Internal Combustion Engine

COMBUSTION POWER CYCLES

Otto Cycle ( Basis of Comparison for Spar!I"nition En"ines # )R (&=C#

)A (&=C#

A$ T

L S=C

S=C

B$ B 

A$ %& an' TS ia"ram

3 P

3

T

S=C

S=C

V=C

V=C 4

2

4

Wnet QT

2

V=C S=C S=C V=C

1 1

V

V2=V3

V1=V4

S

S1=S2

S3=S4

INTERNAL COMBUSTION ENGINE

ANAL*SIS O+ EAC, STATE%/ &/ T/ S/

0 3 0 =

%1 &1 T1 S1

0 = 0 0

%2 &2 T2 S2

3 0 3 =

%4 &4 T4 S4

3 = 3 3

%/ &/ T/ S/

B$ %&T %&T Relat Relatio ions ns.i .ip p Process 1-2 : ( S=C ) 1

k 1 1  k 1  K    T P V  2   2  K    1   P   V    T 1    1  2     

Isentropic Compression Ratio : r ks 

V 1



V 2  V D



cV D  V D

V 2 V 2 Where : c = percent cearance

cV D



C  1 C

Process 2-3 : ( V= C ) P 3



P 2

T 3 P 3 ; T 2 P 2

Presss!re Ratio " r p#=c p#=c = ( $%%ition o& heat) Compression

Process 3 ' 4 ( S = C ) 1

k 1   k 1  K 1  V 3  P 4  K  T 4       P    V    T 3   3  4      

V 4 V 3

= Isentropic e*pansion Ratio"

r es=c es=c

Process 4 ' 1 ( V = C )

P 4 P 1



T 4 P 4 ; T 1 P 1

Press!re Ratio " r p#=c p#=c ( Reection o& eat )


C$ ,eat A''e' 5 )A = 6 7 A Process 2 ' 3 ( V = C ) Q $ = Q2-3 = mc#+T = mc#(T3-T2)

$ ,eat Re8ecte'5 )R = 6 9 A Process 4 '1 : ( V = C ) QR = Q4-1 = - mc#+T = - mc#(T4-T1)

E$ Net :or5 :NET W,T = . Q $ . - . QR . P V  P 1V 1 P 4V 4  P 3V 3  = 2 2 1  K 1  K +$ T.ermal Efficiency5 e

W NET

e= =

Q A

x100%

1 ( r K ) K 1

= 1

T 4  T 1 T 3  T 2

x100%

x100 %

G$ Mean Effecti;e %ress
P/=

W NET V 1  V 2

=

W NET V D


iesel Cycle 9 Basis of Comparison for Compression!I"nition En"ines )A (%=C# )R (&=C#

TC x

L

S=C

S=C

BCC

%&  TS ia"ram 3 P

2

P=C

3

T

S=C

S=C 4

2

P=C 4

Wnet QT V=C S=C S=C

1

V=C 1

1 V

S

ANAL*SIS O+ EAC, STATE-


%/ &/ T/ S/

0 3 0 =

%1 &1 T1 S1

= 0 0 0

%2 &2 T2 S2

3 0 3 =

%4 &4 T4 S4

3 = 3 3

%/ &/ T/ S/

A$ %&T Relations.ip Process 1-2 : ( S=C ) 1

k 1  k 1  K 1     T P V  2   2  K    1    P   V   T 1   1   2     

Isentropic Compression Ratio : r ks 

V 1



V 2  V D



cV D  V D

V 2 V 2 Where : c = percent cearance

cV D



C  1 C

Process 2-3 : ( P= C ) V 3



V 2

T 3 T 2 C!t-o&& Ratio " r CP=C

Process 3 ' 4 ( S = C ) 1

k 1   k 1  K 1  V 3  P 4  K  T 4       P    V    T 3   4  3      

V 4 V 3

= Isentropic *pansion Ratio"

r es=c

Process 4 ' 1 ( V = C )

P 4 P 1



T 4 P 4 ; T 1 P 1

Press!re Ratio " r p#=c

B$ ,eat A''e' 5 )A = 6 7 A


Process 2 ' 3 ( P = C ) Q $ = Q2-3 = mcp+T = mcp(T3-T2)

C$ ,eat Re8ecte'5 )R = 6 9 A Process 4 '1 : ( V = C ) QR = Q4-1 = - mc#+T = - mc#(T4-T1)

$ Net :or5 :NET W,T = . Q $ . - . QR . = . mcp(T 3-T2) . - . - mc#(T4-T1).

