Engine Cycles
Internal Combustion Engines
Air-standard Cycles
Real air-fuel cycles approximated with air-standard cycles due to difficulties in analysis
Differences from the actual cycles
Gas mixtures treated as air
Closed cycles assumed instead of actual open cycles Combustion replaced with heat addition
Exhaust replaced with heat rejection Ideal processes assumed (reversible)
Intake and exhaust: Constant pressure processes Compression and expansion: Isentropic process
Combustion: Constant volume (for SI) and constant pressure (for CI) processes
Exhaust blowdown: Constant volume process
Ideal Gas Relationships
Thermodynamics Air properties
k T T
w R
k v P v
w P TP Tv
Pv
dT c du
dT c dh
RT P
mRT PV
RT Pv
k k k
k v p
1
) (
1
constant constant constant
1 2 2
1
1 1 2
2 2
1
/ ) 1 (
1
K - kJ/kg 287
. 0 1.35 /
K - kJ/kg 821
. 0
K - kJ/kg 108
. 1
v p
v p v
p
c c
R
c c k c c
K - kJ/kg 287
. 0 1.40 /
K - kJ/kg 718
. 0
K - kJ/kg 005
. 1
v p
v p v
p
c c
R
c c k c c
Inside engines in operation and exhaust flows
Inlet flows in turbochargers etc and air flow in radiators
Isentropic process
Variables for Cycle Analysis
air-fuel ratio mass flow rate
heat transfer per unit mass for one cycle heat transfer rate per unit mass
heat transfer for one cycle heat transfer rate
heating value of fuel compression ratio
work for one cycle power
combustion efficiency
Subscripts
m f a
ex
air fuel
exhaust
mixture of all gases
c c HV
W W r Q
Q Q q q m
AF
Otto Cycle
Four-stroke, naturally apsirated SI engines at WOT approximated with an Otto cycle
6 5
1 4 3
2
P0
Pressure, P
Volume, V
TDC BDC
Volume, V
Pressure, P
Otto Cycle: Intake Stroke
Process 6-1: Constant pressure
Intake valve open and exhaust valve closed
1 6
0 1
6
0 6
1
v v
P w
P P
P
6 5
1 4 3
2
P0
Pressure, P
Specific volume, v
TDC BDC
Actual pressure > P0 Temperature rise bet’n 25-35°C
Real cycles
Otto Cycle: Compression Stroke
Process 1-2: Isentropic All valves closed
1 2
2 1
1 2
1 1 2
2 2
1 2 1
1 2
1 1 2
1 1
1 2 1 1 2
1 1
0
/ /
T T
c u
u
k T T
R k
v P v
w P q
r P v
v P P
r T v
v T T
v
k c k
k c k
6 5 1
4 3
2
P0
Pressure, P
Specific volume, v
TDC BDC
Beginning: Slight opening of intake vale aBDC End: Firing of spark plug bTDC
Real cycles
Otto Cycle: Combustion
Process 2-3: Constant-volume heat input All valves closed
max 3
max 3
2 3
2 3
in 3
2
2 3
2 3
2 3
in 3
2 3 2
TDC 2
3
1 AF 0
P P
T T
u u
T T
c q
q
T T
c Q
T T
c m m
T T
c m
Q m Q
Q w
v v
v
v v c
HV
v f a
v m
c HV f
6 5
1 4 3
2
P0
Pressure, P
Specific volume, v
TDC BDC
Otto Cycle: Power Stroke
Process 3-4: Isentropic All valves closed
3 4
4 3
3 4
3 3 4
4 4
3
3 4
3 3 4
1 3
1 4 3 3 4
4 3
1 1
/ 1 /
/ 1 /
0
T T
c u
u
k T T
R k
v P v
w P
r P
v v P P
r T
v v T T
q
v
k c k
k c k
6 5 1
4 3
2
P0
Pressure, P
Specific volume, v
TDC BDC
Beginning: Combustion
End: Exhaust valve opening bBDC
Real cycles
Otto Cycle: Exhaust Blowdown
Process 4-5: Constant-volume heat rejection Exhaust valve open and intake valve closed
