Blade Nomenclature

Blade Nomenclature

Axial and Radial Flow Turbines Differences between turbine and compressor: Compressor

Turbine Blade 1

Long

Last blade

Short

► Work as diffuser

► Work as nozzle

► Direction of rotation is opposite to lift direction

► Direction of rotation is same as Life

► Number of stages are many

► Number of stages is small Pc, the nozzle is not choked. Thus, Pthroat = P2 = 2.49 P ρ 2 = 2 → ρ 2 = 0 .8 3 3 kg / m 3 R T2 m A2 = , o r , m = ρ 2 C a A 2 , A 2 = 0 .0 8 3 3 m 2 ρ 2C a m th ro at area o f n o zzles; A 2 N = ρ 2C 2 o r , m = ρ 2 C 2 A 2 N ⇒ A 2 N = 0 .0 4 3 7 m 2 , also A 2 co s α 2 = A 2 N

Axial Flow Turbine Calculate areas at section (1) inlet nozzle and (3) exit rotor. C a1 = C 1 , b u t C 1 = C 3 a n d C 3 = T1 = T o1 −

C a3 cos α 3

, → C a 1 = 2 7 6 .4 m / s

C 12 → T1 = 1 0 6 7 K 2c p γ

 T  γ −1 P1 =  1  → P1 = 3 .5 4 b a r  To  Po1  1  P1 ρ1 = ⇒ ρ 1 = 1 .1 5 5 k g / m 3 R T1 m = ρ 1 C a1 A1 ⇒ A1 = 0 .6 2 6 m 2

Axial Flow Turbine S im ila rly a t o u tle t o f s ta g e ( ro to r) T o 3 = T o1 − ∆ T o 5 = 1 1 0 0 − 1 4 5 = 9 5 5 K , g iv e n T3 = To3 −

C 32 ⇒ T3 = 9 2 2 K 2c p γ γ −1

 T  P3 =  3  ⇒ P3 = 1 .8 5 6 b a r  To  Po 3  3  P ρ 3 = 3 ⇒ ρ 5 = 0 .7 0 2 k g / m 3 R T5

ρ3 = P3 / RT5 ⇒ ρ5 = 0.702kg / m 2 m = ρ3Ca3 A3 ⇒ A3 = 0.1047 m 2 Blade height and annulus radius ratio

Axial Flow Turbine Mean radius 340 = 0.216 m 2π (250) also for know n (A); A = 2 π rm h

u m = 2π N rm ⇒ rm =

⇒h=

A 2π rm

h h then rt = rm + , rr = rm − 2 2

using areas at stations 1,2,3 thus Location

A1 m h1m rt / rr

2

1

2

3

0.0626

0.0833

0.1047

0.04

0.0612

0.077

1.24

1.33

1.43

Axial Flow Turbine Blade with width W Normally taken as W=h/3 Spacing s between axial blades

space s = = 0.25, should not be less than 0.2 W width w r * t should be 1.2 → 1.4 rr unsatisfactory values such as 0.43 can be reduced by changing axial velocity through φ . increasing Ca will reduce rt check has to be made for mach number M v .

Axial Flow Turbine Vortex Theory The blade speed ( u=ωr) changes from root to tip, thus velocity triangles must vary from root to tip. Free Vortex design axial velocity is constant over the annulus. Whirl velocity is inversely proportional to annulus.

C a2 = cons tan t , Cω 2 r = cons tan t C a3 = cons tan t , Cω 3 r = const, Along the radius.

(

)

Ws = u Cω2 + Cω3 = ω (Cω2 r + Cω3 r ) = cons tan t

Axial Flow Turbine For variable density,

m is given by

δ m = ρ 2 ( 2π r δ r )C a rt

m = 2π C a 2



2

ρ 2 rdr

rr

(C ) r = cons tan t = r (C ω2

a2

tan α 2

)

but Ca 2 is cosntant, thus α 2 changes as r  tanα 2 =  m  tan α 2 m  r 2 similarly r  tan α 3 =  m  tan α 3m  r 3

(a)

(b)

Axial Flow Turbine u = Ca2 tan α 2 − Ca2 tan β 2 , thus, tanβ 2 = tan α 2 −

u Ca2

 r u r  =  m  tan α 2 m −   m (c)  r 2  rm  Ca2 for exit of rotor u = Cas tan α 3 + Ca3 tan α 3  r  u r  thus tanβ3 =  m  tan α 3m +   (d)  r 3  rm 3 Ca3 Ex: Free vortex Results from mean diameter calculations α 2 m = 5 8 .3 8 , β 2m = 2 0 .4 9 , α 3 m = 1 0 o , β 3 m = 5 4 . 9 6 , h 2 = 0 . 0 6 1 2 , rm = 0 . 2 1 6 , h

3

h 2

= 0 . 0 7 7 , rr = rm −

Axial Flow Turbine r  r  r  r ⇒  m  = 1.164, ( m ) 2 0.877,  m  = 1.217,  m  = 0.849 rt  rt  2  rr 3  rt 3 u 1 u also m = = m = 1.25, Results are Ca 2 φ Ca3

