BIODIGESTER Conceptual Design Review December 7 th, 2009 EGGN 491.
Thermodynamics (EGGN 371) Equation Sheet · Thermo Equation Sheet (Cycles) Author: Steven C....
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Thermodynamics (EGGN 371) Equation Sheet Air Standard (variable specific heats) Cold Air Standard (const. specific heats) Process DIESEL 1-2 = 1 2 1 2 v v v v r r ) 1 ( 2 1 1 2 − = k v v T T isentropic compression 2-3 2 3 h h q in − = ) ( 2 3 T T C q p in − = const. P heat addition 3-4 = 3 4 3 4 v v v v r r ) 1 ( 4 3 3 4 − = k v v T T isentropic expansion 4-1 1 4 u u q out − = ) ( 1 4 T T C q v out − = const. V heat rejection in out diesel q q − = 1 η − − − = − ) 1 ( 1 1 ) 1 ( c k c k diesel r k r r η 2 1 v v r = BRAYTON 1-2 = 1 2 1 2 P P P P r r k k P P T T ) 1 ( 1 2 1 2 − = isentropic compression 2-3 2 3 h h q in − = ) ( 2 3 T T C q p in − = const. P heat addition 3-4 = 3 4 3 4 P P P P r r k k P P T T ) 1 ( 3 4 3 4 − = isentropic expansion 4-1 1 4 h h q out − = ) ( 1 4 T T Cp q out − = const. P heat rejection in out brayton q q − = 1 η k k p brayton r ) 1 ( 1 − − = η 1 2 P P r P = 4 3 P P r p = 1 2 1 2 2 1 h h h h a s − − = − η s a h h h h 4 3 4 3 4 3 − − = − η 1 2 1 2 2 1 T T T T a s − − = − η s a T T T T 4 3 4 3 4 3 − − = − η OTTO 1-2 = 1 2 1 2 v v v v r r ) 1 ( 2 1 1 2 − = k v v T T isentropic compression 2-3 2 3 u u q in − = ) ( 2 3 T T C q v in − = const. v heat addition 3-4 = 3 4 3 4 v v v v r r ) 1 ( 4 3 3 4 − = k v v T T isentropic expansion 4-1 1 4 u u q out − = ) ( 1 4 T T C q v out − = const. v heat rejection in out otto q q − = 1 η ) 1 ( 1 k otto r − − = η 2 1 v v r = 3 4 v v r =
Transcript of Thermodynamics (EGGN 371) Equation Sheet · Thermo Equation Sheet (Cycles) Author: Steven C....
Thermodynamics (EGGN 371) Equation Sheet Air Standard
(variable specific heats)
Cold Air Standard (const. specific heats)
Process
DIESEL 1-2 ⎟⎟
⎠
⎞⎜⎜⎝
⎛=
1
212 vvvv rr
)1(
2
112
−
⎟⎟⎠
⎞⎜⎜⎝
⎛=
k
vvTT
isentropic compression
2-3 23 hhqin −= )( 23 TTCq pin −= const. P heat addition
3-4
⎟⎟⎠
⎞⎜⎜⎝
⎛=
3
434 vvvv rr
)1(
4
334
−
⎟⎟⎠
⎞⎜⎜⎝
⎛=
k
vvTT
isentropic expansion
4-1 14 uuqout −= )( 14 TTCq vout −= const. V heat rejection
