Known An air-standard regenerative gas turbine with intercooling and reheat operates at steady state. Operating pressures and temperatures are specified. Turbine and compressor isentropic efficiencies are given and the regenerator effectiveness is known.
Find Determine the thermal efficiency, back work ratio, net power developed, in kW, and total rate energy is added by heat transfer, in kW.
Schematic and Given Data:
Engineering Model
1. Each component is analyzed as a control volume at steady state. The control volumes are shown on the accompanying sketch by dashed lines.
2. There are no pressure drops for flow through the heat exchangers.
3. The compressor and turbine are adiabatic.
4. Kinetic and potential energy effects are negligible.
5. The working fluid is air modeled as an ideal gas.
Analysis Specific enthalpy values at states shown in Fig. E9.11 are provided in the following table. See note 1 for discussion.
| State |
h (kJ/kg) |
State |
h (kJ/kg) |
| 1 |
300.19 |
6 |
1515.4 |
| 2s |
411.3 |
7s |
1095.9 |
| 2 |
439.1 |
7 |
1179.8 |
| 3 |
300.19 |
8 |
1515.4 |
| 4s |
423.8 |
9s |
1127.6 |
| 4 |
454.7 |
9 |
1205.2 |
| 5 |
1055.1 |
|
a. The thermal efficiency must take into account the work of both turbine stages, the work of both compressor stages, and the total heat added. The total turbine work per unit of mass flow is
\begin{aligned}\frac{\dot{W}_{ t }}{\dot{m}} &=\left(h_{6}-h_{7}\right)+\left(h_{8}-h_{9}\right) \\&=(1515.4-1179.8)+(1515.4-1205.2)=645.8 kJ / kg\end{aligned}
The total compressor work input per unit of mass flow is
\begin{aligned}\frac{\dot{W}_{ c }}{\dot{m}} &=\left(h_{2}-h_{1}\right)+\left(h_{4}-h_{3}\right) \\&=(439.1-300.19)+(454.7-300.19)=293.4 kJ / kg\end{aligned}
The total heat added per unit of mass flow is
\begin{aligned}\frac{\dot{Q}_{\text {in }}}{\dot{m}} &=\left(h_{6}-h_{5}\right)+\left(h_{8}-h_{7}\right) \\&=(1515.4-1055.1)+(1515.4-1179.8)=795.9 kJ / kg\end{aligned}
Calculating the thermal efficiency
\eta=\frac{645.8-293.4}{795.9}=0.443(44.3 \%)
b. The back work ratio is
bwr =\frac{\dot{W}_{ c } / \dot{m}}{\dot{W}_{ t } / \dot{m}}=\frac{293.4}{645.8}=0.454(45.4 \%)
c. The net power developed is
\dot{W}_{\text {cycle }}=\dot{m}\left(\dot{W}_{ t } / \dot{m}-\dot{W}_{ c } / \dot{m}\right)
2 =\left(5.807 \frac{ kg }{ s }\right)(645.8-293.4) \frac{ kJ }{ kg }\left|\frac{1 kW }{1 kJ / s }\right|=2046 kW
d. The total rate energy is added by heat transfer is obtained using the specified mass flow rate and data from part (a)
\dot{Q}_{\text {in }}=\dot{m}\left(\dot{Q}_{\text {in }} / \dot{m}\right)
3 =\left(5.807 \frac{ kg }{ s }\right)\left(795.9 \frac{ kJ }{ kg }\right)\left|\frac{1 kW }{1 kJ / s }\right|=4622 kW
1 The enthalpies at states 1, 2s, 3, and 4s are obtained from the solution to Example 9.9 where these states are designated as 1, c, d, and 2, respectively. Thus, h_{1}=h_{3}=300.19 kJ/kg, h_{2 s }=411.3 kJ / kg , h_{4 s }=423.8 kJ / kg.
The specific enthalpies at states 6, 7s, 8, and 9s are obtained from the solution to Example 9.8, where these states are designated as 3, a, b, and 4, respectively. Thus, h_{6}=h_{8}=1515.4 kJ / kg , h_{7 s }=1095.9 kJ / kg , h_{9 s }=1127.6 kJ / kg.
Specific enthalpies at states 2 and 4 are obtained using the isentropic efficiency of the first and second compressor stages, respectively. Specific enthalpy at state 5 is obtained using the regenerator effectiveness. Finally, specific enthalpies at states 7 and 9 are obtained using the isentropic efficiency of the first and second turbine stages, respectively.
2 Comparing the thermal efficiency, back work ratio, and net power values of the current example with the corresponding values of Example 9.6, it should be evident that gas turbine power plant performance can be increased significantly by coupling reheat and intercooling with regeneration.
3 With the results of parts (c) and (d), we get η = 0.443, which agrees with the value obtained in part (a), as expected. Since the mass flow rate is constant throughout the system, the thermal efficiency can be calculated alternatively using energy transfers on a per unit mass of air flowing basis, in kJ/kg, or on a time rate basis, in kW.
Skills Developed
Ability to…
• sketch the schematic of the regenerative gas turbine with intercooling and 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, back work ratio, net power developed, and total rate energy is added by heat transfer.
Quick Quiz
Verify the specific enthalpy values specified at states 4, 5, and 9 in the table of data provided.
