Diffuser of centrifugal compressor

A diffuser of a centrifugal compressor for guiding a fluid flowing from an impeller to a scroll. The diffuser is formed by a pair of oppositely disposed lateral walls. The diffuser is provided at a fluid outlet portion thereof with an outlet throttling portion. This outlet throttling portion is formed by gradually narrowing the passage width downstream from a starting point which is located in a position at which the fluid dynamic pressure is almost perfectly changed to a static pressure. The provision of the outlet throttling portion decreases the risk of a pressure loss, restrains the possibility of flow separation and prevents the fluid from reversely flowing from the scroll. This results in improvements in surge line and partial load efficiency.

BACKGROUND OF THE INVENTION 
The present invention relates to improvements in a diffuser of a 
centrifugal compressor used in a centrifugal refrigerator, an air 
compressor, apparatus for sending natural gas under pressure, or the like. 
A centrifugal compressor generally includes a diffuser for reducing the 
speed of a fluid disposed downstream of the outlet side of an impeller to 
convert the dynamic energy into a static pressure, and a scroll disposed 
as connected to the diffuser. The diffuser is generally formed by a pair 
of parallel lateral walls. 
To improve the efficiency of the diffuser in a centrifugal compressor, 
Japanese Unexamined Patent Publication 156299/1980 proposes a diffuser in 
which the width of the inlet portion is narrowed in order to prevent the 
fluid from reversely flowing at the diffuser inlet portion, thereby to 
reduce the loss due to the fluid eddy. 
Even though the width of the inlet portion is narrowed, the flow separation 
may be restrained only to a limited extent and a portion of the flow may 
be arranged. In particular, when the width of the inlet portion is 
narrowed too much, the conformity of the impeller with the diffuser is 
lost to increase the loss. This may not only impose restrictions on 
improvements in partial load efficiency, but also induce decrease in both 
rated efficiency and maximum flow rate. Further, even though the width of 
the inlet portion is narrowed, the surge line cannot be heightened. 
SUMMARY OF THE INVENTION 
In view of the foregoing, the present invention proposes providing a 
diffuser of a centrifugal compressor capable of providing a good flow of a 
fluid, improving the rated efficiency and the partial load efficiency over 
a wide range, and heightening the surge line. 
The object above-mentioned may be achieved by the providing a centrifugal 
compressor diffuser formed by a pair of lateral walls oppositely disposed 
downstream of a fluid outlet of an impeller and being adapted to guide a 
fluid flowing from the impeller to a scroll. The diffuser includes 
comprising; at a fluid outlet portion thereof, an outlet throttling 
portion of which passage width is gradually narrowed downstream from a 
starting point located in the position where the dynamic pressure of the 
fluid is almost perfectly changed to a static pressure. 
Preferably, the minimum passage width of the outlet throttling portion is 
set to 3/8 or more and 3/4 or less of the passage width upstream of the 
outlet throttling portion. 
Preferably, the starting point from which the outlet throttling portion is 
throttled, is positioned between 70% and 90% of the passage of the 
diffuser. 
Preferably, the diffuser is provided at the inlet portion thereof with an 
inlet throttling portion of which passage width is gradually narrowed 
downstream, and the minimum passage width of the inlet throttling portion 
is set to 75% or more and 95% or less of an outlet width of the impeller 
according to a rated flow amount. 
Preferably, the scroll is disposed as biased toward one of the pair of 
lateral walls, and the outlet throttling portion is formed by inclining 
the one lateral wall toward the passage. 
Preferably, the diffuser includes a movable lateral wall for adjusting the 
passage width which is disposed on at least that portion of either one of 
the lateral walls which forms the outlet throttling portion, and the 
diffuser also includes movable lateral wall operating means for moving the 
movable lateral wall according to a load. In this case, the movable 
lateral wall operating means is preferably adapted to so move the movable 
lateral wall as to narrow the passage width when the vane opening degree 
becomes small. 
Preferably, the movable lateral wall operating means includes a drive shaft 
for rotatingly driving a vane disposed for controlling the flow rate of a 
fluid sucked by the impeller, an eccentric cam rotatable integrally with 
the drive shaft, and a rod for moving the movable lateral wall in such a 
direction as to narrow the passage width when the rod is pressed by the 
eccentric cam. 
