Simulación frigorifico

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Transient simulation of a two-door frost-free refrigerator subjected toperiodic door opening and evaporator frostingq

Bruno N. Borges a, Cláudio Melo a, Christian J.L. Hermes b,⇑

a POLO Research Laboratories for Emerging Technologies in Cooling and Thermophysics, Department of Mechanical Engineering, Federal University of Santa Catarina,

88040900 Florianópolis, SC, Brazilb Laboratory of Thermodynamics and Thermophysics, Department of Mechanical Engineering, Federal University of Paraná, 81531990 Curitiba, PR, Brazil

h i g h l i g h t s

Transient behavior of a refrigerator under periodic door opening is simulated.

The refrigeration loop is modeled following a semi-empirical quasi-steady approach.

Energy and moisture transfer into and within the compartments are modeled.

Key heat and mass transfer parameters were derived from in-house experiments.

Predictions followed closely the experimental trends for power and temperatures.

a r t i c l e i n f o

Article history:

Received 15 September 2014

Received in revised form 20 January 2015

Accepted 21 January 2015

Available online 17 March 2015

Keywords:

Household refrigerator

Transient simulation

Door opening

Evaporator frosting

a b s t r a c t

This paper describes a quasi-steady-state simulation model for predicting the transient behavior of a

two-door household refrigerator subjected to periodic door opening and evaporator frosting. A semi-

empirical steady-state model was developed for the refrigeration loop, whereas a transient model was

devised to predict the energy and mass transfer into and within the refrigerated compartments, and also

the frost build-up on the evaporator. The key empirical heat and mass transfer parameters required by

the model were derived from a set of experiments performed in-house in a climate-controlled chamber.

In general, it was found that the model predictions followed closely the experimental trends for the

power consumption (deviations within ±10%) and for the compartment temperatures (deviations within

±2 K) when the doors are opened periodically and frost is allowed to accumulate over the evaporator.

2015 Elsevier Ltd. All rights reserved.

1. Introduction

Modern refrigerator design is aimed at energy savings and also

at product robustness in relation to evaporator frosting. In this

regard, standardized tests [1,2] as well as tests under real usage

conditions, that is, with doors opened regularly [3,4] allowing

moisture to enter the refrigerated compartment and frost to

accumulate on the evaporator [5] are procedures commonly car-

ried out by most manufacturers.

Nevertheless, since the experimental procedures for frost-free

refrigerators and freezers are costly and time consuming [6,7],

simulation models have been devised to improve the product

development process [8–15]. None of them, however, can predict

the refrigerator performance degradation due to periodic door

opening and consequent evaporator frosting.

Recently, Mastrullo et al. [16] put forward a transient sim-

ulation model that is suitable to predict the time evolution of the

compartment air temperature and the power consumption taking

into account the door opening, and the resulting evaporator frost-

ing. The model was developed and validated for a single-door

upright freezer, which represents a small niche in the realm of

household refrigeration if compared with two-door frost-free

appliances, the so-called ‘‘Combi’’ refrigerators [11,14].

To the best of the authors’ knowledge, none of the models avail-

able in the literature [8–16] are able to predict the performance of

two-door frost-free refrigerators under periodic door opening,

which not only affect the sensible and the latent loads, but also

allows frost to build-up on the evaporator, thus decreasing the

air flow rate supplied by the fan.

To advance a simulation model for predicting the transient

behavior of a two-door frost-free refrigerator subjected to periodic

http://dx.doi.org/10.1016/j.apenergy.2015.01.089

0306-2619/ 2015 Elsevier Ltd. All rights reserved.

q An abridged version of this manuscript was presented at the 15th International

Refrigeration and Air Conditioning Conference at Purdue, July 14–17, 2014.⇑ Corresponding author. Tel./fax: +55 41 3361 3239.

E-mail address: [email protected] (C.J.L. Hermes).

