Download - Heat Engines2
-
8/3/2019 Heat Engines2
1/21
Heat EnginesEnergy Resources:
Fossil fuels, biomass, nuclear, solar, wind, ocean ( waves, ocean temp.
energy conversion OTEC)
Thermodynamic relations:
First Law:
SystemSSSFdHdWdQ
SystemCloseddUdWdQ
.........................
.......................
=
=
Perfect Gas:
)./...(8314
..........................1
................1
....................................
...............................
KkgjG
RTuhM
GR
k
kRC
k
RC
pvuhC
Ck
dTdhC
dTduC
RTpvmRTPV
pv
c
ppv
=
+==
=
=
+====
==
p p
2
1 = pdVW = VdpW
2 1
V V
Second Law: 2
1
Power Plant Generator
Steam power
plants
Hydraulic
power plants
Gas power plants
Gas turbinesReciprocating engines
Petrol Diesel Stirling
-
8/3/2019 Heat Engines2
2/21
TdSdQ = Q
1
2
1
2
12 ln.lnV
VR
T
TCSS v += .(1) 1
1
2
1
212 ln.ln
ppR
TTCSS p = ...(2)
p V=Const
pVn=Const
P=Const (n=0)
T=Const (n=1)
PVk=Const (n=k)
T
PVk=C
V=C
P=C
T=C
S
2
-
8/3/2019 Heat Engines2
3/21
Const.
Volume
(Isochoric)
Const.
Pressure.
(Isobaric)
Const.
Temp.
(Isothermal)
Adiabatic
Reversible
(Isentropic)
Polytropic
Relations V=const
1
2
1
2
T
T
p
p=
2
1
2
1
.
T
T
V
V
Constp
=
=
constU
VpVp
ConstT
=
=
=
2211 .
.
k
k
k
k
p
p
V
V
T
T
ConstpV
ConstS
1
1
2
1
2
1
1
2
.....
=
=
=
= ConstVp n =.
Work W= 0 Vp.
1
2ln.V
VmR
0
..
=
=
Q
UW
TCm v
n
TTRm
1
.(. 12
Heat Q= TCm v .. TCm p ..
WQ
U
V
VTRm
=
= 0
ln...1
2 0 WUQ +=
Entropy=S
1
2ln..
T
TCm v
1
2ln..
T
TCm p
1
2ln..
V
VRm
0 Relations
(1)&(2)
1
2
1
212 ln.ln
V
VR
T
TCSS v += ...(1)
1
2
1
2
12 ln.lnp
pR
T
TCSS p = ..(2)
Air Standard Cycles
Assumptions:
1-The working fluid is air (ideal gas PV=mRT) of fixed mass.
2-Combustion is replaced by a process of heat addition.
3-Cycle is completed by heat transfer to the surrounding.
4-All processes are reversible.
3
-
8/3/2019 Heat Engines2
4/21
5-Constant specific heat.
Important Parameters:
1-Thermal efficiency:
add
netth
QW= p Wnet
2-Mean effective pressure:
s
mV
CycleW
VolumeStroke
CycledoneWork
p ==..
..
V
3-Work Ratio:
WorkGross
WorkNet
W
WWR
positive
net
...
...==
4-Specific Work Transfer:
plantofSizem
WSW
air
net ................=
5-Specific Consumption:
WSW
mCS
net
air
.
1. ==
Carnot Cycle:
4
Source TH
E
Sink TL
W=QH-QL
14
3
2p
32
1
T
V S
TH
TL
4QL
QH
Isothermal
Isentropic
1-2 Isentropic Compression
2-3 Isothermal Heat addition
3-4 Isentropic Expansion
4-1 Isothermal Heat rejection
-
8/3/2019 Heat Engines2
5/21
From p-V diagram:
2
3
1
4
2
3
ln...
ln...ln...
V
VTRm
V
VTRm
V
VTRm
Q
QQ
Q
W
H
LH
H
LH
add
net
th
=
==
but1
4
2
3
V
V
V
V=
H
LLHth
TT
TTT
H
== 1
From T-S diagram:
)(.
).(.)(.
