Chapter 9
Gas Power Systems
Learning Outcomes
►Perform air-standard analyses of internal
combustion engines based on the Otto,
Diesel, and dual cycles, including:
►sketching p-v and T-s diagrams and evaluating
property data at principal states.
►applying energy, entropy, and exergy
balances.
►determining net power output, thermal
efficiency, and mean effective pressure.
Learning Outcomes
►Perform air-standard analyses of gas
turbine power plants based on the Brayton
cycle and its modifications, including:
►sketching T-s diagrams and evaluating
property data at principal states.
►applying mass, energy, entropy, and exergy
balances.
►determining net power output, thermal
efficiency, back work ratio, and the effects of
compressor pressure ratio.
Learning Outcomes
►For subsonic and supersonic flows through
nozzles and diffusers:
►demonstrate understanding of the effects of
area change, the effects of back pressure on
mass flow rate, and the occurrence of choking
and normal shocks.
►analyze the flow of ideal gases with constant
specific heats.
Introducing Power Generation
►To meet our national power needs there are
challenges related to
►Declining economically
recoverable supplies of
nonrenewable energy resources.
►Effects of global climate change
and other environmental and human
health and safety issues.
►Rapidly increasing demand for
power owing to increasing
population.
►Today we are heavily dependent on coal, natural
gas, and nuclear, all of which are nonrenewable.
Introducing Power Generation
►While coal, natural gas, and nuclear will continue to play
important roles in years ahead, contributions from wind power,
solar power, and other renewable sources are expected to be
increasingly significant up to mid-century at least.
Table 8.2
Introducing Power Generation
►This table also shows that thermodynamic cycles are a
fundamental aspect of several power plant types that
employ renewable or nonrenewable sources.
►Vapor power cycles are the focus of Chapter 8. In
Chapter 9 gas turbine power systems and internal
combustion engines are studied as thermodynamic
cycles. The basic building block of gas turbine cycles is
the Brayton cycle.
►Gas power system learning resources are now
provided, including
►Power cycle review
►Area interpretations for work and heat transfer
►Ideal gas model review
Power Cycle Review
►The first law of thermodynamics
requires the net work developed by a
system undergoing a power cycle to
equal the net energy added by heat
transfer to the system:
∙
∙
∙
∙
Wcycle = Qin – Qout
►The thermal efficiency of a power
cycle is
W cycle
 
Q
in
∙
∙
Power Cycle Review
►The second law of thermodynamics requires the thermal
efficiency to be less than 100%.
►Thermal efficiency tends to increase as the average
temperature at which energy is added by heat transfer
increases and/or the average temperature at which energy is
rejected by heat transfer decreases.
►Improved thermodynamic performance of power cycles, as
measured by increased thermal efficiency, for example, also
accompanies the reduction of irreversibilities and losses.
►The extent of improved power cycle performance is limited,
however, by constraints imposed by thermodynamics and
economics.
Area Interpretations for
Work and Heat Transfer
►Ideal cycles formed from internally
reversible processes are used in Chapter 9 to
further understanding of reciprocating internal
combustion engines and gas turbine power
systems.
►Closed systems involving expansion and
compression work are used to model
reciprocating engines. For these applications,
the following area interpretations apply for
internally reversible processes:
Area Interpretations for
Work and Heat Transfer
W 
  
 m int
rev

Q
   Tds
 m int
pdv
rev
p

T
v
s
►Observe that these expressions give work
and heat transfer per unit of mass contained
within the closed system.
Area Interpretations for
Work and Heat Transfer
►One-inlet, one exit control volumes at steady state
are used to model gas turbine power plants. For these
applications, the following area interpretations apply for
internally reversible processes:
p
 W 
    vdp
 m int
 
