Purdue University
Purdue e-Pubs
International Compressor Engineering Conference
School of Mechanical Engineering
1996
A Fundamental Optimum Design for High
Mechanical and Volumetric Efficiency of Compact
Scroll Compressors
N. Ishii
Osaka Electro-Communication University
M. Sakai
Matsushita Electric Industrial Co.
K. Sano
Matsushita Electric Industrial Co.
S. Yamamoto
Matsushita Electric Industrial Co.
T. Otokura
Osaka Electro-Communication University
Follow this and additional works at: http://docs.lib.purdue.edu/icec
Ishii, N.; Sakai, M.; Sano, K.; Yamamoto, S.; and Otokura, T., "A Fundamental Optimum Design for High Mechanical and Volumetric
Efficiency of Compact Scroll Compressors" (1996). International Compressor Engineering Conference. Paper 1176.
http://docs.lib.purdue.edu/icec/1176
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A FUNDAl\1ENTAL OPfiMU M DESIGN
FOR HIGH MECHANICAL AND VOLUMETRIC EFFICIENCY
OF COMPACT SCROLL COMPRESSORS
by
Noriaki Ishii I, Manabu Sakai2, K.iyoshi Sano3, Shuichi Yamamoto3
.
and Takayuki Otokura4
1 Professor,
Faculty of Engineering, Osaka Electro-Communication University,
Neyagawa, Osaka 572, Japan
Tel: +81-720-20-4561; Fax: +81-720-20-4577; E-mail: ishii@is c.osakac .ac.jp
2 Engineer, Compressor Division,
3 Senior Staff Engineer, Air Conditioning Research, Matsushita Electric Industrial Co.,
Ltd.
(Panasonic), Noji-cho, Kusatsu-shi, Shiga 525, Japan
Tel: +81-775-67-9801, Fax: +81-775-61-3201
4 Graduate Student, Faculty of Engineering, Osaka Electro-Communication
University.
ABSTRACT
This paper presents a fundamental optimum design which yields a high compressor
performance in mechanical and volumetric efficiency. The frictional power losses were calculated by
an analytical method revealing the dynamic behavior of scroll compressors, and the refrigerant leakages
were calculated by an incompressive and viscous theory assuming an entire turbulent leakage flow.
Computer calculations were made for a number of combinations of the involute base circle radius and
the scroll depth, where the scroll thickness and the cylinder diameter were fixed at a constant value.
The calculated results for the mechanical and volumetric efficiency indicated that there is a definite
optimum combination of major parameters. Additionally, the effects of the suction volumes and the
clearance values upon the resultant efficiency were carefully examined to clarify a better fundamental
optimum design in compact scroll compressors.
1. INTRODUCTION
The suction volume of scroll compressors is determined by the major parameters, such as the
involute base circle diameter, the scroll depth, the scroll thickness and the number of scroll turns, and,
subsequently, there are many combinations of major parameters that result in a scroll compressor with
the same suction volume. Therefore, one of basically significant designs in scroll compressor is to
determine a combination of these major parameters for high compressor performance.
This paper presents an optimum combination of the major parameters, which yields a high
performance in mechanical and volumetric efficiency of scroll compressors. Depending upon the
selected combination of major parameters, the frictional power loss at each pair of compressor elements
changes, resulting in different mechanical efficiencies [1-3], and simultaneously, the refrigerant
leakage from each clearance also changes, resulting in different volumetric efficiencies. Thus, careful
selection of the optimum combination of major parameters is necessary to ensure a high mechanical and
volumetric efficiency of the scroll compressor.
