dynamic modeling of gas engine driven heat pump system in cooling mode

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Energy xxx (2013) 1e14

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Energy

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Dynamic modeling of Gas Engine driven Heat Pump system in coolingmode

Sepehr Sanaye a,*, Mahmood Chahartaghi b, Hesam Asgari a

a Energy Systems Improvement Laboratory (ESIL), Department of Mechanical Engineering, Iran University of Science and Technology (IUST), Narmak,Tehran 16844, IranbDepartment of Mechanical Engineering, Shahrood University of Technology (SUT), Shahrood, Iran

a r t i c l e i n f o

Article history:Received 25 June 2012Received in revised form3 January 2013Accepted 10 March 2013Available online xxx

Keywords:Gas Engine driven Heat PumpVapor compression refrigeration cycleDynamic modelingTransient heat transferGas engine

* Corresponding author. Tel./fax: þ98 21 77240192.E-mail address: [email protected] (S. Sanaye).

0360-5442/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.energy.2013.03.074

Please cite this article in press as: Sanaye S,http://dx.doi.org/10.1016/j.energy.2013.03.07

a b s t r a c t

The Gas Engine driven Heat Pump (GEHP) operating cycle is a vapor compression refrigeration typewhich includes compressor, condenser, expansion valve, evaporator, and a gas engine to drive thecompressor. In the present work, the dynamic modeling of GEHP system during startup in cooling modeis performed and variation of evaporator and condenser temperatures, shaft power consumed bycompressor, engine fuel consumption, and primary energy ratio of system were determined at varioustime steps. The dynamic modeling included transient heat transfer equations for condenser and evap-orator for computing the evaporator and condenser temperatures. These equations were solved usingRungeeKutta method. In order to validate dynamic modeling, the modeling output results werecompared with the empirical results obtained for a GEHP system. The comparison of modeling resultsand the experimental measured values for various amounts of evaporator and condenser temperatures,cooling capacity, gas engine fuel consumption, shaft power consumed by compressor and primary energyratio of system showed average difference values of 1.73 �C, 1.26 �C, 8.05%, 9.51%, 9.27% and 7.15%respectively.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Gas Engine driven Heat Pump (GEHP) is a significant technologyin providing heating and cooling services. The modeling of GEHP isessential to investigate the proper operation of these systems aswell as to determine their optimum operating conditions. Heatpumps usually consist of two indoor and outdoor heat exchangers.In heating mode, the indoor heat exchanger operates as acondenser and the outdoor heat exchanger operates as an evapo-rator. In cooling mode, the indoor and outdoor heat exchangersswitch their task and play the role of an evaporator and acondenser, respectively. The operating mode switches betweenheating and cooling modes by a reversing valve [1].

Heat pumps are categorized into Electric driven (EHP) and GasEngine driven (GEHP) Heat Pumps [2].

Gas engine heat pumps are used in many modern and industrialcountries in recent years. By considering the capability of GEHPsystems to work in partial load operation, this equipment mayreduce the operating cost of heating and cooling tasks [3,4].

All rights reserved.

et al., Dynamic modeling of G4

Hepbasli et al. [5] reviewed the gas engine heat pump systemsfor residential and commercial applications. A comprehensivehistory of GEHPs and their applications was presented in theirstudy. They modeled the GEHP system using mass and energyconservation equations and predicted the heat exchangers capac-ities and system coefficient of performance. Welsby et al. [6]studied steady state performance of engine driven water-to-waterheat pump. In their work an optimum value for superheating therefrigerant in suction side was proposed. Furthermore the effect ofengine speed on the cooling and heating loads was investigated.

A gas heat pump generally consists of two main parts: heatpump system and a gas engine [2]. The operating cycle of a heatpump system is the same as that for a vapor compression refrig-eration cycle with the main parts of evaporator, compressor,condenser, and expansion valve. An internal combustion gas engineis used to drive the compressor.

Cabello et al. [7] presented a steady model for a vaporcompression refrigeration system using theoretical and empiricalrelations. The refrigerant temperature at evaporator and condenser,and superheating degree at the evaporator outlet were consideredas input data. The refrigerant mass flow rate, evaporator coolingcapacity, compressor power consumption, and coefficient of per-formance (COP) of the cycle were considered as output data. Finally,

as Engine driven Heat Pump system in cooling mode, Energy (2013),

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Nomenclature

A area (m2)AF air to fuel ratio (�)C0 blowby factor (s�1)Cp specific heat at constant pressure (kJ kg�1 K�1)df fin outer diameter (m)dr tube outer diameter at fin root (m)D pipe diameter (m)F correction factor of cross-flowG mass velocity (kg m�2 s�1)h specific enthalpy (kJ kg�1)Hf fin height (m)k thermal conductivity (W m�1 K�1)K ratio of compressor to engine rotational speed (�)L tube length (m)LMTD logarithmic mean temperature difference (�C)M mass (kg)_m mass flow rate (kg s�1)nt number of tubes in a row (�)N total number of tubes (�)Ncomp compressor speed (rpm)P1 tube pitch in plane perpendicular to the flow (m)P2 tube pitch in the flow direction (m)P pressure (MPa)PER primary energy ratioPr Prandtl numberq heat per unit of mass (kJ kg�1)_Q heat transfer rate (kW)rc compression ratio of engine (�)R gas constant (kJ kg�1 K�1)R2 fraction of variance (�)RMS root mean squared (�)Re Reynolds number (�)s specific entropy (kJ kg�1 K�1)T temperature (�C or K)Teva,i initial evaporator temperature (�C)Tcon,i initial condenser temperature (�C)t time (s)U overall heat transfer coefficient (W m�2 K�1)v velocity (m s�1)vm mean velocity of two-phase refrigerant (m s�1)V volume (m3)_V volume flow rate (m3 s�1)w specific work (kJ kg�1)_W shaft power consumed by compressor (kW)x heat release function (�)xm vapor quality in two-phase region (�)

Greek symbolsa convection heat transfer coefficient (W/m2 K)g specific heat ratio (�)r density (kg/m3)h efficiency (%)m dynamic viscosity (N s m�2)s surface tension (N m�1)d fin thickness (m)q angle (rad)uge engine frequency (rad s�1)

Subscriptsa airbelt power transmissionc coolingcomp compressorcon condenserdis dischargeeva evaporatorfuel fuelge gas enginein input valuel liquidlo liquid onlyLHV lower heating valuem mean, mechanicalo output valuer refrigerants isentropicsc subcooledsh superheatsuc suctiont target valueth thermaltp two-phasev vapor

Numbers1 compressor inlet10 evaporator saturated vapor2 compressor outlet20 condenser saturated vapor3 condenser outlet30 condenser saturated liquid4 evaporator inlet(a,1) corresponding air at point 1

S. Sanaye et al. / Energy xxx (2013) 1e142

they validated their modeling results by comparison between themodel outputs and the empirical results.

