Characterization and simulation of an open piston compressor for application on automotive air-conditioning systems operating with R134a, R1234yf and R290

Accepted Manuscript Title: Characterization and simulation of an open piston compressor for application on automotive air-conditioning systems operating with r134a, r1234yf and r290 Author: Paul Ortega Sotomayor, José Alberto Reis Parise PII: DOI: Reference:

S0140-7007(15)00280-7 http://dx.doi.org/doi: 10.1016/j.ijrefrig.2015.09.004 JIJR 3150

To appear in:

International Journal of Refrigeration

Received date: Revised date: Accepted date:

22-11-2014 10-8-2015 10-9-2015

Please cite this article as: Paul Ortega Sotomayor, José Alberto Reis Parise, Characterization and simulation of an open piston compressor for application on automotive air-conditioning systems operating with r134a, r1234yf and r290, International Journal of Refrigeration (2015), http://dx.doi.org/doi: 10.1016/j.ijrefrig.2015.09.004. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

CHARACTERIZATION AND SIMULATION OF AN OPEN PISTON COMPRESSOR FOR APPLICATION ON AUTOMOTIVE AIR-CONDITIONING SYSTEMS OPERATING WITH R134a, R1234yf AND R290 Paul Ortega Sotomayor1, José Alberto Reis Parise2* 1

Pontifícia Universidade Católica do Rio de Janeiro, Department of Mechanical Engineering,

Rua Marquês de São Vicente, 225 22453-900, Rio de Janeiro, RJ, Brazil, e-mail: [email protected] phone: +55 21 983971138 2

Pontifícia Universidade Católica do Rio de Janeiro, Department of Mechanical Engineering,

Rua Marquês de São Vicente, 225 22453-900, Rio de Janeiro, RJ, Brazil, e-mail: [email protected] phone: +5521 35471380, fax: +5521 35471165 * corresponding author

HIGHLIGHTS 

A semi-empirical model for open type compressors was developed and verified



An improved methodology was applied to compressor characterization and simulation



Compressor characterization was carried out with a reduced number of parameters



The model was validated with three different fluids: R134a, R1234yf and R290

ABSTRACT

A semi-empirical characterization and simulation model for automotive air-conditioning open piston compressor is developed. The model is based on fundamental conservation principles and takes into account pressure drop and heat transfer in suction and discharge passages. Fundamental conservation principles equations, as well as volumetric and isentropic efficiencies, pressure drop, heat transfer and property equations are combined to form a system of non-linear algebraic equations. They are worked out so as to identify constants that are sole characteristics of the compressor and should not vary with different operating conditions or refrigerants. A numerical 1 Page 1 of 30

method determines such constants from existing experimental data, thus characterizing the compressor. Experimental data were obtained from tests carried out by Navarro et al. (2013) for a open piston compressor running with fluids R134a, R1234yf and R290. First, the experimental data was employed to determine the characterization parameters of the compressor. Then, the simulation model, with the R134a-based parameters, was applied to simulate the compressor operation with R1234yf and R290. Good agreement was obtained between predicted and experimental values, proving the suitability of the model for the study of new refrigerants.

KEYWORDS: automotive compressors; simulation; semi-empirical model; characteristic parameter, R134a; R1234yf; R290.

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1. Introduction The refrigeration and air conditioning industry has been dedicating a great effort in pursuing refrigerants with lower environmental impact, namely zero ozone depletion potential and very low global warming potential. For the large quantities of refrigerant involved worldwide, an early focus of this effort was put on the automotive air conditioning industry. For that purpose, experimental evaluations are essential and computer simulations, equally important, for improving the accuracy of predictions and reducing development time of new refrigerants and their systems. In this respect, simulation models that are capable of predicting the performance of existing systems operating with new refrigerants may become a valuable design tool. Mathematical models for positive displacement compressors can be divided into three major categories. They are: (i) Empirical or map-based models: performance parameters, that describe capacity, energy consumption and discharge temperature, are determined by polynomial equations that fit experimental data of the compressor – these models are, of course, specific to each compressor and refrigerant tested; (ii) Semi-empirical models: based on fundamental equations, but still relying on empirical data of the compressor, they are comprised by conservation and constitutive equations as well as polynomial fits of experimental data; (iii) Fundamental models: they are strongly based on mass, energy and momentum conservation equations. This division should not be taken strictly, and other forms of compressor model classification exist (Rasmussen and Jakobsen, 2000; Ignatiev, 2000; Groll, 2004). Trade-offs between fundamental and curve fitting equations to be used should be a matter of best addressing the objectives of each simulation effort. As far as modelling of automotive air conditioning compressors is concerned, a number of works can be found in the literature. They range from fundamental (Tojo et al., 1990; Fukuta et al., 1995; Park et al., 2004; Yi et al., 2004; Tian et al., 2004; Tian et al., 2006; Tian et al., 2007; Cavalcante et al., 2008; Tian et al., 2009) to semi-empirical (Darr and Crawford, 1992; Kiatsiriroat and Euakit, 1997; Dirlea et al., 1998; Saiz Jabardo et al., 2002; Cuevas et al., 2007) and empirical (Joudi et al., 2003; Eborn et al., 2005) models. Concerning new refrigerants, the literature on results from automotive AC compressors running on R1234yf, substitute of R134a for new MAC designs, is growing steadily. Comparative R134a-to-R1234yf drop-in and TXV-tuned tests have been reported, for instance, by Minor and Spatz (2008), Mathur (2010), Zilio et al. (2011), Gordon et al. (2011), Zhao et al. (2012), Lee and Jung (2012), Navarro et al (2013), Navarro-Esbrí et al. (2013) and Wang (2014).

