PERFORMANCE SIMULATION OF SINGLE-EVAPORATOR DOMESTIC REFRIGERATOR USING ALTERNATIVE REFRIGERANTS

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1 Engineering Journal o the University o Qatar, Vol. 6, 2003, pp PERFORMANCE SIMULATION OF SINGLE-EVAPORATOR DOMESTIC REFRIGERATOR USING ALTERNATIVE REFRIGERANTS Talib Kshash Murtadha and Salam Hadi Hussain Mechanical Engineering Department University o Technology, Baghdad Republic o Iraq ABSTRACT The search or well-unctioning and energy-optimized rerigeration systems has made modeling and simulation o such systems an important tool or the industry in terms o product development. The present study explores how REFSIM ( a general computer model or simulation o steady-state perormance systems) can be used to handle the physics o a domestic rerigerator. Organization o the model is discussed and approach to modeling o main components with more detailed description in a domestic rerigerator (evaporator, condenser, compressor, capillary tube with and without heat exchange, and suction line) is explained. The modeling eort emphasis was on the local phenomena to be described by undamental thermodynamic, heat transer and luid mechanics relationships. Good agreement is ound with experiments or a wide range o operating conditions to a domestic rerigerator. I. INTRODUCTION Several authors (Cleland 990,Domanski and Didion 984, James and James 986) recognized that the ability to simulate the steady response o rerigeration systems will give engineers in the rerigeration industry the same advantages that simulation has brought to the ields o electronics, luid power, etc. The main advantages o such simulations include better understanding o system and component behavior, and the ability to test ideas without doing experiments. In this way, it is possible to improve control and system perormance, lower energy consumption, and shorten the time it takes to get a product on the market. In spite o this, dynamic modeling and simulation is not yet a commonly used tool within the rerigeration community. The main reason is the complexity and diiculty o the modeling task. Rerigeration systems tend to very diverse, making it diicult to build general simulation models. Furthermore, the basic physical processes o rerigeration systems (evaporation, condensation, throttling, ) are very complex, and diicult to describe on both detail and system levels. Yasuda et al. (98), James and James (987), MacArthur and Gland (989) have done some work in the area o dynamic modeling o thermo-luid systems, but none o this work has, to our knowledge, led to a general methodology or the modeling and simulation o these systems. The emphasis on energy conservation over the past decade has resulted in the development o many domestic rerigerator perormance simulation. Most o these models are composites o a sequence o regression analysis simulations o the major components individual perormance. These models are adequate or simulating a typical domestic rerigerator perormance or even or design change perormance estimation o a speciic domestic rerigerator i all o the component test data are available as input. A totally dierent approach to modeling perormance, one o beginning with irst principles, has also been taken, but in ar ewer cases. These models, one o which is discussed in this paper, incorporate the undamental correlations and laws o thermodynamics, luid mechanics and heat transer into a network o logic that will allow or prediction o the state properties o either the rerigerant or the air at any pre-selected point o their respective circuits. These models are best used when applied to research problems in trying to understand the impact o the 09