Zhang et al. [8] presented a steady state model for a gas enginedriven air to water heat pump system in heatingmode of operation.In their analysis the thermodynamic models of gas engine andcompressor were expressed by using relations obtained fromexperimental data while their heat exchanger models were basedon the mass and energy conservation equations. Finally, the com-parison between the results of the modeling and experimental datawas performed.

Elgendy et al. [9] examined the thermal modeling of the gasengine driven heat pump in coolingmode. Their modeling includeda semi-empirical model for the scroll compressor, a correlation ofgas engine energy consumption as function of compressor power,

Please cite this article in press as: Sanaye S, et al., Dynamic modeling of Ghttp://dx.doi.org/10.1016/j.energy.2013.03.074

engine speed and ambient air temperature as well as modeling ofthe plate evaporator. The corresponding uncertainty values of theirmodeling results in estimating themain parameters such as coolingcapacity, gas engine energy consumption and primary energy ratiowere 7%, 5% and 6% respectively.

Sanaye and Chahartaghi [10] presented a steady state model forevaluating the performance of GEHP usingmain parameters such ascooling/heating capacity and gas engine rotational speed. In theirmodel, the system operating parameters were obtained with a trialand error scheme with guessing the evaporator and condenserpressures and applying conservation laws. The comparison ofmodeling results and the experimental data for various amounts ofsuction and discharge pressures, fuel consumption and coefficientof performance showed 3.4%, 4%, 6.7% and 7.2% average difference


S. Sanaye et al. / Energy xxx (2013) 1e14 3

percentage for cooling mode and 3.7%, 5.4%, 8.1% and 7.8% forheating mode respectively.

Elgendy and Schmidt [11] experimentally evaluated the effect ofseveral important factors (evaporator inlet water temperature,evaporator water volume flow rate, ambient air temperature, andengine speed) on the performance of a GEHP used for water cool-ing, and they concluded that by decreasing the evaporator inletwater temperature and increasing the engine rotational speed, theprimary energy ratio of the system decreased.

Elgendy et al. [12,13] also investigated the performance of aGEHP used for air conditioning and hot water supply. The perfor-mance characteristics of this system were expressed by the outletwater temperatures, total heating capacity, and the PER. The resultsshowed that through the use of gas engine heat recovery, the outletwater temperature of the systemvaries between 35 and 70 �C in theconsidered range of operating parameters.

In these studies the system operating parameters, their in-teractions and ways to increase the system PER or COP were sub-jects of interest. However, with variation of ambient temperature,cooling or heating loads change. The load change results in varia-tions of the engine speed and GEHP other operating parameters.This situation also happens in starting and shutting down operatingconditions as well. Therefore optimal and proper control of GEHP isimportant during these transient conditions and needs GEHP dy-namic modeling.

Chi and Didion [14] presented amodel for air source heat pumpsbased on the transient conservation equations of mass, energy, andmomentum. In their model, the system transient behavior duringstartup was studied in cooling mode, and the system operatingconditions and variation of heat exchanger capacities were inves-tigated. The dynamic behavior of expansion valve was not studiedin their model. Finally, the modeling results were validated byempirical testing output for an air source heat pump in coolingmode.

Salim et al. [15] described a simple algorithm to simulate thetransient behavior of a vapor compression heat pump. Individualmodels were developed for various components of the heat pumpsuch as compressor, evaporator, condenser and expansion valve.

Vargas and Parise [16] presented a mathematical model for aheat pump with variable speed compressor. The time-dependentdifferential equations were solved and the system performancewas modeled during the operation time period. The variations ofshaft power consumed by compressor, COP of the system, and thetemperatures of heat exchangers with timewere illustrated in theirpaper.

Browne and Bansal [17] presented a model to simulate the dy-namic operation of compression refrigeration systems includingchiller in a wide range of operating conditions. Their modelincluded the variations of heat transfer rates in heat exchangers.The compressor was assumed to reach the steady state conditionvery quickly. The model outputs including the system operatingparameters such as the shaft power consumed by compressor, COP,and the refrigerant conditions in the refrigeration cycle were pre-sented versus time.

Fu et al. [18] presented a dynamic model for air to water heatpumps. Ordinary differential equations based on the mass andenergy conservation equations were presented for all componentsversus time. Compressor and expansion valve were modeled in thesteady state condition, however the variations of refrigerant pres-sure and temperature, cooling and heating capacities, and shaftpower consumed by compressor versus time were investigated.Finally, the modeling results were validated with the empiricaltests.

Zhao and Zaheeruddin [19] presented a dynamic model forcompression refrigeration systems based on the mass and energy


conservation relations. All components including evaporator,compressor, condenser, and expansion valve were modeled. Thesystem operating characteristics including cooling capacity andcoefficient of performance were predicted. Furthermore the steadyoperation of the system including refrigerant mass flow rate,superheating degree at evaporator outlet, and compressor speedwas investigated. It was observed that the compressor operatingspeed and refrigerant mass flow rate reached their steady statevalues rapidly.

Llopis et al. [20] presented amathematical model of a shell-and-tube evaporator of a vapor compression refrigeration system. Theirmodel was based on mass and energy conservation equations forany type of evaporator and refrigerant. The model was validated ina wide range of operating conditions.

In GEHP systems, the shaft power consumed by compressor isprovided by an internal combustion gas engine, which is mainlymodeled based on Otto standard air assumption cycle to predict theexhaust gas temperature, engine output power, and thermal effi-ciency [21,22].

Somemodels presented the combustion process and cycle inputheat as a function of crank angle, combustion duration, advancedspark time, and thermal andmass losses from the cylinder chamber[23]. In these models, the pressure change in combustion chamber,engine output power, thermal losses in the cylinder, and the gasengine mixture mass in the combustion chamber were presentedbased on the crank angle.

In this paper, dynamic modeling of heat pump cycle was per-formed using thermodynamic and thermal characteristics of theexisting equipment as well as applying artificial neural network(ANN) and empirical relations. A model was also used to estimatethe gas engine power output in terms of crank angle. The energyequations were presented to compute the time variations ofevaporator and condenser temperatures. The time variations ofevaporator and condenser capacities, shaft power consumed bycompressor, engine fuel consumption, and PER of the heat pumpcycle were computed versus time from the system startup untilreaching the steady state condition using both heat pump and gasengine models simultaneously.

