Compressor efficiency with cylinder slenderness ratio of rotary compressor at various compression ratios

international journal of refrigeration 70 (2016) 42–56

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Compressor efficiency with cylinder slenderness ratio of rotary compressor at various compression ratios Ki-Youl Noh a, Byung-Chae Min a, Sang-Jin Song a, Jang-Sik Yang b, Gyung-Min Choi a,*, Duck-Jool Kim a a

School of Mechanical Engineering, Pusan National University, 30 Jangjeon-dong, Geumjeong-ku, Busan 609735, Republic of Korea b Rolls Royce University Technology Centre, Pusan National University, 30 Jangjeon-dong, Geumjeong-ku, Busan 609-735, Republic of Korea

A R T I C L E

I N F O

A B S T R A C T

Article history:

When the air conditioning and heating systems operate in low speed regions, the effi-

Received 4 September 2015

ciency of inverter compressor is relatively low, owing to the reduction in motor efficiency.

Received in revised form 16 May

Nevertheless, the annual operating time of compressor is largely occupied by low speed regions.

2016

Hence, experimental and numerical analyses were conducted to improve compressor effi-

Accepted 14 June 2016

ciency in these regions, and various pressure conditions were considered. The significant

Available online 17 June 2016

difference in the volumetric efficiency with compression ratios was observed through the experiments. To reduce the decrease in volumetric efficiency at high compression ratio, a

Keywords:

geometric combination of the compression part was considered through a numerical analy-

Compression ratio

sis. The numerical results showed that the volumetric efficiency at small cylinder slenderness

Volumetric efficiency

ratio was relatively high and increased by about 6.3% at a compression ratio of 7. Then the

Rotary compressor

cooling capacity increased by 8.77%, while the input work showed a relatively small in-

Design parameter

crease of 2.44%.

Cylinder slenderness

© 2016 Elsevier Ltd and IIR. All rights reserved.

Rendement d’un compresseur avec rapport d’élancement cylindrique d’un compresseur rotatif à divers taux de compression Mots clés : Taux de compression ; Rendement volumétrique ; Compresseur rotatif ; Paramètre de conception ; Élancement cylindrique

* Corresponding author. School of Mechanical Engineering, Pusan National University, 30 Jangjeon-dong, Geumjeong-ku, Busan 609-735, Republic of Korea. Tel.: +82 51 510 2476; Fax: +82 51 512 5236. E-mail address: [email protected] (G. Choi). http://dx.doi.org/10.1016/j.ijrefrig.2016.06.020 0140-7007/© 2016 Elsevier Ltd and IIR. All rights reserved.

international journal of refrigeration 70 (2016) 42–56

43

Nomenclature A Bt Fn Ft Fh Fd Fm Ffl h Hc Hr k lv, lv2 ltotal lslot mv  m Mb Mc N P Pin,Pout Pr R Rc Rr Recc R1,R2,Rt1Rt2 T Tin,Tout V

1.

flow area [m2] vane thickness [m] normal force between the vane tip and roller [N] tangential force between the vane tip and roller [N] gas force on the vane side [N] gas force on the vane back side [N] inertial force of the vane [N] film load [N] enthalpy [kJ kg−1] cylinder height [m] vane height [m] specific heat ratio vane length protruding into the cylinder [m] total vane length [m] cylinder slot length [m] mass of vane [kg] mass flow rate [kg s−1] friction moment at roller face [N] friction moment between the roller and eccentric [N] revolution per minute [rev min−1] pressure [kPa] suction and discharge pressure [kPa] compression ratio gas constant [J kg−1 K−1] cylinder radius [m] roller radius [m] radius of eccentric [m] reaction force on the vane [N] temperature [K] suction and discharge temperature [K] volume [m3]

Greek letters θ angular position of the crankshaft [rad] δa clearance between the roller face and bearing [μm] clearance between the roller and eccentric part δb [μm] ε eccentricity ratio μ friction coefficient η efficiency ω eccentricity ratio angular velocity of the roller [rev s−1] ωp Subscripts ad b c comp cl cb con dis eb ec lc m mech rb rc sp uc vb v

adiabatic suction chamber compression chamber compressor clearance volume flow between suction chamber and compression chamber control volume flow between clearance volume and muffler flow between back of vane and suction chamber flow between back of vane and compression chamber lower cavity muffler mechanical flow between crank shaft and suction chamber flow between crank shaft and compression chamber suction pipe upper cavity flow passing through top and bottom of vane volumetric