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The semi-empirical models above differ from each other, and from the present model, in the way they predict the basic compressor performance parameters, namely: compressor capacity (mass flow rate), power consumption and gas thermodynamic state at the compressor discharge (temperature or specific enthalpy, in addition to discharge pressure, an input parameter). Kiastsiriroat and Euakit (1997) presented a numerical and experimental study of an automotive air conditioning system, using a compressor of the swash-plate type, operating with a refrigerant mixture R22/R124/R152A. An equation for refrigerant flow rate, with empirically determined coefficients, was derived from that of a centrifugal compressor. The authors did not explain the rationale behind this association between positive displacement (reciprocating) and kinetic (centrifugal) compressor theories. Different mixture compositions (20/23/57% mass fraction; 30/23/47%; 40/23/37%) yielded different coefficients. The compression work equation was that of a polytropic compression of an ideal gas. The empirically determined polytropic exponent was found to be constant for different compositions of the refrigerant. Overall mass and energy balances were carried out for one single control volume. Dirlea et al. (1998) proposed a semi-empirical simulation model for an automotive wobble-plate compressor operating with R134a. Mass and energy balances were applied to one single compressor control volume and the presence of lubricating oil, in the gas stream, and its effect on working fluid properties and compressor performance, were taken into account. Gas mass flow rate was predicted by means of an empirical linear relation, with two parameters to be identified for what the authors called, the "refrigerant flow rate model". Likewise, a "compressor shaft power model" was devised comprising the isentropic compression power plus mechanical losses, resulting in an equation with three parameters to be empirically determined. Identification of the refrigerant mass flow rate parameters was carried out with 55 tests and resulted in predictions within -6% and 8%, and the shaft power parameters, with 80 tests and error globally lower than ±10%. Discharge temperature was not determined. Saiz Jabardo et al. (2002) presented a simulation model for the refrigeration circuit of an automobile air conditioning system. It operated with R134a and had a compressor capacity control system keeping the evaporating temperature constant under any thermal load. Polytropic compression was assumed. The volumetric efficiency due to the re-expansion of the gas trapped in the clearance volume was corrected by a factor that was obtained by curve fitting the compressor catalogue data with a second-order two-variable (compressor speed and displacement) polynomial. Refrigerant state at the compressor discharge was determined from the isentropic compression efficiency, which was determined from a linear fit of the experimental data (efficiency against shaft speed). Brown et al. (2002) modelled an open-type compressor and used empirical correlations for the volumetric and isentropic efficiencies, both in terms of the compression pressure ratio. A single volumetric efficiency was obtained by curve4 Page 4 of 30

fitting data from both CO2 and R134a experiments. A single expression for the isentropic efficiency, derived from a CO2 compressor, was conservatively employed for both refrigerants, to give CO2, according to the authors, a possibly "valid credit". Two other models (Darr and Crawford, 1992; Cuevas et al., 2008) evolved for the application of fundamental and empirical equations to two or four control volumes, respectively, instead of one. Darr and Crawford (1992) followed a traditional compressor model where suction refrigerant state, discharge pressure, compressor shaft speed, ambient temperature as well as swept and clearance volume were input parameters and steady-state refrigerant mass flow rate, compressor power, discharge refrigerant specific enthalpy were the output variables. In addition to the physical parameters, the model also required seven empirical parameters. Isentropic and volumetric efficiencies were employed and heat loss to ambient, considered. A hypothetical shell (consisting of all the physical parts of the compressor, including housing, cylinders and swash plate) exchanged heat with the compressing gas, suction and discharge sides and with ambient, too. Empirical parameters included: two coefficients for the linear relation of the "isentropic volumetric efficiency" with compressor shaft speed, other two for the linear relation of the "isentropic volumetric efficiency" with shaft speed and suction specific volume and the compressor heat loss, through its metallic shell, being a linear function of ambient temperature and the square root of shaft speed. Cuevas et al. (2008) proposed the simulation of an automotive wobble-plate compressor running on R134a. Four control volumes were defined: suction and discharge passages, compression volume and a fictitious metallic isothermal wall exchanging heat with suction and discharge gas as well as with external ambient. Fundamental energy and mass balance equations were applied to each of the control volumes. Presence of lubricating oil was taken into account and isentropic compression process was considered. Eight empirical model parameters were identified and numerically determined from 31 experimental runs. The empirical parameters included two coefficients from a quadratic equation relating power loss to compressor speed, two gas-to-wall overall heat conductances, for suction and discharge passages, respectively, and four other flow and displacement related parameters. Predicted values were compared to experiments and minimal deviations for discharge temperature, mass flow rate and shaft power were found to be -11.3K, 0.005 kg/s and -0.680 kW, respectively. The present model, like Cuevas et al. (2008), also adopts the 4-control volume approach, i.e., suction and discharge passages, compression cylinder and compressor shell. On the other hand, unlike Dirlea et al. (1998) and Cuevas et al. (2008), lubricant flow rate was not taken into consideration. In whatever way, by employing empirical parameters that only apply for the 5 Page 5 of 30

refrigerants they were originally tested, none of the models described above comply with the primary objective of the present work, which is to develop a simulation model capable of predicting the performance of open-type automotive compressors running on new refrigerants (e.g., R1234yf and R290), for which experimental data may not be readily available. It is understood that a semiempirical model, based on refrigerant-independent parameters that characterize a specific compressor and that have been experimentally determined with a conventional refrigerant (e.g., R134a), still not available in the literature, would be most suitable for that objective. This approach, of characterizing a specific compressor with refrigerant-independent empirical parameters, has been originally applied for hermetic compressors by Domanski and Didion (1983). Their model assumed polytropic compression and the volumetric efficiency was due to the reexpansion of the clearance volume gas, corrected for piston and valve leakage and for throttling effect and defined in terms of compressor geometry, polytropic exponent and compression pressure ratio. Mechanical efficiency was assumed to be constant and equal to 0.96. Other features of the model are more specific to hermetic compressors, like electric motor efficiency and rotational speeds as functions of the shaft load fraction. Equations describing the heat transfer and pressure drop processes within the hermetic compressor shell were derived in a way that Q and  P could be expressed in terms of a product of three groups of variables: the first one containing refrigerant properties only; the second group, geometry-based and, therefore, refrigerant independent variables; and the third, operational variables (like refrigerant mass flow rate, average gas to wall temperature difference etc.). Experimental data allowed for the determination of five heat transfer and four pressure drop characterizing parameters, respectively. These nine parameters belonged to the second group above and, in principle, were constant and independent of refrigerant properties and operational conditions. Moreover, no detailed design and geometry information on the compressor was required. Although not explored in the original work (Domanski and Didion, 1983), it becomes clear that the use of refrigerant-independent characterizing parameters would enable the application of the model to the simulation of compressors operating with untested refrigerants. The same approach was utilized by Motta et al. (1996), to determine the "inner" polytropic exponent of a hermetic compressor. Empirical characterization parameters were calculated with results from one single experimental run. To achieve this, authors had to compromise the model by prescribing some estimates for the hermetic compressor internal heat transfer and pressure drop processes, which included: incompressible flow at suction and discharge passages, suction muffler and discharge line pressure drops, temperature gain at suction plenum, pressure drop at shell-side

