Simulation-based design and optimization of refrigeration cassettes

Simulation-based design and optimization of refrigeration cassettes

Applied Energy 88 (2011) 4756–4765 Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy Simu...

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Applied Energy 88 (2011) 4756–4765

Contents lists available at ScienceDirect

Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Simulation-based design and optimization of refrigeration cassettes q Maicon Waltrich b, Christian J.L. Hermes a,⇑, Cláudio Melo b a b

Applied Thermodynamics Research Group, Department of Mechanical Engineering, Federal University of Paraná, P.O. Box 19011, 81531-990 Curitiba-PR, Brazil POLO Research Laboratories for Emerging Technologies in Cooling and Thermophysics, Federal University of Santa Catarina, 88040-970 Florianópolis-SC, Brazil

a r t i c l e

i n f o

Article history: Received 16 April 2011 Received in revised form 8 June 2011 Accepted 11 June 2011 Available online 6 August 2011 Keywords: Refrigeration Design Simulation Optimization Cost Performance

a b s t r a c t A model-driven design and optimization methodology for sizing the components of refrigeration cassettes for light commercial applications (i.e., cooling capacities ranging from 0.5 to 1.5 kW) is presented. Mathematical models were devised for each of the system components and their numerical results were compared with experimental data taken with different cassettes. It was found that the model predictions for the working pressures, power consumption, cooling capacity and coefficient of performance (COP) showed maximum deviations of ±10%. A genetic optimization algorithm was used to design the condenser and evaporator and also to select the compressor model based on an objective function which considers both the COP and cost. The optimization led to two improved cassette designs, which were assembled and tested. One of the optimized cassettes showed a COP/cost ratio approximately 50% higher than that of the baseline system. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction The annual energy consumption due to air conditioning and refrigeration equipment corresponds to approximately 10% of the energy produced worldwide [1]. Light commercial refrigeration appliances (e.g. beverage coolers, chest freezers, vending machines, display cabinets) are one of the major players in this sector. Some of the beverage coolers currently on the market are composed of a thermally insulated cabinet and a compact cooling system, also known as a refrigeration cassette (see Fig. 1) [2]. In comparison to the conventional refrigeration systems, the cassette systems are easier to transport, to replace and to access for cleaning and maintenance. The cassette refrigeration system comprises two fan supplied tube-fin heat exchangers (evaporator and condenser), a hermetic reciprocating compressor, and a thermostatic expansion valve. Additional components such as a pre-condenser and a liquidline/suction-line heat exchanger (also known as internal heat exchanger) are also employed. The air streams through the condenser and evaporator are separated from each other by polyurethane insulation wall. Of these components, the compressor and the heat exchangers are those which have a major impact both on the system coefficient of performance (COP) and cost. The compressor

q An abridged version of this manuscript was presented at the 13th International Refrigeration and Air Conditioning Conference at Purdue, 12–15 July, 2010. ⇑ Corresponding author. Tel.: +55 41 3361 3239. E-mail address: [email protected] (C.J.L. Hermes).

0306-2619/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2011.06.020

selection and the heat exchanger design usually follow standardized test procedures (e.g. SE-SP-200 to 204, [3]), which are costly and time consuming. Alternatively, mathematical models can be employed to reduce the amount of prototypes and experimental runs required [4,5]. Several publications can be found in the literature with an emphasis on the numerical simulation of refrigeration systems [4–20], but optimization studies for component sizing are quite scarce. Furthermore, the reported studies on system optimization treat one component at a time [21–26], neglecting the intrinsic relationship between the system components. In this context, a simulation model focused on the numerical optimization of refrigeration systems was tailored based on the prior work of Hermes et al. [5], validated against reliable experimental data, and then employed to optimize the cassette design by simultaneously varying the compressor, condenser and the evaporator characteristics. The optimization runs let to two cassette designs with a reduced cost and an improved COP.

2. Simulation model The mathematical formulation employed follows that originally proposed by Hermes et al. [5] for household refrigerators. The system simulation model was divided into the following sub-models (see Fig. 2): compressor, pre-condenser, air-supplied heat exchangers (condenser and evaporator), and liquid-line/suction-line heat exchanger.

