multidisciplinary analysis of the operational temperature increase of turbine blades

Computational Materials Science xxx (2010) xxx–xxx

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Computational Materials Science

journal homepage: www.elsevier .com/locate /commatsci

Multidisciplinary analysis of the operational temperature increase of turbine bladesin combustion engines by application of the ceramic thermal barrier coatings (TBC)

T. Sadowski *, P. Golewski **

Faculty of Civil Engineering and Architecture, Department of Solid Mechanics, Lublin University of Technology, Nadbystrzycka 40 Str., 20-618 Lublin, Poland

a r t i c l e i n f o a b s t r a c t

Article history:Received 17 October 2009Received in revised form 7 May 2010Accepted 12 May 2010Available online xxxx

Keywords:Turbine bladesThermal barrier coating (TBC)Computational fluid dynamics (CFD)Computational structural mechanics (CMS)

0927-0256/$ - see front matter Crown Copyright � 2doi:10.1016/j.commatsci.2010.05.032

* Corresponding author. Tel.: +48 81 538 43 86; fax** Corresponding author. Tel.: +48 81 538 43 86; fax

E-mail address: [email protected] (T. Sadowski

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The improvement of the temperature resistance of the aircraft engine elements can be obtained by appli-cation of a single ceramic thermal barrier coating (TBC) (e.g. Noda [1]) or several composite layers (e.g.Sadowski [2]). Engine elements protected by TBC can work safely in elevated temperature range above1000 �C. Continuous endeavour to increase thermal resistance of engine the elements requires, apartfrom laboratory investigations, also numerical study of the different aero-engine parts. The most impor-tant are turbine blades, where high temperatures and stress concentrations during thermal shocks orthermal fatigue can be observed during engine exploitation. The high temperatures and stress concentra-tions can act as the local sources of damage initiation and defects propagation in the form of cracks.

The present paper deals with the solution of the transient temperature transfer problem in bare andthermal barrier coated alloy Inconel 713 for the temperature range up to 1000 �C. The computationalfluid dynamics (CFD) part of analysis was performed by application of ANSYS Fluent code receiving thetemperature field of combustion gas, whereas computational structural mechanics (CMS) part concerningthe temperature distribution inside the turbine blade was done by ABAQUS. Finally, the efficiency of theTBC layer (0.5 mm thickness) protecting and cooling channels was discussed in order to explore the oper-ational temperature increase in the aero-engines.

Crown Copyright � 2010 Published by Elsevier B.V. All rights reserved.

1. Introduction

Description of temperature transfer in the turbine blades(Fig. 1) is a very complex 3-D problem, which requires multidisci-plinary approach including both aerodynamic and structural anal-ysis. The problem can be solved by determination of:

� flow of the fluid around blades,� fluid-structural element interaction,� turbine blade response due to thermo-mechanical loading.

In general solution fluid and structural elements are simulated bycoupled system of equations. This leads to numerical difficulties,like: ill-conditioned nature of the coupled system of matrixes andarduous calculations. Therefore the problem can be decoupled i.e.the fluid and turbine blade can be simulated separately with appli-cation of computational fluid dynamics (CFD) and computationalstructural mechanics (CSM). In the CFD and CSM analyses FEMmeshes at the fluid–structure interface should be the same, other-wise one can apply for instant mapping surface method proposedin [3].

010 Published by Elsevier B.V. All

: +48 81 538 41 73.: +48 81 538 41 73.

).

P. Golewski, Comput. Mater. Sc

In the most general case the blades of the combustion turbineare subjected to:

� high mechanical pressure resulting mainly from: centrifugalforces as well as inlet gas-dynamics,� high gradient of the temperature field taking place in a very

short time,� internal cooling provided by advanced technique, which

includes ejection of a cooling medium from the blade tip.

The heat transfer problem is particularly important during begin-ning of the turbine start-up process, e.g. [4], in the short operatingtime, where the thermal shock takes place. Experimental evidencesand numerical results (e.g. [5–7]) lead to the conclusion that extre-mely high heat transfer rates are observed near the tip and on thetip of the blade. Therefore this part of the turbine blade needs tobe protected by:

� TBC in the form of single layer or several layers (e.g. [1,2,8–18]).� intensive cooling process.

To improve the reliability and durability of the blade, TBC and com-plex cooling system should be applied in the form of a row of chan-nels with the air cooling flow. The effective TBC and cooling designrequires a complete understanding of the flow and heat transfer

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Table 1Thermal conductivity coefficient km for main components of the exhaust gases (atpressure 1 bar).

