The performance of gas turbine engines may be improved by increasing the toleran

Question

The performance of gas turbine engines may be

improved by increasing the tolerance of the turbine

blades to hot gases emerging from the combustor. One

approach to achieving high operating temperatures

involves application of a thermal barrier coating

(TBC) to the exterior surface of a blade, while passing

cooling air through the blade. Typically, the blade is

made from a high-temperature superalloy, such as

Inconel (k = 25 W/m K), while a ceramic, such as

zirconia (k =1.3 W/m K), is used as a TBC.

Consider conditions for which hot gases at T,o=

1700 K and cooling air at T,i 400 K provide outer

and inner surface convection coefficients of ho=

1000 W/m2 K and hi =500 W/m2 K, respectively. If a

0.5-mm-thick zirconia TBC is attached to a 5-mmthick

Inconel blade wall by means of a metallic bonding

agent, which provides an interfacial thermal resistance

of Rt,c =104 m2 K/W, can the Inconel be maintained

at a temperature that is below its maximum

allowable value of 1250 K? Radiation effects may be

neglected, and the turbine blade may be approximated

as a plane wall. Plot the temperature distribution with

and without the TBC. Are there any limits to the thickness

of the TBC?

Explanation / Answer

if Ts,0 and Ts,i <Melting R'', point of incones

eRtotal =1/ho + (L/k)zx +R''t,c + (L/k)in +1/h1

=1/1000+.5x10^-3/1.3 +10^-4 +5X10^-3/25 +1/500

=3.69x10^-3 m^2/K.

q''=(1700-400)/3.69x10^-3

=3.52x10^5 w/m^2

q''= hi(ts,i - Tdaeta, i)

Ts,i= q^v/hi+h daeta,i = 1104K

q''= (Ts,0 - T daeta, i)/R total

=(Ts,o-Tdaeta,i)/(L/k)In+1/hi

then Ts,0=1174K

Note/ I could not write the sign of daeta so u suppose to know it.

good luck

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