Investigation of Cooling Performances of a Non-Film-Cooled Turbine Vane Coated with a Thermal Barrier Coating Using Conjugate Heat Transfer

The aim of this paper is to numerically investigate cooling performances of a non-film-cooled turbine vane coated with a thermal barrier coating (TBC) at two turbulence intensities (Tu = 8.3% and 16.6%). Computational fluid dynamics (CFD) with conjugate heat transfer (CHT) analysis is used to predict the surface heat transfer coefficient, overall and TBC effectiveness, as well as internal and average temperatures under a condition of a NASA report provided by Hylton et al. [NASA CR-168015]. The following interesting phenomena are observed: (1) At each Tu, the TBC slightly dampens the heat transfer coefficient in general, and results in the quantitative increment of overall cooling effectiveness about 16–20%, but about 8% at the trailing edge (TE). (2) The protective ability of the TBC increases with Tu in many regions, that is, the leading edge (LE) and its neighborhoods on the suction side (SS), as well as the region from the LE to the front of the TE on the pressure side (PS), because the TBC causes the lower enhancement of the heat transfer coefficient in general at the higher Tu. (3) Considering the internal and average temperatures of the vane coated with two different TBCs, although the vane with the lower thermal conductivity protects more effectively, its role in the TE region reduces more significantly. (4) For both TBCs, the increment of Tu has a relatively small effect on the reduction of the average temperature of the vane.


