Purdue UniversityPurdue e-Pubs

International Compressor Engineering Conference School of Mechanical Engineering

1994

Heat Transfer Modeling in a ReciprocatingCompressorF. FagottiEmbraco S.A.

M. L. TodescatEmbraco S.A.

R. T. S. FerreiraFederal University of Santa Catarina

A. T. PrataFederal University of Santa Catarina

Follow this and additional works at: https://docs.lib.purdue.edu/icec

This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu foradditional information.Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at https://engineering.purdue.edu/Herrick/Events/orderlit.html

Fagotti, F.; Todescat, M. L.; Ferreira, R. T. S.; and Prata, A. T., "Heat Transfer Modeling in a Reciprocating Compressor" (1994).International Compressor Engineering Conference. Paper 1043.https://docs.lib.purdue.edu/icec/1043

EXPERIMENTAL ANALYSIS OF A VARIABLE-SPEED COMPRESSOR

Manfred Krueger and Marcos Schwarz Embraco S.A.- Research & Development R. Rui Barbosa 1020 (street) C.P. 91 (P.O. Box) 89219-119- Joinville- SC- Brasil Fax: (+55) 474-41 2650

ABSTRACT

An experimental analysis of a variable-speed reciprocating compressor for household refrigeration, with an operating speed range of 2000 to 5000 rpm , is herein presented. The main parameters describing the compressor performance as a function of the shaft speed , are presented for a standard operating condition. A efficiency breakdown analysis is outlined. The motor characteristics and the inverter control system are discussed. It has been identified that the compressor efficiency at low speed, is penalized by the lower compression and motor efficiencies, while at the high speed the negative effects are the low mechanical and valve efficiencies. The maximum compressor efficiency stays around 60 Hz which corresponds to its original design speed.

INTRODUCTION

Experimental evaluations were performed on a regular reciprocating compressor, where the standard induction motor was replaced by a Brushless Permanent Magnet (BPM) motor, providing a capacity variation by controlling the motor speed. Additionally, small changes were introduced on the oil pumping mechanism to assure full lubrication for all the mechanical components, to speed levels below 1500 rpm.

A refrigeration system utilizing the technique of capacity modulation, may reduce its energy consumption by eliminating the on-off cycling losses, enhancing the heat exchangers performance, and allowing the compressor to work on a mor~ favorable condition. Also smaller compressors may be used. Besides the energy consumption aspects, other advantages like better food conservation quality, quick freezing ability and lower noise level, may also be obtained by utilizing a variable speed compressor.

The current analysis is solely based on the compressor itself. The objective is to outline the compressor performance characteristics as function of the operating speed.

MOTOR CHARACTERISTICS

A conventional induction motor for the compressor is not suitable due to the high power losses at low speeds when operated with an inverter, resulting in low electrical efficiency. The BPM motor, on the other hand, has the characteristic of high efficiency and easy control strategy over a wide speed range. Nevertheless, the BPM motor needs a rotor position detector for proper operation . Since the use of internal sensors is not suitable for hermetic compressors, the back EMF structure was chosen for the rotor position detector.

Inverter Design

The control strategy of the inverter design is shown on Figure 1.

599

Figure 1: Inverter Control Strategy

l JcurranUenoor

The inverter main characteristics are the following:

- AC line 115 V AC - Back EMF shaft position detector

- Full bridge rectifier - Microcomputer controlled ( 8 bits)

- DC bus of 160 Volts - Over current protection using shunt resistor

- Three phase full bridge power stage - The control fixed losses as les than 0.7[W)

- Power Mosfet switches - The inverter efficiency stays within a range of 95 to 97%

The back EMF sensor consists of a passive net and voltage comparators that converts the motor voltages into digital

signals as shown on Figure 2.

Figure 2: Back EMF Circuit and Wave Forms

Va v., Vb V<

/Ea

Vb-41 A1 A1 ... UJ· UJ L/Eb

Vc-~ .......... Ec I

Va,Vb,Vc are the phase voltages on the motor, while Ea,Eb.Ec are digital signals that represent Va,Vb and Vc

The inverter main functions are perfonned as follows:

Starting :The microcomputer detennines the correct sequence and timing for the phase currents allowing high starting

torque without physical shaft sensors.

