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Energy and Buildings 47 (2012) 411–420

Contents lists available at SciVerse ScienceDirect

Energy and Buildings

j ourna l ho me p age: www.elsev ier .com/ locate /enbui ld

alidation of a numerical model aimed at the estimation of performance of vaporompression based heat pumps

assimiliano Scarpa, Giuseppe Emmi ∗, Michele De CarliFT – Department of Applied Physics, University of Padua, Via Venezia 1, 35131 Padova, Italy

r t i c l e i n f o

rticle history:eceived 31 October 2011ccepted 12 December 2011

eywords:eat pumphillernergy

a b s t r a c t

HVAC plant designers and energy auditors often face the problem to calculate the performance of heatpumps under various boundary conditions. In this paper a model aimed at that purpose is presented. Inparticular, the model presented is aimed at the simulation of vapor compression based heat pumps orchillers driven by volumetric compressors. It is a numerical model tracing a reference thermodynamicinverse cycle consistent with the specific heat pump or chiller under the requested boundary conditions.The input data necessary are few and easy-to-find, especially if compared with the other simulationmodels proposed in literature. The proposed simplified model makes it possible to use catalog data in

OPecondary fluid temperature

order to get reliable results. Even if the amount of input data required is low, the numerical model showeda good accuracy (within 10%) contrasted against performance declared by manufacturers. Moreover, themodel has low sensitivity to user assumptions so it is valid also for the prediction of the performance in oldHVAC plants. Moreover, this numerical model is fast and suitable for integration within building energysimulation tools. The present model does not take into account air dehumidification at the evaporatornor defrost cycles, whose implementation is currently in progress.

. Introduction

The performance of heat pumps and chillers is strongly influ-nced by boundary conditions, that may be very different fromhe ones used to rate nominal performances, i.e. to determineatalog specifications. Hence, relevant differences between cat-log specifications and performance in real applications mayake place. As a consequence, it is desirable to predict theerformance of heat pumps and chillers under real applica-ion boundary conditions, especially in case of energy auditingnd certification, tailored design or innovative system evalua-ions.

In particular, the performance of heat pumps and chillers mainlyary with the following parameters:

Internal and external secondary fluid mass flow rates, mSF:Int andmSF:Ext

Internal and external secondary fluid inlet temperatures, �SF:Int,Inand �SF:Ext,InThermal capacity requested at the user side, QInt,X

∗ Corresponding author. Tel.: +39 049 827 6884; fax: +39 049 827 6896.E-mail addresses: massimiliano.scarpa@unipd.it (M. Scarpa),

iuseppe.emmi@unipd.it (G. Emmi), michele.decarli@unipd.it (M. De Carli).

378-7788/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.enbuild.2011.12.011

© 2011 Elsevier B.V. All rights reserved.

Of course, the effects of these parameters on the performance ofheat pumps and chillers depend on the operation mode (i.e. heatingor cooling).

In the present document, for the sake of simplicity, heat pumpsand chillers are referred by the general expression “heat pump”,in agreement with the hydraulic analogy, both in heating and incooling performances. Usually, the ratio QInt/QEl,Tot , where QEl,Tot

is the heat pump total electrical consumption, is named COP (coef-ficient of performance), when heating situation is considered, orEER (energy efficiency ratio), when the cooling mode is considered.In the present document, the symbol COP refers to ratio QInt/QEl,Tot

in any operation mode, indeed.The model presented in this paper is used to predict heat pump

performance both at full load and at part load running mode, butthe validation under part load conditions is still in progress andwill be edited in a following paper, thus it is not contained in thepresent work. As a consequence the performance in this paper isintended under full load running mode.

Different kinds of models are available for the prediction ofheat pump performance. Many different approaches were used,from mere curve-fit approximation models to single-componentdetailed simulation. According with Hamilton and Miller [1], a

range of different types of models may be defined: from equation-fitmodels (called “functional fit” models and based on a black-box modeling), to physical models (called “first principle” modelsand developed by the application of detailed models based on

412 M. Scarpa et al. / Energy and Bui

Nomenclature

SymbolsCOP coefficient of performancecp specific heat of fluid (J/(kg K))f factorh specific enthalpy (J/kg)I indexm mass flow rate (kg/s)Q power or heat flow (W)T temperature (K)v specific volume (m3/kg)V volumetric flow rate (m3/s)ε effectiveness� efficiency� temperature (◦C)

SubscriptsAux auxiliary devicesCompr compressorCond condenserCool coolingEl electricEvap evaporatorEx exergeticExt external sideHeat heatingIn inletInt internal sideIs isentropicMotor motorOut outletRF refrigerant fluidSF secondary fluidTot totalX part loadε effectiveness

Superscripts* ideal Carnot cycle

ti

•••

1

addtip

ait

h hourlyNom nominal

hermodynamics and fundamental heat and mass transfer relationsn each component constituting the system).