Some of the new points investigated in this paper are:

� Developing a dynamic model for GEHP with the capability ofpredicting the variation with time of operating characteristicsof GEHP cycle such as evaporator and condenser temperatures,refrigerant mass flow rate, cooling capacity of indoor heat ex-changers, compressor volumetric and isentropic efficiencies,and shaft power consumed by compressor.

� Investigating the engine geometric and operating parametersby applying a gas engine dynamic model which uses four or-dinary differential equations obtained from mass and energyconservation equations in terms of crank angle as the mainparameters. The time-dependent gas engine power and effi-ciency were obtained from this model.

� Investigating simultaneous operation of heat pump and gasengine systems linked by the compressor to compute the time-dependent values of PER and fuel consumption.

� Predicting the variation of engine speed with time duringstartup period until to reach the steady state condition by usingthree input parameters including cooling capacity as well ascompressor suction and discharge pressures using artificialneural network (ANN) method.

� Performing empirical tests to compare the modeling andexperimental results in dynamic operatingmode of the system,as well as to determine the system characteristics in steadystate conditions.

� Providing the uncertainty analysis for the empirical results.


air

condenser

compressor

evaporator

expansion valve (capillary tube)

air

1'

2′3′

Fig. 2. Circulation path of refrigerant and air in vapor compression refrigeration cycle.


2. Dynamic modeling of the gas engine heat pump cycle

A vapor compression refrigeration heat pump includes acompressor, condenser, expansion valve, and evaporator.

In cooling mode, the indoor heat exchanger acts as evaporatorand provides the required cooling load of the building. The maincomponents of heat pump cycle and their operation in coolingmode are shown in Fig. 1. The temperature and pressure sensors arealso indicated in this figure.

In cooling mode, the refrigerant flows through a four-way valveafter exiting the compressor. Then the refrigerant vapor enters theoutdoor heat exchanger, where it condenses. The liquid refrigerantevaporates in indoor heat exchanger after passing through expan-sion value.

The refrigerant circulating path in the refrigeration cycle and itscorresponding Tes diagram are shown in Figs. 2 and 3, respectively.

The presented model can predict and compute the refrigerantmass flow rate, shaft power consumed by compressor, variations ofevaporator and condenser temperature and heat transfer rates aswell as the PER of the cycle in various cooling loads. The followingassumptions were made in the presented model:

� The pipe wall temperature was uniform and the wall thermalresistance was neglected.

� The expansion process was assumed to occur with constantenthalpy.

� Thermal losses from pipes and heat exchangers wereneglected.

All components of heat pump cycle were modeled as follows toinvestigate the cycle operation.

2.1. Compressor

By assuming the adiabatic compression process, shaft powerconsumed ( _Wcomp) by compressor (scroll type) was estimatedfrom:

_Wcomp ¼ _mrwcomp ¼ _mrðh2 � h1Þ ¼ _mr

�h2s � h1

hs

�(1)

where _mr is the refrigerant (R407C) mass flow rate and hs is thecompressor isentropic efficiency.

The refrigerant mass flow rate is expressed as:

_mr ¼ hvr1VcompNcomp

60(2)

Indoor heat

exchanger

Outdoor

heat exchanger

GasEngine

air

air

Expansion Valve

Compressor

Reversing valve

Cooling mode

Refrigerant T, P sensors

1′

2′

Fig. 1. A schematic view of the operating cycle of gas engine heat pump.


where hv is the compressor volumetric efficiency, r1 is the densityof refrigerant at suction line and Vcomp and Ncomp are thecompressor swept volume and rotational speed respectively.

Ncomp in Eq. (2) can be estimated by computing Nge (knowing theK value defined as K ¼ Ncomp/Nge) using neural network analysis asexplained in Section 2.7.

For scroll compressor, the compressor volumetric efficiency wasobtained in terms of the pressure ratio for R407c refrigerant [24]:

hv ¼ 1:053� 0:028�PdisPsuc

�2:5 � Pdis

Psuc� 6:5 (3)

where Psuc and Pdis are the suction and discharge pressuresrespectively.

For scroll compressor, in the mentioned range of pressure ratio,hs was obtained from [24]:

hs ¼ B0 þ B1

�PdisPsuc

�þ B2

�PdisPsuc

�2

(4)

where B0, B1, B2 are the constant coefficients.By assuming no pressure drop in suction and discharge lines

then:

Psuc ¼ Peva (5)

Pdis ¼ Pcon (6)

where Peva and Pcon are the refrigerant pressure in evaporator andcondenser, respectively.

3'3

2s

41

2

1'

2'

Fig. 3. Tes diagram of vapor compression refrigeration cycle.



2.2. Condenser

By assuming the condenser as a finned tube heat exchangersubject to the air flow and the refrigerant flowing through the pipe(coil), the heat transfer rate in the condenser was computed usingLMTD model as:

_Qcon ¼ ðUAÞcon$ðLMTDÞcon (7)

where U is the overall heat transfer coefficient, A is the heatexchanger cross-sectional area in the direction of flow and LMTD isthe logarithmic mean temperature difference.

Considering the cross-flow arrangement for the heat exchangerin the presented model, the correction factor (F) should be used inestimating the heat transfer rate:

Q ¼ U$A$F$LMTD (8)

where F depends on the flow arrangement and geometric con-struction of heat exchanger. For phase change processes incondenser and evaporator, F z1 was assumed due to small regionsof superheating and subcooled sections [25].

In steady state mode, the condenser heat transfer rate wasestimated as:

_Qcon ¼ ðUAÞcon$ðLMTDÞcon ¼ _mrðh2 � h3Þ (9)

Generally, the condenser may be divided into three main sec-tions: superheat section, two-phase section, and subcooled section.Thus, heat transfer rate in condenser was obtained from:

_Qcon ¼ _Qcon;sh þ _Qcon;tp þ _Qcon;sc (10)

The indices of “sh”, “tp”, and “sc” refer to superheat, two-phase,and subcooled sections, respectively.

Heat transfer rates in the above-mentioned sections ofcondenser were obtained from:

_Qcon;sh ¼ ðUAÞcon;sh$ðLMTDÞcon;sh (11)

_Qcon;tp ¼ ðUAÞcon;tp$ðLMTDÞcon;tp (12)

_Qcon:sc ¼ ðUAÞcon;sc$ðLMTDÞcon;sc (13)

The following relations were used for logarithmic mean tem-perature difference (LMTD):

Superheat region:

ðLMTDÞcon;sh ¼�T2 � Ta;2

�� Tcon � Ta;20�

ln�

T2 � Ta;2Tcon � Ta;20

� (14)

where T2 is the refrigerant temperature at the condenser inlet(point 2 in Fig. 2), Tcon is the refrigerant mean temperature in two-phase section of condenser (condenser temperature), Ta,2 and Ta;20

are the condenser exit air temperatures at the corresponding points2 (superheat) and 20 (saturated vapor) of the refrigerant cycle.

