BENG2 APPLIED THERMODYNAMICS
(THER 205)
TUTORIAL EXAMPLES in GAS
TURBINES
(Unless
otherwise indicated use table values for the properties of air.)
1. An ideal gas turbine operating on the
Joule cycle is required to produce an output power of 1MW. Determine the required air-flow and heat
input if the operating pressure ratio is
8, and the maximum cycle temperature is 1000°C and SSL inlet
conditions. [2.942 kg/s; 2.232MW]
2. An ideal gas turbine operating on the
Joule cycle uses air as the working substance.
A thermal efficiency of 40% is required with specific work of 200
kJ/kg. The minimum cycle temperature is
15°C. Determine the cycle
pressure ratio and maximum temperature required. [ 5.98; 975K]
3. Air enters the compressor of a gas
turbine plant at 101 kPa, 17°C and is compressed to 808 kPa with
isentropic efficiency 0.8. The air is heated
in a combustion chamber to 1200 K. The
gases expand in the turbine with isentropic efficiency 0.84 to 101 kPa.
Determine the plant efficiency and the power output with an air mass flow rate
of 30 kg/s. The mass flow rate of fuel
may be neglected.
Use cp = 1.15 kJ/kg K and g = 1.3 for combustion gases. [20.4%, 4.33 MW]
4. A gas turbine plant produces 40 kW with
an air flow rate of 0.5 kg/s. The
compressor pressure ratio is 4 and inlet conditions are 101 kPa, 17°C.
The compressor and turbine isentropic
efficiencies are both 0.82. The pressure
at turbine entry is 5% less than at compressor exit. The mass flow rate of fuel may be neglected.
The turbine exit pressure is 101 kPa.
Determine the maximum cycle temperature and the plant efficiency. Use cp = 1.15
kJ/kg K and g = 1.3 for combustion gases. [1014 K,
12.6%]
5. A gas turbine unit takes in air at 17°C
and 101 kPa and the pressure ratio is 8 to 1. The compressor is driven by the
H.P. turbine and the L.P. turbine drives a separate power shaft. The isentropic efficiencies of the compressor
and H.P. and L.P. turbines are 0.8, 0.85 and 0.83 respectively. Calculate the pressure and the temperature of
the gases entering the power turbine, the net power developed by the unit per
kg/s mass flow and the thermal efficiency of the unit. The maximum cycle temperature is 650°C.
For the combustion and expansion processes use cp = 1.15
kJ/kgK and g = 1.333. [163.2 kPa, 665K, 71.8 kW/kg/s,
18.4%]
6. An automobile company considers the
design of a gas turbine engine to drive a motor car. It is decided that the engine shall be of the
"free turbine" type, in which the first stage turbine is mechanically
coupled to the compressor and the second stage (the free turbine) is actuated
by the gas from the first stage.
Combustion takes place between the compressor and the first stage
turbine. The free turbine, which has no
mechanical connection with the first stage turbine, drives the road wheels of
the car through reduction gearing. Use g and cp for air
throughout.
The following details are agreed:
compressor inlet conditions: 101.5 kPa
and 289 K
compressor pressure ratio: 4
to 1
compressor isentropic efficiency: 0.85
turbine isentropic efficiency: 0.86
(both turbines)
final exhaust pressure: 101.5
kPa
maximum cycle temperature: 1090
K
air mass flow rate (max): 0.908
kg/s
calorific value of fuel: 41.9
MJ/kg
Calculate
the pressure at exit from the first stage turbine. Neglecting all losses, and assuming a
combustion efficiency of 100 per cent, calculate the net power output and the
specific fuel consumption under conditions of maximum air flow rate. [134 kW, 0.375 kg/kWh]
7. A simple gas turbine plant has a pressure
ratio of 6:1 and a maximum gas temperature of
1070K. The inlet temperature is
290 K. If the isentropic efficiency for
the compression and expansion process is 0.87, calculate the overall
efficiency, the net specific work, the fuel-air ratio, and the specific fuel
consumption.
Data: Assume a combustion efficiency of
0.98; a mechanical efficiency of 0.99, and
an inlet pressure of 101.5 kPa.
Appropriate cp values are: compression
=
1013 J/kgK
combustion = 1126
J/kgK
expansion = 1145
J/kgK
Use a specific gas constant (R) for air and
combustion gas = 287 J/kgK
Calorific
value of fuel = 43 MJ/kg
[25%; 161 kJ/kg; 66:1; 0.340
kg/kWh]
8. Show that the work output of a simple
gas-turbine plant of pressure ratio rp in which
the compressor and turbine inlet temperatures are T11 and T33, will be
positive only if the product of the compressor isentropic efficiency (hc) and
turbine isentropic efficiency (ht) is
greater than:-
Show also
that the pressure ratio for maximum work output is given by:-