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flow and, finally, temperature and pressure upper and lower bounds. A system of 36 algebraic equations was obtained and numerically solved. Contrarily to the hermetic compressor models from Didion and Domanski (1983) and Motta et al. (1996), the present simulation is targeted at, of course, open type compressors, a far less complex system, from the thermodynamic point of view. Apart from the obvious differences, polytropic compression was not used (in opposition to Didion and Domanski, 1983) and all heat transfer rates and pressure drops were calculated, instead of prescribed, as in Motta et al. (1996).

2. Mathematical Model 2.1 Control volumes Three refrigerant-side control volumes, suction (s) and discharge (d) passages and compression cylinder (c), and four refrigerant thermodynamic states (1, 2, 3 and 4) are defined, as depicted in Fig.1, which also shows the energy and mass streams. It is assumed that they are all separated from each other and encompassed by a fourth control volume which represents the compressor metallic block (w). Pure refrigerant was assumed as the working fluid. Therefore, the model did not take into account the presence of lubricant oil and its effect on compressor performance (see, for example, Youbi-Idrissi and Bonjour, 2008). 2.2 Energy conservation equations An overall energy balance, encompassing all four control volumes, provides: m h1  W shaft  Q a  m h 4

where

Qa

(1)

is the rate of heat transfer from the compressor block and the surrounding ambient. For

the suction and discharge passages and cylinder control volumes, the energy balance equations are, respectively: m h1  Q s  m h 2

(2)

m h3  Q d  m h4

(3)

m h2  W c  Q c  m h3

(4)

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Finally, the energy balance in the compressor block control volume, in accordance with the heat flow directions outlined in Fig.1, is: Qd  Q f  Qc  Qa  Qs

(5)

The evaluation of Q s , Q d and Q f is outlined next, in eqs. (13), (14) and (21), respectively. . The overall and cylinder energy balances, eqs. (1) and (4) , provide Q a and Q c , respectively. 2.3 Heat transfer rate equations Newton’s law of cooling provides the equation for heat transfer between the gas flow and passage walls, suction or discharge. Q   A T

(6)

where  T is the average temperature difference between the flowing gas and passage walls. Assuming forced convection turbulent flow, the most probable flow regime under typical operating conditions, a dependence of the Nusselt number on the Reynolds and Prandtl numbers based on the Dittus-Boelter correlation (1930) is adopted. Nu  C Re

0 ,8

Pr

0 ,333

(7)

where Nu 

 Dh

(8)

k

Pr 

 cp k

Re 

G Dh

G 

m



A sc

(9)

(10)

(11)

By taking equations (7) to (11) into (6), and following approach by Domanski and Didion (1983), a heat transfer rate equation is obtained in which two groups are identified: one comprising

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variables that depend on operational conditions or refrigerant thermophysical properties, and the other, on variables and parameters that are, in principle, inherent characteristics of the compressor. Q   C A Asc

 0.8

 0.2

Dh

m

0.8

k

0.667

cp

0.333



 0.467



T

(12)

Assuming an homogeneously distributed temperature over the compressor block control volume, T w , and approximating  T to an arithmetic mean temperature difference between gas and walls, the heat transfer rate equations for the suction and discharge passages can be written as, respectively: Qs  C H s  m

0.8

Qd  C H d  m

0.667

ks

0.8

 0.467

c p ,s  s

0.667

kd

0.333



 0.467

c p ,d  d 0.333



 T

w

 T  T2  1  2

  

  T3  T 4     Tw  2   

 

(13)

(14)

where CH s and CH d are compressor heat transfer characteristic parameters, relative to the suction and discharge control volumes, respectively. A linear approximation for the temperature difference , acceptable for small values, is adopted in equations (13) and (14). 2.4 Pressure drop equations The pressure drop across the suction and discharge passages is due to friction, as acceleration and gravitational components are neglected.  L   u2 P  f    Dh  2

(15)

where the dependence of the Fanning friction factor on the Reynolds number, for turbulent flow, is approximated to Blasius equation form: f  0.316 R e

 0.25

(16)

Combining equations (16) and (10) into (15), and separating operation-dependent parameters from compressor characteristics, in a similar way to the heat transfer rate equation, one has:

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 0.316   D h  P      2   Asc 

 0.2

2

 L   1    0.2 m 1.8          D h   Asc  

(17)

Therefore, the pressure drop equations for the suction and discharge passages become, respectively:   0.25 m 1.8   Ps  P1  P2  C Ps  s  s  

(18)

  0.25 m 1.8   Pd  P3  P4  C Pd  d  d  

(19)

2.5 Mechanical, isentropic and volumetric efficiencies equations The mechanical efficiency is defined as m 

Wc W shaft

(20)

so that the rate of heat losses due to mechanical friction can be calculated by: Q f  W shaft (1   m )

(21)

The volumetric efficiency is defined, as usual, from compressor geometry, speed and capacity, with inlet conditions taken at the entry to the cylinder, state 2. v 

m

 2 Vc N

(22)

Equations (1) to (4), (13), (14) and (18), together with refrigerant property equations, for R134a, R1234yf and R290 (Lemmon et al., 2007), form a system of non-linear algebraic equations. In order to be solved numerically, the compressor heat transfer and pressure drop parameters, CH s , CH d , C Ps and C Pd , as well as a curve for  v , have to be determined empirically.