M. Waltrich et al. / Applied Energy 88 (2011) 4756–4765

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Nomenclature Roman $ A C COP cp d e G h H k L m M N Nt NTU p PEC Q t UA W

cost (FMU) area (m2) thermal capacity (W/K) coefficient of performance specific heat at constant pressure (J kg1 K1) tube I.D. (m) thickness (m) mass flux (kg m2 s1) enthalpy (J kg1) heat exchanger height (m) thermal conductivity (K W1) heat exchanger width (m) mass flow rate (kg s1) mass (kg) compressor speed (Hz) number of tube rows number of transfer units pressure (Pa) performance evaluation criterion heat transfer rate (W) temperature (K) thermal conductance (W K1) power (W)

e g

heat exchanger effectiveness efficiency

Subscripts 1–7 positions along the refrigeration loop a ambient, air b booster fan cv control volume d discharge e evaporator g overall h heaters i inlet ihx internal heat exchanger k compressor l liquid pc pre-condenser r refrigerant, return s isentropic process sat saturated sub subcooled sup superheated v volumetric, vapor w calorimeter walls x expansion device

Greek

a

heat transfer coefficient (W m2 K1)

2.1. Fan-supplied tube-fin heat exchangers Two sub-models, one for heat transfer and another for pressure drop (see Fig. 3) were used to simulate the heat exchangers [27]. The thermal sub-model was divided into two domains, namely the air and refrigerant sides. Bearing in mind that the best simulation model is the one which provides the desired results with a minimum computational effort, some minor effects (i.e. two-phase heat transfer coefficient, refrigerant-side pressure drop, coil circuitry) have been overlooked and all modeling efforts have been

placed on factors that actually play important roles on the system performance, such as air-side pressure drop, fan characteristics, heat exchanger geometry. In this fashion, the thermal resistances to conduction through the tube and fin walls were neglected, and both the air and refrigerant flows were assumed to be distributed (one-dimensional), steady-state and purely advective, in order to capture the influences of the different flow regions (i.e. refrigerant superheating, two-phase flow, and sub-cooling). The heat transfer rate Qcv was calculated from the concept of heat exchanger effectiveness, as follows:

Fig. 1. Schematic of the refrigeration cassette.

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Fig. 2. Schematic of the refrigeration loop.

Q cv ¼ ecv C min ðt i;h  t i;c Þ ¼ mr Dhr

ð1Þ

where the ‘‘’’ sign applies to the condenser and the ‘‘+’’ sign to the evaporator, Cmin = min(mrcp,r, ma,cvcp,a) is the lowest thermal capacity (W K1) of the streams, and ti,h and ti,c are the temperatures of the hot and cold streams at the entrance ports (K), respectively. The control volume effectiveness e for a mixed, cross-flow, singlepass heat exchanger was calculated as follows for single-phase refrigerant flow regions [28]:





0:78 ecv ¼ 1  exp NTU0:22 C 1 Þ  1Þ r ðexpðC r NTU

ð2:aÞ

where Cr = Cmin/Cmax, and NTU = UA/Cmin is the number of transfer units. In case two-phase refrigerant takes place, the control volume effectiveness was calculated as follows [28]:

ecv ¼ 1  expðNTUÞ

ð2:bÞ

The fin efficiency was calculated by the procedure introduced by Schmidt [29], and the heat transfer coefficients were obtained from empirical correlations. The air-side heat transfer coefficients were calculated from the correlation proposed by Wang et al.

