Calculos termodinamicos motor diesel
9
Chapter I - Introducton t o t h e Four-Stroke Engine hence: bmep = imep + pmep + fmep) = 17.84 + (-4.46) = 13.38 b a r (1.9.6) I f E q . 1.9.5 i s applied i n this fashion t o a l l o f the simulations conducted in Sec. 1.9.1.6, where t h e A F R i s varied widely from rich t o lean settings, then a n equivalent s e t o f simulation output becomes available which i s related to brake, rather than indicated, data. S o, o n Figs. 1.57-1.59 ar e drawn a ll of t h e simulation output a s brake data t o b e compared a n d contrasted with t h e indicated data. This output may also b e compared with data typical of production s i engines in order t o assess h o w closely this simple simulation i s approaching reality. T h e simu- lation output of brake-relatedvalues i s f or brake mean effective pressure in Fig. 1.57, f o r brake thermal efficiency i n Fig. 1.58, a n d f o r brake specific fuel consumption i n Fig. 1.59. I n Fig. 1.57, t h e friction a n d pumping loss a t a combined 4.46 b a r i s seen drawn on t h e graph, giving a constant difference o f 4.46 b a r between t h e imep a nd bmep lines. When this i s translated into brake thermal efficiency, n b , i t ca n b e seen that t h e effect i s n o longer a hnear shift from indicated thermal efficiency, lit. T h e brake thermal efficiency profile is n o w very much flatter through t h e stoichiometric region, a trend that would b e very typical o f real s i engines. This same trend i s also seen i n thebsfc graph i n Fig. 1.59. T h e peak bmep is n o w observed t o b e around 1 5 bar, a value that i s still o n t h e high side f o r a real s i engine with a delivery ratio of 1.0, b u t that i s n o t s o hugely different from practice. T h e bestbsfc point o f about 2 2 0 g/kWh i s about 14 t o o optimistic compared to o n e of today s production s i automobile engines. Even Closer to Reality I t will b recalled that these simulation data incorporate input data f o r t h e indices o com- pression a n d expansion a t t he ideal value o f 1.4, which i s equal t o t h e ratio o f specific heats f o r air. Recalling t h e discussion i n Sec. 1.9.1.4 above, i f these indices a r e each shifted b y 0.1, t o 1 . 3 a n d 1.5, respectively, a n d t h e present simulationrerun a t a stoichiometric AFR, t he bmep becomes 11.62 b a r a n d t h e bsfc increases t o 2 4 7 g/kWh, both o f which numbers would b e well i n line with current practice. 1.9.2 Power Cycle Analysis o f t h e Diesel Engine Some Fundamental Differences between t h e Diesel a n d t h e Otto Cycles Fig. 1.60 shows t h e measured cylinder traces from a n Otto engine a n d a diesel engine. They ar e roughly a t t h e same imep. T h e diesel engine i s a 6 . 0 liter, six-cylinder, turbocharged, D I unit, a n d t h e Otto engine i s a 2 . 0 liter, four-cylinder, naturally aspirated unit with electronic fuel injection (EFI). Because o n e h as a cylinder swept volume that is twice t h e other, a n d t he diesel engine h a s a C R of 1 7 while t h e Otto engine a CR o f 1 0 , t h e volume scale i s drawn a s volume ratio so that th e engines m a y b e readily compared. T h e higher C R of th e diesel engine shows up during compression a s a volume ratio that i s about half that o f t h e Otto engine. T h e Otto engine would appear t o have combustion a t constant volume, although from t he foregoing above w e know that n o t to b e t h e case. O n the other hand, t h e diesel engine h a s a much higher endof compression pressure and, more importantly i n design terms, temperature. T h e diesel burn also seems to b e a t constant volume, b ut these first impressions will be dis- pelled below. 1 09
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Transcript of Calculos termodinamicos motor diesel
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C h a p t e r
I
-
I n t r o d u c t o n t o
t h e F o u r - S t r o k e
E n g i n e
h e n c e :
b m e p
=
i m e p
+
p m e p
+
f m e p )
=
1 7 . 8 4 +
( - 4 . 4 6 )
=
1 3 . 3 8 b a r
( 1 . 9 . 6 )
I f E q .
1 . 9 . 5
i s
a p p l i e d
i n
t h i s
f a s h i o n
t o a l l o f t h e s i m u l a t i o n s c o n d u c t e d i n S e c .
1 . 9 . 1 . 6 ,
w h e r e
t h e
AFR
i s
v a r i e d
w i d e l y
f r o m
r i c h
t o
l e a n
s e t t i n g s ,
t h e n
a n
e q u i v a l e n t
s e t
o f
s i m u l a t i o n
o u t p u t b e c o m e s a v a i l a b l e
w h i c h i s r e l a t e d t o
b r a k e ,
r a t h e r
t h a n
i n d i c a t e d ,
d a t a .
S o ,
o n
F i g s .
1 . 5 7 - 1 . 5 9 a r e
d r a w n
a l l o f t h e s i m u l a t i o n
o u t p u t
a s
b r a k e d a t a
t o b e
c o m p a r e d
a n d c o n t r a s t e d
w i t h
t h e
i n d i c a t e d
d a t a .
T h i s
o u t p u t
m a y
a l s o b e
c o m p a r e d
w i t h
d a t a
t y p i c a l
o f
p r o d u c t i o n
s i
e n g i n e s
i n o r d e r t o a s s e s s
h o w
c l o s e l y
t h i s
s i m p l e
s i m u l a t i o n
i s
a p p r o a c h i n g
r e a l i t y .