3. Experimental Data Experimental data for compressor characterisation were available in the literature, from tests carried out with an open-type compressor, by Navarro et al. (2013), in supplementary data format. A 10 Page 10 of 30

description of the experimental facility and instrumentation is provided by the authors. The main features were as follows: i) The open piston compressor, driven by an electrical motor, had a swept volume of 660 cm3 and a clearance ratio of 0.05; ii) The test rig was fully automated providing adjustment of refrigerant suction and discharge pressures and inlet temperature within 1 kPa and 0.5 K, respectively; iii) Refrigerant-side instrumentation included temperature sensors (accuracy of ± 0.1oC), pressure transmitters (0.02% FS) and a Coriolis-type flow meter, to measure refrigerant mass flow rate and liquid density (manufacturer-declared uncertainties of

±0.10 % of rate and

±0.0005 g/cm3, respectively) ; iv) Lubricant POE oil ISO68 was used for all tests; iv) The deviation of the torque transducer was lower than 1.5%; v) Tests were conducted with condensing and evaporating temperatures in the 40 to 65oC and -15 to 15oC ranges, respectively, and for two values for rotational speed and suction degree of superheat, 1500 and 2200

rpm and 6 and 15 K,

respectively; vi) Compressor characterization tests were performed according to European Norm EN-13771-1 (2003), for refrigerant mass flow rate evaluation; vii) Oil circulation rate measurements followed ANSI/ASHRAE 41.4 (1996) standard. 4. Compressor Characterization The system of equations that comprise the mathematical model and the experimental data are first employed to determine the compressor characterization parameters and efficiency curves. A combination of the generalized reduced gradient (GRG) method, with routine Solver from Microsoft Excel 2010, was used solve the system of nonlinear equations. The algorithm for the characterization of the compressor is outlined below (see Fig. 2 for flow diagram). i) Enter input data from n experimental runs:  P1 , T1 , P4 , T 4 , m , W sh a ft  i , i  1, n ii) Assume values for mechanical efficiency (constant value, based on Didion and Domanski, 1983, and considering same lubricant for all three refrigerants) and average temperature of compressor block control volume.  m  0.95

(23)

T w  0 .5  T 2  T 3 

(24)

iii) First estimate of enthalpy of refrigerant at inlet {2} and outlet {3} of cylinder, and heat transfer and pressure drop parameters, CH s , CH d , C Ps and C Pd .

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0

h 2  h1

(25)

0

h3  h4

(26)

0

CH s  0 CH d  0

(27)

0

CPs  0 CPd  0

(28)

iv) Calculate other variables for each run: Eqs. (4), (22), (1), (2), (3), (5) and (21), for W c ,  v , s , Q a , Q s , Q d , Q c and Q f , respectively.

v) Calculate the temperature residuals between energy conservation (refrigerant flow) and heat transfer rate equations (between the gas flow and passage walls – suction or discharge and metallic block), at suction and discharge passages. From equations (2) and (13), for suction, and (3) and (14), for discharge, they are defined as:

Fs 

Fd 

m  h 2  h1 

  T  T2  Tw   1 2  

s m  h3  h4 

d

  

(29)

  T  T4     3   Tw  2   

(30)

where  s  CH s  m

0.8

d  CH d  m

0.8

0.667

ks

0.667

kd

 0.467

c p ,s  s 0.333

 0.467

c p ,d  d 0.333



(31)



(32)

Combining the two residuals, Eqs. (29) and (30), with Eq. (24), one has the overall residual of the energy balances, for run i, written in terms of temperature (heat transfer rate per overall control volume conductance):  m ( h1  h 2 )   m ( h 3  h 4 )   T1  T 2   T 3  T 4  Fi         s d      2   2 

(33)

vi) Calculate the objective function, to be minimized, which is the overall temperature residual, calculated for all runs (1 to n). 12 Page 12 of 30

Fobj 

 n 2    Fi   i 1 

(34)

The objective function is, therefore, the square root of the sum of the square of the offsets, i.e., the residuals. vii) Apply restrictions  P1  P2  P3

(35)

Pressure restrictions: 

 P4  P3  h1  h 2  h 3

Enthalpy restrictions: 

(36)

 h4  h3

viii) Check for convergence: is



j

C H s , j C Ps , j C H d , j C Pd , j h 2 , j h 3  ,

Fo b j

below prescribed tolerance? If not, calculate

make j  j  1 and go to instruction (iv).

ix) Results. The application of the method here outlined to the experimental data of Navarro et al. (2013), same compressor and different refrigerants, provided the characterization parameters depicted in table 1. It can be seen that suction and discharge heat transfer parameters differed, between refrigerants R134a and R1234yf, by 2.9% and 0.29%, and between refrigerants R134a and R290, by 5.6% and 0.12%, respectively. Discrepancies for the pressure drop parameters were nil for all cases. These discrepancies that, in principle, from equations (13), (14), (18) and (19), should be equal to zero, are defined as follows:

E I (% ) 

E II (% ) 

x R 134 a  x R 1234 yf

 100

(37)

x R 134 a

x R 134 a  x R 290

 100

(38)

x R 134 a

where x   CH s , CPs , CH d , CPd 

(39)

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The application of the characterization algorithm over a number of experimental runs also allowed for the determination, at each run, of the inner volumetric efficiency,  v 23 , as a function of variable y , defined as the product of critical to atmospheric and "inner" (entrance and outlet of the cylinder) pressure ratios. Figure 3, below, shows the resulting polynomial fit, taking all refrigerants (R134a, R1234yf and R290) into consideration.  v 23   5.14  10

