GAS POWER CYCLES
Chapter 9
Introduction



1.
2.
Two important areas of application for
thermodynamics are power generation and
refrigeration.
Both power generation and refrigeration are
usually accomplished by a system that operates
on a thermodynamics cycle.
Thermodynamics cycles can be divided into
two categories:
Power Cycles
Refrigeration Cycles
Introduction

1.
2.
3.


Power cycles can be categorized as:
Gas power cycles
Vapor power cycle
Combined Power Cycles
In gas cycles, the working fluid remains in the
gaseous phase throughout the entire cycle.
In vapor cycles the working fluid exists in a
vapor phase during one part of the cycle and in
a liquid phase during another part.
Basic Considerations

Closed cycle: the working fluid is returned to the
initial state at the end of the cycle and is re-circulated.

Open cycle: the working fluid is renewed at the end of
each cycle instead of being re-circulated.

Actual Cycle: The cycle encountered in actual devices
are difficult to analyze.

Ideal Cycle: All the internal irreversibilities are
neglected.
Carnot Cycle

1.
2.
3.
4.
The Carnot cycle is composed of 4 totally
reversible processes:
Isothermal heat addition at high temperature
(TH).
Isentropic expansion from high temperature to
low temperature.
Isothermal heat rejection at low temperature
(TL).
Isentropic compression from low temperature
to high temperature.
Gas Power Cycles

In gas power cycles, the working fluid remains a
gas throughout the entire cycle.

Examples of devices that operate on gas power
cycles:
Spark-Ignition Automobile Engines.
Diesel Engines.
Convectional Gas turbines.
1.
2.
3.
Air-Standard Assumptions

1.
2.
3.
4.
To simplify the analysis of actual gas cycles
these assumptions are:
The working fluid is air and assumed to be an
ideal gas.
All the processes are internally reversible.
The combustion process is replaced by a
heat-addition process from an external source.
The exhaust process is replaced by a heat
rejection process that restores the working fluid
to its initial state.
Air-Standard Assumptions

Energy in the form of heat is provided by
burning a fuel within the system boundaries.
Basic components
The basic components are described by the following diagrams
Basic Components

Compression Ratio (r): The ratio of the
maximum volume formed in the cylinder to the
minimum (clearance) volume is called the compression
ratio.
Vmax VBDC
r

Vmin

VTDC
Mean Effective Pressure (MEP): It is a
fictitious pressure that, if it acted on the piston during
the entire power stroke, would produce the same
amount of net work as that produced during the actual
cycle.
Wnet  MEP X Piston Area X Stroke  MEP X Displacement volume
or
MEP 
Wnet
wnet

Vmax  Vmin v max  v min
kPa 
Basic Components
Note:

The mean effective pressure can be used as a
parameter to compare the performances of
reciprocating engines of equal size.

The engine with a larger value of MEP will
deliver more net work per cycle and thus will
perform better.
Classifications
Reciprocating Engines are classified as:

1.
2.

1.
2.
Spark-ignition (SI) engine where:
The combustion of the air-fuel mixture is
initiated by a spark plug.
Otto Cycle is the ideal cycle for the SI Engine.
Compression-ignition (CI) engine where:
The air-fuel mixture is self-ignited as a result of
compressing the mixture above its self-ignition
temperature.
Diesel Cycle is the ideal cycle for CI Engine.
Otto Cycle

The Otto cycle is the ideal cycle for SI engines.

In S I engines, the piston executes 4 complete
strokes.

These engines are called 4 stroke internal
combustion engines.

Initially, both the intake and the exhaust valves
are closed and the piston is at its lowest position
(BDC).
Otto Cycle

The four strokes are:
1.
2.
3.
4.
Compression Stroke.
Expansion or Power Stroke.
Exhaust Stroke.
Intake stroke.
Ideal Otto Cycle
It consists of 4 internally reversible processes:
1-2
2-3
3-4
4-1
Isentropic Compression
Constant volume heat addition
isentropic expansion
Constant volume heat rejection
Diesel Cycle
Read about Diesel Cycle (Text)
Two –stroke engines

All the four functions described above are
executed in just two strokes: The power stroke
and the compression stroke.

The outward motion of the piston is used to
slightly pressurize the air-fuel mixture in the
crankcase.