T h e s i m u -
l a t i o n
o u t p u t
o f b r a k e - r e l a t e d v a l u e s
i s
f o r b r a k e mean
e f f e c t i v e
p r e s s u r e
i n
F i g . 1 . 5 7 ,
f o r
b r a k e
t h e r m a l
e f f i c i e n c y
i n
F i g . 1 . 5 8 ,
a n d f o r
b r a k e
s p e c i f i c
f u e l
c o n s u m p t i o n
i n
F i g .
1 . 5 9 .
I n
F i g .
1 . 5 7 ,
t h e
f r i c t i o n
a n d
p u m p i n g
l o s s a t
a
c o m b i n e d
4 . 4 6
b a r i s s e e n d r a w n o n
t h e
g r a p h ,
g i v i n g
a
c o n s t a n t
d i f f e r e n c e o f
4 . 4 6
b a r b e t w e e n
t h e
i m e p
a n d
b m e p
l i n e s . When
t h i s i s
t r a n s l a t e d
i n t o
b r a k e t h e r m a l
e f f i c i e n c y ,
n b ,
i t
c a n
b e
s e e n
t h a t
t h e
e f f e c t
i s n o
l o n g e r
a
h n e a r
s h i f t f r o m i n d i c a t e d
t h e r m a l
e f f i c i e n c y ,
l i t .
T h e
b r a k e
t h e r m a l
e f f i c i e n c y
p r o f i l e
i s
now
v e r y
m u c h
f l a t t e r
t h r o u g h
t h e
s t o i c h i o m e t r i c
r e g i o n ,
a t r e n d
t h a t
w o u l d
b e
v e r y t y p i c a l
o f
r e a l
s i
e n g i n e s . T h i s s a m e
t r e n d
i s a l s o s e e n
i n
t h e b s f c
g r a p h
i n
F i g .
1 . 5 9 .
T h e
p e a k b m e p
i s now
o b s e r v e d
t o b e
a r o u n d
1 5
b a r ,
a
v a l u e
t h a t i s
s t i l l o n
t h e
h i g h
s i d e f o r
a
r e a l
s i
e n g i n e
w i t h a
d e l i v e r y
r a t i o
o f
1 . 0 ,
b u t t h a t i s
n o t
s o
h u g e l y
d i f f e r e n t
f r o m p r a c t i c e .
T h e b e s t b s f c
p o i n t
o f
a b o u t
2 2 0
g / k W h
i s a b o u t
1 4
t o o
o p t i m i s t i c c o m p a r e d
t o o n e
o f
t o d a y s
p r o d u c t i o n
s i
a u t o m o b i l e
e n g i n e s .
E v e n
C l o s e r
t o
R e a l i t y
I t
w i l l
b e
r e c a l l e d
t h a t
t h e s e
s i m u l a t i o n d a t a
i n c o r p o r a t e i n p u t
d a t a
f o r
t h e
i n d i c e s
o f
c o m -
p r e s s i o n
a n d
e x p a n s i o n
a t
t h e
i d e a l
v a l u e
o f
1 . 4 ,
w h i c h
i s
e q u a l
t o
t h e
r a t i o o f
s p e c i f i c
h e a t s
f o r
a i r .
R e c a l l i n g
t h e d i s c u s s i o n
i n
S e c .
1 . 9 . 1 . 4
a b o v e ,
i f
t h e s e i n d i c e s
a r e e a c h
s h i f t e d
b y 0 . 1 ,
t o
1 . 3 a n d 1 . 5 ,
r e s p e c t i v e l y ,
a n d
t h e
p r e s e n t
s i m u l a t i o n r e r u n
a t
a
s t o i c h i o m e t r i c
A F R ,
t h e
b m e p
b e c o m e s
1 1 . 6 2
b a r
a n d
t h e b s f c i n c r e a s e s
t o
2 4 7
g / k W h ,
b o t h
o f
w h i c h n u m b e r s w o u l d
b e
w e l l
i n
l i n e
w i t h
c u r r e n t
p r a c t i c e .
1 . 9 . 2 P o w e r
C y c l e A n a l y s i s
o f
t h e
D i e s e l
E n g i n e
S o m e F u n d a m e n t a l
D i f f e r e n c e s
b e t w e e n t h e D i e s e l a n d t h e O t t o
C y c l e s
F i g .
1 . 6 0 s h o w s t h e
m e a s u r e d
c y l i n d e r
t r a c e s
f r o m
a n
O t t o
e n g i n e
a n d
a
d i e s e l
e n g i n e .
T h e y
a r e
r o u g h l y
a t
t h e
s a m e
i m e p .
T h e
d i e s e l
e n g i n e
i s a
6 . 0
l i t e r ,
s i x - c y l i n d e r ,
t u r b o c h a r g e d ,
D I
u n i t ,
a n d t h e O t t o
e n g i n e
i s a 2 . 0
l i t e r , f o u r - c y l i n d e r ,
n a t u r a l l y a s p i r a t e d u n i t
w i t h
e l e c t r o n i c
f u e l
i n j e c t i o n ( E F I ) .
B e c a u s e
o n e
h a s
a
c y l i n d e r s w e p t
v o l u m e
t h a t i s t w i c e
t h e
o t h e r , a n d t h e
d i e s e l
e n g i n e
h a s a CR
o f
1 7
w h i l e t h e
O t t o
e n g i n e
a
CR
o f
1 0 ,
t h e
v o l u m e
s c a l e
i s
d r a w n a s
v o l u m e r a t i o s o
t h a t
t h e
e n g i n e s may b e r e a d i l y c o m p a r e d .
