Design of an high loaded stage in an axial steam turbine. We had to build a stage with a certain total-to-total expansion ratio, as precise as possible, starting with few input data and no mechanical, manufacturing or economical constraints. Outline of the work: - Project data and goals - Pros&Cons of impulse stages - Designer choices - Losses in an axial turbine: Ainley&Mathieson formulation and Dunham&Came correction - Iterative procedure in MATLAB - Outputs - Cascade visualisation

1. Design of high pressure stage steam turbine
Milano, 12 dicembre 2018
Design of an high pressure stage
for a steam turbine
Federico Bresciani 876795
Davide Massocchi 883781

2. Nome Cognome, assoc.prof. ABC Dept.
Outlines
1. Project data and goals
2. Pros&Cons of impulse stages
3. Designer choices
4. Ainley&Mathieson + Dunham&Came
5. Iterative procedure
6. Outputs
7. Cascade visualisation

3. Nome Cognome, assoc.prof. ABC Dept.
1. Project data and goals
Data input assigned
• ሶ𝑚STEAM = 200 kg/s
• PT0 =150 bar
• TT0 =700°C
• α0 =0°
Our goal
• βTT obj =2.5
ΔhTT is = 357 kJ/kg
ሶ𝑊is= 71 MW

4. Nome Cognome, assoc.prof. ABC Dept.
2. Impulse stage
The most important goal of an impulse stage is to reduce «quickly» pressure and
temperature. Resisting to high temperature and pressure but also to high
centrifugal stresses is difficult, so it should use some special materials like INCONEL.
PROS
• Less stages (€↓)
• Following stages have no
problems on b
CONS
• Higher force exchange
• Higher losses, but partially
recovered

5. Nome Cognome, assoc.prof. ABC Dept.
3. Designer choices
We choose constant angle blades which is typical for high pressure stages:
Constant angle blades:
• α1 = 61.7°
• β2 = -70°
𝑉1𝑎
𝑉1𝑎 𝑟𝑒𝑓
=
𝑉1𝑡
𝑉1𝑡 𝑟𝑒𝑓
=
𝑟 𝑟𝑒𝑓
𝑟
sin2 α1
𝑊2𝑎
𝑊2𝑎 𝑟𝑒𝑓
=
𝑊2𝑡
𝑊2𝑡 𝑟𝑒𝑓
=
𝑟 𝑟𝑒𝑓
𝑟
sin2 𝛽2

6. Nome Cognome, assoc.prof. ABC Dept.
3. Designer choices
Stator assumptions:
• AR=1.5
• B=0.37 %shrouded
• k=0
• σMID=1.25
Rotor assumptions:
• AR=1.7
• B=0.37 %shrouded
• k=0.05 b2
• σMID = 1.66

7. Nome Cognome, assoc.prof. ABC Dept.
3. Designer choices
Rotational speed optimization:
• to match βTT obj
• to have a feasible Size Parameter and reduce the size effect!
• to manage b/Dm
NOPT = 12 698 rpm
high: 3D effects
low: clearance losses and manufacturing issues

8. Nome Cognome, assoc.prof. ABC Dept.
4. Estimation of losses: Ainley & Mathieson methodology
For the estimation of losses we used Ainley & Mathieson correlation that
estimate the losses in terms of total pressure Y.
We consider the profile losses, the secondary flow losses and also the
clearance losses:
𝑌TOT = [(𝑌𝑃+𝑌𝑆)
Re
2∗105
−0.2
+ 𝑌𝑇𝑐] χTe

9. Nome Cognome, assoc.prof. ABC Dept.
4. Definition used in the evaluation of losses
AINLEY-MATHIESON
𝑌P = 𝑌P 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛
𝑠
𝑐
+
α′1
α2
𝑌P 𝑖𝑚𝑝𝑢𝑙𝑠𝑒
𝑠
𝑐
− 𝑌P 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛
𝑠
𝑐
𝑡𝑚𝑎𝑥
𝑐
0,2
α′1
α2
Profile losses definition
Reaction blade Impulse blade

10. Nome Cognome, assoc.prof. ABC Dept.
4. Definition used in the evaluation of losses
DUNHAM-CAME
𝑌s = 0,334
𝑐
𝑏
4
tan 𝛼in −tan 𝛼ou𝑡
2
𝑐𝑜𝑠α′in
cos3 αout
cos3 αin
Secondary flow losses
Tip clearance losses
𝑌TC = 4𝐵
𝑘
𝑏
0,78 cos2 αout
𝑐𝑜𝑠αm
tan 𝛼in −tan 𝛼ou𝑡
2