T (�C) km (W/m �C)

CO2 H2O O2 N2

400 47,370 56,910 54,110 49,230500 55,220 69,790 60,780 55,070600 62,720 83,640 66,960 60,740700 69,910 98,230 72,870 66,210800 76,700 113,800 78,520 71,490900 83,220 129,830 83,520 76,590

1000 89,440 146,280 88,580 81,5101100 95,420 162,980 93,500 86,1801200 101,050 179,800 98,000 90,680

Table 3Dynamic viscosity coefficient g of main components of the exhaust gas at 1 barpressure.

T (�C) g ((Ns)/m2)

CO2 H2O O2 N2

400 29.91 � 10�6 23.90 � 10�6 36.77 � 10�6 31.21 � 10�6

500 33.16 � 10�6 27.72 � 10�6 40.14 � 10�6 34.02 � 10�6

600 36.20 � 10�6 31.45 � 10�6 43.27 � 10�6 36.64 � 10�6

700 39.06 � 10�6 35.10 � 10�6 46.22 � 10�6 39.11 � 10�6

800 41.77 � 10�6 38.64 � 10�6 49.00 � 10�6 41.43 � 10�6

900 44.35 � 10�6 42.10 � 10�6 51.64 � 10�6 43.64 � 10�6

1000 46.81 � 10�6 45.47 � 10�6 54.16 � 10�6 45.75 � 10�6

1100 49.17 � 10�6 48.74 � 10�6 56.57 � 10�6 47.77 � 10�6

1200 51.43 � 10�6 51.94 � 10�6 58.89 � 10�6 49.72 � 10�6

Fig. 1. Turbine blade and the TBC coating structure.

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characteristics in the whole analysed system, as crossing of admis-sible values of temperature or stress thresholds can lead to prema-ture waste or even to the immediate damage of the turbine blade(e.g. [13–17]) and further the whole engine.

The major task for designers is the continuous endeavour to in-crease the energy efficiency of the modern aircraft jet and indus-trial gas-turbine engines. It can be obtained by allowing for

Table 2Average specific heat cpg of the exhaust gas of normal fuel at constant pressure(p = 1013 � 105 N/m2).

Temperature (�C) cpg (kJ/kg �C)

0 1053100 1079200 1106300 1136400 1167500 1197600 1227700 1255800 1280900 1302

1000 13231100 13411200 13571300 1371

Please cite this article in press as: T. Sadowski, P. Golewski, Comput. Mater. Sc

higher operation temperature and the increase of the structuralintegrity blades by protecting the core from hot gas stress andother aggressive corrosion environment. Therefore the present pa-per deals with the solution of the transient temperature transferproblem in bare and thermal barrier coated alloy Inconel 713 forthe temperature range up to 1000 �C. The CFD part of analysiswas performed by application of ANSYS Fluent code to calculatethe temperature field of combustion gas, whereas CSM part con-cerning the temperature distribution inside turbine blade wasdone by ABAQUS. Finally, the efficiency of the protecting and cool-

Fig. 2. Characteristic dimensions of the blade cross-section.

Fig. 3. Finite element mesh in the CFD analysis (ANSYS Fluent).

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ing channels was discussed in order to explore the operationaltemperature increase in the aero-engines.

Fig. 4. Model of the CFD analysis.

a

b

Fig. 5. (a) Increase of the internal energy (J/kg) and


2. Basic formulas for analytic estimation of temperaturedistribution in the turbine blades

Determination of the temperature field in the blade of rotorwith analytic method is a fairly difficult and time-consuming prob-lem, because of complex shapes and boundary conditions of heatexchange. In order to define the temperature fields in engine parts,one should formulate boundary conditions of the third kind, i.e. itis necessary to know the temperature distribution of gas flowingover the turbine blade surface Tg, and the convective heat transfercoefficients a.

2.1. Temperature of the exhaust gas

The temperature field Tg in blades of the turbine rotor dependson the operating temperature of the exhaust gas T0:

Tg ¼ T0 �c2

1 � rtw21

2cpg; ð1Þ

(b) velocity increase of the exhaust gas (m/s).

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Fig. 7. Finite element mesh for CSM analysis (ABAQUS).