rev

v
T
 Q 
   Td s
 m  int
 

rev
s
►Observe that these expressions give work and heat
transfer per unit of mass flowing through the control
volume.
Ideal Gas Model Review
►Elementary thermodynamic analyses of reciprocating
internal combustion engines and gas turbines use ideal
model principles, as reviewed in Table 9.1.
Ideal Gas Model Review
Ideal Gas Model Review
Considering Reciprocating
Internal Combustion Engines
►What are reciprocating internal combustion engines?
►They are reciprocating engines commonly used in
automobiles, trucks, and buses.
►How do reciprocating internal combustion engines
differ from the vapor power plants considered in
Chapter 8 and the gas turbines considered in later
sections of Chapter 9?
►Processes occur within reciprocating pistoncylinder arrangements rather than by mass flowing
through a series of interconnected components.
Considering Reciprocating Internal
Combustion Engines – Two Types
►Spark-ignition
►A mixture of fuel and air is ignited by a spark
plug.
►This type is
• advantageous for applications up to about
300 hp (225 kW).
• lightweight and relatively low cost.
• predominantly used by automobiles in the
U.S.
Considering Reciprocating Internal
Combustion Engines – Two Types
►Compression-ignition
►Air is compressed to a high pressure and
temperature.
►Combustion occurs spontaneously when fuel is
injected.
►This type is
• preferred for high-power applications and
when fuel economy is required.
• used in heavy trucks and buses, locomotives
and ships, and auxiliary power units.
Introducing Engine Terminology
► Displacement volume: volume
swept by piston when it moves from
top dead center to bottom dead
center
Top dead center
Stroke
Bottom dead center
►Compression ratio, r : volume
at bottom dead center divided by
volume at top dead center
Introducing Engine Terminology
Four-stroke cycle
Four strokes of the piston
for every two revolutions of
the crankshaft
►Intake stroke
With the intake valve open,
piston stroke draws a fresh
charge into the cylinder.
► For spark-ignition
engines, the charge
includes fuel and air.
► For compression-ignition
engines, the charge is air
alone.
Introducing Engine Terminology
►Compression stroke
With both valves closed,
piston compresses charge,
raising the pressure and
temperature, and requiring
work input from the piston to
the cylinder contents.
► For spark-ignition
engines, combustion is
initiated by the spark plug.
► For compressionignition engines,
combustion is initiated
by injecting fuel into the hot
compressed air.
Introducing Engine Terminology
►Power stroke
The gas mixture expands
and work is done on the
piston as it returns to bottom
dead center.
►Exhaust stroke
The burned gases are
purged from the cylinder
through the open exhaust
valve.
Introducing Engine Terminology
►Smaller engines operate on two-stroke cycles
with intake, compression, expansion, and exhaust
accomplished in one revolution of the crankshaft.
►Internal combustion engines undergo
mechanical cycles, but the cylinder contents do
not execute a thermodynamic cycle – matter is
introduced at one composition and is later
discharged at a different composition.
Introducing Engine Terminology
►Mean effective pressure, mep, is an important
performance parameter.
►mep is a theoretical constant pressure that if it
acted on the piston during the power stroke
would produce the same net work as actually
developed in one cycle.
(Eq. 9.1)
►For two engines of equal displacement
volume, the one with a higher mep would
produce the greater net work, and if the engines
run at the same speed, greater power.
Simulating Reciprocating
Internal Combustion Engines
►Detailed study of performance of reciprocating
internal combustion engines requires consideration
of complexities including:
►Combustion processes occurring within the cylinder.
►The effects of irreversibilities related to combustion,
heat transfer, and friction.
►Heat transfer between the gases in the cylinder and
the cylinder walls.
►The work required to charge the cylinder and
exhaust the products of combustion.
►Accurate analyses of reciprocating internal
combustion engines normally requires computer
simulation.
Air-Standard Analysis of Reciprocating
Internal Combustion Engines
►To conduct elementary analyses of reciprocating internal
combustion engines, simplifications are required. Although
highly idealized, an air-standard analysis can provide insights
and qualitative information about actual performance.
►An air-standard analysis has the following elements:
►A fixed amount of air modeled as an ideal gas is the
working fluid. Ideal gas relations are reviewed in Table 9.1.
►The combustion process is replaced by heat transfer from
an external source. Combustion is studied in Chapter 13.
►There are no intake and exhaust processes. The cycle is
completed by a constant-volume heat transfer process while
the piston is at bottom dead center.
►All processes are internally reversible.
►In a cold air-standard analysis, the specific heats are
assumed constant at their ambient temperature values.
Air-Standard Analysis of Reciprocating
Internal Combustion Engines
►For reciprocating internal combustion engines,
three cycles that adhere to air-standard cycle
idealizations are the Otto, Diesel, and Dual cycles.
These cycles differ only in the way the heat addition
process that replaces combustion in the actual cycle
is modeled:
►Otto cycle: Heat addition at constant volume.
►Diesel cycle: Heat addition at constant
pressure.
►Dual cycle: Heat addition at constant volume
followed by heat addition at constant pressure.
Air-Standard Otto Cycle
►The Otto cycle consists of four internally reversible
processes in series:
►Process 1-2: isentropic compression.
►Process 2-3: constant-volume heat addition to the air
from an external source.
►Process 3-4: isentropic expansion.
►Process 4-1: constant-volume heat transfer from the
air.
►The Otto cycle
compression ratio is:
V1 V4
r