E$ T.ermal Efficiency5 e

e=

W NET Q A

=1-

= 1

x100%

C V (T 4  T 1 ) Cp (T 3  T 2 )

x100 %

 (r )  1    x100% ( 1 ) K r    K

1

C

( r K ) K 1

C

G$ Mean Effecti;e %ress
P/=

W NET V 1  V 2

=

W NET V D


at.e Cycle# 9>asis of comparison spar an' compression i"nition en"ines$

P

P=C

T S=C

IP

P=C

V=C

V=C

W,T

S=C

Q $

V=C S=C S=C

V=C

V

SP

T.ermal Efficiency5 e e =1-

1 (r P )

K 1

K   (r C r P )  1   x100% r Kr r    ( 1 ) ( 1 )  P  P C

Where : Compression Rato ( r 0) = C!t-o&& Ratio ( r C ) = Press!re Ratio ( r P) =

V 1 V 2

V 4 V 3 P 3 P 2


IP

%ro>lems  Sol
Sol
k 1  k 1  K 1   V 1  P 2  K  T 2       P    V    T 1    2  1     

r ks 

V 1 V 2



V 2  V D



V 2

cV D  V D



cV D

1

C  1 C

1

 P  K  3250  1.4 r 0S=C =   2      12.02 V 2  100   P 1  V 1

) So#in &or Percent Cearance

r ks 

V 1 V 2



V 2  V D

V 2 c 1 122 = c 122 C = C > 1 122 C - C = 1



cV D  V D cV D



C  1 C

C = ?@ or ?@  C) So#in &or ,etWor6 W,T = . Q $ . - . QR . = . mcp(T 3-T2) . - . - mc#(T 4-T1). 7here : T4 = T1(r C)0 c.o.  c 0.06  0.0907  1.66 r C = = 0.0907 c soA T4 = 31B(199) 14 = 94951 0 an% " T 3 = T1(r 66-1)(r c) = 31B  ( 122) 14-1(199)D T3 = 142@24 0 $so"

T2 = T1(r 6)6-1 = 31B(122) 14-1


T2 = B5?@B 0 There&oreA W,T = . (5)(192)(142@24-B5?@B).-.(5)(@1B9)(31B-94951). W,T = 19@455 0W %) So#in &or the therma e&&icienc< e=

W NET Q A



W NET m air Cp air (T 3  T 2 )



167 .455 KW x100 ( 0.5)(1.0062 )(1427 .24  859 .78 )

e = 5B955  e) So#in &or the /ean &&ecti#e Press!re

P/=

W NET V 1  V 2

r ks  ;!tA

V 1 V 2

=

W NET V D

A V 2 

V 1 r KS C

P1V1 = maRaT1 maRaT 1 (0.5)(0.787)(318) m3   0.456 V1 = P 1 (100) s

So"

m3 0.456 3 V2 = s  0.037 m 12 .02 s There&oreA P/=

167.455  400 KPa (0.456  0.037)


1$ $ heat e*chaner 7as insta p!rpose< to coo 5 6 o& as per secon% /oec!ar 7eiht is 2B an% 6=132 The as is cooe% &rom 15 C to B Water is a#aia;e at the rate o& 3 6.s an% at a temperat!re o& 12 C Cac!ate the e*it temperat!re o& the 7ater in C Ans$ 4? Sol
#as !onstant"  

8.3143 28

 0.297

kJ kg  K

C  k  1.32 C C  1.32 C C  C  R 1.32 C  C  0.297 C  0.928 P V

P

V

P

V

V

V

V

 1.32(0.928)  1.225 P

C

kJ kg  K

HeatBalance : Heat gain by water  Heat loss by gas

$ C w

P W

 T W  $g C P  T g g

0.3( 4.187)(t  12)  0.5(1.225)(150  80) t  46.1C 2$ Eetermine the a#erae C p #a!e in 6F.6-0 o& a as i& 522 6F o& heat is necessar< to raise the temperat!re &rom 30 to B 0 ma6in the press!re constant a$ /$@44 ; 344

c 244 % 444

So!tion: Q = mCpT 522 = 1 Cp (B-3) Cp = 144 6F.6-0


4$ What is the e&&icienc< o& an Gtto c
E  1 

1 k 1

r

k

 1

1 61.4 1

E  0.512  51 .2% $ $ %iese eneratin set cons!mes 235 iters o& &!e %!rin 1 ho!r operation an% pro%!ces ? 67 po7er The %ensit< o& &!e !se% is B?55 6. Eetermine the speci&ic &!e cons!mption o& the %iese eneratin set in 6 per 67-hr Ans$ @$124 a$ @$124 ; 25 Sol
c 24 % 29

