Numerical Study of the Effects of Thermal Barrier Coating and Turbulence Intensity on Cooling Performances of a Nozzle Guide Vane

.


Introduction
It is well-known that internal convection and impingement cooling, film cooling, and thermal barrier coatings (TBCs) are major techniques, which are widely used to protect gas-turbine airfoils from high turbine inlet temperatures (TITs) and achieve the maximum thermal efficiency in state-of the-art gas turbine engines.In fact, the film cooling is an effective method related to the internal cooling, and film cooling performances are influenced by many factors, such as the configuration and position of the film hole, adverse pressure gradient, boundary layer thickness, mainstream turbulence intensity (Tu) and length scale (Lu), and the amount of cooling air consumption.Boyle et al. [1] deemed that Tu and Lu were two physical factors, which naturally and significantly affected the film cooling performances amid those factors.Mayhew et al. [2] expected that real gas-turbine engines were frequently operated under Tu at about 10%-20%.The effects of Tu on the film cooling performance and heat transfer coefficient of turbine airfoils, cylindrical leading edge and flat plate models have been experimentally and numerically investigated by previous researches [3][4][5][6][7][8].To prolong and give good service to the turbine airfoils, TBC has been widely utilized in gas turbine designs as a thermal insulator between hot mainstream and metal surfaces.The insulating thermal capabilities of TBC are affected by many factors, such as porosity, thickness, thermal conductivity, and phase stability of the TBC material as well as the TIT and Tu of hot gas as reported by researches [9][10][11][12][13][14].Recently, CHT analysis has been commonly applied to predict the real metal surface temperatures and cooling performances of turbine vanes.In the numerical investigations of previous works [15][16][17][18], CHT analysis was used to study the film cooled vanes without TBC.Using a Mark II vane provided by Hylton et al. [19], Bohn and Becker [20] used 3D CHT analysis and a Baldwin-Lomax turbulence model [21] to study the aerodynamic and thermal effects of the vane without and with TBC (ZrO 2 , 0.3 mm thickness).Their work indicated that TBC reduced metal temperatures by about 20-29 K in the stagnation area and about 27-43 K in shock area on the suction side (SS).However, TBC hardly affected the metal temperatures near the trailing edge (TE).With the same method and vane model, Bohn and Tümmers [22] investigated the effects of TBC and cooling air flow rate on the thermal stresses within the vane structure, their work concluded that the influence of the thermal resistance added by TBC on the thermal stresses was significantly higher than the influence due to reducing the cooling air flow rate.Alizadeh et al. [23] used CHT analysis and a shear stress transport (SST) k-ω turbulence model to investigate the effects of the thickness and thermal conductivity of TBC on the cooling performances of a turbine blade.Their research indicated that adding a 0.2 mm TBC could result in a 19 K and 34 K fall in the average and maximum temperatures, respectively.But, if the thermal conductivity of TBC increased from 1 W/m•K to 3 W/m•K, the average temperature rose about 10 K. Rossette et al. [24] used CHT analysis and a Spalart-Allmaras turbulence model [25] to investigate the aero-thermal performance of a first stage gas turbine blade with TBC.They concluded that an increase in TBC thickness by about 100-400 µm could reduce the surface temperature by up to 200 K, and TBC could reduce cooling air consumption by about 36% cooling air consumption to maintain the creep life of the blade materials.However, the above literatures focused on the models of the airfoils with a TBC effect only, and no film holes were included.
Nowadays, in advanced gas turbine vane designs, TBC and film cooling are synchronously used, and the real gas-turbine vanes or blades operate in the Tu range of 10%-20%.Therefore, it is necessary to provide the designers and investigators of gas-turbine vanes with relatively comprehensive information related to the combined effects of TBC and Tu on the real cooling performances using a 3D CHT analysis.

Thermal Parameters
Figure 1 illustrates the definitions of thermal parameters in Equations ( 1)- (6).Since the thickness of the TBC layer is thin, therefore a 1D heat conduction effect within the layer is assumed.This means that heat transfers only in the direction normal to the surface.Recently, CHT analysis has been commonly applied to predict the real metal surface temperatures and cooling performances of turbine vanes.In the numerical investigations of previous works [15][16][17][18], CHT analysis was used to study the film cooled vanes without TBC.Using a Mark II vane provided by Hylton et al. [19], Bohn and Becker [20] used 3D CHT analysis and a Baldwin-Lomax turbulence model [21] to study the aerodynamic and thermal effects of the vane without and with TBC (ZrO2, 0.3 mm thickness).Their work indicated that TBC reduced metal temperatures by about 20-29 K in the stagnation area and about 27-43 K in shock area on the suction side (SS).However, TBC hardly affected the metal temperatures near the trailing edge (TE).With the same method and vane model, Bohn and Tümmers [22] investigated the effects of TBC and cooling air flow rate on the thermal stresses within the vane structure, their work concluded that the influence of the thermal resistance added by TBC on the thermal stresses was significantly higher than the influence due to reducing the cooling air flow rate.Alizadeh et al. [23] used CHT analysis and a shear stress transport (SST) k-ω turbulence model to investigate the effects of the thickness and thermal conductivity of TBC on the cooling performances of a turbine blade.Their research indicated that adding a 0.2 mm TBC could result in a 19 K and 34 K fall in the average and maximum temperatures, respectively.But, if the thermal conductivity of TBC increased from 1 W/m•K to 3 W/m•K, the average temperature rose about 10 K. Rossette et al. [24] used CHT analysis and a Spalart-Allmaras turbulence model [25] to investigate the aero-thermal performance of a first stage gas turbine blade with TBC.They concluded that an increase in TBC thickness by about 100-400 μm could reduce the surface temperature by up to 200 K, and TBC could reduce cooling air consumption by about 36% cooling air consumption to maintain the creep life of the blade materials.However, the above literatures focused on the models of the airfoils with a TBC effect only, and no film holes were included.
Nowadays, in advanced gas turbine vane designs, TBC and film cooling are synchronously used, and the real gas-turbine vanes or blades operate in the Tu range of 10%-20%.Therefore, it is necessary to provide the designers and investigators of gas-turbine vanes with relatively comprehensive information related to the combined effects of TBC and Tu on the real cooling performances using a 3D CHT analysis.

