Proposal and Validation of a Model for the Dynamic Simulation of a Solar-Assisted Single-stage LiBrwater Absorption Chiller

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 b 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 a r t i c l e i n f o Article history: R
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  Proposal and validation of a modelfor thedynamic simulationof 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 b 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 a r t i c l e i n f o Article history: Received 28 November 2011Received in revised form21 September 2012Accepted 18 October 2012Available online 1 November 2012 Keywords: Absorption chillerLithium bromideDynamic performanceSimulationExperimental results a b s t r a c t In this paper, a general mathematical model for the dynamic simulation of a single-effectLiBr/water absorption chiller is presented. The model is based on mass and energybalances applied to the internal components of the machine, and it accounts for the non-steady behaviour due to thermal and mass storage in the components. The validation of the mathematical model is performed through experimental data collected on a commer-cial small-capacity water-cooled unit. Due to the peculiar technology adopted in the realchiller, a special effort was made to identify the appropriate values of the main physicalparameters. The validation of the model is based on the values of the water temperature atthe outlet of the machine, as no measurement inside the machine was possible; anyway,a consistency analysis applied to the internal parameters is also presented. The agreementbetween experimental and simulated results is very good, both on a daily and on a seasonalbasis. ª  2012 Elsevier Ltd and IIR. All rights reserved. Proposition et validation d’un mode `le pour la simulationdynamique d’un refroidisseur a ` absorption au LiBr / eausolaire 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 thedescription of the real performance of an energy conversionsystem, especially during the activation stage or part-loadoperation. Such a problem is extremely relevant for absorp-tion chillers, where the high mass of the internal componentsand the accumulation of the fluids inside the vessels usuallymake the transient phase longer than in mechanicalcompression chillers. * Corresponding author. Tel.:  þ 33 47 975 88 58; fax:  þ 33 47 975 81 44.E-mail address: (N. Le Pierre`s).  Available online at journal homepage: international journal of refrigeration 36 (2013) 1015 e 1028 0140-7007/$  e  see front matter  ª  2012 Elsevier Ltd and IIR. All rights reserved.  Very interesting papers on this topic have been presentedin scientific literature. Jeong et al. (1998) propose a dynamicmodel for the simulation of a steam-driven LiBr/waterabsorptionheatpumpthatexploitslow-gradewasteheat.Themodelincludesstoragetermstotakeintoaccountthethermalcapacity of the container and the solution mass storage in thecomponents, but no thermal inertia is attributed to the heatexchangers. Solution and vapour mass flow rates are notconstant, as they are determined as a function of the pressuredifference between the vessels. The simulation time step isautomatically adjusted; the model has been verified, withgoodagreement,throughoperationaldata,butonlybylooking at the thermal power exchanged by the absorber and thecondenser.Ko ¨ hlenbach and Ziegler (2008a, 2008b) paid a lot of atten-tion to the dynamic behaviour, by accounting for heat andmass storage, as well as to the solution transport delaybetween generator and absorber  e  and the way back; on thecontrary, their model is over-simplified as far as the descrip-tionofthesteadystateisconcerned:asanexample,waterandLiBr/water solution have constant property data, anda detailed enthalpy calculation for each state of the system isavoided.Hence, theirmodelis able to describe very accuratelythe shape of the dynamic response to a change in the inputconditions, but a low accuracy on the numerical values isobtained after verification with the experimental measure-ments on a commercial 10 kW single-stage absorption chiller.The work also includes a sensitivity analysis to some internalparameters, which is not supported by experimentalverification.The model developed by Shin et al. (2009) applies to high-capacity double effect absorption chillers. It has been veri-fied against experimental data collected on a commercialdirect-fired chiller of medium capacity during 370 min of operation, with an acquisition time step as high as 5 s. On thewhole, the model proved to be quite reliable at steady opera-tion; on the contrary, during the first 90 min, i.e. when thetransient behaviour was particularly pronounced, differencesup to 10   C were observed between simulated and experi-mental values of the temperatures inside generator andabsorber. Furthermore, during the same period the error onthe determination of the instantaneous capacity reached20%.Other works have been recently presented by Gomri (2010)andBakhtiarietal.