in
outdiesel q
q−=1η ⎥
⎦
⎤⎢⎣
⎡
−
−−= −
)1(11 )1(
c
kck
diesel rkrrη
2
1
vvr =
BRAYTON 1-2
⎟⎟⎠
⎞⎜⎜⎝
⎛=
1
212 PPPP rr k
k
PPTT
)1(
1
212
−
⎟⎟⎠
⎞⎜⎜⎝
⎛=
isentropic compression
2-3 23 hhqin −= )( 23 TTCq pin −= const. P heat addition
3-4
⎟⎟⎠
⎞⎜⎜⎝
⎛=
3
434 PPPP rr k
k
PPTT
)1(
3
434
−
⎟⎟⎠
⎞⎜⎜⎝
⎛=
isentropic expansion
4-1 14 hhqout −= )( 14 TTCpqout −= const. P heat rejection
in
outbrayton q
q−=1η k
k
pbrayton r)1(
1−
−=η 1
2
PPrP =
4
3
PP
rp =
12
1221 hh
hh
a
s
−
−=−η
s
a
hhhh
43
4343 −
−=−η
12
1221 TT
TT
a
s
−
−=−η
s
a
TTTT
43
4343 −
−=−η
OTTO 1-2
⎟⎟⎠
⎞⎜⎜⎝
⎛=
1
212 vvvv rr
)1(
2
112
−
⎟⎟⎠
⎞⎜⎜⎝
⎛=
k
vvTT
isentropic compression
2-3 23 uuqin −= )( 23 TTCq vin −= const. v heat addition
3-4
⎟⎟⎠
⎞⎜⎜⎝
⎛=
3
434 vvvv rr
)1(
4
334
−
⎟⎟⎠
⎞⎜⎜⎝
⎛=
k
vvTT
isentropic expansion
4-1 14 uuqout −= )( 14 TTCq vout −= const. v heat rejection
in
outotto q
q−=1η
)1(1 kotto r −−=η
2
1
vvr =
3
4
vvr =
JET PROPULSION
1-2 DIFUSER: ;
2
21
22
121212 ⎟⎟⎠
⎞⎜⎜⎝
⎛ −+−=−
VVhhwq ;2
)(021
12 ⎟⎟⎠
⎞⎜⎜⎝
⎛−−=VTTCp
;1
2
1
2
PP
PP
r
r = kk
PP
TT
)1(
1
2
1
2
−
⎟⎟⎠
⎞⎜⎜⎝
⎛=
2-3 COMPRESSOR:
;23 PrP p= ;2
3
2
3
PP
PP
r
r = kk
PP
TT
)1(
4
3
2
3
−
⎟⎟⎠
⎞⎜⎜⎝
⎛=
3-4 COMBUSTION: )( 3434 TTChhq pin −=−= 4-5 TURBINE: ;,, outturbincomp ww = ;5423 hhhh −=− );()( 5423 TTTT −=−
;4
5
4
5
PP
PP
r
r = kk
PP
TT
)1(
4
5
4
5
−
⎟⎟⎠
⎞⎜⎜⎝
⎛=
5-6 NOZZLE: ;
2
25
26
565656 ⎟⎟⎠
⎞⎜⎜⎝
⎛ −+−=−
VVhhWq ;2
)(026
56 ⎟⎟⎠
⎞⎜⎜⎝
⎛+−=VTTCp
kk
PP
TT
)1(
5
6
5
6
−
⎟⎟⎠
⎞⎜⎜⎝
⎛=
Propulsion Efficiency in
aircraftinletexit
in
p
qVVV
qw )( −
==
RANKINE
1-2 PUMP: ;1 fhh = ;12 inwhh += 12121 )( hhPPvwin −=−= isentropic compression
2-3 BOILER: ;23 hhqin −= svhh =3 at T & P for S.V. const. P heat addition
3-4 TURBINE: ;43 hhwout −= ;4
4fg
f
sss
x−
= fgf hxhh 44 += isentropic expansion
4-1 CONDENSER: 14 hhqout −= const. P heat rejection
in
outin
in
netrankine q
qqqw −
==η
REFRIGERATION
1-2 COMPRESSOR: );( 12 hhmwin −= ;1ssg = 1hhg = isentropic compression
2-3 CONDENSOR: ;12 ss = ;3 fhh = )( 32 hhmQH −= const. P heat rejection
3-4 THROTTLING: 34 hh ≅ throttling in an expansion device
4-1 EVAPORATOR: )( 41 hhmQL −= const. P heat absorption
12
12
hhhh s
comp −
−=η
in
LR wQPOC
=...