Steady state drive: According to the back EMF signals the microcomputer generates the six inverter drive signals.

Speed control: A software closed loop continuously changes the duty cycle of the PWM in order to keep constant the

speed independently on the load.

Over load protection: Very low speeds or locked rotor state are identified by the microcomputer that runs a protection

routine avoiding compressor damage .

600

BPM Motor Design

The motor is a three phase four pole designed for 300 W .The rotor uses strontiun ferrite magnets assembled on the surface, as shown on Figure 3.

Figure 4: System Efficiency Figure 3: Motor Design

Eff (Y.]

9!1 6000 RPI

95

Sh.tor BB

Core

75

?B

W.,&ng &5 ····················•·····································································································•••·

oa~-'--~--~~--~--~~~~~~~~--~~ .s 1 1.5 2 2.5 3 3.5 4 4.5 s 5.5 6

Torque [Kgf.cm]

The motor has the following characteristics:

- Internal stator diameter : 63mm - Speed range: 2000 to 6000 rpm - Stator height: 48.5mm -Torque: up to l.O[N.m] (10 kgf.cm)

System Efficiency ( inverter + motor)

As shown on Figure 4, the best system efficiency is achieved at the higher speeds. The BPM motor is an economical, efficient and reliable option for variable speed compressors. The microcomputer is a flexible and cheap option, for providing all the compressor features and is also able to incorporate the entire refrigerator control.

EXPERIMENTAL RESULTS

The experimental data were obtained from a 4.85cc displacement reciprocating compressor tested with R-12 refrigerant at the standard ASHRAE test point of -23.3/54.4/32.2C (-10/130/90F). The overall performance characteristics of the cooling capacity, power consumption and COP are shown on Figure 5 as function of the shaft speed.

The lower COP at the extremes of the speed range is notorious. The causes will be identified through the efficiency breakdown analysis presented below. Although not emphasized on Figure 5, also the capacity drops-off at the extremes, which means that the capacity is not purely a function of speed over the entire speed range. This effect can be identified on the mass flow efficiency curve of Figure 7, discussed fun her.

601

300

270

240

~ 210

"' 180 = 0 u 150

g. 120 u

90

60

30 2000

Fig 5: Performance Characteristics

---Cap

--&-cons

-+-coP

2500 3000 3500 4000 4500 5000

Speed [rpm]

1,45

1,4

1,35

1,3

1,25 =-0

1,2 u

1,15

1,1

1,05

1

The efficiency breakdown analysis as shown on Figure 6, indicates that the motor and compression efficiencies

penalize the COP at low speed, while the valve and mechanical efficiencies drop the COP at high speed. The motor

efficiency curve, as shown on Figure 4, drops at low power input (low speed) indicating stronger impact of the constant

losses. The compression efficiency, which accounts for the deviation of the real compression process compared to the

isentropic compression of the actual mass flow, also drops at the low and high speed regions, indicating stronger cylinder

heating, leakage and/or back-flow effects. It has been identified, as shown on Figure 8, that the cylinder-piston leakage

drops majorly the compression efficiency at low speed. At high speed, the back-flow on the valves was identified to be the

major cause. The valve efficiency curve indicates that the flow restrictions and inertia effects have a strong impact on the

high speed region, representing a non-linear grow of the valve losses with the speed increase. Similarly, the mechanical

efficiency decreases with speed due to the stronger effect of the friction losses. Figure 6 also shows the total energy

efficiency curve, which reflects the behavior of the COP.

100

95

90

85

80

~ 75

70

65

60

55

50

1500 2000

Fig 6: Efficiency Breakdown Analysis

2500 3000 3500

Speed [rpm]

602

4000 4500 5000 5500

-----Valve

__...,_Mech.

---*-Motor ~Compr.

--+--T.Emc.

The COP is not only affected by the power losses but also by the mass flow losses, which effect is incorporated by

the compression efficiency factor in Figure 6. As mentioned before, the mass flow efficiency curve of Figure 7 has its value reduced at the low speed due to cylinder-piston leakage, and at the high speed due to valve back-flow. Cylinder­piston leakage was measured, and the result is shown on Figure 8. We identify that the leaked mass flow is independent

of the shaft speed, emphasizing that the cylinder-piston leakage depends mainly on the compression cycle mean pressure.