Applied Energy 147 (2015) 386–395

Contents lists available at ScienceDirect

Applied Energy

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a p e n e r g y

http://dx.doi.org/10.1016/j.apenergy.2015.01.089mailto:[email protected]://dx.doi.org/10.1016/j.apenergy.2015.01.089http://www.sciencedirect.com/science/journal/03062619http://www.elsevier.com/locate/apenergyhttp://www.elsevier.com/locate/apenergyhttp://www.sciencedirect.com/science/journal/03062619http://dx.doi.org/10.1016/j.apenergy.2015.01.089mailto:[email protected]://dx.doi.org/10.1016/j.apenergy.2015.01.089http://crossmark.crossref.org/dialog/?doi=10.1016/j.apenergy.2015.01.089&domain=pdf


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door opening is therefore the main aim of this study. The proposed

model follows a quasi-steady-state approach [14], with a steady-

state sub-model for the refrigeration loop and a transient sub-

model for the energy and moisture transfer into and within the

refrigerated compartments. An additional frost growth and den-

sification sub-model was developed to predict the frost accumula-

tion on the evaporator over time.

2. Simulation model

2.1. Refrigeration loop

A 433-liter top-mount refrigerator, running with R-134a and

comprised of a 6.76-cm3 hermetic reciprocating compressor, natu-

ral draft wire-on-tube condenser, tube-fin evaporator and capillary

tube-suction line heat exchanger, illustrated in Fig. 1, was adopted

in this study.

2.1.1. Compressor

The compressor sub-model uses the volumetric (gv) and overall

(gg) efficiencies to calculate the compression power and the refrig-erant mass flow rate for a given operating condition. The

compressor shell thermal conductance (UAk) is also required for

the heat transfer calculation [12]. The refrigerant specific enthalpy

at the compressor outlet is thus obtained from the following

energy balance [13]:

h2 ¼ h1 þ h2;s h1

gg UAkðT 2 T aÞ

mkð1Þ

Nomenclature

Roman A heat transfer area, m2

C thermal capacity, J K1

c p specific heat at constant pressure, J kg1 K1

D inner diameter, mDfr effective vapor diffusivity in frosted media, m2 s

1

G mass flux, kg/m2 sH height, mh specific enthalpy, J kg1

Ha Hatta number, dimensionlesshlv latent heat of evaporation, J kg

1

hsv latent heat of sublimation, J kg1

k thermal conductivity, W m1 K1

kfr effective thermal conductivity in frosted media,W m1 K1

L length, mLe Lewis number, dimensionlessm mass flow rate, kg s1

N compressor speed, HzNTU number of transfer units, dimensionless p pressure, PaQ heat transfer rate, Wr air flow ratio, dimensionlessS compressor swept volume, m3

T temperature, KUA thermal conductance, Wv specific volume, m3 kg1

V volumetric air flow rate, m3 s1

W compression power, Ww humidity ratio, kgv kga

1

W width, m

Greeka heat transfer coefficient, W m2 K1

d frost thickness, mec emissivity of the condenser wall, dimensionlessex heat exchanger effectiveness, dimensionless/ correction factor, kgvD p pressure drop, Pa

Dt time-step, sgg global compression efficiency, dimensionlessgv volumetric compression efficiency, dimensionlessq density, mr Stefan-Boltzmann constant, W m2 K4

f evaporator dry-out position, m

Subscripts1 compressor inlet2 condenser inlet3 condenser outlet4 evaporator inlet5 evaporator outleta ambient, airc condensercap capillary tubed doore evaporatorf flash-pointff fresh-foodfr frostfz freezerg saturated vapor at the evaporating pressurei inletk compressorl saturated liquidlat latent thermal loadm mulliono outletr refrigerants isentropic processsat saturationsen sensible thermal loadss steady-statesub subcoolingsuc suction linesup superheatingv saturated vaporx internal heat exchanger

Fig. 1. Schematic representation of the refrigeration loop.

B.N. Borges et al. / Applied Energy 147 (2015) 386–395 387

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where (h2,s–h1)/gg is the compression power, whereas the massflow rate displaced by the compressor, mk, is calculated from

[12,13]:

mk ¼ gvNS

v 1

ð2Þ

where N and S are the compressor speed and the swept volume,

respectively. The compression efficiencies were fitted to the experi-

mental data as linear functions of the pressure ratio, and the UAkcoefficient was expressed as a linear fit to the surrounding air tem-

perature data [12,13].

