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Transcript of Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines...
![Page 1: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/1.jpg)
Specific velocity and Re effects
Content:
Specific velocity and turbomachines geometry
Specific diameter
Cordier diagram
Exercise
Reynolds number effects.
![Page 2: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/2.jpg)
Specific velocity and turbomachines
geometry
For a given pump,
a given fluid and
for (rated values for the given
N)
![Page 3: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/3.jpg)
Specific velocity and turbomachines
geometry
These values are constant for the same family of
geometrically similar machines, no matter the values of
![Page 4: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/4.jpg)
Specific velocity
(X)max characterize numerically a given
gemetric family (in what concerns
performance), namely:
and
max
3
ND
Q
max
22
DN
gH
max
43
21
23
gH
QN
- Specific velocity
![Page 5: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/5.jpg)
Same family has identical
Machines with same have approximately
same geometry
Specific velocity -
max
43
21
23
gH
QN
![Page 6: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/6.jpg)
Specific velocity and turbomachines
geometry
1 injector, Pelton Turbines
Pelton Turbines
Several injectors Radial pumps
Radial Turbines
narrow normal large
Kaplan
turbines Prop
. turbines
Mixed
pumps
Axial or Prop.
pumps Radial fans
and compressors Axial fans and compressors
Vapor and gas
turbines
![Page 7: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/7.jpg)
Specific velocity and
turbomachines
geometry
![Page 8: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/8.jpg)
Specific velocity and hydraulic turbines
geometry
![Page 9: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/9.jpg)
Rotors 8 to 12 – pumps
Rotors 13 to 19 - fans
Specific
velocity
and pumps
and fans
geometry
![Page 10: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/10.jpg)
Specific diameter
(X)max characterize numerically a given
geometry (in what concerns performance),
namelly:
and
max
3
ND
Q
max
22
DN
gH
max
4121
21
Q
gHD
- Specific diameter
![Page 11: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/11.jpg)
Specific diameter -
Same family has identical
and
Machines with same and have approximately
the same geometry
max
4121
21
Q
gHD
max
43
21
23
gH
QN
![Page 12: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/12.jpg)
Cordier diagram
Allows to relate
statistically
and
max
4121
21
Q
gHD
max
43
21
23
gH
QN
![Page 13: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/13.jpg)
Exercise
Q = 14,5 m3/s
H = 180 m
N = 333 rpm
Type of pump?
Rotor diameter?
![Page 14: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/14.jpg)
Exercise
Q = 14,5 m3/s
H = 180 m
N = 333 rpm
Type of pump?
Rotor diameter?
Response
58,0
21808,9
25,1460
2333
43
max
43
gH
QN
![Page 15: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/15.jpg)
Cordier diagram
7,4
58,0
mm
gH
QD 2319
max
41
D from figure: 2400 mm
![Page 16: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/16.jpg)
Reynolds number
Reynolds number influence on performance curves
![Page 17: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/17.jpg)
Re influence
FfDN
gHH
22
H
Hk
f1
Re
Under Reynolds influence it is:
Is it be possible to superpose the curves by varying the scale?
Scale factors
Taking
where
where
![Page 18: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/18.jpg)
fH(Re) e f(Re) functions
Reynolds number
![Page 19: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/19.jpg)
Exercise
Centrifugal pump: D = 0,3 m; N = 1450 rpm with water ( =
10-6 m2/s) has the following operation point:
Q = 0,07 m3/s; H = 46 m; = 88%
Compute flow rate, efficiency and head with:
a) Natural oil ( = 810-6 m2/s)?
b) Fuel ( = 20010-6 m2/s)?
Answer:
7
6
22
104,110
3,08,151Re
ag
ag
ND
1)(Re)(Re agagH ff Reynolds number
![Page 20: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/20.jpg)
Exercise
1)(Re pHf
Answer:
62
107,1Re p
p
ND
98,0)(Re pfReynolds number
Centrifugal pump: D = 0,3 m; N = 1450 rpm with water ( =
10-6 m2/s) has the following operation point:
Q = 0,07 m3/s; H = 46 m; = 88%
Compute flow rate, efficiency and head with:
a) Natural oil ( = 810-6 m2/s)?
