1、2008 ASHRAE 319ABSTRACTThis paper presents two simple cooling coil models. Thefirst part of the paper describes and validates the first one(“reference model”). This model only necessitates 3 param-eters, which can be estimated by using commissioning ormanufacturer information. The second part of the
2、 paperpresents and validates the second simple model (“simplifiedmodel”). The paper shows how the latter can be built fromthe reference model, when there is no need to describe whathappens on the refrigerant side. This simplified model can beeasily integrated in the model of a global HVAC system ino
3、rder to calculate the cooling coil energy consumption overlarge time periods. The simplified model is appropriate todecrease the computational time and avoid numerical insta-bilities.INTRODUCTIONMost of the equipment used today for cooling and dehu-midifying an air stream contains cooling coils. The
4、 design andthe operation of cooling coils affect greatly the overall build-ing energy consumption.The literature presents a lot of cooling coil models whichcould be used to optimize their design. These “detailed”models are generally quite complex and require a good knowl-edge of the geometry of the
5、cooling coil (such as the dimen-sions of the fins, the tube thickness, diameter and spacing),which is not always available from the manufacturer. Gener-ally, in these models the coil is discretized in a finite numberof sections (control volumes).Wang and Hihara (2003) presented a method calledequiva
6、lent dry-bulb method (EDT method) to simplify thecalculation in each control volume and distinguish the threecooling modes (totally wet, partially wet and totally dry). Aniterative scheme is then employed for an entire cooling coilsimulation. For any process of cooling and dehumidifying, anequivalen
7、t dry process with the identical cooling capacity isassumed. This equivalent process is defined between the twoconstant enthalpy lines. For the equivalent dry process, thespecific heat is constant due to the constant humidity. Accord-ingly, both the LMTD and effectiveness-NTU method may beused to ca
8、lculate the cooling capacity.Yao et al. (2004) presented a rigorous analysis of theeffect of perturbations of relevant parameters (such as inletwater temperature, water flow rate, inlet air temperature,airflow rate, inlet air humidity) on performances of coolingcoils under different initial conditio
9、ns.More recently, Wang et al. (2007) proposed to decouplethe sensible and the latent heat transfer modes assuming aconstant value of the SHR and the saturation curve slopewithin a small piece of the cooling coil. They developed anumerical cooling coil model using the effectiveness-NTUand the finite
10、element methods. Each element is treated as asmall cross-flow heat exchanger. Both the SHR and the curveslope are determined by the unknown conditions of the air,coil surface and chilled water, so an iterative method must beused.The literature proposes also some simplified or “lumpedgeometrical” mod
11、els, which consider the cooling coil as asingle system and describe it with a limited number of param-eters which represent the lumped geometric terms. Theselumped parameters can be for instance thermal resistances(convective resistance on the air side, conduction resistance ofthe metal and convecti
12、ve resistance on the water side) orlumped thermal masses (in order to account for the dynamicbehavior of the cooling coil). These models are suitable forDevelopment of Simple Cooling Coil Models for Simulation of HVAC SystemsVincent Lemort Jean Lebrun, PhDStudent Member ASHRAE Fellow ASHRAECristian
13、Cuevas, PhD Ion Vladut Teodorese, PhDVincent Lemort is a PhD Student at the Thermodynamics Laboratory of the University of Lige, Belgium. Jean Lebrun is an Applied Ther-modynamics Professor at the University of Lige and Head of the Thermodynamics Laboratory of the University of Lige, Belgium. Cristi
14、anCuevas is an Applied Thermodynamics Professor at the University of Concepcin, in Chile. Ion Vladut Teodorese is a researcher at the Ther-modynamics Laboratory of the University of Lige, Belgium.NY-08-0382008, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashr
15、ae.org). Published in ASHRAE Transactions, Volume 114, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission.320 ASHRAE Transactionsstudying the operation of a cooling coil assoc
16、iated to otherHVAC equipments or carry out real time control.Morisot et al. (2002) proposed to enhance the ASHRAEHVAC 2 Toolkit (Brandemuehl et al. 1993) simplified coolingcoil model in such a way that it accurately determines the cool-ing energy rate and dehumidification rate under nonnominalcondit
17、ions. Their model only necessitates two parameters (theairside and waterside heat transfer coefficients), which can beidentified with one single operating point. They show thatthese heat transfer coefficients can often be assumed to varyonly with flow rates. Consequently, the behavior of the cooling
