Thermal Barrier Coating and Turbulence Intensity Effects ... · THERMAL BARRIER COATING AND...

THERMAL BARRIER COATING AND TURBULENCE INTENSITY EFFECTS ON LEADINGEDGE COOLING USING CONJUGATE HEAT TRANSFER ANALYSIS

Prasert Prapamonthon, Huazhao Xu, Zhaoqing Ke, Wenshuo Yang and Jianhua WangSchool of Engineering Science, University of Science and Technology of China, Hefei, China

E-mail: [email protected]; [email protected]

Received September 2016, Accepted January 2017No. 16-CSME-112, E.I.C. Accession 3998

ABSTRACTThis is a numerical study of thermal barrier coating (TBC) and turbulence on leading edge (LE) cooling of aguide vane. Numerical results were carried out using 3D CFD with conjugate heat transfer analysis. Impor-tant phenomena were revealed. (1) TBC is effective in the LE region especially when free stream turbulence(Tu) increases. (2) At each Tu, TBC near the hub of the vane provides the most effective protection and atthe highest Tu, TBC improves overall cooling effectiveness there by about 25%. (3) Near the exits of filmhole, TBC may have negative effect, because of heat transfer impedance from the solid structure into themixing fluid between mainstream and cooling air emitted from film holes.

Keywords: turbulence intensity; cooling effectiveness; thermal barrier coating.

REVÊTEMENT ISOLANT THERMIQUE ET LES EFFETS DE L’INTENSITÉ DE LATURBULENCE SUR L’ANALYSE DU TRANSFERT DE CHALEUR COMBINÉ AU

REFROIDISSEMENT DU BORD D’ATTAQUE

RÉSUMÉNous présentons une analyse numérique du revêtement isolant thermique (TCB), et la turbulence sur lebord d’attaque de l’aube directrice (LE). Les analyses sont faites en utilisant CFD en 3D combiné avec letransfert de chaleur. Des phénomènes importants ont été constatés. (1) TBC est efficace dans la région dubord d’attaque spécialement quand la turbulence du fluide libre augmente. (2) À chaque turbulence, TBCprès du moyeu de l’aube procure la protection la plus efficace, et au plus fort de la turbulence TBC améliorel’efficacité totale du refroidissement de près de 25%. (3) Près de la sortie du trou du film, TBC peut avoirun effet négatif à cause de l’impédance du transfert de chaleur de la structure solide dans le mélange entrele fluide et le courant dominant et l’air refroidi disséminé par les trous.

Mots-clés : intensité de la turbulence; efficacité du refroidissement; revêtement isolant thermique.

Transactions of the Canadian Society for Mechanical Engineering, Vol. 41, No. 2, 2017 249

NOMENCLATURE

cp, f specific heat capacity of fluid (J/kg K)cp,m specific heat capacity of solid (J/kg K)cp,T BC specific heat capacity of TBC (J/kg K)h heat transfer coefficient without TBC, at vane surface and mainstream (W/m2K)hT BC heat transfer coefficient with TBC, at TBC surface and mainstream (W/m2K)∆h difference between heat transfer coefficient without and with TBC (W/m2K)k f thermal conductivity of fluid (W/mK)km thermal conductivity of solid (W/mK)kT BC thermal conductivity of TBC (W/m K)Ma Mach numberP pressure (Pa)PT total pressure (Pa)PS static pressure (Pa)PR pressure ratio [PR = PT/PS]qflux heat flux between solid and fluid interfaces (W/m2)R percentage of metal temperature reduction (%)T metal surface temperature without TBC (K)Tc,inlet inlet temperature of cooling air (K)Tref temperature at reference (709 K)TT BC metal surface temperature with TBC (K)TW local wall temperature (K)T∞ inlet temperature of mainstream (K)T ′ TBC surface temperature (K)Tu free-stream turbulence intensity (%)(

∂T∂n

)w=0

temperature gradient at interfaces (K/m)

∆T difference between metal surface temperature without and with TBC (K)