In the present study, the mechanical and volumetric efficiencies were computer simulated for a
number of combinations of the involute base circle radius and the scroll depth, where the scroll
thickness and the cylinder diameter were fixed at a constant value. For mechanical efficiency, the
frictional power losses were calculated by an anlytical method for the dynamic behavior of scroll
compressors [4-7]. For volumetric efficiency, the refrigerant leakages through the axial and radial
clearances were calculated by an incompressive and viscous theory assuming an entire turbulent
639
small suction
leakage flow [8]. Additionally computer simulations were made for a number of
design for
optimum
ntal
fundame
a
of
volumes and clearance values, in order to examine a possibility
sors.
high mechanical and volumetric efficiency in compact scroll compres
2. CALCU LATION FOR VOLUM ETRIC EFFICIE NCY
-shaped
A scroll compressor configuration is shown in Figure 1, in which one crescent
by
affected
greatly
is
P,
r,
chambe
compression chambe r is meshed. The pressure in this compression
pressure
lower
the
to
outflow
the leakage inflow from the higher pressure chamber and the leakage
axial clearance
chamber. The leakage inflow is induced by the radial flow velocity Uai through the
by Ti. The
denoted
e
denoted by Ai, and by the tangential flow velocity uri through the radial clearanc
by Ao,
denoted
e
leakage outflow is induced by the radial flow velocity Uao through the axial clearanc
inflow
The
•
T
by
0
and by the tangential flow velocity uro through the radial clearance denoteq
outflow
the
and
r,
velocities are caused by the pressure difference from the higher compression chambe
velocities are by the pressure difference from the lower compression chamber.
by the
For given pressure differences, these inflow and outflow velocities can be calculated
for
valid
be
to
incompressive and viscous flow theory which was ensured in the former study [3]
the
through
refrigerant leakage flows in scroll compressors. Therewith the outflow and inflow rates
ed by
calculat
be
can
Qrj,
and
Qe,
clearanc
radial
the
through
0
those
axial clearance, Qao and Qru, and
the followin g expressions:
Oao :::: P <>aSoUao, Qm :::: poaSillai•}
=
(1)
<1-o p OrBUr0 , <1-i :::: pbrBuri,
B is the
height,
where pis the specific mass, 6a is the axial clearance height, 6r is the radial clearance
1,
Figure
in
Ai
scroll height, and S 0 and Si are the length of the axial clearances denoted by Ao and
the
in
mass
respectively. Using the leakage mass flow rates calculated by (1), the refrigerant
on:
crescent-shaped compression chamber, G, can be calculated by the following integral expressi
G:::: Gs +
!.
1
{
<2ai + <1-i- (Qa0 +Q.o)} dt,
where the time after the instant when
the suction chamber was just closed at
the periphery of the scrolls is represented by t, and the refrigerant mass
in the suction chambe r at t :::: 0 is by
G 8 • Since the inflow mass from the
higher compression chambe r is
normally larger than the outflow mass
to the lower pressure chambe r, the
refrigerant mass in the compression
chamber, G, increase s as the time
elapses, thus inducin g a pressure
non-leakage
in
than
higher
compression. Assumi ng the adiabatic
compression with the specific heat
ratio K , pressure P in the compres sion
chamber with volume V can be
calculated by
¢>, ¢>.
(2)
¢> ;-2 rr
' '
.G.)lC
P -- ps (~(3)
Gs V '
clearances.
where Ps and Vs are the initial values Figure 1. Leakage flow velocities at axial and radial
640
of pressure and volume at t=O, respectively.
If the pressure changes are initially given by the adiabatic change for non-leakage compression,
the refrigerant mass and pressure in the compression chamber can be calculated for one compression
process from suction to discharge, by expressions (2) and (3). Using the calculated pressures,
furthermore, the refrigerant mass and pressure can be newly calculated, and such repeated
calculations can be made to obtain the correct pressure changes and refrigerant gas leakage flow rates.
The resultant refrigerant mass of leakage from the outer two compression chambers to the
suction chamber, llG, can be calculated by
AG = 2 { 0< ( Oao + Q.0 ) dt,
lo
(4)
0
where tr is one period for orbiting motion. Finally the volumetric efficiency l'Jm can be calculated by
the following expression:
_ Gs -AG
.