2 Murthada and Hussain local phenomena on the overall system. Their accuracy is, o course, limited to the accuracy o the correlation used and is not necessarily any better than the accuracy o the regression analysis models, however, the irst principles models, i designed correctly, require ar less and easier to obtain input data. II. DESCRIPTION OF THE MODEL The advancement o this model depends on the act that all rerigerant thermodynamic states in the system are not subject to any restrictions and are ound exclusively as a result o the iteration process in the solution logic o the main program. This lexibility increases the accuracy o the simulation results. During domestic rerigerator operation, there is a one to one relationship between working medium parameters and operation conditions, i.e., or given ambient conditions there is just one rerigerant state at any location within the system, which constitutes steady state operation. This unique set o rerigerant state and low conditions has to be sought by a domestic rerigerator simulation program in an iteration process. In order to set up an iteration procedure or a domestic rerigerator model, balances taking place have to be recognized. The act that the domestic rerigerators thermodynamic cycle is a closed loop makes it convenient to utilize a pressure-enthalpy diagram so that the two properties, enthalpy and pressure, may be explicitly highlighted at the entrance and exit o each component. The explanation o the logic used to iterate these three balances is given below. For sake o clarity, only the our main components, i.e. a compressor, a condenser, a capillary tube and an evaporator are discussed. Required input to the program is restricted to environmental conditions and domestic rerigerator design data as ixed parameters; it also includes initiating guesses o rerigerant states, which will automatically converge to the true state conditions through the iterative process. The simulation process (Fig.) starts with a guessed rerigerant pressure and vapour superheat at the compressor can inlet, and the compressor discharge pressure. From these data and the compressor perormance simulation, the rerigerant mass low rate is determined. Next, the condenser and the capillary tube are simulated and mass low balance is sought by comparing rerigerant mass low rate through the compressor and capillary tube. I compared mass lows are not equal simulation o the compressor, the condenser and the capillary tube is resumed with unchanged rerigerant state at the compressor can inlet and modiied guess o compressor discharge pressure. For instance, in the case o mass low rate through a capillary tube being smaller than mass low rate through a compressor, compressor discharge pressure is increased. Increasing this pressure reduces rerigerant mass low rate through the compressor. Then the condenser is simulated with this smaller mass low rate and at higher saturation temperature. Consequently, rerigerant reaching the expansion device inlet is at higher pressure and has more subcooling. Both actors promote increase o mass low rate through the capillary tube. Thus, an increase in discharge pressure has a clear and opposite impact on mass low rates through the compressor and the capillary tube and the appropriate discharge pressure will be ound or which mass low balance exists. Once a mass low balance is reached, simulation o the evaporator is perormed in a backward scheme with the known rerigerant state at evaporator exit and rerigerant mass low rate. Since the thermodynamic process in a capillary tube is assumed to be adiabatic, rerigerant enthalpy at the evaporator inlet should be equal to the enthalpy at the condenser outlet. I these enthalpies are not equal (enthalpy balance is not reached) a new calculation loop starts rom the beginning with a modiied guess on the rerigerant pressure at the compressor can inlet. From condenser operation point o view, change in compressor suction pressure induces change in rerigerant mass low rate and modiication o condenser saturation temperature caused by the system mass low balance search. These two changes have opposing eects on rerigerant enthalpy at the condenser exit, leaving it relatively unaltered. On the other hand, the same change o compressor suction pressure has a strong eect on rerigerant enthalpy at the evaporator inlet by change in evaporator saturation temperature and rerigerant mass low rate, both working in the same enthalpy change direction, thus an appropriate suction pressure at the compressor inlet can always be ound which enthalpy balance exists. 0

3 Engineering Journal o the University o Qatar, Vol. 6, 2003, pp Start Input: - Rerigerator Data Rerigerant Data Rerigerant Charge Ambient Conditions Guessed Compressor Suction Guessed Compressor Head Pressure Guessed Vapour Superheat at Compressor SIMULATE SIMULATE SIMULATE SIMULATE CHOOSEWY : I=? 2 SIMULATE CA A WITHO HEAT C A G IF MASS BALANOBTAINE SIMULATE SUCTION LINEEXCHAN A G YE SIMULATE IF ENTHALPY A A C OBTAINE? YE MAKE MASS N N AD PR JU ES ST SU HE A AD JU PR ST ES SU SU CT DJ US T VA PO UR SU PE A IS CALCUL A MASS Q A O CHARG? YE N PRINT END Fig. () Simulation process