(2011);bothworksarebasedonasimplifiedsteady-state model of a single or multiple effect absorptionchiller. In the first case, the model is used for evaluating theperformance sensitivity to the main operating parameters,even under a second law perspective, but no validation ispresented, whereas in the second work the model is validatedthrough experimental data and used for the optimization of the chiller design.Myat et al. (2011) presented an effective dynamic model forthe evaluation of temperature and concentration profiles ina single stage LiBr/water absorption chiller; their model also Nomenclature Variables A  surface (m 2 ) c p  specific heat capacity (Jkg   1 K  1 ) C d  discharge coefficient ( e ) D  diameter (m)  f   specific backflow ( e ) F  fouling factor (m 2 kW  1 ) h  specific enthalpy (Jkg   1 ) H  height difference between two components (m) H  daily solar irradiation on the collector plane(kWhm  2 day  1 ) I  solar irradiance on the collector plane (Wm  2 ) _ m  mass flow rate (kgs  1 ) M  mass (kg)Nu Nusselt number ( e )  p  pressure (Pa)Pr Prandtl number ( e )Re Reynolds number ( e ) _ Q   thermal power (W) s  thickness (m) S  pipe section (m 2 ) t  time (s) T  temperature (K) U  heat transfer coefficient (Wm  2 K  1 ) V   volume (m 3 ) _ V   volumetric flow rate (m 3 s  1 ) x  concentration ( e ) z  level of the liquid inside a component (m) Greek letters a  convective coefficient (Wm  2 K  1 ) l  thermal conductivity (Wm  1 K  1 ) r  density (kgm  3 ) z  pressure loss coefficient (-) Subscripts and superscripts a absorberabs absorbedav average valuec condenserd dissipateddes desorbedext externalev evaporatorg generatorhx heat exchangerin inletint internall liquidmax maximum valueo outdoorout outlets solutionsh shellv vapourw water international journal of refrigeration 36 (2013) 1015 e 1028 1016  includessomerelationsforthecalculationoftheheattransfercoefficients and finally leads to an entropy analysis of thechiller, but it is not validated through experimental results.The model described in the present paper has beenconceived in the framework of a research project wherea commercial solar-assisted single-stage absorption chiller isbeing monitored to verify its performance in the air-conditioning of an office space. As a consequence, somespecific features are needed:- the model must be suitable for the simulation of commer-cial 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 precisedescription of the transient response of the machine, but todescribe with good accuracy the time profile of the chillerbehaviour when subject to load variations in the time scaleof a few minutes;- the model must determine the water outlet temperatureand the thermal power at each section of the absorptionchiller;- the model should also present good accuracy in thedescription of the average chiller performance (daily,weekly or even seasonal).For this reason, the validation of the dynamic model is notbased on the application of a load perturbation starting froma steady state, but it is performed by means of real operating conditions, with a continuous change of all the externalparameters over several days of operation.Section 2 describes the equations included in the mathe-matical model, as well as the hypotheses that justify suchequations. Section 3 presents the calculation of the physicalparameters to be adopted in the mathematical model tosimulate the commercial single-stage absorption unitconsidered in this study. Section 4 comments on the experi-mental data and their comparison with the simulated results.Section 5 shows a consistency analysis that investigates intothe capability of the model to correctly describe the internalbehaviourofthemachineanditsresponsetoasuddenchangein the forcing conditions. Section 6 concerns the use of theproposed model to identify some improvements in theexperimental 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 solutionpump, and a solution heat exchanger is normally used tointernally recover thermal energy (see Fig. 1). At the gener-ator, a heat source is supplied, in order to desorb therefrigerant (water vapour) from the solution; the vapourmoves towards the condenser, where it is condensed ata high pressure. The remaining solution, called  strong  as it isrich in LiBr, flows down via the heat exchanger to theabsorber; here it is exposed to the vapour coming from theevaporator, that is absorbed in the solution at low pressureand temperature. The diluted solution is then conveyed tothe generator by the solution pump. The cold productionoccurs at the evaporator.In order to simplify the formulation and the consequentimplementation of the model, some assumptions are made:a temperature, pressure and LiBr concentration arehomogenous inside each component (Myat et al., 2011);b the pressure inside the generator equals that in thecondenser, and the same relation holds between absorberand evaporator;c the cooling water outlet temperature in the absorbercorresponds to the cooling water inlet temperature at thecondenser;d the fluid transport delay between two components isneglected;e each heat exchanger has a constant overall heat transfercoefficient, as already stated by Ko ¨ hlenbach and Ziegler(2008a) and Jeong et al. (1998); f the LiBr/water solution leaving the generator and theabsorber is saturated (Ko ¨ hlenbach and Ziegler, 2008a);g the throttling valves between generator/absorber andcondenser/evaporator are adiabatic;h the vapour produced in the evaporator is saturated, thusno superheating is allowed, as remarked by Shin et al.