Spark Ignition Engine Combustionweb.itu.edu.tr/~sorusbay/SI/LN05.pdf · Spark Ignition Engine...

Prof.Dr. Cem SORUŞBAY - ITU Automotive Laboratories

Spark Ignition Engine Combustion MAK652E Combustion Modelling in Engines Prof.Dr. Cem Soruşbay


Contents

Engine modelling – Introduction

Classification

Thermodynamic Models

Single-zone models

Multi-zone models


Introduction

Currently 90 % of the energy used for transportation, power production and heating is produced by combustion of liquid, solid and gaseous fuels.

Combustion studies;

scientific aspects of combustion process

understanding combustion requires knowledge of thermodynamics, heat and mass transfer and chemical reaction theory

design and performance of specific technologies such

as internal combustion engines, turbines, furnaces etc.


Introduction

Combustion, chemical reaction kinetics

“oxidation reactions which take place very rapidly with conversion of chemical energy to sensible energy, generating heat and light”

Increasing the surface area increses reaction rate – for example liquid sprays in IC engines, flame propagation in turbulent combustion, pulvarised coal combustors etc.

Increasing the temperature also increases reaction rate – the rate of a chemical exothermic reaction increases as the temperature increases.

The rate of such gaseous reaction is often proportional to,

exp (-C/T)

where C is a constant and T is the reaction absolute temperature.

Since fuel reactions are exothermic, thermal energy is released. If the energy release rate is faster than it is transported away by heat transfer, energy release rate increases and eventually explosion occurs.


Introduction

In a spark ignition engine a premixed flame occurs and it is a propagating flame


Introduction


Introduction

Open thermodynamic system


Introduction

Experimental investigation – low and high p


Historical Perspective

In ancient and primitive cultures fire was primarily a mystery to be feared of

It was then accepted as one of the four constituent elements of all matter (earth, air, fire and water) until Renaissance

Carnot (1796 – 1832) and some other scientists began to study key nature of matter, energy and combustion

“Reflections on the Motive Power of Fire” by Carnot : thermodynamic cycle which convert a fraction of energy transfer from a source (such as fire) into work with remaining energy being rejected into a sink.

This provided a theoretical basis for an absolute temperature scale.


Thermal Efficiency

Carnot postulated an ideal thermodynamic cycle having the maximum theoretical thermal efficiency – desired work output to required heat input.

TL is the lowest cycle absolute temperature

TH is the highest cycle absolute temperature

A high Carnot cycle efficiency implies high cycle temperature, which is consistant with combustion process.

addedflux heat

(Power)net work

inputenergy required

outputenergy desired

H

L

T

T1



Formulation of classical thermodynamics

Development of modern heat engine – which was the major factor in Industial Revolution

Development of power systems have raised the material quality of life



Scientific work on combustion started in the 17th century

Early 1800 Joule proved that heat is a form of energy and not a material substance

1855, Robert Bunsen measured flame speed and temperature, collected flame enthalpy data by a calorimeter.

1868, Mallard conducted study on flame propagation (Mallard and Le Chatelier model).

In the 20th century rapid progress has been made on combustion studies

1928 first Combustion Institute meeting – same year first theoretical treatment of diffusion flame height and shape by Burke and Schumann



Combustion modelling started in 1940’s

With the advances in computer technology (high-speed computers) in 1960’s and 1970’s modelling studies were also advanced.

Today computer hardware is suitable for modelling calculation to be performed merging chemical kinetics and fluid dynamics to investigate many aspects of combustion systems.