Greek symbolsρ f density of fluid (kg/m3)ρm density of solid (kg/m3)ρT BC density of TBC (kg/m3)φ overall cooling effectiveness on metal surface without TBCφT BC overall cooling effectiveness on metal surface with TBC∆φ difference between overall cooling effectiveness with and without TBC

1. INTRODUCTION

An increment of thermal efficiency and power output of gas turbines can be achieved through increasingturbine inlet temperature (TIT). However, TIT is limited by the allowable temperatures of current materials.To maintain a reasonable operating life of gas-turbine airfoils, film cooling and thermal barrier coating(TBC) have been widely used in modern gas turbine engines. With advances in numerical simulations, thetechnique of computational fluid dynamics (CFD) with conjugate heat transfer (CHT) analysis has beenwidely applied in gas-turbine fields.

Ni et al. [1, 2] and Mazur et al. [3] deemed that CHT analysis have the following three advantages,firstly, this analysis can provide not only a better understanding on the mixing process of cooling air withmainstream, but also the temperature variation within solid structures; secondly, the results obtained by thisanalysis are able to be easily incorporated into routine analysis of durability; lastly, CHT analysis can givea more accurate approximation of convective boundary conditions, in comparison with given isothermal

250 Transactions of the Canadian Society for Mechanical Engineering, Vol. 41, No. 2, 2017

boundary conditions. Therefore, CHT analysis was used to predict cooling performances of turbine vanesin their works.

Zhang et al. [4] used CHT analysis with thee turbulence models i.e. realizable k-ε , SST k-ω , andV2F models to study cooling performances of the guide vane reported by Timko [5] by comparing coolingeffectiveness obtained by CHT analysis with adiabatic assumption. Their comparisons indicated that heatconduction predicted by CHT analysis uniformly promoted cooling performance. The usable experimentaldata of C3X and Mark II, two cooled vanes of NASA reported by Hylton et al. [6], have been widelyused to validate numerical results obtained by CHT analysis. Yoshiara et al. [7] simulated the aero-thermalcharacteristics of C3X and Mark II using CHT analysis with Spalart-Allmaras, SST k-ω , and SST k-ωcoupled with γ-Reθ transition turbulence models. They found that the numerical results predicted by thethree models gave quite good agreements with the experimental data. Zhang et al. [8] used CHT analysiswith SST k-ω , SST & AGS, and SST & γ-Reθ turbulence models to investigate the cooling characteristicsof Mark II. They concluded that SST & γ-Reθ model improved the prediction accuracies of temperature andheat transfer coefficients in the laminar zone near leading edge (LE).

However, few studies have considered thermal resistance effect of TBC on the gas-turbine airfoils usingCHT analysis thus far. In the previous studies, Bohn and Becker [9] investigated the effect of TBC on theaero-thermal characteristics of Mark II using CHT analysis with a turbulence model provided by Baldwin–Lomax [10]. They found that the relative temperature on the external surface of the coated vane was higherthan that of the uncoated vane about to 4.4%, and the maximum heat transfer coefficient occurring in theshock area on the suction side (SS) was reduced by TBC about 15%, but TBC could not reduce the heat fluxinto the whole vane. With the same simulation approach, Bohn and Tümmers [11] investigated the effectsof TBC and cooling air mass flow on thermal stresses of Mark II coated with two layers of TBC, the topcoating was ZrO2 with a thickness of 0.125 mm, and the bond coating was MCrAlY with a thickness of0.06 mm. They declared that although TBC surface temperature rose, below TBC, the metal temperaturewas reduced and equalized simultaneously. Additionally, the influence of reduction in cooling air massflow on the thermal stresses in the solid structure was significantly lower than the influence of TBC. UsingCHT analysis with SST k-ω turbulence model, Alizadesh et al. [12] studied the effects of the thickness andthermal conductivity of TBC on a turbine blade. They concluded that adding a 0.2 mm of TBC thicknessreduced the blade averaged and maximum temperatures of about 19 and 34 K, respectively. Moreover, therise in thermal conductivity of TBC from 1 to 3 W/(mK) increased the blade averaged temperature about10 K.