(2009) and Gomri (2010); i the volumetric flow rate of diluted solution conveyed bythe solution pump from the absorber to the generator isassumed constant.Most of the above simplifying assumptions are quitereasonable (b,c,g,i) orwellestablishedintheliteratureonthetopic (a, d, e, h). Only the assumption  f   might be questionable:Myat et al. (2011) underline that in a well-designed absorberthesolutioninsidethecomponentandatitsoutletisnormallyslightly sub-cooled. However, when simulating commercialabsorption units, it is not possible to access the inside of themachine, thus there is no way to verify through experimentalmeasurements the accuracy of this last assumption. 2.1. Generator and absorber If looking at the scheme described in Fig. 1, the mass balancefor the solution and the vapour in the generator can berespectively written as follows, by including the storage of both fluids in the vessel: _ m s ; in ; g     _ m s ; out ; g     _ m v ; des  ¼  d M s ; g  d t  (1) _ m v ; des    _ m v ; out ; g   ¼  d M v ; g  d t  (2)The ideal gas law can be used for the vapour, Eq. (3). Thisposition is allowed as the vapour pressure inside a single-stage LiBr/water absorption chiller is normally between 1and 10 kPa, i.e. far lower than the critical pressure; in thisconditions, the error made on the evaluation of the specificvolumebyusingtheidealgaslawislowerthan0.1%,whateverthe vapour temperature, as remarked in (Cengel, 1997). In Eq.(3) the volume  V  v  occupied by the vapour is calculated by international journal of refrigeration 36 (2013) 1015 e 1028  1017  subtracting the volume of the solution from that of the entirevessel, see Eq. (4). M v ; g  $ R v $ T g   ¼  p g  $ V  v  (3) V  v  ¼  V  g    M s ; g  = r s ; g   (4)Furthermore, the mass balance on LiBr, see Eq. (5), and theenergy balance on the solution, see Eq. (6), hold: _ m s ; in ; g  $ x s ; in ; g     _ m s ; out ; g  $ x s ; out ; g   ¼  M s ; g  $ d x s ; g  d t  þ x s ; g  $ d M s ; g  d t  (5) _ Q  hx ; g     _ Q  d ; g   ¼  _ m v ; des $ h v ; des  þ  _ m s ; out ; g  $ h s ; out ; g     _ m s ; in ; g  $ h s ; in ; g  þ  dd t  Mc p ; g  $ T g    (6)In Eq. (6), the convective and radiative heat transferbetween vapour and solution is neglected. The solution isassumed to be fully mixed at each simulation step; asa consequence the enthalpy and the salt concentration in thesolution leaving the vessel correspond to those inside thevessel. Furthermore, according to Alefeld and Radermacher(1993) the temperature of the vapour desorbed in the gener-ator corresponds to the saturation temperature associatedwith the diluted solution entering the component; asaconsequencethevapourwillbesuper-heatedwithrespecttothe solution contained inside the vessel.In addition, the model takes into account the thermalinertia of the shell; the shell is assumed at thermal equilib-rium with the solution ( T sh ¼ T g  ), thus its thermalcapacity canbe composed with that of the solution itself in Eq. (6), where M ¼ M sh þ M s  and  c p  is the average specific heat capacity (Shinet al., 2009), defined as: c p ; g   ¼  M sh $ c p ; sh  þ M s $ c p ; s M sh  þ  M s (7)The thermal power released into the environment can beassessed by introducing an overall thermal resistance  R g  between the solution in the generator and the outdoor air: _ Q  d ; g   ¼  T g     T o  R g   (8)Suchaschemecanbeextendedtotheabsorber,justaccounting for the different direction of the vapour flow, which enters thecomponentandisabsorbedinthesolution.Thethermodynamicstate of the vapour entering the absorber corresponds to that of thevapourproducedintheevaporator;itsenthalpyisassessedasa function of temperature and pressure through the relationsavailable in (Florides et al., 2003), that are derived by fitting thedata presented in (Rogers and Mayhew, 1992).In theequationspreviouslypresented,thethermodynamicproperties of the LiBr/water solution (enthalpy, density,specific heat, thermal conductivity, viscosity) are calculatedthrough 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 vapourinstead of LiBr/water solution; as a consequence, the massbalance on the condensate and the vapour can be written as: _ m l    _ m l ; out ; c  ¼  d M l ; c d t  (9) _ m v ; in ; c    _ m l  ¼  d M v ; c d t  (10) PumpQ hx,g m s,out,g M s,a Q d,a m w,g m s,in,g M v,g m v,in,a Q d,c CONDENSERQ hx,a m s,out,a M l,c M v,a m w,a m s,in,a M v,c m l m l,out,c M l,e Q d.e m w,c Q hx,c m v,in,c m ev Q hx,e M v,e m w,e m l,in,e Solution exchHigh pressureLow pressure m v,out,e EVAPORATOR ABSORBER m v,abs m v,out,g   m v,des GENERATORQ d,g M s,g Fig. 1  e  Description of the main components inside the absorption machine (white arrows: vapour, black arrows: liquid). international journal of refrigeration 36 (2013) 1015 e 1028 1018
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