THE INFLUENCE OF HEAT TRANSFER EFFECTS ON ......Sample result of Calculation in Turbine Cascade 0...

1The Influence Of Heat Transfer Effects On Turbine Performance CharacteristicsProceedings of ASME TURBO EXPO ’06, May 8-11, 2006, Barcelona, Spain

LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

THE INFLUENCE OF HEAT TRANSFER EFFECTS ON TURBINE PERFORMANCE CHARACTERISTICS

K. MathioudakisA. Stamatis

Laboratory of Thermal TurbomachinesNational Technical University of Athens



The Influence Of Heat Transfer Effects On Turbine Performance Characteristics

§Physical reasons for Map Alteration

§Dilatation effect estimation

§Altration of the flow-field

§Application Example

§Summary-Conclusions

§Acknolwdgements



The physics for turbine map constitution The physics for turbine map constitution

• dfs

( )

21

1

t

2

tD

t

t

pp

pp

R12AC

pTm

−

−

=

+γ

γγ

γγ

A turbine blade passage and its equivalent nozzle



Area change effect on turbine mapArea change effect on turbine map

D

DCC

AA

qq δδδ

+=









§Acknolwdgements



Modeling Blade Passage Geometry Change due to DilatationModeling Blade Passage Geometry Change due to Dilatation

Map Change

⇕

Area change

Throat area and its variation due to dilatation



Calculation of metal temperaturesCalculation of metal temperatures (II)(II)

Tc coolant

Tg gas

TBC

Tm

Tw

Blade wall and gas temperature configuration



Calculation of metal temperatures: Simplified 1Calculation of metal temperatures: Simplified 1--D modelD model (II)(II)

Convection

Conduction

Convection

dR



Area Change as a function of flow parameters (1)Area Change as a function of flow parameters (1)

-1

-0.8

-0.6

-0.4

-0.2

00.5 0.6 0.7

convective cooling efficiency (ηc)

% A

rea

chan

ge

-1

-0.8

-0.6

-0.4

-0.2

00 0.2 0.4 0.6

film cooling effectiveness (εf)

% A

rea

chan

ge



-1

-0.8

-0.6

-0.4

-0.2

00 0.001 0.002

TBC thickness (tTBC)

% A

rea

chan

ge

-1

-0.8

-0.6

-0.4

-0.2

01 1.5 2

Cooling Area (Ac)

% A

rea

chan

ge




-1

-0.8

-0.6

-0.4

-0.2

01000 2000 3000 4000

Gas Metal Heat tranfer coef. (hg)

% A

rea

chan

ge

-1

-0.8

-0.6

-0.4

-0.2

05000 6000 7000

Coolant-metal Heat Tran. coef. (hc)

% A

rea

chan

ge




-1

-0.8

-0.6

-0.4

-0.2

00.1 0.2 0.3

Mach Number (Me)

% A

rea

chan

ge

-1

-0.8

-0.6

-0.4

-0.2

0800 850 900

Coolant temperature. (Toc)

% A

rea

chan

ge




-0.5

-0.3

-0.1

0.1

0.3

0.51200 1300 1400 1500

Map Datum Temp. (Tmd)

% A

rea

chan

ge

-0.5

-0.4

-0.3

-0.2

-0.1

0

% A

rea

chan

ge

No cooling no filmno convective Cooling










§Acknolwdgements



Alteration of the flowAlteration of the flow--fieldfield• Flow filed altered due to heat addition to the flow:

• Local density variation → Inviscid flow field altered

• Alteration of boundary layer growth

• Key parameter identified

( )KinT1TT

S0

ww −=

Tw is the wall temperature and T0 is the temperature of the gas.



Alteration of the flowAlteration of the flow--field: encapsulated in discharge coefficientfield: encapsulated in discharge coefficient

0.88

0.9

0.92

0.94

0.96

0.98

1

-1 -0.5 0 0.5 1Sw=(Tw/T0-1)

Cd

0.990.980.960.940.92

Cd,adiab

D41

DRe08,71)C(

DadD

ll ′⋅+−=

( )

w0

w0

ad,D

D

TT22nTTn1

C1C1

−

−=

−− l

l



0

0.2

0.4

0.6

0.8

1

1.2

1.4

-0.5 -0.4 -0.3 -0.2 -0.1 0Sw=(Tw/T0-1)

δCD/C

D (%

)0.990.980.96

Cd,adiab

Discharge coefficient VariationDischarge coefficient Variation



Proposed procedure for incorporating the heat transfer effect Proposed procedure for incorporating the heat transfer effect on boundary layers (I)on boundary layers (I)

Perform calculations of Viscous flow with heat transfer in turbine passage (Navier Stokes Eqns)

to establish a correlation

( discharge coefficient) ↔ Sw



Sample result of Calculation in Turbine CascadeSample result of Calculation in Turbine Cascade

0 0.05

0.1 0.15

0.2 0.25

0.3 0.35

0.4

-0.25 -0.2 -0.15 -0.1 -0.05 0 Sw

Δm

%

Variation of mass flow rate through a cascade, for given inlet total to outlet static pressure ratio and different wall temperatures.



Discharge Coefficient VariationDischarge Coefficient Variation

Comparison of trends established by calculations and viscous flow solutions, to predictions according to the method of [11]

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

-0.25 -0.2 -0.15 -0.1 -0.05 0Sw=(Tw/T0-1)

δCD/C

D (%

).96

CD,ad=.99

.98

calculated



Example ApplicationExample Application

Map Change ↔Area change effect on turbine map

Results from Transient performance Calculation, Results from Transient performance Calculation, incorporating Heat Transfer effectsincorporating Heat Transfer effects



Effect Of Thermal Dilatation On PerformanceEffect Of Thermal Dilatation On Performance


0

0.3

0.6

0.9

1.2

1.5

0 1 2 3 4 5

FUEL

FLO

W (k

g/s)

5

10

15

20

25

0 1 2 3 4 5

HPC

SU

RG

E M

AR

GIN

WITHOUT HPT MAP CORRECTION

WITH HPT MAP CORRECTION-only BL effect

WITH HPT MAP CORRECTION-both effects



Effect Of Thermal Dilatation On PerformanceEffect Of Thermal Dilatation On Performance


0.2

0.3

0.4

0.5

0 1 2 3

FUEL

FLO

W (k

g/s)

5

10

15

20

0 1 2 3

TIME (s)

HPC

SU

RG

E M

AR

GIN

WITHOUT HPT MAP CORRECTION

WITH HPT MAP CORRECTION-only BL effect

WITH HPT MAP CORRECTION-both effects









§Acknolwdgements



Summary Summary -- ConclusionsConclusions

§ Heat Transfer Alters Turbine (mass flow) – (pressure ratio) characteristics, due to geometry changes and flow field alteration

§Geometry Changes can be estimated by assessing material temperatures (A possibility using simplified models has been proposed here)

§Flow field alteration can be expressed through change in the discharge coefficient which can be correlated to an appropriate paramter (S)

§Detailed calculation can be used to establish correlations whichare easily implantable in 1-d engine performance models



AcknowledgementsAcknowledgements

§ The authors would like to express their thanks to SNECMA for

financing the work that led to this paper and for allowing its

publication. Thanks are expresses to X. Ruiz, for many useful comments

and discussions.

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