According to the diffuser of a centrifugal compressor having the 
above-described arrangement, the outlet throttling portion is formed at 
the outlet portion where the change to a static pressure is about to be 
completed. This minimizes the pressure loss. This restrains the flow 
separation and prevents the fluid from reversely flowing from the scroll. 
To heighten the surge line and improve the partial load efficiency, it is 
found advantageous to set the minimum passage width of the outlet 
throttling portion to 3/8 or more and 3/4 or less of the passage width 
upstream of the outlet throttling portion. 
To heighten the surge line and improve the partial load efficiency, it is 
further advantageous that the starting point from which the outlet 
throttling portion is throttled, is positioned between 70% and 90% of the 
passage of the diffuser. 
Further, when the diffuser is provided at the inlet portion thereof with an 
inlet throttling portion of which minimum passage width is 75% or more and 
95% or less of the outlet width of the impeller according to a rated flow 
rate, it is possible to reduce the distortion and inclination of the flow 
at the diffuser inlet portion. Accordingly, such an arrangement is 
preferred not only to improve the general efficiency including the rated 
efficiency and the partial load efficincy, but also to increase the surge 
margin. Further, there is no likelihood that the maximum flow rate is 
decreased. 
When the scroll is disposed as biased toward one lateral wall of the 
diffuser and the outlet throttling portion is formed by inclining the one 
lateral wall toward the passage, such an arrangement effectively prevents 
the fluid from reversely flowing from the scrol. Thus, the efficiency may 
be further improved. 
When the diffuser includes a movable lateral wall for adjusting the passage 
width which is disposed on at least that portion of either one of the 
lateral walls which forms the outlet throttling portion, and the diffuser 
also includes movable lateral wall operating means for moving the movable 
lateral wall according to a load, the movable lateral wall operating means 
is adapted to move the movable lateral wall according to the load, thereby 
to adjust the passage width to the optimum value. Thus, the efficiency may 
be improved regardless of the magnitude of the load, leading to economy of 
energy. In this case, when the movable lateral wall operating means is 
adapted to so move the movable lateral wall as to narrow the passage width 
when the vane opening degree becomes small, the passage width may be 
quickly adjusted in response to variations of the load. 
When the movable lateral wall operating means includes the drive shaft for 
rotatingly driving the vane, the eccentric cam rotatable integrally with 
the drive shaft, and the rod for moving the movable lateral wall, the 
following result may be produced. That is, when the vane is rotatingly 
driven by the drive shaft to reduce the vane opening degree to decrease 
the flow rate of a fluid suctioned by the impeller, the eccentric cam 
rotated with the rotation of the drive shaft causes the rod to push and 
move the movable lateral wall, thereby to narrow the passage width. When 
the vane is rotatingly driven by the drive shaft to increase the flow rate 
of the fluid suctioned by the impeller, the eccentric cam rotated with the 
rotation of the drive shaft permits the rod to retreat. Accordingly, the 
pressure in the diffuser causes the movable lateral wall to be moved in 
such direction as to broaden the passage width. To improve the diffuser 
efficiency, the adjustment of the passage width according to a load is 
made in a mechanical manner. This provides a reliable operation and makes 
the structure simple to reduce the production cost. Further, the 
throttling degree of the passage width according to the vane opening 
degree may be readily adjusted by changing the shape of the eccentric cam.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
The following description will discuss in detail the present invention with 
reference to the attached drawings showing embodiments thereof. 
In FIG. 1, a diffuser generally designated by the reference character A is 
formed by a pair of lateral walls 2 and 3 extending in the discharge 
direction of an impeller 1. A scroll 4 is connected to the diffuser A and 
is formed as biased toward one lateral wall 2. 
The diffuser A is composed of an inlet portion 5, an intermediate portion 6 
and an outlet portion 7 which have different shapes and which are 
successively disposed in the direction from upstream to downstream. 
In FIG. 2, an inlet throttling portion 5a is formed at the inlet portion 5 
by inwardly inclining both lateral walls 2 and 3 to narrow downstream the 
width of the passage formed therebetween. In the intermediate portion 6, 
the lateral walls 2 and 3 are parallel with each other, and the passage 
width t.sub.2 thereat is constant. The minimum passage width of the inlet 
throttling portion 5a (which is equal to the passage width t.sub.2 of the 
intermediate portion 6), is set to 75% or more and 95% or less of the 
outlet width t.sub.1 of the impeller 1. The throttling ratio of the inlet 
throttling portion 5a is the same range of 70% to 95%. 