The intake and exhaust valves are replaced by
openings in the lower portion of the cylinder
wall.
Two –stroke engines



During the latter part of the power stoke, the
piston uncovers first the exhaust port allowing
the exhaust gases to be partially expelled and
then the intake port, allowing the fresh airfuel mixture to rush in and drive most of the
remaining exhaust gases out of the cylinder.
The fresh air-fuel mixture is then compressed
as the piston moves upward during the
compression stroke and is subsequently ignited
by a spark plug.
The two stroke engines are generally less
efficient than four stroke ones.
BRAYTON CYCLE
Brayton Cycle is the ideal cycle for gas turbine engines. Electric power generation and
aircraft propulsion are major applications for gas-turbine engines.
4 PROCESSES:
1-2
2-3
3-4
4-1
Isentropic compression
Constant pressure heat addition
Isentropic expansion
Constant pressure heat rejection
Performing energy balance, we get:
qm  C p T3  T2 
qout  C p T4  T1 
 th 
wnet
q
 1  out
qm
qm
 th  1 
Note:
P2 = P3
P1 = P4
T4
T3
 T1 
 T2 
T

T1 
 4 T  1
1


1
T

T2 
 3 T  1
2


(1)
BRAYTON CYCLE
Also:
T2  P2 
 
T1  P1 

k 1
k
P 
 3
 P4 
k 1
k

T3
T4
T4 T3

T1 T2
Substitute in (1), we get:
 th  1 
T1
1
1
T2
T2
T1
th  1 
1
(2)
or
c 
rpk 1 k
ws
wa
(3)
t 
wa
ws
(4)
BRAYTON CYCLE WITH
REGENERATION
■ Heating the high-pressure air leaving the compressor by the hot exhaust gases in a
counterflow heat exchanger is known as regeneration (see Figure 8.38).
■ The thermal efficiency of the Brayton cycle increases as a result of decrease in the
heat input (thermo-fuel) for the same net power output.
■ Regeneration is used only when the compressor exit temperature is less than the
turbine exit temperature.
■ Referring to the T-s diagram, the regenerator effectiveness is given as:

qreg, act
qreg, max

h5  h2
h4  h2
(5)
BRAYTON CYCLE WITH
REGENERATION
Considering the cold air-standard assumptions, equation (5) reduces to:
T5  T2

T4  T2
(6)
■ Assuming cold air-standard assumptions, show that the thermal efficiency of an ideal
Brayton cycle with regeneration is given as:
 T1  k 1k
th  1     rp 
 T3 
(7)
■ Comment on the effect of temperature and pressure ratios on the thermal efficiencies.
■ See Example 8.7.
BRAYTON CYCLE WITH INTERCOOLING,
REHEATING,
AND REGENERATION
●
Using multistage compression with intercooling reduces the total work of the
compressor operating between two pressures.
●
Similarly using multistage expansion with reheating increases the workout of a
turbine operating between two pressures.

Even-though intercooling and reheating improves the back work ratio of a gas turbine
cycle, but it does guarantee an improvement in the thermal efficiency (why?).
●
Intercooling and reheating have to be used in conjunction with regeneration for the
thermal efficiency to improve.
●
The best performance is achieved when equal pressure ratios are maintained across
each stage. For example (considering Figure 8.44) when
P
P
P2
P
 4 and 6  8 .
P1
P3
P7
P9
●
See Example 8.8.
IDEAL JET-PROPULSION
CYCLES
► Aircrafts are powered by gas turbines that operate on jet-propulsion open cycles.
► In jet-propulsion cycles the gases are expanded in the turbine such that the power
produced is just sufficient to drive the compressor and the auxiliary equipment.
► The thrust to propel the aircraft is provided by a nozzle in which high-pressure gases
exiting the turbine do expand.
► A schematic of turbojet engine is shown in Figure 8.48.
► Aircrafts are propelled by either slightly accelerating a large mass of fluid (propellerdriven engine) or greatly accelerating a small mass of fluid (turbojet engine) in the
opposite direction to motion.
► Gases leave the aircraft at high-velocity after expanding in the nozzle to atmospheric
pressure.
IDEAL JET-PROPULSION CYCLES
Processes in the diffuser, compressor, turbine, and nozzle are assumed to be isentropic in the
ideal turbojet cycle as shown by the T-s diagram (Figure next slide).
► The net thrust developed by the engine is given by:
F  m Vexit  Vinlet 
(N)
where:
Vexit is the exit velocity of exhaust gases relative to aircraft.
Vinlet is the air inlet velocity relative to aircraft.
► The propulsive power, Wp is given as:
Wp  Thrust * Vaircraft
(kW).
The propulsive efficiency, ηp is given by:
p 
Wp
Qm
.
where Q is the thermal energy of the fuel. See Example 8.9.
EXAMPLE8—9 The Ideal Jet Propulsion Cycle
A turbojet aircraft flies with a velocity of 850
ft/s at an altitude where the air is at 5 psia
and —40 The compressor has a pressure ratio
of 10, and the temperature of the gases at the
turbine inlet is 2000T. Air enters the
compressor at a rate of 100 Ibm/s. Utilizing
the cold-air-standard assumptions, determine
(a) the temperature and pressure of the gases
at the turbine exit, (b) the velocity of the
gases at the nozzle exit, and (C) the
propulsive efficiency of the cycle.