Two-phase region:

ðLMTDÞcon;tp ¼�Tcon � Ta;20

�� Tcon � Ta;30�

ln�Tcon � Ta;20

Tcon � Ta;30

� (15)

where Ta;30 is the condenser inlet air temperature at the corre-sponding point 30 (saturated liquid) of the refrigerant cycle.


Subcooled region:

ðLMTDÞcon;sc ¼�Tcon � Ta;30

�� T3 � Ta;3�

ln�Tcon � Ta;30

T3 � Ta;3

� (16)

where T3 is the refrigerant temperature at the condenser outlet(point 3 in Fig. 2) and Ta,3 is the condenser inlet air temperature atthe corresponding point 3 (subcooled) of the refrigerant cycle.

The dynamic form of energy conservation law for condenser(two-phase region) is:

�MCp

�con;tp

dTcondt

¼ _mrðh20 � h30 Þ � ðUAÞcon;tp

�

0BBB@�Tcon � Ta;20

�� Tcon � Ta;30�

ln�Tcon � Ta;20

Tcon � Ta;30

�1CCCA

(17)

where (MCp)con,tp is the refrigerant mean heat capacity in two-phase region of the condenser.

2.2.1. Heat transfer coefficients2.2.1.1. Refrigerant side. For the single-phase regions (superheatand subcooled), DittuseBoelter relation was applied [26]:

a ¼�kD

�ð0:023ÞRe0:8Prn (18)

where a in Eq. (18) is the convection heat transfer coefficient and nis a constant number for condensation process (0.4 [26,27]). Rey-nolds number for refrigerant flow inside the pipe was alsocomputed from:

Re ¼ 4 _mmpD

(19)

The mean value for the two-phase heat transfer coefficient incondenser was obtained from [28,29]:

a ¼ alo

�59þ 2:04

Pr0:38

�(20)

where alo is the heat transfer coefficient for liquid only region(single-phase), as was computed from Eq. (18).

2.2.1.2. Air side. For air passing over the finned tube heatexchanger, the minimum air flow cross-section area (Amin) as wellas finned (Af), un-finned (Au), and the total (At) heat transfer surfacearea were estimated from the following relations [30]:

Amin ¼ ntL�P1 � dr �

2dHf

ðdþ sÞ

(21)

At ¼ Af þ Au ¼ NLpðsþ dÞ

�12

d2f � d2r

�þ df $dþ dr$s

(22)

where nt, N, L, P1, dr, df, d, Hf and s are the number of tubes in a row,total number of tubes, tube length, tube pitch in plane perpendic-ular to the flow, tube outer diameter at fin root, fin outer diameter,fin thickness, fin height and fin spacing respectively.

Reynolds number based on the maximum air velocity over thetube bundle was obtained from:



Re ¼ umax$dr$r (23)
m
umax ¼ _mAmin$r

(24)

Finally the heat transfer coefficient for the air passing over thefinned tube was estimated from [30]:

aa ¼ 0:242kdr

Re0:658

sHf

!0:297�P1P2

��0:091

Pr13F1F2 (25)

where P2 is the tube pitch in the flow direction.

F1, describes the variations of the air thermo-physical propertieswith temperature. This parameter is important at high tem-perature values. This parameter was assumed to be one in ourair conditioning flow heat transfer modeling.F2, is a factor describing the effects of number of rows in heattransfer coefficient. For tube rows less than four this coefficientis one.

2.2.1.3. Overall heat transfer coefficient (U). With estimating theheat transfer coefficient (a), and neglecting thermal resistances forwall and fouling, the overall heat transfer coefficient of condenserwas computed from [2]:

1U

¼ 1ar

þ 1aa

(26)

whereU, ar and aa are overall heat transfer coefficient, heat transfercoefficient of the refrigerant side and heat transfer coefficient of theair side respectively. Eq. (26) was used for both single- and two-phase regions of the condenser.

2.3. Expansion valve

The subcooled refrigerant enters the expansion valve and leavesin two-phase mixture. The enthalpy remains constant during theexpansion (an isenthalpic) process.

h3 ¼ h4 (27)

2.4. Evaporator

Heat transfer rate in evaporator was obtained from:

_Qeva ¼ ðU$A$F$LMTDÞeva (28)

Considering the small regions of single-phase flow in evapo-rator, the flow correction factor F z1 was assumed [25].

Therefore the evaporator heat transfer rate in steady state modewas estimated as follows:

_Qeva ¼ ðUAÞeva$ðLMTDÞeva ¼ _mrðh1 � h4Þ (29)

_Qeva ¼ _Qeva;tp þ _Qeva;sh (30)

where:

_Qeva;tp ¼ ðUAÞeva;tp$ðLMTDÞeva;tp (31)

_Qeva;sh ¼ ðUAÞeva;sh$ðLMTDÞeva;sh (32)


The logarithmic mean temperature difference (LMTD) in two-phase region of evaporator:

ðLMTDÞeva;tp ¼�Ta;10 � Teva

�� Ta;4 � Teva�

ln�Ta;10 � TevaTa;4 � Teva

� (33)

where Teva is the refrigerant mean temperature in two-phase regionof evaporator (evaporator temperature), Ta;10 and Ta,4 are theevaporator inlet and outlet air temperatures at the correspondingpoints 10 and 4 of the refrigerant cycle.

The logarithmic mean temperature difference (LMTD) in su-perheat region of evaporator is defined as:

ðLMTDÞeva;sh ¼�Ta;1 � T1

�� Ta;10 � Teva�

ln�

Ta;1 � T1Ta;10 � Teva

� (34)

where Ta,1 is the evaporator inlet air temperature at the corre-sponding point 1 of the refrigerant cycle.

Therefore the dynamic form of energy conservation law forevaporator (two-phase region) is:

�MCp

�eva;tp

dTevadt

¼ ðUAÞeva;tp

0BBB@�Ta;10 �Teva

��Ta;4�Teva�

ln�Ta;10 �TevaTa;4�Teva

�1CCCA

� _mrðh10 �h4Þ (35)

2.4.1. Heat transfer coefficients2.4.1.1. Refrigerant side. For superheat (single-phase) region ofevaporator, Eq. (19) may be used to compute the heat transfer co-efficient, for cooling process (n ¼ 0.3 [27]).