The diameter D.sub.2 of a tapering end 5c of the inlet throttling portion 
5a is preferably set to about 1.05 to about 1.2 times the outlet diameter 
D.sub.1 of the impeller 1. The inclination angles of the lateral walls 2, 
3 at the inlet throttling portion 5a are preferably about 15.degree. to 
about 30.degree.. 
The diffuser A is provided at the outlet portion 7 thereof with an outlet 
throttling portion 7a which is formed by gradually narrowing the passage 
width downstream from a starting point 10. The passage width of the outlet 
throttling portion 7a is narrowed by inclining, toward the passage, the 
lateral wall 2 toward which the scroll 4 is biased. 
The starting point 10 is located in that position in the vicinity of the 
outlet portion 7 of the diffuser A where the dynamic pressure of a fluid 
is almost perfectly changed to a static pressure, i.e., in the vicinity of 
a point r in FIG. 3 showing how the static pressure is changed from 
upstream to downstream. When the diameter of the impeller 1, the entire 
length of the diffuser and the like are taken into consideration, the 
starting point 10 is preferably located in a position spaced from an inlet 
5b (FIG. 1) by a distance corresponding to about 70 to 90% of the passage 
length of the diffuser. It is required that the position of the starting 
point 10 is moved toward the scroll 4 (i.e., upward in FIG. 1) when the 
rated head is high. 
The tapering angle at the outlet throttling portion 7a is 15.degree. or 
more and 25.degree. or less. The minimum passage width t.sub.3 at the 
outlet throttling portion 7a is set to 3/8 or more and 3/4 or less of the 
passage width t.sub.2 of the intermediate portion 6. At the outlet 
throttling portion 7a, the lateral wall 2 is disposed as projecting to the 
vicinity of the diametrial center of the scroll 4. An outlet 7b is not 
edged but is chamfered. This chamfered face may be parallel with the 
lateral wall 3 or may be round. 
According to this embodiment, there is disposed the outlet throttling 
portion 7a of which passage width is narrowed from the starting point 10 
which is located in a position in the vicinity of the outlet portion 7 
where the static pressure is almost perfectly changed, i.e., in the 
vicinity of the point r in FIG. 3. Accordingly, this outlet throttling 
portion 7a may not only restrain the flow separation, but also increase 
the static pressure and prevent the fluid from reversely flowing from the 
scroll 4. Thus, the surge line may be heightened and the partial load 
efficiency may be improved. 
In particular, the minimum passage width t.sub.3 of the outlet throttling 
portion 7a is 3/8 or more and 3/4 or less of the passage width t.sub.2 of 
the intermediate portion 6. This is of great advantage to increase in 
surge margin and improvements in rated efficiency and partial load 
efficiency. Further, the starting point from which the outlet throttling 
portion 7a is throttled, is located in a position spaced from the diffuser 
inlet by a distance corresponding to 70 to 90% of the passge length of the 
diffuser. Such arrangement is of greater advantage to increase in surge 
line and improvements in partial load efficiency. 
The diffuser is provided at the inlet portion 5 thereof with the inlet 
throttling portion 5a of which passage width is narrowed downstream. The 
passage width t.sub.2 of the intermediate portion 6 is 75% or more and 95% 
or less of the impeller outlet width t.sub.1 according to the rated flow 
rate. This decreases the risk of distortion, inclination or the like of 
the flow at the inlet portion 5 of the diffuser. The multiple effect of 
the inlet throttling portion 5a and the outlet throttling portion 7a may 
not only improve the general efficiency including rated efficiency and 
partial load efficiency, but also increase the surge margin without the 
maximum flow rate lowered. 
Further, the scroll 4 is disposed as biased toward one lateral wall 2, and 
the outlet throttling portion 7a is formed by inclining the one lateral 
wall 2 toward the passage. This effectively prevents the flow from 
reversely flowing from the scroll 4, thereby to further improve the 
partial load efficiency. 
FIG. 4 shows a diffuser which has the same passage configuration and width 
as those of the embodiment in FIG. 1, but which has a movable lateral 
wall. 