Introduction

Due to the increased interest in energy efficiency, inverter system instead of the conventional on/off control is being used in air conditioning and heating systems (Adhikari et al., 2012; Aprea et al., 2009; Chen et al., 2008; Qureshi and Tassou, 1996; Vittorini and Cipollone, 2016). According to the use of inverter system, the analysis of compressor characteristic at variable speeds has also become important. Fig. 1 shows the efficiency and annual operating time for the frequency changes of a DC inverter rotary compressor. The compressor efficiency is usually decreased according to the rise of compression ratio and decrease of operating speed. This behavior is attributed to the characteristics of the motor efficiency, lubrication and the leakage (Ekren et al., 2013; Futani and Shida, 1994; Inada et al., 2000; Piazza and Pucci, 2016; Yang et al., 2011). On the other hand, the annual operating time of a DC inverter rotary compressor tends to be concentrated in the low speed region because of the fine control of room temperature. Therefore, the

Fig. 1 – Compressor operating hours and inverter compressor efficiency. (●: experimental data for a 12.5 cc rotary compressor, △○: experimental data for a 14.1 cc rotary compressor).

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international journal of refrigeration 70 (2016) 42–56

improvement for compressor efficiency at low speed region is needed to maintain the high energy efficiency of system at wide range. Many factors are considered to increase the compressor efficiency. Among them, the optimization of compression part design is the most fundamental and important factor. Several parameters, including the cylinder and roller size, suction and discharge port position angles are considered in the design phase of compressors. It is difficult to determine the optimal design condition by only testing for a prototype compressor. Hence, methods in which a simple physical model and experimental results incorporated are widely used to calculate operation efficiency (Cai et al., 2015; Lee et al., 2015; Shao et al., 2004; Shimizu et al., 1980; Tassou and Qureshi, 1998). Compression part design mainly focuses on the mechanical efficiency. Ooi (2005) used a mathematical model to determine the combination of the design factors of the compression part with minimization of mechanical loss and reported that the optimal compression part design can enhance compressor efficiency. However, the changes in volumetric efficiency as well as minimization of mechanical loss should be considered. Li (2013) predicted the compressor performance at variable speeds through a combination of the volumetric efficiency and adiabatic efficiency based on measurement and mathematical model. The operating pressure is affected by factors such as the operating mode (cooling/heating) and low outdoor temperature, and the leakage characteristics that are dependent on these operating pressures affect the volumetric efficiency directly. In the case of regions with a cold climate, the maintenance of refrigerant flow rate for stable operation is more important than mechanical loss. This is because refrigerant flow rate is considerably decreased by the increase in the specific volume of the refrigerant under low suction pressure and the increase in the inner leakage at a high compression ratio (Bertsch and Groll, 2008).

In this study, the changes of compressor efficiency according to the various compression part design and compression ratios were analyzed by using the mathematical model. And the compression part design based on volumetric efficiency was suggested for improvement of the compressor efficiency at low speed region.

2.

Experimental section

A calorimeter system is used to evaluate the performance of a compressor under the preset operating condition. Fig. 2 shows the secondary fluid calorimeter system used for the experiment. The temperature and the pressure of each part were controlled by proportional integral and derivative control (PID), as shown in Table 1. The compressor performances are measured in stability conditions, and each data set is acquired four times an hour. The standard deviations of the acquired data in two conditions of Fig. 1 are shown in Table 1. The collected data are stored in a PC via general purpose interface bus (GPIB) and ethernet communication. The cooling effect is measured by the heat amount of heat exchange between secondary refrigerant and pipe line in an insulated calorie chamber. The thermal leakage factor (kcal) under controlled condition is calculated by Eq. (1).

kcal =

Wheater Tp − Ta

(1)

where Wheater is the input power of the heater, Ta is the average ambient temperature of calorie chamber, and Tp is the saturation temperature of the secondary fluid. The temperature variation of Ta is kept under 0.1 degrees Celsius, and that of Tp is maintained under 0.5 degrees Celsius.

Fig. 2 – The configuration of a compressor calorimeter.

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international journal of refrigeration 70 (2016) 42–56

Table 1 – The stability of a calorimeter system for the evaluation of compressor performance. Unit

Suction pressure (Pin) Discharge pressure (Pout) Suction temperature (Tin) Expansion valve inlet temperature (Tcal.in) Calorie chamber ambient temperature (Ta) Refrigerant flow Voltage Calorimeter input Cooling capacity

MPa MPa K

kg/h V W Btu/h

Accuracy of measurement device

Wheater + kcal (Ta − Ts ) hcal.out − hcal.in

Stability conditions (variation range)

Standard deviation Pr 3.4 (40 Hz)

Pr 2.3 (40 Hz)

±0.25%

≤0.0005 MPa

0.04

0.04

±1%

≤0.2 K ≤0.2 K ≤0.3 K ≤0.1% ≤2 V ≤1% ≤1%

0.11 0.10 0.10 0.10 0.20 0.88 1.22

0.08 0.10 0.10 0.15 0.22 0.92 1.63

±0.01~0.05% ±0.1%

The mass flow rate of the refrigerant discharged from the  out ) is calculated as shown in Eq. (2). The power compressor ( m consumption was directly measured using a power meter.