V2 V3
Air-Standard Otto Cycle
►Ignoring kinetic and potential energy effects,
closed system energy balances for the four
processes of the Otto cycle reduce to give
W34
W12
 u 2  u1 ,
 u3  u 4
m
m
(Eq. 9.2)
Q23
Q41
 u3  u 2 ,
 u 4  u1
m
m
►The thermal efficiency is the ratio of the net
work to the heat added:
(Eq. 9.3)
Air-Standard Otto Cycle
►Since the air-standard Otto cycle is composed of
internally reversible processes, areas on the T-s and
p-v diagrams can be interpreted as heat and work,
respectively:
►On the T-s diagram, heat transfer per unit of
mass is ∫Tds. Thus,
• Area 2-3-a-b-2 represents
heat added per unit of mass.
• Area 1-4-a-b-1 is the heat
rejected per unit of mass.
• The enclosed area is the net
heat added, which equals the
net work output.
Air-Standard Otto Cycle
►On the p-v diagram, work per unit of mass is
∫pdv. Thus,
• Area 1-2-a-b-1 represents
work input per unit of mass
during the compression
process.
• Area 3-4-b-a-3 is the work
done per unit of mass in the
expansion process.
• The enclosed area is the net
work output, which equals the
net heat added.
Air-Standard Otto Cycle
►The compression ratio, r = V2/V1, is an important
operating parameter for reciprocating internal combustion
engines as brought out by the following discussion
centering on the T-s diagram:
►An increase in the compression ratio
changes the cycle from 1-2-3-4-1 to
1-2′-3′-4-1.
►Since the average temperature of heat
addition is greater in cycle 1-2′-3′-4-1,
and both cycles have the same heat
rejection process, cycle 1-2′-3′-4-1 has
the greater thermal efficiency.
►Accordingly, the Otto cycle thermal
efficiency increases as the
compression ratio increases.
Air-Standard Diesel Cycle
►The Diesel cycle consists of four internally
reversible processes in series:
►Process 1-2: isentropic compression.
►Process 2-3: constant-pressure heat addition to the
air from an external source.
►Process 3-4: isentropic expansion.
►Process 4-1: constant-volume heat transfer from
the air.
►The Diesel cycle
has a two-step
power stroke:
process 2-3 followed
by process 3-4.
Air-Standard Diesel Cycle
V1
►The Diesel cycle compression ratio is: r 
V2
V3
►The Diesel cycle cut-off ratio is: rc 
V2
Air-Standard Diesel Cycle
►Process 2-3 is heat addition at constant pressure.
Accordingly, the process involves both heat and work.
►The work is given by
(Eq. 9.9)
►Introducing Eq. 9.9 into the closed system energy balance
for process 2-3 and solving for Q23/m gives
(Eq. 9.10)
Note: Enthalpy appears only for notational convenience and
does not signal use of control volume concepts.
►The thermal efficiency is the ratio of the net work to the
heat added:
(Eq. 9.11)
Like the Otto cycle, thermal efficiency increases with
increasing compression ratio.
Air-Standard Diesel Cycle
►As for the Otto cycle, areas on the T-s and p-v
diagrams of the Diesel cycle can be interpreted as
heat and work, respectively:
►On the T-s diagram, heat transfer per unit of
mass is ∫Tds. Thus,
• Area 2-3-a-b-2 represents
heat added per unit of mass.
• Area 1-4-a-b-1 is the heat
rejected per unit of mass.
• The enclosed area is the net
heat added, which equals the
net work output.
Air-Standard Diesel Cycle
►On the p-v diagram, work per unit of mass is
∫pdv. Thus,
• Area 1-2-a-b-1 represents work
input per unit of mass during the
compression process.
• Area 2-3-4-b-a-2 is the work
done per unit of mass in the
two-step power stroke: process
2-3 followed by process 3-4.
• The enclosed area is the net
work output, which equals the
net heat added.
Air-Standard Dual Cycle
►By considering heat transfer to the air
undergoing the power cycle as occurring in two
steps: constant volume followed by constant
pressure, the air-standard Dual cycle aims to
mimic the pressure-volume variation of actual
internal combustion engines more closely than
achievable with the Otto and Diesel cycles.
Air-Standard Dual Cycle
►The air-standard Dual cycle consists of five internally
reversible processes in series:
►Process 1-2: isentropic compression.
►Process 2-3: constant-volume heat addition to the air
from and external source.
►Process 3-4: constant-pressure heat addition to the air
from an external source.
►Process 4-5: isentropic expansion.
►Process 5-1: constant-volume heat transfer from the air.
►As for the Diesel
cycle, the Dual cycle
has a two-step
power stroke:
process 3-4 followed
by process 4-5.
Air-Standard Dual Cycle
►Using closed system energy balances for each of
the processes, the following expression for thermal
efficiency for the air-standard Dual Cycle can be
developed:
(Eq. 9.14)
Note: As for the Diesel cycle, enthalpy appears only for
notational convenience and does not signal use of control
volume concepts.
►Like the Otto and Diesel cycles, thermal efficiency
increases with increasing compression ratio.
Air-Standard Dual Cycle
►The specific internal energies and temperatures
at each principal state are determined using
methods similar to those used for the Otto and
Diesel Cycles.
►Areas on the T-s and p-v diagrams of the Dual
cycle can be interpreted as heat and work,
respectively, as in the cases of the Otto and Diesel
cycles.
Actual Reciprocating Internal
Combustion Engines
►As implied by the discussion of the Otto, Diesel,
and Dual cycles, it is advantageous for actual
reciprocating internal combustion engines to have
high compression ratios.
►However, since the temperature of the fuel-air
mixture being compressed in spark-ignition
engines also increases with compression ratio,
the possibility of autoignition or “knock” limits
the compression ratio of such engines to the
range 9.5-11.5, when fueled with unleaded
gasoline.
Actual Reciprocating Internal
Combustion Engines
►Since only air is compressed in the cylinder,
compression-ignition engines do not experience
engine knock due to premature autoignition of fuel.
Accordingly, such engines can
►operate at higher compression ratios than sparkignition engines.
►use less refined fuels having higher ignition
temperatures than the volatile fuels required by sparkignition engines.