As referred by Undapalli and Leylek [13], film cooling performances were influenced by many factors,such as configuration of film holes, adverse pressure gradient, boundary layer thickness and free streamturbulence. Among these factors, Boyle et al. [14] pointed out that turbulence intensity (Tu) and turbulencelength scale could be physically significant. Mayhew et al. [15] predicted that Tu of real gas turbineswas usually in a range of 10–20%. Ou and Han [16] experimentally investigated the effects of Tu on filmeffectiveness and heat transfer coefficient in the LE of a cylindrical leading edge model, at Tu = 0.75, 5.07,and 9.67%, and blowing ratios of 0.4, 0.8, and 1.2. They concluded that when Tu increased, heat transfercoefficient increased, and film effectiveness decreased, but at high blowing ratios, the effects of Tu werereduced. Besides, Ekkad et al. [17] studied film effectiveness and heat transfer coefficient of a cylindricalleading edge model using a transient liquid crystal technique. They found that at lower blowing ratios, ahigher Tu might reduce film effectiveness, but this effect was not significant at higher blowing ratios. Ames[18, 19] experimentally investigated the influences of Tu (Tu = 1–12%) on cooling performances of C3X,and they found that the higher Tu evidently augmented the averaged heat transfer coefficient on the pressureside (PS), and reduced film effectiveness and quickened the dissipation of film effectiveness on SS. Tholeet al. [20] investigated experimentally the heat transfer performances of a first stage nozzle guide vane at


Tu = 0.6 and 19.5%. Their results indicated that when Tu was at 19.5%, heat transfer coefficient achievedthe largest value in stagnation region.

Up to now, rarely has the use of numerical techniques with CHT analysis to investigate the combinedeffects of Tu and TBC on cooling performance of the gas-turbine airfoils been reported. The objective ofthis work is to study and provide a better understanding of the effects of Tu and TBC on surface temperature,heat transfer coefficient and overall cooling effectiveness in the LE region and its vicinity of a film-cooledturbine vane with a technical aspect of the numerical simulation using CHT analysis. Furthermore, thiswork can be practically applied by gas-turbine engineers to obtain better design of gas-turbine vanes andimprovement of cooling performances in the LE region and its vicinity when the film-cooled vanes coatedwith TBC operate under real conditions with various Tus of hot gas from the combustion chamber.

2. THERMAL PARAMETERS

Three important thermal parameters used in this work are as follows:

(a) The heat transfer coefficient; it is defined by

h =qflux

T∞−Tw=−k f

(∂T∂n

)w=0

T∞−Tw(1)

where

Tw =

{T, vane without TBCTT BC, vane with TBC

a negative h means that qflux transfers from the vane surface to the mainstream, on the other handwhen qflux transfers from the mainstream to the vane surface, h is positive.

(b) Overall cooling effectiveness, this parameter is used to describe the normalized solid temperatureunder a wall with heat conduction. It is calculated by

φ =T∞−Tw

T∞−Tc,inlet(2)

where

Tw =

{T, vane without TBCTT BC, vane with TBC

(c) The percentage of metal temperature reduction, this parameter is used to evaluate the ability of TBCto protect metal surfaces from the hot gas. This is defined by

R =

(∆TT

)×100% =

(1− TTBC

T

)×100%. (3)

Since TTBC is always lower than T , R is always positive.

3. VANE CONFIGURATION

The film-cooled guide vane used in this work is adapted from Timko [5]. It is a slightly twisted vane with aspan of 4 cm. There are 7 film-hole rows in the LE and its vicinity, as shown in Fig. 1a, two rows are placedon the LE (LE1 and LE2), two rows are located on the SS (SS1 and SS2), and three rows are positioned on


Fig. 1. (a) Vane configuration; (b) its cross-section area at 52.5% midspan.

Fig. 2. Temperature distributions along vane surface at midspan.

the PS (PS1, PS2, and PS3). Each row has 12 film holes with an equal distance of 1 mm. All of the filmholes are cylindrical with the same diameter of 0.48 mm, and the same angle of 45◦ as reported by Nasiret al. [21]. There are two cavities, aft and forward cavities in the vane to supply coolant. This numericalstudy focuses on the cooling performances in the LE and its vicinity limited within the region of 0≤ x/C0.4,0≤ y/D≤ 0.4, and 0≤ z/H ≤ 1, as shown in Fig. 1.