[30], and the heat transfer coefficients for the refrigerant side were derived from Gnielinski’s [31] correlation for single-phase flows, and assumed to be infinite for condensing and evaporating flows of HFC-134a. It worthy of note that when the refrigeration cassette is running in steady-state conditions and with the doors closed – i.e. the regular test standard conditions – there is practically no air infiltration into the cabinet and, therefore, no latent heat transfer. The hydrodynamic sub-model considers the heat exchanger pressure drop and also the fan-supplied air flow rate. The air flow rate is dependent on both (i) the fan characteristics and (ii) the system impedance created by the evaporator, supply and return ducts, refrigerated compartment and fan hood, arranged in a closed loop for the cold air stream; and the condenser, fan hood and grills, arranged in an open-loop for the warm air stream. Therefore, the evaporator fan pressure head is calculated from Dpe = Dp1– 2 = Dp2–3 + Dp3–1, where the term Dp2–3 corresponds to the pressure drop in the evaporator coil, and Dp3–1 is the pressure loss in the refrigerated compartment (see Fig. 4). The condenser fan pressure head is calculated from Dpc = Dp6–7 = Dp5–6 + Dp7–8, where the term Dp5–6 corresponds to the pressure drop in the condenser coil, and Dp7–8 is the pressure drop at the outlet port (see Fig. 4). The operation point is found through the intersection of the heat exchanger pressure drop curve with the fan performance curve, expressed as a third–order polynomial. The solution algorithm employs two loops. First, the hydrodynamic sub-model is iteratively solved to obtain the fan-supplied air flow rate. Then the thermal sub-model is iteratively solved for each control volume following the refrigerant circuit. This procedure is repeated until convergence is achieved, i.e. when the largest temperature difference between two successive iterations is less than 0.1 K. Comparisons with experimental results showed that the model was able to predict 92% of the experimental data for the heat transfer rate with a maximum deviation of ±10%, and 88% of the experimental data for the pressure drop with a maximum deviation of ±15%. More details can be found in [27].

2.2. Compressor, pre-condenser and internal heat exchanger In most reciprocating compressors, the refrigerant passes successively through the compressor shell, the suction muffler, and the suction valve before entering the compression chamber from where it is pumped through the discharge valve and then through the discharge muffler to the condenser. The refrigerant enthalpy at

Fig. 3. Physical model of the tube-fin heat exchangers.

M. Waltrich et al. / Applied Energy 88 (2011) 4756–4765

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Fig. 4. Schematic of the air circuit.

the compressor discharge, h2, is calculated from an energy balance at the compressor shell,

h2 ¼ h1 þ ðW k  Q k Þ=mr

ð3Þ

The compressor mass flow rate, mr , and the compression power, Wk, are obtained from

mr ¼ gv V k N=v 1

ð4Þ

W k ¼ mr ðh2;s  h1 Þ=gg

ð5Þ

transfer coefficient was assumed to be constant (=38 W m2 K1), and obtained empirically from experimental tests carried out with the cassettes under investigation. The cassette employs a lateral liquid-line/suction-line heat exchanger (see Fig. 6.a). The refrigerant enthalpy at the entrance of the expansion device (see Fig. 2), h6, was obtained from the following energy balance:

h6 ¼ h5 ¼ h4 þ h7  h1

ð8Þ

The rate of heat released from the compressor shell, Qk, is calculated from

where t1 = t7 + eihx(t4  t5), and eihx was calculated from a epsilonNTU relation for double-pipe counterflow heat exchangers [28] using the following conductance,

Q k ¼ U k Ashell ðt 2  t a Þ

1 1 UA1 ihx ¼ Rv þ Rl ¼ ðaAgÞv þ ðaAgÞl

ð6Þ

The volumetric and overall efficiencies, gv and gg, of the compressor were obtained from the compressor maps supplied by the manufacturer, and fitted as linear functions of the pressure ratio, pc/pe, with maximum deviations of 10% for both power consumption and mass flow rate. The thermal conductance, Uk, on the other hand, was reduced from experimental tests carried out with the cassette, and assumed to be constant (=14 W m2 K1). The shell surfaces area, Ashell, was obtained from the compressor manufacturer. The pre-condenser is a gas cooler placed between the compressor and the condenser (see Fig. 5), and thus an equation is required to calculate the refrigerant enthalpy at the condenser inlet:

_ r cp;r Þ h3 ¼ h2 þ cp;r ðt2  ta Þ½1  expðU pc Apc =m

ð9Þ

where the indexes l and v stand for the liquid line and the suction line, respectively. The heat transfer coefficients of superheated vapor, av, and subcooled liquid, al, flowing through the suction line and liquid line, respectively, were obtained from the Gnielinski cor-

ð7Þ

where the heat transfer coefficient at the refrigerant side was calculated from the Gnielinski [31] correlation, and the air side heat

Fig. 5. Schematic of pre-condenser.

Fig. 6. Internal heat exchanger: (a) physical model and (b) thermal resistance.