Introduction
The performance of a gas turbine engine is evaluated by two thermomechanical quantities, that is, thermal efficiency and output power.A key factor to obtain this performance is that turbines' airfoils need to be able to operate under serious circumstances from high thermal loads at the turbine inlet.Therefore, thermal barrier coatings (TBCs) and cooling techniques (internal cooling and film cooling) are widely used in advanced gas turbines to thermally protect the airfoils, to maintain and prolong a useful life of the airfoils, from the turbine inlet temperature (TIT).However, the cooling techniques are limited by cooling air consumption.Hence, TBC is essential for the airfoils as an insulator to avoid direct contact with hot gases.In fact, several factors may influence the protective ability of TBC, that is, thermal conductivity, thickness, porosity, phase stability, surface roughness of the TBC, temperature of the hot gas, matching of thermal expansion coefficients with the metal surface coated with TBC, and coating method.Meier and Gupta [1] highlighted that the TBC could be applied to reduce the surface temperature of a turbine part by 167 • C. Maikell et al. [2] experimentally investigated the TBC effect on overall effectiveness of a leading-edge model based on cylindrical geometry.They found that at the interface of the TBC, the TBC significantly increased overall effectiveness.Boyle [3] studied the effects of TBC on improving the thermal efficiency of an engine; he concluded that TBC had an impact on vane sensitivity to the external heat transfer coefficient.Boyle and Senyitko [4] indicated that the presence of TBC added the skin roughness, which was a physical factor of TBC, and had significant results on the heat transfer rate on the turbine vane surface.
Recently, the technique of computational fluid dynamics (CFD) with fluid-solid interaction analysis, also called conjugate heat transfer (CHT), has been commonly used by many researchers [5][6][7][8][9] to obtain a better understanding of the phenomena of fluid flow and heat transfer happening from fluid-solid interfaces in gas turbine engines.Furthermore, CHT analysis has been applied to predict the effect of TBC on thermal and mechanical phenomena of turbine airfoils, also, Na et al. [10] used CHT analysis with realizable k-ε turbulence to study the effects of TBC on a flat plate model with cylindrical holes.They indicated that TBC reduced the lateral conductive heat transfer of the surface.Also, TBC made temperature gradients more discrete under the coolant jets.Bohn and Becker [11] both aerodynamically and thermally investigated the Mark II vane reported by Hylton et al. [12], the vane without TBC and with TBC with a constant thickness of 0.3 mm of ZrO 2 , using a 3D CHT approach with the Baldwin-Lomax turbulence model [13].They found that TBC resulted in the reduction of the surface temperaturesabout 27-43 K in the shock area on the suction side (SS) and about 20-29 K in the stagnation area.With the same simulation technique, Bohn and Tümmers [14] expanded their work by studying thermal stresses in the vane under the effects of mass flow rate of coolant and TBC.They used the Mark II vane coated with two layers of TBC: a constant thickness of 0.125 mm of ZrO 2 as the top coat (TC) and 0.06 mm of MCrAlY as the bond coat (BC).They indicated that the influence of the TBC was significantly higher than that of the reduction of coolant mass flow.Alizadeh et al. [15] investigated the effects of thermal conductivity and thickness of TBC on the temperature sensitivity of a turbine blade with internal cooling, using CHT analysis with the SST k-ω model.They concluded that the inclusion of a 0.2-mm thickness of TBC resulted in a 34 K and 19 K drop in the maximum and average blade temperatures, respectively.Moreover, the blade average temperature could be increased about 10 K when the thermal conductivity of the TBC changed from 1 W/m•K to 3 W/m•K.Yongbin et al. [16] used CHT analysis with an SST k-ω model to investigate the effects of TBC and the mass flow rate of cooling air on a gas turbine blade coated with a uniform TBC thickness of 0.3 mm.Their results indicated that the TBC effect was weakened in the trailing edge (TE), but the TBC played a major role in the region cooled effectively by internal cooling.Rossette et al. [17] used CHT analysis with the turbulence model of Spalart-Allmaras [18] to aerodynamically and thermally investigate the performances of a gas turbine blade coated with TBC.They concluded that the inclusion of a thickness of about 100-400 µm of TBC reduced the surface temperature of the blade by as much as 200 • C, and using TBC reduced 36% of the coolant need to maintain the creep life of the blade material.
Incidentally, one recognizes that turbulence intensity (Tu) and turbulence length scale (Lu) are physical factors that play prominent roles in the performance of a film-cooled turbine airfoil and flow field.In fact, real gas turbine engines are frequently run under Tu by about 10% to 20%, as predicted by Mayhew et al. [19].Effects of Tu on the performance of film cooling of the turbine vanes and blades, flat plate, and cylindrical leading-edge models were numerically and experimentally investigated by many groups of researchers [20][21][22][23][24][25][26][27][28].However, few experimental and numerical studies have hitherto been focused on a real situation regarding the cooling performances of turbine airfoils from simultaneous effects of TBC and Tu.Davidson et al. [29] experimentally investigated TBC and film cooling on the C3X scaled up 12× at Tu = 0.5% and 20%.Their results indicated that with no film cooling, TBC increased the overall effectiveness by as much as 200%.When Tu increased from 0.5% to 20%, overall effectiveness changed insignificantly.For the film-cooled vane with round holes, overall effectiveness was increased significantly by TBC, and the effect of the blowing ratio on the overall cooling effectiveness of the turbine vane with TBC was minimal.Prapamonthon et al. [30,31] simultaneously studied the effects of Tu and TBC on the cooling performance of a leading-edge cooling guide vane and a real film-cooled vane, using 3D CHT analysis at Tu = 3.3%, 10%, and 20%.Their works indicated that TBC was more effective when the level of Tu increased.Namely, at Tu = 20% with film cooling, overall effectiveness was improved as much as about 24% in the regions cooled ineffectively.For the leading-edge cooling guide vane, overall cooling effectiveness at the hub increased by about 25%.
Hence, there is a demand to provide gas turbine engineers and designers with useful numerical studies of real phenomena from the effects of Tu and TBC on the cooling performance of a turbine airfoil.This research proposes a numerical investigation of the cooling performance of the C3X vane, an extensively non-film-cooled turbine vane reported by Hylton et al. [12], coated with TBC at different Tus using the analysis of 3D CHT linked with CFD.