 out = m

Data acquisition (four times a hour)

(2)

where Ts is the temperature of the secondary fluid, and hcal.in and hcal.out are the enthalpy at the inlet and outlet of the calorie chamber, respectively. The experiments were performed at 40 Hz using a twin rotary compressor with displacement volume of 12.5 cc for six operating conditions. The operating conditions were selected from the compressor operation map shown in Fig. 3, and divided by the condensing temperature and the evaporating temperature, which are listed in Table 2. The compressor operation map was created based on a simple calorimeter experiment for an

absolute suction pressure of 0.34 to 1.42 MPa, a compression ratio of 1.4 to 13, and a frequency of 15 to 90 revolution per second (RPS).

3.

Compressor analysis model

3.1.

Refrigerant material property

Fig. 4(a) shows the cross sectional view and compression part of a hermetic rotary compressor, respectively. The motor and compression parts are coupled on the same shaft, and the eccentric part of each compression part rotates by the motor. The compression process in upper and lower cylinder happens by rotation of eccentric part with a phase difference of 180 degrees. Hence, a cycle takes two motor revolutions to be finished. The vane exists to divide the suction and compression chamber

Fig. 3 – The compressor operation map.

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international journal of refrigeration 70 (2016) 42–56

Table 2 – Experimental conditions of the calorimeter at 40 Hz. Case no.

1

2

3

4

5

6

Pin (MPa) Pout (MPa) Pr Tin (K) Tcond (K) Tvi (K) Teva (K)

1.42 2.25 1.58 303.81 310.14 301.84 292.71

1.13 2.77 2.45 295.63 318.71 310.41 284.53

0.99 3.38 3.4 289.23 301.34 293.04 278.13

0.93 3.79 4.08 289.23 332.73 324.43 278.13

0.74 3.68 5 281.76 331.28 322.98 270.66

0.54 3.78 7 272.53 332.47 324.17 261.43

in a cylinder. The general vane is separated with the roller, and the spring at the back of vane is inserted to maintain the contact between the vane and the roller. In this study, the structure combined vane and roller were adopted to decrease friction and leakage on the vane tip. The vane tip leakage was ignored by increase of leakage flow path, and the vane spring for prevention of vane tip leakage was not considered (Okur and Akmandor, 2011; Wu and Chen, 2015). Since the space behind the vane is connected to the space inside the shell, the pressure that acts on the back of vane was defined by discharge

(a)

(b) Fig. 4 – The (a) cross sectional view and shape of compression part of compressor and (b) definition of the control volume and inner leakages (2-cylinders).

international journal of refrigeration 70 (2016) 42–56

 gasdt Mgas = Mgas initial + ∫ m

(5)

 oildt Moil = Moil initial + ∫ m

(6)

P=

Mgas Pin ⎛ ⎞ ⋅ ρink ⎜⎝ Vcon − Moil ρoil ⎟⎠

⎛ P⎞ T = Tin ⋅ ⎜ ⎟ ⎝ Pin ⎠

k=

Fig. 5 – Definition of the angle for volume calculation.

pressure (Pout). The structure except vane part was applied same structure with a conventional rolling piston compressor. The refrigerant flows into the chamber through a suction pipe. After compression, the refrigerant is discharged to the muffler when the valve opens. Suction and compression progress simultaneously, and each chamber is divided by the vane. To predict the changes in pressure during compression, the refrigerant flow paths were defined by control volume, and the leakages depending on the pressure difference between each control volume were considered, as shown in Fig. 4(b). The volumes of the suction and compression chambers were determined by crank shaft rotation (θ), as shown in Fig. 5. The compression chamber volume is defined in Eq. (3). The relationship between suction and compression chamber volume is shown by Eq. (4).

(3)

Vb (θ ) = Vc (2π − θ )

(4)

where Rc is the cylinder radius, Rr is the roller radius, Hc is the cylinder height, Bt is the vane thickness, e is the eccentric length (Rc−Rr), and α is the angle formed by the lines joining Ov to Oc and Or as shown in Fig. 5 ( α = sin −1 ( esin θ Rr ) ). lv is the vane length projecting into the chamber ( lv = Rc − Rr cosα + ecosθ ). Compression process was assumed as isentropic process, and the changes of refrigerant pressure and temperature in each control volume were calculated by Eqs. (5)–(9). The initial concentration of oil was assumed by 1% of mass of each control volume.

k

(7)

(k − 1) k

(8)

Cp (t ) Cv (t )

(9)

where Mgas, Moil are gas and oil mass in each control volume, respectively.Cp is specific heat at constant pressure and Cv is specific heat at constant volume. For calculation, leakage can be modeled using the nozzle flow model, Fanno flow model, and incompressible viscous flow model under different conditions. To calculate the mass flow rate for an oil free structure, Wu and Chen (2015) investigated the leakage characteristics of changes in the refrigerant using the Fanno flow model and incompressible viscous flow model. In this study, the simple orifice flow for an isentropic change of state was considered to calculate the leakage flow between the control volumes. Flow coefficient (Cm) for valve system used the function of discharge port diameter and valve lift (Min et al., 2014).