5

y  2.46  10 4

3

y  4.27  10 3

2

y  0.341 y  0.409 2

(40)

where Pcrit y

Patm



R 32

R 32 

Pcrit



P2

Patm

(41)

P3

P3

(42)

P2

or, generally,  v 23  a 4 y  a 3 y  a 2 y  a 1 y  a 0 4

3

2

(43)

It should be noted that the use of the inner pressure ratio, P2 P3 , corrected by a critical to atmospheric pressure ratio, Pcrit Patm , allowed for the construction of a volumetric efficiency equation that is independent of the gas being compressed, as implied by Fig. 3, for the present experimental data, with three different refrigerants. 5. Compressor Simulation With the compressor empirical parameters defined, the mathematical model can now be solved to simulate the compressor performance. In addition to the compressor characterization parameters and volumetric efficiency curve, CH s , CH d , C Ps , C Pd , and  v , operational and geometry parameters, ( P1 , T1 , P4 and N ) and V c , respectively, are taken as input data. Main output variables are, m , W shaft and T 4 . The algorithm for the compressor simulation is presented next. See Fig. 4 for flow diagram. i) Enter input data: empirical parameters, volumetric efficiency curve, operating conditions and swept volume; 14 Page 14 of 30

ii) First estimate of T 2 , T3 and T 4 : j0

T  T1

(44)

T  T4

(45)

T  Tcond  P4    Tcond

(46)

0 2

0 3

0 4

iii) First estimate of refrigerant mass flow, 0 m (initial guess 0.01). iv) Calculate variables P2 , P3 and  v 23 , from Eqs. (18), (19) and (43), respectively and thermodynamic properties at refrigerant states at inlet {2} and outlet {3} of the cylinder. v) Recalculate the new value for refrigerant mass flow rate, j m , from equation (22) .

vi) Check for convergence:

j

m j

j 1

m

m

  . If not, then: calculate j m ; j  j  1 ; and go to (iv).

vii) Calculate other variables. Eq. (1): W shaft ; Eq. (2):

Qs

; Eq. (3): Q d ; Eq. (4):

Qc

; Eq. (21): Q f .

 m ( h1  h 2 )   m ( h 3  h 4 )   T1  T 2   T 3  T 4  9   10 .     2    2    s d     

vi) Check for convergence: 

If not: re-

calculate jT 2 , jT 3 and jT 4 ; go to (iii). vii) Results. 6. Validation of the simulation model

The simulation model was made to run with characterization parameters and volumetric efficiency to refrigerant R134a, R1234yf and R290 experimental data. Numerically predicted results, for refrigerant mass flow rate, discharge temperature and shaft power, were compared with the available experimental data, as depicted in Figs. 5 to 13. Discrepancies between experimental and predicted values of the discharge temperature,  T , refrigerant mass flow rate,  m , and shaft 4

power  W

shaft

, were defined as follows: 15 Page 15 of 30

 T  T 4 ,pred  T 4 ,exp

(47)

4

m 

W

m

pred

 m exp 

 100

(48)

m exp



W

shaft,pred

 W shaft,exp 

 100

(49)

W shaft,exp

shaft

The following limits were found for  T ,  W 4

shaft

and  m with R134a, R1234yf and R290 data

points:   2.23 o C   T  2.21 o C 4  R 134a:   1.5%   m  1.2%   1.7%    1.2% W shaft 

  2.4 o C   T  0.3 o C 4  R 1234yf:  2.0%   m  7.5%   1.3%    1.3% W shaft 

  1.7 o C   T  1.3 o C 4  R 290:   3.2%   m  2.0%   1.0%    2.5% W shaft 

It can be observed that, in general, agreement for R134a data was reasonably good (Figs. 5,8 and 11). As for R1234yf (Figs. 6 and 12) or R290 (Figs. 7 and 13), data scattering was equivalent to that found for the baseline refrigerant (Figs. 5, 8 and 11). And, for Figs, 8, 9 and 10, predicted results with R134a have shown a better agreement for the obvious reason that compressor characterization was carried out with own R134a data. A for R1234yf and R290 results, they present, overall, higher and equivalent (in magnitude) discrepancies. From the limits above, it can be inferred that the discrepancies found between predicted and experimental results (discharge temperature, refrigerant mass flow rate and power consumption) confirm the model capability to predict compressor performance with untested refrigerants, in case tests with a known refrigerant are available.

7. Simulation Results

A sensitivity analysis was carried out with refrigerant R134a to determine pressure drop and temperature variation across the four control volumes used in the simulation model. One test 16 Page 16 of 30

condition was chosen from the data taken from Navarro et al (2013), with evaporating and condensing temperatures of 0oC and 65oC, respectively, as well as an inlet degree of superheat of approximately 5oC. These values reflect cabin and outdoor/engine bay operating conditions, respectively. The same operational conditions were used with R1234yf and R290 fluids. Table 2 summarizes the input data for the analysis. Gas pressure and temperature values at four compressor thermodynamic states (1, 2, 3 and 4) are shown in Figs. 14 and 15, respectively. The expected trend is observed, i.e., with suction and discharge passages pressure drops, as well as discharge temperature, T 4 , and, consequently, internal pressure ratio, P3 P2 . Pressure drop in suction passage was always small and temperature variation (due to heat transfer with passage walls) was of the same order for both suction and discharge passages. Figure 16 shows the variation of predicted suction,  P1 2  P1  P2 , and discharge,  P3  4  P3  P4 , pressure drops, for all three refrigerants, against compressor rotational speed. Input

data for the simulation model, Table 3, was taken from experimental operational conditions from Navarro et al. (2013). Compared to R134a, refrigerant R1234yf presented higher pressure drops for both suction and discharge sides. As for R290, still comparing with R134a, higher losses were found in the discharge side, but an opposite trend was found in the suction side. These were findings for specific compressor geometry and operating conditions and must not necessarily be generalized. Pressure losses across suction and discharge passages increase, of course, with compressor rotational speed. The same input data of Table 2 was used to compare results of mass flow rate, m , and shaft power, W shaft , respectively, of an automotive compressor using refrigerants R134a , R1234yf and R290. For all operational conditions, runs with refrigerant R1234yf indicated a mass flow rate increase of approximately 16% and, with refrigerant R290, a mass flow rate decrease 18%, in comparison to R134a (Fig. 17). The shaft power of an automotive compressor running with refrigerant R1234yf decreased 2% and, with fluid R290, increased 45%, if compared to R134a (Fig.18). 8. Conclusions