Thermal Parameters
Figure 1 illustrates the definitions of thermal parameters in Equations ( 1)- (6).Since the thickness of the TBC layer is thin, therefore a 1D heat conduction effect within the layer is assumed.This means that heat transfers only in the direction normal to the surface. .This parameter is used to evaluate the cooling performance on the outside metal surface using the CHT analysis.(2) TBC effectiveness (τ): (1) Overall cooling effectiveness (φ): where T w = T , uncoated vane ⇒ φ T TBC , coated vane ⇒ φ TBC .This parameter is used to evaluate the cooling performance on the outside metal surface using the CHT analysis.
Energies 2017, 10, 362 3 of 16 (2) TBC effectiveness (τ): This parameter is defined to discuss the effect of TBC on the outside temperature of TBC.(3) Percentage of temperature reduction (R): This parameter is used to evaluate the ability of TBC to reduce the metal temperature of the vane.(4) Increment of overall cooling effectiveness (∆φ): This parameter is used to evaluate the effect of TBC on the metal temperature at each Tu.(5) Variation of heat transfer coefficient (∆h): where It is worth noting that the heat transfer coefficient defined by Equation ( 6) is based on the local wall surface temperature and mainstream temperature.A negative h means that heat transfers from the surface to the mainstream.On the other hand, h is positive when heat transfers from the mainstream to the vane surface.

Geometric Configuration
The geometry referenced in this work is a modified vane of the film-cooled nozzle guide vane (NGV) reported by Timko [26], which consists of enhanced internal cooling with a forward and an aft cavity, and external film cooling with a total of 13 rows with 199 holes, as shown in Figure 2a,b.The height of NGV is 4 cm, and a constant cross-section view at midspan is given in Figure 2c.Two rows of diffusion shaped-holes, R1 and R2, are placed on the SS.Rows R3 to R9 of the film holes are cylindrical with the same size and angle in the radial direction, and all of them are located at the leading edge (LE) and its vicinity.Two rows of the compound angled type, R10 and R11, and one row of the film holes in the axial direction, R12, are drilled on the pressure side (PS), and one row of slot, R13, is positioned at the TE.More details about the film holes are presented in Table 1.The height of NGV is 4 cm, and a constant cross-section view at midspan is given in Figure 2c.Two rows of diffusion shaped-holes, R1 and R2, are placed on the SS.Rows R3 to R9 of the film holes are cylindrical with the same size and angle in the radial direction, and all of them are located at the leading edge (LE) and its vicinity.Two rows of the compound angled type, R10 and R11, and one row of the film holes in the axial direction, R12, are drilled on the pressure side (PS), and one row of slot, R13, is positioned at the TE.More details about the film holes are presented in Table 1.

Computational Mesh
All numerical meshes are of a hexahedral unstructured type, which are generated by ANSYS ICEM V.15 using the tools of blocking manipulation.To obtain high qualities, the meshes are further adapted by R and H refinement procedures.In addition, the O-grid scheme is applied to the fluid region in the immediate vicinity of the vane walls to resolve the boundary layer flows.Three numbers of elements with coarse mesh 9,143,910 (9.1 M), medium mesh 10,672,683 (10.6 M), and fine mesh 13,171,055 (13 M) are compared to assure that the numerical results are independent of the mesh strategy.Figure 3a,b shows the dimensionless pressure and surface temperature distributions along the vane surface at midspan, respectively.The medium and fine mesh strategies give acceptable agreements to each other.The maximum difference for the temperature is less than 2%.Therefore, it is reasonable to choose the medium mesh with 10.6 M elements for the following calculations.The value of y + in the current simulation is less than 5, which is generally acceptable.Detailed reviews of some computational meshes and the quality distribution of the computational mesh are depicted in Figure 4a,b, respectively.