23
1423
SSTm
SSTmSSTm
Q
QQ
Q
W
H
LH
H
LH
add
netth
=
==
but 1423 SSSS =
H
LLH
th
T
T
T
TT
H
=
= 1
gross
net
W
WWR =
== ))(( 23 SSTTmQW LHnet
isentropicisothermalgross WWW += U=0 Q=0
W=Q W=U
))((
)()(
))((
)(.)(.
23
23
23
23
SSTTSW
TTCSST
SSTTWR
TTCmSSTmW
LH
LHvH
LH
LHvHgross
=
+
=
+=
Reciprocating engines cycles:Stirling Cycle:
5
1
S
2
3
41
43
2
V
Tp V=Const
Isothermal T=Const
1-2 Isothermal Compression2-3 Const. Volume Heat addition
3-4 Isothermal Expansion
4-1 Const. Volume Heat rejection
-
8/3/2019 Heat Engines2
6/21
1
S
2
3
4 1
43
2
V
Tp V=Const
Isothermal T=Const
1-2 Isothermal Compression
2-3 Const. Volume Heat addition
3-4 Isothermal Expansion4-1 Const. Volume Heat rejection
4
3
1
2
1
2
12
3
434
...........ln..
ln..
V
V
V
Vbut
V
VTRmQ
V
VTRmQ
L
H
==
=
6
-
8/3/2019 Heat Engines2
7/21
===
=
+=
==
LimitsTempsamethebetweenWorking
Carnot
H
L
H
LHth
H
HL
H
HL
add
th
TT
TTT
V
VTRm
V
VTRm
V
VTRm
V
VTRm
V
VTRm
V
VTRm
Q
WW
Q
dW
...................
1
2
1
2
1
2
3
4
3
4
1
2
34
3412
1
ln..
ln..ln..
ln..
ln..ln..
2
1234
34
1234
1ln)(
1
V
VTTRWWSW
T
T
W
WW
W
WWR
Lh
H
L
gross
net
=+=
=+
==
Both WR & SW are greater than the values for Carnot cycle.
+
=+
=
H
LHvH
L
LHvH
LH
T
TT
SS
CTT
TTCSSTSSTTWR
)(.
)(1
1)1()()(
))((
23
23
23
.Carnot
[ ] onethanloweris ................
CarnotStirling WRWR >
3-4ColdHot
Regenerator CoolerHeater
?
Expansion Compression
7
Stirling
Engine
0 90 180 270 360 Crank angle
Total
Volume
4-1 1-2 2-3 3-4
Compression Expansion
4-1 Transfer of working fluid to the cold space..Const vol.heat rejection to
the regenerator
2-3 Transfer of working fluid to the hot space..Const vol. Heat addition
from the regenerator
-
8/3/2019 Heat Engines2
8/21
Otto Cycle:
8
p
V S
4
3
2
4
3
2
1
T
1
V1
V2
Isentropic Const. Volume
Wnet
Qadd
Qrej
-
8/3/2019 Heat Engines2
9/21
Carnotk
v
th
k
v
kk
th
v
vv
th
vvnet
vrej
vadd
rT
T
V
V
T
T
RationCompressior
V
V
T
T
T
T
T
T
V
V
V
V
T
Tbut
T
T
T
T
T
T
TT
TT
TTCm
TTCmTTCm
TTCmTTCmW
TTCmvolconstQQ
TTCmvolconstQQ
-
8/3/2019 Heat Engines2
10/21
Diesel Cycle:
10
1
V S
1
2
Tp
4
2 3
3
4
P=Const
V=Const
Isentropic
P=Const
T=Const
-
8/3/2019 Heat Engines2
11/21
)1(
)1(1
1).(.
).(.1
).(.
).(.)(.
).(.)(.
).(.
).(.
2
3
2
1
4
1
23
14
23
1423
1423
1414
2332
=
=
=
=
==
==
T
TT
T
TT
kTTCm
TTCm
TTCm
TTCmTTCm
TTCmTTCmW
TTCmQQ
TTCmQQ
p
v
p
vp
th
vpnet
vrej
padd
..........)1(
1
.
11
1
1
.
11
...........
.................