Thermal Parameters
The evaluation method of four thermal parameters which relate to temperatures on the metal surface with and without TBC is demonstrated in Figure 1, as established by Prapamonthon et al. [31].The presence of a bond coat is neglected by a simplified assumption that it is a part of the vane surface with a relatively thin thickness.Thus, its thermal resistance on heat transfer through the vane surface is disregarded.(1) Heat transfer coefficient (h): where T w = T, without TBC ⇒ h T , with TBC ⇒ h TBC , if h is positive, it means that heat flux transfers into the solid structure.On the other hand, if heat flux transfers into the fluid, h is negative.However, in this work, h is expected to be positive because T ∞ > T w .
(2) Overall cooling effectiveness (ϕ): where T w = T, without TBC ⇒ ϕ T TBC , with TBC ⇒ ϕ TBC , with a conduction wall and CHT analysis, the cooling performance on the vane metal surface is evaluated by this parameter.
(3) Thermal barrier coating effectiveness (τ): The effect of TBC on the cooling performance is discussed by this parameter through the external surface of TBC.
(4) Percentage of metal temperature reduction (R): This parameter is used to consider the TBC ability to protect the metal surface from the hot gas.

Geometric Configuration
In this work, the geometry of the C3X vane reported by Hylton et al. [12] is used.Figure 2 depicts the mainstream cascade, the configuration of the C3X vane with a constant cross section, and ten cylindrical cooling passages where air flows from the hub to the tip.Its height is 76.2 mm in the spanwise direction.

Computational Mesh and Mesh Independence
In this work, computational meshes are generated by ICEM, ANSYS V.15.In order to obtain simple and high-quality meshes, all computational domains are formed as hexahedral unstructured meshes.All meshes are improved by the O-grid technique to attain high-quality meshes and suffice to resolve the boundary layer near surfaces in fluid domains.The value of y+ for the computational mesh of the first cell is less than 5. Comparisons of the distributions of surface temperatures along the vane surface at midspan with three mesh number strategies, that is, 4,834,244 (4.8 M, coarse mesh), 5,574,920 (5.5 M, medium mesh), and 6,655,148 (6.6 M, fine mesh), are considered to confirm mesh independence.Figure 3 shows that most of the numerical results of 5.5 M and 6.6 M give a very good agreement, with the maximum error about 1%.Therefore, it is not necessary to increase the quantity of mesh elements, and the 5.5 M is selected as the computational mesh throughout the following calculations.

Techniques of Calculation
Numerical results in this research are conducted by using ANSYS FLUENT v15 under the appropriate implementation of the pressure-based segregated algorithm with the SIMPLE method and SST k-ω turbulence model.The second-order accuracy of the discretization scheme is determined in the solid and fluid regions.The convergence process and its stability are improved by under-relaxation factors, and the accuracy of the results is furthered by an option of low-Reynolds number corrections for low speed flows and four correction factors for the compressibility effect, curvature correction, viscous heating, and production limiter.The convergence criteria are that the residuals of the scaled continuity and energy equations must be lower than 10 −3 and 10 −6 , respectively.To confirm the convergence of the numerical results, the mass-flow-rate balance at all inlets and outlets is checked carefully.Moreover, the six-point temperatures on the vane surface are monitored until the larger changes of these parameters disappear with subsequent iterations.As per previous works done by Prapamonthon [30,31], it is expected that the converged solutions are obtained after 17,000-18,000 iterations.With CHT analysis, the Navier-Stokes equations and equation of energy are solved within the fluid domain, whereas the heat conductive equation by Fourier's law is only solved in the solid domain under a suitable thermal conductive effect to associate the calculation of heat flux.The mesh interface technique (MIT) with the couple wall option is exploited at all interfaces of the solid and fluid domains to allow heat flux to transfer at the interfaces, whereas fluid cannot flow across these interfaces, as presented in Figure 6a.To consider the effect of TBC at all interfaces, a constant thickness of 0.03556 cm of yttria-partially-stabilized zirconia (ZrO 2 ) is used as a TBC insulator, as used by Halila et al. [32], and named as TBC 1. Figure 6b illustrates the application of the thermal condition provided by FLUENT to address the TBC effect at the interfaces of the solid and fluid domains.Due to a very thin layer of TBC, only 1D heat conduction is considered in the TBC.In order to further study the thermally protective effect of TBC, a new TBC proposed by Wang et al. [33] is used as the candidate TBC, named as TBC 2. Table 1 gives the important properties of the TBC materials used to take account of the heat conduction through TBC.Air is used as the mainstream and the coolant in the passages, and the vane structure is assumed as being made of steel, and their properties in this work are given in Table 2.

