에너지변환특론
Advanced Energy Conversion
Chapter 3. Otto cycle and Diesel cycle
교수
박 수 한
참고 .
- http://www.youtube.com/playlist?list=PLX2gX- ftPVXXMDW2aoPCk7nM-58n7nW5M
2
Operation of IC Engines
How to make the analysis of the engine cycle much more manageable?
- Actual Cycles:
• Mechanical cycle
• Thermodynamics point of view, non-cyclic, open cycle, quasi steady-flow
• Variable composition (combustion) with gas mixtures (Fuel, CO2, H2O, O2, N2)
4
Simplify to the Air Standard Cycle
Mechanical Cycle Thermodynamic Cycle
Fuel, Air CO2, N2, H2O
Air
Qin Qout
Air Standard Cycle
- Air-Standard Cycle:
• Simplified and more manageable
• Determines important design parameters
• Reasonable accuracy, particularly w.r.t. sensitivity to design parameters
• Error involves
6
Air Standard Assumptions
- Working fluid is Air
- Mass of air (gas phase) is constant (actually variation up to 7%)
- Closed cycle
• Recalculated Air
• Heat Exchangers for heat rejection and addition - No Internal Combustion
Air Standard Assumptions
- Ideal Processes
• Constant pressure exhaust at 1 atms.
• N/A cycles have constant pressure intake at 1 atms
• Turbo/Supercharged cycles have constant pressure >
1 atms.
- Compression and Expansion are Isentropic with constant specific heats
- Heating is at constant volume (SI), constant pressure (CI), or both (high speed CI)
8
Thermodynamics - review
- Ideal Gas:
- The First Law of Thermodynamics
- The Second Law of Thermodynamics dT
c du
dT c
dh
RT P
mRT PV
RT Pv
v
p
,
,
,
w du
q
T
ds q
Thermodynamics – Work and Heat
- For a closed system:
P
w
1
2 T
q
1
2
21
Pdv
w q
12Tds
10
Thermodynamics - symbols
sound of
speed
work spcific
/
heats speific
,
energy internal
specific
enthapy specific
density
cylinder in
gas of mass
e temperatur
air of constant gas
gas of volume specific
cylinder in
volume
cylinder in
presure gas
c w
c c k c c
u h m T R v V
P
v p v
p
efficiency combustion
power
cycle one
for work
ratio n compressio
fuel of value heating
rate fer heat trans
cycle one
for fer heat trans
mass unit per rate fer heat trans
cycle one
for mass unit per fer heat trans
rate flow mass
ratio fuel air
AF
c c HV
W W r Q
Q Q q q m
exhaust ex
fuel, air,
:
f
a
Subscripts
Polytropic Process
const
Pv
n1 1
1 2
2
2 1 1
2
n n n n
v P
T
v v P
P
RT Pv
from
polytropic 1
const) (
isochoric
const) (
isentropic
const) (T
isothermal
1
const) (
isobaric
0
k n
v n
s k
n n
P n
12
Polytropic Process
v
P n 0 (isobaric)
l) (isotherma
1 n
) (isochoric
n
c) (isentropi k
n
s T
n
0 n k
n
1 n
Thermodynamics - review
- Isentropic process:
- Speed of sound
system closed
for )
1 (
) (
) 1
(
) (
constant constant constant
1 2
1 1 2
2 2
1
) 1 (
1
k T T
R k
v P v
w P TP Tv
Pv
k k k
k
14
Thermodynamic Properties - Air
- Engine operating conditions:
- Standard conditions:
K - kJ/kg 287
. 0
35 . 1 /
R - BTU/lbm 196
. 0 K - kJ/kg 821
. 0
R - BTU/lbm 265
. 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
4 . 1 /
R - BTU/lbm 172
. 0 K
- kJ/kg 718
. 0
R - BTU/lbm 240
. 0 K
- kJ/kg 005
. 1
v p v
p
c c
R
c c
k c c
Otto Cycle
Real Otto
스파크 점화 기관의 공기표준 사이클
정적 사이클 (constant volume cycle), 일정체적 하에서 연소
1876년 Nikolaus August Otto, 독일
참고.