Gs
l']v =
(5)
3. CALCULATED RESULTS
YQlumetrk.EfficieiJC~
In numerical calculation, the specific heat ratio was assumed to be 1.32, the suction pressure to
be 0.62 MPa, the suction temperature to be 18 °C, the specific mass of refrigerant in the suction
chamber to be 24.71 kg/m3 and the discharge pressure to be 2.17 MPa. The cylinder diameter and the
scroll thickness were fixed at the values of75.7 mm and 4 nun, respectively, and the combinations of
the involute base circle radius rb and the scroll height B were adjusted at various values.
Calculated results for refrigerant leakage at a
suction volume of 10.3 cm3 and an involute base circle
radius of 2.0 mm are shown in Figure 2, where both the
axial and radial clearances were fixed at 10 ~tm. The
abscissa is the orbiting angle e, and its zero value
corresponds to the angle when the suction chamber was
closed. One compression cycle is about 79Qo. The
leakage flow velocities are less than about 74 m/s at the
axial clearance, and less than about 117 m/s at the radial
clearances, as shown in diagram (b). The leakage flow
velocities at the axial clearances are less than the radial
clearance, but the leakage mass flow rates from the axial
clearance is larger than the radial clearance, as shown in
diagram (c).
By integrating the calculated mass flow rates for
one cycle of orbiting motion, as given by (4), the
resultant refrigerant mass of leakage from the outer two
compression chambers to the suction chamber, L1G, can
be calculated, thus resulting in the volumetric efficiency
given by (5). Similar calculations were made for various
72D
e (deg]
values of the involute base circle radius from 1.3 nun to
3.6 nun, and the calculated results were obtained, as Figure 2. Refrigerant leakage in scroll
shown in Figure 3, where the suction volume Vs was
compressor with involute base circle
fixed at 4 different values from 10.3 cm3 to 2.5 cm3.
radius of 2.0 mm and axial and radial
Figure 3a shows the scroll height over the suction
clearances of 10 ~tm: (a) pressure in
volume, B/Vs, which increases with decreasing the
compression chamber; (b) leakage ininvolute base circle radius fb. The refrigerant mass of
flow and outflow velocities; (c) leakage
mass inflow and outflow rates.
641
leakage for Vs=10.3 cm3 is shown in Figure 3c, where
the leakage mass AGa from the axial clearance is larger
than AG r from the radial clearance, corresponding well to
the calculated data of the leakage mass flow rates shown
in Figure 2c. The resultant refrigerant mass of leakage,
AG, shows a minimum value around at rb=l.7 mm, thus
resulting in the volumetric efficiency which shows its
maximum value of 76.2 % for Vs=10.3 cm3. As the
suction volume becomes smaller , the volumetric
efficiency decreases wholly. When the suction volume
takes on a small value of 2.5 cm3, the volumetric
efficiency is less than about 20 %.
o.a.---- -------- --.
"""
"'~0.6
>"' 0.4
I
~0.2
o:l
..,_-- VS=1 0.3cm3
7.5cm3
5.0cm 3
2.5cm3
0 L...:::=§§§~~_j
(a)
90r-----------------~
80
70
,......., 60r
£so
'---'
~17"2
~cm3
~cm3
~Ocrn3
> 40
I
Mechanical Efficiency
~
I
An analytical method for dynamic behavior of
I
30
scroll compressors has been established with regard to the
20
fundamental dynamics of machinery, in the previous
studies [4-7], where it was assumed that the frictional
10
I
forces at any pair that is not well lubricated by a thick oil
0'-----'---.c....... ..J--'-----'---'---- --' (b)
film are subject to Coulomb's law of friction. As for the
frictional coefficient at each pair, it was quite difficult to
evaluate each precise value for practically used scroll
Thereupon, it was a quite rough
compressors.
assumption but the previous study made use of the
frictional coefficient of 0.013 which were determined
I
'\l 4
I
numerically in a study [9] for a compact rolling-piston
I L1Gr
r
c!5
rotatory
crankshaft
the
Therewith,
rotary compressor.