2.1.2. Capillary tube suction line heat exchanger

The internal heat exchanger was modeled according to the

semi-empirical approach introduced by Hermes et al. [17], who

considered the refrigerant flow and the heat transfer as indepen-

dent phenomena, and derived explicit algebraic expressions for

the refrigerant mass flow rate as follows:

mxmad

¼ 1:29 LsucLcap

0:145DsucDcap

0:315e0:285x

v f lf v glg

!0:214ð3Þ

where mad is the mass flow rate of an adiabatic capillary tube withthe same bore and length, calculated as follows:

mad ¼ 6:0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiD5capLcap

pc pf v f

þ pf pe g

þ f

g 2ln gpe þ f

gpf þ f

s ð4Þ

where f = v f pf k, g = v f (1k), and k = 1.67 105 pf

0.72 [17], v f and pf are the specific volume and pressure at the flash-point, respectively,

whereas pc and pe stand for the condensing and evaporating pres-

sures. The correlation is valid for internal heat exchangers with

capillary tube inner diameters ranging from 0.553mm to

2.154 mm, and tube lengths from 2 m to 4 m [17].

The specific enthalpy at the evaporator inlet and the tempera-

ture at the compressor inlet are thus expressed as:

h4 ¼ h3 exc p;1ðT 3 T 5Þ ð5Þ

T 1 ¼ T 5 þ exðT 3 T 5Þ ð6Þ

where ex = NTU/(1 + NTU) is the heat exchanger effectiveness

(0.65), whereas NTU stands for the number of transfer units, cal-

culated as follows [17]:

NTU ¼ 1:4m0:57ad Lsuc

D0:43suc

k2=3g

l0:1g c 2=3p;g

ð7Þ

2.1.3. Condenser

The natural draft wire-and-tube condenser was divided into

three domains, namely superheating, saturation and subcooling

[12–14]. The overall heat transfer in the condenser is therefore cal-culated from:

Q c ¼ Q c; sup þ Q c;sat þ Q c;sub ¼ UAcðT c T aÞ ð8Þ

where T c is the condensing temperature, calculated implicitly by the

model thus ensuring that the same amount of mass flows through

the compressor and the capillary tube, whereas T a is the surround-

ing air temperature, which is an input data with a constant value.

The specific refrigerant enthalpy at the condenser outlet is

expressed as:

h3 ¼ h2 Q cmk

ð9Þ

As the heat transfer is governed by free convection and radiation on

the air-side, the thermal conductance was approximated asUAc (ac + arad) ( At + Aw) [12–14]. The combined heat transfer

coefficient was calculated from the correlation proposed by Melo

and Hermes [18],

ac þaradarad

¼5:68 Aw At þ Aw

0:60 pt dtdt

0:28 pw dwdt

0:492T c T aT c þT a

0:08ð10Þ

where dt and dw are the tube and wire diameters, respectively, pt

and pw are the tube and wire pitches, respectively, and At and Aware the overall heat transfer surface due to the tubes and the wires,

respectively. The correlation is valid for wire-and-tube condensers

with tube outer diameter ranging from 4.8 to 6.2 mm, number of

tube rows from 13 to 25, and number of wire pairs from 10 to 90

[18]. The radiative heat transfer coefficient is calculated from the

following linearized model:

arad ¼ ecrðT c þ T aÞðT 2c þ T

2aÞ ð11Þ

where r is the Stefan–Boltzmann constant, whereas ec (=0.81) is theemissivity of the condenser walls.

2.1.4. Evaporator

The no-frost evaporator, illustrated in Fig. 2, was divided into

two domains, namely refrigerant flow and air-side heat and masstransfer. The specific refrigerant enthalpy at the evaporator outlet

can be expressed as [12–14]:

h5 ¼ h4 þ Q sen þ Q lat

mxð12Þ

where h5 = h( pe, T 5) and T 5 = T e + DT sup. The evaporator superheat-

ing, DT sup, varies with time due to the periodic door opening. To

address this issue, a moving-boundary approach, as introduced by

Wedekind and Stoecker [19], was adopted:

f ¼ fss ðfss f

Þ expðsDt Þ ð13Þ

where fss is the two-phase boundary position in the steady-state

regime, and s is a time constant, calculated respectively from

fss ¼ ð1 x4Þmoxhlvq0

ð14Þ

s ¼ ð1 cÞqlð

14pD2eÞhlv

q0 ð15Þ

where mxo (=3.8 kg/h) is the initial mass flow rate evaluated at

steady-state conditions, c is the mean void fraction of the two-phase region, calculated as suggested by Cioncolini and Thome

[20], De is the inner diameter of the evaporator coil, and q0 is the

heat transfer rate per unit length in the two-phase region, calcu-

lated from

q0 ¼ mxðhv h4Þ

fo ð16Þ

where f = Le at t = 0.

