Known An ideal air-standard gas turbine cycle operates with reheat and regeneration. Temperatures and pressures at principal states are specified.
Find Determine the thermal efficiency.
Schematic and Given Data:
Engineering Model
1. Each component of the power plant is analyzed as a control volume at steady state.
2. The compressor and turbine processes are isentropic.
3. There are no pressure drops for flow through the heat exchangers.
4. The regenerator effectiveness is 100%.
5. Kinetic and potential energy effects are negligible.
6. The working fluid is air modeled as an ideal gas.
Analysis We begin by determining the specific enthalpies at each principal state of the cycle. States 1, 2, and 3 are the same as in Example 9.4: h_{1}=300.19 kJ / kg , h_{2}=579.9 kJ / kg , h_{3}=1515.4 kJ / kg.
The temperature at state b is the same as at state 3, so h_{ b }=h_{3}.
Since the first turbine process is isentropic, the enthalpy at state a can be determined using p_{ r } data from Table A-22 and the relationship
p_{ ra }=p_{ r 3} \frac{p_{ a }}{p_{3}}=(450.5) \frac{300}{1000}=135.15
Interpolating in Table A-22, we get h_{ a }=1095.9 kJ/kg.
The second turbine process is also isentropic, so the enthalpy at state 4 can be determined similarly. Thus,
p_{ r 4}=p_{ rb } \frac{p_{4}}{p_{ b }}=(450.5) \frac{100}{300}=150.17
Interpolating in Table A-22, we obtain h_{4}=1127.6 kJ/kg. Since the regenerator effectiveness is 100%, h_{ x }=h_{4}=1127.6 kJ/kg.
The thermal efficiency calculation must take into account the compressor work, the work of each turbine, and the total heat added. Thus, on a unit mass basis
\eta=\frac{\left(h_{3}-h_{ a }\right)+\left(h_{ b }-h_{4}\right)-\left(h_{2}-h_{1}\right)}{\left(h_{3}-h_{ x }\right)+\left(h_{ b }-h_{ a }\right)}
=\frac{(1515.4-1095.9)+(1515.4-1127.6)-(579.9-300.19)}{(1515.4-1127.6)+(1515.4-1095.9)}
1 = 0.654 (65.4%)
1 Comparing the present value with the thermal efficiency determined in part (a) of Example 9.4, we can conclude that the use of reheat coupled with regeneration can result in a substantial increase in thermal efficiency.
Skills Developed
Ability to…
• sketch the schematic of the regenerative gas turbine with reheat and the T–s diagram for the corresponding air-standard cycle.
• evaluate temperatures and pressures at each principal state and retrieve necessary property data.
• calculate the thermal efficiency.
Quick Quiz
What percentage of the total heat addition occurs in the reheat process? Ans. 52%.
