1. Axial Flow Compressors

2. Axial Flow Compressors
Elementary theory

3. Axial Flow Compressors

4. Axial Flow Compressors
Comparison of typical forms of turbine and compressor rotor blades

5. Axial Flow Compressors
Stage= S+R
S: stator (stationary blade)
R: rotor (rotating blade)
First row of the stationary blades is called guide vanes
** Basic operation
*Axial flow compressors:
series of stages
each stage has a row of rotor blades followed by a row of stator blades.
fluid is accelerated by rotor blades.

6. Axial Flow Compressors
In stator, fluid is then decelerated causing change in the kinetic energy to static pressure.
Due to adverse pressure gradient, the pressure rise for each stage is small. Therefore, it is known that a single turbine stage can drive a large number of compressor stages.
Inlet guide vanes are used to guide the flow into the first stage.
Elementary Theory:
Assume mid plane is constant r1=r2, u1=u2
assume Ca=const, in the direction of u.
, in the direction of u.

7. Axial Flow Compressors
Inside the rotor, all power is consumed.
Stator only changes K.E.P static, To2=To3
Increase in stagnation pressure is done in the rotor.
Stagnation pressure drops due to friction loss in the stator:
C1: velocity of air approaching the rotor.
: angle of approach of rotor.
u: blade speed.
V1: the velocity relative t the rotor at inlet at an angle 1 from the axial direction.
V2: relative velocity at exit rotor at angle 2 determined from the rotor blade outlet angle.
2: angle of exit of rotor.
Ca: axial velocity.

8. Axial Flow Compressors
Two dimensional analysis:
Only axial ( Ca) and tangential (Cw). no radial component

9. Axial Flow Compressors

10. Axial Flow Compressors
from velocity triangles
assuming
the power input to stage
where
or in terms of the axial velocity
From equation (a)

11. Axial Flow Compressors
Energy balance
pressure ratio at a stage

12. Axial Flow Compressors
Degree of reaction
is the ratio of static enthalpy in rotor to static enthalpy rise in stage
For incompressible isentropic flow Tds=dh-vdp
dh=vdp=dp/ Tds=0
h=p/ ( constant )
Thus enthalpy rise could be replaced by static pressure rise ( in the definition of )
but generally choose =0.5 at mid-plane of the stage.

13. Axial Flow Compressors
=0: all pressure rise only in stator
=1: all pressure rise in only in rotor
=0.5: half of pressure rise only in rotor and half is in stator. ( recommend design)

14. Axial Flow Compressors
special condition
=0 ( impulse type rotor)
from equation 3
1=-2 , velocities skewed left, h1=h2, T1=T2
=1.0 (impulse type stator from equation 1)
=1-Ca(tan1+tan2)/2u, 2=1
velocities skewed right, C1=C2, h2=h3T2=T3
=0.5
from 2

15. Axial Flow Compressors
Three dimensional flow
2-D
1. the effects due to radial movement of the fluid are ignored.
2. It is justified for hub-trip ratio>0.8
3. This occurs at later stages of compressor.
3-D are valid due to
1. due to difference in hub-trip ratio from inlet stages to later-stages, the annulus will have a substantial taper. Thus radial velocity occurs.
2. due to whirl component, pressure increase with radius.

16. Axial Flow Compressors

17. Axial Flow Compressors
Design Process of an axial compressor
(1) Choice of rotational speed at design point and annulus dimensions
(2) Determination of number of stages, using an assumed efficiency at design point
(3) Calculation of the air angles for each stage at the mean line
(4) Determination of the variation of the air angles from root to tip
(5) Selection of compressor blades using experimentally obtained cascade data
(6) Check on efficiency previously assumed using the cascade data
(7) Estimation on off-design performance
(8) Rig testing

18. Axial Flow Compressors
Design process:
Requirements:
A suitable design point under sea-level static conditions (with =1.01 bar and , N as take off thrust, may emerge as follows:
Compressor pressure ratio 4.15
Air-mass flow kg/s
Turbine inlet temperature K
With these data specified, it is now necessary to investigate the aerodynamic design of the compressor, turbine and other components of the engine. It will be assumed that the compressor has no inlet guide vanes, to keep weight and noise down. The design of the turbine will be considered in Chapter 7.

19. Axial Flow Compressors
Requirements:
choice of rotational speed and annulus dimensions;
determination of number of stages, using an assumed efficiency;
calculation of the air angles for each stage at mean radius;
determination of the variation of the air angles from root to tip;
investigation of compressibility effects

20. Axial Flow Compressors
Determination of rotational speed and annulus dimensions:
Assumptions
Guidelines:
Tip speed ut=350 m/s
Axial velocity Ca= m/s
Hub-tip ratio at entry
Calculation of tip and hub radii at inlet
Assumptions Ca=150 m/s
Ut=350 m/s to be corrected to 250 rev/s

21. Axial Flow Compressors
Equations
continuity
thus

22. Axial Flow Compressors
procedure

23. Axial Flow Compressors
From equation (a) N
260.6
0.2137
0.4
246.3
0.2262
0.5
227.5
0.2449
0.6

24. Axial Flow Compressors
Consider rps250
Thus rr/rt=0.5, rt=0.2262, ut=2rt*rps=355.3 m/s
Is ok. Discussed later. Results r-t=0.2262, r-r=0.1131, r-m= m

25. Axial Flow Compressors
At exit of compressor

26. Axial Flow Compressors
No. of stages
To =overall = =164.5K
rise over a stage K for subsonic
4.5 for transonic
for rise over as stage=25
thus no. of stages =164.5/25
- normally To5 is small at first stage
de haller criterion V2/V1 > 0.72
- work factor can be taken as 0.98, 0.93, 0.88 for 1st, 2nd, 3 rd stage and 0.83 for rest of the stages.

27. Axial Flow Compressors
Stage by stage design;
Consider middle plane
stage 1
for no vane at inlet

28. Axial Flow Compressors
Angles
check de Haller

29. Axial Flow Compressors

30. Axial Flow Compressors
Second stage

31. Axial Flow Compressors

32. Axial Flow Compressors

33. Axial Flow Compressors

34. Axial Flow Compressors6 5 4
Stage
2.968
2.447
1.992
405
381
357
1.199
1.213
1.228
3.560
429
0.592
0.521
0.455

35. Axial Flow Compressors
Stage 7
At entry to the final stage the pressure and temperature are 3.56 bar and 429 K. the required compressor delivery pressure is 4.15*1.01=4.192 bar. The pressure ratio of the seventh stage is thus given by

36. Axial Flow Compressors
the corresponding air angles, assuming 50 per cent reaction, are then 1=50.98,

37. Design calculations using EES
"Determination of the rotational speed and annulus dimensions"
"Known Information"
To_1=288 [K]; Po_1=101 [kPa]; m_dot=20[kg/s]; U_t=350 [m/s]
$ifnot ParametricTable
Ca_1=150[m/s];r_r/r_t=0.5;cp=1005;R=0.287;Gamma=1.4
$endif
Gamr=Gamma/(Gamma-1)
m_dot=Rho_1*Ca_1*A_1 "mass balance"
A_1=pi*(r_t^2-r_r^2) "relation between Area and eye dimensions"
U_t=2*pi*r_t*N_rps
C_1=Ca_1
T_1=To_1-C_1^2/(2*cp)
P_1/Po_1=(T_1/To_1)^Gamr
Rho_1=P_1/(R*T_1)
$TabStops in

38. Design calculations using EES

39. Design calculations using EES

40. Design calculations using EES

41. Design calculations using EES

42. Design calculations using EES

43. Design calculations using EES