19

New technologies

Power consumption analysis of rotary vane compressor

Ryusuke Yamada* Keita Sato* Hiroki Takesashi*

Abstract In recent years, improvement in energy efficiency of each component is desired for the fuel efficiency of any car. In the previous paper, we introduced the more efficient fixed displacement rotary vane compressors (new CR series) for car air conditioners. This paper describes the technology involved in analysis of compressor power, used in development of new series of Compressors .

Key Words : Efficiency, Environment, Simulation／Rotary Vane

1. Introduction The concern about environmental issues such as CO2 emission has been increasing. As a consequence, the improvement of fuel efficiency during a car air conditioning operation is required. To fulfill this requirement, high energy efficiency is necessary from our product (the Rotary Vane) type compressor. In the previous paper, we introduced a new CR compressor that has improved the efficiency. This paper describes the technology involved in analyzing power consump-tion, used in the new CR compressor.

2. Structure of CR compressor The CR compressor has a fixed-displacement concen-tric rotary vane structure. Fig. 1 shows the exploded view of CR compressor. Fig. 2 shows the sectional view of a compressor body. Fig. 3 shows the flow of refriger-ant gas and oil. The refrigerant is fed from an intake port installed at the front head to the compressor body, through an intake chamber sandwiched by the front head and front side block. A rotor with five vanes is provided in the compressor body enclosed by an oval cylinder and side blocks. Compression is performed for 10 times per revolution. The compressed refrigerant is discharged from a case port after passing through a reed valve and a centrifugal type oil separator. The refrigerant and oil are separated in the oil separator.

Fig. 1 Structure of vane rotary compressor

Fig. 2 Compression chamber

Fig. 3 Refrigerant and oil* Compressor Business Unit　Compressor Development Group

20

CALSONIC KANSEI TECHNICAL REVIEW vol.12 2016

3. Factorial analysis of power consumption Formula (1) expresses overall adiabatic efficiency that shows the ratio between theoretical power and actual power. In this study, power transmission loss by belt driving is excluded from the calculation. The factor of power consumption loss is classified into ① Volume efficiency, ② Adiabatic compression loss, and ③ Sliding friction loss. The following sections explain the detailed calculation method of each factor.

= ℎ

∆ + + ℎ ・・・(1)

ℎ

∆

∆

: Overall efficiency: Theoretical compression power in ideal flow rate: Volume efficiency: Sliding friction loss: Adiabatic compression loss

3.1. Volume efficiency

It is a ratio between ideal and actual flow rates. In this paper, the volumetric efficiency is calculated on the basis of the formula (2), defining the efficiency as a ratio between ideal and actual discharge masses in one compression chamber for the descriptive purposes.

=− ∆ − ∆

・・・(2)

∆

∆

: Ideal refrigerant mass per compression chamber: Refrigerant density lowered by intake heat and pressure loss

: Refrigerant density lowered by leak from clearance

The causes of volume efficiency loss are ① intake air heating and pressure loss that are expressed by ideal gas law and ② leak that lowers refrigerant charging ratio in the compression chamber due to its structure.

3.1.1. Heating from conduit wall and pressure loss by conduit resistance

Intake heating and pressure loss is generated at the area between an intake port and a compression cham-ber inlet. The heat is generated when heat quantity of the parts forming the conduit is transmitted to refrigerant. The heat increases the volume flow rate and pressure loss. The formula (3) can be derived from converting these losses into mass.

∆ = 1 1 − 1 2

2 1・・・(3)

V

1

1

2

1

2

: Volume in compression chamber: Refrigerant density in intake port: Refrigerant temp. in intake port: Refrigerant temp. in front of compression chamber: Refrigerant pressure at intake port: Refrigerant pressure in front of compression chamber

3.1.2. Leak lowering charging ratio

Refrigerant leaks from the clearance between the sliding vanes and cylinder. Refrigerant influx and its efflux of the compression chamber are separately con-sidered in the calculation. The influx is a phenomenon where refrigerant flows into the compression chamber during intake and reduces the charging ratio compared with the ideal intake volume. The efflux is a phenom-enon where refrigerant leaks out of the compression chamber during the period from refrigerant intake end to discharge end and lowers the charging ratio. The leak flow rate is calculated by the formula (4) or (5). The formula (4) is used for the leak from the clearance markedly affected by fluid viscosity. The formula (5) is used for the leak slightly affected.