Fig. 2. Schematic representation of the ‘‘no-frost’’ evaporator coil.

388 B.N. Borges et al./ Applied Energy 147 (2015) 386–395


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2.2. Evaporator frosting

The evaporator sub-model calculates the cooling capacity from

the following heat and mass balances on the air-side (see Fig. 2). In

the case of a uniform coil temperature, i.e. evaporator filled with

two-phase refrigerant, the heat and mass balances yield:

Q sen ¼ mac p;aðT fr T iÞ 1 exp ae Aemac p;a

ð17Þ

Q lat ¼ mahsvðwfr wiÞ 1 exp ae Ae

mac p;aLe

2=3 !" # ð18Þwhere Q e = Q sen + Q lat, T fr is the frost surface temperature,

wfr = wsat(T fr) is the humidity ratio at the frost surface, Le is the

Lewis number and ae is the air-side heat transfer coefficient calcu-lated as suggested by Barbosa et al. [21],

aeGmaxc p

¼ 0:6976 Re0:4842D Ae Ato

0:3426Pr2=3 ð19Þ

where Gmax = ma/ Amin is the mass flux at the minimum free flow

passage, i.e. the cross-section area obtained from a transversal cut

including tubes and fins, and Ato is the surface area of the tube only.

One should note that the evaporator of the refrigerator under study

is similar to sample #6 tested by Barbosa et al. [21]. In addition, one

should note that, in the cases where superheated refrigerant takes

place, the terms between brackets in equations (17) and (18) must

be modified to account for the refrigerant temperature variation, as

described in [22].

The frost formation model was based on the work of Hermes

et al. [23], which was originally developed for horizontal flat sur-

faces and later adapted by [5] for finned-tube heat exchangers

(Fig. 2). According to [23], the frost surface temperature is calcu-

lated from:

T fr ¼ T e þ ðQ sen þ Q latÞd

kfr Aeþ wsat;ehsvqaDfr

kfrð1 coshHaÞ ð20Þ

where Ha is the Hatta number, and kfr and Dfr are the effective ther-

mal conductivity and vapor diffusivity of the frost layer, respec-

tively, calculated as described in [23]. In addition, the growth rate

of the frost layer of thickness d is calculated from:

dd

dt ¼

2kfrbqfrdhsv

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 þ bdQ senkfr Ae

2þ4bdhsvkfr

Gfr

s 1 þ

bdQ senkfr Ae

2435

ð21Þ

where Gfr is the total mass flux of the vapor transferred to the

frosted medium, and b is an empirical parameter that comes from

the frost density correlation in the following form [24]:

Fig. 3. Schematic representation of the air flow during a door opening event.

0,000 0,002 0,004 0,006 0,008 0,010 0,01240

42

44

46

48

50

52

54

56

58

60

∆ P t

[ P a ]

Va [m³/s]

∆Pe = 5 Pa∆Pe = 5 Pa

∆Pe = 15 Pa∆Pe = 15 Pa

∆Pe = 25 Pa∆Pe = 25 Pa

∆Pe = 35 Pa∆Pe = 35 Pa∆Pe = 45 Pa∆Pe = 45 Pa

Fig. 4. Characteristic curve of the fan.

Fig. 5. Schematic representation of the wind-tunnel facility.


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qfr ¼ a expðbTfrÞ ð22Þ

The accumulated frost mass and the frost thickness are calculated,

respectively, from mfr = mfro + Gfr AeDt and d = d

o + (dd/dt )Dt [5,23].

In addition, the frost density is obtained from qfr(t > 0) = mfro / Aed

o,

where the superscript ()o represents the values at the previous

time-step. The defrost process has not been accounted for by the

model.

2.3. Refrigerated compartments

The model for the refrigerated compartments, which was based

on the work of Borges et al. [14], is aimed at determining the psy-

chrometric conditions of the moist air inside the fresh-food and

freezer (frozen-food) compartments over time by means of tran-

sient energy and mass balances, which yield the following expres-

sions for the air temperature and humidity of the fresh-food and

freezer compartments, respectively:

T ¼ T ss; ðT ss; T oÞ exp

ADt

C

ð23Þ

w ¼ wss; ðwss; woÞ exp B

Dt q/

ð24Þ

where T o

and wo

are the air temperature and humidity ratio

of the compartment at the beginning of the time-step,

A⁄

= UA⁄

+ UAm + md,⁄c p,a + m⁄c p,a and B⁄ = md,⁄ + m⁄. The asterisk ()⁄indicates either the freezer (fz) or the fresh-food (ff) compartment.