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relation [31]. The liquid-to-suction line heat exchanger was modeled considering the tube walls as extended surfaces, whose effectivenesses gv and gl were calculated from the surface effectiveness definition considering the following characteristic length (see Fig. 6b): l = (pdi + et)/2 [32]. 2.3. Working pressures Two additional equations are required to determine the evaporating and condensing pressures. In general, the working pressures are obtained implicitly and iteratively from the following mass balances

_ r;k  m _ r;x ¼ 0 m M

X

ð10Þ

Mn ¼ 0

ð11Þ

n

where mr,k and mr,x are the compressor and the expansion device (the latter has not been modeled in this study) mass flow rates, respectively, M is the actual refrigerant charge and Mn is the calculated amount of refrigerant in each of the n components of the refrigeration loop (not modeled). It is worth noting that Eqs. (10) and (11) are non-linear functions of the working pressures, leading to time-consuming calculations and also to convergence issues. In order to keep a reasonable level of complexity, Eqs. (10) and (11) were replaced by fixed values of refrigerant superheating and subcooling at the evaporator and condenser exits, respectively. The working pressures were then calculated directly from

pe ¼ psat ðt7  Dt sup Þ

ð12Þ

pc ¼ psat ðt4 þ Dt sub Þ

ð13Þ

This procedure not only eliminates potential convergence issues, but also brings the numerical analysis closer to the design practice, where both the expansion valve and the refrigerant charge are adjusted a posteriori to guarantee a certain degree of superheating and subcooling. 2.4. Solution algorithm The code was implemented using the EES platform [33] and the REFPROP7 software [34]. The solution algorithm follows the procedure introduced by Hermes et al. [5], where two iterative loops were adopted. The input parameters are the air temperature at the condenser and evaporator inlets, the evaporator superheating and condenser subcooling, the compressor speed, and all the empirical parameters obtained from the experiments. In the outer loop, the condensing and evaporating pressures, and the refrigerant temperature at the compressor inlet are calculated by the Newton–Raphson method. In the inner loop, a successive substitution scheme was adopted for each of the system components. Thus, for a given set of values for pe, pc and t1, the compressor sub-model calculates h2, the condenser sub-model estimates h4 and t4 = t(pc, h4), the internal heat exchanger sub-model calculates h6

and t1, and the evaporator sub-model calculates h7 and t7 = t(pe, h7). The calculation procedure continues until convergence is achieved. 3. Optimization scheme The optimization of a refrigeration system is strongly dependent on the choice of an objective function (also known as performance evaluation criterion, PEC). In this study, the following PEC was devised in order to consider both the thermodynamic (COP) and economic (cost, $) performances:

PEC ¼

COP =$tot COP =$tot

ð14Þ

where the superscripts  and ° refer to the optimized and original cassette configurations, respectively, and $tot is the total cost, which considers the cost of each system component based on the following assumptions:  Cost data: The cost analysis was based on real cost data so that the real trends are properly reproduced by the model. However, a fictitious monetary unit (FMU) was employed.  Compressor: The compressor cost was estimated from $k = F$(COP  Qe)1/2, where both 1.5 < COP < 2.75 and 460 < Qe < 750 W were obtained from catalog data for evaporating and condensing temperatures of 10 °C and 45 °C, respectively. A fictitious monetary correction factor F$ = 0.68 FMU W1/2 was employed.  Heat exchangers: The costs of the heat exchangers were obtained based on the amount of raw material employed (80%) and on the cost of manufacturing (20%), thus: $hx = 1.25(MCu$Cu + MAl$Al), where $Cu = 4.5$Al, in (FMU/kg), MCu and MAl are given in (kg), and the indexes ‘Cu’ and ‘Al’ stand for copper and aluminum, respectively.  Fans and accessories: The cost of the fans were kept constant (7.20 FMU each), and the costs of the other accessories were considered to be 44.30 FMU. The optimization analyzes were conducted varying the evaporator and condenser geometries, and considering five different compressor models, as indicated in Table 1. The optimization constraints were imposed by the test standards for ‘‘small’’ refrigeration cassettes [3]. According to these standards, the system COP shall not be less than 1.0 under ‘‘C’’ condition, whereas the cooling capacity shall not be less than 230 W under ‘‘D-2’’ condition, as depicted in Table 2. The optimization was carried out using the genetic algorithm procedure available in EES [33]. 4. Experimental work 4.1. Experimental facility The experimental activities were carried out using a calorimeter to test refrigeration cassettes, as shown in Fig. 7 [35]. The air supplied by the evaporator fan (R) is cooled down by the evaporator coil and then directed towards a polyurethane-insulated chamber,