Computational Mesh
All numerical meshes are of a hexahedral unstructured type, which are generated by ANSYS ICEM V.15 using the tools of blocking manipulation.To obtain high qualities, the meshes are further adapted by R and H refinement procedures.In addition, the O-grid scheme is applied to the fluid region in the immediate vicinity of the vane walls to resolve the boundary layer flows.Three numbers of elements with coarse mesh 9,143,910 (9.1 M), medium mesh 10,672,683 (10.6 M), and fine mesh 13,171,055 (13 M) are compared to assure that the numerical results are independent of the mesh strategy.Figure 3a,b shows the dimensionless pressure and surface temperature distributions along the vane surface at midspan, respectively.The medium and fine mesh strategies give acceptable agreements to each other.The maximum difference for the temperature is less than 2%.Therefore, it is reasonable to choose the medium mesh with 10.6 M elements for the following calculations.The value of y + in the current simulation is less than 5, which is generally acceptable.Detailed reviews of some computational meshes and the quality distribution of the computational mesh are depicted in Figure 4a,b, respectively.

Calculation Techniques
ANSYS FLUENT V.15 is used as the solver, and the SST k-ω turbulence model with a Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm is implemented appropriately.The spatial discretization with second order accuracy is used to solve momentum and energy equations in the fluid domains, whereas in the solid domain only the energy equation is solved on the basis of Fourier's law.Under-relaxation factors are adjusted attentively to obtain the converged results.The convergence criteria of the results are that the residual magnitudes of energy and continuity equations must reduce to the levels of 10 −6 and 10 −3 , respectively.Moreover, the converged results are substantiated by proving the balance of mass flow rates at all inlets and outlets, and observing the traces of temperature variation at monitoring points on the vane surfaces.The Mesh Interface Technique (MIT) is applied to deal with all couple interfaces of solid-fluid domains.In order to numerically study the effects of TBC, all elements at the interfaces of the vane and fluid mainstream are applied to a layer of TBC with a uniform thickness of 0.3556 mm, as reported by Halila et al. [27].For this thin layer of TBC, only 1D heat conduction equation is solved.
The fluid domain consists of cooling air and a hot mainstream, the vane is made of steel, and TBC is ZrO2, and the thermal properties are given in Table 2.

Property of Material
Air: Mainstream and Cooling Air Steel: Vane Structure ZrO2: TBC Three-equation of Sutherland model --

Boundary Conditions
Numerical simulations are carried out under the boundary conditions reported by Timko [26], as shown in Table 3.It should be noted that five exact pressure ratios (PRs), i.e., PR = 1.67, 2.0, 2.3, 2.5, and 2.7 were used in Timko's report [26], but it lacks the specification of the exact PR used to obtain the experimental results.Therefore, it is worth testing simulations at those PRs.To save the computational cost and time, PR = 1.67, 2.3 and 2.7 are tested, and the designed PR of 1.67 is used for all simulations.Three Tus (Tu = 3.3%, 10% and 20%) at the mainstream inlet are added to study the Tu effects on the cooling performances in the following section.Due to the lack of exact values from Timko [26], the length scale, Lu, is set at a constant value of 6 cm at the inlet of the mainstream following the instruction of FLUENT V.15.

Calculation Techniques
ANSYS FLUENT V.15 is used as the solver, and the SST k-ω turbulence model with a Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm is implemented appropriately.The spatial discretization with second order accuracy is used to solve momentum and energy equations in the fluid domains, whereas in the solid domain only the energy equation is solved on the basis of Fourier's law.Under-relaxation factors are adjusted attentively to obtain the converged results.The convergence criteria of the results are that the residual magnitudes of energy and continuity equations must reduce to the levels of 10 −6 and 10 −3 , respectively.Moreover, the converged results are substantiated by proving the balance of mass flow rates at all inlets and outlets, and observing the traces of temperature variation at monitoring points on the vane surfaces.The Mesh Interface Technique (MIT) is applied to deal with all couple interfaces of solid-fluid domains.In order to numerically study the effects of TBC, all elements at the interfaces of the vane and fluid mainstream are applied to a layer of TBC with a uniform thickness of 0.3556 mm, as reported by Halila et al. [27].For this thin layer of TBC, only 1D heat conduction equation is solved.
The fluid domain consists of cooling air and a hot mainstream, the vane is made of steel, and TBC is ZrO 2 , and the thermal properties are given in Table 2.
Three-equation of Sutherland model --

Boundary Conditions
Numerical simulations are carried out under the boundary conditions reported by Timko [26], as shown in Table 3.It should be noted that five exact pressure ratios (PRs), i.e., PR = 1.67, 2.0, 2.3, 2.5, and 2.7 were used in Timko's report [26], but it lacks the specification of the exact PR used to obtain the experimental results.Therefore, it is worth testing simulations at those PRs.To save the computational cost and time, PR = 1.67, 2.3 and 2.7 are tested, and the designed PR of 1.67 is used for all simulations.Three Tus (Tu = 3.3%, 10% and 20%) at the mainstream inlet are added to study the Tu effects on the cooling performances in the following section.Due to the lack of exact values from Timko [26], the length scale, Lu, is set at a constant value of 6 cm at the inlet of the mainstream following the instruction of FLUENT V.15.