The heat transfer coefficient for the two-phase region of evap-oration was estimated from [29]:

aDL

kl¼ 0:087 Re0:6m Prl

�rvrl

�0:2�kWkl

�0:09

(36)

where DL in the above relation is defined as:

DL ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

s

g ðrl � rvÞr

(37)

and s is the surface tension force and Reynolds number for two-phase refrigerant was computed from:

Rem ¼ rlvmDL

ml(38)

The velocity of two-phase refrigerant inside the pipe was ob-tained from:

vm ¼ Grl

�1þ xm

�rlrv

� 1��

(39)

where vm is the mean velocity of two-phase refrigerant, G is themass flux, equal to 4 _m=pD2 and xm is the mixture quality.

2.4.1.2. Air side. The heat transfer coefficient for the air passingover the finned tube was estimated from Eq. (25).



2.4.1.3. Overall heat transfer coefficient (U). By knowing the heattransfer coefficient (a), and neglecting thermal resistances of wallsand fouling, the overall heat transfer coefficient of evaporator wasalso computed from Eq. (26).

For two separated regions of evaporator, the overall heattransfer coefficient can be computed knowing the heat transfercoefficients of air and refrigerant sides.

2.5. Gas engine

A spark ignition internal combustion gas engine was used todrive the compressor of the heat pump with vapor compressioncycle.

The heat release process during combustion of fuel and airmixture in the cylinder was expressed as a function of crank angle[23]:

x ¼ 1� exp��q� qsqd

�n�qs < q < qs þ qd (40)

where x is the fraction of the heat release from the input fuel energyand q, qs and qd are the crank angle, the angle (time) of the begin-ning of heat release process and the duration of heat releaserespectively. n is a constant obtained for ordinary spark ignitioncombustion engines.

The values of qs, qd and nwere obtained based on awide range ofempirical data for spark ignition combustion engines [23].Assuming the gases inside the cylinder as ideal gases, we have:

PV ¼ mRT (41)

By differentiation of the above equation based on the crankangle (q), and using the first law of thermodynamic in differentialform, and considering thermal and mass losses in engine cylinder,four ordinary dimensionless differential equations were obtained.By solving these equations simultaneously the pressure, outputwork, and the gas mass and thermal losses inside the cylinder wereobtained. These equations were:

dP

dq¼ �g

P

V

dV

dqþ ðg� 1Þ

V

264Q dx

dq� a

�1þ bV

�0B@P

V

m� T

w

1CA375

� gC0P

uge

(42)

dW

dq¼ P

dV

dq(43)

dQ

loss

dq¼ a

�1þ bV

�0B@P

V

m� T

w

1CA (44)

dm

dq¼ � C0m

uge(45)

where Pis dimensionless pressure of combustion chamber, T

is

dimensionless temperature, Vis cylinder dimensionless volume at

each crank angle, Wis dimensionless indicator work, g is the ratio

of specific heats, Q

loss is dimensionless combustion heat loss, mis

dimensionless mass inside cylinder and a, b and C0 are the constant

values as explained in Ref. [10]. Solving these four simultaneous


equations provided pressure, work, heat loss and mass of gas incylinder.

The indicated work per cycle at the end of combustion processwas obtained and the indicated thermal efficiency (hth) of enginewas computed from:

hth ¼ W

Q

(46)

2.6. The combined heat pump and gas engine system

Shaft power consumed by compressor and engine indicatedpower ( _Wge;i) were related by the following relation:

_Wcomp ¼ _Wge;ihmhbelt (47)

The indicated thermal efficiency of engine was estimated from:

hth ¼_Wge;i_Qin

¼_Wge;i

_VfuelqLHV(48)

where _Wge;i is the gas engine indicated power, hm is the gas enginemechanical efficiency, hbelt is the power transmission efficiencybetween engine and compressor and _Vfuel is the volumetric flowrate of fuel consumption. Combining the above equations, the fuelvolumetric flow rate can be expressed as:

_Vfuel ¼_Wge;i

hthqLHV¼

_Wcomp

hmhbelththqLHV(49)

Therefore the system primary energy ratio (PER) was obtainedfrom:

PER ¼ output cooling energyinput fuel energy

(50)

Thus:

PERc ¼_Qeva;c_Qin;c

¼_Qeva;c

_Vfuel;cqLHV(51)

Or by combining Eqs. (48), (49) and (51):

PERc ¼_Qeva;c_Wcomp;c

$hm$hbelt$hth;c ¼ qeva;cwcomp;c

$hm$hbelt$hth;c (52)

where PERc, _Qeva;c and _Wcomp;c are GEHP primary energy ratio,evaporator capacity and shaft power consumed by compressor incooling mode, respectively.

2.7. Artificial neural network (ANN)

In this study, a multi-layer perceptron neural network is used topredict rotational speed of gas engine during the system startupuntil reaching the steady state operating condition.

Perceptron network is composed of different layers while eachlayer has its number of neurons or cells. The first layer, final layerand the middle layer of the network are called input layer, outputlayer and hidden layers respectively. Neurons in each layer areconnected to all neurons of the adjacent layers. Information istransmitted between neurons through these connections. Each ofthese connections has its own weighting factor, which are multi-plied in transferring data from one neuron to another neuron. For



computing a neuron output, an activation function work on inputvalues (sum of the weighted information). Neural network de-termines the relationship between input and output data throughtraining (learning) procedure [31]. Creation of a neural network formodeling and prediction consists of three stages; creation of thedata needed for network training, assessment of different struc-tures of neural networks to select the optimal structure and finallyevaluation of neural network performance by checking a group ofdata that are not used in the network training.

By changing the cooling load of GEHP system the engine rota-tional speed changes. Due to the fact that compressor in heat pumpcycle is driven by gas engine, any change in engine speed results inchange in refrigerant mass flow rates passing through compressor.

Therefore for correct system modeling, variation of enginespeed and effective parameters should be taken into account. Inthis system analysis it was found that several parameters such ascooling capacity as well as suction (evaporator) and discharge(condenser) pressures change the engine speed. Hence, for givenvalues of the above three parameters, one may consider a uniquevalue for the engine speed. The relations among three mentionedparameters and engine speed in this analysis were obtainedthrough using Neural Network. To perform this job the GEHP sys-tem was run, and more than 50 groups of data (engine speed,cooling capacity, and suction and discharge pressures) werecollected at various cooling loads.

The data were randomly separated into three groups of sixtypercent, twenty percent and twenty percent, used for training,validating and testing respectively.