Boundary Conditions
In this work, the boundary conditions of the external mainstream and internal coolant passages are set as those of the run number 4112 of the experiment reported by Hylton et al. [12] at Tu = 8.3% and 16.6% as given in Tables 3 and 4, respectively.However, it should be noted that this research is conducted under a simple assumption that any physical change in the faces of TBC, which may occur in any experiment, is not considered.

Validation of Turbulence Model
The experimental data reported by Hylton et al. [12] is used to validate the numerical results of the pressure and surface temperature at midspan obtained by the SST k-ω turbulence model, as presented in Figure 7. From Figure 7a, it is obvious that the SST k-ω model predicts a good pressure distribution compared to the experimental data.Only a slight difference happens on the SS in the range of 0.7 < x/C < 0.9.Besides, this turbulence model overestimates the surface temperature in the range of −0.7 < x/C < 0.4, and underestimates in the two ranges of −1.0 < x/C < −0.7 and 0.4 < x/C < 1.0, as seen in Figure 7b.However, the model gives the trend of the surface temperature distribution well, with the maximum error about 3%.So, it is acceptable and reasonable to use the SST k-ω model in the following simulations.

Percentage of Metal Temperature Reduction
Figure 8 presents the distributions of the surface temperature reduction (R) at midspan, which indicates that at both Tu values, TBC plays a major role in thermal protection in the range of about −0.65 < x/C < 0.8, and TBC can reduce the metal surface temperature by as much as 3.2% (about 25 K) at x ≈ −0.45 on the PS and Tu = 16.6%.However, R drops dramatically near the TE, that is, the range of −1.0 < x/C < −0.65 on the PS and 0.8 < x/C < 1.0 on the SS.With increasing Tu, R distribution at Tu = 16.6% has a similar trend to that at Tu = 8.3%.However, R rises in the range of −0.65 < x/C < 0.2 and stays unchanged in the other regions.These phenomena suggest that although the TBC is effective in protecting the metal surface, the role of the TBC in the TE is small because the T TBC is a little lower than T in such regions.This phenomenon may be explained by the fact that the TE is the smallest and thinnest part of the vane, so it is coated with the smallest amount of TBC.Moreover, this region obtains relatively high temperatures, but is cooled by the lower rates of coolant with the relatively high inlet temperatures, namely, the holes H9 and H10 seen in Figure 2, and Table 4. Additionally, the protective ability of TBC increases with Tu in the LE and its neighborhood on the SS, as well as the region from the LE to the front of the TE on the PS, but hardly changes in the other regions.

Overall and TBC Effectiveness
Figure 9 shows comparisons between ϕ, ϕ TBC , and τ distributions at midspan for two Tus.At each Tu, it is clear that τ < ϕ < ϕ TBC because T' > T > T TBC .The trends of ϕ, ϕ TBC , and τ distributions are similar to one another.The maximum ϕ, ϕ TBC , and τ are located at the same position, that is, at x/C = −0.45 on the PS.This is reasonable because it is the closest position to the coolant passage H5, where has the lowest inlet temperature and a relatively higher coolant flow rate, as seen in Table 4.With the increase in Tu, it is observed that ϕ, ϕ TBC , and τ decrease due to the fact that T, T TBC , and T' increase with Tu.Another observation is that the reductions of ϕ, ϕ TBC , and τ with Tu are very small near the TE.The general trends of the characteristics of overall and TBC effectiveness distributions at different Tus are captured by the contours in Figures 10 and 11.The contours indicate that at each Tu, the inclusion of TBC leads to the quantitative increment of overall cooling effectiveness by about 16% to 20%, and about 8% at the TE.The reduction of ϕ TBC is lower than that of ϕ when Tu increases.The reason is that the presence of TBC mitigates the reduction of overall cooling effectiveness by significantly reducing TBC effectiveness on the external surface of the TBC.