 = Cm Pu A m

2k

(k − 1) RTu

(S2 k − S(k+1) k )

(10)

where k is the specific heat ratio as function of the pressure and the temperature, A is the leakage area, and Pu, Tu are the pressure and the temperature of upstream, respectively. S is the ratio between the upstream (Pu) and downstream (Pd) pressures. A choked flow occurs when the pressure ratio falls below a critical point (rc).

S= 1 1 Vc (θ ) = π ( Rc2 − Rr2 ) Hc − ⎡⎢ Rc2θ − Rr2 (θ + α ) 2 ⎣2 B2 Tanα 1 1 − e ( Rr cosα + ecosθ ) siinθ ⎤⎥ Hc − Bt lvHc + t Hc 2 2 8 ⎦

47

2 ⎞ k (k −1) Pd ≥ rc = ⎛ ⎝ Pu k + 1⎠

(11)

Valve system was considered by a single degree of freedom system, as shown in Fig. 6. Valve lift was calculated from Eq. (12), and discharge area according to valve lift was calculated. The mass flow rate pass through the valve system was calculated by Eq. (10). Over-compression occurred by valve stiffness at the beginning of discharge, and it is also affected by factors such as pressure difference and effective area of discharge port.

F (t ) = meff ⋅  y + Cdamp ⋅ y + k ⋅ ( y − δ 0 ) = Aeff ⋅ ( Pm − P)

(12)

where meff is effective mass, Cdamp is damping value, k is valve  are valve lift, velocity and acceleration, restiffness. y, y , y spectively. δ0 is initial valve lift, Aeff is effective area of discharge port and Pm is pressure in muffler.

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international journal of refrigeration 70 (2016) 42–56

∑F

y

= − μ fric R1 − μ fric R2 − Fn cosα 2 − Ft sinα 2 + Fd = Fm

∑ M = −R

1

+

(lv + rv ) + R2 (lv + lslot + rv ) −

μ fric R2 Bt ⎛ lv + ⎜ + rv ⎞⎟ Fh = 0 ⎠ ⎝2 2

μ fric R1Bt 2

(15)

(16)

where μfric is the friction coefficient, rv is the vane tip radius, and lv is vane acceleration. Fh, Fd and Fm were obtained, as shown in Eqs. (17)–(19).

Fig. 6 – Schematic diagram of valve dynamics.

3.2.

Dynamics analysis

Many studies for the dynamic analysis of the rotary compressors have been progressed. Yanagisawa and Shimizu (1985) analyzed the motion of a rolling piston through dynamic equations, and verified the analytic results by comparing them with experimental results. In this study, a dynamic analysis was carried out for the vane and roller assembled structure, and loss calculation was based on the existing studies for the rotary compressor (Ooi, 2008). The analysis of the forces acting on the driving part was based on the changes in pressure during compression. The analysis part can be divided into analyses on the vane, roller, and the crankshaft.

3.2.1.

Vane

Fig. 7(a) shows the forces acting on the vane, and the force and moment equilibrium equations are used to obtain the values of R1, R2, and Fn. The reaction forces of R1 and R2 occur between the cylinder and the side of vane face. Fn is a normal force which is acting at the contact point of the vane tip and the roller. The contact point is moved by the motion of vane and roller with the crank angle advances. Sawai et al. (2014) calculated the contact angle between the vane tip and the roller by solving simultaneously the equation of motion for the vane, the roller and the crankshaft. The pressure distributions around the vane tip were defined by the contact angle, and variable forces based on these pressure distribution were applied for dynamic analysis of vane. In this study, the contact point between the vane tip and the roller was simply assumed as a point on a line connected between the vane tip center and the roller center. It was calculated by α2, and α2 is represented by Eq. (13).