As is shown in Fig. 4, with knowing 30 groups of three param-eters cooling loads, evaporator and condenser pressures as inputvalues and engine speed as output values, the learning procedure ofNeural Network analysis was completed.

In this article, back-propagation algorithm and LevenbergeMarquardt (LM) method was used for neural network training.With assistance of back-propagation algorithms neural networkwas trained through changing the middle layers weight. Further-more the hyperbolic tangent activation function and linear activa-tion functions were applied for middle and final layers respectively.

To evaluate the performance of neural network, two checkingcriteria named root mean squared (RMS, Eq. (53)) and the fractionof variance (R2, Eq. (54)) were used [31].

RMS ¼24�1

n

�Xj

tj � oj 2351=2 (53)

R2 ¼ 1�P

j�tj � oj

�2P

j�oj�2 (54)

where n is the number of data, t is the target value and o is theoutput value of ANN.

Different structures were evaluated in the training network andthe best structure was obtained based on the minimum values ofRMS or the maximum values of R2 respectively.

Fig. 4. ANN architectures for engine rotational speed expectancy.


The optimum ANN architecture, fraction of variance (R2) for thevalues predicted by the neural network in comparison with realdata and the RMS value of the tested data set, are presented inTable 1. Results shown in Table 1 prove that the applied ANNmodeland its prediction procedure were accurate enough for estimatingthe required parameters.

2.8. The algorithm of computations

The properties of refrigerant R407c were computed by the in-house developed software at Energy Systems Improvement Labo-ratory (ESIL). Dynamic equations for computing the condenser andevaporator temperatures (Eqs. (17) and (35)) were solved by 4thorder RungeeKutta numerical method and the variation ofcondenser and evaporator temperatures (as well as their corre-sponding saturated pressures)with time were predicted for GEHP.

The engine rotational speed in each time stepwas also predictedby using the artificial neural network and knowing the condenserand evaporator saturated pressures as well as by computing thecooling capacity at each time step.

By the computed evaporator and condenser temperatures(or pressures) and engine rotational speed, the refrigeration cyclestate points, the heat transfer rate for evaporator and condenser(Eqs. (10) and (30)), and the shaft power consumed by compressor(Eq. (1)) were obtained. The fuel consumption (Eq. (49)) and theprimary energy ratio of system (Eq. (52)) were also computed foreach time step.

The flowchart of computation procedure is shown in Fig. 5.

3. Experimental tests

After modeling the gas engine heat pump system and deter-mining the capacities of heat exchangers and the system operatingparameters, experimental tests were needed to evaluate the nu-merical values of experimental system real operating parameters.

For this purpose a gas engine heat pump systemwas installed atEnergy Systems Improvement Laboratory and experimental testswere performed to record the operating parameters and to checkthe modeling output. The outdoor unit included the gas engine,compressor and outdoor heat exchanger with nominal capacity of28.0 kW in cooling mode. The cooling capacity of GEHP waschanged by the type and number of three available indoor heatexchangers which could run simultaneously.

There were two compressors in the system. When the load ca-pacity increased, the second compressor started to run with thesame thermodynamic states at their both inlets (with doubledisplacement volume). The compressor revolution range was2280e4085 min�1 in cooling mode.

The dynamic operation of GEHP system from the starting-upuntil reaching the steady state mode was investigated. Duringsystem startup, the evaporator and condenser temperature varia-tions were recorded by the inflow installed temperature sensorswith specification given in Table 2. The fuel volume flow rate wasmeasured and recorded by the gas flowmeter. There were a controlunit with three loggers for displaying the inlet/outlet temperatures,humidity and air flow speed. For decreasing the accidental errors in

Table 1The optimum ANN architecture, fraction of variance (R2) and the RMS value for thevalues predicted by the neural network.

Numberof hiddenlayers

Optimum ANN architecture Trainingalgorithm

Error (%)

1st hiddenlayer

2nd hiddenlayer

RMS R2

Network 2 4 6 LM 0.006881 0.999887


Start

, eva conT T

,, , ( .55)eva con eva testP P Q Eq

Artificial Neural Network: Nge

Ncomp=K.Nge

P (Eq.42)

W (Eq.43)

lossQ (Eq.44)

m (Eq.45)

Heat pump cycle:

v Eq.3) , s (Eq.4)

rm (Eq.2)

Differential equation for new temperatures:Eq.17 – Eq.35

Heat transfer coefficients:

r

a

, ( .26)e cU U Eq

End

No

Yes

fuelV (Eq.49)

PER (Eq.52) t = t +

1 1 1 1, , , , , , , , sup sub c d sT T r V T P mθ θΔ Δ

0, , , , , , m belt ge AF C Kη η γ ω

(Eq.1)

(Eq.30)

thη (Eq.46)

tΔ

compW 1

evaQ

conQ (Eq.10)

Fig. 5. Algorithm of dynamic modeling of GEHP.Start

Input parameters:

a,1 a,1 a,3 a,4T , T , T , T (by air temperature sensor )

eva conT , T (by refrigerant temperature sensor )

aV (by velocity sensor)

a aP , A

aa

, , , .57a eva a conm m Eq , .57m ,a eva ,

.55 , .56eva conQ Eq Q Eq.56Q Eq Q.55 ,

( .58)compW Eq( .5W (


measuring inlet and outlet air temperature/humidity, the averagevalues of simultaneous measured values for temperature/humidityat six points was used to find the final average temperature/hu-midity values. The average air velocity were also estimated byinserting a thermal bulb sensor on the heat exchanger frontalsurface area and performing data acquisition at six points. The listof measuring instruments and their corresponding uncertainty isgiven in Table 2.

Then the capacities of heat exchangers were obtained from thefollowing relations:

_Qeva ¼ _ma;evaCp;a�Ta;1 � Ta;4

�(55)

where _ma;eva is the air mass flow rate in evaporator, Cp,a is the airspecific heat in constant pressure, Ta,1 is the air temperature atevaporator inlet, Ta,4 is the air temperature at evaporator outlet.

Table 2Specifications of measuring devices [33,34].

Sensor Operating range Maximumuncertainty (%)

Air temperature sensor �20 to 70 (�C) �1Barometer 50 to 110 (kPa) �1Thermal bulb velocity sensor 0 to 10 (m/s) �1Tachometer 0 to 10,000 (rpm) �0.1Gas flow meter 0.5 to 240 (l/min) �5Refrigerant temperature sensor �30 to 100 (�C) �1Refrigerant pressure sensor 3 to 30 (bar) �2


_Qcon ¼ _ma;conCp;a�Ta;2 � Ta;3

�(56)

where _ma;con is the air mass flow rate in condenser, Ta,3 is the airtemperature at condenser inlet, Ta,2 is the air temperature atcondenser outlet.