T h e h i g h e r
CR
o f t h e d i e s e l
e n g i n e
s h o w s
u p d u r i n g c o m p r e s s i o n a s
a
v o l u m e r a t i o t h a t i s a b o u t
h a l f
t h a t o f t h e
O t t o
e n g i n e .
T h e
O t t o
e n g i n e w o u l d a p p e a r
t o
h a v e
c o m b u s t i o n
a t c o n s t a n t
v o l u m e ,
a l t h o u g h f r o m t h e
f o r e g o i n g
a b o v e
we
k n o w
t h a t
n o t
t o
b e
t h e
c a s e .
On
t h e o t h e r
h a n d , t h e d i e s e l
e n g i n e
h a s a
m u c h
h i g h e r
e n d o f
c o m p r e s s i o n
p r e s s u r e
a n d ,
m o r e
i m p o r t a n t l y
i n
d e s i g n
t e r m s , t e m p e r a t u r e .
T h e
d i e s e l
b u r n
a l s o
s e e m s
t o
b e
a t
c o n s t a n t
v o l u m e ,
b u t
t h e s e
f i r s t
i m p r e s s i o n s
w i l l
b e
d i s -
p e l l e d
b e l o w .
1 0 9
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D e s i g n
a n d S i m u l a t i o n
o f
F o u r - S t r o k e
E n g i n e s
1 4 0
6 . O L
1 6 4 V
TC D I
D I E S E L
s a
1 2 0
I M E P = 1 2 . 4 3
b a r
L i
a
1 0 0
2 . O L
1 4
4 V
NA
S i
O T T O
I
8 0 I M E P = 1 4 . 2 6 b a r
C O
w
8 0
a -
c
6 0
MEASURED
C Y L I N D E R
PRESSURES
2 0
0
S
0 . 0 0 . 1
0 . 2
0 . 3 0 . 4
0 . 5
0 . 6
0 . 7
0 . 8
0 . 9
1 . 0
CYLINDER
VOLUME
RATIO
F i g .
1 6
M e a s u r e d p -
V
d i a g r a m s f o r
a
d i e s e l
a n d a n O t t o
e n g i n e .
T h e r e
i s
n o
d e n y i n g
t h a t
t h e
t w o
p - V d i a g r a m s
a r e
n o t
a l i k e ,
e i t h e r
i n
s h a p e
o r
c h a r a c t e r .
T h e O t t o
d i a g r a m
i s s h o r t
a n d
s q u a t
c o m p a r e d
t o
t h e
l o n g e r ,
l e a n e r
D i e s e l
d i a g r a m .
T h e
D e f i n i t i o n
o f
t h e
I d e a l
D i e s e l
C y c l e
T h e
i d e a l
D i e s e l
c y c l e
i s
p r e s e n t e d
i n
s o m e
t h e o r e t i c a l
d e t a i l
i n A p p e n d i x A l
. 1 ,
S e c . A . 1 .
1 . 0 .
I t
i s i l l u s t r a t e d
t h e r e
b y F i g s .
A.4
a n d
A 1 . 5 ,
s h o w i n g
p r e s s u r e - v o l u m e c h a r a c t e r i s t i c s a n d
t e m p e r a t u r e - v o l u m e
c h a r a c t e r i s t i c s ,
r e s p e c t i v e l y .
T h e r e i s
a
common
b o n d
i n
f u n d a m e n t a l
t h e r m o d y n a m i c
t h i n k i n g
b e t w e e n
t h e i d e a l
D i e s e l
a n d t h e i d e a l
O t t o
c y c l e ,
t h e
l a t t e r
b e i n g
d e s c r i b e d i n S e c .
1 . 6 . 9 . T h e
e l e m e n t s o f t h e
i d e a l D i e s e l
c y c l e
a r e ,
r e f e r r i n g
t o
F i g s .
A 1 . 4 a n d
A 1 . 5 :
( a )
A d i a b a t i c
a n d
i s e n t r o p i c c o m p r e s s i o n
f r o m s t a t e c o n d i t i o n 1 - 2
( b )
C o n s t a n t v o l u m e
c o m b u s t i o n
a s h e a t
t r a n s f e r f r o m
2 - 3
( c ) C o n s t a n t
p r e s s u r e
c o m b u s t i o n a s
h e a t
t r a n s f e r
f r o m 3 - 4
( d )
A d i a b a t i c
a n d
i s e n t r o p i c
c o m p r e s s i o n
f r o m
s t a t e
c o n d i t i o n
4 - 5
( e )
C o n s t a n t
v o l u m e h e a t
r e j e c t i o n
t o
r e p r e s e n t e x h a u s t
p r o c e s s f r o m 5 - 1
T h u s , t h e r e i s a n e x t r a
h e a t a d d i t i o n
p r o c e s s f o r
d i e s e l
c o m b u s t i o n
c o m p a r e d t o t h e
i d e a l
O t t o
c y c l e ,
o t h e r w i s e
t h e
t w o
c y c l e s
a r e
i d e n t i c a l .
T h e
o r i g i n a l
d e f i n i t i o n
o f
t h e
i d e a l D i e s e l
c y c l e
w a s
t h a t i t
h a d
o n l y
c o n s t a n t
p r e s s u r e
c o m b u s t i o n w h e r e a s
t h a t
d e s c r i b e d
a b o v e i s
o f t e n
c a l l e d t h e
D u a l
c y c l e
[ 1 . 2 ] .
I
d e f i n e
e i t h e r ,
o r
b o t h ,
a s a n i d e a l
D i e s e l
c y c l e .