상사점 (Top Dead Center, TDC):
피스톤이 크랭크축으로부터 가장 먼 위치 (TDC 이전 –BTDC, TDC 이후-ATDC)
하사점 (Bottom Dead Center, BDC):
피스톤이 크랭크축으로부터 가장 가까운 위치 (BDC 이전 –BTDC, BDC 이후-ATDC)
보어 (Bore): 실린더의 직경 또는 피스톤면의 직경
행정 (Stroke): 피스톤이 상사점에서 하사점 또는 하사점에서 상사점으로 움직인 거리
간극체적 (Clearance Volume):
피스톤이 상사점에 있을 때 연소실의 최소체적
배기량 (Displacement), 행정체적(Displacement Volume)
: 피스톤이 상사점과 하사점을 움직이면서 배제하는 체적
TDC
BDC
l B
L
s
a
Vc
Vd
Vc: clearance volume
Vd: displaced or swept volume B : cylinder bore
L : piston stroke l : connecting rod length
참고.
압축비 (compression ratio, rc)
C C d
C V
V
r V
volume cylinder
minimum
volume cylinder
Maximum
SI engine : rc = 8 ~ 12
CI engine : rc = 12 ~ 24
보어 행정비 (bore to stroke ratio, Rbs)
L Rbs B
Small & medium size engine = 0.8 ~ 1.2
Large slow speed CI engine = ~ 0.5
B L : under square engine, 저속 대형엔진
TDC
BDC
l B
L
s
a
Vc
Vd
Otto Cycle
냉각손실 :
압축 후반, 연소 중, 팽창과정에서 연소실 내의
작동유체와 연소실 벽면 등의 온도차로 인해 발생하는 열손실
시간손실 :
이론 사이클에서는 상사점에서 순간적으로 연소가 일어나 지만, 실제로는 그렇지 못하다. 연소에 필요한 시간은 대략 크랭크 각도로 40~60CA가 필요하다. 이처럼 정적연소가 아니라서 생기는 열손실을 말한다.
펌프손실 :
공기가 흡입되는 과정에서 이동통로의 조도, 공기청정기, 인젝터, 스로틀밸브 등을 거치면서 손실되는 양.
스로틀밸브에 의한 손실량이 가장 크다.
배기손실 :
배출가스를 통한 열손실
Air Standard Otto Cycle
1-2: Isentropic Compression
2-3: Constant Volume Heat Addition 3-4: Isentropic Expansion
4-5: Constant Volume Heat Rejection 5-6: Exhaust at 1 atm
6-1: Intake at 1 atm
20
Otto Cycle: P-v & T-s Diagrams
Otto Cycle Thermodynamic Analysis at WOT
(6-1: Constant-pressure intake) 1-2: Isentropic compression
2-3: Constant volume heat addition 3-4: Isentropic expansion
4-5: Constant volume heat rejection
(5-6: Constant-pressure exhaust)
22
Isentropic Compression (1-2) Process
) (
) (
1 0
) (
) ( const.
2 1
1 1 2
2 2 2 1
1 2 1
1 2
1 1 2
1 1
1
2 1 1 2
T T
c
u u
k v P v
Pdv P w
q
r v P
P v P
r v T
T v T
Pv
k c k
k c k
k
Constant Volume Heat Addition (2-3) Process
) (
) (
0
2 3
3 2
2 3
2 3
3 2
3 2
2 3
T T
c m Q
Q
T T
c u
u q
q w
v v
v m in
v in
24
Isentropic Expansion (3-4) Process
) (
) (
1 0
1 1 const.
4 3
4 3
3 3 4
4 4 4 3
3 4 3
3 4
3 3 4
1 3
1
4 3 3
4
T T
c
u u
k v P v
Pdv P w
q
P r v
P v P
T r v
T v T
Pv
v
k
c k
k
c k
k
Constant Volume Heat Rejection (4-1) Process
) (
) (
0
4 1
5 4
4 1
4 1
4 5
5 4
1 4 5
4
1 4
5
T T
c m Q
Q
T T
c u
u
u u
q q
w w
v v
v
v m out
v out
26
Thermodynamic Properties
r
cv v v
v
v v
v v
3 4 2
1
3 2
1
4
and
2 3 1
4
T T T T
1-2 & 3-4 processes are isentropic
Indicated Thermal Efficiency of Otto Cycle
12 1 2
3 1 4 2
1
2 3
1 4
2 3
1 4
in out in
net OTTO
/ 1 1
1 1 ) / (
1 ) / 1 (
) (
) 1 (
) (
) 1 (
1
k c v v t
r
T T T
T T T T
T
T T
T T
T T
c
T T
c
q q q
w
• k = 1.3 ~ 1.4 and rc > 1
Thermal efficiency increases with compression ratio
28
Example Problem 3-1
- Given
• 4-Cylinder, 2.5L, SI engine, WOT, 4-Stroke
• Air standard Otto cycle, 3000 RPM
• Compression ratio = 8.6:1, mech. eff. = 86 %
• S/B = 1.025, AF = 15
• iso-octane: HV = 44,300 kJ/kg, comb. eff. = 100 %
• Initial conditions: P1 = 100 kPa, T1 = 60°C
• Exhaust residual: 4%
- Calculate parameters for one cylinder
- Do a complete thermodynamic analysis
Example Problem 3-1
30
Real Air-Fuel Engine Cycles
1. Real engines operate on an open cycle
• Changing gas composition via combustion