More generally, the following approaches may be considered:

Numerical approximation approachGeneral thermodynamic approachDetailed thermodynamic approach

.1. Numerical approximation

The models based on numerical approximation approaches usu-lly consist in equation-fit models. In brief, the heat pump isescribed as a black box whose operation is predicted by equationserived from maps of performance data. Hence the determina-ion of heat pump performance at specific boundary conditionss based on equation parameters derived from performance mapsreviously assumed.

Many models are based on this approach, that has somedvantages, such as the high accuracy in predictions, but evenmportant drawbacks, such as the need of many performance datao define accurate performance maps and consequent long time for

ldings 47 (2012) 411–420

performance map data input. Moreover, the prediction is not reli-able out of the data ranges used for the input of performance maps,for instance in case of different secondary fluid mass flow rates.The performance maps may be referred to the heat pump as awhole (system approach) or to each single part of the heat pump(component approach).

Stoecker and Jones [2] introduced an equation-fit modelbased on a component approach. It consists in the simultane-ous solution of a set of equations by successive substitutiontechnique. In this model the compressor electric power andrequired heat rejection are determined via an equation-fit approach(versus refrigerant fluid evaporation and condensation temper-atures), whereas the condenser heat transfer rate is assumedconstant and the evaporator heat transfer rate is a simplefunction of inlet water temperature and evaporation tempera-ture.

The same general approach is contained in [1], where anequation-fit steady state model is presented to predict the per-formance of each component of air-conditioning systems. In thismodel each component is represented by an energy balance and amass balance at steady state conditions, expressed via equation-fitbasing on refrigerant and secondary fluid temperatures, pressuresand qualities.

The model by Lash [3] is based on the equation-fit approach aswell. It is able to calculate heat pump performance starting frominlet air and water temperatures and mass flow rates, by equationsderived by least squares approximation from manufacturer’s per-formance data. Then Shenoy [4] modified the Lash model to takeinto account variable air flow rates and splitting into latent andsensible cooling capacities.

1.2. General thermodynamic approaches

Examples of general thermodynamic approaches come fromStandards, such as EN 15316-4-2 [5] and ISO/WD 13612-2 [6].They are based on correlations between ideal heat pumps andreal heat pumps. In a few words, these models define the behav-ior of a real heat pump as a function of the performance of areference heat pump. Usually, such a reference consists in theCarnot reversible heat pump and the relation is simple, such asthe one in Eq. (1), where multiplier �Ex is the so-called exergeticefficiency and resumes the decrease in COP consequent to irre-versibilities.

COP = f (COP∗) = �Ex · COP∗ (1)

Basing on this approach, as a first step in the calculation proce-dure, the COP of the real machine is compared with the referenceCOP (COP*), related to the reversible Carnot cycle, under ratedboundary conditions, thus obtaining �Ex:

�Ex = COP∗Nom

COPNom(2)

These models are very simple and show good accuracy whenvarious rated operating conditions are known.

1.3. Detailed thermodynamic approaches

These models are based on the detailed description of thethermodynamic phenomena taking place in each heat pump com-ponent. The components usually considered are evaporator andcondenser, compressor and expansion valve.

Some models, such as Fischer and Rice [7], Domanski and Didion

[8], Cecchini and Marchal [9], Stefanuk et al. [10], and Bourdouxheet al. [11] require a detailed description of the components, whereasother models, such as [12], adopt a parameter estimation method,in order to determine the internal parameters of the components

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M. Scarpa et al. / Energy an

y an optimization procedure via multi-variable objective func-ions.

The first set of models are difficult in use because they require aot of data, often out of HVAC planner availability, but ensure highccuracy in calculations, so that they can be used also for heat pumpesign.

The second set of models can be used via detailed manufactureratalogs, where performance under many boundary conditionsre specified, so that the input data procedure is not straightfor-ard.

Detailed thermodynamic approaches are usually implementedor specific kinds of components. For instance, as regards com-ressors, such models often focus on reciprocating compressors,ence the prediction of performance of heat pumps driven byifferent kinds of compressors may suffer intrinsic “systematic”rrors.

To get the order of magnitude for heat pump model accu-acy, the study by Damasceno et al. [13] is cited. There, threeodels are compared: the Fischer and Rice model, the Doman-

ki and Didion model, and the Nguyen and Goldschmidt model.he best accuracy in heating was shown by the model by Fis-her and Rice (accuracy on capacity: 6.5%; accuracy on COP:.5%), whereas the model by Domanski and Didion showed theest accuracy in cooling (accuracy on capacity: 3.0%; accuracyn COP: 7.5%). Therefore it is evident that even the most accu-ate models generally cannot score better than 5%, and that 10%an be considered as a good accuracy level. Moreover, the studyhowed that, even in the case of good agreement with perfor-ance experimental data, the programs were not able to calculate

efrigerant pressures and temperature distributions with similarccuracy.

