**4. External heat transfer of cooled turbine airofoils**

The aerodynamics of the gas path flows through the static turbine vanes and rotating blades consist of a range of flow phenomena and flow structures such as accelerating sonic and transonic flows, unsteady flows, separated flows, secondary flows, overtip leakage flows, and interacting flows between the main gas path flows and coolant and leakage flows. To enhance the turbine aerodynamic efficiency and manage the external heat loads, significant research efforts have been made over the past decade to minimize the energy losses which are associated with the latter flow phenomenon. Similarly, there has been a significant research effort [4–6, 11, 12], in understanding and minimizing the external heat transfer on the turbine airofoils and endwalls, which is essentially defined by the gas path aerodynamics, thermodynamics, turbine geometrical annulus, and the geometrical profiles of the airofoils.

#### **4.1. Airofoil external heat loads**

airofoil metal temperature equal the gas temperature, and when *ε* = 1, *Tm* = *Tc*

by the lowest effectiveness and efficiency values.

118 Heat Exchangers– Design, Experiment and Simulation

**3.2. Detailed aerothermal designs**

**Figure 8.** Heat transfer performance chart for gas turbine blades.

0.1–0.7.

metal temperature equals the coolant temperature. For most gas turbine blades ranging from the rear to the front turbine stages, the effectiveness values are respectively in the range of

**Figure 8** shows the relationship between the cooling effectiveness, mass flow function and the cooling efficiency, which is shown in an alternative form to that normally highlighted in Refs. [4–6]. Here, the cooling efficiency and the massflow function parameters are plotted on the horizontal and vertical axis respectively, which makes it easier to compare the cooling efficiencies of different turbines. From **Figure 8**, it is clear the front stages of the gas turbine, which are exposed to the highest hot gas temperatures, will generally have the highest cooling effectiveness and efficiency levels as their cooling designs will include film cooling, thermal barrier coatings, impingement cooling, turbulator convective cooling, and advanced alloys. The rear stages which are generally exposed to the lowest hot gas temperatures are generally convectively cooled, consume the least amount of cooling air, and are represented

During the detailed design phases, the design of cooled turbine airofoils is normally done using design systems which incorporate the effect of all three-dimensional geometrical and aerothermal effects. There is extensive use of computational fluid dynamics, as part of the overall turbine design process and the thermal analyses are based on conjugate heat transfer-based model. **Figure 9(a)** shows a typical example of a gas turbine blade conjugate heat transfer model [9], where both the internal coolant flows in the internal cooling passages and the external heat

and the airofoil

The aerodynamic development of the boundary layer on the turbine static and rotating airofoils is highly nonuniform, and it largely determines the absolute levels of the external heat transfer coefficient to which it will be exposed. Other factors that significantly influence the airofoil heat transfer include the mainstream turbulence, profile curvature, streamwise pressure gradients, surface roughness, upstream wakes, and film cooling. **Figure 10** shows the Mach number measured on a turbine vane and blade [13], and highlights; (a) the strong Mach

**Figure 10.** Aerodynamic measurements and predictions on a 1st stage (a) vane and (b) blade [12].

number variations near the leading edge stagnation point, (b) accelerating flow on the pressure and suction sides immediately downstream of the leading edge, (c) region of transitional boundary layer, (d) regions of accelerating turbulent flows on the pressure side, and (e) regions of peak Mach numbers on the suction side followed by decelerating flows towards the trailing edge. It is this variation in the profile Mach number which largely determines the vane and blade external heat transfer coefficients.

The detailed distribution of the heat transfer coefficients on the turbine vane and blade of a high pressure turbine was measured by Tallman et al. [12] for a range of operating conditions. **Figure 11** shows the distribution of the measured and predicted Stanton numbers, (St = Nu/ Re.Pr) at 50% airofoil span and at Re/L = 3.1 e6, and clearly highlights the differences in the heat transfer distribution between the vane and the blade. This is largely due to the different profile shapes, leading edge diameters, Mach number distributions, and the overall pressure ratio across the vane and blade. **Figure 11** highlights the heat transfer distribution associated with the various aerodynamic flow regimes on the airofoil. For the vane, the heat transfer coefficient increases from the leading edge to the suction side, reaches a peak value, and then decelerates towards the trailing edge. On the pressure side, it reduces from the leading edge and after transition, continuously accelerates up to the trailing edge. For the blade, the peak heat transfer coefficient value is at the leading edge, which then decreases gradually on the

**Figure 11.** External heat transfer measurements at 50% span, (a) 1st stage vane, and (b) 1st stage blade. [12].

suction side until the trailing edge. However, on the pressure side, the heat transfer coefficient reduces rapidly from the leading edge, and then there is a transition to higher values until the trailing edge. These typical trends in the nonuniformity of the heat transfer coefficient are generally observed on most turbine vanes and blades. However, in addition to these generalized airofoil heat transfer distributions, actual industrial gas turbines blades are also affected by several other parameters, such as; inlet pressure and temperature profiles, airofoil shape and curvature, position of film cooling holes, thermal barrier coating roughness, transient wakes from upstream vanes, and blade passage turbulence intensity levels.

