Thermodynamics of internal combustion Engine

7/29/2019 Thermodynamics of internal combustion Engine

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Thermodynamic Design of Engine

P M V Subbarao

Professor

Mechanical Engineering Department

Design for Performance..


2/66

Mean Effective Pressure

The constant pressure that would have to exist to do the

same work over Vd as is done by the actual cycle.

A better measure of engine work than torque

Depends more on engine design than engine size

At maximum torque:

Naturally aspirated: 850 to 1050 kPa

Turbocharged: 1250 to 1700 kPa These are about 10% lower at maximum power


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SI Engine Cycle vs Thermodynamic Otto Cycle

A

IR

Intake

Stroke

FUEL

Ignition

Power

Stroke

Fuel/Air

Mixture

Compression

Stroke

Combustion

Products

Exhaust

Stroke

TC

Qin QoutAir

Compression

Process

Const volume

heat addition

Process

Expansion

Process

Actual

Cycle

OttoCycle BC

Const volume

heat rejection

Process


4/66

Early CI Engine Cycle and the Thermodynamic Diesel Cycle

A

IR

Intake

Stroke

Fuel injected

at TC

Power

Stroke

Exhaust

Stroke

Air

Compression

Stroke

Combustion

Products

Air

Compression

Process

Expansion

Process

Actual

Cycle

DieselCycle BC

Qout

C

onst volume

heat rejection

Process

Qin

Const pressure

heat addition

Process


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Transient I.C. Engine Processes : Control Mass

)()()()(

tWtQdt

mud

dt

mudCMCM

CM

fuelair

irrCM Wdt

tdV

tptW

)(

)()(

atmcylCM TtTtUAtQ

)()()(

Parameters that require Process Rate model


6/66

Actual SI Engine cycle

Ignition

Total Time Available ~ 10 msec


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Early CI Engine Cycle

A

I

R

Combustion

Products

Fuel injected

at TC

Intake

Stroke

Air

Compression

Stroke

Power

Stroke

Exhaust

Stroke

Actual

Cycle

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

Fuel injection starts

Early CI engine

The combustion process in the early CI engines is best

approximated by a constant pressure heat addition

processDiesel Cycle


8/66

Modern CI Engine Cycle

Combustion

Products

Fuel injected

at 15o bTC

Intake

Stroke

A

I

R

Air

Compression

Stroke

Power

Stroke

Exhaust

Stroke

Actual

Cycle

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

Fuel injection starts

Modern CI engine

The combustion process in the modern CI engines is best approximated

by a combination of constant volume and constant pressureDual Cycle


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Thermodynamic Design : A tradition of Post Carnot

Research

Major portion of motive power generation occurs in any Reciprocating IC

engine in a control mass (closed system).

The thermal operation of any IC engine is a transient cyclic process.

Even at constant load and speed, the value of thermodynamic parameters atany 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 aknown 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 Model.

Air standard Thermodynamic Model.


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Irreversible I.C. Engine Cycle


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First Law Analysis: Transient Compression of

Control Mass

Compression Process

Fuel/Air

Mixture Air

SI Engine CI Engine


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Ideal Compression Process

)()()()( tWtQdt

muddt

mud CMCMCM

fuelair

dt

tdVptptW ccCM

)()()(

atmcylCMTtTtUAtQ

)()()(

Parameters that require Process Rate model

Reversible displacement work:

Instantaneous Rate of heat transfer:


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Actual Compression Process : Control mass :

Variable Property Single Fluid , heat transfer , frictional losses

)()()()(

tWtQdt

mud

dt

mudCMCM

CM

fuelair

)()(

)(

tWtQdt

mud

CMCMCM

air


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Isentropic Compression Process

For a infinitesimal compression process:

pdVdUTdS

dVV

mRTmRdTpdVdTmcVdpdU v

110

VdV

TdTdV

VTdT

1

11

1


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kgKkJT

CT

CT

CCcp /100010001000

3

3

2

210

Rc

c

p

p

V

dVT

T

dT)(1

For infinitesimal compression from initial state.

Variable Properties of Working fluid

11 TT dVVdTTTV


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1V

11 d

dVV

i

i

d

dVV

12 VrV c


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Friction Force

pSf

Friction force is directly proportional to piston velocity

1

sin

cossin

60 22

R

LNSp

1sin

cossin60 22

R

LNf

where is a coefficient of friction that takes into

account the global frictional losses


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The extra instantaneous power during Compression

2

221

sin

cossin

60

R

LNSfP p


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1V

12 VrV c

iV

ii dVV

Frictional Adiabatic Compression


20/66

VdV

TT

dT

comp

fri

)(11

,

For Irreversible Adiabatic Compression


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p

dp

Tn

Tn

T

dT

comp

irr

)(

1)(1

,

For Irreversible Polytropic Compression


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For another infinitesimal compression fromp+idp:

idpp

dp

dTTn

dTTn

dTT

dTi

j

j

i

jj

comp

i

j

j

i

1

1

1

11

,

1

1

1

)(

1)(1

Evaluation of Polytropic efficiency, hcomp,.


