**2. Design consideration of cooled turbine blades**

In the design of air cooled gas turbine blades, there are several different factors related to the integration of a turbine blade thermal design into the overall gas turbine. Some of the key factors which influence the overall design of the turbine blade include [4–6, 51],


In **Figure 5**, some of the above parameters are highlighted, such as the impact of the coolant extracted from the different stages of the compressors. The front stage of the turbine will normally use the coolant extracted with the highest pressures, while the middle and rear turbine stages progressively use coolant extracted with lower pressures and temperatures. For the rear stage airofoils, the cooling systems are normally low pressure drops systems and do not have features such as film cooling and impingement cooling. The front stage airofoils however do have cooling systems with film cooling and impingement, as they are generally fed with the high pressure compressor end air. In addition to the impact of the air flow system, another major interface parameter for designing the airofoil cooling system is the combustor hot gas temperature and its distribution [8]. **Figure 5** shows a schematic of the hot gas distribution at the turbine inlet, which is generally nonuniform, and dependant on the upstream combustor and burner design. As **Figure 5** shows, typically there is a radial distribution of the hot gas temperature, which is commonly referred to as the profile factor or the radial temperature distortion factor (RTDF). In addition to this, there is also a circumferential temperature distribution which is referred to as the pattern factor or the outer temperature distortion factor (OTDF). In the thermal design of gas turbine airofoils, blade tips, and endwalls, these radial and circumferential temperature distributions are always considered in the design process, and are normally based on in-situ engine measurements and high fidelity CFD predictions.

**Figure 5.** Major design factors influencing the gas turbine overall aerothermal design, (a) coolant supply system, (b) combustor hot gas temperature profiles.

**Figure 6.** Major design interfaces for overall airofoil designs.

**2. Design consideration of cooled turbine blades**

expansion characteristics of the hot gas within the turbine.

• Blade material and its properties at elevated temperatures.

• Maintenance methods and reconditioning of the turbine blades.

operating envelope of the gas turbine.

• Geometrical clearances and gaps.

CFD predictions.

lifetime requirements.

114 Heat Exchangers– Design, Experiment and Simulation

In the design of air cooled gas turbine blades, there are several different factors related to the integration of a turbine blade thermal design into the overall gas turbine. Some of the key fac-

• Overall gas turbine performance (power output and efficiency) and airofoil component

• Variation of ambient conditions, start-up load gradients, and shut-down conditions.

• Turbine aerodynamics, external heat loads to airofoils and turbine inlet temperatures.

• Hot gas temperature, pressure, and velocity profiles from the combustor chamber, and the

• Choice of coolant from the compressor bleeds and the supply conditions over the entire

• Manufacturing capability of the blade internal cooling core, machining of film cooling

In **Figure 5**, some of the above parameters are highlighted, such as the impact of the coolant extracted from the different stages of the compressors. The front stage of the turbine will normally use the coolant extracted with the highest pressures, while the middle and rear turbine stages progressively use coolant extracted with lower pressures and temperatures. For the rear stage airofoils, the cooling systems are normally low pressure drops systems and do not have features such as film cooling and impingement cooling. The front stage airofoils however do have cooling systems with film cooling and impingement, as they are generally fed with the high pressure compressor end air. In addition to the impact of the air flow system, another major interface parameter for designing the airofoil cooling system is the combustor hot gas temperature and its distribution [8]. **Figure 5** shows a schematic of the hot gas distribution at the turbine inlet, which is generally nonuniform, and dependant on the upstream combustor and burner design. As **Figure 5** shows, typically there is a radial distribution of the hot gas temperature, which is commonly referred to as the profile factor or the radial temperature distortion factor (RTDF). In addition to this, there is also a circumferential temperature distribution which is referred to as the pattern factor or the outer temperature distortion factor (OTDF). In the thermal design of gas turbine airofoils, blade tips, and endwalls, these radial and circumferential temperature distributions are always considered in the design process, and are normally based on in-situ engine measurements and high fidelity

holes, application of thermal barrier coatings, and overall manufacturing costs.

tors which influence the overall design of the turbine blade include [4–6, 51],

At the airofoil component level design, **Figure 6** shows an overview of several other interface considerations which needs to be accounted for in the overall optimization of the airofoil thermal design. The major design drivers for an optimized airofoil design include engine performance targets, aerothermal targets, component lifetime and mechanical integrity targets, and the manufacturing and cost constraints. Within these global requirements, **Figure 6** also highlights that are also many subtargets, such as manufacturing capability and field experience.