Enthalpy carried away, limiting thermal efficiency
1 4
4 5
4 5
out 5
4
4 1
4 5
out 5
4 5 4
BDC 1
4 5
0
T T c u
u
T T
c q
q
T T c m
T T
c m Q Q
w
v v
v v
v v v m
v m
6 5 1
4 3
2
P
0
Pressure, P
Specific volume, v
TDC BDC
Otto Cycle: Exhaust Stroke
Process 5-6: Constant pressure
Exhaust valve open and intake valve closed
Processes 6-1, 5-6
sometimes left off since these cancel each other
6 1
0
5 6
0 6
5
0 5
6
v v
P
v v
P w
P P
P
6 5 1
4 3
2
P0
Pressure, P
Specific volume, v
TDC BDC
Actual pressure < P0
Real cycles
Otto Cycle: Thermal Efficiency
Thermal efficiency: Depending only on temperature
Using relations for processes 1-2, 3-4
Therefore,
34 21
34 21OTTO
1 1
/ 1
/
T T
T T
T T
c
T T
c
q q
q w
v v
in out
in net
t
2 3 1
4
4 3 1
3 4 1
2 1 1
2
/ /
/ /
/ /
T T T
T
T T v
v v
v T
T k k
11 2 1
2 OTTO 1
/ 1 1
/ / 1 1
/ 1
k c
k t
r v v T
T
Compression ratio, rc Thermal efficiency, t (%)
Prob. 3-1
1
4 3
2
Entropy, s
Temperature, T
Real Air-fuel Cycles
Open cycle with changing compositions
Gas compositions change during combustion Molar quantities change
Fuels added sometimes during the cycles (CI, some SI) Liquid fuel droplets introduced sometimes
Crevice flows and blowby past the pistons
Non-ideal and no air
Inlet flow: Air with up to 7% fuel
Exhaust flow: CO2, H2O, N2, CO, HC, part, etc.
Non-ideal gas behavior during combustion (high pressure)
Non-constant specific heats: As high as 30% change in the engine temperature range
Real Air-fuel Cycles
Heat loss during the cycle
Power stroke starts at a lower pressure and work output is decreased Lowered temperature and pressure at the power stroke end
Lower indicated thermal efficiency
Short but finite combustion time
Finite time desirable; e.g. supersonic detonation would result in a rough cycle and shorten engine life
Starts bTDC: Negative work in the compression stroke Completes aTDC: Some power lost in the power stroke
Combustion efficiency of >100%: incomplete mixing, local variations in temperature, turbulence, quenching, etc. (SI: ~95%, CI: ~98%)
Real Air-fuel Cycles
Finite blowdown time
Exhaust valves open 40-60° bBDC → Some work lost
Intake valves open bTDC
Due to flow restriction (lowered volumetric efficiency otherwise) Compression delayed → lowered temperature and pressure rise before combustion
Finite valve times: Smooth cam profiles
Valve overlap
Errors with QLHV since different property values Approximation
t actual 0.85
t OTTOSI Engine Cycle at Part Throttle
Flow restriction with a partially closed throttle
Pressure drop in the incoming air (Temperature similar)
The lower loop: negative work
The lower pressure →
lower pressures throughout the rest of the cycle (exception: atmospheric press at exhaust stroke)
Less air, fuel → Less thermal energy, work out (similar temperature rise)
pump
net d i ex dex net i
pump
d ex ex
d i i
P P
V W
V P P
W
V P V
V P W
V P V
V P W
/ pmep
5 6
6 5
6 1
1 6
Specific volume, v
Pressure, P
P0
TDC BDC
1 5 4 3
2
6
6a
Part Throttle SI w/Super-, Turbochargers