Air mass flow rate was computed from:

_ma ¼ ravAAa (57)

where ra, vA and Aawere density, mean velocity, and surface area ofthe air flow, respectively.

Shaft power consumed by compressor based on test results wasestimated as:

_Wcomp ¼ _Qcon � _Qeva (58)

Primary energy ratio of gas engine heat pump in cooling modewas computed from Eq. (51).

The flowchart of output results using input measurement valuesis shown in Fig. 6.

4. Case study

A software program was developed to support the modelingprogram to compute the properties of refrigerant R407c.

Based on the results of empirical tests obtained for refrigerantR407c in the operating range of scroll compressor, the constants ofisentropic efficiency in Eq. (4) were obtained as follows:

B0 ¼ 1:2328; B1 ¼ �0:1802; B2 ¼ 0:0147

Our interested dynamic variables of the system included theevaporator and condenser temperatures were obtained using Eqs.(17) and (35). Evaporator and condenser heat transfer rates, shaft

fuelV f lV f (by gas flow meter)

.52cPER Eq

End

Fig. 6. Algorithm of experimental test.



power consumed by compressor, engine fuel consumption, andprimary energy ratio of GEHP system were also estimated in thenext step.

In order to validate the modeling results, they were comparedwith the test results obtained for a system with the specificationslisted in Table 3 in cooling mode.

Through a curve fitting process to the experimental data, thevariations with time of the recorded values of inlet/outlet airtemperatures to/from the heat exchangers were predicted as:

Ta;1 ¼ 3:397�10�8t3�3:603�10�5t2�0:005051tþ27 (59)

where Ta,1 is the evaporator inlet air temperature (�C) and t is thetime elapsed from the startup. Similarly for Ta,4, the evaporatoroutlet air temperature (�C) or Ta,2, the condenser outlet air tem-perature (�C), the following relations were obtained:

Ta;4 ¼ � 1:58� 10�13t5 þ 4:608� 10�10t4 � 5:334

� 10�7t3 þ 3:015� 10�4t2 � 0:09791t þ 26:8(60)

Ta;2 ¼ 34:802 t0:0125 (61)

The condenser (outdoor heat exchanger) inlet air temperature,Ta,3, is the ambient temperature.

The gas engine rotational speed could be predicted bycomputing the evaporator capacity (using Eq. (55) by knowing theair temperatures from Eqs. (59) and (60)), as well as using therecorded data for evaporator and condenser pressures at each timestep, which were three input values to the ANN model.

The ratio of heat transfer surface area in superheat, two-phase,and subcooled regions to the total surface area in condenser andevaporator were obtained as:

Aeva;sh ¼ 0:15Aeva (62)

Aeva;tp ¼ 0:85Aeva (63)

Acon;sh ¼ 0:15Acon (64)

Acon;tp ¼ 0:8Acon (65)

Acon;sc ¼ 0:05Acon (66)

Table 3Input data of the system general specifications [33].

Parameter Dimension Value

Ambient temperature (�C) 34Ambient pressure (kPa) 85Compressor displacement volume (Vcomp) (m3/rev) 0.0000605 � 2Superheating degree at evaporator outlet (Tsh) (K) 5Subcooling degree at condenser outlet (Tsc) (K) 5Engine displacement volume (V) (cc) 952Engine mechanical efficiency (hm) (�) 0.8Engine volumetric efficiency (hv,ge) (�) 0.85Power transmission efficiency (hbelt) (�) 0.95Lower heating value of the fuel (qLHV) (kJ/m3) 36,200b coefficient (�) 2.18a

(�) 0.2Leakage factor (C0) (s�1) 0.8Air o fuel ratio (AF) (�) 16.5Spark advance degree (qs) (deg) �16Heat release duration (qd) (deg) 40Ratio of compressor to engine rotational

speed (K)(�) 1.9


5. Uncertainty analysis

Assuming that R as the desired result of some experiments isgiven as a function of independent variables x1, x2,., xn as follows:

R ¼ Rðx1; x2;.; xnÞ (67)

If U1, U2, ..., Un are the corresponding uncertainty of the inde-pendent variables, the uncertainty of the R, UR, is determined as[32]:

UR ¼��

vRvx1

U1

�2þ�vRvx2

U2

�2þ .þ

�vRvxn

Un

�2�1=2(68)

For estimating the air side cooling capacity of indoor heatexchanger ( _Qa) sources of uncertaintywere air density, velocity andenthalpy difference. Thus:

_Qa ¼ Rðra;Va;DhaÞ (69)

where density depends on temperature and pressure (r¼ P/RT) andthe enthalpy is a function of atmospheric temperature, pressureand relative humidity. Therefore, the maximum uncertainty forcapacity is:

U _Qa¼"

v _Qa

vVUV

!2

þ v _Qa

vPUP

!2

þ v _Qa

v4U4

!2

þ v _Qa

vTUT

!2#1=2

(70)

PER of GEHP depends on the capacity and fuel volume flow rate(Eq. (51)). Considering the constant value of qLHV, the uncertainty ofPER was estimated as:

PER ¼ R_Qeva;

_Vf

�(71)

UPER ¼"

v PER

v _QevaU _Qeva

!2

þ v PER

v _VfU _Vf

!2#1=2(72)

Consequently from Eqs. (70) and (72) and Table 2, the maximumuncertainty for the cooling capacity, fuel consumption and PER are3.18%, 5% and 5.9% respectively.

6. Discussion and results

The presented model was used to obtain the condenser andevaporator temperatures as well as their capacities, shaft powerconsumed by compressor, fuel consumption, and PER of the cycle.Finally, the modeling results were compared with experimentalresults.

By solving dynamic Eqs. (17) and (35), the variations of evapo-rator and condenser temperatures from startup point until reach-ing the steady state conditions are shown in Fig. 7 from bothmodeling and experimental results.

Referring to Fig. 7, it was observed that after startup, the vari-ations of condenser and evaporator temperatures were fast at thebeginning and then it approached the steady state conditiongradually. The refrigerant pressure and temperature increase dur-ing compression in the compressor. During startup the refrigeranttemperature in condenser increased while the evaporator pressuredecreased gradually with time until they reached to their steadystate values. The average difference value between the modelingand measured data for the condenser and evaporator temperatureswere 1.26 �C and 1.73 �C respectively.


Fig. 7. Variations of condenser and evaporator temperature during startup.


