Turbomachines: Unsteadiness and Manufacturing Tolerances

F. Montomoli, PhD

Whittle Laboratory

University of Cambridge

• Increase Aircraft Performance

• Reduce component weight

• Axial space reduced, higher blade loading

- higher unsteady interactions

- unsteady design

Unsteadiness

Courtesy of Rolls-Royce

Manufacturing Tolerances

• Increase GT performance – Higher reliability

• Smaller core, higher TET

– more complex systems (coolant, geometry etc)

– manufacturing deviations: critical

Courtesy of Mitsubishi Heavy Industry

High Pressure Turbines: higher temperature

Salvadori S, Montomoli F, Martelli F, Adami P, Chana K., Castillon L.: “Aero-thermal study of the unsteady flow field in a transonic gas turbine with inlet temperature distortions”, J. of Turbomachinery, 2010

Salvadori S, Montomoli F, Chana K, Martelli F, Povey T., Qureshi I., “Analysis of the Effect of a Non-uniform Inlet Profile on Heat Transfer and Fluid Flow in Turbine Stages” J. of Turbomachinery, 2011

Courtesy of Rolls-Royce: The Jet Engine

Combustion Chamber: Exit Temperature Distribution

Courtesy of Rolls-Royce: The Jet Engine

Nozzle Location

Hot Streaks Migration

rotor is critical, unsteady simulation must be used!

Uncertainty on temperature distribution

Better for the rotor tip

Low Pressure Turbines: less blades

Montomoli F., Hodson, H.P., Haselbach, F.: “Effect of roughness and unsteadiness on the performance of a new LPT blade at low Reynolds numbers”, Journal of Turbomachinery, 2010

Courtesy of Rolls-Royce

Low Pressure Turbines: No Unsteady Wakes

S/S01

1

0M

ach

is i=0 g=21 Re=30.000

S/S01

1

0M

ach

is i=0 g=21 Re=30.000i=0 g=24 Re=30.000

separation

Low Pressure Turbines: No Unsteady Wakes

Wake Induced Transition

High loading blade can be usedWake passing reduces the separation

Low Pressure Turbines: hot gas ingestion

Montomoli F. “Interaction of Wheel Space Coolant and Main Flow in a New Aeroderivative LPT”, J. of Turbomachinery 2010, GE award.

Unsteadiness and Real Geometry: GE LM2500+G4

Monte Carlo analysis

Simplified network

stator

Prediction Hot Gas Ingestion: life + 40%

25% pitchPS

50% pitch

@LE75% pitch

SS

0.26

0.28

0.3

0.32

0.34

0.36

f(teta) [deg]

f(p

) [-

]

φφφφ=0.2φφφφ=0.4

φφφφ=0.6

Axial Compressors: stall margin

Montomoli F., H.P. Hodson, L. Lapworth: “RANS-URANS in axial compressors, a design methodology”, IMECHE Seminar: Grand review in the state-of-the-art in the numerical simulation of fluid flow 2, London, 2009, J. Power and EnergyMontomoli F., E. Naylor, H.P. Hodson, L. Lapworth “Unsteady effects in cantilevered axial compressors: a multistage simulation”, ISABE 2009, Montreal Canada.

Courtesy of Rolls-Royce

Low Speed Compressor - BRR1

Two simulations: steady (mixing plane)unsteady (sliding plane)

Reduced count ratio 3-4 (75 rotor- 96 stator blades)

20 times more doing the right problem!

Flow

rotor 1

rotor 2

rotor 3

rotor 4

stator 1

stator 2

stator 3

stator 4

BRR1

X [m]0 0.1 0.2 0.3 0.4 0.5 0.6

r 1 r 2 r 3 r 4s 1 s 2 s 3 s 4

0

20

40

60

80

100

120

140

elements, M cores iterations, K

RANS

URANS

Computational cost

100 times more expensive

Characteristic Steady vs Unsteady

0.10

0.20

0.30

0.40

0.50

0.38 0.43 0.48 0.53 0.58

Va/Umid

Pre

ssu

re R

ise C

oeff

icie

nt,

ψψ ψψ

65

70

75

80

85

90

95

Eff

icie

ncy, ηη ηη

η η η η

ψψψψ

exp stall point

Exp

RANS

URANS

unsteady stall limit

steady stall limit

Radial distribution stator losses

r 1 r 2 r 3 r 4s 1 s 2 s 3 s 4

0

10

20

30

40

50

60

70

80

90

100

0.450 0.500 0.550 0.600 0.650

(P0-P0in)/(0.5ρρρρU2) [-]