2
3
1
2
3
2
3
1
2
3
1
2
3
2
31
1
2
1
4
3
2
3
1
4
1432
1
4
3
3
4
1
1
2
2
1
ratiooffcutV
Vwhere
kr
V
V
V
V
rk
VV
VV
VV
V
VV
V
TT
TT
VVVV
V
V
T
Tand
V
V
T
Tbut
k
k
k
kth
kk
k
k
kk
==
=
=
=
=
=
=
=
=
)..........(...................... smallisloadslowinhigherisloadondepends th
[ ]
ratiocomphighatoperateEnginesDieselBut
rratiocompsametheforOttoDiesel
Diesel
unitythangreaterOtto
kr
thth
k
kth
....................
..............)....()(
..
....................................
)1(
1
.
11
1
-
8/3/2019 Heat Engines2
12/21
12
3
2
1
T
V
1
5
43p
S
5
4V=Const
Otto
Diesel
Isentropic
P=Const
ratiopressurep
pLet
TTkTT
TT
TTCmTTCm
TTCmTTCmTTCm
Q
W
TTCmVVpW
QQW
TTCmQQ
TTCmTTCmQQQ
th
pv
vpv
add
net
th
vpositive
rejaddnet
vrej
pvadd
.............
)()(
)(1
)(.)(.
)(.)(.)(.
)(.)(
)(.
)(.)(.
2
3
3423
15
3423
153423
5434
1551
34233423
=
+
=
+
+
==
+=
=
==
+=+=
12
-
8/3/2019 Heat Engines2
13/21
k
k
k
k
k
k
k
kk
k
Tr
rTT
VVrVV
VV
VV
VV
V
V
V
V
V
VrT
V
VTT
rTV
VTT
rTp
pTTrT
V
VTT
......
......................
.
.
.
....
...
..,...........
1
1
1
15
32
13
24
13
34
1
4
5
4
1
5
41
1
1
5
4
45
1
1
3
4
34
1
1
2
3
23
1
1
1
2
1
12
=
=
=====
=
=
=
=
===
=
)(.)(
)(.)(.)(.
)(.)()(
tan................
............1................................................................
............1.........)1.(.()1(
1.11
5434
153423
153423
...
.
.1
TTCmVVp
TTCmTTCmTTCmWR
TTCTTCTTCSW
timporrsamethefor
rsamethefor
rsametheforif
kr
v
vpv
vpv
DieselthDualthOttoth
Dieselth
Ottoth
k
kth
+
+=
+=
>>
=
=
+
=
Gas Turbine Cycles: (Brayton or Joule)
13
1
2
3
2
1
T
V
1 4
3p
S
4
V=Const
P=Const
Isentropic
P=Const
44
C T
C.C
Qrej
Qadd
14
32
Wnet
Gas Turbine Cycle (Brayton cycle, or Joule cycle)
-
8/3/2019 Heat Engines2
14/21
23
14
23
1423
1
)(.
)(.)(.
TT
TT
TTCmQ
TTCmTTCmW
th
padd
ppnet
=
=
=
powerOutputpowerTurbinepowerCompressor
powerTurbine
powerOutput
W
WWRNB
rT
T
TT
TTTTWr
r
p
p
T
T
T
TT
T
TT
T
T
p
p
p
p
T
Talso
r
rT
Tr
TT
ratioessurep
prand
rationCompressioV
VrLet
ve
net
k
k
p
k
k
p
th
k
k
th
k
k
k
k
k
v
th
k
v
k
v
p
v
.........
...
...........:
.1)(
)()(
.............1
1
11
)1(
)1(
1
.....
................1
1
........,
....Pr.......
............
1
2
1
43
1243
1
1
2
1
2
1
2
3
2
1
4
1
4
3
1
4
3
1
1
2
1
2
1
12
113
4
1
2
2
1
=
==
=
=
=
==
=
=
=
=
=
==
=
=
+
14
-
8/3/2019 Heat Engines2
15/21
Report (M-1):
Hold a comparison among Otto, Diesel and Dual cycles in the following
conditions:
1-Same compression ratio and same heat input.2-Same maximum pressure and same heat input
3-Same maximum pressure and maximum temperature.
Draw the 3 cycles on the same P-V and T-S diagrams, compare the net
power and thermal efficiency.
15
-
8/3/2019 Heat Engines2
16/21
16
-
8/3/2019 Heat Engines2
17/21
17
-
8/3/2019 Heat Engines2
18/21
18
-
8/3/2019 Heat Engines2
19/21
19
-
8/3/2019 Heat Engines2
20/21
20
-
8/3/2019 Heat Engines2
21/21