Table 1 Heat exchanger and compressor characteristics. Evaporator

Condenser

Compressor

Parameter

Min

Max

Parameter

Min

Max

Model

Vk (cm3)

Qe (W)

COP

Width (m) Height (m) Depth (m) Fin pitch (m) Tube O.D. (m)

0.3 0.076 0.044 0.002 0.0075

0.38 0.175 0.088 0.008 0.0115

Width (m) Height (m) Depth (m) Fin pitch (m) Tube O.D. (m)

0.2 0.152 0.044 0.001 0.0075

0.304 0.275 0.088 0.006 0.0115

Comp1 Comp2 Comp3 Comp4 Comp5

16.8 10.6 7.95 7.95 7.69

747 643 599 620 457

1.49 2.21 2.15 2.74 1.92

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M. Waltrich et al. / Applied Energy 88 (2011) 4756–4765 Table 2 Testing conditions. Condition

Qe (W)

COP

ti,e (°C)

ta (°C)

/a (%)

‘‘C’’ ‘‘D-2’’ ‘‘D-20’’ ‘‘D-38’’

n/a 230 n/a n/a

1.0 n/a n/a n/a

2 2 20 38

32.2 40.5 40.5 40.5

65 75 75 75

where a booster fan sets the pressure drop inside the chamber, whilst PID-controlled electrical heaters regulate the air temperature. A plenum is also employed to homogenize both the chamber air velocity and temperature. The cassette is attached to the cabinet in order to avoid any air and moisture infiltration. T-type thermocouples are placed at several positions within the chamber to provide the temperature distribution along the air circuit. A differential pressure transducer is also used to measure the pressure drop between the chamber inlet (I) and outlet (R) ports. The calorimeter operating limits are: maximum air side pressure drop of 125 Pa, and maximum heating power of 1.9 kW. The cassette is instrumented with pressure transducers and T-type thermocouples according to the recommendations of the SE-SP-200 to 204 standards [3]. The compressor power input is measured by a power analyzer. The condenser and evaporator fan power inputs are measured beforehand. A computer-based data acquisition system (96-channels, sampling rate of 5 s) is used to gather and process the experimental information. The calorimeter is placed inside an environmental room, with controlled indoor air temperature, humidity and velocity. The test conditions are then adjusted, and the cassette is kept on for 4 h until the steady-state regime is achieved. 4.2. Test conditions The test conditions are defined by the SE-SP-200 to 204 standards [3] for ‘‘small’’ cassettes [0.324 m (height), 0.508 m (width), 0.559 m (depth) and 22 kg (weight)], as summarized in Table 2. The minimum approval criteria are: (i) COP > 1 under ‘‘C’’ condition; (ii) Qe > 230 W under ‘‘D-2’’ condition; and (iii) (Qe,D-2 + Qe,D-20 + Qe,D-38)>1500 W. Moreover, the minimum evaporator air flow rate and pressure drop relationships are 255 m3/h (0 Pa), 212 m3/h

(25 Pa) and 190 m3/h (37 Pa). Hence, the product approval requires that at least five experimental tests are conducted. In this study, four different refrigeration cassettes running with HFC-134a were tested according to the recommendations of the SE-SP-200 to 204 standards [3] using various expansion valve and refrigerant charge adjustments, and also different compressors and heat exchanger configurations. In total, 59 experimental data points were collected. The geometric characteristics of the components tested (evaporators, condensers, fans and compressors) are summarized in Table 3. 4.3. Data acquisition The cassette input power corresponds to the sum of the compressor power, Wk, with the power of the heat exchanger fans, We and Wc.. The cassette cooling capacity was calculated using the three different approaches, described below. The first approach considers an overall energy balance involving both the chamber and the cassette,

Q e ¼ UAw ðt a  t i Þ þ

  kr Ar ta þ td t r þ t i  þ Wh þ Wb þ We lr 2 2

ð15Þ

where UAw ¼ 4:20  0:00978  ðt a  t i Þ (W K1). The first term of the right-hand side refers to the heat gain through the cabinet walls, the second term to the heat transfer from the hot spots (condenser and compressor shell) to the cold air circuit, Wh is the power dissipated inside the cabinet through the electric heaters, Wb and We are the power consumed by the booster and the evaporator fans, respectively. The second and third approaches consider an energy balance on the refrigerant and air sides, respectively.