G =( 2 − 1)ℎ3

12 ・・・(4)

G = A 2 − 1 1 12

1

2

− 2

1

( +1)

・・・(5) � �( ) ( )G

h

ν

A

1

2

1

: Leak flow rate: Clearance height : Width of conduit: Kinematic viscosity: Length of conduit: Cross section of conduit: Pressure at upstream: Pressure at downstream: Ratio of specific heat: Refrigerant density at upper stream

3.2. Adiabatic compression loss

It is an energy caused by a load exceeding an ideal adiabatic compression. The load arises from refrigerant leak between adjacent compression chambers and from the conduit loss at the discharge portion after refriger-ant intake. Work of the compression chamber can be calculated by obtaining the area of PV diagram on the basis of

21

Power consumption analysis of rotary vane compressor

compression chamber pressure and volume. The com-pression chamber pressure is derived from the formula (6) after calculation of change in the refrigerant density in the compression chamber caused by re-compression, leak from the clearance, and the conduit resistance.

= ・・・(6)

: Compression chamber pressure: Compression chamber density

Fig. 4 shows the calculation results of the compression chamber pressure. The hatched area shows the ideal PV relation. The area difference between the ideal work and the actual one is work loss.

Pumping loss

leak

repressing

Fig. 4 Pressure-volume diagram

3.3. Mechanical loss

Mechanical loss is an energy caused by ① sliding friction and ② viscous fluid friction.

3.3.1. Sliding friction force

It is generated by slide between a vane and a rotor, and a cylinder and a rotor. Fig. 5 shows these friction forces. The forces are obtained by the force balance formulas of (7), (8), and (9) based on the vectors that are determined by shape factors and forces such as vane back pressure and centrifugal force. The PV diagram in the section 3.2. is used to obtain the compression chamber pressure and back pressure. Friction coef-ficient is estimated from the Stribeck curve because of intervenient oil.

− 3 − 4 + 4 + 5 − 6 5

+ ( − ) 7 − 8 + 8 = 0 ・・・(7)

1 − 2 + 2 + 3 − 56 5 − 56 6

− ( − ) 7 = 0 ・・・(8) 1 1 + 2 2 − 2 2 + 3 3 + 4 4 − 4 4

− 5( 5 + 56 5′) 5 + 6( 6 + 56 6′) 6

− 7′ 7 + 8 8 − 8 8 = 0 ・・・(9)

( )

Fig. 5 Force acting on the vane

1

2

3

4

5, 6

7

8

5

6

56

: Symbol showing force application direction: Symbol showing force application direction

5

6

5, 6

: Force applied to vane back surface by back pressure ( ): Force applied to vane tips by compression chamber pressure ( )

: Normal force at contact point between rotor and vane: Normal force at contact point between cylinder and vane : Force applied to vane side by pressure between rotor and vane

: Symbol showing friction force application direction

: Centrifugal force: Force applied to vane side by compression chamber ( )

: Coefficient of friction at contact point between rotor andvane

: Coefficient of friction at contact point between cylinder and vane

3.3.2. Viscous fluid friction force

It occurs between a vane and a side block, a rotor and a side block, a rotor and a cylinder, and a shaft and bearings. These friction forces are calculated by formula (10) called Newton’s law of viscosity.

22

CALSONIC KANSEI TECHNICAL REVIEW vol.12 2016

= ・・・(10)

: Change in viscosity in vertical direction

: Shearing force: Viscosity of lubricant where refrigerant is dissolved

4. Calculation results Using the calculation techniques from the section 3.1 to 3.3, we obtained overall adiabatic compression efficiency (formula (1)), which is an index of consump-tion energy. Fig. 6 shows the calculation results and measurement results using a calorimeter.

Fig. 6 Overall adiabatic efficiency

The calculation results correlate with the measurement ones. Fig. 7 shows the breakdown of the cause analysis based on the results.

Fig. 7 Breakdown of Overall adiabatic efficiency

As Fig. 7 shows, we identified contribution ratios of each loss factor. The ratio of the adiabatic compression loss is the highest at high revolution speed. This is due to the effect of the discharge valve and discharge con-duit. In light of the calculation results in the above Fig. 7 and shape factor in each part, we reached 9% energy reduction in the new CR series.

5. Conclusion We clarified the factors of the energy loss and contri-bution ratios by modeling the loss of the vane rotary type compressor at a steady operation. Thus we can narrow down the methods for efficiency improvement and conduct development work efficiently. We will make efforts to continue the development work so that this technique can also be applied to a ransient operation state. With this technique, we will also con-tribute to the improvement of compressor efficiency to respond to more strict environmental regulations and the needs of actual fuel efficiency improvement.

Reference(1) Mitsuhiro Fukuda, Tadashi Yanazawa, Takashi

Shimizu, and Tatsuro Shikada：Compression charac-teristic of mixture of refrigerant and oil in refriger-ant compressor Transactions of the JSME, Vol. 61, No. 582, p．191-197 (1995)

(2) Refrigerant compressor compiled by Compressor Engineering Committee, Japan Society of Refrigerat-ing and Air Conditioning Engineers, Tokyo, Japan Society

(3) of Refrigerating and Air Conditioning Engi-neers，2013，264p

Ryusuke Yamada Keita Sato Hiroki Takesashi