Sp

an

%

RANS

Exp

URANS

Unsteady effects at midspan-casing

Wakes at Midspan: RANS

r 1 r 2 r 3 r 4s 1 s 2 s 3 s 4

U

rotor stator

W

U

C

Wakes at Midspan: URANS

r 1 r 2 r 3 r 4s 1 s 2 s 3 s 4

U

rotor stator

Slip velocity

Wake convection at midspan

5m/s

a’

b’c‘

d‘

1<=∆

∆

'b'a

ab

U

'U

a

b

c

d

UabdsUdsU

d

c

b

a

w∆Γ ⋅=⋅+⋅= ∫∫

Decay of Velocity Defect

0.0

0.5

1.0

0 20 40 60 80 100 120

X/Chord %

Re

lati

ve

Wa

ke

De

pth

LE TE

Invis

cid

vis

cousCFD

Smith’s model

2

1

−=

exit

inlet

L

LR Smith’s recovery 1966

a

’

b’c‘

d‘

1<=∆

∆

'b'a

ab

U

'U

a

bc

d

Smith’s recovery effect

0.0

0.5

1.0

0 20 40 60 80 100 120

X/Chord %

Re

lati

ve

Wa

ke

De

pth

LE TE

Invis

cid

vis

cousCFD

Smith’s model

• Losses URANS < Losses RANS

a

’

b’c‘

d‘

1<=∆

∆

'b'a

ab

U

'U

a

bc

d

Adamczyk (1996) mixing loss proportional to square of the wake deficit

Casing – tip leakage vortex

r 1 r 2 r 3 r 4s 1 s 2 s 3 s 4

Casing - tip leakage vortex recovery

0

20

40

60

80

100

0.43 0.45 0.47 0.49 0.51 0.53Vax/Umid

Re

co

ve

ry

a

’

b’c‘

d‘

1<=∆

∆

'b'a

ab

U

'U

a

bc

d

r 1 r 2 r 3 r 4s 1 s 2 s 3 s 4

Casing at design point

RANS URANS

r 1 r 2 r 3 r 4s 1 s 2 s 3 s 4

Casing near stall

RANS URANS

r 1 r 2 r 3 r 4s 1 s 2 s 3 s 4

0.10

0.20

0.30

0.40

0.50

0.38 0.43 0.48 0.53 0.58

Va/Umid

Pre

ssu

re R

ise C

oeff

icie

nt,

ψψ ψψ

65

70

75

80

85

90

95

Eff

icie

ncy, ηη ηη

η η η η

ψψψψ

exp stall point

Exp

RANS

URANS

unsteady stall limit

steady stall limit

Explanation on stability margin

The cause is the flow near the casing

• Midspan unsteadiness reduces the losses

• Casing modifies stall margin

Cost: 100 times!

Is there any cheaper solution?

Lesson learnt

Coupled steady-unsteady?

Steady

Unsteady

Is it possible?

Not directly

Hybrid RANS-URANS

Steady

Unsteady Unsteady time averaged

Computational cost

Reduced computational cost

020406080

100120140160

elements, M iterations, K CPU cost

(CPUs It)

URANS

URANS-RANS

• Unsteadiness plays a role in axial compressor

• Computational cost of URANS calculation very high

• RANS-URANS hybrid method developed

• Reduced computational cost

Conclusions

HP Turbines: Manufacturing Tolerances

Montomoli F., Massini M, Salvadori S., Martelli F: "Geometrical Uncertainty and Film Cooling: Fillet Radii", J. of Turbomachinery

Courtesy of Mitsubishi Heavy Industry

• General Electric: hole accuracy 10% of diameter

• variation +20°C metal temperature about -33% component life(Bunker R.: GT2008-50124)

• i.e. Laser Percussion Drilling(Smith W. R., “Models for solidification and splashing in laser percussion drilling”, Journal on Applied Mathematics, Vol.