The thermal conductance of each compartment, UA⁄

, and of the

mullion, UAm, and the equivalent thermal capacity and mass of each

compartment, C ⁄

and /⁄, respectively, were all obtained from

experimental data. In addition, the terms T ss,⁄ and wss,⁄ are related

to the steady-state condition, and calculated as follows:

T ss; ¼ ðUA þ md;c p;aÞT a þ UAmT r þ ma;c p;aT o

A

ð25Þ

wss; ¼ md;wa mwo

Bð26Þ

where

T o ¼ rTfz þ ð1 r ÞT ff Q senmac p;a

ð27Þ

wo ¼ rwfz þ ð1 r Þwff Q latmahsv

ð28Þ

where r is the freezer air flow ratio.

The air flow rate entering the cabinet during a door opening

event is calculated as described by Wang [25], and shown in

Fig. 3, as follows:

md; ¼ 2

3K qW d;H d;

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffi2gHd;ð1 qa=qÞ

ð1 þ ðq=qaÞ1=3Þ

3

v uut ð29Þwhere K ⁄ is an empirical discharge coefficient determined from

experimental data.

The air-side hydrodynamics was modeled according to the

methodology outlined in Hermes et al. [13]. The overall pressure

drop was thus correlated to the air flow rate through the following

expression:

D pt ¼ c qaV 2 þ D pe ð30Þ

where c is an empirical coefficient obtained from experimental data,

and D pe is the pressure drop in the frosted evaporator, calculated asfollows:

D p ¼

fG2max

2qa

Ae Amin ð31Þ

where f is the friction factor calculated from [21]:

f ¼ 5:965 Re0:2948D Ae At

0:7671N lo2

0:4436ð32Þ

The characteristic curve for the fan, depicted in Fig. 4, wasfitted toa

third-order polynomial using experimental data obtained in a wind-

tunnel facility [13], illustrated in Fig. 5.

2.4. Solution algorithm

The model was coded in EES [26]. The solution algorithm, illus-

trated in Fig. 6, is based on a sequential solution for the models forthe refrigerated compartments and the refrigeration loop, whose

Fig. 6. Information flow diagram of the simulation model.



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sub-models are in turn solved simultaneously by the Newton–

Raphson technique. The evaporator frosting and dry-out sub-mod-

els are solved implicitly in the inner loop, whereas the models for

the refrigerated compartments are solved explicitly in an outer

loop, as depicted in Fig. 6. The on–off cycles were implemented

by means of an IF-THEN-ELSE loop that emulates a thermostat.

The door opening patterns are included in the model in an outer

loop, as shown in Fig. 6. More information can be obtained in [22].

3. Experimental work

The refrigerator was carefully instrumented as illustrated in

Fig. 7. The evaporating and condensing pressures were measured

by means of strain gauge pressure transducers ranging from 0 to

10 bar (±2 mbar uncertainty) and from 0 to 20 bar (±4 mbar uncer-

tainty), respectively. A Coriolis-type mass flow meter with a mea-

surement uncertainty of ±0.03 kg/h was installed at the

compressor discharge. The compressor and fan power consump-

tion were monitored using a digital power analyzer with a mea-

surement uncertainty of ±0.1%. Capacitive relative humidity

transducers (±2% uncertainty) were installed at the evaporator

inlet and outlet together with pressure takes for air-side pressure

drop measurements using a differential pressure transducer rang-ing from 0 to 62.5Pa (±0.3 Pa uncertainty). All T -type

thermocouples employed in this study have a measurement uncer-

tainty of ±0.3 C. More details can be found in [22].

The experimental plan, summarized in Table 1, was designed to

provide all of the empirical information required for the sake of

model closing. The doors were opened and closed using a pur-

pose-built door-opening device attached to both the freezer and

fresh-food doors [3], so that they could be operated independently.

The arrangement is placed within a climate chamber, depicted in

Fig. 8, which provides a strict control of temperature, humidity

and air velocity.The time between door opening events and the length of time of

the event are both easily programmed. Patterns comprised of 4

cycles of door opening events, each cycle lasting 1 h and applied

in sequence, were adopted, with a 4-h interval between cycles.