Since the leakage flow remains constant, its effect at low speed becomes very significant due to the low pumped mass

flow rate, as indicated by the curve of percentage leak effect of Figure 8.

Fig 7: Mass Flow Efficiency

72 r-------------------------~ 70

68

66

~ 64

62

60

58

56~~~-+--~--+-~--~--~~

1500 2000 2500 3000 3500 4000 4500 5000 5500

Speed [rpm]

25

20

:c 15

= -=:l 10

5

0

Fig 8: Leakage Flow Rate

7

6

5

4 ~ ~

3 ......

l=:=:u/hl 2

1

0

2000 2500 3000 3500 4000 4500 5000

Speed [rpm)

The efficiency analysis also required the knowledge of some compressor temperatures. Figure 9 shows the trend of some temperatures as functions of the compressor speed. As expected, the temperatures grow with speed, reflecting a

higher compressor energy throughput. The suction temperature, however, is less sensitive to speed change, which may

reflect the gas dynamic effect through the suction system.

Fig 9: Temperatures

85

80

75

70

65 [C)

60

55 • Suet

50 • Oil

• Motor

45 )( Bearing

40 )I( Shell

1500 2000 2500 3000 3500 4000 4500 5000 5500

Speed [rpm)

603

CONCLUDING REMARKS

A efficiency breakdown analysis of a variable-speed, hennetic reciprocating compressor, for application on household refrigeration was presented. The relevant concluding remarks are outlined as follows:

• The compressor efficiency at low speed is penalized by the lower compression and motor efficiencies. At high speed the negative effects are the low mechanical and valves efficiencies.

• The cylinder-piston leakage has a strong impact on reducing the mass flow efficiency at low speed, while the valves back-flow reduce the mass flow efficiency at high speed.

• The major compressor changes refer to the BPM motor design, which incorporates magnets on the rotor, requiring new rotor manufacturing and assembling processes.

• The microcomputer electronic board provides the operation and protection functions for the compressor, and the software flexibility allows programming for extra abilities, like the entire refrigeration system control or adjustment of specific parameters according to the application conditions.

REFERENCES

[1] Tizuka K., Uzuhashi H., Kano M., Endo T., Mohri K. Microcomputer control for sensorless brushless motor, IEEE 1984.

[2] Persson E.K., Meshkat S., Brushless motor and controls, Motor-con Conference, Geneva, Switzerland, sept 13-15, 1983

(3] Roerig C.S., Smith RJ., Brushless D.C. motors for systems control, Purdue Compressor Conference, 1982. 124-129 [4] Itami T., Okoma K., Misawa K., An experimental study of frequency-controlled compressors. [5] Serizawa Y., Iizuka K., Senou M., Inverter controlled rotary compressors, Hitachi Review Vol.36, 1987,

N.3 177-185 [6] Scalabrin G., Bianco G., Experimental thermodynamic analysis of a variable-speed open reciprocating refrigeration

compressor, Int. 1. Refrig. 1994 Vol17 N. 1 [7] Davoine J., Perret R., Le-Huy H., Operation of a self-controlled synchronous motor without a shaft position sensor,

IEEE Transactions on Industry Applications Vol1A-19 no.2, marchlapril1983.

604

Heat Transfer Modeling in a Reciprocating Compressor

Fabian Fagotti, Marcio Luiz Todescat Embraco- EmpretJa Brasileira de CompretJtJoretJ S. A.

Rua Rui BarbotJa, 1020, Cz. P. 91, 89219-901 - Join ville - SC - Brazil

Rogerio Tadeu da Silva Ferreira, Alvaro Toubes Prata Federal UnivertJity of Santa Catarina, Department of Mechanical Engineering,

Cz. P. 476, 88040-900- Florian6politJ- SC- Brazil

ABSTRACT

This work presents a study on the gas-to-wall heat transfer model in a compressor simulation program. Widely used heat transfer models, available in the literature are assessed. The simulation program used in this study has been previously validated, presenting reliable results when compared comparing to theoretical and experimental data. The application of the first law of thermodynamics in the case of a reciprocating compressor modeling is discussed, and various heat transfer models are compared to experimental data. Program validation is extended to a wide range of working conditions. Finally, the most reasonable model for the case in study is established. This paper also deals with the improvements in a thermal energy analysis program and its companion compressor simulation program, both previously published.