### **3. Turbine blade thermal analysis**

#### **3.1. Global thermal assessments**

Due to the large number of operating and geometrical parameters that influence the heat transfer mechanism in gas turbine blades, simplified zero-dimensional relationships and design charts are often utilized. This allows for assessing the impact of various operational and geometrical parameters on a given blade cooling system. For such zero-dimensional analysis, it is important to have the detailed 2D and 3D thermal analysis results of the specific turbine blade or vane, and which has effectively been proven for meeting the design performance and lifetime in field gas turbines. This is commonly referred to as the reference blade from which new designs and concepts can be developed with a sufficient degree of confidence.

The thermal analysis is based on a simplified conjugate heat transfer analysis of flow in a cooling passage of a turbine blade as shown in **Figure 7** and assumes that the airofoil; (a) metal temperature is the average surface temperature at the airofoil midspan, (b) is exposed to the maximum hot gas temperature profile at the blade inlet, and (c) the coolant enters at the blade root and exits at the blade trailing edge. Then by performing a simple energy balance, it can be observed that,

Heat transferred from the hot gas to the airofoil = heat gained by the airofoil = heat gained by the coolant in the airofoil.

$$Q = h\_{\underline{c}} S\_{\underline{c}} L \left( T\_f - T\_m \right) = h\_{\underline{c}} S\_{\underline{c}} L \left( T\_m - T\_c \right) = m\_{\underline{c}} C\_{\underline{pc}} \left( T\_{\underline{co}} - T\_{\underline{c}} \right) \tag{1}$$

where *Q* is the total heat transferred to the airofoil, *h*<sup>g</sup> and *hc* are respectively the hot gas and coolant heat transfer coefficients, L is the airofoil height, *Sg* and *Sc* are respectively the total airofoil perimeter on the gas and coolant sides, *Tf* is the average film cooling temperature, *Tm* is the average airofoil metal temperature, and *Tci* and *Tco* are the coolant inlet and out temperatures. *Tc* is the average of the coolant inlet and outlet temperatures. For film-cooled airofoils, a film cooling effectiveness is additionally defined, which essentially modifies the driving hot gas temperature, *Tg* , with a film temperature, which is defined by;

$$\text{Fillm Cooling Efficiency}, \qquad \eta\_f = \frac{T\_g - T\_f}{T\_g - T\_w} \tag{2}$$

After rearranging the above equations, the following relationships can be derived;

$$\text{Cooding Efficiency}, \qquad \qquad \varepsilon = \frac{T\_g - T\_n}{T\_g - T\_{\dot{a}}} \tag{3}$$

$$\text{Mass flow function}, \qquad \qquad m^\* = \frac{m\_\epsilon \cdot C\_{pc}}{h\_g \cdot S\_g \cdot L} \tag{4}$$

**Figure 7.** Thermal design parameters of a gas turbine airofoil.

At the airofoil component level design, **Figure 6** shows an overview of several other interface considerations which needs to be accounted for in the overall optimization of the airofoil thermal design. The major design drivers for an optimized airofoil design include engine performance targets, aerothermal targets, component lifetime and mechanical integrity targets, and the manufacturing and cost constraints. Within these global requirements, **Figure 6** also highlights that are also many subtargets, such as manufacturing capability and field experience.

Due to the large number of operating and geometrical parameters that influence the heat transfer mechanism in gas turbine blades, simplified zero-dimensional relationships and design charts are often utilized. This allows for assessing the impact of various operational and geometrical parameters on a given blade cooling system. For such zero-dimensional analysis, it is important to have the detailed 2D and 3D thermal analysis results of the specific turbine blade or vane, and which has effectively been proven for meeting the design performance and lifetime in field gas turbines. This is commonly referred to as the reference blade from which

The thermal analysis is based on a simplified conjugate heat transfer analysis of flow in a cooling passage of a turbine blade as shown in **Figure 7** and assumes that the airofoil; (a) metal temperature is the average surface temperature at the airofoil midspan, (b) is exposed to the maximum hot gas temperature profile at the blade inlet, and (c) the coolant enters at the blade root and exits at the blade trailing edge. Then by performing a simple energy balance, it can be observed that, Heat transferred from the hot gas to the airofoil = heat gained by the airofoil = heat gained by

is the average airofoil metal temperature, and *Tci* and *Tco* are the coolant inlet and out tempera-

a film cooling effectiveness is additionally defined, which essentially modifies the driving hot

