A regenerative gas turbine with intercooling and reheat operates at steady state. Air enters the compressor at 100 kPa, 300 K with a mass flow rate of 5.807 kg/s. The pressure ratio across the two stage compressor is 10. The pressure ratio across the two stage turbine is also 10. The intercooler and reheater each operate at 300 kPa. At the inlet to the turbine stages, the temperature is 1400 K. The temperature at inlet to the second compressor stage is 300 K. The isentropic efficiency of each compressor and turbine stage is 80%. The regenerator effectiveness is 80%. The back work ratio is ______

Take, $h_{1} = h_{3} = 300.19 k J / k g$

$h_{2 s} = 411.3 k J / k g, h_{4 s} = 423.8 k J / k g$

$h_{6} = h_{8} = 1515.4 k J / k g$

$h_{7 s} = 1095.9 k J / k g$

$h_{g s} = 427.6 k J / k g$

$h_{9 s} = 1127.6 k J / k g$

All symbols carry their usual meaning

0.454

Open in App

Solution

The correct option is A 0.454
$η_{c} = \frac{h_{4 s} - h_{3}}{h_{4} - h_{3}}$

$\Rightarrow h_{4} = h_{3} + \frac{h_{4 s} - h_{3}}{η_{c}} = 300.19 + (\frac{423.8 - 300.19}{0.8}) = 454.7 k J / k g$

also, $η_{c} = \frac{h_{2 s} - h_{1}}{h_{2} - h_{1}}$

$h_{2} = h_{1} + \frac{h_{2 s} - h_{1}}{η_{c}}$

$\Rightarrow h_{2} = 439.1 k J / k g$

$η_{i} = \frac{h_{8} - h_{9}}{h_{8} - 4_{g s}}$

$h_{9} = h_{8} - η_{i} (h_{g} - h_{g s})$

= 1515.4 - 0.8 (1515.4 - 1127.6) = 1205.2 kJ/kg

Similarly

$h_{j} = h_{6} - η_{i} (h_{6} - h_{7 s}) = 1179.8 k J / k g$

$η_{r e g} = \frac{h_{3} - h_{4}}{h_{9} - h_{4}}$

$h_{5} = h_{4} + η_{r e g} (h_{9} - h_{4})$

= 454.7 + 0.8 (1205.2 - 454.7) = 1055.1 kJ/kg

Now, $\frac{W_{j}}{m} = (h_{6} - h_{7}) + (h_{3} - h_{9}) = (1515.4 - 1179.8) + (1515.4 - 1205.2)$

= 645.8 kJ/kg.

and $\frac{W_{c}}{m} = (h_{2} - h_{1}) + (h_{4} - h_{3}) = (439.1 - 300.19) + (454.7 - 300.19) = 293.4 k J / k g$

$∴ B W R = \frac{W_{c} / m}{W_{t} / m} = \frac{293.4}{645.8} = 0.454$ = 45.4%

Suggest Corrections

Similar questions

Q. A gas turbine power plant working on the Brayton cycle with regeneration of 80% effectiveness. The air at the inlet to the compressor is at 1 bar and 300 K the pressure ratio is 6 and maximum cycle temperature is 1200 K. The turbine and compressor each have an efficiency of 80%.
The efficiency of the cycle with the regeneration is_______%.

In simple gas turbine cycle following data are given: Isentropic efficiency of compressor = 80%. Turbine isentropic efficiency = 100%. All shafts have mechanical efficiency = 90%. Turbine output shaft is coupled to compressor and generator. Pressure ratio of compression = 3 : 1.

Maximum turbine temperature = 1000 K. Ambient condition 1 bar, 327 K. Net specific power output from the turbine is ____ KJ/kgk. Take generator efficiency = 95%, cp = 1.005 kJ/kgk.

Q. The following data relate to a high pressure ratio single shaft gas turbine cycle with reheat. Total ambient condition = 1.01 bar, 288 K, total compressor pressure ratio = 32, polytropic efficiency = 0.9 for compressor and turbine both, turbine both, turbine inlet temperature = 1600 K pressure loss in first combustor = 2% of compressor delivery pressure loss in second combustor = 4% of HP turbine, exhaust pressure, total turbine exhaust pressure = 1.05 bar, mechanical efficiency for assembly = 0.97, combustion efficiency of both combustor = 0.96, alternator efficiency = 0.97, alternator power output = 240 MW, lower calorific value of fuel = 42000 kJ/kg,

C_{P_{a}} = 1.005 k J / k g k, C_{p_{g}} = 1.15 k J / k g K .

For optimum power output, the reheating pressure under. ideal condition should be

Common Data Question:
In a simple Bryaton cycle, the pressure ratio is $8$ and temperature at the entrance of compressor and turbine are $300 K$ and $1400 K$ respectively. Both compressor and gas turbine have isentropic efficiencies equal to $80$ %. or the gas, assume a constant value of $c_{p}$ (specific heat at constant pressure) equal to $1 k J / k g K$ and ratio of specific heats as $14$ . Neglect changes in kinetic and potential energies

The power required by the compressor in $k W / k g$ of gas flow are is

Q. In a three stage reciprocating air compressor with perfect intercooling the air enters the compressor at 100 kPa, 22°C and pressure at the outlet is 4 MPa. The compression process follows

p v^{1.32} = C

. The isothermal efficiency of the compressor is _____%.(Take Rs.=0.287 kj/kgK) (Correct to two decimal place)

Join BYJU'S Learning Program