Heat Transfer Coefficient
Figure 12a,b show the h and h TBC distributions at midspan and at the same Tu for two Tus, respectively.One can observe that at each Tu, h and h TBC have similar trends and match the distributions of R. Another observation is that h TBC is lower than or equal to h, and both h and h TBC decrease near the TE. Figure 12c,d present comparisons of h and h TBC at midspan and at two Tus, respectively.It is clear that when Tu rises up from 8.3% to 16.6%, both h and h TBC increase in the range of −0.75 < x/C < 0.3, but the increment of h is stronger than that of h TBC .However, the effects of increasing Tu on h and h TBC are slight in the other regions.These phenomena suggest that the heat transfer coefficient may be slightly dampened by TBC and that TBC causes the lower augmentation of the heat transfer coefficient in the LE and its neighborhoods on the SS, as well as the region from the LE to the front of the TE on the PS when the level of Tu rises.The overall effects of TBC on h and h TBC at the different Tus are illustrated by holistic contours in Figure 13.It confirms that the inclusion of TBC slightly dampens the heat transfer coefficient and causes the reduction of the heat transfer coefficient in general; that is, h TBC < h.However, the trends of h and h TBC distributions are similar to each other.At different Tus, the increase in Tu is the cause of increases in h and h TBC , but the augmentation of h TBC remains lower than that of h in general.

Vane Internal Temperature
In order to further study of the effect of TBC on cooling performance, the different TBCs, that is, TBC 1 and TBC 2, are used to evaluate the temperature within the vane material in this section.At first, distributions of R on the vane surface with TBC 1 and TBC 2 are considered, as depicted in Figure 14.One can observe that TBC 2 gives a higher R than TBC 1, and the highest R of TBC 2 is about 6.5% if Tu = 16.6%, but about 3.2% for TBC 1 at the same Tu.However, R obtained by TBC 2 drops more severely than that by TBC 1 in the range of −1.0 < x/C < −0.65 on the PS and 0.8 < x/C < 1.0 on the SS, namely, 6.5% to 2% for TBC 2 and 3% to 1% for TBC 1. Also, there is no significant difference of R in such regions, though Tu increases.This indicates that although the lower thermal conductivity of TBC protects the vane surface more effectively, at the same time, the role of TBC in the TE region and its vicinity decreases more seriously.Moreover, it is likely that R obtained by both TBCs is independent of Tu in such regions as well.Next, the vane internal temperatures with the two different TBCs are compared against those without TBC using the contours of three-section planes at three spans, that is, 10%, 50%, and 90%, as illustrated in Figures 15 and 16 for Tu = 8.3% and 16.6%, respectively.From these figures, it is indicated that the vane internal temperature increases with the spanwise direction, following the direction of coolant flowing in the 10 passages.Another phenomenon is that the relatively high temperatures inside the vane are still observed in the TE region of each section area, although TBC with a lower thermal conductivity is employed.This corresponds to the lowest cooling effectiveness happening on the surface of the TE, including the role of TBC in this region.With the increment of Tu, overall and TBC effectiveness decreases as described previously.Hence, the vane surface and internal temperatures increase.Figure 17 shows the effect of TBC on reductions of the average vane temperature at Tu = 8.3% and 16.6%.It should be noted that the "average vane temperature" is the volume-average temperature of the vane.The negative value on the ordinate means that TBC reduces the average vane temperature.It is found that TBC 2 reduces the average vane temperature about two times more than TBC 1 (about 38% for 2 and 19% for TBC1), due to its lower thermal conductivity.However, the effect of Tu on this reduction is very slight for both TBCs.This may be explained by the fact that the heat transfer coefficient increases with Tu as shown in Figure 12c,d, so the average vane temperature increases.Nevertheless, it is found that the increment of the average vane temperature obtained without TBC, TBC 1, and TBC 2 are similar to each other.So, the reductions of the average vane temperature for both TBCs change insignificantly when Tu increases.