INTRODUCTION

In the design and development of compressors, it is frequently desired to evaluate operating characteristics with­out experimentation. Most of the work on compressor and/or system optimization can be done through simulation programs. Comparing with experimental trial-and-error method, this procedure is much less time-consuming, re­quires fewer investiments on facilities and generates more knowledge. However, it does not substitute experiments in some cases; both tools are perfectly compatible and one fulfill the other's deficiencies. The choice on what is the best routine for each situation is a strategic point in designing compressors and refrigerating systems.

Todescat et alli (1992) developed a model based on steady state control volumes energy balances, including the compressor simulation as a companion program, in order to evaluate mass flows, enthalpies, pressures, etc. This procedure was adopted aiming to minimize the amount of experimental data inputs. With some improvements, this program is used throughtout the present work.

Whatever the way to model the control volume heat transfer coefficients, the gas-to-cylinder is the most difficult model to establish. Experimental validation is very difficult to carry out in various aspects, and the combination of intrinsically complicated phenomena generates a very expensive theoretical analysis. In spite of that, it is necessary to determine the gas-to-wall heat transfer model that better fits to the compressor global simulation model, since there are a number of works in the field.

In the present investigation, a pragmatic approach was used: various models were investigated and the best one was chosen based on comparative results of overall compressor working characteristics. This procedure was adopted in absence of experimental data relative to the parameters involved in the gas-to-cylinder heat transfer phenomenum. In what follows, the correlation of thermal model with the compressor simulation program is also discussed. Through this approach, one could conclude which model that provides the best fit to experimental results.

COMPRESSOR SIMULATION MODEL

The compressor simulation program is used to evaluate all the main parameters concerning the compressor operating. The original program was developed by Ussyk (1984), based on Soedel & Wolverton (1974). Since then, several improvements have been included in the original program. The following characteristics are now considered in the model: piston displacement as a function of time, thermodynamic processes inside the cylinder, fluid flow through the valves, valve dynamics, piston-cylinder clearance leakage, gas pulsation inside mufflers, motor momentum-power­efficiency relationship, bearing simulation, thermal simulation and refrigerant thermodynamic and thermophysical

605

properties evaluation. The program calculates various parameters along the whole compressor cycle, some of them

are: instantaneous pressures throughout the compressor, mass flow rates, valves dynamics, energy and mass losses,

refrigerating capacity, energy consumption, etc.

The various differential equations, associated to the process modeling, are solved via a fourth order Runge-Kutta

method. Thermodynamic properties can be evaluated using four different equations: perfect gas, Martin-Hou,

Carnahan-Starling-DeSantis and modified Bennedict-Webb-Rubin. The last two equations are available through

program linking to REFPROP database (see Gallagher et alii, 1993), which seems to be the state-of-the-art in the

field. Martin-Hou equation of state is available linking to an in-house developed database, based on Reynolds (1979).

Valves displacements are modeled by modal superposition or by single degree of freedom mass-spring model. Mass

flow through valves is modeled considering one-dimensional isentropic flow. Effective flow and force areas must be

previously measured. Gas pulsation is acoustically modeled considering mufflers as Helmholtz resonators. Bearings

are modeled through short bearing theory. Optionally, a fixed value can be set for the bearing power losses. Finally,

thermodynamic processes for the gas inside the cylinder can be evaluated either by the well-known polytropic model

or by the first law of thermodynamics. As the compressor internal temperatures are input data for the program, there must be an interface between

the compressor simulation program and the thermal simulation program (see Todescat et alli, 1992). The latter

evaluates the temperatures, performing energy balances in eight control volumes, representative of the compressor

parts, using some of the compressor simulation program outputs. Optionally, the temperatures can be set by the

user, in order to simulate just the compressor pump operation.

Since electric motor efficiency and bearings power losses are now considered functions of their respective temper­

atures, their representative control volumes must be taken int account in the global model simultaneous solution.

In this scenario, eight temperatures are considered whithin the compressor: gas in the suction muffler (index "sc"),

cylinder walls ("w"), gas in the discharge muffler ("de"), discharge gas ("d"), internal environment ("ie"), compres­

sor housing ("h"), electric motor ("m") and bearings ("b"). Temperatures are considered in steady-state conditions

in all points except in-cylinder gas. The control volume balance equations are simultaneously and iteratively solved,

since they depend on all compressor energy fluxes. The only modification with respect to the program described by

Todescat et alli (1992), are the inclusion of the equations below.

