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1、Applied Thermal Engineering 29 (2009； 1622-1630 Contents lists available at ScienceDirect Applied Thermal Engineering ELSEVIER journal homepage: A semi-empirical model for steady-state simulation of household refrigerators Joaquim M. GoncalvesClaudio Melob, Christian J.L. Hermesb, IVleasmecI disclia

2、iage temp*erafluiae C Fig. 3. Validation of the compressor sub-model: (a) mass flow rate, (b) power consumption and (c) compressor discharee temperature 40 40 sssu P3pd b 三 uo-dumsug.u乡 od P8J一pid c bo-srIU芒 ddEE 胡fe-ss 一 p WWH-d I HI IVleasured power consumption IW1 8 3.2. Heat exchangers: condense

3、r and evaporator The condenser is a natural draft wire-and-tube heat exchanger, in which the air-side temperature is assumed to be uniform The condenser was divided into three regions depending on the refrigerant state: superheated, saturated or subcooled (Fig 4a) The heat transfer rate in each regi

4、on was then modeled following the &NTU method 9 The refrigerant at the condenser exit was obtained from the following energy balance: /I4 = 3 Qc.su p + Qcsat + Qc.sub (7) W where the heat transfer rates were calculated as follows: Qc,SUp = w(居 一 hv) = Wfpy佝 一 G)l - exp(UAgp/wCp,v), (7a) Qcsat = W知=U

5、A昭：一 fa),(7b) Qc価=w(h| -h4) = wcp,i(tc - ta)l - exp(-U/lsllb/wCp,i). (7c) Note that Eqs. (7a) - (7c) are constrained by the overall condenser area, Ac = Ac* 1201 3I140150 Refrigerant charsc gl 4O4H2CEM 1 I 2 2 a L) -iin 一5Nh=-二 w1.5三 IM -SES-SSUWtMQd 170 -17- 9( -；tnibiei)t temperature = 32 C Svstci

6、n # -AJ.WlMhulH 二氏 IBlrw 二 1002.0(M2.5(M 3JKMI 3.5004.5005.0(H Compressor speed |rpin| 2( o o J o o o o o o 3 2 112 4 c -u - msvdujf,sxuf Fig. 9. Model validacion vaiying Q) the refrigerant charge, (b) the compressor speed and (c) the valve opening. -18- 90 0.10.20.30.4 仇5 0.60.7(.0.91 Capillary tub

7、c-siictiaii line lieat excluinger effectiveness Fig. 10. Effect of the capillary tube-suction line heat exchanger effectiveness. 5 o 1 I 1 1 20 5 1 1 o n )5 n 95 105 Fig. 10 depicts the effect of capillary tube to suction line heat exchanger effectiveness on the compressor power. It can be seen that

8、 both compressor power and refrigerant charge decrease with increasing effectiveness, which is due to the reduction in the vapor quality at the evaporator inlet and, thus, a lower amount of refrigerant is needed In practical terms, the proposed effectiveness enhancement can be performed by increasin

9、g the heat exchanger length or reducing the suction line diameter. Fig. 11 shows the effect of the finned surface of the heat exchanger on the compressor power. It can be noted that the compression power decreases with increasing condenser surface, although a higher amount of refrigerant is required

10、 to keep the internal air temperature constant (Fig. 11a). It can also be noted that the heat transfer surface was considerably increased, although the power consumption changed only 5%. When the number of evaporator fins was changed (Fig. lib), not only the refrigerant charge but also the compresso

11、r speed needed to be adjusted to keep the internal air temperature constant. Also, it is worth noting the asymptotic power consumption reduction with the increase in either the condenser or evaporator heat transfer surface -19- 7 11 90100111)12()IM140ISO160 Refrigerant charge |g| Fig. 12. Map of the

12、 refrigerator states. 1 1 9 9 8 Fig. 12 shows the map of refrigerator states considering the refrigerant charge, compressor speed and capillary tube inner diameter as state variables. This map shows a region where the compressor power reaches an optimum value In this region, both the condenser and t

13、he evaporator are fully charged, with their exits are approximately in the saturated state. Increasing the compressor speed also increases the refrigerant charge band between an undercharged condenser and an overcharged evaporator, always with a penalty with regard to the compressor power consumptio

14、n. This result shows an opportunity not only for the design of an almost optimum system but also for the implementation of a multi- variable control system to explore the advantages of 什“s behavior. 5 Concluding remarks The conclusions of this study can be summarized as follows: Experiments: A top-m

15、ount refrigerator was tested under a wide range of operating conditions. Thirteen variables were experimentally evaluated that led to over 160 data points. Refrigerant pressure and temperature measurements were taken at seven locations along the refrigeration loop with a minimum effect on system per

16、formance These data were essential for the development and validation of the component sub-models. Models: The mass, energy and momentum conservation equations were used as a framework for the component sub-models. Parametric and lumped models were also developed and fitted to the experimental data.

17、 The main empirical parameters were the friction factors and the heat transfer coefficients Numerical procedures: The sub-models were implemented in the EES software The computer code was written in a modular format, using a specific procedure for each of the components When all the routines are run

18、 together the program solves a set of four non-linear equations The program predictions were compared to the measured data and a reasonable level of agreement was achieved -21- Analysis: The effects of some key parameters on the system performance were determined. During this analysis the internal a

19、ir temperature was held constant reflecting a design requirement. A map of the system states which provides insights into both the design and control procedures was also presented This type of analysis provided a realistic insight into the systemic behavior, which is otherwise laborious and costly t

20、o carry out experimentally. Acknowledgements The authors are grateful to Empresa Brasileira de Compressores (EMBRACO S.A.) for sponsoring this research program. The continued support from Conselho Nacional de Desenvolvimento Cientlfico (CNP ) is also duly acknowledged. References 1 GL Davis, TC Scot

21、t, Component modeling requirements for refrigeration system simulation: large effort, little effect? in: Compressor Technology Conference at Purdue, West Lafayette, IN, USA, 1976, pp. 401 - 40& 2 D. Arthur, Little, Inc., Refrigerator and Freezer Computer Model User s Guide,U.S. Department of Energy,

22、 Washington, DC, 1982. 3 DS Abramson, I. Turiel, A. Heydari, Analysis of refrigerator-freezer design and energy efficiency by computer modeling: DOE perspective, ASHRAE Transactions 96 (Part I) (1990) 1354 - 1358. 4 R.N Reeves, C.W. Bullard, R.R. Crawford, Modeling and experimental paiameter estimat

23、ion of a refrigeration/freezer system, ACRC TR-9, University of Illinois at Urbana-Champaign, Urbana, IL, 1992 5 FH Klein, C Melo, ME Marques, Steady-state simulation of an all refrigeratorjn: Proc of the 20th International Congress of Refrigeration, Sydney, 1999, vol.Ill, Paper 073. 6 M.M. Mezavila, C. Melo, CAPHEAT: an homogeneous model to simulate refrigerant flow through non-adiabatic capillary tub