18、coil can be predicted under nonnominal conditions, such asthose encountered with variable air and/or water flow rateoperations.Wang et al. (2004) proposed a simple, yet accurate, steadystate cooling coil model that can be used for real time controland optimization of HVAC systems. The model is chara
19、cter-ized by 3 characteristic parameters. A procedure for determin-ing the unknown parameters using commissioning or cataloginformation is given. Jin et al. (2006) extended the work ofWang et al. (2004) to develop a simple dynamic model topredict the performance of the cooling coil in time varyingop
20、eration conditions. Their model requires no more than 6parameters that represent the lumped geometric terms.Recently, Zhou (2005) and Braun (2006) developed andvalidated computationally and well-documented transientcooling coil models. A forward and an inverse model weredeveloped. The forward model
21、solves the governing differen-tial equations involving energy storages and transfers within acooling and dehumidifying coil, using physical parametersthat characterize the coil. The inverse model is typically asimpler formulation where lumped parameters are determinedfrom regression using experiment
22、al training data or datagenerated by a detailed forward model. These models werecompared with existing simplified models available in theliterature and confirmed to provide improved predictions ofcooling coil transient performance. The developed models areuseful for testing feedback controllers and
23、fault detection anddiagnostic methods.The first part of this paper presents and validates a coolingcoil model built over the proposals of Braun et al. (1989) andLebrun et al. (1990). This model introduces a limited number ofparameters. The second part of this paper shows how it is possi-ble to simpl
24、ify even more this (“reference”) model when thereis no need to describe what happens on the refrigerant side.Actually, the determination of the refrigerant flow rate and therefrigerant exiting temperature is only necessary if the chillerperformances and energy consumption have to be modeled andif th
25、ey are significantly affected by the return refrigeranttemperature. The simplified model, which only focuses on theair side, can be easily integrated in the model of a larger HVACsystem. Using this model instead of the reference modeldecreases the computational time and avoids numerical insta-biliti
26、es. Moreover, it is appropriate for simulating the operationof a global HVAC system over large time periods.REFERENCE MODEL OF A COOLING COILDescription of the Reference ModelThis reference model is based on a model previouslyproposed and partially validated by Lebrun et al. (1990). Thismodel threat
27、s the cooling coil as a one-zone counter-flow heatexchanger. Fully dry and fully wet regimes are describedsimultaneously and the regime to be considered is the oneleading to the maximal cooling capacity (Braun et al. 1989).(1)In dry regime, the overall heat transfer coefficient iscalculated by consi
28、dering three resistances in series: theconvective resistance on the air side, the conduction resistanceof the metal and the convective resistance on the refrigerantside:(2)The influence of the cooling coil geometry, which is notknown “a priori”, is lumped into the thermal resistances on therefrigera
29、nt and on the air sides. By assuming a correlation ofthe typeNu = CRemPrn(3)the heat transfer coefficient can be expressed by(4)where(5)To define the exponent m, the internal and external flowsare assumed to be turbulent and laminar respectively. For theexponent n, a value of 0.3 is used. Figure 1 s
30、hows the valuesof the coefficient K*for pure water and different aqueous solu-tions of ethylene glycol. According to these results, it isconcluded that the thermal resistance on the refrigerant sidemust take into account the effect of the fluid properties, sincethe coefficient K*varies significantly
31、. Figure 1 shows also thatthe heat transfer coefficient is largely degraded when higherethylene glycol concentrations are used (by 70 % for an ethyl-ene glycol concentration of 50% in mass).Figure 2 shows that on the air side, the thermal resistancecould be calculated by taking only into account the
32、 effect ofthe air mass flow rate. The coefficient K*is not very sensitiveneither to the air temperature nor to the air pressure.Both thermal resistances are consequently defined as(6)QcoilMAX Qcoil dry,Qcoil wet,()=1AUcoil dry,- Racoildry,Rmcoil,Rrcoil,+=hC*M mK*=K*nmk1 ncn=Racoildry,Racoiln,Macoiln
33、,Macoil,-0.6=ASHRAE Transactions 321(7)Where Ra,coil,nand Rr,coil,nare the parameters of themodel, which must be identified on the basis of experimentalresults or catalogue data. , , and areconstant parameters, imposed by the choice of the nominalpoint.In dry regime, the cooling coil capacity is giv