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where T0 is the temperature of the exhaust gas in front of the row ofblades in engine (�C), c1 is absolute speed of the outflow of the ex-haust gas from the nozzle (m/s), w1 is relative speed of the inflow ofthe exhaust gas on the blades of rotor (m/s), rt = 0.85�0.95 is coef-ficient of the temperature recovery, and cpg is the specific heat ofthe exhaust gas at the constant pressure (J/kg �C).

2.2. Heat transfer coefficients

Heat flows to the tongue of a blade from the exhaust gasthrough the whole boundary edges from the tip of blade to theshield of the rotor. Description of this process is possible by def-inition of the convective heat transfer coefficient a. Generally, adepends on the current temperature of the hot gas stream andchanges along the circuit and along the height of the blade ton-gue. The value of the convective heat transfer coefficient for manygases and liquids overflowing any engine part, is expressed byseveral characteristic numbers: Nusselt (Nu), Prandtl (Pr), Rey-nolds (Re). a (W/(m2 �C)) is calculated from the followingformula:

a ¼ Nukm

dh; ð2Þ

where

Nu ¼ CðPrAReBÞ: ð3Þ

Here, km is thermal conductivity of the heat transfer medium(W/(m �C)). The values km for the main components of the exhaustgas versus temperature are presented in Table 1.

For the mixture of gases, km is calculated from the followingformula:

km ¼Xn

i¼1

zikiPnj¼1zjUij

: ð4Þ

The accuracy of km estimation by formula (4) is approximately 4%. zi

is the molar part of the gas component ‘‘i”, whereas function Uij isequal to:

Uij ¼1ffiffiffi8p 1þMi

Mj

� ��0:5

1þ gi

gj

!0:5Mj

Mi

� �0:2524

35

2

: ð5Þ

One can point out that when i = j, then Uij = 1 as well as Uij – Uji. Mi

is the molar mass of the gas component ‘‘i”.

Fig. 6. Temperature (�C)


Moreover, in the formula (2) dh denotes the hydraulic diameter(the computational size), (m). C in relation (3) is a proportionalitycoefficient, whereas A, B are power indexes, all determinedempirically.

The Prandtl number Pr in (3) is equal to:

Pr ¼ cpggkm

; ð6Þ

where the values of specific heat cpg for the exhaust gas versus tem-perature were included in Table 2. g is the dynamic viscosity ofmedium, ((Ns)/m2). The values of g of the main components ofthe exhaust gas in relation to temperature are presented in Table 3.

For the mixture of gases, the dynamic viscosity coefficient is cal-culated from the following formula:

g ¼Xn

i¼1

zigiPnj¼1zjUij

: ð7Þ

The accuracy of g assessed by formula (7) is approximately equal to2%.

The Reynolds number Re in (3) was calculated according to:

Re ¼_mdn

g; ð8Þ

of the exhaust gas.

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Fig. 8. Temperature (�C) distribution for t = 200 s on the pressure side of the: (a) unprotected blade and (b) blade with TBC.

Fig. 9. Temperature (�C) distribution for t = 200 s on the suction side of the: (a) unprotected blade and (b) blade with TBC.


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where _m is a mass flow rate in (kg/s) and dn is a characteristiclength-scale parameter in (m).


The above presented formulas and data from Tables 1–3 wereapplied in numerical modelling of the problem, presented below.

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3. Numeric method of calculating temperature distribution inblades of the turbine

3.1. FEM models

To obtain the temperature of the exhaust gas flowing aroundthe blade surface the ANSYS Fluent 12 [19] commercial code wasapplied.

Pre-processing in numerical modelling was divided in threesteps:

1. Generation of the blade shape within ANSYS. In the paper, oneblade from the rotor of engine JP-67PL including 29 blades,made from alloy Inconel 713, was modelled. The characteristicshape and dimensions of the blade were shown in Fig. 2. Bladeswithout internal cooling and possessing cooling system in theform of set of channels were considered.

2. Creation of thin TBC layer (made of ZrO2 + 7 wt.% Y2O3, e.g. [8]).It was done with SolidWorks 2009 after importing data fromANSYS. In the first step 0.5 mm thickness side surface layer

Fig. 10. Temperature (�C) distributions and placement of chara

Fig. 11. Comparison of temperature change i


was removed from the blade and then surface of the bladewas be elongated in such a way that it cut solid figure, sepa-rately for the upper and bottom surface. Finally the blade con-sisted of two separate solids: core of blade and TBC. Then themodel was imported to program ABAQUS, [20].