Validation of the Turbulence Model
All of the numerical results in this work are carried out using a SST k-ω turbulence model, which has been tested successfully in predicting flow and thermal fields by several researchers [17,18,23,30].To validate the results obtained from the SST k-ω turbulence model, the numerical Mach number (Ma) along the vane surface at midspan is compared against the experimental data reported by Timko [26] at PR = 1.67, 2.3, and 2.7, as shown in Figure 5.For the three PRs, in the regions of 0 < x/C < 0.4 on the SS and 0 < x/C < 0.5 on the PS, the numerical results of Ma give acceptable agreements with the experimental data, and the effect of PR on Ma is insignificant.But, at PR = 1.67, the numerical result of Ma is underestimated at x/C ≈ 0.61 and 0.68 on the PS.With PR increasing up to 2.3 and 2.7, the numerical results of Ma at those positions rise up close to the experimental data with a maximum error of about 10%.This indicates that the differences between the numerical results and the experimental results of Ma meaningfully decrease with PR, and the SST k-ω turbulence model can provide acceptable results in this work.However, it should be noted that PR = 1.67 is used for all simulations in this work because it was the design condition reported by Timko [26].

Validation of the Turbulence Model
All of the numerical results in this work are carried out using a SST k-ω turbulence model, which has been tested successfully in predicting flow and thermal fields by several researchers [17,18,23,30].To validate the results obtained from the SST k-ω turbulence model, the numerical Mach number (Ma) along the vane surface at midspan is compared against the experimental data reported by Timko [26] at PR = 1.67, 2.3, and 2.7, as shown in Figure 5.For the three PRs, in the regions of 0 < x/C < 0.4 on the SS and 0 < x/C < 0.5 on the PS, the numerical results of Ma give acceptable agreements with the experimental data, and the effect of PR on Ma is insignificant.But, at PR = 1.67, the numerical result of Ma is underestimated at x/C ≈ 0.61 and 0.68 on the PS.With PR increasing up to 2.3 and 2.7, the numerical results of Ma at those positions rise up close to the experimental data with a maximum error of about 10%.This indicates that the differences between the numerical results and the experimental results of Ma meaningfully decrease with PR, and the SST k-ω turbulence model can provide acceptable results in this work.However, it should be noted that PR = 1.67 is used for all simulations in this work because it was the design condition reported by Timko [26].

Overall Cooling Effectiveness and TBC Effectiveness
Figure 6a compares the φTBC and φ distributions at midspan for the three Tus.It is observed that at the same Tu, φTBC is always higher than φ, because TTBC is always lower than T.However, the distributions of φ and φTBC are similar to each other.The higher φ and φTBC are at the exits of the film holes, and the highest φ and φTBC are found at the same position, i.e., x/C = 0.38 on the SS.It means that this position has the lowest T and TTBC.The reason is that the position is just downstream of shaped-holes R1 and R2, where the combined effects of the larger number of film holes and the lower pressure on the SS, including reduced effective blowing ratio at the hole exits [31] can effect more cooling air to be emitted from the film holes.When Tu increases, φ and φTBC decrease, because T and TTBC increase with Tu.But, these effects on φ and φTBC are relatively smaller in the region of 0.4 < x/C

