1

Internal Combustion Engines

Lecture-7

Ujjwal K Saha, Ph.D.Department of Mechanical Engineering

Indian Institute of Technology Guwahati

Prepared underQIP-CD Cell Project

2

Air Standard Cycles

1. Carnot - maximum cycle efficiency2. Otto - spark-ignition (SI) engine 3. Diesel - compression-ignition (CI) engine4. Brayton - gas turbine

3

• Air standard cycles are idealized cycles based on the following approximations:

– the working fluid is air (ideal gas)

– all the processes are internally reversible

– the combustion process is replaced by heat input from an external source

– heat rejection is used to restore fluid to initial state

Air Standard Cycles

4

Thermodynamic Cycles

• Air-standard analysis is used to perform elementary analyses of IC engine cycles.

• Simplifications to the real cycle include:1) Fixed amount of air (ideal gas) for working fluid2) Combustion process not considered3) Intake and exhaust processes not considered4) Engine friction and heat losses not considered5) Specific heats independent of temperature

5

SI Engine Cycle vs Thermodynamic Otto Cycle

AI

R

CombustionProducts

Ignition

IntakeStroke

FUEL

Fuel/AirMixture

AirTC

BC

CompressionStroke

PowerStroke

ExhaustStroke

Qin Qout

CompressionProcess

Const volume heat addition

Process

ExpansionProcess

Const volume heat rejection

Process

ActualCycle

OttoCycle

6

Process 1 2 Isentropic compressionProcess 2 3 Constant volume heat additionProcess 3 4 Isentropic expansionProcess 4 1 Constant volume heat rejection

v2TC TC

v1BC BC

Qout

Qin

Air-Standard Otto cycle

3

4

2

1

vv

vvr ==

Compression ratio:

7

Otto cycle efficiency

)1T/T(T)1T/T(T

1TTTT

1qq

1qw

232

141

23

14

in

out

in

net

−−−=

−−−=−==η

In Otto cycle, the combustion is so rapid that the piston does not move during the process, and therefore, combustion is assumed to take place at constant volume.

8

Otto Cycle (Contd.)For isentropic process:pvk = constant with k=cp/cv

For process 1-2: p1 v1

k = p2 v2k

2

1

1

2

1

1

2

2

1

2k2

k1

vv

TT

vRTv

RT

pp

vv

===

1k

2

11k

2

1k1

1

2

1

2

1

2k2

k1

vv

vv

TT

TT

vv

vv

−

−

−

⎟⎟⎠

⎞⎜⎜⎝

⎛==

=

9

Since m = constant:

For process 3-4, using the same analysis:

Then

1k

1k

TDC

BDC

1k

2

1

1k

2

1

1

2 rVV

VV

vv

TT −

−−−

=⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟

⎠

⎞⎜⎝

⎛=⎟

⎠

⎞⎜⎝

⎛=

1k

1k

TDC

BDC

1k

3

4

4

3 rVV

VV

TT −

−−

=⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛=

1k

1

4

2

3

4

3

1

2

r1

1

TT

TT

orTT

TT

−−=η

==

10

Increasing Compression RatioIncreases the Efficiency

Typical Compression Ratios for Gasoline Engines

11

Higher Compression Ratios?

• Higher compression ratio leads to auto-ignition (without spark)

• Causes knock• Engine damage• Thus, there is an upper limit of high

compression ratio

12

CI Engine Cycle and the Thermodynamic Diesel Cycle

AI

R

CombustionProducts

Fuel injectedat TC

IntakeStroke

Air

Air

BC

CompressionStroke

PowerStroke

ExhaustStroke

Qin Qout

CompressionProcess

Const pressure heat addition

Process

ExpansionProcess

Const volume heat rejection

Process

ActualCycle

DieselCycle

13

Process 1 2 Isentropic compressionProcess 2 3 Constant pressure heat additionProcess 3 4 Isentropic expansionProcess 4 1 Constant volume heat rejection

Air-Standard Diesel cycle

Qin

Qout

2

3vvrc =

Cut-off ratio:

v2TC

v1BC TC BC

14

• Cycle efficiency,

in

out

in

net

qq

1qw

−==η

Due to ignition delay and finite time required for fuel injection, combustion process continues till the beginning of power stroke. This keeps the cylinder pressure at peak levels for a longer period. Therefore, the combustion process can be approximated as constant pressure heat addition. Remaining processes are similar to that of Otto cycle.

15

3

2

1

2

4

3

,

,

,

c

e

VCutoff Ratio rV

VCompression Ratio rV

VExpansion Ratio rV

=

=

=

Cutoff Ratio Expansion Ratio Compression RatioΧ =

16

assuming constant specific heats:

for isentropic process 1-2:

for constant pressure process 2-3: p2 = p3

ideal gas law:

)1T/T(k)1T/T(

TT

1)TT(k)TT(

1)TT(c)TT(c

123

14

2

1

23

14

23p

14v

−−−=

−−−=

−−−=η

−⎛ ⎞

= ⎜ ⎟⎝ ⎠

k 1

1 2

2 1

T vT v

c

2

3

2

3

3

3

2

2 rvv

TT

vRT

vRT ===>=

17

for isentropic process 3-4:

but diesel cycle has higher r!

kc

k

2

3

1k

2

3

2

3

1k

2

3

2

3

1

4

1k

3

2

1

21k

3

1k2

1

2

1k3

1k1

1k

3

1

1k

3

4

4

3

rvv

vv

vv

vv

TT

TT

vv

TT

v

vTT

vv

vv

vv

TT

=⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛===>

⎟⎟⎠

⎞⎜⎜⎝

⎛===⎟⎟

⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛=

−−

−

−

−

−

−−−

Ottodiesel

c

kc

c

kc

1k

rgivenfor,1)1r(k

1rcesin

)1r(k1r

r1

1,then

η≤η

≥−−

−−

−=η−

18

( )( )1

11 111

kc

Diesel kc

rr k r

η −

⎡ ⎤−⎢ ⎥= − ⋅

−⎢ ⎥⎣ ⎦

Thermal Efficiency

111 −−= kOtto r

ηRecall,

Note that the term in the square bracket is always larger than one so for the same compression ratio (r), the Diesel cycle has a lower thermal efficiency than the Otto cycle.