3. Generation of the FEM mesh. A multi block structured grid(Fig. 3) of about 20,000 cells was adopted to discretize the com-putational domain. An H-type grid was used for both the inletand outlet blocks, while a composite J/O-grid was utilized forpassage block in order to reduce grid skewness and facilitatesolving the boundary layer around the blade.

3.2. Numerical examples

The CFD analysis was performed with ANSYS Fluent 12, usingdata from Tables 1–3 and data from literature. The followingparameters for the exhaust gas were introduced: density, heatcapacity, thermal conductivity and dynamic viscosity coefficient.Steady state solutions were computed using the k–e turbulencemodel along with scalable wall functions. The total pressure, the

cteristic points in the cross-section of the blade in t = 29 s.

n characteristic points chosen in Fig. 10.

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total temperature and the flow angle were fixed at the inflowboundary, while the average static-pressure was imposed at theoutflow. The walls were treated as smooth and adiabatic. The inlettotal pressure and total temperature were fixed at p = 101,325 Paand T = 1000 �C. Fig. 4 shows the blade placed in the flow channel,whereas Fig. 5 presents the variation of internal energy of the gasand its velocity. The red arrows indicate the characteristic placeswhere the considered functions reached the maximum values.The temperature distribution around the turbine blade was pre-sented in Fig. 6. The maximum of the function is in the frontal ver-tical edge of the blade.

CSM analysis was performed with ABAQUS after exporting tem-perature field obtained in CFD. Three models for structural analysiswere created:

Fig. 12. Temperature (�C) distributions in the bla


1. Unprotected turbine blade. For the creation of surface gases1240 DS4 elements were used, whereas the core blade wasmodelled by 29,730 of DC3D4 elements.

2. Protected by TBC turbine blade. TBC layer of 0.5 mm thicknesswas modelled by 103,982 of DC3D4 elements. Fig. 7 presentsthe mesh of finite elements for blade and TBC.

3. Protected by TBC turbine blade with additional system of fivecooling channels placed in the central part of the blade.

In the numerical modelling the simulation obeys transient heatingof the blade by flowing combustion gases. The unsteady tempera-ture increase was studied until 200 s. Temperature transfer in theturbine blade is very complex 3-D problem. In the real problem itis necessary to consider two kinds of heat exchange:

de cooled by system of channels (t = 200 s).

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1. The outflow of heat was simulated from the bottom part of theblade to the scarf, introducing the thermal conductivitycoefficient.

2. For the bottom surface of the blade, where convection to therotor took place, the heat transfer coefficient was defined.

The numerical results concerning distribution of temperatures forthe blade with TBC were presented in Fig. 8 (concerning the pres-sure side of the blade) and Fig. 9 (the suction side) after 200 s fromthe beginning of the heating. One can notice the significant reduc-tion of the temperature field due to ZrO2 + 7 wt.% Y2O3 TBC. In thetip of the blade, where maximum of the function takes place, thereduction of the temperature level is equal to 154.6 �C, i.e. the de-crease of the temperature due to introduction of the TBC is approx-imately equal to 18%. The temperature maps show lower values oftemperature on the bottom side of the blade – due to heat transferto the rotor.

Fig. 10 shows the top surface of the blade with temperature dis-tribution for t = 29 s. On this surface three points: A, B, C were cho-sen in order to plot the temperatures evolution in time t for the

Fig. 13. (a and b) Temperature difference DT (�C) for the characteristic points of the cropressure and suction sides.


unprotected blade and protected one. The variations of the temper-ature functions are presented in Fig. 11. One can observe highlynonlinear behaviour in the first 50 s. Steady state of temperaturedistribution takes place after 200 s. The most effective protectionis at the beginning of the heating process, where the differencesbetween corresponding points for unprotected and protectedblades are greatest. In the steady state after t = 200 s the appropri-ate differences are much less due to the heat absorption. This resultpoints out the significance of the suitable designed TBC for efficientimprovement of the structural element due to the thermal shock orthermal fatigue.