Overall Cooling Effectiveness and TBC Effectiveness
Figure 6a compares the φ TBC and φ distributions at midspan for the three Tus.It is observed that at the same Tu, φ TBC is always higher than φ, because T TBC is always lower than T.However, the distributions of φ and φ TBC are similar to each other.The higher φ and φ TBC are at the exits of the film holes, and the highest φ and φ TBC are found at the same position, i.e., x/C = 0.38 on the SS.It means that this position has the lowest T and T TBC .The reason is that the position is just downstream of shaped-holes R1 and R2, where the combined effects of the larger number of film holes and the lower pressure on the SS, including reduced effective blowing ratio at the hole exits [31] can effect more cooling air to be emitted from the film holes.When Tu increases, φ and φ TBC decrease, because T and T TBC increase with Tu.But, these effects on φ and φ TBC are relatively smaller in the region of 0.4 < x/C < 0.7 on the SS, the reason is that the effect of Tu on the SS is much less sensitive than that on the PS. Figure 6b illustrates the noteworthy differences between τ and φ TBC at midspan for the three Tus.At the same Tu, τ is lower than φ TBC except at the exits of the film holes, where τ may be equal to or higher than φ TBC .Moreover, τ is close to φ TBC in the region of 0.38 < x/C < 0.6 on the SS, and the distributions of τ are consistent with T .These phenomena suggest that the TBC does not play a major role near the exits of the film holes and the effectively cooled regions.Like φ and φ TBC , an increase in Tu only causes a quantitative reduction in τ, and the trends of the τ distributions retain the same.
Energies 2017, 10, 362 7 of 16 < 0.7 on the SS, the reason is that the effect of Tu on the SS is much less sensitive than that on the PS. Figure 6b illustrates the noteworthy differences between τ and φTBC at midspan for the three Tus.At the same Tu, τ is lower than φTBC except at the exits of the film holes, where τ may be equal to or higher than φTBC.Moreover, τ is close to φTBC in the region of 0.38 < x/C < 0.6 on the SS, and the distributions of τ are consistent with T′.These phenomena suggest that the TBC does not play a major role near the exits of the film holes and the effectively cooled regions.Like φ and φTBC, an increase in Tu only causes a quantitative reduction in τ, and the trends of the τ distributions retain the same.
(a) (b) Figures 7 and 8 present the holistic contours of φ, φTBC, and τ on the PS and the SS, for the three Tus, respectively.From those figures, the following interesting phenomena can be observed: (1) at the same Tu, τ is of the lowest effectiveness in general except at the exits of the film holes, and φTBC is always higher than φ.Moreover, the distributions of φ and φTBC are more uniform than that of τ due to the lower thermal conductivity of TBC.The distribution of τ is similar to the distributions of the adiabatic film effectiveness obtained by adiabatic assumption in our previous work [28,29].This phenomenon is reasonable because the thermal conductivity of TBC is much lower than that of the vane's material, and TBC reduces the heat flux transferred into the solid structure; (2) At each Tu, the relatively lower τ, φ, and φTBC always happen near the tip and the hub of the vane, because it is difficult to cool those regions effectively by the cooling air emitted from the film holes.However, the relatively higher τ, φ, and φTBC always happen at the exits and downstream of the diffusion shapedholes R1 and R2 on the SS; (3) When Tu increases, the regions with the relatively lower effectiveness at the tip and hub expand significantly, which is as expected since more heat is transferred to the vane with higher Tus.Figures 7 and 8 present the holistic contours of φ, φ TBC , and τ on the PS and the SS, for the three Tus, respectively.From those figures, the following interesting phenomena can be observed: (1) at the same Tu, τ is of the lowest effectiveness in general except at the exits of the film holes, and φ TBC is always higher than φ.Moreover, the distributions of φ and φ TBC are more uniform than that of τ due to the lower thermal conductivity of TBC.The distribution of τ is similar to the distributions of the adiabatic film effectiveness obtained by adiabatic assumption in our previous work [28,29].This phenomenon is reasonable because the thermal conductivity of TBC is much lower than that of the vane's material, and TBC reduces the heat flux transferred into the solid structure; (2) At each Tu, the relatively lower τ, φ, and φ TBC always happen near the tip and the hub of the vane, because it is difficult to cool those regions effectively by the cooling air emitted from the film holes.However, the relatively higher τ, φ, and φ TBC always happen at the exits and downstream of the diffusion shaped-holes R1 and R2 on the SS; (3) When Tu increases, the regions with the relatively lower effectiveness at the tip and hub expand significantly, which is as expected since more heat is transferred to the vane with higher Tus.
Energies 2017, 10, 362 7 of 16 < 0.7 on the SS, the reason is that the effect of Tu on the SS is much less sensitive than that on the PS. Figure 6b illustrates the noteworthy differences between τ and φTBC at midspan for the three Tus.At the same Tu, τ is lower than φTBC except at the exits of the film holes, where τ may be equal to or higher than φTBC.Moreover, τ is close to φTBC in the region of 0.38 < x/C < 0.6 on the SS, and the distributions of τ are consistent with T′.These phenomena suggest that the TBC does not play a major role near the exits of the film holes and the effectively cooled regions.Like φ and φTBC, an increase in Tu only causes a quantitative reduction in τ, and the trends of the τ distributions retain the same.
(a) (b) Figures 7 and 8 present the holistic contours of φ, φTBC, and τ on the PS and the SS, for the three Tus, respectively.From those figures, the following interesting phenomena can be observed: (1) at the same Tu, τ is of the lowest effectiveness in general except at the exits of the film holes, and φTBC is always higher than φ.Moreover, the distributions of φ and φTBC are more uniform than that of τ due to the lower thermal conductivity of TBC.The distribution of τ is similar to the distributions of the adiabatic film effectiveness obtained by adiabatic assumption in our previous work [28,29].This phenomenon is reasonable because the thermal conductivity of TBC is much lower than that of the vane's material, and TBC reduces the heat flux transferred into the solid structure; (2) At each Tu, the relatively lower τ, φ, and φTBC always happen near the tip and the hub of the vane, because it is difficult to cool those regions effectively by the cooling air emitted from the film holes.However, the relatively higher τ, φ, and φTBC always happen at the exits and downstream of the diffusion shapedholes R1 and R2 on the SS; (3) When Tu increases, the regions with the relatively lower effectiveness at the tip and hub expand significantly, which is as expected since more heat is transferred to the vane with higher Tus.Additionally, the ability of TBC is quantitatively evaluated by the percentage of temperature reduction, R, defined in Equation ( 3), for the three Tus, as shown at midspan in Figure 9.It is obvious that for each Tu, the value of R increases in the region of 0.6 < x/C < 0.9 on the SS and −0.8 < x/C < −0.2 on the PS, but rapidly drops near the TE, i.e., −1.0 < x/C < −0.9 and 0.95 < x/C < 1.0.The highest values for R (R = 5% at Tu = 3.3% and R = 6% at Tu = 20%) are at the same position, i.e., x/C = −0.8,which is between the film rows R12 and R13 on the PS.The lowest R is about 1.1% at Tu = 3.3% and 1.7% at Tu = 20% in the region from x/C = 0.38 to x/C = 0.6 on the SS, where T′, T, and TTBC are at the lowest values, because those are the positions of the exits and are downstream of the shaped-holes in R1.Moreover, the results also indicate that the value of R on the PS is generally higher than that on the SS.This result is different from the conclusion drawn by Meitner [13], which concluded that TBC was more effective on the SS than on the PS because the heat flux was higher on the uncoated SS.Nevertheless, the conclusion in this work is still reasonable because the amount of film-hole rows on the SS is much less than that in Meitner [13].Therefore, the heat flux is higher on the uncoated PS, as shown in Figure 10.These phenomena indicate that the role of TBC on the PS is more dominant than that on the SS due to a fewer number of film holes, and this role decreases in the regions cooled effectively by the cooling air discharged from the film holes as well as the TE.With increasing in Tu, it is found that the increases of R in the effectively cooled regions near R1 and the TE are smaller than those in other regions.Additionally, the ability of TBC is quantitatively evaluated by the percentage of temperature reduction, R, defined in Equation ( 3), for the three Tus, as shown at midspan in Figure 9.It is obvious that for each Tu, the value of R increases in the region of 0.6 < x/C < 0.9 on the SS and −0.8 < x/C < −0.2 on the PS, but rapidly drops near the TE, i.e., −1.0 < x/C < −0.9 and 0.95 < x/C < 1.0.The highest values for R (R = 5% at Tu = 3.3% and R = 6% at Tu = 20%) are at the same position, i.e., x/C = −0.8,which is between the film rows R12 and R13 on the PS.The lowest R is about 1.1% at Tu = 3.3% and 1.7% at Tu = 20% in the region from x/C = 0.38 to x/C = 0.6 on the SS, where T , T, and T TBC are at the lowest values, because those are the positions of the exits and are downstream of the shaped-holes in R1.Moreover, the results also indicate that the value of R on the PS is generally higher than that on the SS.This result is different from the conclusion drawn by Meitner [13], which concluded that TBC was more effective on the SS than on the PS because the heat flux was higher on the uncoated SS.Nevertheless, the conclusion in this work is still reasonable because the amount of film-hole rows on the SS is much less than that in Meitner [13].Therefore, the heat flux is higher on the uncoated PS, as shown in Figure 10.These phenomena indicate that the role of TBC on the PS is more dominant than that on the SS due to a fewer number of film holes, and this role decreases in the regions cooled effectively by the cooling air discharged from the film holes as well as the TE.With increasing in Tu, it is found that the increases of R in the effectively cooled regions near R1 and the TE are smaller than those in other regions.Additionally, the ability of TBC is quantitatively evaluated by the percentage of temperature reduction, R, defined in Equation ( 3), for the three Tus, as shown at midspan in Figure 9.It is obvious that for each Tu, the value of R increases in the region of 0.6 < x/C < 0.9 on the SS and −0.8 < x/C < −0.2 on the PS, but rapidly drops near the TE, i.e., −1.0 < x/C < −0.9 and 0.95 < x/C < 1.0.The highest values for R (R = 5% at Tu = 3.3% and R = 6% at Tu = 20%) are at the same position, i.e., x/C = −0.8,which is between the film rows R12 and R13 on the PS.The lowest R is about 1.1% at Tu = 3.3% and 1.7% at Tu = 20% in the region from x/C = 0.38 to x/C = 0.6 on the SS, where T′, T, and TTBC are at the lowest values, because those are the positions of the exits and are downstream of the shaped-holes in R1.Moreover, the results also indicate that the value of R on the PS is generally higher than that on the SS.This result is different from the conclusion drawn by Meitner [13], which concluded that TBC was more effective on the SS than on the PS because the heat flux was higher on the uncoated SS.Nevertheless, the conclusion in this work is still reasonable because the amount of film-hole rows on the SS is much less than that in Meitner [13].Therefore, the heat flux is higher on the uncoated PS, as shown in Figure 10.These phenomena indicate that the role of TBC on the PS is more dominant than that on the SS due to a fewer number of film holes, and this role decreases in the regions cooled effectively by the cooling air discharged from the film holes as well as the TE.With increasing in Tu, it is found that the increases of R in the effectively cooled regions near R1 and the TE are smaller than those in other regions.