G#er-a spec cons!mption = (235 i.? 67-hr)(B?55 6.i) = 234 6.67-hr ?$ The entrop< o& p!re s!;stance at a temperat!re o& a;so!te Hero is: a Gne c$ ero ; In&init< % $7a
c 555 % 545

Solatic efficiency of t.e compressor c Q=> ; Q=% Isentropic So!tion:


$%ia;atic e&&icienc< o& the compressor = (isentropic 7or6.act!a &!i% 7or6) F$ What is the area o& the %iaram &rom the reation o& temperat!re an% entrop< pane a$ :or ; P/

c eat % ner<

/@$ The &irst a7 o& thermo%$ $ So!tion: Lrom: 1 x100 % e=1( r K ) K 1 7here : e=

W NET 1000  Q A Q A

So#in &or Q $ : Q $ = mc#( T3 ' T2 ) Q $ = (1) (@19)(31@3 '@@3 ) Q $ = 1@1B4

KJ Kg

Then A e=

1000  0.5819  58 .19% 1718.4

th!sA 5B1? = 1 -

1 r k

1.4 1

A r k  8.85

/1$ The compression ratio o& an GTTG c
c 2 2511 0Pa '$ 2 1/$/@ %a

So!tion : k

 V  k   1    r k  P 1  V 2 

P 2


P 2  P 1 ( r k ) k

P 2  150(9) th!sA

1.4

P 2  3251.10 KPa

/2$ What is the &ina temperat!re a&ter compression o& a Eiese C
T 2  V 1    T 1  V 2 

k 1

 ( r k ) k 1

T 2  T 1 ( r k ) k 1 7here : T 1  32  273  305 K 1  C 1  0.08  C 0.08 r k  13 .5 r k  th!sA

T 2  305(13.5)1.4 1 T 2  863.84 K /4$ $n I%ea E!a Com;!stion C<ce operates on 5 ram o& air $t the ;einnin o& the compression" the air is at 1 0Pa" 45 C I& r p  1.5" r c  1.65" an! r k  10" %etermine the c
e 

P

W NET Q A

P=C

T S=C

IP

P=C

V=C

V=C

W,T

S=C

Q $

V=C S=C S=C

V=C

7here : W NET  Q A  Q R

V

SP


IP

Q A  Q A#  Q A" So#in &or Q A# an% Q A" Q A#  mC V (T 3  T 2 ) Q A"  mC P (T 4  T 3 )

$t point 1

V 1 

mRT 1 P 1

0.5 0.287  45  273   0.456 m 3 100



$t point 2

V 2 

V 1 r k

0.456  0.0456m 3 10



T 2  V 1    T 1  V 2 

k 1

  r k  k 1

T 2   45  273 10 

1.4 1

 798 .78 K

K

 V  k 1.4 P 2  P 1  1   P 1  r k   10010   2511 .89 KPa  V 2  $t point 3 P 3  P 2  r p  2511 .891.5  3767.84 KPa

 P 3  3767.84    798.78    1193 .17 K  2511 .89   P 2 

T 3  T 2 

$t point 4 V 4  V 3 r c   0.0456 1.65  0.075m 3

 V 4    T 3 r c  1198.17 1.65   1976.98 K V  3 

T 4  T 3  $t point 5

 V  T 5  T 4  4   V 5 

k 1

 0.075  T 5  1976.98   0.456 

1.4 1

 960.375 K

ThenA

Q A#  mc $  T 3  T 2    0.5  0.7186  1198 .17  798 .78   143 .50 KJ Q A"  mc p  T 4  T 3    0.5 1.0062  1976 .98  1198 .17   391 .82 KJ Q A  143 .50  391 .82  535 .32 Q R  mc $  T 3  T 1    0.50   0.7186  960 .375  318   230 .81 KJ W NET  Q A  Q R  535 .32  230 .81  304 .51 KJ th!sA e