Intake pressure > Atmospheric pressure → Higher pressure throughout the cycle
Positive net pumping work Increased air and fuel
Increased temperature (compressive heating)
Sometimes, self-ignition or knocking
Aftercooler or
Lower compression ratio
Exhaust Process
Consists of blowdown and exhaust stroke Blowdown: A large % of gases leaving
Approximated with ideal gas isentropic relationship Temperature decrease due to expansion cooling
Modeling an actual open system as a closed system
(7: Hypothetical state)
ex
k k
k kk k k
k
P P T P
P T
P P T P
P T T
/ ) 1 ( 4 4 0
/ ) 1 ( 4 4
/ ) 1 ( 3 3 7
/ ) 1 ( 4 4 7
7
/ /
/ /
Specific volume, v
TDC BDC
7 7c 7b 7a 5
1 4
Exhaust Residual
Mass bet’n blowdown and exhaust stroke Mass after the exhaust stroke
Mass in the cylinder during the entire cycle Exhaust residual
7 1 7
5 5
7 V /v V /v V /v
m ex
7 2 7
6 /v V /v
V
mex
7 7 4
4 3
3 2
2 1
1 /v V /v V /v V /v V /v
V
mm
7 2 7
7 7
2 / )/( / ) /
(V v V v V V
xr
) / )(
/ )(
/ 1 (
) / /(
) / (
) / 1 (
) / )(
/ 1 ( ) / )(
/ ( ) / /(
) / (
4 4
7 7 4
4
7 4 7
4 4 6 4
4 7
6
P P
T T r
P RT
P RT
r
v v r v
v V V v
V v
V x
ex ex
c c
c r
OR
m ex
r m m
x /
Gases leaving during blowdown have high kinetic energy due to high velocity
Enthalpy (temperature) rise in exhaust manifold This rise is progressively reduced
It is desirable to mount the turbine of a turbocharger close to the exhaust manifold
Exhaust Kinetic Energy
Specific volume, v
TDC BDC
7 7c 7b 7a 5 1
4
Energy Balance during Intake
Total enthalpy conserved for incoming and exhaust air
Temperature of the gas mixture at the compression stroke start
Volumetric efficiency is reduced due to hot exhaust residual, which reduces incoming air density
exex p mex
exa
p aa mm
pa m mm m a
a ex
ex
T T
m m
T m m
T c m T
c m T
c m
h m h
m h
m
/ /
Tm 1 xrTex
1 xr
T aProb. 3-2,3
Diesel Cycle: Combustion
Combustion lasts into the expansion stroke due to ignition delay and finite injection time
→ Constant-pressure process for combustion Combustion: Process 2-3 (heat input)
Cutoff ratio: V3 /V2 v3 /v2 T3 /T2
max 3
2 3 2 2
3 3
2 3
2
2 3 2
3 in
3 2
2 3
2 3 2 3 in
3 2
) (
) (
1 AF
T T
v v P u
u q
w
h h T
T c q
q
T T c Q
T T c m m
T T c m
Q m Q
Q
p p c
HV
p f a
p m
c HV f
0
Specific volume, v
TDC BDC
Pressure, P
Entropy, s
Pressure, P
Diesel Cycle: Thermal Efficiency
Thermal efficiency
With rearrangements
The number in the bracket > 1
Thermal efficiency: Otto > Diesel for a given compression ratio Compression ratio: CI > SI
34 12
43 12
DIESEL
1 1
/ 1
/
T T
k
T T
T T
c
T T
c
q q
q w
p v
in out
in net
t
1 1 1 1
1
DIESEL
k r
k k
c t
Prob. 3-4
Dual Cycle
Modern CI engine: Injection of fuel ~20° bTDC
Const. P heat combustion + const. V heat combustion
Modern CI: Dual cycle
Historic CI: Diesel cycle
Volume, V Volume, V
Pressure, P
Dual Cycle: Combustion
Process 2-x: Constant-volume heat input
Pressure ratio
2
2 max
2 2
2
2 2
2 2
2
/ 0
T T P P
P
u u
T T
c q
T T
c m m
T T
c m Q
w
V V
V
x x
x x
