Gas Turbine Power Cycles [3]

4.5. Exhaust Heat Exchanges

Because the gas leaving the turbine is hotter than the gas leaving the compressor, it is
possible to heat up the air before it enters the combustion chamber by use of an exhaust gas
heat exchanger. This results in less fuel being burned in order to produce the same
temperature prior to the turbine and so makes the cycle more efficient. The layout of such a
plant is shown on fig.8.

In order to solve problems associated with this cycle, it is necessary to determine the temperature prior to the combustion chamber (T3).

A perfect heat exchanger would heat up the air so that T3 is the same as T5. It would also cool down the exhaust gas so that T6 becomes T2. In reality this is not possible so the
concept of THERMAL RATIO is used. This is defined as the ratio of the enthalpy given to the air to the maximum possible enthalpy lost by the exhaust gas. The enthalpy lost by the exhaust gas is

∆H = mgcpg(T5-T6)

This would be a maximum if the gas is cooled down such that T6 = T2. Of course in reality
this does not occur and the maximum is not achieved and the gas turbine does not perform
as well as predicted by this idealisation. ∆H(maximum) = ∆H = mgcpg(T5-T6)

The enthalpy gained by the air is ∆H(air) = macpa(T3-T2)
Hence the thermal ratio is T.R. = macpa(T3-T2)/ mgcpg(T5-T2)

The suffix ‘a’ refers to the air and g to the exhaust gas. Since the mass of fuel added in the
combustion chamber is small compared to the air flow we often neglect the difference in
mass and the equation becomes

WORKED EXAMPLE No.5
A gas turbine uses a pressure ratio of 7.5/1. The inlet temperature and pressure are
respectively 10oC and 105 kPa. The temperature after heating in the combustion
chamber is 1300 oC. The specific heat capacity cp for air is 1.005 kJ/kg K and for the
exhaust gas is 1.15 kJ/kg K. The adiabatic index is 1.4 for air and 1.33 for the gas.
Assume isentropic compression and expansion. The mass flow rate is 1kg/s.
Calculate the air standard efficiency if no heat exchanger is used and compare it to the
thermal efficiency when an exhaust heat exchanger with a thermal ratio of 0.88 is used.

SOLUTION
Referring to the numbers used on fig.8 the solution is as follows.

In order find the thermal efficiency, it is best to solve the energy transfers.
P(in)= mcpa(T2-T1) = 1 x 1.005 (503.6-283) = 221.7 kW
P(out) = mcpg(T4-T5) = 1 x 1.15 (1573-953.6) = 712.3 kW
P(nett) = P(out) - P(in) = 397.3 kW
Φ(in)combustion chamber) = mcpg(T4-T3)
Φ(in)= 1.15(1573-953.6) = 712.3 kW
ηth = P(nett)/Φ(in) = 494.2/712.3 = 0.693 or 69.3%

Self Assessment Exercise No. 5
1. A gas turbine uses a pressure ratio of 7/1. The inlet temperature and pressure are
respectively 10oC and 100 kPa. The temperature after heating in the combustion
chamber is 1000 oC. The specific heat capacity cp is 1.005 kJ/kg K and the adiabatic
index is 1.4 for air and gas. Assume isentropic compression and expansion. The mass
flow rate is 0.7 kg/s.
Calculate the net power output and the thermal efficiency when an exhaust heat
exchanger with a thermal ratio of 0.8 is used.
(Answers 234 kW and 57%)

2. A gas turbine uses a pressure ratio of 6.5/1. The inlet temperature and pressure are
respectively 15oC and 1 bar. The temperature after heating in the combustion chamber
is 1200 oC. The specific heat capacity cp for air is 1.005 kJ/kg K and for the exhaust
gas is 1.15 kJ/kg K. The adiabatic index is 1.4 for air and 1.333 for the gas. The
isentropic efficiency is 85% for both the compression and expansion process. The mass
flow rate is 1kg/s.