304.51 535.32

 56.88%


/$ The sto6e o& a petro enine is B@5 mm an% the cearance is eM!a to 125 mm$ compression pate is no7 &itte% 7hich has the e&&ect o& re%!cin the cearance to 1 mm $ss!min the compression perio% to ;e the 7hoe stro6e" the press!re at the 1 .35  C " ;einnin o& compression as ?B2? 0Pa an% the a7 o& compression PV 135 an% the a7 o& compression PV =C" Cac!ate the press!re at the en% o& compression ;e&ore an% a&ter the compression pate is &itte% a$ /?1$/@ %a c 1@2B1 0pa ; 152B1 0Pa % 1B2B1 0Pa So!tion : 1.35

P 1V 1

 P 2V 2

1.35 1

98.29 87.5  12.5 th!sA P 2  1628.10 KPa

1.35

 P 2 12.5

1.35

/?$ The compression ratio o& a petro enine 7or6in on the constant #o!me c
T 2  V 1  T 2       8.5  1.35 1  40  273  T 1  V 2  T 2  661.97 K th!sA T 2  388.97C


/D$ When the piston is mo#in !p in a t7o-stro6e %iese enine" the sca#ene ports are cose% 7hen the piston is 9@5 mm &rom the top o& its stro6e" the press!re an% temperat!re o& the air in the c<in%er 7hen ;ein 13B 0Pa an% 43 C The cearance is eM!a to 95 mm an% the %iameter o& the c<in%er is 95 mm Cac!ate the mass o& air compresse% in the c<in%er ta6in the atmospheric press!re as 11325 0Pa an% R &or air as 2B@ 0F.6-0 a 21 6 >$ @$2/ " So!tion :

c 41 6 % 51 6

P1V1 = mRT1 Where : P 1  13.8  101.325  115.125 KPa T 1  43  273  316 K V 1 



4

 0.65 2  0.675  0.065  0.2456m 2

R  0.287

KJ kg  K

S!;stit!te

115 .125  0.2456  m 0.287  316  th!sA m= 31 6 /$ I& the compression ratio an% the c!t-o&& ratio o& a Eiese nine are 15 an% 3 respecti#e<" 7hat is the e*pansion ratio a$ 4 c 9 >$  % @ So!tion : V r k  1  15 V 2

r c  r e 

V 3 V 2 V 4 V 3

3 

r k r c



15 3

r e  5


/F$ The air is compresse% to 1.5 o& its oriina #o!me in an Gtto c
 V    1  T 1  V 2 

T 2

k 1

7here: T 1  25  273  298 K V 2 

1 5

V 1 1.4 1

   V  T 2  1  298  1   V 1  5   T 2  561.58 K T 2  288.58C 1@$ $t the ;einnin o& compression in an i%ea %!a com;!stion c

1/$ $n i%ea %!a com;!stion c$ @$D/  % 45@1  So!tion : c

e  1

a

7here:

A  r k

k 1

 12  1.31  2.11 r p r c  1 k

C 

1.6 1.5 1.3  1   1.04  1  r p k ( r c  1) 1.6  1  1.61.5  1

r p

e 1

1.04 2.11

 50.71%

or K   (r C r P )  1 e =1  x100%  50.71% (r P ) K 1  (r P  1)  Kr P (r C  1) 

1

11$ What is the press!re ratio in an i%ea %!a com;!stion c
12$ In an i%ea com;!stion c
r c 

V 4 V 3



V 4 0.055

 1.5; t&'s; V 4  0.0825m 3


14$ In an air stan%ar% GTTG c
1 A

(&ere : A  r k

k 1

sol$ing or r k : r k 

1 c c

1  0.18



0.18

 6.556

t&en; A   6.556 

1.4 1

 2.12

t&'s ; e  1

1 2.12

 0.53

1$ The compression ratio o& an i%ea GTTG c
c 12445 0Pa" 9 C % 12445 0Pa" 5???9 C

So!tion : k

 V  k   1    r k  P 1  V 2  k P 2  P 1  r k  P 2

P 2  101 .3 6 

1.4

P 2  1244.5 KPa

 V    1  T 1  V 2 

T 2

T 2  T 1  r k 

k 1

  r k 

k 1

k 1

T 2   20  273 6 

1.4 1

T 2  599.96 K



Internal Combustion Engine

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