Q e ¼ mr ðh7  h6 Þ ¼ mr ðh1  h4 Þ

ð16Þ

Q e ¼ ma cp;a ðt r  t i Þ þ W e

ð17Þ

where h7  h6 ¼ h1  h4 is obtained from an energy balance in the liquid-to-suction line heat exchanger. It is worth noting that the refrigerant side cooling capacity was calculated from the refrigerant enthalpies at points (1) and (4) (see Fig. 2), where there are only single-phase refrigerant. Fig. 8 compares the calculated cooling capacities derived from the three methodologies for all 59 experiments. It

Fig. 7. Schematic representation of the calorimeter.

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Table 3 Construction characteristics of the cassettes. Cassette Compressor Condenser Width Height/No. of transversal tubes Depth/No. of longitudinal tubes Fin pitch/No. of fins Tube O.D. Evaporator Width Height/No. of transversal tubes Depth/No. of longitudinal tubes Fin pitch/No. of fins Tube O.D.

C1 Comp1

C2 Comp3

O1 Comp5

O2 Comp5

0.304 0.250/10 0.066/3 0.0031/99 0.0095

0.304 0.200/8 0.066/3 0.0034/90 0.0095

0.304 0.275/11 0.088/4 0.0025/120 0.0075

0.210 0.200/8 0.044/2 0.00175/120 0.0075

0.380 0.200/8 0.066/3 0.0035/108 0.0080

0.380 0.150/6 0.066/3 0.0042/90 0.0080

0.380 0.175/7 0.088/4 0.0025/150 0.0095

0.300 0.150/6 0.044/2 0.0020/150 0.0095

Cooling capacity, W

1000 cabinet walls air side refrigerant side

800

600

400

200

0

5

10

15

20

25

30

35

orator design parameters and compressor characteristics) on the overall system performance. The following boundary conditions were assumed based on the mean values of the experimental results obtained for cassette C2: evaporator superheating of 4 °C, condenser subcooling of 5 °C, ambient temperature of 32.2 °C, and air return temperature of 2.2 °C. Fig. 10 explores the effect of the evaporator geometry on the cooling capacity with this component apart (Fig. 10a) and integrated into the system (Fig. 10b). It is worth noting that, albeit both analyses have similar trends, the evaporator is more sensitive to the modifications when it is apart from the system. For instance, a higher fin pitch reduces the cooling capacity by 38% and 19% with the evaporator apart and integrated into the system, respectively. This is so because with the evaporator integrated into the system,

Experimental run

can be seen that the results are similar for most of the data runs with a maximum deviation of 10%, the same magnitude of the measurement uncertainties reported by Marcinichen et al. [35].

(a)

5. Results 5.1. Model validation exercise

12 + 10%

8

A sensitivity analysis was carried out with cassette C2 to study the effect of changes at the component-level (condenser and evap-

- 10%

4

0

4

8

12

16

20

Measured pressure, bar

(b) 1200 cooling capacity power consumption

1000

+ 10%

800

- 10%

600 400 200 0

5.2. Parametric analysis

discharge suction

16

0

Calculated energy transfer rate, W

The experimental data used for the model validation exercise were obtained from the refrigeration cassettes C1 and C2 assembled with different and heat exchangers, but with all other components remaining unchanged (e.g. fans, thermostatic expansion valve and internal heat exchanger). The experimental runs were carried out under the ‘‘C’’ and ‘‘D’’ conditions of standards SESP-200 to 204 [3], and with the condenser subcooling varying from 1 to 11 °C (i.e. the condenser outlet temperature subtracted from the condensing temperature) and the evaporator superheating from 1 to 18 °C (i.e. the evaporating temperature substracted from the evaporator outlet temperature). The experimental data was used to calibrate the empirical parameters of the model, (i.e., the pre-condenser air-side heat transfer coefficient, and the compressor shell conductance) in order to improve the model predictions. Fig. 9 compares the measured working pressures (a), cooling capacities and power consumptions (b) with their simulated counterparts. It can be seen that the model predictions are close to the experimental data with a maximum deviation of ±10%.