A p p e n d i x A I . 1 , S e c . A l . 1 . 1 0
c o n t a i n s a l l
o f t h e
t h e r m o d y n a m i c t h e o r y
r e q u i r e d t o r e s o l v e
a
g i v e n
d e s i g n
i n t e r m s o f
i t s
p e r f o r m a n c e
c h a r a c t e r i s t i c s ,
o r
i t s s t a t e
c o n d i t i o n s
a t
p o i n t s 1 - 5
t h r o u g h o u t
t h e
c y c l e .
T h i s
t h e o r y
w i l l
b e u s e d
b e l o w
t o
e x a m i n e a
t e s t
c a s e
f o r t h e
i d e a l D i e s e l
c y c l e .
1 1 0
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C h a p t e r
1
-
I n t r o d u c t i o n
t o
t h e F o u r - S t r o k e
E n g i n e
T h e
T e s t
E n g i n e
U s e d a s
t h e
C o m p r e s s i o n - I g n i t i o n E n g i n e
E x a m p l e
T h r o u g h o u t
t h i s s e c t i o n
o n
t h e
d i e s e l
e n g i n e ,
a
s i n g l e c y l i n d e r
u n i t o f
9 9 7 . 5
c m 3
c a p a c i t y ,
r u n n i n g
a t 1 8 0 0
r p m ,
i s u s e d
t o
i l l u s t r a t e
t h e
t h e r m o d y n a m i c
p o i n t s
t o b e m a d e .
I t
i s ,
i n
f a c t ,
o n e
c y l i n d e r
o f
a
s i x - c y l i n d e r
t u r b o c h a r g e d
D I d i e s e l
t r u c k
e n g i n e
o f 6 l i t e r s n o m i n a l
c a p a c i t y .
I t
h a s
a
b o r e
o f 1 0 0
mm,
a
s t r o k e
o f 1 2 7
mm,
a n d
a
c o n n e c t i n g
r o d
w i t h
2 1 7
mm c e n t e r s . T h e
g u d g e o n
p i n
o f f s e t
i s
z e r o . F r o m t h e
b o r e
a n d
s t r o k e
v a l u e s ,
i t
i s
s e e n t o b e a n
u n d e r - s q u a r e
e n g i n e ,
t h e
common
f e a t u r e
o f w h i c h h a s
a l r e a d y
b e e n
c o m m e n t e d
o n i n S e c .
1 . 8 . 1 .
T h e
p i s t o n
p o s i t i o n
a t
a n y p o i n t
o n
t h e r o t a t i o n o f t h e
c r a n k i s f o u n d
u s i n g
t h e
t h e o r y
o f
S e c .
1 . 4 . 4
a n d
t h e
c y l i n d e r v o l u m e b y
E q .
1 . 4 . 1 . T h e
s w e p t
v o l u m e i s 9 9 7 . 5
c m 3 ,
b u t i s
u s e d
i n a l l
t h e r m o d y -
n a m i c e q u a t i o n s
a s
9 9 7 5 x
1 0 - 6
m 3 .
c o m p r e s s i o n
r a t i o o f
1 7
i s
u s e d ,
s o
t h e c l e a r a n c e v o l u m e i s o b t a i n e d f r o m
E q .
1 . 4 . 3 . T h i s
c l e a r a n c e
v o l u m e i s
6 2 . 3
c m 3 ,
b u t
i s
u s e d
i n
a l l
t h e r m o d y n a m i c e q u a t i o n s
a s 6 2 . 3
x
1 0 - 6
m 3 .
T h e m a x i m u m a n d
m i n i m u m
c y l i n d e r
v o l u m e s ,
i . e . ,
a t
b d c a n d
t d c ,
f o r
t h i s
d i e s e l
e n g i n e
a r e
1 0 5 9 . 8
a n d
6 2 . 3
c m 3 ,
t o
b e
u s e d
i n
s t r i c t
S I
u n i t s
a s
1 0 5 9 . 8
x
1 0 - 6
a n d
6 2 . 3
x
1 0 - 6
m 3 .
T h e
f u e l
i s
d o d e c a n e
w i t h
a d e c l a r e d
c a l o r i f i c v a l u e
o f
4 3 . 5
M J / k g .
F r o m
E q .
1 . 6 . 1 7 ,
t h e
c a l c u l a t e d s t o i c h i o m e t r i c
a k r - f u e l
r a t i o
f o r d o d e c a n e i s
1 4 . 9 5 . T h e t e s t
e n g i n e
i s
t o b e e x a m -
i n e d a t
a
l i g h t
l o a d
p o i n t ,
w h e r e
t h e
e q u i v a l e n c e
r a t i o , X ,
i s
2 . 9 5 .
C o n s e q u e n t l y ,
t h e a i r - f u e l
r a t i o
i n t h e c h a m b e r
i s
4 4 . 1 .
L e t
i t
b e a s s u m e d t h a t 1 0 o f t h e f u e l
i s
t o b e
b u r n e d a t
c o n s t a n t
v o l u m e , l e a v i n g 90
f o r c o m b u s t i o n
a t c o n s t a n t
p r e s s u r e .
T h e
w o r k i n g
f l u i d
w i t h i n
t h e
e n g i n e
c y l i n d e r
i s
c o n s i d e r e d
t o b e
a i r
w i t h t h e
p r o p e r t i e s
g i v e n
i n
A p p e n d i x
Al
l ,
S e c s .
A 1 .
1 .
I
a n d A 1 . 1 . 2 .
A s s t a t e d b e f o r e
i n
S e c .