'\l 2
behavior, the constraint force and the frictional power
loss at each pair could be calculated to reveal the
(Vs==10.3cm3) (c)
_L
~ 01
mechanical efficiency.
4
3
2
The mechanical efficiency calculated for 4
rb [mm]
different values of suction volume are shown in Figure 4.
for axial
Some of the mechanical efficiencies were cited from the Figure 3 .. Volumetric efficiency
and radial clearances of 10 !Am: (a)
previous study [3]. In computer calculations, the motor
scroll height; (b) volumetric efficiency;
power was adjusted to keep the mean crankshaft speed at
refrigerant mass of leakage from
(c)
.56.4 Hz, and an optimum intermediate pressure was led
two compression chambers.
outer
to
to the back surface of the orbiting scroll end plate
[4bearing
95.------------~-----.
minimize the frictional power loss at the thrust
7].
With decreasing the involute base circle radius,
90
the frictional power losses at the crankshaft and crank pin
height.
scroll
in
increase
the
of
increases because
Furthermore, with increasing involute base circle radius,
a 85
the frictional power loss at the thrust bearing increases
1;:.::[2].
area
chamber
compression
in
because of the increase
That is why the mechanical efficiency shows its highest
80
value at a moderate involute base circle radius.
~-'
f::
\v-----
Jr~
\LS----_l_
Mechanical and Volumetric Efficiency
751r-~--,2~_.--,3~~--~4
The product of the volumetric efficiency shown in
lb[mm]
Figure 3b and the mechanical efficiency shown in Figure
4, termed a mechanical and volumetric efficiency TJ, are Figure 4. Mechanical efficiency for fricshown in Figure Sa. The efficiency curves for the suction
tional coefficient of 0.013.
642
volumes of 10.3 cm3 , 7.5 cm3 and 5.0 cm3 increase rapidly with increasing the involute base circle
radius rb, showing each peak value at the involute base circle radius of 2.0 mm to 2.1 mm. These
curves gradually decrease with increasing further the involute base circle radius. The decrease
magnitude from each peak value is not so large .. As shown in Figure Sb, however, the crankshaft
speed fluctuation ratio a increases rapidly, with increasing the involute base circle radius, and takes
on a value more than 1% for Ib> about 2.5 rom. Conclusively, a fundamental optimum value for the
involute base circle radius has to be determined around at 2.0 mm to 2.1 mm. The efficiency curve for
the suction volume of 2.5 cm3 does not exhibit a peak value, since the volumetric efficiency took on too
small values, as shown in Figure 3b.
80r----------...,
4. POSSIBILITY OF FUNDAMENTAL OPTIMUM
DESIGN FOR COMPACT SCROLL COMPRESSORS
.........,
70
;:::] 66.6
60
59.1
Vs,10.3cw 3
~Scw 3
£50
4ll
"--"
In order to examine the possibility of fundamental
~.Ocw 3
~40
optimum design for compact scroll compressors, similar
30
calculations were made for various reduced values of the
axial clearance. The leakage mass from the axial
20
15.7%
clearance was far larger than from the radial clearance, as
10
shown in Figure 3c. That is why the axial clearance only
~.____.._ _.__ _.___,______.__..J(a)
was reduced and the radial clearance was kept at the same
value of 10 !lm- The calculated results are shown in
.........,3
Figure 6. As the axial clearance decreases, the efficiency
~2
curves for a larger suction volume of 10.3 cm3 increase
(j 1
wholly, exhibiting each peak value at the involute base
circle radius of about 2.2 to 2.4 mm, as shown in
1~~~~~~3~--'--~4.~)
diagram (a). The efficiency curves for a smaller suction
Ib(mm]
volume of 2.5 cm3 also exhibit each peak value at the
involute base circle radius of about 1.9 to 2.1 mm, which Figure 5. Mechanical and volumetric efficiency for axial and radial clearances of
becomes higher with decreasing the axial clearance, as
10 !liD: (a) mechanical and volumetric
shown in diagram (b).
efficiency; (b) crankshaft speed fluctuation ratio.
