Chapter 1: Gas Power Cycles
Power cycles review:
The net work developed by a system undergoing a power cycle to equal the net
energy added by heat transfer to the system according to the 1st law of
thermodynamics.
Ẇ cycle = Q̇ in − Q̇ out
The thermal efficiency of the power cycle:
Ẇ cycle
η=
Q̇ in
Reciprocating Internal Combustion Engines:
There are two types of reciprocating internal ignition engines which are:
1. Spark-ignition: A mixture of fuel and air is ignited by a spark plug.
2. Compression-ignition: Air is compressed to a high pressure and
temperature then combustion occurs spontaneously when fuel is
injected.
Engine Terminology:
• Displacement volume: volume swept by piston
when it moves from top dead center to bottom
dead center.
• Compression ratio, r: volume at bottom dead
center divided by volume at top dead center.
• 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.
o For spark-ignition engines, the charge includes fuel and air.
o For compression-ignition engines, the charge is air alone.
 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.
o For spark-ignition engines,
combustion is initiated by the
spark plug.
o For compression-ignition
engines, combustion is
initiated by injecting fuel into
the hot compressed air.
 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.
• Smaller engines operate on two-stroke cycles with intake, compression,
expansion, and exhaust accomplished in one revolution of the crankshaft.
• Mean effective pressure: It 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.
mep =
Wnet
Vdisplacement
An air-standard analysis has the following elements:
• A fixed amount of air modeled as an ideal gas is the working fluid.
• The combustion process is replaced by heat transfer from an external
source.
• 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.
For reciprocating internal combustion engines, three cycles that adhere
to air-standard cycle idealizations:
• 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:
r=
V1 V4 𝑉𝑉𝑚𝑚𝑚𝑚𝑚𝑚
=
=
V2 V3 𝑉𝑉𝑚𝑚𝑚𝑚𝑚𝑚
Ignoring kinetic and potential energy effects, closed system energy balances for
the four processes of the Otto cycle reduce to give:
W12
= u2 − u1
m
W34
= u3 − u4
m
Q 23
= u3 − u2 = cv (T3 − T2 )
m
Q 41
= u4 − u1 = cv (T4 − T1 )
m
The thermal efficiency is the ratio of the net work to the heat added:
η𝑡𝑡ℎ,𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 =
,𝑤𝑤ℎ𝑒𝑒𝑒𝑒𝑒𝑒 𝑘𝑘 =
(u3 − u2 ) − (u4 − u1 )
u4 − u1
𝑇𝑇4 − 𝑇𝑇1
1
=1−
=1−
= 1 − 𝑘𝑘−1
𝑟𝑟
u3 − u2
𝑇𝑇3 − 𝑇𝑇2
u3 − u2
𝑐𝑐𝑝𝑝
𝑐𝑐𝑣𝑣
The T-s diagram:
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.
The p-v diagram:
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.
The compression ratio:
• 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 34.
The Diesel cycle compression ratio is:
The Diesel cycle cut-off ratio is:
r=
V1
V2
rc =
V3
V2
Process 2-3 is heat addition at constant pressure. Accordingly, the process
involves both heat and work.
The work is given by:
3
W23
= � p dv = p2 (v3 − v2 )
m
2
From the closed system energy balance for process 2-3 and solving for Q23/m
gives
Q 23
= (u3 − u2 ) + p(v3 − v2 ) = (u3 − pv3 ) − (u2 − pv2 ) = h3 − h2
m
= 𝑐𝑐𝑝𝑝 (𝑇𝑇3 − 𝑇𝑇2 )
𝑄𝑄41
= 𝑢𝑢4 − 𝑢𝑢1 = 𝑐𝑐𝑣𝑣 (𝑇𝑇4 − 𝑇𝑇1 )
𝑚𝑚
The thermal efficiency is the ratio of the net work to the heat added:
η𝑡𝑡ℎ,𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷
Wcycle
Q 41
u4 − u1
𝑇𝑇4 − 𝑇𝑇1
= m =1− m =1−
=1−
Q 23
Q 23
h3 − h2
𝑘𝑘(𝑇𝑇3 − 𝑇𝑇2 )
m
m
1
𝑟𝑟𝑐𝑐𝑘𝑘 − 1
= 1 − 𝑘𝑘−1 �
�
𝑟𝑟
𝑘𝑘(𝑟𝑟𝑐𝑐 − 1)
Like the Otto cycle, thermal efficiency increases with increasing compression
ratio.
The T-s diagram:
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.
The p-v diagram:
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 twostep 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.
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.
Thermal efficiency for the air-standard Dual Cycle can be developed:
η𝑡𝑡ℎ,𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 =
Wcycle /m
Q 51 /m
=1−
(Q 23 /m + Q 34 /m)
(Q 23 /m + Q 34 /m)
(u5 − u1 )
=1−
(u3 − u2 ) + (h4 − h3 )
Like the Otto and Diesel cycles, thermal efficiency increases with increasing
compression ratio.
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 auto ignition or “knock” limits the compression ratio of such
engines to the range 9.5-11.5, when fueled with unleaded gasoline.
• Since only air is compressed in the cylinder, compression-ignition engines
do not experience engine knock due to premature auto ignition of fuel.
Accordingly, such engines can:
 Operate at higher compression ratios than spark-ignition engines.
 Use less refined fuels having higher ignition temperatures than the
volatile fuels required by spark-ignition engines.