Fig. 12 presents the turbine blade without TBC, but addition-ally cooled by the system of five channels. For calculation itwas assumed, that the interaction between cooling medium andthe blade is described by surface film condition with convectionheat transfer coefficient a = 300 W/(m2 �C). The sink temperaturewas taken 100 �C at the advanced stage of heating. The tempera-ture distribution showed in Fig. 12 concerns the end of the heat-ing process, i.e. t = 200 s. Comparison with the results presentedin Figs. 8a and 9a for unprotected blade leads to the conclusion

ss-section (Fig. 12) between a cooling wall of channels and the blade surface on the

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that the system of cooling channels decreases the maximum tem-perature about 7.26%. It means that protection by TCB is moreeffective (Figs. 8b and 9b). However, the synergism of both ana-lysed effects gives the very high level of reduction of the maxi-mum temperature about 25%. More detailed information in theseveral characteristic lines across the channels presents Fig. 13.DT is the temperature difference between a cooling holes walland the bucket surface at both suction and pressure sides. Ascan be seen from Fig. 13 the temperature gradients have similartendency for all crossing lines as gas flow temperature increases.The largest temperature gradients in the considered cross sectionare observed for lines s2-sh2, p2-ph2, p3-ph3 and s3-sh3. The re-gion between the cooling channels two and three is the thickestzone of the blade. Therefore it generates the largest temperaturegradients in the cross section and it is the reason that thermal fa-tigue cracks can be created, e.g. [21]. The smallest temperaturedifferences are registered along the lines p5-ph5 and s5-sh5. Thisis due to the fact that the blade wall has the smallest thickness.The maximum temperature gradients appear between points of

Fig. 14. Temperature difference DT (�C) for the characteristic points of the cross-sectionblade with the system of cooling channels.

Fig. 15. Temperature difference DT (�C) for the characteristic points of the cross-sectionblade without the system of cooling channels.


leading and trailing edges of the cross section. This difference isequal to 267 �C for t = 200 s. It is important to notice that trailingedge temperature is much higher in comparison to the leadingedge. Fig. 14 presents the similar temperature gradients for corre-sponding points at pressure and suction side of the bucket. Themaximum values are two times smaller in comparison toFig. 13. The comparative calculations were done for the bladewithout cooling system. Fig. 15 shows variation in time of tem-perature gradients in the same cross lines. The curves shapesare quite different in case of lines p4-s4 and p5-s5. Moreover,the sign changes from plus to minus.

The represented numerical results indicate that the thermalheat transfer in the turbine blades is very complex problem, dueto the fact that internal structure of the blades is build up fromthe core material, coating and system of cooling channels. The tem-perature fields in the blade vary in time, but the tip of the airfoil isthe most exposed to the thermal gradients. The maximum temper-ature appears on the trailing edge. The application of TBC and cool-ing system of channels reduce the maximum temperature about

(Fig. 12) between the blade surface on the pressure and suction sides for the turbine

(Fig. 12) between the blade surface on the pressure and suction sides for the turbine

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25%. This results in significant increase of the operation tempera-ture in the turbines of aero-engines.

4. Conclusions

Multidisciplinary analysis of the thermal heat transfer of theturbine blades in combustion engines was done. Two kinds of theturbine blades: unprotected and protected by the ceramic thermalbarrier coatings (TBC) were analysed. The problem was solved intwo steps by CFD and CSM analysis. The major conclusions aresummarised as follows:

� the temperature transfer in the turbine blade is very complex 3-D problem, which depends on thermo-mechanical properties ofthe applied composites, shapes of the analysed blades andboundary conditions of heat transfer process,� application of 0.5 mm thickness YSZ thermal barrier coating sig-

nificantly reduces the operation temperature – in the analysednumerical example about 18%,� the system of cooling channels leads to significant reduction of

the maximum surface temperature – about 7% in the numericalexample.

The total reduction of the TBC and the system of cooling chan-nels is very effective. Presented numerical results estimate thiseffectiveness at the level of 25%, i.e. the increase of the operationaltemperature of the engine can be significant or life-time of the safeexploitation can be prolonged. It is important in case of crack ini-tiation and propagation under thermal shock or thermal fatiguein TBC.

Acknowledgement

The research leading to these results has received funding from:(1) Financial support of Structural Funds in the Operational Pro-


gramme - Innovative Economy (IE OP) financed from the EuropeanRegional Development Fund - Project ‘‘Modern material technolo-gies in aerospace industry”, No. POIG.0101.02-00-015/08 is grate-fully acknowledged. (task: ZB-10: Modern thermal barriercoatings for critical parts of engines), (2) The European Union Sev-enth Framework Programme (FP7/2007 – 2013), FP7 - REGPOT –2009 – 1, under Grant agreement No. 245479.

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multidisciplinary analysis of the operational temperature increase of turbine blades

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