5. CONCLUSIONS
The present study performed
computer simulations for the mechanical and volumetric efficiency, thus
resulting in the following conclusions. The volumetric efficiency is
more significantly affected by the refrigerant leakage from the axial clearance than from the radial clearance. A
fundamental optimum design for
higher mechanical and volumetric efficiency would be possible for compact scroll compressors, by reducing
the axial clearance and by selecting
the optimum combination of the major
parameters. An extremely compact
and
high
efficiency
scroll
compressor, for example, with a
suction volume of2.5 cm3, would be
::r---~-~---0-2-...,
70
........
~60
90r-----------.
80
~
1!-
o,dO!Lm
~
70
~60
~
50
50
40
40
301_......__'*2____..____*3___.---.J.4
(a)
l"b[mm]
~
~
~
3 ~--~*2~~3~~~4
(b)
l'b[mm]
Figure 6. Improvement of mechanical and volumetric efficiency:(a) for suction volume of 10.3 cru3; (b) for suction
volume of 2.5 cm3.
643
highly possible, by utilizing the present optimum design simulations.
ACKNOVVLEDGMlliNTS
The authors would like to express their gratitude to Mr. Jirou Yuuda, Head of the Air
Conditioning Research Laboratory, and Mr. Tomio Kawabe, Head of the Compressor Division, for
their financial support in carrying out this work and their permission to publish these results. The
authors also would like to express their sincere thanks to Mr. Hiraku Matsui and Mr. Noriyuki Morita
for their energetic works for leakage tests and computer simulations.
REFERENCES
( 1) Ishii, N. et al., Optimum Combination of Dimensions for High Mechanical Efficiency of a RollingPiston Rotary Compressor, Proc. International Compressor Engineering Conference at Purdue,
July, 1990, pp.418-424.
(2) Ishii, N. et al., Optimum Combination of Parameters for High Mechanical Efficiency of a Scroll
Compressor, Proc. International Compressor Engineering Conference at Purdue, July, 1992,
pp.l18al-118a8.
(3) Ishii, N. et al., A Study on High Mechanical Efficiency of a Scroll Compressor with Fixed
Cylinder Diameter, Proc. International Compressor Engineering Conference at Purdue, July,
1994, pp.677-682.
(4) Ishii, N. et al., Mechanical Efficiency of Various Large Capacity Scroll Compressors, Proc.17th
International Congress of Refrigeration, Wien, Aug., 1987, pp.468-474; Transactions of the
Japan
Society of Mechanical Engineers (in Japanese), Series C, Vol.53, No.495, 1987, pp.2295-2302.
(5) Ishii, N. et al., Dynamic Behavior of a Scroll Compressor (Dynamic Analysis), JS.ME
International Journal, Series 3, Vol.31, No.1, March, 1988, pp.58-67; Proc. International
Compressor Engineering Conference at Purdue, Vol.3, Aug., 1986, pp.901-916.
(6) Ishii, N. et al., On the Superior Dynamic Behavior of a Variable Rotating Speed Scroll
Compressor, Proc. International Compressor Engineering Conference at Purdue, Vol.l, July,
1988, pp.75-82; Transactions of the Japan Society of Mechanical Engineers (in Japanese), Series
C, Vol. 55, No.517, 1989, pp.2436-2445.
(7) Ishii, N. et al., Mechanical Efficiency of a Variable Speed Scroll Compressor, Proc. International
Compressor Engineering Conference at Purdue, Vol.l, July, 1990, pp.192-199.
(8) Ishii, N. et al., Refrigerant Leakage Flow Evaluation for Scroll Compressors, Proc. International
Compressor Engineering Conference at Purdue, July, 1996.
(9) Ishii, N. et al., The High Mechanical Efficiency of Rolling-Piston Rotary Compressors, Proc. 2nd
World Congress on Heating, Ventilating, Refrigerating and Air Conditioning (CLIMA2000) at
Sarajevo, Yugoslavia, 1989, p.91.
644