1 . 9 . 1 ,
I
d e f i n e
t h a t
a t
b d c
t h e
s w e p t
v o l u m e i s
r e g a r d e d
t o
b e
f i l l e d w i t h
f r e s h
a i r
b e c a u s e t h e c l e a r a n c e
v o l u m e
i s
c o n s i d e r e d
t o
b e f i l l e d w i t h a g a s t h a t i s
i n e r t , e x h a u s t ,
b u t t h a t
a l s o h a s t h e p r o p e r t i e s
o f a i r .
I n
s h o r t ,
o n l y
t h e
s w e p t
v o l u m e
a t
b d c
i s
d e f i n e d
t o
c o n t a i n
a
t r u e
f r e s h
a i r . B e c a u s e
m a n y
o f
t h e d a t a c a l c u l a t e d
b y
t h e
s i m p l e
s i m u l a t i o n s b e l o w
a r e
t o b e
c o m p a r e d w i t h m e a s u r e d
d a t a
f r o m
a
f i r i n g e n g i n e ,
t h e
s t a t e
c o n d i t i o n s s e l e c t e d
a t
b d c
a t
t h e o n s e t
o f
t h e c o m p r e s s i o n s t r o k e
r e f l e c t t h e
r e a l i t y
o f
t u r b o c h a r g i n g
a
d i e s e l
e n g i n e , c o m p a r e d
t o
t h e s t a n d a r d
r e f e r e n c e
p r e s -
s u r e a n d
t e m p e r a t u r e
c o n d i t i o n s s e l e c t e d f o r t h e
n a t u r a l l y a s p i r a t e d
s p a r k - i g n i t i o n
u n i t .
T h e
s t a t e
c o n d i t i o n s t o b e u s e d
a t p o i n t
I
i n F i g s .
A 1 . 4
a n d A l . 5
i n A p p e n d i x A l . 1
a r e
2 . 3 3
b a r a n d
7 0 ° C .
T h e
p r e s s u r e
i s k n o w n f r o m t h e
m e a s u r e d
c y l i n d e r p r e s s u r e
d a t a
t o
b e
2 . 3 3
b a r ,
b u t
t h e
t e m p e r a t u r e
I
h a v e h a d t o e s t i m a t e
b a s e d o n
e x p e r i e n c e , d u e t o t h e a b s e n c e o f
r e a l
d a t a .
1 . 9 . 2 . 1
T h e r m o d y n a m i c
N a v i g a t i o n
a r o u n d
t h e
I d e a l D i e s e l
C y c l e
I n i t i a l
V a l u e s f o r
T o t a l
M a s s ,
A i r
M a s s ,
D e n s i t y ,
D R ,
a n d
H e a t f r o m
F u e l
a t
S t a t e
P o i n t
1
T h e
e n g i n e
i s
t u r b o c h a r g e d
s o t h e s t a t e
c o n d i t i o n
1
i s
a t 2 . 3 3
b a r
a n d
7 0 ° C .
F r o m
t h e s t a t e
e q u a t i o n ,
E q .
A l . 5 , m a s s
o f
g a s
i n
c y l i n d e r ,
m l :
= p 1 V 1
_
2 . 3 3
x
1 0 5
x
1 0 5 9 . 8
x
1 0
= 2 5 . 0 8 4 x 10 k g
R T 1
2 8 7
x
3 4 3
1 1 1
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D e s i g n
a n d S i m u l a t i o n
o f
F o u r - S t r o k e
E n g i n e s
T h e
m a s s
o f
a i r
t r a p p e d
i n
c y l i n d e r ,
m t a :
m t a = P l V s v
=
2 . 3 3 x 1 0 5 x
9 9 7 . 5
x
1 0
=23.61x10
k g
R T ,
2 8 7
x
3 4 3
F r o m
E q . 1 . 6 . 1 ,
r e f e r e n c e
m a s s ,
m d r e f ,
f o r
D R
i s :
p=
P a t
-
1 0 1 3 2 5
= 1 . 2 0 5 k g / n 3
a
R T a t
2 8 7
x
2 9 3
F r o m
E q s .
1 . 6 . 3 a n d
1 . 6 . 4 ,
d e l i v e r y
r a t i o i s :
DR-
m a s
Mt a
=
2 3 . 6 1 x
1 0
=
1 . 9 6
m d r e f
P a t V s v
1 . 2 0 5
x
9 9 7 . 5
x
1 0 4
T h e
d e l i v e r y r a t i o , D R ,
i s
1 . 9 6
a n d
s h o w s
t h e c o n s i d e r a b l e
a m o u n t
o f
a i r
b l o w n
i n t o
t h e
e n g i n e
f r o m t h e
c o m p r e s s o r
s e c t i o n
o f
t h e
t u r b o c h a r g e r .
F r o m
E q .
1 . 6 . 2 0 ,
t h e
m a s s
o f f u e l
t r a p p e d ,
m t f :
m t f = t a
2 3 . 6 1
x
1 0
-
5 . 3 5 4 x 1 0 5
k g
F r o m
E q . 1 . 6 . 2 1 ,
t o t a l
h e a t t r a n s f e r
a r o u n d
t d c
i s
e q u i v a l e n t
t o
h e a t
e n e r g y
i n
f u e l :
Q R
=
T l C m t f C f l
= 1 . 0 x 5 . 3 5 4
x 1 0 x
4 3 . 5 x
1 0 6
=
2 3 2 9 J
As t h e
bum
p r o p o r t i o n
a t c o n s t a n t
v o l u m e ,
k c v ,
i s d e c i d e d a t
0 . 1 ,
t h e n
f r o m
E q .