The main objective of the paper was to characterize a compressor from experimental data taken from operation with a known refrigerant, for example, R134a. The simulation model was then developed in such a way that the pressure drop and heat transfer characterizing parameters do apply

17 Page 17 of 30

to new, eventually untested, refrigerants, e.g., R1234yf. The success of this approach was confirmed by characterization, see Table 1, as well as by simulation results, Figs. 5 to 13. The following conclusions can be drawn from the present work: 

Semi-empirical models, based on fundamental equations and empirical data, can

simulate open-type compressors with reasonable accuracy; 

Previously

available

semi-empirical

models

for

automotive

air-conditioning

compressors were unable to present characterization parameters that were independent from the refrigerant tested; 

By providing good agreement when simulating a MAC compressor running with

R1234yf and R290, yet based on R134a characterization data, the model proved to be a useful tool for the simulation of compressors with new refrigerants, for which laboratory data may not be readily available. ACKNOWLEDGEMENTS Thanks are due to CAPES (Brazilian Ministry of Education, PNPD post-doctoral scholarship), CNPq (from the Brazilian Ministry of Science and Technology, grant 456360/2013-1) and to FAPERJ (State of Rio de Janeiro Research Funding Agency, E-26/110.849/2011), for the financial support provided. The authors also express their gratitude to Dr Samuel Yana Motta and Dr Elizabet Vera Becerra, for their support and encouragement.

18 Page 18 of 30

REFERENCES ANSI/ASHRAE 41.4, 1996. Standard Method for Measurement of Proportion of Lubricant in Liquid Refrigerant. Brown, J. S., Yana-Motta, S. F., Domanski, P. A., 2002, Comparitive analysis of an automotive air conditioning systems operating with CO2 and R134a, International Journal of Refrigeration, vol. 25, pp. 19–32. Cavalcante, P., Farsterling, S., Tegethoff, W., Stulgies, N., Köhler, J., 2008. Transient modeling and sensitivity analysis of a controlled R744 swash plate compressor, International Compressor Engineering Conference. Purdue University, Paper 1880, pp. 1-8. Cuevas, C., Winandy, E., Lebrun, J., 2007. Testing and modelling of an automotive wobble plate compressor. International Journal of Refrigeration, vol. 31, pp. 423 – 431. DOI: 10.1016/j.ijrefrig.2007.008. Darr, J.H., Crawford, R.R., 1992. Modeling of an automotive air conditioning compressor based on experimental data, report ACRCTR-14, Air Conditioning and Refrigeration Center University of Illinois, pp. 1-82. Dirlea, R., Gauthy, L., Grodent, M., Khamsi, Y., Lebrun, J., Negoiu, D., 1998. Modeling of wobble plate compressors used in automotive air-conditioning. International Compressor Engineering Conference. Purdue University, Paper 1249, pp. 255-260. Domanski, P., Didion, D., 1983. Computer modelling of the vapour compression cycle with constant flow area expansion device. NBS Building Science Series 155. NIST, Gaithersburg, USA, pp. 1-148. Eborn, J., Tummescheit, H., Prölß, K., 2005. AirConditioning - a Modelica library for dynamic simulation of AC systems. 4th International Modelica Conference, March 7-8, 2005, Hamburg University of Technology, Hamburg-Harburg, Germany, pp.185-192.

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European Norm EN-13771-1, 2003. Compressor and Condensing Units for Refrigeration. In: Performance Testing and Test Methods. Refrigerant Compressors. Fukuta, M., Yanagisawa, T., Shimizu, T., Suzuki, Y., 1995. Mathematical-model of vane compressors for computer simulation of automotive air conditioning cycle. JSME International Journal

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and

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http://dx.doi.org/10.1299/jsmeb.38.199. Gordon, T., Eustice, H., and Brooks, W., 2011. Automotive AC System Oil Migration HFO1234yf Vs. R134a, SAE Technical Paper. DOI: 10.4271/2011-01-1173. Groll, E.A., 2004. Modeling of compressors. USCN/IIR short course: Simulation tools for vapor compression systems and component analysis. Purdue University. July 10-11. Incropera, P., Dewitt, P., Bergman, L. Lavine, S., Fundamentos de Transferência de Calor e de Massa, Livros Técnicos e Científicos Editora S.A., sexta edição, 2008. Ignatiev, K.M., 2000. Compressor simulation. USCN/IIR short course: Simulation tools for vapor compression systems and component analysis. Purdue University. July 23-24. Joudi, K.A., Mohammed, A.S.K., Aljanabi, M.R., 2003. Experimental and computer performance study of an automotive air conditioning system with alternative refrigerant. Energy Conversion and Management, vol. 44, 2959-2976. DOI: 10.1016/S0196-8904(03)00051-7. Kiatsiriroat, T., Euakit, T., 1997. Performance analyses of an automobile air-conditioning system with R22/R124/R152A refrigerant. Applied Thermal Engineering, vol. 17, pp. 1085-1097. DOI: 10.1016/S1359-4311(97)80003-8. Lee, Y., Jung, D., 2012. A brief performance comparison of R1234yf and R134a in a bench tester for automobile applications, Applied Thermal Engineering, vol. 35, 240-242. DOI: 10.1016/j.applthermaleng.2011.09.004. Lemmon E.W., Huber, M.L., McLinden, M.O., 2007. NIST Standard Reference Database 23. NIST Reference Fluid Thermodynamic and Transport Properties -REFPROP, Version 8.0. 20 Page 20 of 30