The model described in the present paper predicts the per-ormance of heat pumps by tracing a reference thermodynamicnverse cycle, under the actual boundary conditions, taking intoccount the specific refrigerant fluid used in the heat pump. Forhis purpose detailed characteristics of the heat pump shoulde inputted, such as, at least, compressor isentropic efficiency,vaporator and condenser effectivenesses, and refrigerant fluid vol-metric flow rate. Since these data are usually not included in dataheets and catalogs available to HVAC plant designers and buildingnergy auditors, they are defined by the numerical model itself, thatnfers these characteristics starting from specifications reportedn catalogs. For this purpose the model adopts assumptions andpproximations typical in heat pump design. The consequent opti-al compromise between amount of input data and accuracy

onstitutes one of the most relevant results in the present paper.he model is implemented in Fortran and provides a good level ofccuracy, even more if the low amount of required input data isonsidered. The final results do not show a critical sensitivity toser-defined input data.

After the initial assessment of basic heat pump characteristicsdescribed in Section 2.1.1), the model traces the thermody-amic inverse cycle for the specific heat pump under full

oad with each specific set of boundary conditions (see Section.1.2).

The model is fast in calculations (about 3.5 s to calculate heatump performance for 8760 sets of boundary conditions, by a com-uter with the following specifications: Microprocessor – Intel2uo T7300 2.00 GHz; RAM – 2 GB; OS – MS Vista) and provides

eliable results with few input data for heat pumps equipped witholumetric compressors, so it is particularly suitable for the integra-ion into building energy simulation software for detailed energy

onsumption prediction. The current release of the model cannotake properly into account air dehumidification and defrost, thatre included in the next model upgrade, currently under develop-ent.

ldings 47 (2012) 411–420 413

2. Methods

2.1. Description of the model

The present model is able to estimate heat pump performance,in terms of COP, user side and ambient side heat flow rates, andelectrical power consumption, under boundary conditions far dif-ferent from the nominal ones. For this purpose the model startsfrom inputted catalog data to determine the basic characteristics ofthe heat pump. This part of the simulation constitutes the first cal-culation phase, when the parameters to be used in the next hourlycalculations are achieved. The prediction of performance at specificboundary conditions constitutes the second calculation phase. Forthis reason the description of the model is split into 2 sub-sections:

- First calculation phase: determination of the basic heat pumpparameters aimed at full load performance calculation, shownin Section 2.1.1

- Second calculation phase: calculation of heat pump full loadperformance at inputted hourly boundary conditions, shown inSection 2.1.2.

2.1.1. Determination of the basic parameters of the specific heatpump

The model requires the following basic catalog data, from whichthe main parameters of the heat pump can be inferred:

• Secondary fluids (options: “Water–Water”, “Water–Air”,“Air–Water”, or “Air–Air”).

• Refrigerant fluid (options: “R134a”, “R407C”, or “R410A”).• Rated coefficients of performance (typically under nominal

boundary conditions), for heating mode and/or for cooling mode(COPNom,Heat and COPNom,Cool).

• Rated internal thermal capacities (typically under nominalboundary conditions), for heating mode and/or for cooling mode(Q Nom,Heat

Int and Q Nom,CoolInt ).

• Rated electric power consumed by the auxiliary components(typically under nominal boundary conditions), for heating modeand/or for cooling mode (Q Nom,Heat

Auxiland Q Nom,Cool

Auxil).

• Total efficiency of the electric motor driving the compressor(�Motor).

• Temperatures of the secondary fluids at the inlet and outlet ofthe user side and ambient side heat exchangers (evaporator andcondenser), at nominal conditions: �Nom,Heat

SF:Int,In , �Nom,HeatSF:Int,Out , �Nom,Heat

SF:Ext,In ,

�Nom,HeatSF:Ext,Out , �Nom,Cool

SF:Int,In , �Nom,CoolSF:Int,Out , �Nom,Cool

SF:Ext,In , and �Nom,CoolSF:Ext,Out .

• Effectiveness index of the heat pump under examination, Iε.This parameter is a user-defined input used to qualify thethermal effectiveness of the evaporator and condenser. The pos-sible values range from 0 (low effectiveness, hence lower heatexchanger performance) to 10 (high effectiveness, hence higherheat exchanger performance).

At first, the numerical model starts from the inputs abovementioned to calculate the basic parameters concerning the maincomponents of the heat pump. The calculation procedure is sum-marized below and is performed for each operation mode (heatingand cooling):

(1) Computation of the power applied to the cycle by the compres-sor, at nominal conditions:(

Q Nom)

Q NomCompr = Int

COPNom− Q Nom

Aux · �Motor (3)

(2) Calculation of the mass flow rates of the secondary fluids atthe user- and ambient-side heat exchangers, basing on declared

414 M. Scarpa et al. / Energy and Buildings 47 (2012) 411–420

Table 1Ranges defined for temperature differences between refrigerant fluid and secondary fluids, at condenser and evaporator, for heating and cooling cases.

