Question 14.8: For a forced convection cooling of an axial flow turbine bla......

1. The blade temperature is expressed by the relation (14.90), from which

T_{\text{b}}=T_{\text{cr}}+(T_{\text{g}}-T_{\text{cr}})\left[1-\frac{e^{-Kl/L}}{1+h_{\text{g}}S_{\text{g}}/h_{\text{c}}S_{\text{c}}} \right] =320+1180\left[1-\frac{e^{-Kl/L}}{3} \right] \\ \frac{K}{L} =\frac{h_{\text{g}}S_{\text{g}}}{\dot{m}_{\text{c}}C_{\text{pc}}[1+(h_{\text{g}}S_{\text{g}}/h_{\text{c}}S_{\text{c}})]} =\frac{1500 \times 0.15}{1.0 \times 1005(1+2)} =0.0746 \\ \therefore T_{\text{b}}=320+1180\left[1-\frac{e^{-0.0746 \ l}}{3} \right] \quad \quad \quad (1)

The coolant temperature is to be calculated from the relation

T_{\text{C}}=T_{\text{g}}-(T_{\text{g}}-T_{\text{b}})[1+(h_{\text{s}}S_{\text{g}}/h_{\text{c}}S_{\text{c}})] \\ T_{\text{C}}=1500-3(1500-T_{\text{b}}) \quad \quad \rightarrow (2)

From Equations 1 and 2, T_{\text{b}} \text{ and } T_{\text{g}} are calculated at different blade heights

The blade and coolant temperature distribution along the blade height are plotted in Figure 14.43.
Variation of blade and coolant temperatures along the blade height.

2. Calculate the parameter (φ) and (T_{\text{M}})

\text{Since} \ \phi = \frac{T_{\text{G}}-T_{\text{M}}}{T_{\text{G}}-T_{\text{C}}} \\ T_{\text{M}}=T_{\text{G}}-\phi(T_{\text{G}}-T_{\text{C}})

Since \dot{m}_{\text{c}}/\dot{m}_{\text{g}} = 3%, from Figure 14.39, the value of Φ is determined and the maximum blade temperature for different cooling techniques is calculated and listed in Table 14.6.
As seen from the table, transpiration method gives the minimum value of the maximum temperature, which assures that it is the best cooling technique.