4. COMPUTATIONAL PROCEDURES

4.1. Computational StrategyThe commercial software, ANSYS ICEM V.15, is used to generate computational grids. To achieve a highquality, the entire calculation domain is decomposed into five blocks, i.e. mainstream, film hole, forwardcavity, aft cavity, and solid vane. The grids in each block are hexahedral. O-grid is used to improve all gridsnear the surfaces to suffice for resolving fluid flow in boundary layer. To confirm the grid independence ofnumerical results, three strategies with grid elements of 4,834,244 (4.8M), 5,123,256 (5.1M), and 6,489,129(6.4M) are tested.

Figure 2 exhibits the metal surface temperature distributions along the vane’s midspan. Most portions ofthe numerical results in 5.1M and 6.4M give acceptable agreements, and the highest difference is less than


Fig. 3. Computational grid.

Table 1. Properties of TBC material.Property Value

ρTBC 5500 kg/m3

cp,TBC 418 J/kgKkTBC 1.04 W/mK

Table 2. Specific heat capacity and thermal conductivity of air and steel.Specific heat capacity (J/kg K) Thermal conductivity (W/m K)

Air cp, f = 938+0.196T k f = 0.0102+5.8×10−5TSteel cp,m = 438.5+0.177T km = 11.2+0.0144T

2%. Therefore, it is not necessary to further the elements, and it is reasonable to use the grid with 5.1Melements in the following calculations.

Figure 3 shows some computational grids in mainstream, two cavities, film hole, and solid vane. Theaveraged and the minimum quality of the whole computational grid are about 0.7815 and 0.135, respectively.

4.2. Computational SetupThe commercial software, FLUENT V.15, with SST k-ω turbulence model, the pressure-based segregatedalgorithm, and SIMPLE method are used in this work. The discretization scheme with second order ac-curacy is utilized in all fluid and solid regions. In order to increase the accuracy of the results, low-Recorrections, compressibility effect, curvature correction, viscous heating, and production limiter are con-sidered. Equations of mass, momentum and energy are solved within fluid domains, but in solid domain,only the energy equation based on Fourier’s law is solved. Convergence criteria of the results are that theresidual values of the scaled energy and continuity equations must be less than 10−6 and 10−3, respectively.To confirm the convergence, mass flow rate balance between all inlets and outlet, and residual histories oftemperature at six monitor points on the vane surfaces are checked. The coupled wall option is applied atfluid-solid interfaces to ensure that the heat flux and temperature on both fluid and solid sides are equivalent.

To combine the effect of TBC, TBC made of typical ZrO2 with a thickness of 0.3556 mm is used, asreferred by Halila et al. [22]. Due to the thin thickness of TBC, only 1D heat conduction equation is solvedin TBC. It this study, a bond coat is not considered in all calculation, the bond coat is presumed to be a partof the vane surface with a relatively thin thickness. Consequently, it cannot have a major role in conductiveheat transfer through the wall. The physical properties of TBC used in this study are listed in Table 1.

Air with the ideal gas assumption is used as working media in the mainstream and coolant, the vaneis made of steel with a density of 8055 kg/m3, and the thermal properties of the air and steel within atemperature range from 339 to 1000 K are calculated by the equations given in Table 2.


Table 3. Boundary conditions used in this work.Boundary ConditionMainstream inlet T = 709K, PT = 344.74 kPa, Tu = 3.3, 10, and 20%Mainstream outlet Pressure-outlet, PR = 1.67Forward cavity inlet Tc,inlet = 339 K, PT = 350.95 kPaAft cavity inlet Mass flow rate, 0.007 kg/s

Fig. 4. Boundary conditions.

Fig. 5. Mach number distributions along vane surface at midspan.

4.3. Boundary ConditionsThe experimental conditions reported by Timko [5] are used as the simulation conditions, as listed in Table 3.

As shown in Fig. 4, periodic condition at two side surfaces, adiabatic and non-slip wall conditions at thetop and bottom of the entire mainstream domain are used.


Fig. 6. Temperature distributions at three Tus.