A 1 . 7 6 :
Q 3 =
kVQR
=
0 . 1
X
2 3 2 9
=
2 3 2 9
J
Q
=
1 - k C V ) Q R
= 0 . 9
x
2 3 2 9
=
2 0 9 6 . 1
J
P r o c e s s
1 - 2 ,
A d i a b a t i c
a n d
I s e n t r o p i c
C o m p r e s s i o n
F r o m
E q s .
A 1 . 2 6
a n d
A 1 . 5 0 , p r e s s u r e
a t
e n d
o f
c o m p r e s s i o n ,
P 2 :
P 2
= p 4
2 - J
=
p l C R Y
=
2 . 3 3 x 1 0 5
x
1 7
= 2 . 3 3 x 1 0 5
x 5 2 . 8
=
1 2 3 . 0 2
x 1 0
P a
i e . ,
1 2 3 . 0 2
b a r )
1 1 2
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C h a p t e r
I
-
I n t r o d u c t i o n t o
t h e
F o u r - S t r o k e E n g i n e
F r o m E q . A 1 . 5 5 ,
t e m p e r a t u r e
a t e n d o f
c o m p r e s s i o n ,
T 2 :
T _ _
V I .
)
= C R ) Y -
T 2
=
3 4 3 x 3 . 1 0 6
=
1 0 6 5 . 4
K
F r o m E q s .
A 1 . 2 1
a n d
A 1 . 2 3 ,
t h e
w o r k d o n e d u r i n g c o m p r e s s i o n
i s
n e g a t i v e :
W I
=
- m C v ( T 2
T = - 2 5 . 0 8 4
x
7 1 8
x
1 0 6 5 . 4
3 4 3
=
- 1 3 0 1 . 1 J
F r o m
E q .
A 1 . 2 3 , t h e c h a n g e
o f
i n t e m a l e n e r g y d o n e
d u r i n g c o m p r e s s i o n
i s
p o s i t i v e :
U2
-
U l
=
m l C v ( T 2
-
T i )
=
2 5 . 0 8 4
x
1 0 4
x 7 1 8
x
( 1 0 6 5 . 4
-
3 4 3 )
=
1 3 0 1 . 1
J
P r o c e s s
2 - 3 ,
C o n s t a n t
C o l u m e
C o m b u s t i o n
T h e
f i r s t
l a w
o f
t h e r m o d y n a m i c s
i s
a p p l i e d
t o
t h e
c o n s t a n t
v o l u m e c o m b u s t i o n p r o c e s s
w h e r e
t h e
w o r k
o u t p u t
i s
z e r o .
Q 2
=
U 3
U 2
+ w 2
=
m l C v T 3 - T 2
+ 0
t h e n
s o l v i n g
f o r
T 3 :
T 3 = T 2 +
Q 2
1065.4232.9
= 1 1 9 4 . 7
K
m I C V
2 5 . 0 8 4
x
1 0 4
x 7 1 8
U s i n g
t h e
s t a t e
e q u a t i o n ,
a s
i n
E q . A 1 . 4 4 ,
s o l v i n g
f o r
p 3 :
P 3
P 2
x
2
T 3
T 3
=
1 2 3 . 0 2
x
1 0 5
x
1
9 4 . 7
=
1 3 7 . 9 5
x
1 0 5
P a
-
=TPp X
- l = 3 P O 2 X l -
1 0 6 5 . 4
i . e . ,
1 3 7 . 9 5
b a r )
C h a n g e
o f
i n t e r n a l
e n e r g y d u r i n g
t h e
p r o c e s s
f r o m
2 - 3 :
U 3
-
U 2
=
Q2=2329
J
1 1 3
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D e s i g n
a n d
S i m u l a i o n
o f F o u r - S t r o k e
E n g i n e s
P r o c e s s
3 - 4
C o n s t a n t
P r e s s u r e
C o m b u s t i o n
T h e
f i r s t
l a w
o f
t h e r n o d y n a m i c s
i s
a p p l i e d
t o t h e
c o n s t a n t
p r e s s u r e
c o m b u s t i o n
p r o c e s s .
F r o m
E q .
A 1 . 7 7 ,
s o l v i n g
f o r
T 4 :
_ _
2 0 9 6 . 1
= 2 2 .
T4=T3+
= 1 1 9 4 . 7 +
2 0 2 6 . 1
K
m , C p
2 5 . 0 8 4 x
1 0 - 4
x 1 0 0 5
F r o m
E q .
A 1 . 7 8 , s o l v i n g
f o r
p 4 :
N
=
P 3
i e . ,
1 3 7 . 9 5
b a r
F r o m
E q .
A 1 . 7 9 :
T 4
4~
2 0 2 6 . 1
3
V 4
=
V 3
4= 6 2 . 3 x l O
x
= 1 0 5 . 6 6 x I 0 m
T 3
1 1 9 4 . 7
T h e
c h a n g e
o f
i n t e r n a l
e n e r g y
d u r i n g
t h e
p r o c e s s
f r o m 3 - 4
i s
a n a l y z e d u s i n g
t h e
f i r s t
l a w
o f
t h e r m o d y n a m i c s
f o r
t h e
c l o s e d
s y s t e m ,
f r o m
E q s .
A 1 . 7 7
a n d
A l . 8 3 :
U4
-
U 3
=
m Cv ( T 4
-
T 3 )
=
2 5 . 0 8 4
x
1 0 4
x 7 1 8x 2 0 2 6 . I - 1 1 9 4 . 7 ) =
1 4 9 7 . 4
J
B y
E q .