In FIG. 4, a lateral wall 2 toward which a scroll 4 is biased, has a base 
lateral wall 20 and a movable lateral wall 8 which is movably attached to 
the base lateral wall 20. The diffuser in FIG. 4 further has movable 
lateral wall operating means 9 for moving the movable lateral wall 8. 
The movable lateral wall operating means 9 has a vane 91 disposed at the 
suction port of a compressor and adapted to be rotatingly driven by a 
drive shaft 92, an eccentric cam 93 rotatable integrally with the drive 
shaft 92, and a rod 94 having one end 94a which comes in contact with the 
eccentric cam 93, and the other end 94b which passes through the base 
lateral wall 20 and which is secured to the reverse surface of the movable 
lateral wall 8. 
The embodiment in FIG. 4 produces not only the same operational effects as 
those in the embodiment in FIG. 1, but also the following operational 
effects. 
More specifically, when the drive shaft 92 rotates the vane 91 in such a 
direction as to close the suction port, the flow rate of a fluid suctioned 
by the impeller 1 is decreased. On the other hand, with the rotation of 
the drive shaft 92, the eccentric cam 93 is rotated clockwise from the 
state shown in FIG. 5 (a) to the state shown in FIG. 5 (b), causing the 
rod 94 to be pushed and moved. This causes the movable lateral wall 8 to 
be moved rightward in FIG. 4, so that the passage width is narrowed. 
When the vane 91 is rotated in such a direction as to open the suction 
port, the flow rate of a fluid suctioned by the impeller 1 is increased. 
On the other hand, with the rotation of the drive shaft 92, the eccentric 
cam 93 is rotated counterclockwise from the state shown in FIG. 5 (b) to 
the state shown in FIG. 5 (a), thus allowing the rod 94 to be moved toward 
the eccentric cam 93. Accordingly, the pressure in the diffuser causes the 
movable lateral wall 8 to be moved in such a direction as to broaden the 
passage width. Thus, the passage width may be adjusted according to 
increase/decrease in load. This may not only improve the diffuser 
efficiency regardless of the magnitude of the load, but also save the 
energy consumption. In particular, the passage width may be adjusted 
according to the opening degree of the vane 91. This enables such 
adjustment to be quickly made in response to variations of the load. 
Further, to improve the diffuser efficiency, the adjustment of the passage 
width according to the load may be made in a mechanical manner. This 
provides a reliable operation and makes the structure simple to reduce the 
production cost. Further, the adjustment of the drawing degree of the 
passage width according to the vane opening degree may be readily made by 
changing the shape of the eccentric cam. 
According to this embodiment in FIG. 4, the movable lateral wall may be 
disposed only at the outlet throttling portion 7a of the diffuser, as 
shown in FIG. 6. 
Alternately, the rod 94 may be hydraulically moved, assuring the movement 
of the movable lateral wall 8. 
Further, provision may be made such that the rod 94 is moved by deformation 
of a spring made of a shape memory alloy as heated by a heater. Such an 
arrangement eliminates the drive means such as a motor or the like, thus 
reducing the cost. 
COMATIVE EXAMPLES I to IV 
There were made diffusers of Comparative Examples I to III in which only 
the inlet portions were respectively throttled at the throttling ratios 
(t.sub.1 /t.sub.2) shown in the following Table 1. In a diffuser of 
Comparative Example IV, the inlet portion was not throttled at all. 
TABLE 1 
______________________________________ 
Inlet Throttling Ratio 
t.sub.1 /t.sub.2 
______________________________________ 
Comparative Example I 
0.95 
Comparative Example II 
0.8 
Comparative Example III 
0.7 
Comparative Example IV 
1.0 
______________________________________ 
The partial load efficiency was measured on each of the Comparative 
Examples I to IV. The results are shown in FIG. 7. 
As shown in FIG. 7, Comparative Example II presenting the throttling ratio 
of 0.8 produces the optimum result for a normal rated flow rate which 
corresponds to about 80 to 90% of the maximum flow rate, while Comparative 
Example I presenting the throttling ratio of 0.95 produces the optimum 
result for a flow rate higher than the normal rated flow rate. In 
Comparative Example III presenting the throttling ratio of 0.70, the inlet 
portion was throttled too much so that the conformity of the diffuser with 
the impeller 1 was lost, thereby to increase the loss. Thus, it is found 
that Comparative Example III cannot be practically used. 