### **4.2. Endwall external heat loads**

number variations near the leading edge stagnation point, (b) accelerating flow on the pressure and suction sides immediately downstream of the leading edge, (c) region of transitional boundary layer, (d) regions of accelerating turbulent flows on the pressure side, and (e) regions of peak Mach numbers on the suction side followed by decelerating flows towards the trailing edge. It is this variation in the profile Mach number which largely determines the

**Figure 10.** Aerodynamic measurements and predictions on a 1st stage (a) vane and (b) blade [12].

The detailed distribution of the heat transfer coefficients on the turbine vane and blade of a high pressure turbine was measured by Tallman et al. [12] for a range of operating conditions. **Figure 11** shows the distribution of the measured and predicted Stanton numbers, (St = Nu/ Re.Pr) at 50% airofoil span and at Re/L = 3.1 e6, and clearly highlights the differences in the heat transfer distribution between the vane and the blade. This is largely due to the different profile shapes, leading edge diameters, Mach number distributions, and the overall pressure ratio across the vane and blade. **Figure 11** highlights the heat transfer distribution associated with the various aerodynamic flow regimes on the airofoil. For the vane, the heat transfer coefficient increases from the leading edge to the suction side, reaches a peak value, and then decelerates towards the trailing edge. On the pressure side, it reduces from the leading edge and after transition, continuously accelerates up to the trailing edge. For the blade, the peak heat transfer coefficient value is at the leading edge, which then decreases gradually on the

**Figure 11.** External heat transfer measurements at 50% span, (a) 1st stage vane, and (b) 1st stage blade. [12].

vane and blade external heat transfer coefficients.

120 Heat Exchangers– Design, Experiment and Simulation

At the vane and blade endwall or platform, the aerodynamic flows are highly three-dimensional, transonic, and consist of areas where the hot gas flow strongly interacts with cooler rim purge and leakage flows. **Figure 12(a)** highlights the salient features of the hot gas path flow interactions on the platforms, which are largely pressure driven flows generated by the crosspassage pressure differences on the pressure and suction side of neighbouring airofoils. Over the last decade, there has been a significant experimental and numerical research effort to understand the behavior and impact of these high speed endwall flows on the platform heat transfer [4–6, 11, 16, 17]. Some of the key factors which define the platform heat transfer include the inlet profile of hot gas temperature, pressure and turbulence intensities, film cooling, platform contouring, and impact of leakage and rim purge flows.

**Figure 12(b)** shows the heat transfer and film cooling distributions on a first stage vane [15]. The heat transfer coefficient distribution shows that the suction side shoulder and the pressure side trailing edge regions experience the highest heat transfer coefficients, which also correspond to the areas with the highest Mach numbers. For the vane platform film cooling effectiveness without the upstream purge flows, **Figure 12(c)** shows that the measured and predicted film cooling effectiveness compares quite well, and the films remain attached to the passage wall and are very effective in cooling the platform. Due to the three-dimensional nature of the endwall flows, **Figure 12** highlights that the magnitude and directions of the local velocity, temperature, and pressure distributions play a dominant role in the heat transfer distributions on airofoil platforms.

**Figure 12.** Endwall flow and heat transfer, (a) flow structures [14], (b) heat transfer coefficients [15], and (c) film cooling effectiveness [15].

#### **4.3. Blade tip and endwall external heat loads**

The blade tip and its neighbouring endwall regions are one of the most complex aerodynamic and heat transfer areas of the gas turbine. **Figure 13** shows some typical blade tips designs ranging from flat tips, squealers and shrouded tips, and its impact on the turbine efficiency. For flat tip and squealer tip designs, this region is dominated by the pressure driven overtip leakage flow from the airofoil pressure side to the suction side. This flow then travels through the narrow gap between the rotating blade and the static casing endwall, and subsequently interacts with the main cross passage flows to form a high speed vortex on the tip suction side. For the shrouded blade, the gas flow is from the leading to the trailing edge. The hot gas flows then interact within the rotating shroud fins with the shroud cooling air. Due to the complex flow structure and high heat loads at the blade tips, an accurate knowledge of the local aerodynamics and heat transfer is important for ensuring that the mechanical integrity of the blade tips are ensured for long operating periods, especially at higher gas turbine operating temperatures.