62, No. 6, 2002, pp. 1899-1923)

Film cooling: how accurate is our geometry?

manufacturing uncertainty

without in service variations

Film cooling test case

(Saumweber and Shultz 2008)

r/D=0.0,1.25,2.5, 5%

D=5mm

Computational domain

Inlet coolant

0.15<Mac<0.6

Outlet coolant

Inlet hot gas

Outlet hot gas

Viscid wall

Periodic

Inviscid wall

x

z

y

• 2M elements for geometry• 64 simulations

Discharge coefficient, sharp edge r/D=0%

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.2 1.7 2.2

Ptc/Pm [-]

Cd

[-]

Mac 0.60

Mac 0.30

r/D=0%

exp

exp

Mac 0.60

Mac 0.30

Discharge coefficient, sharp edge r/D=0%

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.2 1.7 2.2

Ptc/Pm [-]

Cd

[-]

Mac 0.60

Mac 0.45

Mac 0.15

Mac 0.30

r/D=0%

exp

exp

Mac 0.60

Mac 0.30

Flow structures, 0.15<Mach<0.45

Mach=0.15 Mach=0.30 Mach=0.45

Z/D

Vorticalmotion

vortex vortexvortex0

Coolant

• What is the difference with a “standard” plenum condition?

Effect of fillet on discharge coefficient, Mach=0.30

0.6

0.7

0.8

0.9

1.2 1.7 2.2

Ptc/Pm [-]

Cd

[-]

r/D=5.00% r/D=2.50%

r/D=1.25%

r/D=0.00%

exp

Effect of fillet on discharge coefficient

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.2 1.7 2.2

Ptc/Pm [-]

Cd

[-] Mach 0.60

Mach 0.45

Mach 0.15

Mach 0.30

r/D=5%

r/D=0%

exp

0.15<Mac<0.60

• code prediction: lower Cd for Mach=0.60, higher for Mach= 0.30

0.6

0.7

0.8

1.2 1.7 2.2

Ptc/Pm [-]

Cd

[-]

r/D=5.00% r/D=2.50%

r/D=1.25%

r/D=0.00%

exp

Cd for 0%<r/D<5%

Probability distribution of fillet radius

0.00

0.05

0.10

0.15

0.20

0.25

0 1 2 3 4 5r/D %

Pro

bab

ilit

y

r/D probability

distribution

Cd – probability distribution

• For r/D=0.0% , Cd=0.68

• For r/D=0.5% , Cd=0.71, diff. 4%

0.00

0.05

0.10

0.15

0.20

0.25

0 1 2 3 4 5r/D %

Pro

bab

ilit

y

0.68

0.70

0.72

0.74

0.76

0.78

0.80

0.82

Cd

[-]

Cdr/D probability

distribution

Cd · probability

distribution

r/D=0.5%

0.00

0.05

0.10

0.15

0.20

0.25

0 1 2 3 4 5r/D %

Pro

bab

ilit

y

0.68

0.70

0.72

0.74

0.76

0.78

0.80

0.82

Cd

[-]

Cdr/D probability

distribution

Cd=0.68

Cd=0.71

r/D=0.5%

Cd – probability distribution

• Cd – probab. distr., Cd=0.73, diff. 7%

• In order to obtain Cd=0.73, equivalent r/D=1%

0.00

0.05

0.10

0.15

0.20

0.25

0 1 2 3 4 5r/D %

Pro

bab

ilit

y

0.68

0.70

0.72

0.74

0.76

0.78

0.80

0.82

Cd

[-]

Cdr/D probability

distribution

Cd · probability

distribution

r/D=0.5%

0.00

0.05

0.10

0.15

0.20

0.25

0 1 2 3 4 5r/D %

Pro

bab

ilit

y

0.68

0.70

0.72

0.74

0.76

0.78

0.80

0.82

Cd

[-]

Cdr/D probability

distribution

r/D=0.5%

-9.00

-7.00

-5.00

-3.00

-1.00

1.00

3.00

5.00

0 1 2 3 4 5

r/D % [-]

Cd

Err

or

%error including the mean r/D

with determinsitc analysis 2%

σσσσ=0.5%

σσσσ=1.0%

σσσσ=1.5%σσσσ=2.0%

σσσσ=2.5%

error with sharp edge and

determinstic analysis 9%

• r/D=2% is “robust”

• r/D=0%, error up to 11%

Cd error as function of σ σ σ σ and r/D

• Sharp edge modifies up to 11% Cd respect to r/D=5%

• Including the manufacturing distribution a mean value for Cd can be obtained

• An equivalent r/D is defined to take into account the manufacturing variations

• It is possible to identify robust configurations, less dependent from modifications

Conclusions

Conclusions

• Unsteady Effects in Compressors are Important for Stall Margin

• Robust Design: reduce-take into account unknowns