4 Murthada and Hussain In the third iterative loop, the rerigerant mass balance in the system is used to adjust rerigerant superheat (or quality) at the entrance to the compressor can. Speciically, rerigerant mass inventory is made. It is based on rerigerant states in the system, which were ound to satisy enthalpy and pressure balances with assumed vapour superheat (or quality) at the compressor can inlet. The amount o rerigerant obtained rom mass inventory calculations is compared to the rerigerant charge. I the amount o rerigerant calculated is smaller than rerigerant input into the domestic rerigerator, the superheat (or quality) guess is decreased and all calculations are automatically resumed rom the beginning. As explained above, the inal solution is obtained by searching or pressure balance, energy balance and by satisying the mass conservation law. This is realized in three iteration loops in which rerigerant discharge pressure, rerigerant pressure and superheat (or quality) are being iterated. All three loops are being iterated using the secant method. In the course o the computing process the main program gathers inormation about the domestic rerigerator particular component s perormance, updated at each iteration loop and applies them to anticipate changes in state property value which is being iterated. This allows or the iteration process to converge aster with each iteration loop. III. DESCRIPTION OF SUBMODELS AND MASS INVENTORY The ollowing domestic rerigerator components have individual algorithms subroutined into main program logic: hermetic compressor, condenser, evaporator, capillary tube, connecting tubings. Models o these components have been explained in (Hussain, 2000). An abbreviated description o the ist our major components and the rerigerant mass inventory is all that is discussed here. The hermetic compressor was designed so that the suction inlet pipe was directed towards the inlet port o the intake muler. Gas drawn into the cylinder was a mixture o heated gas rom the housing, and that came directly rom the suction line. It was desirable that the intake be as direct as possible, since additional superheat added within the compressor has a negative eect on both capacity and eiciency (Dossat, 99). The volume low rate was calculated using a volumetric eiciency ζ v : o m comp ρs N rpm = ζ v. Vstroke. () 60 The volumetric eiciency is compressor, and rerigerant (R2 & R34a) speciic, and depends moderately on the pressure ratio (P c /P e ) (Cullimore et al. 996). However, in the present work this dependency was neglected. The work (W) delivered by the compressor to the luid was calculated using an isentropic eiciency (ζ is ) that depends on the actual compressor and rerigerant (Domonski and Didion 984), such that W = p c P e N rpm γ... V ζ 60 γ stroke is P n c p P e γ γ γ P e (2) The approximated values o the volumetric and isentropic eiciency were ound rom experiments perormed by Rasmussen (997), where both eiciencies were determined as unctions o compressor speed ( rpm) at dierent condensing/evaporating temperatures. The isentropic eiciency decreased slightly as speed increased, and was also ound to decrease with decreasing condensation temperature. The volumetric eiciency was ound to decrease with both increased speed as well as increased pressure ratio. 2

5 Engineering Journal o the University o Qatar, Vol. 6, 2003, pp Shortly ater compressor start-up, the pressure exceeds the saturation pressure and ilm condensation begins in the condenser. Ater a while, the irst part o the condenser becomes a superheated zone, ollowed by a two-phase zone, and then inally, beore the capillary tube, a sub-cooled zone is present. The general technique used by the simulation program or the condenser model is to divide the condenser coil into a user-speciied number o segments, which in turn, are divided into a number o modules. The inlet conditions to the segment are provided and a Newton-Raphson iteration is perormed to determine the outlet conditions or each module in the segment. During this procedure, each module is treated as an individual heat exchanger and local rerigerant-side heat transer coeicients are determined based on the module outlet conditions. The governing equation or each module are the conservation o energy and momentum equations. The operating conditions at the condenser coil inlet that must be speciied or the simulation are the rerigerant inlet pressure, temperature, and mass low rate and the environmental conditions. The eectiveness-ntu method, as described in conventional heat transer texts, is used in the condenser simulation to determine the heat rejected by each module (Q mod ). The general orm o the equation is: Q mod = ε. C min.( T Rin T Ain ) (3) Further details on how the eectiveness-ntu method is applied in this model are contained in Ragazzi (99). In the present research two model are developed or the capillary tube, one o them or adiabatic low which is produced when the capillary tube is placed in the rerigeration system without getting heat transer to the suction line, and another model with heat transer between them. For each model, the capillary tube is assumed to be a straight, horizontal, constant inner diameter with a homogeneous, one-dimensional low. The set o assumptions allow the two phase low in a capillary tube with adiabatic low to be treated as the Fanno low and rerigerant properties and critical pressure can be computed accordingly. Flow resistance due to a capillary tube with an adiabatic low is subdivided into resistance due to entrance eect and due to low in the tube itsel. Flow in the capillary is evaluated by solving the equation o motion (Domonski and Didion 984): P i + L i + 2 G P i 2 ρ. dp + D ρ ln i = 0 ρ i+ L i. dl + (4) Single-phase low and two-phase low in the tube are considerd separately. For single-phase low (liquid only) the above equation o motion reduces to the Fanning pressure drop ormula, while or two-phase low the equation o motion has to be solved in its ull orm. In a practical application, rerigerant low in a capillary tube may be liquid only, two-phase only or both liquid and two-phase separated by a lash point. The developed model will simulate a capillary tube or either o these cases. In the non-adiabatic low model, the capillary tube is placed inside the suction line, orming an eicient counter low heat exchanger. An important eature o the heat exchanger is increased mass low in the capillary tube by increasing sub-cooling o liquid leaving the condenser. The luid network or this model is built in the same manner as the condenser, only with much smaller dimensions. The thermal network diered since the rerigerant in the suction line lows on the outside o the capillary tube. In the developed model, the evaporator model is based on the equation o conservation o energy that can be expressed in the ollowing equation: 3