⎛ e ⋅ sinθ ⎞ α 2 = sin −1 ⎜ ⎝ Rr − rv ⎠⎟

(13)

Fh = lvHr ( Pc − Pb )

(17)

B B Fd = ⎛ Bt Pout − ⎛ t + rvsinα 2 ⎞ Pc − ⎛ t − rvsinα 2 ⎞ Pb ⎞ Hr ⎝ ⎝2 ⎠ ⎝2 ⎠ ⎠

(18)

Fm = −mvlv

(19)

At first, Ft was selected arbitrarily as initial value at first, and it was recalculated using the equilibrium equation of the moment acting on the roller. Fig. 7(b) shows the forces and moments acting on the roller. Mb represents the torque resulting from the shearing force generated by the velocity gradient in the oil film of the upper and lower sides of the roller. Oil viscosity (μoil) was defined by solubility, discharge pressure and temperature. Oil viscosity for discharge pressure (Pin) of 3.38 MPa was 0.008869 Pa·s

Mb =

πμoilω p ( Rr4 − ri4 ) δb

(20)

where ri is radius of the eccentric part, μoil is the oil viscosity coefficient, ωp is the angular velocity of the roller, and δb is the clearance between the roller and the bearing face, as shown in Fig. 4(a). Mc represents the friction torque generated between the roller and the eccentric part, and it is calculated by the mobility method. This method is suitable for compact structures and has the advantages that it does not need pressure distribution calculation and recursive calculation (Booker, 1971; He et al., 2013; Hirani et al., 1997; Mayer, 2004).

Mc =

μoil (ω − ω p ) ri2 Heccπ ⎛ 2 + ε ⎞ δ a ε + F sinφ ⎝ 1 + ε ⎠ 2ri fl δa 1 − ε 2

(21)

where Ffl is the film load, Hecc is the height of the eccentric part, ω is the angular velocity of the crank shaft, ε is the eccentric ratio, ϕ is the attitude angle, and δa is the clearance between inner face of the roller and the eccentric part as shown in Fig. 4(a). Ft is recalculated by calculating of Mb and Mc as shown in Eq. (22).

Friction coefficient used experimental results of literature (Yanagisawa et al., 1982). Friction coefficient (μdis) for vane tip and side was defined by 0.1 and 0.15, respectively.

Ft =

∑F

where Ip is the moment inertia of the roller and ω p is the angular acceleration of the roller.

x

= − R1 + R2 − Fn sin α 2 + Fh + Ft cos α 2 = 0

(14)

Mc − Mb − I pω p Rr − rv

(22)

international journal of refrigeration 70 (2016) 42–56

49

(a)

(b) Fig. 7 – Force acting on the (a) vane and (b) roller.

Ip =

ρroller Hrπ ( Rr4 − ri4 ) 2

(23)

eω cos (α 2 + θ ) (Rr − rv )

(24)

ωp = −

ω p =

eω sin (α 2 + θ ) (α 2 + ω ) (Rr − rv )

3.2.2.

θ +α⎞ Fr = Fp cos ⎛ − F cos (α 2 − α ) cos (θ + α ) ⎝ 2 ⎠ n − Ft cos (α 2 − α ) sin (θ + α ) + Fe

(26)

θ +α⎞ Fθ = −Fp sin ⎛ + Fn cos (α 2 − α ) sin (θ + α ) ⎝ 2 ⎠ − Ft cos (α 2 − α ) cos (θ + α )

(27)

Froller = Fr2 + Fθ2

(28)

(25)

Roller

Fig. 7(b) represents the force acting on the roller, and it is defined as follows using Fn, Ft , Fp, and Fe .

where Fp is the pressure force acting on the roller and Fe is the centrifugal force of the roller.

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international journal of refrigeration 70 (2016) 42–56

Fp = 2Rr Hc ( Pc − Pb ) sin ⎛ ⎝

θ +α⎞ 2 ⎠

Fe = mroller eω 2

3.2.3.

(29)

(30)

4.

Crankshaft

A twin rotary compressor has two cylinders with a phase difference of 180°. The compression process of each cylinder is calculated using Eqs. (3)–(30). Fig. 8 shows the forces acting on the crank shaft of the twin rotary compressor. Deformation and inclination of crank shaft are not considered. The forces acting on the center of each journal (Fmj, Fsj) are calculated using the force acting on the roller. Reference point for moment calculation of crank shaft is A–A line. • The force in the radial direction

Fmjr − Fsjr + Fr + Fec1 − Fr 2 − Fec2 = 0

(31)

Fmjr (lmj + lsj ) + (Fr + Fec ) ⋅ lsj − (Fr 2 + Fec2 ) ⋅ lsj2 = 0

(32)

• The force in the tangential direction

Fmjt − Fsjt + Fθ − Fθ 2 = 0

(33)

Fmjt (lmj + lsj ) + Fθ ⋅ lsj − Fθ 2 ⋅ lsj2 = 0

(34)

• The resultant force

Fmj = Fsj =

2 2 Fmjr + Fmjt

2 Fs2jr + Fsjt

cylinder and that of the sub journal, and lsj2 is distance between the center of lower cylinder and that of the sub journal.