• Motor energy balance: W, = Qm = U Am(Tm- T;e) (1)

(2)

FIRST LAW OF THERMODYNAMICS APPLIED TO CYLINDER PROCESSES

The use of a polytropic transformation model is theoretically valid just for closed systems. In a compressor,

its applicability is restricted to the compression and expansion processes along the cycle, where there is no mass

flow through the control volume boundaries, excluding the leakages. Using the first law of themodynamics, one can

discriminate the heat transfer effects, besides the fact that the model is valid for general purposes.

Application of the first law of thermodynamics to the in-cylinder gas yields the equation below.

dT dt

(3)

Here, T represents in-cylinder gas mean temperature, t is the time, m is the mass of gas inside the cylinder, Cv

is the specific heat at constant volume, Ac and V are the cylinder internal area and volume respectively, m is a

mass flow rate, h represents enthalpies, with exception to the gas-to-wall heat transfer coefficient, hw. P is the

cylinder pressure, and v is the specific volume. Enthalpy index sc and de are relative to suction and discharge

mufflers; no index denote in-cylinder gas. Mass flow rates index J, bJ, d and bd are relative to suction, suction

back-flow, discharge and discharge back-flow; vis relative to leakages. For more details, see Todescat et alli (1993).

The solution of the equation above yields the gas instantaneous temperature as a function of various compressor

606

operating characteristics, and it has to be simultaneously solved with other equations governing the global model.

Here the main concern consists in determining the heat transfer coefficient, h.,. A fair amount of work has been

done on this subject, none of them completely successful. Experimental determination of h., shows some problems,

like small space for probes, highly position·dependent phenomenum and fast response measurements. Numerical

modeling presents also a number of strorig restrictions. Various heat transfer models have been tested in compressor simulation programs in order to establish the best

one. Annand (1963) proposed the following correlation for internal combustion engines.

(4)

In the preceding equation, "A" and "b" are experimentally determined. The author suggests values around 0. 7 for

both constants, which are used throughout the present work. He also mentioned the possibility of considering Peclet

number (Pe = ReP-r) instead of Reynolds; this procedure is also considered here. The extension to compressors is

direct, not taking into account combustion terms. Adair et alli (1972) determined the correlation below, originally for compressors.

(5)

This equation did not furnished a good agreement with experiments for instantaneous measured data, nonetheless

the average heat flux predictions were quite good. Velocities calculation -inside the cylinder aims to include heat

transfer improvements in the suction period, due to turbulence enhancement.

Hamilton (1974) made use of the Dittus· Boelter correlation, widely used to evaluate heat transfer in inner duct

turbulent flow, in the following form.

(6)

Brok et alli (1980) proposed a correlation based on Adair's work; the only difference was on the swirl velocity

evaluation. In spite of this difference, results of both models are almost identical for most of the cases.

Polman (1981) solved analitically the conservation equations in a boundary layer to evaluate the heat flux in the

gas·t~wall interface, as follows.

>.a [ •sy,: w D cos(wt + r;) + T.I.T"'] q( t) - ----''------:-------;------;--~

- 1 + 6r + cos(wt) (7)

where the parameters lth and l. are related to the thermal and hydrodynamic boundary layers thicknesses, respec·

tively. The parameter 6r is evaluated by the expression 6r = (; - 1 )6v, where 6v is associated to the mechanism

dimensions; for the slider-crank mechanism its value is one. In spite of Polman's equation is valid just for 6v « 1,

it was also considered here.· Parameter r; is a phase angle between temperature and heat flux.

Lin & Zhou (1984) proposed an equation quite similar to Adair's, as follows.

N u = 0. 75Re0·8 Pr0·6 (8)

Like Brok et alli, they used a methodology similar to Adair et alli to evaluate the swirl velocity.

Table 1 shows results considering the various models. The compressor simulated is a small reciprocating com·

pressor for domestic appliances, working at the ASHR~E low back pressure check·point condition.

