Specific velocity and Re effects

Content:

Specific velocity and turbomachines geometry

Specific diameter

Cordier diagram

Exercise

Reynolds number effects.

Specific velocity and turbomachines

geometry

For a given pump,

a given fluid and

for (rated values for the given

N)

Specific velocity and turbomachines

geometry

These values are constant for the same family of

geometrically similar machines, no matter the values of

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

Same family has identical

Machines with same have approximately

same geometry

Specific velocity -

max

43

21

23

gH

QN

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

Specific velocity and

turbomachines

geometry

Specific velocity and hydraulic turbines

geometry

Rotors 8 to 12 – pumps

Rotors 13 to 19 - fans

Specific

velocity

and pumps

and fans

geometry

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

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

Cordier diagram

Allows to relate

statistically

and

max

4121

21

Q

gHD

max

43

21

23

gH

QN

Exercise

Q = 14,5 m3/s

H = 180 m

N = 333 rpm

Type of pump?

Rotor diameter?

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

Cordier diagram

7,4

58,0

mm

gH

QD 2319

max

41

D from figure: 2400 mm

Reynolds number

Reynolds number influence on performance curves

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

fH(Re) e f(Re) functions

Reynolds number

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

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)?

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)?

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)?

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)?

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

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)?

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)?

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)?

Bibliography

Capítulos 7, 8 and 9

Turbomáquinas, A. F. O. Falcão, Folhas

AEIST, 2004.