v x
x v f a
x v m x
x
TDC x
3 1
2 2
3
2 / / 1/ /
/P P P T T r P P
Px x c k
TDC BDC
Specific volume, V
Pressure, P 2
x 3
Temperature, T
Entropy, s 2
x
3
Dual Cycle: Combustion
Process x-3: Constant-pressure heat input
Cutoff ratio Heat in
max 3
3 3 3
3 3
3
3 3
3
3 3
3
max 3
) (
) (
) (
T T
v v
P v
v P
u u
q w
h h
T T
c q
T T
c m m
T T
c m Q
P P
P
x x
x
x x
x
x x
p x
x p
f a
x p
m x
x
TDC BDC
Specific volume, V
Pressure, P 2
x 3
Temperature, T
Entropy, s 2
x
3 x
x v v V V T T
v
v3 / 3 / 2 3 / 2 3 /
x x
x x
in
c HV f x
x in
h h u
u q
q q
Q m Q
Q Q
3 2
3 2
3
2
Dual Cycle: Thermal Efficiency
Thermal efficiency:
With rearrangements
For real diesel engines
x p x x x
v
v
in out in
net t
T T k T T
T T T
T c T T c
T T c
q q
q w
3 2
1 4 3
2
1 4 DUAL
1 1
/ 1
/
1 1
1 1 1
1
DUAL
k r
k k
c t
actualactual 0.85
DUALDIESEL85 . 0
t t
t t
: History engines
: Modern engines
Comparison of Different Engines
For a given compression ratio:
Heat transfer:
Area under the process line
t OTTO
t DUAL
t DIESELin out
q
q : Identical : Different
Comparison of Different Engines
For a given peak pressure:
Heat transfer:
Area under the process line
For the most efficient engine
Combustion as close to constant volume
Higher compression ratio
t DIESEL
t DUAL
t OTTOin out
q
q : Identical : Different
Prob. 3-5
Two-stroke Cycles
Very small and large engines in two-stroke cycles
Small engines: No valves etc. → Lightweight and inexpensive
Large engines: One power stroke per cycle → Smooth operation at low RPM
No exhaust stroke and imperfect scavenging
Large amount of exhaust residual
Air-fuel mixture diluted and combustion temperature lowered Reduces NOx emissions but creates other problems in catalytic systems
Two-stroke SI Engine Cycles
Process 1-2: Isentropic power or expansion All ports closed
Process 2-3: Exhaust blowdown Exhaust port open, intake closed
Process 3-4-5:
Intake and exhaust scavenging Exhaust and intake ports open
k T T R k
v P v
w P q
v v P P
v v T T
k k
1 1
0 / /
1 2 1
1 2 2 2
1 2 1
2 1 1 2
1 2 1 1 2
Volume, V
Two-stroke SI Engine Cycles
Process 5-6: Exhaust scavenging Exhaust open, intake closed
Process 6-7: Isentropic compression all ports closed
Process 7-1: Constant-volume heat input (combustion)
All ports closed
Volume, V
k 1
T T R k
1
v P v
w P
0 q
/v v P P
/v v T T
6 7 6
6 7 7 7
6 7 6
k 7 6 6 7
1 k 7 6 6 7
1 7
7 max 1
max 1
7 1 v m c
HV f in 1
7 1 7
TDC 1
7
/T T P P
P T T
T T c η m
Q m Q
Q
0 W
V V V
Two-stroke CI Engine Cycles
Combustion approximated by a two-step process Process 7-x:
Constant-volume heat input
Process x-1:
Constant-pressure heat input
7
7 max
7 7
7 7
/ 0
T T P P
P
T T c m Q
W
V V V
x x
x v m x
x
TDC x
max 1
1 1
1 1 1
max 1
T T
T T c m Q
V V P W
P P P
x v
m x
x x
x
Prob. 3-7
Miller Cycle
Modern modification of the Atkinson cycle Expansion ratio > compression ratio
Utilizing a unique valve timing
Intake valve closed bBDC or aBDC
Read 3.9, 3.10 Prob. 3-6
Atkinson cycle Miller cycle Super- or turbocharged