11. Nome Cognome, assoc.prof. ABC Dept.
4. Estimation of supersonic losses
DUNHAM-CAME
Huge change in the slope
of losses after M1=1.4
If Mout > 1: 𝑌P = 𝑌P AM 1 + 60 Mout − 1 2

12. Nome Cognome, assoc.prof. ABC Dept.
5. Iterative procedure
First guess:
λ =2.65
ɸ =0.9
ηTT =88%
V2t MID =0
𝐿 𝑒𝑢 𝑀𝐼𝐷 = ηTT ΔhTT is

13. Nome Cognome, assoc.prof. ABC Dept.
5. Iterative procedure: general overview
while |βTT - βTT,old|>ε
while |L - Lold|>ε
UMID= 𝐿 𝑒𝑢 𝑀𝐼𝐷/λ
DMID =60 UMID /πN
V1t MID = V2t MID +λ UMID → α1
Cycles on D1 and b1
P2 HUB = P1 HUB
h2 HUB = h1 HUB
Cycles on D2 and b2𝐿 𝑒𝑢 = U1 V1t – U2 V2t
L = mass_average(𝐿 𝑒𝑢)
βTT =mass_average(βTT)
If |βTT - βTT,obj|>ε
λ updated
Stator
Rotor
→ W2 HUB

14. Nome Cognome, assoc.prof. ABC Dept.
5. Iterative procedure: cycles on D and b
D1 =f (b1 ;DMID) for each section
U1 (D1) and VT1 are fixed
→ MV1 ,h1 from energy balance
c1 =b1/AR1 → YP ref
→ P1 ,PT1 , properties first guess
b1 by continuity
b1 =
ሶ𝑚 NSECTIONS
π σ 𝑖 ρ1 𝑖
𝑉1𝑎 𝑖
𝐷1 𝑖
YS (b1), YTC (b1) → YTOT
→ P1 ,PT1 → properties
D1 =f (b1 ;DMID)
For rotor it’s the
same but outlet
velocity triangle is
computed differently!
𝑖0 = 𝑖1 = +5°
𝛿1=3°
𝛿2=2°

15. Nome Cognome, assoc.prof. ABC Dept.
6. Outputs
Stator V_1a V_1t P1 P_T1 T1 M_V1
HUB 365.662 678.403 64.338 138.550 552.319 1.129
MID 360.550 668.919 66.314 139.629 556.587 1.110
TIP 355.599 659.734 68.179 140.513 560.637 1.093
Rotor W_2a W_2t P2 P_T2 T2 M_W2 solidity_r Re2 10-5
Ysec_r Y_TC_r Ytot_r L_eu reaction degree
HUB 154.951 -425.723 54.964 57.016 548.429 0.663 1.757 59.190 0.383 0.422 0.767 284.109 0.001
MID 148.042 -406.742 58.096 59.903 556.411 0.631 1.668 58.576 0.367 0.410 0.742 270.433 -0.027
TIP 141.758 -389.478 60.985 62.790 563.923 0.602 1.588 57.774 0.351 0.399 0.718 255.885 -0.056
Stator solidity_s Re1 10-5
Ytot_s
HUB 1.272 47.483 0.154
MID 1.249 47.739 0.141
TIP 1.227 47.917 0.131

16. Nome Cognome, assoc.prof. ABC Dept.
6. Outputs
ηTT =75.5%
βTT=2.5 with a tolerance of 10-5
DMID = 0.602 m
ሶ𝑊= 54 MW → ηis =54/71=76%
Stator Rotor
ηFDN 90% 52%
b/DMID 0.027 0.075
NBLADES 218 118
Δα - Δβ 60° 105°
c/DMID 0.018 0.044

17. Nome Cognome, assoc.prof. ABC Dept.
7. Cascade visualisation

18. Nome Cognome, assoc.prof. ABC Dept.
Bibliography
• Corso di Turbomachinery A; Gaetani (2017)
• Sviluppo di un codice 1D per il calcolo di turbine assiali; De
Nicola, Jacoub (2013)
• Investigation of Losses Prediction Methods in 1D for Axial Gas
Turbines; Dahlquist (2008)
• Corso di motori aeronautici; Valorani (2012)