Kind of temperature difference Air Water

Min �� (◦C) Max �� (◦C) Min �� (◦C) Max �� (◦C)

�Nom,CoolSF:Int

− �Nom,CoolRF:Int

11.0 20.0 4.0 8.0�Nom,Cool

RF:Ext− �Nom,Cool

RF:Ext6.0 20.0 5.0 12.0

�Nom,CoolSF:Ext

− �Nom,CoolRF:Ext

6.0 15.0 5.0 12.0

(

(

(

(

side) secondary fluid (mhSF:Int and �h

SF:Int,In);• Running mode (cooling or heating);• Electrical power consumed by the auxiliary components (Q h

Aux).

�Nom,CoolRF:Int

− �Nom,CoolSF:Int

18.0

With �NomSF:Int

=�Nom

SF:Int,In+�Nom

SF:Int,Out2 and �Nom

SF:Ext=

�NomSF:Ext,In

+�NomSF:Ext,Out

2

capacities, on Q NomCompr , and on declared inlet/outlet temperatures

of the secondary fluids at evaporator and condenser:

mNomSF:Int = Q Nom

Int

cp,SF:Int · |�NomSF:Int,Out − �Nom

SF:Int,In| (4)

and

mNomSF:Ext = Q Nom

Ext

cp,SF:Ext · |�NomSF:Ext,Out − �Nom

SF:Ext,In|(5)

3) Calculation of the evaporation and condensation temperatures.Depending on the kind of heat pump and on the operationmode (heating or cooling), the model chooses a range of designtemperature differences between the refrigerant fluid and thesecondary fluids, according with Table 1, that is based on tem-perature differences used in typical evaporator and condenserdesign.

Then the effectiveness index is used to set the relatedtemperature differences at evaporator and condenser, via inter-polation. For instance, value 10 makes the software to assignthe lowest values of the temperature differences betweenthe refrigerant fluid and the secondary fluids, whereas value0 implies the use of the worst temperature differences. Asa consequence, the software interpolates between the mini-mum value of the range and the maximum one, for each heatexchanger and for each operation mode (heating or cooling).This way the condensation and the evaporation temperaturesof the refrigerant fluid are estimated under nominal boundaryconditions.

4) Calculation of the thermal effectivenesses of evaporator andcondenser, for each running mode:

εInt =|�Nom

SF:Int,In − �NomSF:Int,Out |

|�NomSF:Int,In − �Nom

RF:Int |(6)

and

εExt =|�Nom

SF:Ext,In − �NomSF:Ext,Out |

|�NomSF:Ext,In − �Nom

RF:Ext |(7)

For this purpose the refrigerant fluid is assumed to perform anisothermal process inside the heat exchangers; this hypothesisis considered acceptable, since the heat flows associated to pureevaporation and pure condensation represent the main fractionof the total heat transferred at the evaporator and the condenserrespectively.

5) Calculation of the reference points of the nominal thermo-dynamic inverse cycle, basing on the previously computedevaporation and condensation temperatures and using thethermo-physical properties of the specific refrigerant fluid. Thereference points of the cycle are shown in Fig. 1.

6) Calculation of the refrigerant fluid volume flow rate:

V = mNomRF · vNom

2 =Q Nom

SF:Evap

hNom2 − hNom

7

· vNom2 (8)

27.0 4.0 8.0

This volume flow rate is assumed constant in any operatingcondition, since the present model is aimed at the descriptionof the thermal behavior of heat pumps driven by volumetriccompressors.

(7) Calculation of enthalpy at reference point 3:

hNom3 = hNom

2 +Q Nom

Compr

mNomRF

(9)

(8) Determination of the isentropic efficiency of the compressor attest conditions:

�NomIs = mNom

RF · (hNom3i

− hNom2 )

Q NomCompr

(10)

This way every basic parameter of the machine is calculated attest conditions. These parameters are then used for the estimationof the heat pump performance at full load conditions.

2.1.2. Calculation of heat pump full load performance at inputtedhourly boundary conditions

The previously calculated parameters are used to predict thebehavior of the specific heat pump under actual boundary condi-tions. To characterize each boundary condition (for instance theboundary condition assumed to be acting during a particular hour“h” of the year), the present software needs the following inputs:

• Mass flow rate and inlet temperature of the external side (ambi-ent side) secondary fluid (mh

SF:Ext and �hSF:Ext,In);

• Mass flow rate and inlet temperature of the internal side (user

Fig. 1. Main points of the reference cycle.