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)()()()(

tWtQdt

mud

dt

mudCMCM

CM

fuelair

)()(

)(

tWtQdt

mud

CMCMCM

air


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)()()( tWtQdt

Tmcd CMCMCM

airv

CI Engine

Compressions:


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dt

tdvp

dt

Tcd

CM

airv )(

dt

dv

v

RT

dt

dTR 11

Ideal Gas Model

dt

dv

v

T

dt

dT

1

1

v

dv

T

dT

1

1


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kgKkJT

CT

CT

CCcp

/100010001000

3

3

2

210

)(

)(

)( RTc

Tc

Tp

p

vdvT

TdT )(1


27/66

Properties of Gases

kgKkJ

T

C

T

C

T

CCcp /100010001000

3

3

2

210

Gas C

0C

1C

2C

3

Air 1.05 -0.365 0.85 -0.39Methane 1.2 3.25 0.75 -0.71

CO2 0.45 1.67 -1.27 0.39

Steam 1.79 0.107 0.586 -0.20

O2 0.88 -0.0001 0.54 -0.33

N2 1.11 -0.48 0.96 -0.42


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Variable Properties of Air

0.5

0.7

0.9

1.1

1.3

1.5

0 200 400 600 800 1000 1200 1400

Temperature, K

g

cp

cv


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Properties of Fuels

kgkJT

CTC

TC

TCCC fp /100010001000 2

4

3

3

2

210,

Fuel C0 C1 C2 C3 C4

Methane -0.29149 26.327 -10.610 1.5656 0.16573

Propane -1.4867 74.339 -39.065 8.0543 0.01219

Isooctane -0.55313 181.62 -97.787 20.402 -0.03095

Gasoline -24.078 256.63 -201.68 64.750 0.5808

Diesel -9.1063 246.97 -143.74 32.329 0.0518

I t i C i V i bl P t M d l


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Isentropic Compression : Variable Property Model

s

T

11 dvv

1v

2

1

1

i

idvv

j

i

idvv1

1

1

11

n

iidvv

2v

For a small compression ratio: )(1

11

T

i

i

i

i

v

v

T

T


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I t i C i V i bl P t M d l


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Isentropic Compression : Variable Property Model

s

T

11 dvv

1v

2

1

1

i

idvv

j

i

idvv1

1

1

11

n

iidvv

2v

For a small compression ratio:

)(1

1

1

1

T

i

i

i

i

i

v

v

T

T


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Explicit Method:

)(1111

iT

ivii rTT

)(1

1

1

1

1

iT

i

i

i

i

i

v

v

T

T

)(11)(1

1

)(1

11

iii T

iv

T

ivi

T

ivii rrTrTT


34/66

Pressure Profile During Compression

Ideal Gas Model:

V

mRTp

)(1111

iT

ivii rTT


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Initial Conditions

Engine Respirator S stem


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Engine Respiratory System

Pexh,cyl

Exhaust Valve : Operation Schedule


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Exhaust Valve : Operation Schedule

Pcyl

Patm

I l t V l O ti S h d l


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Inlet Valve : Operation Schedule

Pcyl

Patm

C li d P Di


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Cylinder Pressure Diagram

q

Aexhaust Aintake


40/66

Work Required for Compression

dVV

mRTdVpW

TDC

BDC

TDC

BDC

TDC

BDCVdVTmRdVpWW ncompressio

TDC

IVCV

dVTmRW ncompressio


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Global Isentropic Compression Process

The overall isentropic process between states 1 & 2:

2

1

12 pdvmUU 2

1

12 pdvUU

N

i

T

v

i

rTT1

)(1

12

1

N

i

iT

vrTT 11)(1

12


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Basics of Combustion


43/66

23 Complete combustion at constant volume

0

)()()( tWtQdt

mud CMCMCM

air

)(tQdt

dum

CM

CM

air

..)( VCtmdt

dum fuel

CM

air


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23 Complete combustion at constant volume

inQUU 23

..2

0

2

0

3

0

VCmdTmcQdTmcdTmc fuel

T

T

vin

T

T

v

T

T

v

..2

0

3

0

VCAFdTcmdTmc

T

T

v

T

T

v


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23 Complete & Finite Duration combustion