, with a film temperature, which is defined by;

After rearranging the above equations, the following relationships can be derived;

*Tg* − *Tco*

*Tg* − *Tci*

is the average of the coolant inlet and outlet temperatures. For film-cooled airofoils,

and *hc*

and *Sc*

) (1)

(2)

(3)

are respectively the hot gas and

is the average film cooling temperature, *Tm*

*hg Sg <sup>L</sup>* (4)

are respectively the total

new designs and concepts can be developed with a sufficient degree of confidence.

*Q* = *hg Sg L* (*Tf* − *Tm*) = *hc Sc L* (*Tm* − *Tc*) = *mc Cpc* (*Tco* − *Tci*

where *Q* is the total heat transferred to the airofoil, *h*<sup>g</sup>

airofoil perimeter on the gas and coolant sides, *Tf*

Film Cooling Effectiveness, *η<sup>f</sup>* <sup>=</sup> *Tg* <sup>−</sup> *<sup>T</sup>* \_\_\_\_\_*<sup>f</sup>*

Cooling Effectiveness, *<sup>ε</sup>* <sup>=</sup> *Tg* <sup>−</sup> *<sup>T</sup>* \_\_\_\_\_*<sup>m</sup>*

Mass flow function, *<sup>m</sup>* \* <sup>=</sup> *mc <sup>C</sup>* \_\_\_\_\_*pc*

coolant heat transfer coefficients, L is the airofoil height, *Sg*

**3. Turbine blade thermal analysis**

116 Heat Exchangers– Design, Experiment and Simulation

**3.1. Global thermal assessments**

the coolant in the airofoil.

tures. *Tc*

gas temperature, *Tg*

$$\text{Cooding Efficiency}\_{\prime} \tag{5}$$

$$\eta = \frac{T\_{\text{co}} - T\_{\text{o}}}{T\_{\text{n}} - T\_{\text{o}}} \tag{6}$$

By further combining for the effectiveness, massflow function and efficiency, the following practical engineering formulations can be derived.

$$\text{Overall effectiveness}, \qquad \qquad \varepsilon = \frac{m^\*}{1 + m^\*\eta} \tag{6}$$

$$\text{Overall efficiency,}\\
\text{ }\qquad \eta = 1 - \exp\left[-\frac{A}{m^\*}\right] \quad \text{Where} \ A = \frac{h\_\circ \cdot S\_\circ}{h\_\circ \cdot S\_\circ}\tag{7}$$

To represent thermal barrier coatings (TBC) and the airofoil wall thickness, the hot gas and coolant heat transfer coefficients in the above equations are replaced by effective heat transfer coefficients, i.e.,

$$h\_{g.gt} = \frac{h\_{\text{g}}}{1 + B\,i\_{\text{th}}} \tag{8}$$

$$h\_{c.gt} = \frac{h\_{\text{c}}}{1 + B\,i\_{\text{w}}} \tag{9}$$

$$h\_{c.gt} = \frac{h\_{\text{c}}}{1 + B\,i\_{w}} \tag{9} \text{ where wall Biot number, B } i\_{w} = \frac{h\_{\text{c}}t\_{w}}{k\_{w}}$$

Where, *t tbc* and *ktbc* are the thermal barrier coating thickness and thermal conductivity, respectively. Similarly, *t <sup>w</sup>* and *kw* are the metal wall thickness and thermal conductivity. From the above relationship, it can be observed that for the extreme cases, when *ε* = 0, *Tm* = *Thg*, the airofoil metal temperature equal the gas temperature, and when *ε* = 1, *Tm* = *Tc* and the airofoil 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 0.1–0.7.

**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 by the lowest effectiveness and efficiency values.

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

#### **3.2. Detailed aerothermal designs**

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

**Figure 9.** Detailed airofoil aerothermal design using (a) conjugate thermal modelling [9], and (b) 3D thermal modelling and comparisons with measured engine data [2, 10].

loads on the airofoil hot gas surfaces are directly simulated. **Figure 9(b)** shows a typical example of the predicted metal temperature on a turbine vane based on a conjugate heat transfer model and compared to measured metal temperatures from a test engine [2, 10].