Note: CI needs higher r compared to SI to ignite fuel

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When rc (= v3/v2) 1 the Diesel cycle efficiency approaches the efficiency of the Otto cycle

Remark

Compression ratio = 10-22 (Diesel)Compression ratio = 6-10 (Otto)Thus, efficiency of Diesel Cycle is greater than Otto Cycle.

Higher efficiency and low cost fuel makes diesel engine suitable for larger power units such as larger ships, heavy trucks, power generating units, locomotives etc.

20

Diesel Cycle Otto Cycle

The only difference is in process 2-3

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Both Otto cycle (Constant volume heat addition) and Diesel cycle (Constant pressure heat addition) are over-simplistic and unrealistic. In actual case, combustion takes place neither at constant volume (time required for chemical reactions), nor at constant pressure (rapid uncontrolled combustion).

Dual cycle is used to model the combustion process. It is a compromise between Otto and Diesel cycles, where heat addition takes place partly at constant volume and partly at constant pressure. This cycle is also known as mixed cycle. In fact, Otto and Diesel cycles are special cases of Dual cycle.

Remark

22

Modern CI Engine Cycle and the Thermodynamic Dual Cycle

AI

R

CombustionProducts

Fuel injectedat 15o bTC

IntakeStroke

Air

AirTC

BC

CompressionStroke

PowerStroke

ExhaustStroke

Qin Qout

CompressionProcess

Const pressure heat addition

Process

ExpansionProcess

Const volume heat rejection

Process

ActualCycle

DualCycle

Qin

Const volume heat addition

Process

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Process 1 2 Isentropic compressionProcess 2 2.5 Constant volume heat additionProcess 2.5 3 Constant pressure heat additionProcess 3 4 Isentropic expansionProcess 4 1 Constant volume heat rejection

Dual Cycle

Qin

Qin

Qout

11

2

2

2.5

2.5

33

44

24

Thermal Efficiency

)()(11

5.2325.2

14

hhuuuu

mQmQ

in

out

cycleDual −+−

−−=−=η

( )⎥⎦⎤

⎢⎣

⎡−+−

−−= − 1)1(

111 1 c

kc

kcconst

Dual rkr

rv αααη

111 −−= kOtto r

η( )( )⎥⎦

⎤⎢⎣

⎡

−−

⋅−= − 11111 1

c

kc

kconst cDiesel r

rkrV

η

Note, the Otto cycle (rc=1) and the Diesel cycle (α=1) are special cases:

3 2.5

2.5 2where and c

v Pr v Pα= =

25

The use of the Dual cycle requires information about either:i) the fractions of constant volume and constant pressure heat

addition (common assumption is to equally split the heat addition), or

ii) maximum pressure P3.

For the same inlet conditions P1, V1 and the same compression ratio:

DieselDualOtto ηηη >>

For the same inlet conditions P1, V1 and the same peak pressure P3(actual design limitation in engines):

ottoDualDiesel ηηη >>

26

For the same inlet conditions P1, V1and the same compression ratio P2/P1:

For the same inlet conditions P1, V1and the same peak pressure P3:

Diesel

Dual

Otto

DieselDualOtto

“x” →“2.5”

Pmax

Tmax

Po

Po

Pres

sure

, P

Pres

sure

, P

Tem

pera

ture

, T

Tem

pera

ture

, T

Specific VolumeSpecific Volume

Entropy Entropy

27

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The MIT Press, Cambridge, Massachusetts.

References

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1. http://www.mne.psu.edu/simpson/courses2. http://me.queensu.ca/courses 3. http://www.eng.fsu.edu4. http://www.personal.utulsa.edu5. http://www.glenroseffa.org/6. http://www.howstuffworks.com7. http://www.me.psu.edu 8. http://www.uic.edu/classes/me/ me429/lecture-air-cyc-web%5B1%5D.ppt9. http://www.osti.gov/fcvt/HETE2004/Stable.pdf10. http://www.rmi.org/sitepages/pid457.php11. http://www.tpub.com/content/engine/14081/css12. http://webpages.csus.edu13. http://www.nebo.edu/misc/learning_resources/ ppt/6-1214. http://netlogo.modelingcomplexity.org/Small_engines.ppt15. http://www.ku.edu/~kunrotc/academics/180/Lesson%2008%20Diesel.ppt16. http://navsci.berkeley.edu/NS10/PPT/ 17. http://www.career-center.org/ secondary/powerpoint/sge-parts.ppt18. http://mcdetflw.tecom.usmc.mil19. http://ferl.becta.org.uk/display.cfm20. http://www.eng.fsu.edu/ME_senior_design/2002/folder14/ccd/Combustion21. http://www.me.udel.edu22. http://online.physics.uiuc.edu/courses/phys14023. http://widget.ecn.purdue.edu/~yanchen/ME200/ME200-8.ppt -

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