4.4. Validation of Numerical MethodTo validate numerical method, the experimental data obtained by Timko [5] at PR = 1.67 are used. CHTsimulation is carried out by SST k-ω turbulence model. Figure 5 presents a comparison between Machnumber (Ma) distributions along the vane’s midspan predicted by the numerical method against the Maobtained by the experimental approach.

It is clear, on the PS in the region −0.4 < x/C < 0, and on the SS in the region 0 < x/C < 0.05, thenumerical results exhibit a very good agreement with the experimental data. On the SS, after x/C = 0.04, the


Fig. 7. Contours of ∆T at three Tus.

difference between experimental and numerical results increases with the maximum averaged error about10%. This validation seems reasonable and acceptable. Therefore, in the following simulations, CHTanalysis with SST k-ω turbulence model at PR = 1.67 is used.

5. RESULTS AND DISCUSSIONS

5.1. Effects of TBC and Tu on Temperature DistributionsFigure 6 presents temperature distributions over TBC surface (T ′), on the metal surface without TBC(T ),and on the metal surface with TBC (TTBC) at three Tus. From the three series of Fig. 6, one can find thefollowing three important phenomena: (1) At the same Tu,T ′ is always the highest, and TTBC is alwayslower than T , and T ′ countor is quite different from T countor, but T ′ countor is similar to the temperaturedistribution obtained by adiabatic assumption in our past work [23]. This phenomenon is reasonable becausethe very large thermal resistance of TBC blocks heat flux transferring into the solid structure. (2) At eachTu, the maximum temperatures of T ′,T and TTBC always happen in the tip region of the vane because thisregion is the hardest region to be cooled by cooling air. (3) When Tu increases, the regions with highertemperatures, especially near stagnation line, extends significantly. The reason for this pheomenon is that itis more difficult to cool these regions by cooling air when the level of Tu is elevated.

For distinguishing the real TBC effect, Figs. 7a–c are used, which show the temperature differences,∆T = T −TTBC, at three Tus. From these figures, one can find two important phenomena: (1) ∆T is alwaysgreater than zero. It means that TBC plays a positive role of thermal protection. Furthermore, the maximum∆T happens near the hub region of the vane, namely the maximum ∆T is about 36, 38 and 42 K at Tu = 3.3,10, and 20%, respectively. This is expected because the hub region is closest to the coolant inlet of theforward cavity, which has the lowest temperature. (2) With increasing in Tu, this positive role is moresignificant.

Figure 8 exhibits a quantitative comparison of TBC effect in term of the percentage of temperature reduc-tion, R, at 52.5% span. From this figure, one can find that at each Tu,R decreases in streamwise direction,and R gradually decreases after PS3, but drastically decreases after SS2. When Tu increases, R increasesin general, and the increment of R in the region from PS3 to stagnation line is larger than that in the regionfrom SS2 to stagnation line. This can be explained by the fact that the increase in T and TTBC in the regionfrom PS3 to stagnation line is more serious than that in the region from SS2 to stagnation line, as shown inFig. 9. Additionally, R can achieve the highest value about 6.8% at Tu = 20% and about 5.8% at Tu = 3.3%near stagnation line. Therefore, the TBC technique is effective in LE, and the thermally protective effect onthe PS is better than that on SS, especially near stagnation line and at higher Tus.


Fig. 8. Distribution of R at 52.5% span.

Fig. 9. Effects of Tu on T and TTBC at 52.5% span.

5.2. Effects of TBC and Tu on Heat Transfer CoefficientFigure 10 illustrates distributions of heat transfer coefficients on the metal surface without TBC(h) and overTBC surface (hTBC) at three Tus.

It is clear that at the same Tu,h and hTBC are similar in general, but most hTBC are lower than h. Therelatively higher h and hTBC exist in LE, as marked as region 1. The highest h and hTBC appear nearthe tip and the hub of the vane, as indicated in regions 2 and 3, respectively. This is reasonable becausethese regions are hardly cooled by the cooling air ejected from film holes. When Tu increases, h enlargesmuch more rapidly than hTBC in the three regions. This can be explained by the fact that in these regionsthe boundary layer is very thin and the cooling air ejected from film holes is hardly to form an effectivecoverage film at higher Tus. Therefore, TBC can play an important role to reduce the effect of Tu throughits very large thermal resistance.