)()(

)(

tWtQdt

mudCMCM

CM

air

dt

tdVtpVCtm

dt

tTdcm combfuel

CM

v

..)(

)(,

dt

dVpVCm

dt

Tdcm combfuel

CM

v

..)(

)(,

dt

dV

V

RTVCm

dt

Tdcm combfuel

CM

v

..)(

)(,

Fi it H t R l


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Finite Heat Release

A typical heat release curve consists of an initial spark ignition phase,

followed by a rapid burning phase and ends with burning completion phase

The curve asymptotically approaches 1 so the end of combustion is defined

by an arbitrary limit, such as 90% or 99% complete combustion where

xb = 0.90 or 0.99 corresponding values for efficiency factora are 2.3 and 4.6

The rate of heat release as a function of crank angle is:

1

1

n

d

sb

d

inb

in xna

Q

d

dxQ

d

dQ

bindxQdQ

.99


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dt

dV

V

RTVCm

dt

Tdcm combfuel

CM

v

..)(

)(,

dt

dV

V

RT

d

dQ

dt

Tdcm

CM

v

)(

Ideal gas model: mRTpV

d

dQ

Vd

dV

V

p

d

dp 1


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3 4 Isentropic Expansion

AIR

)(tw

dt

duCM

CM

air

Isentropic Expansion : Variable Property Model


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Isentropic Expansion : Variable Property Model

s

T

1

1

3

n

i

idvv

4v

j

i ij

dvv1

2

1

3

i

idvv

13

dvv

3v

For a small compression ratio:

)(1

1

1

1

T

i

i

i

i

i

v

v

T

T


50/66

Explicit Method:

)(1111

iT

ivii rTT

)(1

1

1

1

1

iT

i

i

i

i

i

v

v

T

T

)(11)(1

1

)(1

11

iii T

iv

T

ivi

T

ivii rrTrTT


51/66

Pressure Profile During Expansion

Ideal Gas Model:

V

mRTp

)(1111

iT

ivii rTT


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Work Delivered during Expansion

dV

VmRTdVpW

BDC

TDC

BDC

TDC

BDC

TDCVdVTmRdVpWW ansion

exp

TDC

IVCV

dVTmRW ansion

exp


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Global Isentropic Expansion Process

The overall isentropic process between states 3 & 4:

4

3

12 pdvmUU 4

3

12 pdvUU

N

i

T

v

i

rTT1

)(1

43

1

N

i

iT

vrTT 11)(1

43


54/66

Constant Volume Heat Removal

1

1

4

4

T

P

T

P

AIR

Qout

BC

)()()(

tWtQdt

mudCMCM

CM

air

0

)(tQdt

dum

CM

CM

air

TUAdt

dum

CM

air


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41 Complete Cooling at constant volume

outQUU 41

out

T

T

vout

T

T

v

T

T

v QdTmcQdTmcdTmc 1

0

1

0

4

0


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41 Complete & Finite Duration Cooling

)()(

)(

tWtQdt

mudCMCM

CM

air

dt

tdVtptTtUA

dt

tTdcm

CM

v

)(

dt

dVpTTUA

dt

Tdcm amb

CM

v

)(

dt

dV

V

RTTTUA

dt

Tdcm amb

CM

v

)(

Surface Area for Cooling


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Surface Area for Cooling


58/66

Engine Heat Losses

For many engines, the heat losses can be subdivided:

ambientoilcoolantloss QQQQ

General range of various heat losses are:

Type of loss Range Remarks

Cooling 10 30 %

5 15%

Diesel engines on

higher side

Oil At low load higherlosses

Ambient 2 10%

Engine Cooling System


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Measurement of Engine Heat Transfer


60/66

Measurement of Engine Heat Transfer

S I Engine Temperatures


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S I Engine Temperatures

Three of the hottest points are

around the spark plug,

the exhaust valve and port, and

the face of the piston.

Highest gas temperatures during

combustion occur around the spark

plug. This creates a critical heat transfer

problem area.

The exhaust valve and port operate hot

because they are located in pseudo-

steady flow of hot exhaust gases. The piston face is difficult to cool

because its is separated form the water

jacket or finned surface.

Computed Temperature of A Piston


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Computed Temperature of A Piston


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Heat Transfer in Combustion Chambers


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cg

coolantgas

hk

x

h

TT

A

Qq

11

Gas to Surface Heat Transfer


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Heat transfer to walls is cyclic.

Gas temperature Tg in the combustion chamber varies greatly over and

engine cycle.

Coolant temperature is fairly constant.

Heat transfer from gas to walls occurs due to convection & radiation.

Convection Heat transfer:

Radiation heat transfer between cylinder gas and combustion chamber

walls is

wallgasgcconvconv TThA

Qq

w

w

g

g

wallgas

wallgasgrrad

rad

F

TTTTh

A

Qq

111

21

44


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The Cyclic Integral

dVpWcycle

dVpWcycle

kNWP cycleengine

60

k=1:for two-strokecycle

k=2:for four-stroke

cycle

Thermodynamics of internal combustion Engine

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