From the foregoing, it is found that the diffuser presenting the throttling 
ratio of about 0.8 is most preferred among the diffusers having throttled 
inlet portions. It is presumed that diffusers of which inlet portions are 
throttled at a ratio from 0.75 to 0.95, are practically preferred. 
TEST EXAMPLES I and II, and COMATIVE EXAMPLE II 
In addition to Comparative Example II producing the most preferred result 
among the diffusers of which only inlet portions were throttled, there 
were made a diffuser of Test Example I of which only outlet portion was 
throttled, and a diffuser of Test Example II of which inlet portion was 
throttled at the same ratio as that of Comparative Example II and of which 
outlet portion was throttled at the same ratio as that of Test Example I 
(See Table 2). 
TABLE 2 
______________________________________ 
Throttling t.sub.1 /t.sub.2 
t.sub.3 /t.sub.2 
Ratio at the inlet 
at the outlet 
______________________________________ 
Test Example I 1.0 0.5 
Comparative 0.8 0.5 
Example II 
Test Example II 0.8 1.0 
______________________________________ 
With the use of Test Examples I, II and Comparative Example II, the surge 
lines were measured. The results are shown in FIG. 8. Also, the partial 
load efficiencies were measured. The results are shown in FIG. 9. 
As shown in FIG. 8, the surge lines of Test Example I of which only outlet 
portion was throttled and Test Example II of which both inlet and outlet 
portions were throttled, are higher, throughout the range from a low flow 
rate to a high flow rate, than the surge line of Comparative Example II of 
which only inlet portion was throttled. This proves that provision of the 
outlet throttling portion improves the surge line. The surge line of Test 
Example II is slightly higher than the surge line of Test Example I. It is 
presumed that such a result is produced by the multiple effect that both 
inlet and outlet portions are throttled. 
As shown in FIG. 9, throughout the range from a low flow rate to a high 
flow rate, the partial load efficiencies of Test Examples I and II are 
higher than that of Comparative Example II, and the partial load 
efficiency of Test Example II is higher than that of Test Example I. This 
proves that the diffuser of which outlet portion is throttled at a 
predetermined ratio, may be improved in partial load efficiency more than 
the most preferred diffuser among the diffusers of which inlet portions 
are throttled. Further, it is found that the diffuser of which both inlet 
portion and outlet portion are throttled, is improved in partial load 
efficiency more than the diffuser of which only outlet portion is 
throttled. It is presumed that the improvement in efficiency over a wide 
range is achieved by the multiple effect of the inlet throttling portion 
5a and the outlet throttling portion 7a. 
TEST EXAMPLES II, III and COMATIVE EXAMPLES II, V 
In addition to Test Example II and Comparative Example II, there were made 
diffusers of Test Examples III and Comparative Example V respectively 
having the dimensional relationships among the passage width t.sub.2, the 
passage width t.sub.3 and the outlet width t.sub.1 as shown in Table 3. 
TABLE 3 
______________________________________ 
t.sub.1 /t.sub.2 
t.sub.3 /t.sub.2 
Throttling Ratio 
at the inlet 
at the outlet 
______________________________________ 
Test Example II 0.8 0.5 
Test Example III 
0.8 0.75 
Comparative 0.8 1.0 
Example II 
Comparative 0.8 0.25 
Example V 
______________________________________ 
To clarify the influence exerted by the fact that the outlet throttling 
portion 7a was throttled, the inlet throttling portions 5a presented the 
same ratio. 
The surge lines of Test Examples and Comparative Examples above-mentioned 
were measured. The results are shown in FIG. 10. Also, the partial load 
efficiencies of Test Examples and Comparative Examples above-mentioned 
were measured. The results are shown in FIG. 11. FIG. 12 shows the maximum 
efficiencies of respective Examples above-mentioned. 
As shown in FIG. 10, throughout the range from a low flow rate to a high 
flow rate, the surge lines of Test Examples II, III and Comparative 
Example V of which both inlet portion and outlet portion were throttled, 
are higher than that of Comparative Example II of which only outlet 
portion was throttled, and the surge line is higher as the throttling 
ratio at the outlet is greater in the order of Test Example III, Test 
Example II and Comparative Example V. 
