Page 431 - Advanced thermodynamics for engineers

17.6 PROBLEMS 421

P17.4 Air at 290 K flows into the compressor of a gas turbine engine. The temperature increases to
1350 K when it flows into the turbine. The pressure ratio is 15 and power output is 5 MW.
Assume the whole process is isentropic, evaluate
1. Thermal efficiency.
2. Fuel consumption. The lower calorific value of the fuel, Q , is 44,000 kJ/kg.
0
p
3. Ratio of turbine work and compressor work.
Take heat capacity ratio, k air ¼ 1.38; c p ¼ 1.05 kJ/kgK.
[0.526, 0.114 kg/s, 2.2]
P17.5 A gas turbine operates at a pressure ratio of 8. The air flows into the compressor at 290 K and
flows out of the combustion chamber at 1400 K. The efficiency of compressor and turbine
are 0.8 and 0.9 respectively. A heat exchanger with effectiveness of 0.85 is used. Assuming
an isentropic process, calculate the thermal efficiency and net power output of the engine.
The mass flow rate is 1 kg/s. Take heat capacity ratio k air ¼ 1.38; c p ¼ 1.005 kJ/kgK.
[0.61, 653.9 kW]
P17.6 Prove that the optimum pressure ratio for intercooling of gas turbines with heat exchange is
given below:

1=2
p 2 p i p 2 0
¼ ¼ :
p 1 p 1 p 1
Assume that the processes in the turbine and compressor are both isentropic, and that the
heat exchanger effectiveness, ε ¼ 1.0.
P17.7 Air flows into the compressor of a gas turbine engine at 0.1 MPa, 300 K and is compressed
to 0.8 MPa. The air is heated to a maximum temperature of 1100 K and then expanded
through two stages each with a pressure ratio of 3. The intermediate reheating temperature is
1100 K. Assuming C p is constant and independent of temperature, determine the cycle
efficiency. Take heat capacity ratio k ¼ 1.4.
[0.41]
P17.8 A turbojet is travelling at high Mach number and the ambient pressure, p a , and temperature,
T a , are 0.5 bar and 220 K respectively. It is also known that the stagnation temperature at the
inlet of the compressor is T 01 ¼ 400 K. If the intake nozzle isentropic efficiency, h i ¼ 0.8,
find the pressure ratio, p 01 /p a .
[5.8]
P17.9 If the compressor pressure ratio of the turbojet in P17.8 is 13.0 and the isentropic efficiency
is 0.8, calculate the stagnation pressure p 02 and the stagnation temperature T 02 at the
compressor outlet.
[37.7 bar, 940.5 K]
P17.10 If the compressor (for the turbojet in P17.8 and P17.9) consumes 7500 kW of power,
calculate the turbine temperature drop (T 03 T 04 ) and the mass flow rate of intake air. The
mechanical transmission efficiency is 0.99 and the mass flow rate of the fuel is negligible.
[483.7 K, 13.74 kg/s]
P17.11 Assume that the turbine inlet temperature T 03 (for the engine considered in P17.8–P17.10) is
1700 K, and that the propelling nozzle has an inlet pressure p 04 of 2.1 bar and an isentropic