A 1 . 8 4
t h e w o r k
o u t p u t
i s
g i v e n b y :
4
=
m j R ( T 4
-
T 3 )
=
2 5 . 0 8 4
x
1 0 - 4 x 2 8 7
x
( 2 0 2 6 . 1
1 1 9 4 . 7 )
=
5 9 8 . 5
J
P r o c e s s
4 - 5 ,
A d i a b a t i c a n d
I s e n t r o p i c E x p a n s i o n
F r o m
E q .
A 1 . 8 0 , t e m p e r a t u r e
a t
e n d o f
e x p a n s i o n ,
T 5 ,
a f t e r
p r o c e s s
3 - 4 :
__ _
-. Y
-0.4
T4
V T
T 6l
1059 8
x l1 0
5 5 = 6 2 0 2 6 . 1 0
= 8 0 5 . 6
K
F r o m
E q .
A 1 . 8 1 , p r e s s u r e
a t
e n d o f
e x p a n s i o n , p 5 :
V 4
1 7 . 9 5
1 0 5 [ 1 0 5 . 6 6 x I 1
0
=
5 . 4 7
x
1 0 5 P a
( w h i c h
i s 5 . 4 7
b a r )
1 3 7 9
i 0 V 5
1 0 5 9 . 8
x
1 0 4
=
t ) O S 9 . 8 x l O ~ ~ ~ ~ J
= 7Xi5P
wihi
.7br
1 1 4
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C h a p t e r
1
-
I n t r o d u c t i o n
t o
t h e
F o u r - S t r o k e
E n g i n e
F r o m
E q s .
A l . 8 4 ,
t h e
w o r k
d o n e
d u r i n g
e x p a n s i o n
i s
p o s i t i v e :
W 5 =
-mCv(T
-
T 4 ) =
- 2 5 . 0 8 4 x
1 0 4
x
7 1 8 x
( 8 0 5 . 6
-
2 0 2 6 . 1 )
=
2 1 9 8
J
F r o m
E q . A 1 . 2 3 ,
t h e
c h a n g e
o f
i n t e r n a l
e n e r g y
d o n e
d u r i n g
e x p a n s i o n
i s
n e g a t i v e :
U 5 - U 4 = m i C v T
-
T 4 )
=
2 5 . 0 8 4
x
1 0 4
x
7 1 8
x
( 8 0 5 . 6
-
2 0 2 6 . 1 )
=
- 2 1 9 8 J
P r o c e s s
5 - 1 ,
t o
C o m p l e t e
t h e
C y c l e b y
C o n s t a n t
V o l u m e
H e a t
R e j e c t i o n
F r o m t h e f i r s t
l a w
o f
t h e r m o d y n a m i c s , a s i n
E q .
A 1 . 8 5 :
Q ,
=
m I C V 4 T i
-
T 5 )
=
2 5 . 0 8 4
x
1 0 4
x
7 1 8
x
( 3 4 3
8 0 5 . 6 )
=
- 8 3 3 . 1
J
C h a n g e
o f
i n t e r n a l
e n e r g y
d u r i n g
h e a t
r e j e c t i o n
f r o m
4 - 1 :
U 1
-
U 5
=
Q
=
m l C v T
T 5 )
=
- 8 3 3 . 1
J
O b t a i n i n g
N e t
V a l u e s
f o r
t h e
C y c l e
N e t w o r k o u t p u t
f r o m
t h e
c y c l e ,
f r o m
E q s .
A 1 . 7 0 a n d
A 1 . 7 1 :
W n e t
=
W 2
+
W 3
+
W 5 = - 1 3 0 1 . 1 +
5 9 8 . 5
+
2 1 9 8
=
1 4 9 5 . 4 J
I d e a l D i e s e l
c y c l e
t h e r m a l
e f f i c i e n c y
i s
g i v e n
b y E q .
A l . 7 1 :
n e t
w o r k
=
n
-
1 4 9 5 . 4
h e a t
i n p u t
Q R
2 3 2 9
T h e m e a n
e f f e c t i v e
p r e s s u r e ,
i m e p ,
c a n
b e f o u n d
u s i n g
E q .
1 . 6 . 3 1
o r
E q .
A 1 . 8 6 :
m e - -
1 4 9 5 . 4
5
imVp
9 9 7 . 5 x 1 0 @
= 1 4 . 9 9 x 1 0 5 P a ( i . e . , 1 4 . 9 9 b a r )
V S V
9 9 7 . 5
x
1 0 4
T h e
p o w e r o u t p u t
o f
o n e
e n g i n e
c y l i n d e r
c a n
b e
f o u n d
u s i n g E q .
1 . 6 . 3 3 :
r p m
5
1 8 0 0
W = W n e t
X
= 1 4 9 5 . 4
x
=
2 2 . 4 3
x
1 0 3
i . e . ,
2 2 . 4 3
k W )
1 2 0
1 2 0
1 1 5
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D e s i g n
a n d S i m u l a t i o n
o f
F o u r S t r o k e
E n g i n e s
T h e
f u e l
c o n s u m p t i o n
r a t e
p e r c y l i n d e r
m i i f
i s
f o u n d f r o m :
r n f =
m a s s p e r
p o w e r c y c l e x
p o w e r c y c l e s p e r s e c o n d
1 8 0 0
=
0 . 8 0 3
x
1 0 3
k g /
s
2 x 0
=535x FX12
F r o m
E q .