• Changing mass for CI cycle via fuel addition
2. Properties differ from air
• Fuel & combustion products
• Specific heat varies by up to 30 % (300 K to 3000 K)
3. Heat losses during the cycle (up to 12 %)
Real Air-Fuel Engine Cycles
4. Combustion requires finite time (~ 6 %)
• 30 to 60 degrees of crank rotation
• More compression work, Less expansion work
Finite time combustion losses
32
Real Air-Fuel Engine Cycles
5. Blowdown process requires a finite time (~2 %)
• Exhaust valve opens bBDC
• Work loss at the end of power stroke
Early Exhaust Valve Opening Loss
Real Air-Fuel Engine Cycles
6. Intake valve closes aBDC
• Improves volumetric efficiency
• Momentum of entering air continues flow through intake valve after piston starts up
• Reduces effective compression ratio
• Reduces T and P due to compression
7. Finite valve opening and closing times
• To assure the fully opened valves at TDC
• Valve overlap at TDC
34
Real Air-Fuel Cycle vs. Ideal Cycle
- Errors due to the differences between real air-fuel cycles and ideal air standard cycles
- Some errors tend to cancel, e.g., specific heats
- The efficiency of real cycle efficiency is less than that of air standard cycle
t actual 0 . 85
t OTTOSI Engine Cycle at Part Throttle
Negative pump work – P1 is lower than Po
?
36
SI Engine Cycle with T/C or S/C
Positive pump work – P1 is higher than Po
?
Part Throttle, T/C or S/C
– Part throttled: Negative – T/C or S/C: Positive
Wpump
net ( P
i P
ex ) V
d
38
Exhaust Process
Exhaust stroke
Blowdown
EVO
Real Exhaust Blowdown P-v
KE h
h
o
s
40
Real Exhaust Blowdown T-s
KE h
h
o
s
Real Exhaust Blowdown Equations
o ex
k k k o
k ex
P P
P
P T P
P T P
T
7
) 1 (
4 4
) 1 (
4 4
7
where,
-
Approximated by Isentropic Process
42
Exhaust Residual
-
Residual exhaust gas in clearance volume, V
c, at TDC starting intake stroke
m ex
r
m
x m
Mass of exhaust gas carried into the next cycle
Mass of gas mixture within the cylinder for the entire cycle
Calculating Exhaust Residual
o ex
k
o ex
k
P P P
P v
v P
P
P P P
P v
v P
P
3 3
3 7 7
3
4 4
4 7 7
4
7 1 7
5 5
7
v
V v
V v
m V
ex
44
Calculating Exhaust Residual
4
7 2 7
7 7
2
1
/
P P T
T x r
V V v
V v
V m
x m
ex r
m ex r
7 2 7
6
7 7 2
2 1
1
and v
V v
m V
v V v
V v
m V
ex m
Calculating Exhaust Residual
a r
ex r
m
x T x T
T ) ( 1 )
(
1
m m
a a ex
ex
h m h m h
m
a
ex
T T
T
7
where,
46
Exhaust Residuals in Real Engines
- Exhaust residual amount
• SI engine at WOT: 3~7 %
• SI engine at part throttle: up to 20 %
• CI engine: Generally less than for SI engine
- The effect of exhaust residual
• Less heat addition
• Dilution Max. temperature decreases
• Volumetric efficiency decreases
Diesel Cycle
Real Diesel
48
Air Standard Diesel Cycle
1-2: Isentropic Compression 2-3: Constant Pressure Heat Addition
3-4: Isentropic Expansion 4-5: Constant Volume Heat Rejection
5-6: Exhaust at 1 atm 6-1: Intake at 1 atm
Diesel Cycle: P-v & T-s Diagrams
50
Diesel Cycle Thermodynamic Analysis
(6-1: Constant-pressure intake) 1-2: Isentropic compression
2-3: Constant pressure heat addition 3-4: Isentropic expansion
4-5: Constant volume heat rejection
(5-6: Constant-pressure exhaust)
Isentropic Compression (1-2) Process
1 0
) (
) ( const.