Table 1: Comparison of results among the models Adair Ann and Brok Lin Hamilton Polman Adiabatic

s.v.o.p. 165.2 165.2 165.4 159.7 166.3 163.7 166.2

d.v.o.p. 41.2 40.9 40.8 40.6 41.0 41.0 41.0

t.l. 6.5 7.3 6.5 10.7 5.7 7.9 5.6

r.c. -4.8 ·4.7 ·4.8 ·5.4 ·4.1 +5.4 ·5.5

p.c. +1.5 +0.4 +1.5 -5.0 +2.0 +0.1 +2.2 s.v.o.p.: suctiOn valve openmg penod (degrees), d.v.o.p.: d1scharge valve openmg penod (degrees),

t.l.: thermodynamic loss, r.c.: refrigerating capacity, p.c.: power consumption, (deviation from experimental data.,%)

607

Figure 1 shows the instantaneous gas-to-wall heat flux for the cases of table 1. Brok's model results are almost identical to those of Adair's modeL The model used by Hamilton results in almost no heat transfer. Liu & Zhou's model presents a discontinuity in two points in consequence of swirl velocity evaluation.

200

100

" ---~--0

s:

Q) ......, -100 rc ....

......, rc Q)

-200 ..<:::

-300

-400 0

' -....,

'I" \ \ \ \ I \ I \ I \

60 120 180

Adair et alli Ann and Brok et alli Liu & Zhou Hamilton Pol man

240 300 crank angle from BDC (degrees)

Figure 1: Gas-to-wall heat rate for various models

GLOBAL THERMAL SIMULATION

......... -

360

It has been also calculated the various global heat transfer coefficients for the compressor control volumes, in the same way described by Todescat el alli (1992). Since the complete modeling is described in the abovementioned reference, it will be omitted here. With exception of the film coefficients to the cylinder and discharge chamber control volumes, all other coefficients resulted in virtually same values, whatever the model considered. Som~

inconsistent aspects have also been observed. As example, for Polman's model the coefficient for the cylinder control volume resulted negative. Large dispersion of values were observed for the cylinder and the discharge muffler control volumes, where the influence of cylinder gas temperature is clear (see the energy balances in Todescat et alli, 1992). Differences in the order of ten times were observed in the cylinder control volume film coefficient.

Making use of the heat transfer coefficients calculated, the compressor was thermally simulated. Table 2 shows the deviation between predicted results and experimental data. Results using Polman's model were omitted, since its cylinder control volume global heat transfer coefficient resulted negative.

Table 2: Predicted temperatures deviation from experimental data (degrees Celsius) Adair An nand Brok Liu Hamilton Adiabatic

cylinder -15.2 -8.0 -15.2 -0.1 -15.0 -16.3 suction chamber -1.4 -1.1 -1.4 +0.4 -1.6 -1.6

discharge chamber -2.9 -3.2 -3.0 -1.6 -2.0 -1.5 internal environment -2.2 -2.0 -2.2 -1.0 -2.4 -2.4

discharge -1.6 -1.9 -1.6 -2.6 -1.6 -1.5 housing -1.4 -1.4 -1.5 -0.7 -1.6 -1.6

Except one, all differences are negative, as a consequence of underestimation of power losses. Actually, short­bearing model was not applicable in the present case, as well as gas friction losses have not been modeled. Some

608

improvements on these subjects are required, although the results are qualitatively quite good.

In spite of the best results were presented by Liu & Zhou model for temperatures evaluation, it was observed

that their model drives to inconsistent results for some cases. Table 3 shows the variation of cylinder-to-internal

environment heat transfer coefficient for Adair et alli, Annand and Liu & Zhou models. Since the last one yielded

negative values for this parameter, it has been discarded.

Table 3· U Ac in W / K for three models at six operating conditions

-35°C/40°C -15°C/40°C -5°C/40°C -35°C/70°C -l5°C/70°C -5°C/70°C

Annand 0.577 0.448 1.07 0.511 0.474 0.305

Adair 0.293 0.453 1.19 0.177 0.380 0.340

Liu 0.483 -1.57 -3.17 0.267 -1.31 -4.00 ..

operating condition = evaporating temperature / condensmg temperature

For each operating condition, the heat tranfer coefficients for the other control volumes did not present a con­

siderable variation, whatever the model used for the cylinder. Todescat et alli (1993) compared results of Adair's, Annand's and Liu & Zhou's models with the numerical

solution presented by Recktenwald (1989). The authors concluded that Liu & Zhou's model overestimates heat

fluxes, Adair's underestimates it. Annand's model presented the best fit comparing to numerical results of the

complete Navier-Stokes equations performed by Recktenwald. This conclusion reinforces the adoption of Annand's

as the best amog the models analyzed here.