Referring to Fig. 8, after the system startup and flowing therefrigerant in the cycle, due to the variations of refrigerant and airtemperatures, the logarithmic mean temperature difference andheat transfer rate in evaporator increased rapidly based on Eqs.(28), (33) and (34). However the rate of change of refrigerant andair temperatures deceased with time. Thus, with decreasing thevariations of evaporator cooling capacity it reached the steady statevalues.

Based on the experimental results, after the system startup andby passing the air through the evaporator coils, the air temperaturedifference between the evaporator inlet and outlet increased whichresulted in rising the evaporator cooling capacity (Eq. (55)). Thevariations of cooling capacity with time due to small temperaturedifference between evaporator inlet and outlet reached the steadystate situation after about 3 min. The average difference value be-tween the modeling and measured data for evaporator coolingcapacity was about 8.05%.

The variation of heat rejection rate of condenser with time fromits startup is shown in Fig. 9.

In condenser, similar to the evaporator, after the systemstartup and flowing the refrigerant in the cycle, based on Eqs. (7)

Fig. 8. Variations of evaporator co


and (14)e(16), the logarithmic mean temperature difference andheat transfer rate in condenser increase rapidly due to the varia-tions of refrigerant and air temperatures. However the variationrates of refrigerant and air temperatures decrease with time whichcause small variations of heat rejection rate of condenser and fasterreaching the steady state condition.

Based on the experimental results, after the system startup andwith passing the air over the condenser coils, the air temperaturedifference between the condenser inlet and outlet increases, whichresults in increase the heat transfer rate in condenser (Eq. (56)). Thevariations of heat transfer rate decrease with time due to smallertemperature difference between condenser inlet and outlet. Thecondenser temperature reaches the steady state mode after about2min. The average difference percent points between themodelingprediction and corresponding values obtained from experimentalresults for the condenser heat rejection rate was about 6.01%.

Variation of shaft power consumed by compressor is shown inFig. 10. The shaft power consumed by compressor at the initialmoments of system starting-up had its lowest value. Due toincreasing the compress pressure ratio (compression ratio) as wellas the compressor rotational speed, the cycle refrigerant mass flow

oling capacity during startup.


Fig. 9. Variations of condenser heat rejection rate during startup.


rate and the shaft power consumed by compressor increased(which provides increasing the specific compressor work). Theaverage difference value between the modeling and measured datafor shaft power consumed by compressor was about 9.27%.

The variation of engine fuel consumption during starting-up isshown in Fig. 11. Referring to Eq. (49) and considering constantvalues for the gas engine mechanical efficiency, the power trans-mission efficiency and lower heating value of fuel, the enginefuel consumption depends on the shaft power consumed bycompressor and the engine cycle indicated thermal efficiency.

The change in thermal efficiency during startup is mainly due tochange in gas engine rotational speed. The increase of cooling ca-pacity during startup is due to increase in compressor (or engine)speed which provides more refrigerant mass flow rate to someextent. However after circulating specific refrigerant mass flowrate, the second compressor starts to run and the speed for twocompressors (or engine) decreases. Results of gas engine modelingin Section 2.5 show that the efficiency increases mildly with risingthe engine speed. Therefore during the starting-up with increasingthe compressor (or gas engine) speed, the engine thermal efficiency

Fig. 10. Variations of shaft power consumed


rises mildly. With mild increase of thermal efficiency and sharpincrease of shaft power consumed by compressor with increasingspeed, a sharp increase in gas engine fuel consumption was ex-pected as shown in Fig. 11.

The mean values of difference percent point in comparison ofmodeling and experimental data was about 9.51% for gas enginefuel consumption rate.

The GEHP variation of PER is also shown in Fig. 12. The PER ofGEHP depends on the evaporation heat transfer rate (capacity),shaft power consumed by compressor and the engine thermal ef-ficiency as indicated by Eq. (52). Therefore these three parametersrise during first running time periods while the thermal efficiencyfall later on. Due to the fact that the slope of increase in coolingcapacity was bigger than that for the shaft power consumed bycompressor during startup, the system PER increased sharply inabout first 30 s. With increasing the shaft power consumed bycompressor (as well as fuel consumption) later on, the PER of GEHPdecreased.

Experimental results also show that considering the constantvalue for fuel lower heating value, the PER of heat pump

by compressor of GEHP during startup.


Fig. 12. Variations of PER of GEHP during startup.

Fig. 11. Variations of engine fuel consumption during startup.


refrigeration cycle depends on the evaporator cooling capacity andengine fuel consumption as described by Eq. (52).

The percent difference value between modeling and test resultsfor PER was 7.15%.

Finally, the system operating parameters in steady state modewere presented in Table 4. The comparison between experimental

Table 4System characteristics at steady state.

Parameter Dimension Test result Modelingresult

Difference

Evaporator temperature (�C) �2.5 �3.76 1.26 (�C)Condenser temperature (�C) 44.6 46.04 1.44 (�C)Evaporator cooling capacity (kW) 11.7 11.91 1.79%Condenser heat rejection

rate(kW) 16 15.88 0.75%

Shaft power consumed bycompressor

(kW) 4.3 3.91 9.07%

Engine rotational speed (rpm) 1300 1291 0.7%Fuel mass flow rate (kg/s) 2.69 � 10�4 2.48 � 10�4 7.8%PER of GEHP (�) 1.015 1.087 7.09%


and modeling results shows an accepted consistency between twogroups of results.

7. Conclusions

In this paper, the dynamic modeling of gas engine heat pump(GEHP) system was investigated in cooling mode consideringcondenser and evaporator temperatures as the time variables.

The output results of GEHP starting-up until reaching the steadystate condition as well as system specifications such as heat ex-changers capacities, shaft power consumed by compressor, fuelmass flow rate, and PER of GEHP were computed and comparedwith experimental data.

Variations of condenser and evaporator temperatures show thatthe system reaches the steady state condition in more than aboutfive minutes. This estimation is important in both aspects of GEHPsystem application as well as system design/analysis. In the lattercase the appropriate time interval for data acquisition (data fre-quency), for designing the control units as well as time period ofwarming up and cooling down the engine, heat exchangers andaccessories could be predicted fromGEHP dynamicmodeling results.



The comparison between empirical andmodeling results showedan acceptable agreement. The average difference values of themodeling and the measured outputs for evaporator and condensertemperatures, cooling capacity, gas engine fuel consumption, shaftpower consumed by compressor and primary energy ratio of systemshowed 1.73 �C, 1.26 �C, 8.05%, 9.51%, 9.27% and 7.15% respectively.

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