Effects of TBC and Tu on Overall Cooling Effectiveness
Figure 11 presents the effects of TBC on increasing in the overall cooling effectiveness in percentage on the vane surfaces for the three Tus.One can find three important phenomena: (1) at each Tu, the values of Δφ are always positive.This means that TBC plays a constructive role to protect the vane, especially at the tip and the hub as marked as A to F, which are the locations cooled poorly by cooling air; (2) at each Tu, this constructive role is weaker at the exits and downstream of the diffusion shaped-holes R1 on the SS, and the regions near the TE as marked as X and Y; (3) With increasing in Tu, the constructive role is more significant, namely at higher Tus, the overall cooling effectiveness demonstrates a significant improvement by TBC in the regions near the tip (Region A, Δφ = 18%, 24% and 24% or ΔT = 32 K, 38 K and 38 K for Tu = 3.3%,10% and 20%, respectively) and near the hub (Region C, Δφ = 16%, 19% and 21% or ΔT = 34 K, 36 K and 38 K for Tu = 3.3%, 10% and 20%, respectively) on the LE-SS.But, the improvement becomes slight in the regions of downstream of the diffusion shaped-hole R1 on the SS (Δφ = 2%, 2%-3% and 3% or ΔT = 6 K, 6-8 K and 8 K for Tu = 3.3%, 10% and 20%, respectively) and near the TE.These results exhibit the benefits of introducing TBC to protect NGV from harsh mainstream flows, especially for the regions which are insufficiently cooled by cooling air, and TBC effects an increase in the overall cooling effectiveness when Tu increases.