6 Murthada and Hussain Q evap + + Qcan Q disline Q sucline + E + Q can = Q cond + Q Lqline = E W (6) Mass inventory o rerigerant is used or iteration o rerigerant superheat or quality at the compressor can inlet. Accuracy o mass inventory results depends on accuracy o evaluation o mean rerigerant density in particular domestic rerigerator components and accuracy o internal volume determinations. In order to minimize the error o computations, mass inventory results are used on a relative basis, i.e. calculated charge is compared not to the actual rerigerant charge only, but to the mass o rerigerant calculated or operating conditions at which superheat at the compressor can inlet is known as a design parameter. In a domestic rerigerator compressor and connecting tubes rerigerant low is single-phase or two-phase with vapour/liquid velocity slip ratio close to. Mean density is known or these components rom perormed calculations during iterative process closing enthalpy and pressure balances. In the case o both coils, the rerigerant is in part by single-phase, While, in most o the coil some type o two phase annular low prevails. For this low regime, mean density is evaluated in terms o densities o saturated liquid and vapour, and the void raction as correlated by (Tandon et al., 985) based on (Lisa et el.,995) results: (5) α R e R e = + F ( X ) 2 tt F ( X tt ) (7) or 50 < R e < 25 α or R e R e = + F ( X ) 2 tt F ( X tt ) R e 25 (8) where F ( X tt ) = [ / / ] X tt X tt and R e = G re ( x) D i µ Mean rerigerant density is calculated or each tube individually. This is possible since the program employs tube-by-tube simulation model or a condenser. 4

7 Engineering Journal o the University o Qatar, Vol. 6, 2003, pp IV. PRESSURE DROP CORRELATIONS Single-phase pressure drops are calculated using churchill s equation (Churchill 977)or the Darcy riction actor as ollows: /2 2 8 = 8 + Re 3/ 2 ( A + B) where = λ A ln + Re D B = ( / Re) 6 (9) This unction agrees very well with experiments at both high and low Reynolds number, but overestimated the riction actor somewhat in the transition region. In the case o two-phase low, rerigerant pressure drop inside a tube is calculated by (Jung and Radermacher, 989, 993) with evaporation and (Lockhart-Martinelli, 949) with condensation. V. CONVENTIONAL HEAT-TRANSFER CORRELATIONS Convective heat transer between luid and thermal sub models here is characterized by the heat-transer coeicient α HT (Cullimore et al. 996): Qconv=α HT AHXI T (0) Where A HXI and T are the inside heat-transer area and temperature dierence between rerigerant and tube wall temperature, respectively. In the case o single-phase low, HT is calculated rom the Nusselt number according to α D Nu = HT () k Where: Nu Nu Nu = 3.66 Re < 960 = 0.8 n Re Pr Re > 6420 = 0.67 n 0.6 (Re 25) Pr 960 < Re < 6420 (2) Here the coeicient n= 0.3 corresponds to cooling and n= 0.4 corresponding to heating. In the present research, two undamental boiling heat-transer regimes are considered: nucleate and ilm. Nucleate boiling is characterized by the bubbles that orm at the wall and then drit into the bulk liquid stream. This regime exists or qualities 0.0 to 0.7 only. Film boiling, however, is characterized by vapour-dominated heat-transer (Dittus-Boelter Correlation). For qualities between 0.7 and.0, an interpolation between the two regime corrlations is used. 5

