Page 155 - Handbook of Energy Engineering Calculations

4. Find the temperature at the exhaust of the gas turbine
Using an approach similar to that above, determine T from (T /T ) =
4
3′
4′
[(P /P )] k–k .Substituting and solving for T4′ = 1661[(14.9/56)] (1.4-1)/1.4 =
4′
3′
1137.9°R, or 677.8°F (358.8°C).
Now use the equation for gas-turbine efficiency, namely, turbine efficiency
= c (T − T )/c (T − T ) = 0.85, and solve for T , the temperature after
4″
p
3′
4′
4″
p
3′
expansion, at the exhaust. Substituting as earlier, T = 1218.2°R, 758.2°F
4″
(403.4°C). This is the temperature after expansion, i.e., at the exhaust of the
gas turbine.
5. Determine the work of compression, expander work, and thermal
efficiency
(b) The work of compression = c (T − T ) = 0.24(828 − 520) = 74.16 Btu
1
2′
p
(78.23 J).
The work delivered by the expander = c (T − T ) = 0.24 (1661 − 1218) =
1
p
2′
106.32 Btu (112.16 J).
The net work = 106.3 − 74.2 = 32.1 Btu (33.86 J). Then, the thermal
efficiency = net work/heat supplied = 32.1/200 = 0.1605, 16.6 percent
thermal efficiency.

Related Calculations. With the widespread use today of gas turbines in a
variety of cycles in industrial and central-station plants, it is important that an

engineer be able to analyze this important prime mover. Because gas turbines
can be quickly installed and easily hooked to heat-recovery steam generators
(HRSG), they are more popular than ever before in history.
Further, as aircraft engines become larger—such as those for the Boeing

787 and the Airbus 380—the power output of aeroderivative machines
increases at little cost to the power industry. The result is further application
of gas turbines for topping, expansion, cogeneration, and a variety of other
key services throughout the world of power generation and energy

conservation.
With further refinement in gas-turbine cycles, specific fuel consumption,
Fig. 15, declines. Thus, the complete cycle gas turbine has the lowest specific
fuel consumption, with the regenerative cycle a close second in the 6-to-1

compression-ratio range.