(35)

(36)

where Fec is the centrifugal force of the eccentric part. lmj is distance between the center of the upper cylinder and that of the main journal, lsj is distance between the center of the upper

Results and discussion

4.1. Compressor performance according to the compression ratio Fig. 9 shows the experimental and numerical analysis results under the operating conditions listed in Table 2. The results were normalized by the result for a compression ratio of 2.45. The results of the numerical analysis show tendency similar to those of the experiments, and the discrepancy is within 3% under all conditions, except at a compression ratio of 1.58. In the case of a compression ratio of 1.58, a difference of 7% in the power input was caused by the loss of over-compression that the pressure in the compression chamber is higher than the discharge pressure. The over-compression loss was overestimated because the calculated pressure change during the discharge process was relatively slower than practical. Fig. 9(a) shows the actual mass flow rate according to the compression ratio, and the x-axis shows the evaporator and condenser temperatures for each compression ratio. The mass flow rate was mainly influenced by the evaporation temperature. For a compression ratio of 7, the very low mass flow rate was attributed to the increase in the refrigerant specific volume under the low suction pressure and the increase in the inner leakage caused by a high pressure difference. Fig. 9(b) and (c) shows the cooling capacity and the power input, respectively. Both performance values are expressed as the product of mass flow rate and enthalpy difference. The change in power input at a high compression ratio is nonlinear. This is because the mass flow rate decreases significantly even though the enthalpy difference increases by rising condensing temperature. Fig. 9(d) shows the energy efficiency ratio (EER) which represents the ratio of cooling capacity in the British thermal unit (BTU) and power input. The compressor efficiency can be predicted from the calorimeter experiment results using Eqs. (37) to (39). The product of the adiabatic and mechanical efficiency is expressed as the factor for the power input. If the change in pressure in the compression chamber is measured by the pressure sensor, two efficiencies can be distinguished by calculating the actual gas work (Wactual). The motor efficiency that is more influenced by the operating speed is also affected by the compression ratio. However, a constant motor efficiency of 94% was applied in this efficiency calculation because the influence of compression ratio was small.

ηv =

 out  out m m =  theoretical ρin ⋅ Vc (0) ⋅ N 60 m

ηad ⋅ ηmech =

(37)

 m − hcal.in ) Wtheoretical Wactual (h ⋅ = theoretical cal.out Wactual (Wactual + Wmechanical ) Wcomp ⋅ ηmotor (38)

Fig. 8 – Force acting on the crank shaft.

ηcomp = ηv ⋅ ηad ⋅ ηmech ⋅ ηmotor

(39)

international journal of refrigeration 70 (2016) 42–56

(a)

(b)

(c)

(d)

51

Fig. 9 – Comparison of analysis result and experiment result depending on the compression ratio for (a) mass flow rate, (b) cooling capacity, (c) power input and (d) energy efficiency ratio (EER) at 40 Hz.

where ηv, ηad, ηmech, ηmotor and ηcomp are the volume efficiency, adiabatic efficiency, mechanical efficiency, motor efficiency, and compressor efficiency, respectively. Wtheoretical is the theoretical adiabatic compression work, Wactual is the actual gas compression work, Wmechanical is the mechanical loss in friction part, and Wcomp represents the power input measured using a power meter. Fig. 10 shows the efficiency of compressor for the compression ratio at 40 Hz. ηv, ηad ∙ ηmech, ηcomp of compression ratio of 7 showed a maximum reduction of 24%, 13% and 30% against compression ratio of 1.58, respectively.ηv is largely affected by the inner leakage in the compression chamber. In particular, these leakages increase in proportion to the compression ratio. The amounts of leakage at the radial clearance of the roller and the axial clearance of the roller are the largest among the inner leakages (Shimizu et al., 1980). The changes in ηad ∙ ηmech with the changes in the compression ratio are relatively small because the mechanical loss (Wmechanical) and the actual gas work (Wactual) increase simultaneously (Ooi, 2008). Accordingly, the

Fig. 10 – Change of compressor efficiency according to compression ratios at 40 Hz.

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international journal of refrigeration 70 (2016) 42–56

port and discharge port, vane length, and the diameter of the eccentric part have to be changed accordingly. The following criteria were applied to some limited design conditions, and the results are presented in Table 3: (1) The displacement volume was maintained as 12.5 cc. (2) All the factors, except the factors accompanying changes in the cylinder radius and height, were kept constant. (3) When the cylinder diameter is changing, the position angles of the suction and discharge ports were defined as the fixed distances from the y-axis as shown in Fig. 11. (4) The length of the vane protruding into the cylinder (lv) was defined to be less than 40% of the total vane length. (5) The surface pressure acting on the eccentric part was kept constant based on the maximum gas force (Fp). (6) The height of the eccentric part was proportional to the height of the cylinder.

Fig. 11 – Position angles at the suction port and discharge port.

reduction in ηv at a high compression ratio is big as compared with ηad ∙ ηmech.