**Figure 14** shows the sensitivity of the key parameters which influence the metal temperature of a typical squealer blade tip design. The main parameters influencing the tip metal temperatures are the hot gas temperatures and the cavity mixed temperatures. Other parameters such as the wall thickness and the heat transfer coefficients also play a major role in determining the tip metal temperatures. The heat transfer distribution on the blade tip and the endwall is highly nonuniform and driven largely by the local Mach number distributions and the tip geometry [4–6, 11, 53].

**Figure 15** shows the flow distributions for two squealer tip designs and highlights the complex flow structure within the tip crown and the flow interactions between the tip leakage, main hot gas flows, and the coolant within the blade passage [18]. For these two blade tip designs, **Figure 16** also shows the measured and predicted heat transfer coefficients on the

**Figure 13.** Typical blade tip designs and performance characteristics.

**Figure 14.** Sensitivity of operating conditions on blade tip heat transfer.

**4.3. Blade tip and endwall external heat loads**

122 Heat Exchangers– Design, Experiment and Simulation

**Figure 13.** Typical blade tip designs and performance characteristics.

temperatures.

[4–6, 11, 53].

The blade tip and its neighbouring endwall regions are one of the most complex aerodynamic and heat transfer areas of the gas turbine. **Figure 13** shows some typical blade tips designs ranging from flat tips, squealers and shrouded tips, and its impact on the turbine efficiency. For flat tip and squealer tip designs, this region is dominated by the pressure driven overtip leakage flow from the airofoil pressure side to the suction side. This flow then travels through the narrow gap between the rotating blade and the static casing endwall, and subsequently interacts with the main cross passage flows to form a high speed vortex on the tip suction side. For the shrouded blade, the gas flow is from the leading to the trailing edge. The hot gas flows then interact within the rotating shroud fins with the shroud cooling air. Due to the complex flow structure and high heat loads at the blade tips, an accurate knowledge of the local aerodynamics and heat transfer is important for ensuring that the mechanical integrity of the blade tips are ensured for long operating periods, especially at higher gas turbine operating

**Figure 14** shows the sensitivity of the key parameters which influence the metal temperature of a typical squealer blade tip design. The main parameters influencing the tip metal temperatures are the hot gas temperatures and the cavity mixed temperatures. Other parameters such as the wall thickness and the heat transfer coefficients also play a major role in determining the tip metal temperatures. The heat transfer distribution on the blade tip and the endwall is highly nonuniform and driven largely by the local Mach number distributions and the tip geometry

**Figure 15** shows the flow distributions for two squealer tip designs and highlights the complex flow structure within the tip crown and the flow interactions between the tip leakage, main hot gas flows, and the coolant within the blade passage [18]. For these two blade tip designs, **Figure 16** also shows the measured and predicted heat transfer coefficients on the

**Figure 15.** Flow structure and Mach number distributions for full and partial squealer blade tips [18].

blade with film cooling [18]. Both measurements and predictions show that on the blade tip, very high values exist in the leading edge regions and on the suction side rims. However, on the neighbouring endwall, the high heat transfer regions are largely location on the blade pressure side and towards the trailing edge.

#### **4.4. Thermal barrier coatings**

The use of high temperature thermal barrier coatings (TBC) for reducing the incident heat flux on both static and rotating gas turbines blades is extensive in gas turbines, particularly

**Figure 16.** Heat transfer coefficient distributions on blade tip and endwall for full and partial squealer blade tips [18].

in the first and second turbine stages. There are essentially two main types of TBC, which are in widespread use in the gas turbine industry, namely air plasma sprayed (APS) and electron beam physical vapour deposition (EBPVD) [7]. For heavy duty gas turbines, the APS TBC is widely used with thickness which can range from 100 to up to 600 μm. The thermal impact of thermal barrier coatings on the turbine blade thermomechanical integrity is significant, and they therefore play an important role as a thermal protection system for gas turbine components. As highlighted previously, in the thermal analysis of turbine blades, the thermal barrier coating is generally represented as a thermal resistance to the incident heat flux, by modifying the hot gas transfer coefficient via the thermal barrier coating Biot number. **Figure 17** shows that by increasing the thickness of the thermal barrier coating and reducing its thermal conductivity, the effective hot gas heat transfer coefficient can be significantly reduced. This results in a direct reduction of the incident heat flux on the turbine blade.

