Turbine blades mounted to a rotating disc in a gas turbine engine are exposed to a gas stream that is at Tinfinity=1200 deg. C and maintains a convection coefficient of h=250W/m2K over the blade. The blades, which are fabricated from Inconel, k=6*10-4 m2 and a perimeter of P=110mm. A proposed blade-cooling scheme, which involves routing air through the supporting disc, is able ot maintain the base of each blade at a temperature of Tb=300 deg. C.

A. If the maximum allowable blade temperature is 1050 deg. C and the blade tip may be assumed to be adiabatic, is the proposed cooling scheme satisfactory?

B. For the proposed heating scheme, what is the rate at which heat is transferred from each blade to the coolant?

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cjmejiab cjmejiab · Answer 1 · 2019-11-08T22:15:09+01:00

a) We start calculating the temperature through the Temperature Distribution equation, which is

First with our values, we calculate the parameter m,

[tex]m=(\frac{hP}{kA_c})\{0.5} = (\frac{250*110*10^{-3}}{20*(6*10^{-4})})=47.87/m[/tex]

[tex]\frac{T-T_{\infty}}{T_b-T_{\infty}} = \frac{1}{cosh mL}[/tex]

Replacing ,

[tex]\frac{T-1200}{300-1200} = \frac{1}{cosh(47.87*0.05)}[/tex]

[tex]T=(-900)(0.81109)+1200[/tex]

[tex]T=1037\°c[/tex]

We realize that the temperature is below the 1050 allowed. Using techniques to reach the target temperature are recommended.

b) To calculate the heat rate, we only apply its equation, that is,

[tex]Q_f = (hpkA_c)^{0.5}(T_b-T_{\infty})tanh mL[/tex]

[tex]Q_f = (250*100*10^{-3}*20*6*10^{-4})^{0.5}(300-1200)(47.87-0.05)[/tex]

[tex]Q_f = -508W[/tex]

There is a loss of 508W