M. Scarpa et al. / Energy and Buildings 47 (2012) 411–420 415

General da ta:• Secondar y fluids• Refrigerant flui d• Total efficiency of the electric motor drivin g thecompress or• Effec� veness index

Performances rated under no minal bound ary cond i�ons:• Coefficient of performan ce• Th ermal ca pacity• El ectric power con sumed by the auxil iary compon ents• Temperatures of the second ary fluid at the inlet an doutlet of the user side heat exc hanger• Temperatures of the second ary fluid at the inlet an doutlet of the ambi ent side heat exchanger

Input data

Hourly dat a:• Mass flo w rate and inlet temperature of user -side second ary fluid• Mass flo w rate and inlet temperature ofambient-side secondar y flui d• El ectric po wer consumed by the au xilia rydevic es, if different from the one rated und ernominal boundar y condi �on s• Runnin g mode (h ea�ng or coolin g)

Input data

General data:• Thermal effec�veness of the user -side heat exchanger• Thermal effec�veness of the ambi ent-side heat exchanger• Refrigerant flu id volume flo w rate• Isentropic efficiency of the compress or

Performances rated und er nominal boundar y condi �on s:• Mass flo w rates of the secondar y flu ids

Output data

Hou rly data:• Maximum thermal capacity• CO P• Outlet tempe rat ures of the second ary flui ds

Output data

PHASE 1

PHASE 2

e of

tfds

sdactd

(

(

TM

Fig. 2. General schem

In order to estimate the COP at the imposed boundary condi-ions, the present model assumes constant thermal effectivenessesor both the evaporator and the condenser, whereas the user canecide whether the isentropic efficiency must be maintained con-tant or must be varied by a user-defined function..

At this point, the software performs an iterative process: theoftware changes the thermal capacities at evaporator and con-enser (and hence the evaporation and condensation temperaturesnd the rest of points in the reference thermodynamic inverseycle) until the global energy balance is fulfilled, consistently withhe thermo-physical properties of the refrigerant fluid. More inetail, the main steps of the calculation are summarized as follows:

1) At first, the model assumes the nominal thermal capacities as

starting values of the heat flows transferred at the condenserand the evaporator.

2) Based on such thermal powers, and assuming constant effec-tivenesses of the heat exchangers, the model calculates the

able 2ain parameters and performance under nominal conditions for the heat pumps conside

Type ofmachine

Model Refrigerantfluid

Heating

Q NomInt

(kW) COP �hSF:Ext,In

/�hSF:Ext,Out

(◦C)/(◦C)

AW

A R410A 9.0 3.90 2/–

B R410A 5.8 4.24 7/–

C R407C 29.9 3.19 7/–

D R410A 41.0 2.93 7/–

WW

E R410A 8.6 4.10 12/7

F R407C 32.1 3.41 12/7

G R410A 50.5 3.92 12/7

H R410A 18.7 3.40 12/7

model input/output.

condensation and evaporation temperatures of the workingfluid:

�hRF:Cond = Q h

Cond

mhSF:Cond

· Cp,SF:Cond · εCond

+ �hSF:Cond,In (11)

�hRF:Evap = �h

SF:Evap,In −Q h

Evap

mhSF:Evap · Cp,SF:Evap · εEvap

(12)

(3) Based on the previously determined parameters of the machine,the whole thermodynamic inverse cycle can be traced, consis-tently with the first principle of thermodynamics.

(4) Then, the software compares the thermal powers transferred bythe current thermodynamic cycle through both the evaporatorand the condenser with the ones assumed at the beginning of

the current iteration. If the difference between those thermalpowers is within a predefined tolerance (in the case of thesesimulations: 1%), then the process stops and the iteration loop isnot performed any longer. Otherwise, the process begins a new

red in the validation (AW, Air–Water; WW, Water–Water).

Cooling

�hSF:Int,In

/�hSF:Int,Out

(◦C)/(◦C)Q Nom

Int(kW) COP �h

SF:Ext,In/�h

SF:Ext,Out(◦C)/(◦C)

�hSF:Int,In

/�hSF:Int,Out

(◦C)/(◦C)

30/35 8.6 3.12 27/– 12/730/35 7.0 3.66 35/– 23/1840/45 25.0 2.81 35/– 12/740/45 37.0 2.64 35/– 12/7

30/35 10.5 5.00 30/35 12/740/45 27.2 3.61 30/35 12/740/45 43.4 4.25 30/35 12/735/40 20.9 4.35 30/35 12/7

416 M. Scarpa et al. / Energy and Buildings 47 (2012) 411–420

ba

dc

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Sim

ulat

edCO

P[-

]

Declared COP [-]

AW - He a�ng

ABCD

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Sim

ulat

edCO

P[-

]

Declared COP [-]

AW - Coo ling

ABCD

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Sim

ulat

edCO

P[-

]

Declared COP [-]

WW - He a�ng

EFGH

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Sim

ulat

edCO

P[-

]

Declared CO P [-]

WW - Coo ling

EFGH

Fig. 3. COP: comparison between declared and calculated values: Air–Water in heating mode (a), Air–Water in cooling mode (b), Water–Water in heating mode (c), andWater–Water in cooling mode (d).