Mathur, G., "Experimental Investigation of AC System Performance with HFO-1234yf as the Working Fluid," SAE Technical Paper 2010-01-1207, 2010, doi:10.4271/2010-01-1207. Minor, B., Spatz, M., 2008. HFO-1234yf Low GWP Refrigerant Update, International Refrigeration and Air Conditioning Conference, paper 937, Purdue University. Motta, S.Y., Braga, S.L., Parise, J.A.R., 1996. A study on the polytropic exponent of reciprocating hermetic compressors, International Compressor Engineering Conference. Purdue University. Paper 1088, pp. 89-94. Navarro, E., Coberan, J.M, Martínez, I.O., Gonzalvez, J., 2013, Comparative experimental study of an open piston compressor working with R-1234yf, R-134a and R-290, International Journal of Refrigeration, vol. 36, pp.768-775. DOI: 10.1016/j.ijrefrig.2012.11.017. Navarro-Esbrí, J., J.M. Mendoza-Miranda, J.M., Mota-Babiloni, A., Barragán-Cervera, A., Belman-Flores, J.M., 2013, Experimental analysis of R1234yf as a drop-in replacement for R134a in a vapor compression system, International Journal of Refrigeration, vol. 36, pp. 870-880. DOI: 10.1016/j.ijrefrig.2012.12.014. Park, J. I., Adams, D. E., Ichikawa, Y., Bayyouk, J., 2004. Modeling and simulation of the suction process in a multi-cylinder automotive compressor, International Compressor Engineering Conference, Purdue University, Paper 1623, pp. 1-8. Rasmussen, B. D. and Jakobsen, A., 2000. Review of compressor models and performance characterizing variables, International Compressor Engineering Conference, Purdue University, Paper 1429, pp. 515-522. Saiz Jabardo, J.M., Gonzales Mamani, W., Ianella, M.R., 2002. Modeling and experimental evaluation of an automotive air conditioning system with a variable capacity compressor. International Journal of Refrigeration, vol. 25, pp. 1157–1172. DOI: 10.1016/S01407007(02)00002-6.

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Tian, C., Dou, C., Yang, X., Li, X., 2004. A mathematical model of variable displacement wobble plate compressor for automotive air conditioning system. Applied Thermal Engineering, vol. 24, pp. 2467–2486. DOI: 10.1016/j.applthermaleng.2004.04.011. Tian, C., Liao, Y., Li, X., 2006. A mathematical model of variable displacement swash plate compressor for automotive air conditioning system. International Journal of Refrigeration, vol. 29, pp. 270–280. DOI: 10.1016/j.ijrefrig.2005.05.002. Tian, C., Xu, H., Xianting Li, X., Liao, Y., 2007. Simulation and performance analysis of control mechanism in variable displacement swash plate compressor. Applied Thermal Engineering, vol. 27, pp. 1868–1875. DOI: 10.1016/j.applthermaleng.2007.01.001. Tian, C., Xu, H., Zhang, L., Li, X., 2009. Experimental investigation on the characteristics of variable displacement swash plate compressor. Applied Thermal Engineering, vol. 29, pp. 2824– 2831. DOI: 10.1016/j.applthermaleng.2009.02.002. Tojo, K., Takao, K., Ito, M., Hayase, I., Takahashi, Y., 1990. Dynamic behaviour of variable displacement compressor for automotive air conditioners. SAE Technical Paper Series, International Congress and Exposition, Detroit, USA, paper 900084, pp 1-9. Wang, C., 2014, System performance of R-1234yf refrigerant in air-conditioning and heat pump system – An overview of current status, Applied Thermal Engineering, vol. 73, Issue 2, pp.1412–1420. doi:10.1016/j.applthermaleng.2014.08.012. Yi, F.S., Groll, E.A., Braun, J.A., 2004. Modeling and testing of an automobile ac scroll compressor, Part I: model development. International Compressor Engineering Conference. Purdue University. Paper 1657, pp. 1-8. Youbi-Idrissi, M., Bonjour, J., 2008. The effect of oil in refrigeration: Current research issues and critical review of thermodynamic aspects, International Journal of Refrigeration, Volume 31, Issue 2, Pages 165–179. doi:10.1016/j.ijrefrig.2007.09.006.

22 Page 22 of 30

Zhao, Y., Chen, J., Xu, B., He, B., 2012, Performance of R-1234yf in mobile air conditioning system under different heat load conditions, International Journal of Air-Conditioning and Refrigeration, vol. 20, pp. 1-8. DOI: 10.1142/S2010132512500162. Zilio, C., Brown, J.S., Schiochet, G., Cavallini, A., 2011. The refrigerant R1234yf in air conditioning systems. Energy. 36, 6110-612. DOI: 10.1016/j.energy.2011.08.002.

23 Page 23 of 30

NOMENCLATURE A

heat transfer area, m2

Asc

cross-sectional area, m2

a 4 , a 3 , a 2 , a1 , a 0

constant of Nu  f  Re, Pr  correlation, -

C CH

coefficients of polynomial fit for volumetric efficiency, -

j

compressor heat transfer characteristic parameter relative to control volume j, m0.2

C Pj

compressor pressure drop characteristic parameter relative to control volume j, m-3.75

cp

specific heat at constant pressure, kJ kg-1 K-1

Dh

hydraulic diameter, m

E

relative discrepancy between characteristic parameter of different refrigerants, %

f

friction factor, -

F

residual of the energy conservation equation applied over suction and discharge volumes, K

Fo b j

objective function

G

mass flux, kg s-1 m-2

h

specific enthalpy, kJ kg-1

k

thermal conductivity, kW m-1 K-1

L

characteristic length, m

m

refrigerant mass flow rate, kg s-1

n

number of experiments

N

compressor rotational speed, s-1

Nu

Nusselt number, -

P

Pressure, kPa

Pr

Prandtl number, -

Q

heat transfer rate, kW 24 Page 24 of 30

Qf

rate of heat losses due to mechanical friction, kW

R ij

pressure ratio between control volumes i and j

Re

Reynolds number, -

T

temperature, oC

Tj

average temperature of control volume j, oC

u

velocity, m s-1

Vc

swept volume, m3

Wc

power input to cylinder control volume, kW

W shaft shaft power, kW

x

one of the compressor heat transfer or pressure drop characteristic parameters

y

product of pressure ratios, as defined in eq. (41)