After this period, the system was kept running for 8 h with the

doors closed. The pattern was repeated every 24 h. In a door open-

ing cycle, the freezer door was opened every 12 min for 10 s over a

period of 1 h, totalizing 5 opening events per hour. On the other

hand, the fresh-food door was opened every 2.5 min for 30 s, tota-

lizing 20 opening events per hour.

4. Results

The model predictions were compared with the correspondingexperimental data for ambient conditions of 32 C and 70% RH.

Fig. 7. Summary of the instrumentation.

Table 1

Summary of experimental tests.

Experiment Test facility Ambient conditions Empirical parameter

Fan characteristics Wind-tunnel 21 C, 50% RH 3rd-order polynomial

Cabinet hydrodynamics Wind-tunnel 21 C, 50% RH c Refrigeration loop Chamber 6 runs, doors closed, 25 < T < 38 C, 8 < w < 32g/kg r , gv, gg, UAk, UA⁄, UAm, C ⁄Door opening tests Chamber 3 runs, door openings, 25 < T < 38 C, 12 < w < 21g/kg K ⁄, /⁄, qfr

o , mko, b


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The simulations were initiated at the compressor start up immedi-

ately after a defrost cycle and lasted until the next defrost cycle

began. Fig. 9 shows the predicted and experimental results for

the refrigerated compartment temperatures for the whole period.

Two door opening cycles can be clearly seen, the first from 30

to 90 min and the second from 330 to 390 min. It should be

noted that the model follows closely the experimental trends, with

an average deviation of around ±2 C, the maximum discrepancies

occurring during door opening.

Fig. 10 compares the predictions of the working pressures with

the experimental data. It can be observed that the model predic-

tions for the evaporating pressure are within a ±5% error band,

while the condensing pressure is under predicted with an offset

of approximately 0.5 bar during the whole period, but with devia-

tions within a ±10% band. Consequently, the power consumption is

also reasonably well predicted by the model, with deviations not

exceeding ±5%, as shown in Fig. 11.

Fig. 12 shows the time-evolution of the evaporator superheat-

ing. Five peaks can be observed during the test period, which

Fig. 8. Schematic representation of the climate chamber.

0 60 120 180 240 300 360 420 480 540

-25

-20

-15

-10

-5

0

5

10

15

20

25

Time [min]

Tfz, Experimental

Tfz, Simulated

Tff, Experimental

Tff, Simulated

T e m p e r a t u r e [ ° C ]

Fig. 9. Time evolution of the refrigerated compartment temperatures.

0 60 120 180 240 300 360 420 480 5407

8

9

10

11

12

13

14

15

16

17

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.71.8

1.9

2.0

Time [min]

E v a p o r a t i n g p r e s s u r e [ b a r ]

C o n d e n s i n g p r e s s u r e [ b a r ]

Pc, Experimental Pc, SimulatedPc, Simulated

Pe, ExperimentalPe, Exper imen tal Pe, SimulatedPe, Simulated

Fig. 10. Time evolution of the condensing and evaporating pressures.



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appear when both doors are opened concurrently, thus increasing

the thermal loads and pushing the dry-out position downstream of

the evaporator. Small variations in the evaporator superheating

occur when only the door of the fresh-food compartment is

opened. It can also be noted that the model predictions follow

the experimental trends satisfactorily, although errors of up to

3 K can be observed in the peaks.

Fig. 13 shows the time-evolution of the air-side pressure drop

due to evaporator frosting and Fig. 14 explores the air-side predic-

tion capabilities of the model. For a clean evaporator coil, a 5 Pa

pressure drop is observed, increasing steadily to 15 Pa during the

first cycle of door opening events. This value does not change dur-

ing the period when the doors are kept closed, since there is no

moisture infiltration and, therefore, no frost growth. During the

second cycle of door openings the evaporator air-side pressure

drop increases to around 25 Pa. During the whole period the model

predicted satisfactorily the experimental trends, although absolute

errors of up to 5 Pa can be observed.

Fig. 14 shows the calculated frost mass for each of the five evap-

orator rows. The rows are numbered from bottom to top, according

to the air flow direction, as illustrated in Fig. 2, and comprised 27

(1st), 34 (2nd), 67 (3rd), 66 (4th), and 67 (5th) fins. It can be noted

that the frost is mostly accumulated along the first three rows,

which is due to the higher humidity gradient at the evaporator

inlet. It can also be noted that there is more frost accumulated

along the 3rd row than along the 1st row, which is due to thehigher heat transfer (finned) area of the former.