Effects of TBC and Tu on Overall Cooling Effectiveness
Figure 11 presents the effects of TBC on increasing in the overall cooling effectiveness in percentage on the vane surfaces for the three Tus.One can find three important phenomena: (1) at each Tu, the values of ∆φ are always positive.This means that TBC plays a constructive role to protect the vane, especially at the tip and the hub as marked as A to F, which are the locations cooled poorly by cooling air; (2) at each Tu, this constructive role is weaker at the exits and downstream of the diffusion shaped-holes R1 on the SS, and the regions near the TE as marked as X and Y; (3) With increasing in Tu, the constructive role is more significant, namely at higher Tus, the overall cooling effectiveness demonstrates a significant improvement by TBC in the regions near the tip (Region A, ∆φ = 18%, 24% and 24% or ∆T = 32 K, 38 K and 38 K for Tu = 3.3%,10% and 20%, respectively) and near the hub (Region C, ∆φ = 16%, 19% and 21% or ∆T = 34 K, 36 K and 38 K for Tu = 3.3%, 10% and 20%, respectively) on the LE-SS.But, the improvement becomes slight in the regions of downstream of the diffusion shaped-hole R1 on the SS (∆φ = 2%, 2%-3% and 3% or ∆T = 6 K, 6-8 K and 8 K for Tu = 3.3%, 10% and 20%, respectively) and near the TE.These results exhibit the benefits of introducing TBC to protect NGV from harsh mainstream flows, especially for the regions which are insufficiently cooled by cooling air, and TBC effects an increase in the overall cooling effectiveness when Tu increases.

Effects of TBC and Tu on Heat Transfer Coefficient
Figure 12 shows the contours of Δh for the three Tus.It is shown that at each Tu, Δh is positive in the regions to be poorly cooled by cooling air, particularly between holes R12 and R13, R2 and R3, and the front of the TE on the SS as marked as regions 1, 2, and 3, respectively.This phenomenon suggests that TBC decreases the heat flux from the mainstream into the vane, and plays a positive role.However, the negative Δh is observed in the effectively cooled regions, especially at the exits of the film holes and the downstream regions of the shaped-hole R1.At this time TBC shows an opposite role and TBC blocks the heat flux from being released from the solid vane into the mixing fluid of cooling air with the mainstream.At the higher Tus, the roles of TBC on the heat transfer coefficient are more significant, as shown in Figure 13.The temperature distributions at midspan of the vane and mainstream are displayed at three Tus both with and without TBC.For each Tu, the effects of TBC on the mixing process of the mainstream and coolant is insignificant.However, the increase in Tu disturbs the cooling air near the exit and downstream of the film holes, and intensifies the mixing of the mainstream with cooling air.This causes higher temperatures in the vane and higher heat transfer.Therefore, the role of TBC increases, and this phenomenon is evident on the PS.The enhanced mixing of the mainstream with cooling air is more clearly shown in Figure 14.

