Specific velocity and Re effects

Transcription

1 Seciic velocity and Re eects Content: Seciic velocity and turbomachines geometry Seciic diameter Cordier diram Exercise Reynolds number eects.

2 Seciic velocity and turbomachines geometry For a given um, a given luid and or (rated values or the given N)

3 Seciic velocity and turbomachines geometry These values are constant or the same amily o geometrically similar machines, no matter the values o

4 Seciic velocity (X) max characterize numerically a given gemetric amily (in what concerns erormance), namely: ND 3 max and gh N D max 3 1 N 3 4 gh max - Seciic velocity

5 Seciic velocity - Same amily has identical gh max Machines with same have aroximately same geometry N

6 Seciic velocity and turbomachines geometry 1 injector, Pelton Turbines Pelton Turbines Several injectors Radial Turbines narrow normal large Radial ums Mixed ums Radial ans and comressors Kalan turbines Pro. turbines Axial or Pro. ums Axial ans and comressors Vaor and gas turbines

7 Seciic velocity and turbomachines geometry

8 Seciic velocity and hydraulic turbines geometry

9 Seciic velocity and ums and ans geometry Rotors 8 to 1 ums Rotors 13 to 19 - ans

10 Seciic diameter (X) max characterize numerically a given geometry (in what concerns erormance), namelly: ND 3 max and gh N D max 1 1 D gh 1 4 max - Seciic diameter

11 Seciic diameter - Same amily has identical and D gh N Machines with same and have aroximately the same geometry 1 4 max 3 4 gh max

12 Cordier diram Allows to relate statistically 3 1 N 3 4 gh max and 1 1 D gh 1 4 max

13 Exercise = 14,5 m 3 /s H = 180 m N = 333 rm Tye o um? Rotor diameter?

14 Exercise = 14,5 m 3 /s H = 180 m N = 333 rm Tye o um? Rotor diameter? Resonse N , gh 9,8 180 max 0,58

15 Cordier diram 0,58 4,7 D 319mm 1 4 gh max D rom igure: 400 mm

16 Reynolds number inluence on erormance curves Reynolds number

17 Re inluence Under Reynolds inluence it is: Is it be ossible to suerose the curves by varying the scale? Scale actors Taking where gh N D H F where H Re 1 k H

18 H (Re) e (Re) unctions Reynolds number

19 Exercise Centriugal um: D = 0,3 m; N = 1450 rm with water ( = 10-6 m /s) has the ollowing oeration oint: = 0,07 m 3 /s; H = 46 m; = 88% Comute low rate, eiciency and head with: Answer: a) Natural oil ( = m /s)? b) Fuel ( = m /s)? Re H (Re ND ) 151,8 0, (Re ) 1 1, Reynolds number

20 Exercise Centriugal um: D = 0,3 m; N = 1450 rm with water ( = 10-6 m /s) has the ollowing oeration oint: = 0,07 m 3 /s; H = 46 m; = 88% Comute low rate, eiciency and head with: a) Natural oil ( = m /s)? Answer: Re H (Re (Re ND ) 1 ) 0,98 1, Reynolds number

21 Exercise Centriugal um: D = 0,3 m; N = 1450 rm with water ( = 10-6 m /s) has the ollowing oeration oint: = 0,07 m 3 /s; H = 46 m; = 88% Comute low rate, eiciency and head with: Answer: a) Natural oil ( = m /s)? Re H (Re ND ) 1 1, No change in head: H H 46m

22 Exercise Centriugal um: D = 0,3 m; N = 1450 rm with water ( = 10-6 m /s) has the ollowing oeration oint: Answer: Re = 0,07 m 3 /s; H = 46 m; = 88% Comute low rate, eiciency and head with: (Re a) Natural oil ( = m /s)? ND ) 0,98 1, Re Re I = thus ( ) = ( ) and Re Re 0,980,88 0,864

23 Exercise Centriugal um: D = 0,3 m; N = 1450 rm with water ( = 10-6 m /s) has the ollowing oeration oint: = 0,07 m 3 /s; H = 46 m; = 88% Comute low rate, eiciency and head with: a) Natural oil ( = m /s)? Answer: I = thus N gh 4 gh 3 4 N 3 H H 0,07 m 3 s

24 Exercise Centriugal um: D = 0,3 m; N = 1450 rm with water ( = 10-6 m /s) has the ollowing oeration oint: = 0,07 m 3 /s; H = 46 m; = 88% Comute low rate, eiciency and head with: b) Fuel ( = m /s)? Answer: Re H (Re ND ) 0,95 6, (Re ) 0,74 Reynolds number

25 Exercise Centriugal um: D = 0,3 m; N = 1450 rm with water ( = 10-6 m /s) has the ollowing oeration oint: Answer: Re H = 0,07 m 3 /s; H = 46 m; = 88% Comute low rate, eiciency and head with: (Re b) Fuel ( = m /s)? ND ) 0,95 6, gh N N gh D D H H Re F Re F I = thus F( ) = F( ) and H Re H H 0, , 7m Re H

26 Exercise Centriugal um: D = 0,3 m; N = 1450 rm with water ( = 10-6 m /s) has the ollowing oeration oint: Answer: Re = 0,07 m 3 /s; H = 46 m; = 88% Comute low rate, eiciency and head with: (Re b) Fuel ( = m /s)? ND ) 0,74 6, Re Re I = thus ( ) = ( ) and Re Re 0,740,88 0,65

27 Exercise Centriugal um: D = 0,3 m; N = 1450 rm with water ( = 10-6 m /s) has the ollowing oeration oint: = 0,07 m 3 /s; H = 46 m; = 88% Comute low rate, eiciency and head with: b) Fuel ( = m /s)? Answer: I = thus N gh 4 gh 3 4 N 3 H H ,7 0, ,065m 3 s

28 Bibliograhy Caítulos 7, 8 and 9 Turbomáquinas, A. F. O. Falcão, Folhas AEIST, 004.