Table 3Number of simulations executed for each heat pump model (AW, Air–Water; WW, Water–Water).

Type of machine AW WW Total

Model A B C D Subtotal E F G H Subtotal

fl

e

TA

Number of simulationsHeating 11 16 20 20 67

Cooling 4 8 28 24 64

iteration, setting the just calculated condenser and evaporatorheat flows as starting values and performing the iteration fromstep 2.

At the end of the iterative process, the user side and ambient heatows and the coefficient of performance at full load are obtained.

To sum up, the general flow and main input/output variables forach calculation phase are summarized in Fig. 2.

able 4mount of validation points within 10% accuracy.

Secondary fluids AW

Model A B C D Subtotal

HeatingAmount of points 11 16 20 20 67

Amount of pointswithin 10% accuracy

9 (82%) 9 (56%) 15 (75%) 20 (100%) 53 (79%)

CoolingAmount of points 4 8 28 24 64

Amount of pointswithin 10% accuracy

2 (50%) 3 (38%) 28 (100%) 24 (100%) 57 (89%)

21 18 30 18 87 15418 15 15 15 63 127

2.2. Validation

The model was validated against detailed technical datadeclared by European heat pump manufacturers. The collected

technical data consisted in general technical parameters, perfor-mance rated under nominal conditions (usually according withStandard EN 14511 [14–17]), and performance declared under var-ious boundary conditions.

WW Total

E F G H Subtotal

21 18 30 18 87 15414 (67%) 18 (100%) 30 (100%) 18 (100%) 80 (92%) 133 (86%)

18 15 15 15 63 12713 (72%) 15 (100%) 15 (100%) 15 (100%) 58 (92%) 115 (91%)

M. Scarpa et al. / Energy and Buildings 47 (2012) 411–420 417

0

5

10

15

20

25

30

35

40

45

50

…÷

-20

-20

÷-1

5

-15

÷-1

0

- 10

÷-0

5

-05

÷00

00÷

05

05÷

10

10÷

15

15÷

20

20÷

…

Rela

�ve

Freq

uenc

y[%

]

Err or Range [% ]

AW - Hea�ng

0

5

10

15

20

25

30

35

40

45

50

…÷

-20

-20

÷-1

5

-15

÷-1

0

- 10

÷-0

5

-05

÷00

00÷

05

05÷

10

10÷

15

15÷

20

20÷

…

Rela

�ve

Freq

uenc

y[%

]

Err or Range [% ]

AW - Cooli ng

0

5

10

15

20

25

30

35

40

45

50

…÷

-20

-20

÷-1

5

-15

÷-1

0

- 10

÷- 0

5

-05

÷00

00÷

05

05÷

10

10÷

15

15÷

20

20÷

…

Rela

�ve

Freq

uenc

y[%

]

Err or Range [%]

WW - Hea�ng

0

5

10

15

20

25

30

35

40

45

50

…÷

-20

-20

÷-1

5

-15

÷-1

0

-10

÷-0

5

-05

÷00

00÷

05

05÷

10

10÷

15

15÷

20

20÷

…

Rela

�ve

Freq

uenc

y[%

]

Error Range [% ]

WW - Cooling

a b

c d

F followW

pc

thrmvfmhcIt

3

3

mda

artdtuo

ig. 4. Relative frequencies for calculation accuracy in case of heat pumps in theater–Water in heating mode (c), and Water–Water in cooling mode (d).

The validation regarded Air–Water and Water–Water heatumps whose main parameters and performance under nominalonditions are shown in Table 2.

The model was validated both in heating and in cooling opera-ion modes. The simulations did not regard Water–Air and Air–Aireat pumps because they will be considered in a next step of theesearch activity, after the conclusion of the validation on dehu-idification performance and frost/defrost cycles. Moreover, the

alidation in heating mode for Air–Water heat pumps is not per-ormed at low ambient temperatures because the defrost forecast

odel is currently under development. Thus the temperature andumidity ranges used in the validation were chosen in order to limitases in which heat pumps work under such boundary conditions.n particular, the air source temperatures in heating mode are downo 2 ◦C.

. Results and discussion

.1. Accuracy in the evaluation of COP and maximum capacities

The overall amount of simulations executed for each heat pumpodel are summarized in Table 3. The correspondences between

eclared and predicted COP are summarized in Fig. 3, for Air–Waternd Water–Water heat pumps respectively.