8 Murthada and Hussain In the case o two-phase low in a condensation process, heat transer is calculated using a Rohsenow correlation (Rohsenow and Hartnett 973) or rerigerant (R2) and a Dobson correlation (Dobson, 994) or rerigerant R34a. VI. HEAT TRANSFER-SECONDARY SIDE OF TUBE The dominant heat-transer mechanism rom the condenser, compressor, and the evaporator (see Figure 2) to the surrounding air is due to a combination o natural convection and radiation: Q& = Q& conv + Q& rad where Q& conv = H c A Q& rad = σ ε A HXO HXO ( T w T a ) 4 4 ( T w T a ) = H r A HXO ( T w T a ) (3) (4) (5) Assuming a cabinet-wall temperature o rerigerator approximately equal to the ambient temperature. Following the work o (Jakobsen, 995) on a domestic rerigerator o the type considered here, the total air heat-transer coeicient [in W/m 2.K] or the condenser can be itted as H cond 0.46 = H c + H r = T (6) Similarly, or the compressor H comp T = (7) and or the evaporator H evap T = 8) However, as temperature variations are relatively small, all heat-transer coeicients, that include both convection and radiation are modeled as constants. Actual values are listed as air-side heat-transer coeicients along with other model parameters in the section results and validation. The heat-transer between the capillary tube and the suction line is calculated by this research ollowing the prescription described in the section on conventional heat transer. Here, we have assumed that the most important contribution to this heat transer is a consequence o the capillary tube being co-axially aligned within the section line. VII. RESULTS AND VALIDATION In this section key results rom simulation o rerigeration cycle are presented and compared to measurements rom a 9 t 3 ( m 3 ) top-mount rerigerator-reezer, with a static condenser using R2 and R34a rerigerants. All rerigeration components remained the same throughout the test, except that the length o the capillary tube, compressor size and the amount o charge were changed or each rerigerant. One o the eatures o the simulation model is that the results contain much more inormation than measurements provide. Example o this include the detailed inormation about pressure and temperature distribution along capillary tube and condenser tubes. The main advantages o such simulation include better understanding o system and component behavior when they are used dierent alternative rerigerants or comparison purpose. Numerical results o condenser (type o wire and tube) simulation are illustrated in Figures 3,4,5 and 6 where rerigerant (R2 or R34a) enters the condenser (total tubes length 7.65 m subdivided into 00 nodes o equal length 6

