Thermodynamic Analysis of Internal Combustion Engines

P M V SUBBARAOProfessor

Mechanical Engineering DepartmentIIT Delhi

Work on A Blue Print Before You Ride on an Actual Engine….It is a Sign of Civilized Engineering….

SI Engine Cycle

A I R

CombustionProducts

Ignition

IntakeStroke

FUEL

Fuel/AirMixture

CompressionStroke

PowerStroke

ExhaustStroke

ActualCycle

Actual SI Engine cycle

Ignition

Total Time Available: 10 msec

Early CI Engine Cycle

A I R

CombustionProducts

Fuel injectedat TC

IntakeStroke

Air

CompressionStroke

PowerStroke

ExhaustStroke

ActualCycle

Modern CI Engine Cycle

CombustionProducts

Fuel injectedat 15o bTC

IntakeStroke

A I R

Air

CompressionStroke

PowerStroke

ExhaustStroke

ActualCycle

Thermodynamic Cycles for CI engines

• In early CI engines the fuel was injected when the piston reached TC and thus combustion lasted well into the expansion stroke.

• In modern engines the fuel is injected before TC (about 15o)

• The combustion process in the early CI engines is best approximated by a constant pressure heat addition process Diesel Cycle

• The combustion process in the modern CI engines is best approximated by a combination of constant volume and constant pressure Dual Cycle

Fuel injection startsFuel injection starts

Early CI engine Modern CI engine

Thermodynamic Modeling

• The thermal operation of an IC engine is a transient cyclic process.• Even at constant load and speed, the value of thermodynamic

parameters at any location vary with time.• Each event may get repeated again and again.• So, an IC engine operation is a transient process which gets

completed in a known or required Cycle time.• Higher the speed of the engine, lower will be the Cycle time.• Modeling of IC engine process can be carried out in many ways.• Multidimensional, Transient Flow and heat transfer Model.• Thermodynamic Transient Model USUF.• Fuel-air Thermodynamic Mode.• Air standard Thermodynamic Model.

Ideal 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

• The two types of reciprocating engine cycles analyzed are:1) Spark ignition – Otto cycle2) Compression ignition – Diesel cycle

AirTC

BC

Qin Qout

CompressionProcess

Const volume heat addition

Process

ExpansionProcess

Const volume heat rejection

Process

OttoCycle

Otto CycleA I R

CombustionProducts

Ignition

IntakeStroke

FUEL

Fuel/AirMixture

CompressionStroke

PowerStroke

ExhaustStroke

ActualCycle

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

v2TC

TCv1BC BC

Qout

Qin

Air-Standard Otto cycle

3

4

2

1

vv

vvr

Compression ratio:

First Law Analysis of Otto Cycle

12 Isentropic Compression

)()( 12 mW

mQuu in

2

1

1

2

1

2

vv

TT

PP

AIR

)()( 1212 TTcuum

Wv

in

23 Constant Volume Heat Addition

mW

mQuu in )()( 23

)()( 2323 TTcuum

Qv

in

2

3

2

3

TT

PP

AIR Qin

TC

11

2

1

1

2

k

k

rvv

TT

3 4 Isentropic Expansion

AIR)()( 34 mW

mQuu out

)()( 4343 TTcuum

Wv

out

4

3

3

4

3

4

vv

TT

PP

4 1 Constant Volume Heat Removal

AIR QoutmW

mQuu out )()( 41

)()( 1414 TTcuum

Qv

out

1

1

4

4

TP

TP

BC

1

1

4

3

3

4 1

k

k

rvv

TT

23

1243

uuuuuu

QW

in

cycleth

23

14

23

1423 1uuuu

uuuuuu

Cycle thermal efficiency:

thin

thincycle

rr

umQ

krr

VPQ

Pimep

VVW

imep

1/

11

1 111121

Indicated mean effective pressure is:

Net cycle work:

1243 uumuumWWW inoutcycle

First Law Analysis Parameters

12

1

23

14 111)()(1

kv

v

rTT

TTcTTc

Effect of Compression Ratio on Thermal Efficiency

• Spark ignition engine compression ratio limited by T3 (autoignition) and P3 (material strength), both ~rk

• For r = 8 the efficiency is 56% which is twice the actual indicated value

Typical SI engines9 < r < 11

k = 1.4

111 k

const cth rV

Effect of Specific Heat Ratio on Thermal Efficiency

111 k

const cth rV

Specific heat ratio (k)

Cylinder temperatures vary between 20K and 2000K so 1.2 < k < 1.4k = 1.3 most representative

The net cycle work of an engine can be increased by either: i) Increasing the r (1’2)ii) Increase Qin (23”)

P

V2 V1

Qin Wcycle

1

2

3

(i)

4

(ii)

Factors Affecting Work per Cycle

1’

4’

4’’

3’’th

incycle

rr

VQ

VVW

imep

1121

Effect of Compression Ratio on Thermal Efficiency and MEP

k

in

rrr

VPQ

Pimep 11

1111

k = 1.3

Ideal Diesel Cycle

Air

BC

Qin Qout

CompressionProcess

Const pressure heat addition

Process

ExpansionProcess

Const volume heat rejection

Process

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

23

1411hhuu

mQmQ

in

out

cycleDiesel

11111 1

c

kc

kconst cDiesel r

rkr

V

For cold air-standard the above reduces to:

Thermal Efficiency

111 kOtto r

recall,

Note 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 efficiencythan the Otto cycle

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

Typical CI Engines15 < r < 20

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

Thermal Efficiency

Higher efficiency is obtained by adding less heat per cycle, Qin, run engine at higher speed to get the same power.

AirTC

BC

Qin Qout

CompressionProcess

Const pressure heat addition

Process

ExpansionProcess

Const volume heat rejection

Process

DualCycle

Qin

Const volume heat addition

Process

Thermodynamic Dual Cycle

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

)()()()( 5.2325.25.2325.2 TTcTTchhuum

Qpv

in

Thermal Efficiency

)()(11

5.2325.2

14

hhuuuu

mQmQ

in

out

cycleDual

1)1(

111 1 c

kc

kcconst

Dual rkr

rv

111 kOtto r

11111 1

c

kc

kconst cDiesel r

rkr

V

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

2

3

5.2

3 and where PP

vvrc

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), orii) maximum pressure P3.

Transformation of rc and into more natural variables yields

1

1111 111 krVP

Qk

kr kin

c

1

31PP

r k

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

DieselDualOtto

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

ottoDualDiesel

For the same inlet conditions P1, V1 and the same compression ratio P2/P1:

For the same inlet conditions P1, V1 and the same peak pressure P3:

32

141

1

TdsTds

QQ

in

outth

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