20

Calculated pressure, bar

Fig. 8. Comparison among the cooling capacity calculation procedures.

0

200

400

600

800

1000

1200

Measured energy transfer rate, W Fig. 9. Comparison between calculated and measured values: (a) working pressures and (b) energy transfer rates.

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Cooling capacity, W

500

(a) 600

max min

450 400 350 300

Depth

450 400

Width

(b) 600

100 max min

80

450

60 57%

400

50%

40

350 25%

30%

20

15%

0

250 Width

Height

Depth

Fig. 10. Effect of evaporator geometry on cooling capacity and cost: (a) apart and (b) integrated.

the log-mean temperature difference increases, thereby attenuating the reduction of the cooling capacity. Fig. 10b also shows the influence of the evaporator parameters on the component cost, where it can be seen that variations in height, depth and width may reduce the cost by 60%, without a significant effect on the cooling capacity. A similar analysis was also carried out with the condenser, which is shown in Fig. 11 with this component apart and integrated into the system. Again, it is noteworthy that the condenser heat transfer duty is more sensitive to the geometric modifications with the condenser apart of the system. Fig. 12 shows the effect of the compressor model on the cassette COP. As depicted in Table 1, Comp1 has the higher cooling capacity and lower COP, Comp2 and Comp3 have medium cooling capacities and COPs, Comp4 has a medium cooling capacity and a high COP and Comp5 has the lowest cooling capacity and a medium COP. The COP and cooling capacity provided in the figure legend were obtained from compressor catalogues for an evaporating temperature of 10 °C and condensing temperature of 45 °C. It should be noted that by replacing compressor Comp3 by Comp4, the system COP experiences an increase of 15%, although a 22% increase is inferred from the compressor maps. It should also be noted that by replacing Comp2 by Comp3, the system COP increases 9%, instead of the 3% COP reduction inferred from the compressor maps. These results show the importance of selecting compressors models based on their effects on the system performance. 5.3. Cassette optimization Cassette C2 was chosen as the baseline for the optimization task since it provided a higher COP/cost ratio when compared to Cassette C1. The optimizations were performed under condition ‘‘C’’ assuming that both the evaporator superheating and the condenser subcooling are equal to 3 °C. Two optimization criteria were

Height

Depth

Fin pitch Tube O.D. 100

max min

550

80

500

60 45%

450 400

50%

40 25%

22%

28%

20 0

350

Fin pitch Tube O.D.

Width

Height

Depth

Fin pitch Tube O.D.

Fig. 11. Effect of condenser geometry on heat transfer rate and cost: (a) apart and (b) integrated.

2.00 1.80

Cassette COP

300

500

Fin pitch Tube O.D.

Cost reduction (gray bars) %

Cooling capacity, W

Height

Heat transfer duty, W

Width

500

550

350

250

(b) 550

max min

Cost reduction (gray bars), %

550

Heat transfer duty, W

(a)

1.60

Compressor data at -10ºC / 45ºC Comp 1 = 747 W / 1.49 Comp 2 = 643 W / 2.21 Comp 3 = 599 W / 2.15 Comp 4 = 620 W / 2.74 Comp 5 = 457 W / 1.92

1.40 1.20 1.00 0.80 Comp 1

Comp 2

Comp 3

Comp 4

Comp 5

Fig. 12. Effect of compressor model on cassette COP.

adopted: (i) maximum COP and (ii) maximum PEC = COP/$tot, giving rise to two different cassette configurations, namely O1 (COPbased) and O2 (PEC-based). It is worthy noting that there is no need to explore conditions other than those used for designing the cassette (condition ‘‘C’’) during the optimization task, as the intention is to select the best design in terms of cost and COP among hundreds of options and then construct a prototype. Once the prototype is constructed, the full set of tests shall then be performed. The optimized cassette characteristics are presented in Table 3. Each optimization process required almost 3 h to be completed. The results are summarized in Table 4 and presented graphically in Fig. 13. It is worth noting that the cassette O1 COP is 52% higher than that of the baseline with additional evaporator and condenser costs of 31% and 42%, respectively, and with a compressor cost

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Table 4 Comparison between experimental and calculated results. Variable

C2

Variation with respect to cassette C2, %

pe (bar) pc (bar) Wtot (W) Qe (W) COP

O1

Exp.