Effects of TBC and Tu on Heat Transfer Coefficient
Figure 12 shows the contours of ∆h for the three Tus.It is shown that at each Tu, ∆h is positive in the regions to be poorly cooled by cooling air, particularly between holes R12 and R13, R2 and R3, and the front of the TE on the SS as marked as regions 1, 2, and 3, respectively.This phenomenon suggests that TBC decreases the heat flux from the mainstream into the vane, and plays a positive role.However, the negative ∆h is observed in the effectively cooled regions, especially at the exits of the film holes and the downstream regions of the shaped-hole R1.At this time TBC shows an opposite role and TBC blocks the heat flux from being released from the solid vane into the mixing fluid of cooling air with the mainstream.At the higher Tus, the roles of TBC on the heat transfer coefficient are more significant, as shown in Figure 13.The temperature distributions at midspan of the vane and mainstream are displayed at three Tus both with and without TBC.For each Tu, the effects of TBC on the mixing process of the mainstream and coolant is insignificant.However, the increase in Tu disturbs the cooling air near the exit and downstream of the film holes, and intensifies the mixing of the mainstream with cooling air.This causes higher temperatures in the vane and higher heat transfer.Therefore, the role of TBC increases, and this phenomenon is evident on the PS.The enhanced mixing of the mainstream with cooling air is more clearly shown in Figure 14. Figure 14 demonstrates, for the vane without TBC at the three Tus, streamtraces of the cooling air released from the inlets of the film holes at midspan and contours of temperature in the plane perpendicular to the axial chord and immediately downstream of film-hole rows R1, R6 and R10.As Tu increases from 3.3% to 20%, the streamtraces coming out of film-hole rows R6 and R10 are disturbed more strongly than those of film-hole rows R1.Furthermore, the enhanced mixing at higher Tus of the mainstream and cooling air can be evidenced from the contours of temperature.These phenomena show that the higher mainstream Tus cause higher disturbances to the cooling air emitted on the PS than on the SS. Figure 14 demonstrates, for the vane without TBC at the three Tus, streamtraces of the cooling air released from the inlets of the film holes at midspan and contours of temperature in the plane perpendicular to the axial chord and immediately downstream of film-hole rows R1, R6 and R10.As Tu increases from 3.3% to 20%, the streamtraces coming out of film-hole rows R6 and R10 are disturbed more strongly than those of film-hole rows R1.Furthermore, the enhanced mixing at higher Tus of the mainstream and cooling air can be evidenced from the contours of temperature.These phenomena show that the higher mainstream Tus cause higher disturbances to the cooling air emitted on the PS than on the SS.  Figure 14 demonstrates, for the vane without TBC at the three Tus, streamtraces of the cooling air released from the inlets of the film holes at midspan and contours of temperature in the plane perpendicular to the axial chord and immediately downstream of film-hole rows R1, R6 and R10.As Tu increases from 3.3% to 20%, the streamtraces coming out of film-hole rows R6 and R10 are disturbed more strongly than those of film-hole rows R1.Furthermore, the enhanced mixing at higher Tus of the mainstream and cooling air can be evidenced from the contours of temperature.These phenomena show that the higher mainstream Tus cause higher disturbances to the cooling air emitted on the PS than on the SS.

Conclusions
This paper presents a numerical investigation on the combined effects of TBC and Tu on the cooling performances of a modified vane of the film-cooled nozzle guide vane (NGV).The overall cooling effectiveness, TBC effectiveness and heat transfer coefficient are analyzed and discussed at Tu = 3.3%, 10% and 20%.Through the comparisons and discussions, the following conclusions are drawn.However, it should be noted that because of the lack of experimental data for heat transfer in the report of Timko [26], a heat transfer comparison with the experimental data is not drawn.Therefore, the conclusions drawn here should be extended cautiously.
(1) TBC increases significantly the overall cooling effectiveness on the basis of the vane metal surface, but it does not alter the trends of distribution of the overall cooling effectiveness for all three Tus.(2) For this test case, with only two rows of film holes on the SS, TBC is more effective on the PS than on the SS.The role of TBC on the increment in the overall cooling effectiveness is relatively higher in the ineffectively cooled regions, i.e., the tip and hub of the vane, but is relatively lower in the regions close to the exits of film holes, the downstream of the diffusion shaped-holes on the SS, and the TE.
(3) When Tu increases, the increment in the overall cooling effectiveness due to TBC in the ineffectively cooled regions can reach up to 24% or 38 K at Tu = 20%, but increases slightly in the exits and downstream of the diffusion shaped-holes on the SS, as well as the TE.(4) TBC can block heat flux from mainstream into the vane, but it can also blocks the heat flux transferred from the solid vane into the mixing fluid of cooling air and the mainstream.When Tu increases, these effects becomes more significant.
φ TBC overall cooling effectiveness on the metal surface with TBC τ TBC effectiveness ∆φ increment of overall cooling effectiveness on the vane surface

Figure 1 .
Figure 1.Evaluation thermal parameters on vane surface with and without thermal barrier coating.

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

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

Figure 9 .
Figure 9.Effect of Tu on the percentage of temperature reduction (R) at midspan.

Figure 9 .
Figure 9.Effect of Tu on the percentage of temperature reduction (R) at midspan.Figure 9. Effect of Tu on the percentage of temperature reduction (R) at midspan.

Figure 9 .
Figure 9.Effect of Tu on the percentage of temperature reduction (R) at midspan.Figure 9. Effect of Tu on the percentage of temperature reduction (R) at midspan.

Figure 10 .
Figure 10.Heat flux on the uncoated vane (a-c) on the PS; (d-f) on the SS at three Tus.

Figure 10 .
Figure 10.Heat flux on the uncoated vane (a-c) on the PS; (d-f) on the SS at three Tus.

Figure 11 .
Figure 11.Effects of TBC on overall cooling effectiveness (a-c) on the PS; (d-f) on the SS at three Tus.

Figure 11 .
Figure 11.Effects of TBC on overall cooling effectiveness (a-c) on the PS; (d-f) on the SS at three Tus.

Figure 12 .Figure 13 .
Figure 12.Effect of TBC on heat transfer coefficient (a-c) on the PS; (d-f) on the SS at three Tus.

Figure 12 .Figure 12 .Figure 13 .
Figure 12.Effect of TBC on heat transfer coefficient (a-c) on the PS; (d-f) on the SS at three Tus.

Figure 13 .
Figure 13.Effect of Tu on cooling air emitted from film holes at midspan.

Figure 14 .
Figure 14.Effect of Tu on streamtraces of cooling air emitted from the film holes at midspan.

Table 3 .
Basic boundary conditions used in all simulations.

Table 3 .
Basic boundary conditions used in all simulations.