34、en by Equa-tion (8), involving the humid inlet air and refrigerant temper-atures. The cooling coil effectiveness coil,dryis expressed as afunction of the heat transfer coefficient AUcoil,dryby means ofthe classical -NTU method,(8)When the cooling coil works in wet regime, the air can bereplaced by a
35、 fictitious perfect gas, whose enthalpy is fullydefined by the actual wet bulb temperature. The air sidethermal resistance and the total cooling power are defined byEquations 9 and 11 (Lebrun et al. 1990).(9)with(10)(11)To determine the air state at the cooling coil outlet in wetregime, a fictitious
36、 semi-isothermal heat exchanger is defined,according to the ASHRAE classical procedure (ASHRAE2000). One of the two fluids supplying this heat exchanger isthe air; the other one is a fictitious fluid of infinite capacityflow rate, whose uniform temperature is supposed tocorrespond to the average tem
37、perature of the external surfaceof the coil, also called “contact” temperature Tc,coil,wet. The“contact” effectiveness is defined by:(12)(13)Enthalpy and specific humidity of the air at the coolingcoil outlet can easily be defined through the following rela-tionships:(14)(15)where hc,coil,wetand Wc,
38、coil,wetcorrespond to the enthalpy andthe specific humidity of the air at the coil surface defined atsaturated state.A block diagram representation of the cooling coilmodel is given in Figure 3. Some variables are considered asinput values, whereas the output values are calculated by themodel. The m
39、odel only necessitates three parameters: thethree thermal resistances. As mentioned before, the twonominal flow rates and the nominal coefficient areimposed by the choice of the nominal point. Some otherparameters have to be added in order to characterize therefrigerant: its density, its specific he
40、at, its dynamic viscosityand its thermal conductivity.Figure 1 Variation of the coefficient K*with the refrigeranttemperature.Figure 2 Variation of the coefficient K*with the airtemperature and pressure.Rrcoildry,Rrcoiln,Krn,*Kr*-Mrcoiln,Mrcoil,-0.8=Macoiln,Mrcoiln,Krn,*Qcoil dry,coil dry,Cmin coil
41、dry,Tasucoil,Trsucoil,()=Rafcoil,Racoildry,cpacoil,cpafcoil,-=wetcoilexwbcoilsuwbwetcoilexacoilsuacoilfapTThhc,=Qcoil wet,coil wet,Cmin coil wet,Twb su coil,Trsucoil,()=ccoilwet,1NTUccoilwet,()exp=NTUccoilwet,1Racoil,Cacoil,-=hasucoil,haexcoilwet,ccoilwet,hasucoil,hccoilwet,()=Wsu coil,Wex coil wet,
42、ccoilwet,Wsu coil,Wccoilwet,()=Krn,*322 ASHRAE TransactionsThis model can be easily adapted to a direct expansioncoil. In this case, the coolant fluid is the refrigerant and themodel must account for its vaporization.(16)The enthalpy (hr, s u , ev) at the coil (or evaporator) inlet is thesame as the
43、 enthalpy at the outlet of the expansion device of therefrigeration cycle. If the expansion can be considered as isen-thalpic, this enthalpy is also the same as at condenser outlet. Itcan then be calculated as a function of the condensing pressureand of the condenser exit subcooling. This subcooling
44、 essen-tially depends on the amount of refrigerant introduced in therefrigeration system (refrigerant “charge”).The enthalpy at the outlet of the evaporator is calculatedon the basis of the refrigerant pressure and the temperature atthe outlet of the evaporator. The exiting temperature iscomputed by
45、 imposing a refrigerant superheating at the outletof the cooling coil. This superheating is usually imposed bythe expansion device.A convenient approximation is to consider that the refrig-erant is isothermal inside the coil:(17)And this evaporation temperature can be defined as theweighted average
46、of the actual refrigeration temperatures (inorder to take into account the effects of the evaporator pressuredrop and the evaporator superheating):(18)Where and are the mean refrigerant temper-atures in respectively the two-phase and the superheatingzones of the evaporator.Validation of the Referenc
47、e ModelThe cooling coil model is validated in the frame of acommon simulation exercise, where modelers have the oppor-tunity to tune, validate and evaluate their simulation models(Felsmann 2007). The experimental setup used to validate themodels consists in an instrumented cooling coil located insid
48、ean air handling unit.As it is the case in most of the situations, only one perfor-mance point is given by the manufacturer. This operating pointcorresponds to a wet regime of the coil. The refrigerant is anaqueous solution of ethylene glycol, whose concentration isassumed to be 35% in mass. Enterin
49、g and leaving dry and wetbulb temperatures, glycol water flow rate, entering and leavingglycol water temperatures and total cooling power corre-sponding to this point are given by the manufacturer (Table 1).The sensible and latent cooling capacities as well as the airflow rate can be estimated from these values.Theoretically, since this point corresponds to a wet regimean