Figure 11 shows a comparison between h and hTBC distributions from LE2 to SS2, at Tu = 10%, asmarked as region X in Figs. 10b and 10e. The difference between h and hTBC conspicuously appears near


Fig. 10. Contours of (a–c) h and (d–f) hTBC at three Tus.

Fig. 11. Contours of region X in Figs. 10b and 10e at Tu = 10%.

the exits of film hole LE1, SS1, and SS2, i.e. h and hTBC are negative, but h is lower than hTBC. Thisphenomenon may be explained by the fact that on the surface with TBC, the thermal load transferring fromthe solid vane into cooling air-mainstream mixing fluid in these regions are reduced by the lower thermalconductivity of TBC.

This phenomenon can be more explained by Fig. 12, which presents the differences between h and hTBC,∆h = h− hTBC, at three Tus. A positive value of h means that TBC blocks the heat flux from mainstream


Fig. 12. Effect of TBC on ∆h at three Tus.

Fig. 13. Contours of (a–c) φ and (d–f) φTBC at three Tus.

entering the vane structure, and TBC plays a positive role; whereas a negative value means that TBC blocksthe heat releasing from solid vane into the mixing fluid of cooling air and mainstream, at this time TBCplays an opposite role. From Fig. 12, one can observe that for all Tus, h is positive in most regions, but nearthe exits of film hole LE1, SS1, and SS2, is negative. Therefore, although TBC technique is effective in theLE region, TBC can block the heat releasing from solid structure into the mixing fluid close to the exits offilm holes, this is a negative effect. This remarkable difference can be also observed at Tu = 3.3 and 20%.


Fig. 14. Effects of TBC on ∆φ at three Tus.

5.3. Effects of TBC and Tu on Overall Cooling EffectivenessFigure 13 shows contours of overall cooling effectiveness on the metal surface of the vane without TBC(φ)and with TBC(φTBC) at the three Tus. At the same Tu, it is clear that φ is always lower than φTBC becauseTTBC is always lower than T . Generally, φ and φTBC decrease with an increase in Tu, and the reduction of φ

is more than that of φTBC.Figure 14 illustrates the effect of TBC and Tu on the increment of overall cooling effectiveness, ∆φ =

φTBC− φ , at the three Tus. It is clear that when Tu increases, the increment of ∆φ rises. The maximum∆φ exists at the hub of the vane, where ∆φ can reach a value of 0.11 or the reduction of the metal surfacetemperature is about 40–42 K at Tu = 20%. This phenomenon indicates that TBC can increase overallcooling effectiveness about 25% at the hub of the vane near the LE at the highest Tu.

6. CONCLUSIONS

This paper presents a numerical investigation on the cooling performances in the LE and its vicinity of a filmcooled vane with TBC at three Tus using 3D CFD technique with CHT analysis in FLUENT V.15. Only 1Dheat conduction in TBC is considered because the thickness of TBC is very thin. Through the discussionand analysis of numerical results, the following conclusions can be drawn:

1. TBC is effective in the LE and its vicinity, especially when the level of Tu of the mainstream increases.

2. At each Tu, TBC at the region near the hub of the vane gives the most effective thermal protectionagainst thermal load.

3. At the highest Tu, TBC can reduce the metal surface temperature at the region near the hub about40–42 K, this leads to the improvement of overall cooling effectiveness at that region about 25%.

4. In the vicinity of the LE, the ability of TBC on the PS is better than that on the SS, this phenomenonis clearer at higher Tus.

5. Near the exits of film holes, TBC may play a negative effect, because TBC may block the heat releas-ing from solid structure to the mixing fluid between cooling air and mainstream.


ACKNOWLEDGMENTS

The research is supported by the Natural Science Foundation of China (contract no. 51376168). The firstauthor is grateful to Chinese Academy of Sciences and World Academy of Sciences for the CAS-TWASPresident’s Fellowship Programme to support his PhD study and research at the University of Science andTechnology of China.

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