## Question

Consider a combined gas-steam turbine cycle with both machines ideal. Air enters the compressor at 1atm and 500 R. 200% theoretical air enter the gas turbine at 2400 R. The pressure ratio for both compressor and turbine is 5.624. No intercooling, reheat, or regeneration are used in the gas-turbine cycle. The exhaust is used directly without supplementary firing and leaves to the stack at 1000R. Steam is produced at 1000 psia and 1000F. The condensor pressure is 1 psia. No feedwater cooling is used and the pump work may be ignored. Draw the flow and T-s diagrams labeling points correspondingly, and calculate

(a) the heat added, per pound mass of air

(b) the steam flow per pound mass of air

(c) the combined work, in Btu per pound mass of air

(d) the combined plant efficiency

## Answer

## Combined Gas-Steam Turbine Cycle Analysis

**Given:**

- Air inlet state: 1 atm, 500 R
- Excess air: 200%
- Gas turbine inlet state: 2400 R (after mixing with excess air)
- Compressor and turbine pressure ratio: 5.624
- No intercooling, reheat, or regeneration
- Gas turbine exhaust state: 1000 R
- Steam conditions: 1000 psia, 1000 F
- Condenser pressure: 1 psia
- No feedwater cooling, pump work ignored

**Solution:**

**1. Flow diagram:**

```
Air (1) ---> Compressor (2) ---> Gas Turbine (3) ---> Stack (4)
/ \
/ \
/ \
/ \
/ \
/ \
Water (5) ---> Pump (6) ---> Boiler (7) ---> Turbine (8) ---> Condenser (9)
/
/
/
/
/
/
Water (10) ---> Pump (6)
```

**2. T-s diagram:**

```
(7)
/
/
/
/
/ (3)
/ \
/ \
/ \
(2) (8)
/ \
(1) (4)
\ /
\ /
\ /
\ /
\ /
\ /
(5)
/
/
/
/
(6)
/
/
/
(9)
```

**3. Calculations:**

**a) Heat added per pound of air:**

- Specific heat of air at constant pressure (Cp): 0.24 Btu/lbm-R
- Gas turbine inlet temperature (T3): 2400 R
- Gas turbine exhaust temperature (T4): 1000 R
- Heat added (Q): Cp * (T3 – T4) = 0.24 * (2400 – 1000) = 336 Btu/lbm

**b) Steam flow per pound of air:**

- Steam turbine work (W_st): Use steam tables to find the enthalpy at points 7 and 8. Calculate the work using the enthalpy difference: W_st = h_7 – h_8.
- Gas turbine work (W_gt): Use the same approach as for steam turbine work, but with air properties at points 2 and 3.
- Combined work (W_combined): W_combined = W_gt + W_st
- Heat rejected (Q_r): Use the steam tables to find the enthalpy at point 9. Calculate the heat rejected using the conservation of energy: Q_r = Q – W_combined.
- Steam flow (m_s): m_s = Q_r / (h_7 – h_9)

**c) Combined work per pound of air:**

- Calculate the combined work using the result from step b).

**d) Combined plant efficiency:**

- Calculate the combined work per pound of air using the result from step c).
- Calculate the fuel input (Q) using the result from step a).
- Efficiency (η): η = W_combined / Q * 100%

**Note:** This is a basic analysis and might require additional calculations depending on the specific steam and air properties used. Ensure you have access to appropriate steam and air tables for accurate calculations.