4.2.

Compression part design

Various combinations of the main dimensions, including cylinder radius, cylinder height, and roller radius, are considered for the decision of the displacement volume. The decision of the main dimensions in design phase is important because the characteristics of the friction loss and the inner leakage are different in each combination. In this study, the performance characteristics of the compressor for cylinder slenderness ratio (H/D) were investigated using a verified numerical model under limited design conditions. When the cylinder radius and height were changed, the changes in the position angles of the suction

Fig. 12(a) shows the results of the performance calculation according to the cylinder radius and height for a compression ratio of 3.4. The roller size was proportional to the cylinder size and height because the same displacement volume was considered. The EER, cooling capacity, and power input with geometrical configuration, showed maximum differences of 7.9%, 4.7%, and 3.6%, respectively. The differences in the cooling capacity are closely related to the cylinder height. This is because the area of the radial leakage between the roller and the cylinder is determined by the cylinder height and clearance. The radial leakage caused by the pressure difference between the suction chamber and compression chamber forms a large part of the compression part leakage (Cai et al., 2015). Wu and Chen (2015) reported that the compression part leakage of 70% to 80% occurred at radial and axial clearance of the roller based on calculations using a mathematical model. Further, the amount of refrigerant ingested in the suction chamber was considered an influencing factor of the cooling capacity. Fig. 12(b) shows the change in suction chamber volume with crankshaft rotation angle (θ). The displacement volume (Vs(360)) was the same. However, the volume change (Vs(θ)) with crankshaft rotation is different according to the combination of cylinder radius and height. Mass flow rate between control chambers is calculated by Eq. (10), and pressure difference is

Table 3 – Changes in the main design factors depending on the cylinder diameter and height (reference model no. 5). No.

1 2 3 4 5 6 7 8 9 10 11 12 13

Design factor Rc (mm)

Rr (mm)

Hc (mm)

Recc (mm)

lv/ltotal

lslot (mm)

θsuc (°)

θdis (°)

23.5 23.5 23.5 26.5 26.5 26.5 29.5 29.5 23.5 23.5 29.5 29.5 29.5

20.25 20.69 21.02 22.43 23.16 23.67 25.48 25.91 18.19 18.80 26.98 27.31 27.56

14 16 18 10 12 14 9 10 9 10 14 16 18

9.52 9.73 9.88 10.56 10.90 11.15 12 12.20 8.63 8.89 12.66 12.79 12.9

0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31

15.89 13.99 12.55 19.46 16.29 14.08 19.27 17.39 24.86 22.25 12.69 11.26 10.16

24.99 24.99 24.99 21.99 21.99 21.99 19.66 19.66 24.99 24.99 19.66 19.66 19.66

11.29 11.29 11.29 10.00 10.00 10.00 8.97 8.97 11.29 11.29 8.97 8.97 8.97

international journal of refrigeration 70 (2016) 42–56

(a)

(b)

(c)

(d)

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Fig. 12 – Calculation results with compression part design at 40 Hz (12.5 cc compressor and compression ratio 3.4): (a) compressor performance, (b) suction chamber volume with crank angle, (c) suction chamber pressure with crank angle and (d) intake and discharge flow rates.

one of the influence factors. The flow between control volumes is resulted in the change of suction and discharge chamber volume. This is because suction and compression chamber volumes are changed by crank shaft rotation, unlike other fixed control volume. If the suction chamber volume was relatively large in the early stage of the suction process, the low pressure in suction chamber may be formed due to the low density. The increase in the pressure difference between the suction pipe and suction chamber causes the increase in the intake flow rate, as shown in Fig. 12(c). The pressure of chamber during discharge process is decreased by discharge and inner leakage. In case of the increased intake flow in suction process, the decrease of pressure in chamber was relatively slow against other conditions. The maintenance of high pressure during discharge process plays an important role in discharge flow. The difference in power input is caused by the gas losses. The gas losses include the pressure loss in suction process, the pressure rise by intake flow increase, and over-compression loss in discharge process. The discharge process is completed when

the rollers passed the discharge port completely. Although the discharge port of same size is applied, the crank angle passing through discharge port is different because the roller movement per degree is different for each cylinder size. This angle decreases with increasing cylinder size, and the overcompression loss increases owing to the smaller angle, as shown in Fig. 12(a). In case of a cylinder radius of 29.5 mm and a height of 9 mm, the amount of remaining refrigerant in the compression chamber during the compression process was larger than the other conditions because of the increased intake flow rate and reduced leakage flow. The pressure in the compression chamber during the discharge process was maintained high by this remaining refrigerant, and the valve opening time was longer than other conditions. This advantage acted as the reduction factor of the over-compression loss even though the crank angle passing through the discharge port is small. As a result, the cooling capacity can be changed by the combination of cylinder height and radius, and it increases at a relatively low cylinder slenderness ratio (H/D). Similar trends are ob-