1 . 6 . 3 6 t h e
s p e c i f i c
f u e l
c o n s u m p t i o n
c a n b e c a l c u l a t e d :
iffimf
0 . 8 0 3
x 1 0 3
xl kgW
i s f c
iLOS l
= 3 . 5 8 x 1 o 8
k g / W s
2 2 . 4 3
x
1 0 3
H o w e v e r
i n m o r e c o n v e n t i o n a l
u n i t s o f
k g / k W h
t h i s b e c o m e s :
i s f c
=
3 . 5 8
x
1 0 8
k g
3 . 5 8
x
1 0 8
x
1 0 3
x
3 6 0 0
k g
W
s
1 2 9
k g / k W h
Ws
Ws
kW h
G r a p h i c a l
O u t p u t f f r o m
a
C o m p u t e r
S i m u l a t i o n
o f
t h e I d e a l
D i e s e l
C y c l e
F i g s .
A 1 . 4 a n d
A l . 5
i n A p p e n d i x A l . l
s h o w t h e r e s u l t s
o f
t h e
a b o v e c a l c u l a t i o n s
f o r
t h e
i d e a l
O t t o
c y c l e
b u t d e r i v e d o n
a
c o m p u t e r .
T h e
p r o c e d u r e
a n d c o m m e n t s
t h a t
a r e
g i v e n
i n
S e c . 1 . 9 . 1 . 1
p e r t a i n i n g
t o s i m i l a r
c o m p u t a t i o n s
f o r
t h e i d e a l O t t o
c y c l e
a r e
e q u a l l y g e r m a n e
h e r e
s o
t h e y
d o n o t
n e e d t o b e
r e p e a t e d .
B e c a u s e
F i g s .
A A . 4
a n d
A 1 . 5
a r e
d r a w n
t o
s c a l e
t h e
n u m b e r s
f o r
p r e s s u r e t e m p e r a t u r e
a n d v o l u m e
w h i c h
a r e d e r i v e d a b o v e c a n
b e
s e e n a t
t h e
r e l e v a n t
s t a t e
p o s i t i o n s
n u m b e r e d a s
1 5 .
F i g .
1 . 6 1
s h o w s
t h e
c u m u l a t i v e
w o r k
h e a t
t r a n s f e r
a n d i n t e r n a l
e n e r g y d i a g r a m s
f o r t h i s
i d e a l D i e s e l
c y c l e .
T h e
1 0
j u m p
i n h e a t
t r a n s f e r
a n d a c c u m u l a t e d i n t e r n a l
e n e r g y
c a n b e
s e e n a t t h e t d c
p o i n t
w h e r e t h e c o n s t a n t v o l u m e h e a t
i n p u t
t a k e s
p l a c e .
T h e
e x t r a w o r k
r e q u i r e d
t o
c o m p r e s s
t h e
a i r
i n t h e D i e s e l
c y c l e c o m p a r e d
t o t h a t
f o r
t h e O t t o
c y c l e
i n
F i g .
1 . 4 0
i s
e v i d e n t .
I t
t o o k
j u s t
2 1 3 J o f
w o r k
t o
c o m p r e s s
t h e
O t t o
c y c l e c h a r g e
a t
a
c o m p r e s s i o n
r a t i o
o f
1 0
b u t
i t
t o o k
1 3 0 1
J
i n
t h e
d i e s e l
e n g i n e
w i t h
t h e m u c h
h i g h e r
c o m p r e s s i o n
r a t i o o f 1 7 .
A l t h o u g h
t h e d i e s e l
e n g i n e
i s
d o u b l e t h e
c a p a c i t y
o f t h e
g a s o l i n e e n g i n e
t h a t s t i l l
t r a n s l a t e s
t o
a b o u t
t h r e e t i m e s
t h e
c o m p r e s s i o n
w o r k
f o r
a n
e q u i v a l e n t
d i e s e l
u n i t .
T h i s e x p l a i n s
w h y
a
m u c h
m o r e r o b u s t
s t a r t e r
m o t o r a n d
b a t t e r y
a r e
r e q u i r e d
t o
s u p p l y
t h e
n e c e s s a r y e n e r g y
t o
g e t
a c a r
d i e s e l
e n g i n e
g o i n g
a s
c o m p a r e d
t o i t s
s p a r k i g n i t i o n c o u n t e r p a r t .
I g n i t i o n
o f t h e f u e l
i n
t h e
d i e s e l
e n g i n e
o c c u r s
b y
h e a t i n g
t h e
i n j e c t e d l i q u i d
t o
v a p o r
a n d
t h e n
h e a t i n g
t h a t
v a p o r
t o
i t s
s e l f i g n i t i o n t e m p e r a t u r e .
T h e e n d
o f
c o m p r e s s i o n
t e m p e r a t u r e
c a l c u l a t e d
a b o v e
a s
T 2
i s
1 0 6 5 . 4
K
o r 7 9 2 . 4 ° C .
A
t e m p e r a t u r e
a t t h i s l e v e l i s
m o r e
t h a n
s u f f i
c i e n t t o
c a r r y
o u t t h e
t w o
h e a t i n g p r o c e s s e s d e s c r i b e d
a n d
t o i n i t i a t e i g n i t i o n .
H o w e v e r
u n d e r
n o r m a l c o l d s t a r t
c o n d i t i o n s t h e
i n i t i a l
t e m p e r a t u r e a t
b d c w o u l d b e m o r e l i k e
2 0 ° C a n d a
r e c a l c u l a t i o n
o f t h e
e n d o f
c o m p r e s s i o n
t e m p e r a t u r e g i v e s 9 1 0 K o r
6 3 7 ° C ; s t a r t i n g i s now
m o r e
p r o b l e m a t i c .
U n d e r
a r c t i c a i r
c o n d i t i o n s o f 3 0 ° C
t h e e q u i v a l e n t
e n d o f
c o m p r e s s i o n
1 1 6