Conclusions
The numerical investigation of cooling performances of a non-film-cooled turbine vane coated with a thermal barrier coating are conducted at the different Tus of Tu = 8.3% and 16.6% using 3D CHT analysis.Through the analysis and discussion of the overall effectiveness, TBC effectiveness, heat transfer coefficient, and comparison between the vane internal temperature and average vane temperature obtained by two different TBCs, the interesting findings can be concluded as follows: (1) At midspan, for both Tus, TBC is effective in protecting the metal surface, but TBC does not play a major role near the TE.The contours indicate that at each Tu, the inclusion of TBC leads to the quantitative increment of overall cooling effectiveness of about 16-20%, but about 8% at the TE.(2) At midspan, when Tu increases, the reduction of the metal surface temperature at midspan increases in the LE and its neighborhoods on the SS, as well as the region from the LE to the front of the TE on the PS, but hardly changes in the other regions.Also, the effective contours show that TBC alleviates the reduction of the overall effectiveness of the vane.(3) When the level of Tu rises, the presence of TBC slightly dampens the heat transfer coefficient in general, and causes the lower augmentation of the heat transfer coefficient in the LE and its neighborhoods on the SS, as well as the region from the LE to the front of the TE on the PS.(4) The use of two different TBCs indicates that the vane with the lower thermal conductivity provides the lower internal and average temperatures, but its role reduces more significantly in the TE.(5) For both TBCs, the difference of the average temperature of the vane changes insignificantly as Tu increases.
Ladkrabang also.The first author would like to thank Professor Guowei Yang and Associate Professor Bo Yin, Institute of Mechanics, Chinese Academy of Sciences (CAS), for their extraordinary support.
Author Contributions: In this paper, Prasert Prapamonthon build the vane geometry, designed the methodology of simulation, carried out and analyzed the numerical results, and wrote this paper; Soemsak Yooyen improved the discussions; Suwin Sleesongsom gave suggestions during the calculation; Daniele Dipasquale suggested the computational technique; Huazhao Xu proposed the idea of applying FLUENT to simulate the effect of TBC; Jianhua Wang improved the manuscript overall; and Zhaoqing Ke checked the numerical results.

Conflicts of Interest:
The authors declare no conflict of interest.

Figure 1 .
Figure 1.Evaluation of the thermal parameters used in this work [31].TBC: thermal barrier coating.

Figure 2 .
Figure 2. Mainstream cascade and C3X geometric configuration and its cross-section area at midspan.

Figure 3 .
Figure 3. Comparisons of three mesh number strategies for surface temperature distributions at midspan.PS: pressure side; SS: suction side.

Figures 4
Figures 4 and 5 show a part of the generated mesh of the solid and fluid domains, and the mesh quality distributions of the solid and fluid domains, respectively.

Figure 7 .
Figure 7. Comparisons between experimental and numerical results at midspan (a) pressure and (b) temperature distributions.

Figure 8 .
Figure 8. Effects of turbulence intensity (Tu) and TBC on surface temperature reduction (R) at midspan.

Figure 14 .
Figure 14.Percentage of metal temperature reduction (R) of two TBCs at midspan and Tu = 8.3% and 16.6%.

Table 1 .
Properties of TBC materials.

Table 3 .
Boundary conditions of the external mainstream.

Table 4 .
Boundary conditions of the internal coolant passages.
f specific heat capacity of mainstream and coolant (J/kg•K) c m specific heat capacity of metal (J/kg•K) c TBC specific heat capacity of TBC (J/kg•K) h heat transfer coefficient without TBC, between metal surface and mainstream (W/m 2 •K) h ref reference heat transfer coefficient (1135 W/m 2 •K) h TBC heat transfer coefficient with TBC, between TBC surface and mainstream (W/m 2 •K)