conditioning using an air-cooled single-effect lithium bromide absorption chiller: results of a trial conducted in Madrid in August 2005. Appl. Therm. Eng. 28, 1074e1081. Jeong, S., Kang, B.H., Karng, S.W., 1998. Dynamic simulation of an absorption heat pump for recovering low-grade waste heat. Appl. Therm. Eng. 18, 1e12. Ko¨hlenbach, P., Ziegler, F., 2008a. A dynamic simulation model for transient absorption chiller performance. Part I: the model. Int. J. Refrigeration 31, 217e225. Ko¨hlenbach, P., Ziegler, F., 2008b. A dynamic simulation model for transient absorption chiller performance. Part II: numerical results and experimental verification. Int. J. Refrigeration 31, 226e233. Massey, B., Ward-Smith, J., 1998. Mechanics of Fluids. Taylor & Francis, UK. Monne´, C., Alonso, S., Palacin, F., Guallar, J., 2011. Stationary analysis of a solar LiBr e H2O absorption refrigeration system. Int. J. Refrigeration 34, 518e526. Myat, A., Thu, K., Kim, Y.D., Chakraborty, A., Chun, W.G., Ng, K.C., 2011. A second law analysis and entropy generation minimization of an absorption chiller. Appl. Therm. Eng. 31, 2405e2413. Rivera, W., Xicale, A., 2001. Heat transfer coefficient in two phase flow for the water/lithium bromide mixture used in solar absorption refrigeration systems. Solar Energy Mater. Solar Cells 70, 309e320. Rogers, G., Mayhew, Y., 1992. Thermodynamic and Transport Properties of Fluids: SI Units, fourth ed. Blackwell Publishers, UK. Shin, Y., Seo, J.A., Cho, H.W., Nam, S.C., Jeong, J.H., 2009. Simulation of dynamics and control of a double-effect LiBreH2O absorption chiller. Appl. Therm. Eng. 29, 2718e2725.