α2

β2

α3

β3

Tip

54.93

0

8.52

58.33

Root

62.15

39.32

12.12

51.13

mean

58.38

20.49

10

54.96

Axial Flow Turbine U = tan α 2 − tan β2 = tan β3 − tan α3 Ca & cp∆Tos == m & cp (To1 − To3 ) = m & UCa (tan α 2 + tan α3 ) == m & UCa (tan β2 + tan β3 ) W=m & UCa (tan α 2 − tan α1) = m & UCa (tan β2 − tan β1) =m T' p ∆Tos = To1 − To3 = ηsTo1(1 − o3 ) = ηsTo1(1 − ( o3 ) γ /(γ −1) ) To1 po1 T −T where ηs = o1 o3 To1 − To' 3

EES Design Calculations of Axial Flow Turbine Known Information To 1 = 1100

[K]

P ratio =

1.873

DelTs =

145

Etta turbine

=

0.9

Assumptions U = 340 N rps

=

φ =

0.8

α3 =

[m/s]

250

10

Loss nozzle

=

0.05

EES Design Calculations of Axial Flow Turbine cp =

1148

DelTs =

φ =

γ

=

1.333

Po 1 Po 3 C2 · cos ( α 2 )

Ca U γ γ – 1

Gamr =

Epsi

0.287

To 1 – To 3

P ratio = Ca =

R =

=

DelTs

2 · cp ·

2

U Epsi = Reaction

2 · φ · ( tan ( β 2 ) + tan ( β 3 ) ) φ · ( tan ( β 3 ) – tan ( β 2 ) ) 2

=

U =

Ca · ( tan ( α 2 ) – tan ( β 2 ) )

U =

Ca · ( tan ( β 3 ) – tan ( α 3 ) )

EES Design Calculations of Axial Flow Turbine Calculate A2 Loss nozzle

T2 – T2dash

=

C2

2

2 · cp To 2 =

To 1

To 2 – T2 = Po 1

Po 1

Pth = Rho2 =

A2

=

Gamr

T2dash γ + 1 2

=

Pc

2

2 · cp

To 1

=

P2

C2

Gamr

P2 Pth R · T2 m Rho2 · Ca

A2 · cos ( α 2 ) =

A2N

EES Design Calculations of Axial Flow Turbine Calculate A3 Calculate A1 To 1 – T1 = Po 1

To 1

=

P1

A1

=

2

C3

To 3 – T3 =

2

2 · cp

2 · cp Gamr

T1 P1

Rho1 = C1 =

C1

Po 3

To 3

=

P3

T3 P3

Rho3 =

R · T3

R · T1

C3 =

Ca m Rho1 · Ca

A3

Gamr

Ca m

=

Rho3 · Ca

EES Design Calculations of Axial Flow Turbine Blade height at section 2

Blade height U =

A2 =

2 · π · r m · h2

r t2 =

rm +

r r2 =

rm –

rratio 2

=

2 · π · N rps · r m

Blade height at section 1 A1 =

2 · π · r m · h1

r t1 =

rm +

r r1 =

rm –

rratio 1

=

h1 2 h1 2

2 h2 2

r t2 r r2

Blade height at section 3 A3 =

2 · π · r m · h3

r t3 =

rm +

r r3 =

rm –

rratio 3

=

r t1 r r1

h2

r t3 r r3

h3 2 h3 2

EES Design Calculations of Axial Flow Turbine

A1 = 0.06345

A2 = 0.08336

A2N = 0.04372

A3 = 0.1046

α 3 = 10

β2 = 20.49

β 3 = 54.97

C1 = 272

α 2 = 58.37 C2 = 518.7

C3 = 272

Ca = 272

cp = 1148 [J/kgK]

DelTs = 145

Epsi = 2.88

Ettaturbine = 0.9

γ = 1.333

Gamr = 4.003

h1 = 0.04666

h2 = 0.06129

h3 = 0.07692

Loss nozzle = 0.05

m = 20 [kg/s]

Nrps = 250 [rev per sec]

P1 = 355.1

P2 = 248.8

P3 = 186.1

Pc = 215.9

φ = 0.8

Po1 = 400 [kPa]

Po3 = 213.6

Pth = 248.8

Pratio = 1.873

R = 0.287 [kJ/kgK]

Reaction = 0.4211

Rho1 = 1.159

Rho2 = 0.8821

Rho3 = 0.7029

rratio1 = 1.242

rratio2 = 1.33

rratio3 = 1.432

rm = 0.2165

rr1 = 0.1931

rr2 = 0.1858

rr3 = 0.178

rt1 = 0.2398

rt2 = 0.2471

rt3 = 0.2549

T1 = 1068

T2 = 982.8

T2dash = 977

T3 = 922.8

To1 = 1100 [K]

To2 = 1100 [K]

To3 = 955

U = 340 [m/s]

Axial Flow Turbine

Axial Flow Turbine