9 Engineering Journal o the University o Qatar, Vol. 6, 2003, pp and 6 return bends) in a superheated state and exit either in a subcooled state or two-phase state depending on the type o rerigerant used. From these igures it is evident that the results are consistent with the physics o the system. The numerical analysis showed that the rerigerant vapour condenses in about 70-80% o the condenser tube length when rerigerant (R2) was used. Meanwhile R34a leaves the condenser tubes in the two-phase state, indicating that this condenser needed an increase o about 20-30% o its tubes length to get the same perormance as compared with R2. In all test runs the outlet rerigerant temperature o the condenser tube within standard deviation o 4.2K o those measured experimentally. Numerical results o capillary tube simulation are illustrated in Figures 7 and 8 where both rerigerant R2 and R34a enter with the same inlet diameter (0.7 mm) and inlet state or both cases adiabatic and diabatic tubes. When comparing both cases, the adiabatic region cannot be distinguished rom the diabatic region by observing the pressure proiles. This is a characteristic o single-phase low only and not necessarily so or two-phase low, which occurred closer to the exit. As shown in Figure 8, it is not possible to locate the lash points by observing temperatures. This illustrates a signiicant dierence between adiabatic capillary tubes and capillary tube-suction line heat exchangers. The dierence is that in adiabatic tubes the capillary tube luid temperature is constant until a sharply decreasing luid temperature marks the lash point. In contrast, the capillary tube luid temperature in a heat exchanger does not reveal where the lash point occurs. In comparison with the experimental results obtained, the computational model yield results accurate to within (4.54%) or the compressor input power and (5.74%) or the coeicient o perormance (COP) using R2 and (4.3%) or the compressor input power and (5.32%) or COP using R34a. The veriication is done or within domestic rerigerator operation within range o ambient room conditions rom (20 o C to 35 o C) or as shown in Figures 9 to 2. Figure 3 and 4 present the computational results o three ambient room temperatures, plotted in a simple cycle orm on the pressure-enthalpy diagram. Note that rerigerant vapour superheat at the compressor inlet decreases with the increase o the ambient room temperature. This superheat variation is reasonably well simulated by this model demonstrating a reasonable intercycle simulation accuracy. Evaporator Capillary tube Heat Exchanger Suction line Compressor Condenser Fig. (2) Schematic o component interaction. 7

10 Murthada and Hussain.6 TIN=90 o C m =.5 g/s R2-Tam b=25 C R2-Tam b=35 C R34a-Tam b=25 C R34a-Tam b=35 C Pressure (bar) Node Number Fig. (3) Nodal Distribution o Pressure From Computational Results o Condenser Subroutine Using R2 and R34a at Dierent Ambient Temperatures Temperature ( o K ) Pin=.5 bar m=.5 g/s R2-Tamb=25 C R2-Tamb=35 C R34a-Tamb=25 C R34a-Tamb=35 C Node Number Fig. (4) Nodal Distribution o Rerigerant Temperature From Computational Results o Condenser Subroutine Using R2 and R34a at Dierent Ambient Temperatures 2 0 Pin=.5 bar m=.5 g/s Tin=90 o C R2-Tamb=25 C R2-Tamb=35 C R34a-Tamb=25 C R34a-Tamb=35 C Node Heat Rejected (W) Node Number Fig. (5) Nodal Distribution o Heat Transer From Computational Results o Condenser Subroutine Using R2 and R34a at Dierent Ambient Temperatures 8

11 Engineering Journal o the University o Qatar, Vol. 6, 2003, pp TIN=90 o C m=.5 g/s Pin=.5 bar R2-Tamb=25 C R2-Tamb=35 C R34a-Tamb=25 C R34a-Tamb=35 C Rerigerant Quality Node Number Fig. (6) Nodal Distribution o Rerigerant Quality From Computational Results o Condenser Subroutine Using R2 and R34a at Dierent Ambient Temperatures Adiabatic-R2 Adiabatic-R34a Nonadiabatic-R2 Nonadiabatic-R34a Pressure (bar) Capillary Tube Length (m) Fig. (7) Rerigerant Pressure Distribution From Computational Results o Capillary Tube Subroutine With Adiabatic and diabatic Flow Temperature ( o K ) Adiabatic-R2 Adiabatic-R34a Nonadiabatic-R2 Nonadiabatic-R34a Capillary Tube Length (m) Fig. (8) Rerigerant Temperature Distribution From Computational Results o Capillary Tube Subroutine With Adiabatic and diabatic Flow 9

12 Murthada and Hussain 00 R2 Expe r ime ntal Computational Tamb=20 o C Pressure (bar) Enthapy (kj/kg) Fig. (9) Comparison Between Experimental and Computational Results Using R2 at Ambient Temperature (20 o C) 00 R-34a Experimental Computational Tamb=20 o C Pressuer (bar ) Enthalpy ( kj/kg) Fig. (0) Comparison Between Experimental and Computational Results Using R34a at Ambient Temperature (20 o C) 00 R2 Computational Experimental Tamb=35 o C Pressure (bar) Enthapy (kj/kg) Fig. () Comparison Between Experimental and Computational Results Using R2 at Ambient Temperature (35 o C) 20