Sim.

Diff.

Exp.

Sim.

Diff.

Exp.

Sim.

Diff.

2.2 10.3 299.4 419.5 1.40

2.3 10.6 303.1 423.6 1.40

0.1 0.3 1.2% 1.0% 0.0%

2.1 10.4 279.5 561.2 2.01

2.1 10.5 266.1 567.5 2.13

0 0.1 4.8% 1.1% 6.0%

1.8 10.9 264.7 439 1.66

1.9 11.7 270 469.4 1.74

0.1 0.8 2.0% 6.9% 4.8%

with differences of ±5% for all the relevant parameters (COP, cooling capacity, working pressures, power consumption). Finally, it should be noted that the optimized cassettes surpassed the standardized requirements (see Fig. 14), with higher cooling capacities (33.8% (O1) and 4.7% (O2)) and higher COPs (43.6% (O1) and 18.6% (O2)) than the benchmark cassette C2. Another point to be noted is that during the tests under condition ‘‘D-38’’ the compressor thermal fuse, originally of 2.4 A, was replaced by another of 2.7 A, in order to keep the compressor running.

160 cassette COP compressor cost evaporator cost condenser cost

140 120 100 80 60 40

6. Conclusions

20 0

Cassette O1

Cassette O2

Fig. 13. Optimization results.

reduction of 18%. Although the heat exchangers became more expensive, the final cost of cassette O1 is lower than that of the baseline (see Table 4). Cassette O2, on the other hand, showed a COP 24% higher than that of the baseline, with cost reductions of 44%, 48% and 18% for the evaporator, condenser and compressor, respectively. Cassettes O1 and O2 were manufactured and tested in order to validate the optimization methodology. The expansion device opening and the refrigerant charge of these cassettes were adjusted beforehand, so that the cassettes O1 and O2 were tested with a refrigerant charge of 500 g and 200 g, respectively, whereas cassette C2 has required 260 g. The differences between the refrigerant charges of cassettes C2, O1 and O2 are mostly due to the different internal volumes of the heat exchanger coils. Table 4 compares the experimental (condition ‘‘C’’) and calculated results for cassettes C2, O1 and O2. It can be observed that the simulation results are in good agreement with the experimental counterparts,

1200 1000

A computer-aided methodology for the design, analysis and optimization of refrigeration cassettes for light commercial applications was introduced. Mathematical models were proposed for each of the system components, particularly the fan-supplied tube-fin heat exchangers (condenser and evaporator) as they affect significantly both the system performance and product cost. Furthermore, the component sub-models were applied together in order to simulate the thermal behavior of the refrigeration cassette. It was found that the model predictions for the working pressures, power consumption, cooling capacity and COP are very close to the experimental data with maximum deviations of ±10%. The system simulation model was invoked by a genetic optimization algorithm that searches for COP and cost improvements by simultaneously changing the heat exchanger design characteristics and the compressor model. The optimization exercise provided two improved cassette configurations, which were assembled and tested in a calorimeter apparatus. The optimized cassette configuration showed a COP/cost ratio approximately 50% higher than that of the baseline cassette. It is worth noting that a COP higher than 2 was obtained with the optimized cassette running with HFC-134a. Acknowledgements 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 CNPq Agency. Thanks are also addressed to Mr. Paulo C. Sedrez, undergraduate student of mechanical engineering at the POLO Labs, for his help with drawings and figures. The authors are also grateful to Dr. Jackson B. Marcinichen, presently at the École Polytechnique Fédérale de Lausanne, for his support with the experiments. Financial support from Embraco S.A. is also duly acknowledged.

C2 O1 O2

1100

Cooling capacity, W

O2

900 800 700 600

References

500 400

standardized lower limit

300 200

0

5

10

15

20

25

30

Air return temperature, °C Fig. 14. Product approval under condition ‘‘D’’.

35

40

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