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international journal of refrigeration 70 (2016) 42–56

(a)

(a)

(b)

(b) Fig. 13 – The compressor performance with cylinder slenderness ratio (H/D): (a) numerical analysis and (b) experiment for the condition of compression ratio 2.3.

served in experimental results. Fig. 13 shows the experimental and numerical results according to the cylinder slenderness ratio (H/D) of a twin rotary compressor of 8.5 cc. The experiments were performed at a compression ratio of 2.3. The cylinder slenderness ratio (H/D) was changed by the aforementioned criteria, and the fixed cylinder height was used. The cooling capacity at lower cylinder slenderness ratio (H/D) was up more than 1%, even though the compression ratio is low. On the other hand, the power input showed a little difference of maximum 0.4%. The numerical results showed the similar trends, and the maximum relative error between experimental and numerical results was 6.6% for the cooling capacity of 60 Hz. The difference in intake flow rate and leakage flow according to the cylinder slenderness ratio (H/D) was higher at high compression ratios. Fig. 14(a) shows the calculated results at a pressure ratio of 7 in a previous compressor model of 12.5 cc.

Fig. 14 – Calculation results for the compression part design under new conditions of 40 Hz: compressor performance (a) for a high compression ratio of 7 and (b) with new compressor model (24 cc).

A positive difference of 8.77% in the cooling capacity was observed. The air-conditioning and heating systems used at low outdoor temperatures can lower the driving speed by causing an increase in the mass flow rate of the refrigerant. Fig. 14(b) shows the calculated results for the new compressor model of 24 cc at a compression ratio of 3.4. Various design conditions were obtained in the same manner as in the previous compressor model of 12.5 cc. Although the effect of the leakage flow was observed, the difference in the intake flow rate was small. Hence, the overall trend was similar, but the change in cooling capacity was relatively small. The experimental and calculation results for the 12.5 cc compressor model (Rc = 26.5 mm/Hc = 12 mm) at 40 Hz are shown in Fig. 15. The change in the efficiency in the compressor with changes in the compression ratio was generally similar, but the difference in the efficiency at a low compression ratio of 1.58 was caused by the aforementioned over-compression loss. In the calculation results for the 12.5 cc compressor model (Rc = 29.5 mm/Hc = 9 mm) which showed the high

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rise of pressure, and the variation is smaller compared with cooling capacity. (4) The total compressor efficiency also shows the results improved by increase in the volumetric efficiency. Each efficiency shows the maximum variations at a compression ratio of 7. The volumetric efficiency (ηv) showed an increase of 6.8%, and the adiabatic and mechanical efficiencies (ηad ∙ ηmech) relatively decreased by 2%. The compressor efficiency (ηcomp) increased by 3.7% with an increase in volumetric efficiency.

Acknowledgments

Fig. 15 – Changes in the efficiency with an improved combination of the main dimensions at 40 Hz.

compressor performance, the volumetric efficiency (ηv) showed an increase of 6.8% at a compression ratio of 7. The adiabatic and mechanical efficiency (ηad ∙ ηmech) relatively decreased by 2%. The compressor efficiency (ηcomp) increased by 3.7% with an increase in volumetric efficiency.

5.

Conclusions

To improve the energy consumption efficiency in the operation of an inverter of a domestic air-conditioning and heating system, calorimeter experiments were performed to check the performance characteristics in the low speed region for which the annual operating time is long. In addition, a numerical analysis was carried out to evaluate the effect of the main dimensions. The results are as follows: (1) As the pressure ratio increases, the compressor efficiency is largely influenced by the change in volumetric efficiency. The volumetric efficiency at high compression ratio is less than that at low compression ratios by about 24% because of the leakage in the compression part. On the other hand, the adiabatic and mechanical efficiencies, which are related to the power input, decreased by about 14%. (2) Even while maintaining the displacement volume constant, the compression part can be designed in various shapes. The volumetric efficiency varies with the design of compression part. The mass flow rate discharging from compression part increases at a relatively low cylinder slenderness ratio (H/D) due to the low leakage and much intake flow. (3) The effect of cylinder slenderness ratio (H/D) became sensitive at relatively high compression ratio conditions. At a compression ratio of 7, the EER, cooling capacity, and power input with geometrical configuration show positive maximum variations of 6.2%, 8.77%, and 2.44%, respectively. The increase of power input occurs from the

This work was supported by “Human Resources Program in Energy Technology” of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), granted financial resource from the Ministry of Trade, Industry and Energy, Republic of Korea (No. 20144030200570), and was also supported by the Human Resources Development program (No. 20144010200780) of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korean government Ministry of Trade, Industry and Energy. REFERENCES

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