1 1 2
2 2 2 1
1 2 1
1 2
1 1 2
1 1
1
2 1 1 2
k v P v
Pdv P w
q
r v P
P v P
r v T
T v T
Pv
k c k
k c k
k
52
Constant Pressure Heat Addition (2-3) Process
) (
) (
) (
) (
1) AF
(
) (
2 3
2 2
3 3
2 3
2
2 3
2 3
3 2
2 3
2 3
3 2
v v
P u
u q
w
h h
T T
c q
q
T T
c Q
T T
c m Q
m Q
Q
p in
p c
HV
p m c
HV f
in
– Cutoff ratio (Load ratio)
2 3 2
3 2
3
T T v
v V
V
• Heat addition period
r
1
Cut-off Ratio for Indicated Thermal Efficiency
54
Isentropic Expansion (3-4) Process
) (
) (
1 0
1 1 const.
4 3
4 3
3 3 4
4 4 4 3
3 4 3
3 4
3 3 4
1
3 1
4 3 3 4
T T
c
u u
k v P v
Pdv P w
q
P r v
P v P
T r v
T v T
Pv
v
k
c k
k
c k
k
2 1 3
: 4
Note v
v vv
Constant Volume Heat Rejection (4-1) Process
) (
) (
0
4 1
5 4
4 1
4 1
4 5
5 4
1 4 5
4
1 4
5
T T
c m Q
Q
T T
c u
u
u u
q q
w w
v v
v
v m out
v out
56
) 1 (
) 1 (
1 1
) (
) 1 (
1
1 DIESEL
2 3
1 4
in out in
net DIESEL
k r
T T
c
T T
c q
q q
w
k k c t
p t v
Indicated Thermal Efficiency of Diesel Cycle
• β 1, then (βk -1) 0
• β rc, then state 3 state 4
t DIESEL
t OTTO
decreases to the lowest valueCut-off Ratios and Thermal Efficiencies
58
Dual Cycle
Real
Dual
Pre-mixed Combustion
Non-premixed Combustion
Air Standard Dual Cycle
1-2: Isentropic Compression 2-x: Constant Volume Heat Addition
x-3: Constant Pressure Heat Addition
3-4: Isentropic Expansion 4-5: Constant Volume Heat Rejection
5-6: Exhaust at 1 atm
60
Dual Cycle: P-v & T-s Diagrams
Dual Cycle Thermodynamic Analysis
(6-1: Constant-pressure intake) 1-2: Isentropic compression
2-x: Constant volume heat addition x-3: Constant pressure heat addition 3-4: Isentropic expansion
4-5: Constant volume heat rejection
62
Constant Volume Heat Addition (2-x) Process
2 2
2
2 3
2 3
2 2
2
) (
) (
) (
) (
0
u u
T T
c q
T T
c m m
T T
c m Q
w
v v
v
x x
v x
v f a
v m x
x
TDC x
– Pressure ratio
1 3 2
2 3 2
1
P P r
T T P
P P
P k
c x
x
Constant Pressure Heat Addition (x-3) Process
) (
) (
) (
) (
1) AF
(
) (
2 3
2 2
3 3
2 3
2
2 3
2 3
3 2
2 3
2 3
3 2
v v
P u
u q
w
h h
T T
c q
q
T T
c Q
T T
c m Q
m Q
Q
p in
p c
HV
p m c
HV f
in
– Cutoff ratio (Load ratio)
x
x T
T V
V v
v v
v 3
2 3 2
3
3
64
Indicated Thermal Efficiency of Dual Cycle
1 )
1 (
) 1 (
1 1
) (
) (
) 1 (
1
1 DUAL
3 2
1 4
in out in
net DUAL
k r
T T
c T
T c
T T
c q
q q
w
k k c t
x p
x v
v t
− Heat in
) (
)
( 2 3
3
2 x x x x
in q q u u h h
q
− Thermal efficiency
Comparison of Otto, Diesel, and Dual Cycles
α 1: dual cycle Diesel cycle β 1: dual cycle Otto cycle
1 )
1 (
) 1 (
1 1
1
DUAL
k r
k k c t
66
Comparison of Cycles – Fixed r
c
t OTTO
t DUAL
t DIESELComparison of Cycles – Fixed P
max
t DIESEL
t DUAL
t OTTO68
Atkinson Cycle
Miller Cycle
N/A T/C
70
Comparison of Miller Cycle and Otto Cycle
New Design and New Product
- What is all about the design in mechanical engineering?
• Optimization with constraints including
performance, cost, endurance, operation etc.
- How can the new technology/product be accepted by customers?
• No sacrifice on old functions
• Additional functions, convenience, price
72