13 Engineering Journal o the University o Qatar, Vol. 6, 2003, pp R-34a Expperimental Computational Tamb=35 o C Pressuer (bar ) Enthalpy ( kj/kg) Fig. (2) Comparison Between Experimental and Computational Results Using R34a at Ambient Temperature (35 o C) 00 R2 Tamb=27.5 C Tamb=32.5 C Tamb=37.5 C Pressure (bar) Enthapy (kj/kg) Fig. (3) Simpliied Thermodynamic Cycle Realized By a Domestic Rerigerator Using R2 at Dierent Ambient Temperatures 00 R-34a Tamb=27.5 C Tamb=32.5 C Tamb=37.5 C Pressuer (bar ) Enthalpy ( kj/kg) Fig. (4) Simpliied Thermodynamic Cycle Realized By a Domestic Rerigerator Using R34a at Dierent Ambient Temperatures 2

14 Murthada and Hussain VIII. CONCLUSIONS The model described here is capable o simulating a domestic rerigerator with a constant low area expansion device at imposed operating conditions without restrictions on rerigerant state at any system location. The model can be used or a wide variety o applications. It has been used or perormance evaluation o systems with matched and mismatched components. It has also been used to test how certain modiications o components aect overall perormance o a domestic rerigerator. Perormance o a domestic rerigerator illed with dierent rerigerants has been also analyzed with the aid o the model. The model absolute accuracy is limited (as with all irst principle models) and may not be any better than a regression analysis model particularly that the model is based on component good empirical data. The ability or a irst principle model to predict overall system perormance is to varying degrees dependent on the accuracy o dierent correlations simulation o the local phenomena which is sometimes unknown in a real machine. For example, the heat transer correlations or internal two phase low is not available or tubes with elbows and branches. Also this model is not particularly amenable as an open ended design tool but rather a design analysis tool. However, it is convenient that the input data required are only that which can be determined rom external measurements and inormation normally supplied by the manuacturer. Nomenclature A HX(I or O) C nim D E G H C H r L o m n p N rpm Nu comp P c P e Q can Q cond Q disline, Q lqline Q evap Q mod Q sucline Re T Ain T Rin T w V stroke W x x tt ( I:inside & O:outside )heat transer area Minimum heat capacity rate Capillary tube inside diameter Electrical energy input rate to the compressor Friction actor Rerigerant mass lux Radiation heat transer coeicient Convection heat transer coeicient Length Mass low-compressor Relative compressor clearance Nominal number o revolutions per minute-compressor Nusselt number Pressure-condenser Pressure-evaporator Heat rejection rate rom a compressor to ambient air Heat rejection rate rom condenser tubes to ambient air Heat rejection rate rom discharge line and liquid line to ambient air Cooling duty Module total heat transer Heat transer rate rom ambient air to the suction line Renold number Air inlet temperature Rerigerant inlet temperature Tube wall temperature Stroke volume-compressor Mechanical Power available or compression Process Rerigerant quality Lockhard-Martinelli parameter 22