Greek symbols 

heat transfer coefficient, kW m-2 K-1



dimensional groups as defined in Eqs. (31) and (32), kW K-1

T

4

m W

discrepancy between predicted and experimental discharge temperature, K relative discrepancy between predicted and experimental refrigerant mass flow rate, relative discrepancy between predicted and experimental shaft power, -

shaft

 Pi  j

pressure drop between i and j, kPa

T

average temperature difference between flowing gas and passage walls, K

T

temperature increase to estimate compressor discharge temperature, K



tolerance, -

25 Page 25 of 30

m

mechanical efficiency, -

s

isentropic efficiency, -

v

volumetric efficiency, -



dynamic viscosity, kg m-1 s-1



density, kg m-3

Subscripts a

ambient

atm atmospheric c

cylinder or compression space control volume

crit

critical

cond condensation d

discharge passages control volume

f

friction

evap

evaporation

exp experimental i

experiment number

j

iteration number

pred predicted s

suction passages control volume

w

compressor metallic block control volume

1

refrigerant thermodynamic state at compressor suction

26 Page 26 of 30

2

refrigerant thermodynamic state at cylinder (or compression space) entry

23

between states 2 and 3

3

refrigerant thermodynamic state at cylinder (or compression space) exit

3s

refrigerant thermodynamic state at cylinder exit from isentropic compression

4

refrigerant thermodynamic state at compressor discharge

I

R1234yf compared to R134a

II

R290 compared to R134a

Abbreviations AC

air conditioning

MAC

mobile air conditioning

27 Page 27 of 30

LIST OF FIGURES Figure 1. Control volumes of the automotive AC compressor with mass (dashed lines) and energy (solid lines) streams. Figure 2. Flow chart for the calculation of compressor characterization parameters. Figure 3. Inner volumetric efficiency for the same compressor running on R134a, R1234yf and R290 with corresponding polynomial fit of characterization model. Figure 4. The flow chart for the simulation of automotive compressor. Figure 5. Comparison between predicted and experimental discharge temperature, for refrigerant R134a, with discrepancies upper and lower limits. Figure 6. Comparison between predicted and experimental discharge temperature for refrigerant R1234yf, with discrepancies upper and lower limits. Figure 7. Comparison between predicted and experimental discharge temperature for refrigerant R290, with discrepancies upper and lower limits. Figure 8. Comparison between predicted and experimental refrigerant mass flow rate for refrigerant R134a, with discrepancies upper and lower limits. Figure 9. Comparison between predicted and experimental refrigerant mass flow rate for refrigerant R1234yf, with discrepancies upper and lower limits. Figure 10. Comparison between predicted and experimental refrigerant mass flow rate for refrigerant R290, with discrepancies upper and lower limits. Figure 11. Comparison between predicted and experimental shaft power for refrigerant R134a, with discrepancies upper and lower limits. Figure 12. Comparison between predicted and experimental shaft power for refrigerant R1234yf, with discrepancies upper and lower limits. Figure 13. Comparison between predicted and experimental shaft power for refrigerant R290, with discrepancies upper and lower limits.

28 Page 28 of 30

Figure 14. Pressure distribution across compressor control volumes, for refrigerant R134a, with operational conditions of Table 2. Figure 15. Temperature distribution across compressor control volumes, for refrigerant R134a, with operational conditions of Table 2. Figure 16. Suction and discharge pressure drop versus compressor rotational speed, for R134a, R1234yf and R290. Operational conditions of Table 3. Figure 17. Refrigerant mass flow comparison with different fluids and operational conditions of Table 2. Figure 18. Shaft power consumption comparison with different fluids and operational conditions of Table 2.

29 Page 29 of 30

Table 1 – Compressor characterization parameters. CH s

CH d

C Pd

C Ps  3.75

[m ] [m ] [m ] [ m  3.75 ] 4 3 5 3 R134a 0.279±0.0006 0.617±0.007 4.90 × 10 ±9.03 × 10 1.56 × 10 ±4.36 × 10 4 3 5 3 R1234yf 0.271±0.0006 0.619±0.007 4.90 × 10 ±9.03 × 10 1.56 × 10 ±4.36 × 10 R290 0.263±0.0006 0.617±0.007 4.90 × 104±9.03 × 103 1.56 × 105±4.36 × 103 E I (% ) 2.9 0.32 0.0 0.0 E II (% )

0.2

0.2

5.7

0.0

0.0

0.0

Table 2 – Operational conditions for sensitivity analysis. P1

R134a R1234yf R290

kPa 292.80 315.00 474.46

T1 o

C 5.00 5.84 6.02

P4

N

kPa 1889.82 1834.80 2342.95

rpm

1500 1500 1500

Table 3 – Input data  P1 , T1 , P4 , N  for pressure drop   P1 2 ,  P3  4  vs. compressor rotational speed calculations.

P1 kPa 163.94 R134a 243.34 292.80 183.72 R1234yf 265.63 315.82 291.62 R290 406.04 474.46 Fluid

T1 C -8.95 1.01 6.02 -9.13 0.99 5.84 -8.92 1.08 5.97 o

P4 kPa 1889.82 1889.82 1889.82 1834.80 1834.80 1834.80 2342.95 2342.95 2342.95

N rpm 900 1500 2200 900 1500 2200 900 1500 2200

ΔP12 kPa 0.08 0.20 0.37 0.11 0.27 0.52 0.05 0.13 0.23

ΔP34 kPa 1.18 2.96 5.95 1.34 3.29 7.21 1.34 3.46 7.08

30 Page 30 of 30