Calculate the thermal efficiency when an exhaust heat exchanger with a thermal ratio
of 0.75 is used.
(Answer 48.3%)

Worked Example No.6
A gas turbine has a free turbine in parallel with the turbine which drives the
compressor. An exhaust heat exchanger is used with a thermal ratio of 0.8. The
isentropic efficiency of the compressor is 80% and for both turbines is 0.85.
The heat transfer rate to the combustion chamber is 1.48 MW. The gas leaves the
combustion chamber at 1100oC. The air is drawn into the compressor at 1 bar and
25oC. The pressure after compression is 7.2 bar.
The adiabatic index is 1.4 for air and 1.333 for the gas produced by combustion. The
specific heat cp is 1.005 kJ/kg K for air and 1.15 kJ/kg K for the gas. Determine the
following.
i. The mass flow rate in each turbine.
ii. The net power output.
iii. The thermodynamic efficiency of the cycle.

Solution

T1 = 298 K
T2= 298(7.2)(1-1/1.4) = 524 K
T4 = 1373 K
T5 = 1373(1/7.2)(1-1/1.333) = 838.5 K

COMPRESSOR
ηi = 0.8 = (524-298)/(T2-298) hence T2= 580.5 K

TURBINES
Treat as one expansion with gas taking parallel paths.
ηi = 0.85 = (1373-T5)/(1373-838.5) hence T5 = 918.7 K
HEAT EXCHANGER
Thermal ratio = 0.8 = 1.005(T3-580.5)/1.15(918.7-580.5)
hence T3= 890.1 K

COMBUSTION CHAMBER
Φ(in)= mcp(T4-T3) = 1480 kW
1480 = m(1.15)(1373-890.1) hence m = 2.665 kg/s

COMPRESSOR
P(in) = mcp (T2-T1) = 2.665(1.005)(580.5-298) = 756.64 kW

TURBINE A
P(out) = 756.64 kW = mAcp(T4-T5)
756.64 = = 2.665(1.15)(1373-918.7) hence mA= 1.448 kg/s
Hence mass flow through the free turbine is 1.2168 kg/s
P(nett) = Power from free turbine =1.2168(1.15)(1373-918.7) = 635.7 kW

THERMODYNAMIC EFFICIENCY
ηth = P(nett)/Φ(in)= 635.7/1480 = 0.429 or 42.8 %

Self Assessment Exercise No. 6
1. List the relative advantages of open and closed cycle gas turbine engines.
Sketch the simple gas turbine cycle on a T-s diagram. Explain how the efficiency can be improved by the inclusion of a heat exchanger. In an open cycle gas turbine plant, air is compressed from 1 bar and 15oC to 4 bar. The
combustion gases enter the turbine at 800oC and after expansion pass through a heat
exchanger in which the compressor delivery temperature is raised by 75% of the
maximum possible rise. The exhaust gases leave the exchanger at 1 bar. Neglecting
transmission losses in the combustion chamber and heat exchanger, and differences in
compressor and turbine mass flow rates, find the following.
(i) The specific work output.
(ii) The work ratio
(iii) The cycle efficiency
The compressor and turbine polytropic efficiencies are both 0.84.
Compressor cp = 1.005 kJ/kg K γ= 1.4
Turbine cp = 1.148 kJ/kg K γ= 1.333

2. A gas turbine for aircraft propulsion is mounted on a test bed. Air at 1 bar and 293K
enters the compressor at low velocity and is compressed through a pressure ratio of 4
with an isentropic efficiency of 85%. The air then passes to a combustion chamber
where it is heated to 1175 K. The hot gas then expands through a turbine which drives
the compressor and has an isentropic efficiency of 87%. The gas is then further
expanded isentropically through a nozzle leaving at the speed of sound. The exit area
of the nozzle is 0.1 m2. Determine the following.
(i) The pressures at the turbine and nozzle outlets.
(ii) The mass flow rate.
(iii) The thrust on the engine mountings.
Assume the properties of air throughout.
The sonic velocity of air is given by

The temperature ratio before and after
the nozzle is given by
T(in)/T(out) = 2/(γ+1)