As shown in FIG. 11, the partial load efficiency of Comparative Example V 
presenting a throttling ratio of 0.25 at the outlet portion, is higher for 
a low flow rate and lower for a high flow rate than that of Comparative 
Example II of which only inlet portion was throttled. The partial load 
efficiency of Test Example II presenting a throttling ratio of 0.5 at the 
outlet portion is higher, throughout the flow rate range, than that of 
Comparative Example II of which only inlet portion was throttled. The 
partial load efficiency of Test Example III presenting a throttling ratio 
of 0.75 at the outlet portion is higher than that of Comparative Example 
II for the range from a low flow rate to an intermediate flow rate, and is 
substantially equal to that of Comparative Example II for a high flow 
rate. On the other hand, the Examples of which outlet portions were 
throttled at a ratio from 0.5 to 1.0, present substantially the same 
maximum efficiency, as shown in FIG. 12. 
When the use of a diffuser of which both inlet and outlet portions are 
throttled, for a normal rated flow rate and the use thereof with a partial 
load are taken into consideration, it is presumed that both rated 
efficiency and partial load efficiency may be improved in a good balance 
by setting the minimum passage width t.sub.3 of the outlet throttling 
portion 7a to 3/8 to 3/4 of the passage width t.sub.2 of the intermediate 
portion 6. 
TEST EXAMPLES I, IV and COMATIVE EXAMPLES II, VI 
In addition to Test Example I and Comparative Example II, there were made 
diffusers of Test Example IV and Comparative Example VI of which only 
outlet portions were respectively throttled at ratios shown in Table 4. 
The surge lines of these Examples were measured. The results are shown in 
FIG. 13. The partial load efficiencies of these Examples were also 
measured. The results are shown in FIG. 14. 
TABLE 4 
______________________________________ 
t.sub.1 /t.sub.2 
T.sub.3 /t.sub.2 
Throttling Ratio 
at the inlet 
at the outlet 
______________________________________ 
Test Example I 1.0 0.5 
Test Example IV 1.0 0.75 
Comparative 0.8 1.0 
Example II 
Comparative 1.0 0.25 
Example VI 
______________________________________ 
As shown in FIG. 13, the surge lines of Test Examples I, IV and Comparative 
Example VI of which only outlet portions were throttled, are higher than 
that of Comparative Example II which had produced the best result among 
the diffusers of which only inlet portions were throttled. As the outlet 
portion is throttled more, the surge line is higher in the order of Test 
Example IV, Text Example I and Comparative Example VI. As shown in FIG. 
14, the partial load efficiency of Comparative Example VI presenting a 
throttling ratio of 0.25 at the outlet portion, is higher for a low flow 
rate and much lower for an intermediate flow rate and a high flow rate 
than that of Comparative Example II of which only inlet portion was 
throttled. The partial load efficiency of Test Example I presenting a 
throttling ratio of 0.5 at the outlet portion is higher, throughout the 
flow rate range, than that of Comparative Example II of which only inlet 
portion was throttled. The partial load efficiency of Test Example IV 
presenting a throttling ratio of 0.75 at the outlet portion is higher than 
that of Comparative Example II for the range from a low flow rate to an 
intermediate flow rate, and is substantially equal to that of Comparative 
Example II for a high flow rate. 
When the use of a diffuser of which only outlet portion is throttled, for a 
normal rated flow rate and the use thereof with a partial load are taken 
into consideration, it is presumed that both rated efficiency and partial 
load efficiency may be improved in a good balance by setting the minimum 
passage width t.sub.3 of the outlet throttling portion 7a to 3/8 to 3/4 of 
the passage width t.sub.2 of the intermediate portion 6. 
It is noted that the efficiencies in FIGS. 7, 9, 11 and 14 are those as 
measured on lines having a predetermined margin with respect to the surge 
lines. 
In the measurements above-mentioned, Freon 11 was used as a refrigerant. 
However, even though Flon 12, Freon 22, Flon 123, Flon 134a or the like is 
used as a refrigerant, the equivalent results may be produced in a 
quantitative analysis Further, the equivalent results may also be produced 
when, instead of a refrigerant of a refrigerator, air, natural gas or the 
like is used as the fluid. That is, the present invention may also be 
applied to a centrifugal compressor for an air compressor or apparatus for 
sending natural gas under pressure.