**Figure 17.** Effect of thermal barrier coatings (TBC) on heat transfer.

For typical heavy duty gas turbines, **Figure 17** shows that the thermal barrier coating reduces the effective heat transfer coefficient by almost 50% compared to no application of the TBC. Additionally, **Figure 17** shows that, for the new generation of advanced TBC's [6, 7], with lower thermal conductivity, the effective heat transfer coefficient can be further reduced. It is clear from **Figure 17**, that thermal barrier coatings are an integral and significant part of the overall blade thermal design system.

### **4.5. Film Cooling**

in the first and second turbine stages. There are essentially two main types of TBC, which are in widespread use in the gas turbine industry, namely air plasma sprayed (APS) and electron beam physical vapour deposition (EBPVD) [7]. For heavy duty gas turbines, the APS TBC is widely used with thickness which can range from 100 to up to 600 μm. The thermal impact of thermal barrier coatings on the turbine blade thermomechanical integrity is significant, and they therefore play an important role as a thermal protection system for gas turbine components. As highlighted previously, in the thermal analysis of turbine blades, the thermal barrier coating is generally represented as a thermal resistance to the incident heat flux, by modifying the hot gas transfer coefficient via the thermal barrier coating Biot number. **Figure 17** shows that by increasing the thickness of the thermal barrier coating and reducing its thermal conductivity, the effective hot gas heat transfer coefficient can be significantly reduced. This

**Figure 16.** Heat transfer coefficient distributions on blade tip and endwall for full and partial squealer blade tips [18].

For typical heavy duty gas turbines, **Figure 17** shows that the thermal barrier coating reduces the effective heat transfer coefficient by almost 50% compared to no application of the TBC. Additionally, **Figure 17** shows that, for the new generation of advanced TBC's [6, 7], with

results in a direct reduction of the incident heat flux on the turbine blade.

**Figure 17.** Effect of thermal barrier coatings (TBC) on heat transfer.

124 Heat Exchangers– Design, Experiment and Simulation

Film cooling is generally applied at different locations along the perimeter of an airofoil by rows of discrete holes, through which coolant air is discharged into the airofoil external boundary layer. The coolant, which is several hundred degrees colder than the hot gas, then creates a film of air on the airofoil surface, whose temperature is significantly lower than the surrounding hot gas. Consequently, the incident hot gas temperature for heat transfer is reduced. **Figure 18** shows an example of the application of a film row at the blade trailing edge and the key parameters which define the performances of film cooling. **Figure 19** shows that as the average film cooling effectiveness on a turbine blade is increased, the film to hot gas temperature ratio reduces and the film temperature close to the wall can be reduced by several hundred degrees relative to the surrounding hot gas temperature.

**Figure 18.** Film cooling of gas turbine blades.

Increasing the average film cooling effectiveness can be achieved by using many film rows, but this would be at the expense of high coolant consumption and reduced turbine efficiencies. Alternatively, increased film cooling effectiveness can also be achieved by using advanced film cooling hole designs without increasing the coolant consumption [4, 6, 11, 13, 20, 21].

The film cooling effectiveness depends on the complex aerothermal interaction between the high speed hot gas flow and the ejected film cooling jets in the external gas boundary layer. It is also dependent on several geometrical and operational parameters such as film cooling hole shape, hole angle, velocity and temperature of the ejected coolant, temperature and velocity of the surrounding hot gas, blade curvature, and local turbulence levels. As highlighted in **Figure 19**, increasing the film cooling effectiveness results in significant reduction in the film to hot gas temperature ratio, and hence there continues to be a significant research effort on developing film cooling technology due to its significant benefits in reducing local near wall

**Figure 19.** Effect of film cooling effectiveness on hot gas temperatures.

hot gas temperatures [4–6, 11, 16, 17, 20, 21]. Over the last decade, there has been a significant focus on airofoil, platform, and blade tip film cooling with more recent focus on advanced shapes of film cooling holes, such as three-dimensional shaped holes and trench holes. In a recent study [13], the multirow film cooling characteristic on a high lift vane and blade were demonstrated. **Figure 20** shows that the use of three-dimensional advanced fan shaped holes can provide high airofoil average film cooling effectiveness and the use of only one or two row of shaped holes located upstream of the suction side shoulder can provide high film cooling effectiveness until the trailing edge.

**Figure 20.** Multi row film cooling characteristics on a gas turbine (a) vane and (b) blade [13].