0 60 120 180 240 300 360 420 480 540

0

20

40

60

80

100

120

140

160

180

200

Time [min]

C o m p r e s s i o n p o w e r [ W ]

SimulatedSimulated

ExperimentalExperimental

Fig. 11. Time evolution of the compression power.

0 60 120 180 240 300 360 420 480 540

0

2

4

6

8

10

12

Time [min]

E v a p o r a t o r s u p

e r h e a t i n g [ K ]

Experimental

SimulatedSimulated

Fig. 12. Time evolution of the evaporator superheating.

0 60 120 180 240 300 360 420 480 540

0

5

10

15

20

25

30

Time [min]

Experimental

SimulatedSimulated

E v a p o r a t o r a i r - s i d e p r e s s u r e d r o p [ P a ]

Fig. 13. Time evolution of the evaporator air-side pressure drop.

0 60 120 180 240 300 360 420 480 540

0

20

40

60

80

100

120

Time [min]

A c c u m u l a t e d f r o

s t m a s s [ g ]

2nd

Row2nd

Row

1st Row

3rd

Row3rd

Row

4th

Row4th

Row

5th

Row5th

Row

Fig. 14. Time evolution of the accumulated frost mass along each evaporator row.


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5. Summary and conclusions

A quasi-steady-state semi-empirical mathematical model was

developed to predict the transient behavior of the key operating

parameters (i.e., working pressures, compression power, compart-

ment temperatures, and accumulated frost mass on the evap-

orator) of a two-door frost-free refrigerator subjected to periodic

door opening. The model predictions were compared with a setof in-house experimental data collected in a climate-controlled

chamber. The door opening were carried out by a purpose-built

apparatus according to a predefined pattern.

It was found that the model predictions followed closely the

experimental trends, with deviations for the working pressures

and power consumption not exceeding the 10% thresholds and pre-

dictions for the compartment air temperatures being within ±2 C

error bands. The model was also used to predict the frost dis-

tribution over the evaporator coil and it was observed that the frost

accumulates mostly in the first three rows, the third row being cru-

cial in terms of frost clogging because of the higher number of fins

and thus lower free flow passage of air.

Acknowledgments

This study was carried out at the POLO facilities under National

Grant No. 573581/2008-8 (National Institute of Science and

Technology in Refrigeration and Thermophysics) funded by the

Brazilian Government Agency CNPq. The authors are grateful to

Mr. Rafael Gões for his valuable support in the experiments.

Financial support from Whirlpool Latin America S.A. is also duly

acknowledged.

Appendix A. Refrigerator characteristics

Refrigerator

Type: Top-mount frost-free.

Refrigerant type/charge: HFC-134a/100 g.

Cabinet internal volume: 439 liters.

Fan power consumption: 7 W.

Compressor

Type: Hermetic reciprocating compressor.

Stroke: 6.76 cm3.

Speed: 60 Hz.

Condenser

Type/material: wire-and-tube/steel.

Length of the discharge line: 1600 mm.

Condenser height/length of the wires: 1210 mm.Condenser width: 540 mm.

Tube outer diameter: 5.1 mm.

Bend radius: 28.8 mm.

Number of tubes: 21.

Wire diameter: 1.4 mm.

Number of wires: 90.

Surface emissivity: 0.81.

Internal heat exchanger

Type/material: concentric/copper.

Capillary tube outer diameter: 1.90 mm.

Capillary tube inner diameter: 0.80 mm.

Capillary tube length: 2.55 m.

Heat exchanger length: 1.34 m.

Approximate heat exchanger effectiveness: 65%.

Suction line inner diameter: 7 mm.

Evaporador

Type/material: no-frost tube-fin/aluminium.

Coil length: 7.585 m.Inner diameter: 6.7 mm.

Outer diameter: 7.9 mm.

Number of tubes: 10 (longitudinal)/2 (transversal).

Evaporator height: 189 mm.

Evaporator width: 340 mm.

Evaporator depth: 59 mm.

Number of fins (1st row): 27.

Number of fins (2nd row): 34.

Number of fins (3rd row): 67.

Number of fins (4th row): 66.

Number of fins (5th row): 67.

Fin dimensions: 35 mm (height)/59 mm (width)/0.125 mm

(thickness).

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