RESULTS

Figures 2 and 3 show numerical results (curves) deviation from experimental data (points) for the same compressor

mentioned in table 1. Superheating, subcooling and compressor entry temperatures were maintained constant at

32.2°C. It becomes evident that the simulation program works very well throughout the range explored. The

experimental data evaluated represent the mean value of a number of data with at least 95% statistical confidence

interval. Annand's model was used to model the gas-to-wall heat' transfer phenomena.

~ .B e

-~ .. ~ CJ>

·~ ~ "' -: ~

2250

1150

1250

750

250 -40

/" / Cl / '

/ ' '

/ ' ' ' ' / ' ' ' J?) ' '

/ . . . / .I<T'

/ ' .

/ . . . / . . .

/ . . / .......... . 0 condenslng

/

~-~--:-----·· --temperature ~

Cl------- condensing temperature = o -

-35 -30 -25 -15 -10 -5 evaporating temperature ldeq. Celsius)

Figure 2: Refrigerating capacity: theoretical versus experimental data

~ "' .::: a. "' ., "' 8

~ 40 c :;

70 c

350

300

250

200

150

.......... ...-" .---~-- ................ {)

.-· ...... -__ .. - ./-'()

.--· ........... ••• ·:;.. .....- r:O:::-· -_----::c-==ona=•en:-:s""l.n:-:g,------,

_.;.:? ...-- temperature = 40 c ~- Cl ···--·· condensing 8 temperature = 70 c

100~--~--~~--~--~----._ __ _. ____ ._ __ ~ -40 -35 -30 -25 -20 -15 -10 -5

evaoorating temperature ldeg. Celsius)

Figure 3: Energy consumption: theoretical versus experimental data

Figure 4 shows the energy fluxes along the compressor manifolds. This figure illustrates the type of information

available in the output of a simulation program that can not be easily obtained by experimental methods.

609

300

2 00

§: ,.... ;'l ,., ::z: "" 100

~ ., ... .... ... .,~ ... "'

., "' ., """., .., :;;{l

,. '<> "'., ..... ~ "' 0 "' ..: "' ... ., "' ""

_..., "' !;l tl 0. --< :'! ... ., ...

u .... ..... "' u .., ..., .., Figure 4: Energy fluxes in the compressor manifolds

CONCLUSIONS

Polman (1981) and Liu & Zhou (1984) models lead the global compressor model to inconsistent results in some

working conditions. Brok et alli (1980) model presents the same behaviour of Adair et alli (1972) model. Contrary to

Brok et alli (1980) conclusion, heat transfer modeling may assume an important role in the compressor simulation.

Annand (1963) model showed the best fit to experimental data concerning the compressor simulated by the authors.

The overall simulation program works very well when evaluating thermal behaviour, as well as performance

characteristics. It was tested over a wide range of operating conditions, presenting very reliable results.

REFERENCES

• Adair, R. P., Qvale, E. B. & Pearson, J. T., 1972, "Instantaneous Heat Transfer to the Cylinder Wall on

Reciprocating Compressors", Proc. Purdue Comp. Tech. Conf., 521-526

• Annand, W. J. D., 1963, "Heat Transfer in the Cylinders of Reciprocating Internal Combustion Engines", Proc.

In6tn. Mech. Engr6. 1 117, 973-996 • Brok, S. W., Touber, S. & van der Meer, J. S., 1980, "Modeling of Cylinder Heat Transfer- Large Effort,

Little Effect?", Proc. Purdue Comp. Tech. Conf., 43-50

• Gallagher, J., McLinden, M., Morrison, G. & Huber, M., 1993, "NIST Thermodynamic Properties of Refriger­

ants and Refrigerants Mixtures Database (REFPROP)", Thermophy6ic6 Divi6ion, National ln6titute of Standard.!

and Technology, US Department of Commerce • Hamilton, J. F., 1974, "Extensions of Mathematical Modeling of Positive Displacement Type Compressors",

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