Fig. 3 shows that the in most of the validation points the modelgrees with declared values within ±10%. The authors consider thisesult appreciable. As a matter of fact, that is the accuracy encoun-ered by Damasceno et al. [13] in the validation of much more

etailed models as well. And it is even more interesting to notehat such a result is achieved using just catalog parameters and anser-defined index (the effectiveness index), with no exploitationf additional features present in the model and aimed to improve

ing conditions: Air–Water in heating mode (a), Air–Water in cooling mode (b),

the model accuracy, such as the use of typical correlations for thedetermination of compressor efficiency versus the pressure ratio.

Table 4 shows that an average of 79% of the validation points iswithin 10% accuracy in case of Air–Water heat pumps in heatingmode. That is the worst model accuracy encountered in this set ofvalidations, because of the occurrence of some validation pointswithin defrost boundary conditions. In fact, the model accuracy isfar higher when referring to Water–Water heat pumps in heatingmode (92%), and in case of heat pumps used in cooling mode (89%for Air–Water and 92% for Water–Water). Moreover, Fig. 4 showsthat the model has no general tendency towards over- or under-estimation.

Anyway, the accuracy in the calculation of COP is not sufficientto determine whether the model is able to predict the performanceof heat pumps. As a matter of fact, the heat pump performancestrongly depends on part load control, that is defined startingfrom the ratio between the target capacity and the maximumheating/cooling capacity at the actual boundary conditions. As aconsequence, it is important to achieve high accuracy in the calcu-lation of maximum heating/cooling capacities, in order to achievereliable predictions of performances at part load conditions.

For this purpose the same heat pumps and boundary conditionswere used to validate the model in the calculation of the maximumheating/cooling capacities. The results of the comparison are sum-marized in Fig. 5. As can be seen, the model accuracy in maximumcapacity calculation is higher than in case of COP calculation.

The validation results have been summarized via a statisticalanalysis based on the estimation of the coefficient of determination,

R2. The R2 values are calculated for COP and maximum capacities,in heating and in cooling modes, and are shown in Tables 5 and 6.

Tables 5 and 6 show a good correlation between declared andcalculated values, with the best results in case of Water–Water heat

418 M. Scarpa et al. / Energy and Buildings 47 (2012) 411–420

ba

0

10

20

30

40

50

60

0 10 20 30 40 50 60

Sim

ulat

ed C

apac

ity

[kW

]

Declared Capacity [k W]

AW and WW - Hea�ng

ABCDEFGH

0

10

20

30

40

50

60

0 10 20 30 40 50 60

Sim

ulat

ed C

apac

ity

[kW

]

Declared Capacity [k W]

AW and WW - Cooling

ABCDEFGH

Fig. 5. Validation of the model in maximum capacity calculation in heating (a) and in cooling (b) modes.

Table 5Coefficients of determination R2 in COP predictions.

COP

Heating Cooling

AW WW AW WW

Declaredvalues

Calculatedvalues

Declaredvalues

Calculatedvalues

Declaredvalues

Calculatedvalues

Declaredvalues

Calculatedvalues

Mean 3.79 3.65 4.07 4.12 2.81 2.82 3.14 3.14.10

pp

auraomibno

cepiiho

TC

Variance 1.01 0.56 1.10 1Covariance 0.72 1.05

R2 0.92 0.92

umps, especially in cooling operation mode, confirming the resultsresented in, Table 4 and according with Damasceno et al. [13].

The results above shown were achieved with no exploitation ofdditional features available in the developed model, such as these of isentropic efficiency adjustment via user-defined curves. Asegards this specific feature, Fig. 6 shows the improvements achiev-ble via the application of isentropic efficiency adjustments basedn a typical compressor efficiency curve, applied to heat pumpodel B. In particular, the efficiency curve used in this calculation

s contained in [2] and refers to a rotary screw compressor withuilt-in volume ratio equal to 3.0. The curve contained in [2] wasormalized and referred to the isentropic efficiency instead to theverall compression efficiency. It is shown in Fig. 7.

From Fig. 6 it is clear that the use of typical isentropic efficiencyorrection curves may help to significantly improve the final result,ven if the correction curves are not referred to the specific com-ressor present in the heat pump. That is an interesting result, since

t allows the user to define a set of typical correction curves depend-ng on compressor kind and size, without specific input for eacheat pump, since manufacturer and model of the compressor areften out of data available to HVAC planners and energy auditors.

able 6oefficients of determination R2 in maximum capacity predictions.