![Page 21: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/21.jpg)
Exercise
1)(Re pHf
Answer:
62
107,1Re p
p
ND
No change in head:
mHH agp 46
Centrifugal pump: D = 0,3 m; N = 1450 rpm with water ( =
10-6 m2/s) has the following operation point:
Q = 0,07 m3/s; H = 46 m; = 88%
Compute flow rate, efficiency and head with:
a) Natural oil ( = 810-6 m2/s)?
![Page 22: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/22.jpg)
Exercise
98,0)(Re agf
Answer:
62
107,1Re p
p
ND
agag ff Re
ppp ff Re
If p = ag thus f(p) = f(ag) and
8624,088,098,0Re
Re
ag
p
agpf
f
Centrifugal pump: D = 0,3 m; N = 1450 rpm with water ( =
10-6 m2/s) has the following operation point:
Q = 0,07 m3/s; H = 46 m; = 88%
Compute flow rate, efficiency and head with:
a) Natural oil ( = 810-6 m2/s)?
![Page 23: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/23.jpg)
Exercise
Answer: If p = ag thus 4343
ag
ag
p
p
gH
QN
gH
QN
smH
HQQ
ag
p
agp
307,0
Centrifugal pump: D = 0,3 m; N = 1450 rpm with water ( =
10-6 m2/s) has the following operation point:
Q = 0,07 m3/s; H = 46 m; = 88%
Compute flow rate, efficiency and head with:
a) Natural oil ( = 810-6 m2/s)?
![Page 24: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/24.jpg)
Exercise
95,0)(Re fHf
Answer:
42
108,6Re f
f
ND
74,0)(Re ff
Centrifugal pump: D = 0,3 m; N = 1450 rpm with water ( =
10-6 m2/s) has the following operation point:
Q = 0,07 m3/s; H = 46 m; = 88%
Compute flow rate, efficiency and head with:
b) Fuel ( = 20010-6 m2/s)?
Reynolds number
![Page 25: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/25.jpg)
Exercise
95,0)(Re pHf
Answer:
42
108,6Re f
f
ND
agagH
agFf
DN
gHRe
22
ffH
fFf
DN
gHRe
22
If f = ag thus F(f) = F(ag) and
mf
fHH
agH
fH
agf 7,434695,0Re
Re
Centrifugal pump: D = 0,3 m; N = 1450 rpm with water ( =
10-6 m2/s) has the following operation point:
Q = 0,07 m3/s; H = 46 m; = 88%
Compute flow rate, efficiency and head with:
b) Fuel ( = 20010-6 m2/s)?
![Page 26: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/26.jpg)
74,0)(Re ff
Answer:
42
108,6Re f
f
ND
agag ff Re
fff ff Re
If f = ag thus f(f) = f(ag) and
65,088,074,0Re
Re
ag
f
agff
f
Exercise Centrifugal pump: D = 0,3 m; N = 1450 rpm with water ( =
10-6 m2/s) has the following operation point:
Q = 0,07 m3/s; H = 46 m; = 88%
Compute flow rate, efficiency and head with:
b) Fuel ( = 20010-6 m2/s)?
![Page 27: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/27.jpg)
Answer: If f = ag thus 4343
ag
ag
f
f
gH
QN
gH
QN
smQQ ag
f
H
H
agf
32
3
2
3
065,046
7,4307,0
Exercise Centrifugal pump: D = 0,3 m; N = 1450 rpm with water ( =
10-6 m2/s) has the following operation point:
Q = 0,07 m3/s; H = 46 m; = 88%
Compute flow rate, efficiency and head with:
b) Fuel ( = 20010-6 m2/s)?
![Page 28: Specific velocity and Re effects - ULisboa · PDF fileSpecific velocity and turbomachines geometry These values are constant for the same family of geometrically similar machines,](https://reader031.fdocuments.us/reader031/viewer/2022030503/5aaf817c7f8b9a6b308d644f/html5/thumbnails/28.jpg)
Bibliography
Capítulos 7, 8 and 9
Turbomáquinas, A. F. O. Falcão, Folhas
AEIST, 2004.