15 Engineering Journal o the University o Qatar, Vol. 6, 2003, pp α Void raction α HT Heat transer coeicient γ Polytropic coeicient ε Eectiveness ρ Fluid speciic density ρ s Fluid speciic density-inlet compressor ζ is Isentropic eiciency-compressor ζ v Volumetric eiciency-compressor λ Surace roughness parameter σ Stean-Boltzman constant κ Fluid thermal conductivity µ Rerigerant liquid viscosity REFERENCES. Churchill, S.W Frictional Equation Spans all Fluid Flow Regions Chemical Engineering, Vol.84, pp Cleland, A.C Food Rerigeration Process-Analysis, Design, and Simulation. Essex, UK: Elsevier Science Publishers Ltd. 3. Cullimore, B., S.G. Ring R.G. Goble, and C.L. Jensen Sinda/Fluint Users Manual or Version 3.2. Cullimore and Ring Technologies. Inc. Littleton, CO. 4. Dobson, M. 994, A Dimensionless Correlation or Heat Transer in Forced Convection Condensation Technical Report 42 or the Air-Conditioning and Rerigeration Center. Urbana: University o Illinois at Urbana-Champaign. 5. Domonski, P., and Didion, D Mathematical Model o an Air-to-Air Heat Pump Equipped with a Capillary Tube. International Journal o Rerigeration, Vol. 7, No. 4,pp. ( ). 6. Dossat, R.J. 99. Principles O Rerigeration, Chapter 2, 3rd Edition Englewood Clis, N.J : Prentice Hall. 7. Hussain, S.H Simulation o Vapour-Compression Rerigeration System using Ozone Layer-Save Rerigerants. M.Sc. Thesis, Technology University, Mechanical Engineering Department, Iraq. 8. Jakobsen, A Energy Optimization o Rerigeration Systems. Ph.D. Thesis No. F-79-, Rerigeration Laboratory, Technical University o Denmark, Copenhagen. 9. James, K.A., and James, R.W A Critical Survey o Dynamic Mathematical Models o Rerigeration System and Heat Pumps and Their Components. Technical Memorandum No. 97, Inst. o Environmental Eng., Polytechnic o The South Bank, London. 0. James, K.A., and James, R.W Transient Analysis o Thermostatic Expansion Valves or Rerigeration Systems Evaporators using Mathematical Models. Trans. Inst. M. C9: Jung, D. S., and R. Radermacher Prediction o Evaporation Heat Transer Coeicient and Pressure Drop o Rerigerant Mixture in Horizontal Tubes. Int. J. Rerig. Vol. 6, No. 3,pp. (20-209). 2. Jung, D.S., and R. Radermacher A Study o Flow Boiling Heat Transer with Rerigerant Mixtures. Int. F. Heat and Mass Transer, Vol. 32, No. 9, pp. (75-764). 3. Lisa, A.O., Zietlow, D.C., and Pedersen, C.O Predicting Rerigerant Inventory o R34a in Air- Cooled Condensers. ASHRAE Technical Data Bulletin, Vol., No. 4, pp. (27-35). 4. Lockhard, R. W., and R. C. Martinelli Proposed Correlation o Data or Isothermal Two-Phase Two- Component Flow in Pipes. Chemical Engineering Progress, Vol. 45, No., pp. (39-48). 5. Macarthur,J.W., and Grald, E.W Unsteady Compressible Two-Phase Flow Model or Predicting Cyclic Heat Pump Perormance and a Comparison with Experimental Data. Rev Int. Froid 2: Ragazzi, F.99. Modular-Based Computer Simulation o an Air-Cooled Condenser. M.Sc. Thesis. Urbana : University o Illinois at Urbana-Champaign. 7. Traviss, D. P., Rohsenow, W.M., and Baron, A.B Forced Convection Condensation Inside Tubes: A Heat Transer Equation or a Condenser Design. ASHRAE Trans., Vol. 79, pp. (57-65). 8. Yasuda, H., Machielsen, C.H., Touber, S., and Brujin, M.D. 98. Transient Behavior o a Compression- Evaporation Rerigeration System. WTHD No. 33, Department o Mechanical Engg., Delt University o Technology, Delt, The Netherlands. 23

16 Murthada and Hussain 9. Rasmussen, B.D Variable Speed Hermetic Reciprocating Compressor or Domestic Rerigerators. Ph.D. Thesis No. ET-Ph-D , Department o Energy Engineering, Technical University o Denmark, Copenhagen. 20. Tandon, T.N., Varma, H.K., and Gupta, C.P A Void Fraction Model or Annular Two-Phase Flow. International Journal o Heat and Mass Transer, Vol. 28, No., pp. (9-98). 24