Maximum capacity

Heating

Air–Water Water–Water

Declaredvalues

Calculatedvalues

Declaredvalues

Calcuvalue

Mean (kW) 26.4 25.8 34.6 33.6Variance (kW2) 237 218 359 336

Covariance (kW2) 223 342

R2 0.97 0.97

0.36 0.34 1.16 1.170.33 1.090.88 0.95

3.2. Sensitivity analysis

As shown in the previous results of the validation, the model isreliable and considerably accurate, but the influence of user deci-sions and assumptions must be determined. In particular, the useris asked to input Iε, i.e. the index that qualifies the thermal effec-tiveness of the evaporator and condenser heat exchangers. As aconsequence, the influence of such an assumption is analyzed inthis sub-section.

In Fig. 8 an example of COP values for model D with two differentassumptions for Iε (i.e. 4 and 10) are shown.

This figure shows significant improvements in results for highCOP values, whereas at low COP values the differences are far lower.Hence the user assumption about Iε value is critical only for highvalues of COP. Such values are encountered with boundary condi-tions typical of midseason operation, when the heat loads are farlower than in full heating and cooling conditions. As a consequence,

the influence of Iε assumption on season energy consumption forheating and cooling is not critical.

Table 7 shows the percentage of COP values within 10% accuracyfor each model, consequent to different assumptions on Iε. It can be

Cooling

Air–Water Water–Water

lateds

Declaredvalues

Calculatedvalues

Declaredvalues

Calculatedvalues

26.4 26.6 22.2 22.9132 128 161 162

127 1590.96 0.96

M. Scarpa et al. / Energy and Buildings 47 (2012) 411–420 419

Table 7Percentage of validation points within 10% accuracy, depending on the value of the effectiveness index (Iε = 4, Iε = 6, Iε = 8 and Iε = 10).

Secondary fluids AW (%) WW (%) Total (%)

Model A B C D Subtotal E F G H Subtotal

HeatingIε = 4 45 50 55 85 61 62 56 90 83 75 69Iε = 6 45 50 60 90 64 71 56 100 83 80 73Iε = 8 45 50 75 95 70 71 61 100 100 85 79Iε = 10 82 56 75 100 79 67 100 100 100 92 86CoolingIε = 4 100 88 79 92 86 61 73 80 80 73 80Iε = 6 100 100 93 96 95 67 87 87 87 81 88Iε = 8 75 100 96 100 97 83 87 100 93 90 94Iε = 10 50 38 100 100 89 72 100 100 100 92 91GlobalIε = 4 60 63 69 89 73 62 64 87 82 74 74Iε = 6 60 67 79 93 79 69 70 96 85 81 80Iε = 8 53 67 88 98 83 77 73 100 97 87 85Iε = 10 73 50 90 100 84 69 100 100 100 92 88

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

Calc

ulat

edCO

P[-

]

Declared CO P [-]

COP - w/- isent ropic efficiency ad justment COP - w/o isent ropic efficiency adj ustment

Fe

sIsATTra

ar

F

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Sim

ulat

edCO

P[-

]

Declared CO P [-]

Model D - Comparison of COP

Ie = 4Ie = 10

ig. 6. Comparison of COP calculated without and with correction of isentropicfficiency versus declared COP values.

een, the most accurate results are achieved with the assumptionsε = 8 and Iε = 10. The results for different values of Iε show someudden variation, for instance in heating operation mode for model, where sudden increase in accuracy is achieved when using Iε = 10.hat is due to the position of some results, near the lines of ±10%.hus even a low increase in accuracy makes it possible to shift someesults within the region of ±10% accuracy assumed by the authors

s reference accuracy.

After the results of Table 7, considered that the best results arechieved with Iε ≥ 8, the next release of the model will adopt nar-ower ranges of temperature differences between the refrigerant

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 1 2 3 4 5 6 7 8

Isentr

opic

effic

iency [-]

Pressure ratio [ -]

ig. 7. Normalized typical curve for compressor isentropic efficiency correction [2].

Fig. 8. Comparison of COP values for AW model D: calculated values (with Iε = 4 andIε = 10) versus declared values.

fluid and secondary fluids than the ones shown in Table 1. That willmake the choice of the values of Iε less critical and will prevent fromwrong user assumptions.

4. Conclusions

This paper presents a new model for the prediction of energyperformance of heat pumps and chillers, aimed to achieve goodaccuracy results by the use of catalog data. The model wasvalidated with Water–Water and Air–Water heat pumps andchillers.

The validation showed that, despite the low amount of inputparameters needed, the model is able to predict the performancewithin 10% in accuracy, the same accuracy range found in previ-ous literature for more complex models. Better accuracy can beachieved via the use of typical curves for isentropic efficiency cor-rection, with no detailed reference to efficiency curves for eachspecific compressor. The model shows a low sensitivity to userassumptions, making the model robust and easy to use.

Moreover, the program is extremely fast in calculations and isable to predict the performance of heat pumps in heating and cool-ing modes even when boundary conditions, in terms of mass flowrates and secondary fluid inlet temperatures are far from ratednominal conditions.

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