Energy and Combustion

We will look at gas-phase chemical reactions that liberate

substantial energy as heat

The chemistry and physics of combustion take place within few millionths of a second -

destruction and rearrangement of molecules which rapidly release energy, require temperatures of 1600 – 2200 oC

High speed computers and laser anemometers are required to investigate microscopic nature of combustion


Fuel

Fuel can be considered as a finite resource of chemical potential energy in which energy stored in the molecular structure of particular compounds is released by complex chemical reactions

Fuels should have,

high energy density (content)

high heat of combustion (heat release)

good thermal stability (storage)

low vapour pressure (volatility)

nontoxicity (environmental impact)


Fuel – Engine Interface

combustion driven heat engines

intermittent combustion continuous combustion

internal external internal external

Diesel – Brayton

compression ign gas turbine Rankine Stirling

direct inj indirect inj

Otto – spark ignition

homogeneous stratified charge

charge


Fuel – Engine Interface

The state of the art in engineering of current power and propulsion

systems in use is in the increasing the combustion and thermal efficiencies, and to develop new fuels and engines to operate

Developments in future engine technology to,

minimize pollutant emissions

maximize energy efficiency

optimize tolerance to a wider variety of fuels


Engine Modelling

Two different approaches :

Thermodynamic models

Multidimensional models

Unburned gas

Flame front

Piston

Burned gas


Engine Modelling


based on the First Law of Thermodynamics, used to analyse the performance and emissions of SI-engines

classified into two groups : single zone models and multi zone models

In single –zone models the mixture composition, pressure and temperature of the combustion chamber are assumed to be uniform. The chemical heat release is either specified (predictive analysis) or calculated from pressure diagrams (heat release analysis).

In multi-zone models the mixture in the combustion chamber is divided into two or three regions : unburnt and burnt regions and the quench layer. These models require the specification of the burning velocity and flame front geometry.


Engine Modelling

One-zone approach Two-zone approach


Engine Modelling

Dimensional Models (CFD approach)

dimensional models consider the spatial and temporal variations of the velocity, temperature and pressure fields in one, two or three dimensions.

In thermodynamic models, spatial flow variations are considered – local velocity and temperature fields are not calculated.

Governing equations for the flow field are solved – various coordinate systems can be used according to the formulation of the geometrical conditions of the specified problem.

Turbulence model equations are also solved simultaneously.

Requires more computer storage memory and speed.



Single-zone Models

cylinder charge is assumed to be uniform in pressure, temperature and composition.

heat release analysis : experimentally determined pressure diagrams are used as an input to predict the heat release rate or the mass burning rate – they ignore the flame propagation and combustion chamber geometry

if the mass burning rate is specified, they can be used as predictive tools – mass burning rate depends on combustion duration, ignition angle, engine geometry, equivalence ratio, residual mass etc. – therefore tuning may be required to predict the pressure diagrams in different engines or different operating conditions for the same engine



If mass transfer into and out of the cylinder during intake and exhaust, the heat transfer between in-cylinder gases and cylinder head, piston, and cylinder liner, and the rate of charge burning (energy release from fuel) are all known, the energy and mass conservation equations permit the cylinder pressure and work transfer to the piston to be calculated.

These models predict engine operating characteristics - indicated power, mean effective pressure, specific fuel consumption etc,

They effectively follow the changing thermodynamic and chemical state of the working fluid through the four strokes of the cycle - they are called engine cycle simulations.



Thermodynamic analysis Phenomenological models

Intake

Compression

Combustion

Expansion

Exhaust

Cylinder and valve geometry

Thermodynamic properties

Flow rates

Heat transfer

Transport properties

Combustion rate

Emission mechanism



Starting point is the First Law of Thermodynamics applied to an open system.

During each process, submodels are used - describing geometric features of the cylinder and valves or ports, thermodynamic properties of the unburnt and burnt gases, mass and energy transfer across system boundaries and the combustion process.



Single-zone Models

define the state of the cylinder charge in terms of average properties, do not distinguish between burnt and unburnt gases and assume the cylinder charge is homogeneous.

heat transfer and gas flow phenomena can be included in simple approaches.

combustion in a single zone model can be considered as a heat addition process – cylinder charge is regarded as a simple fluid.

The 1st Law of Thermodynamics applied to an open system,

(1)

p, T and m are the pressure, temperature and mass of the cylinder charge respectively, u is the mixture specific internal energy

iihmd

dQ

d

dVp

d

mud

)(


Single-zone Models

cv specific heat at constant volume,

V combustion chamber volume,

dQ/d heat loss,

hi specific enthalpy of the gases flowing into the cylinder with mass flow rate of mi

To reference temperature,

uo internal energy of formation at ref temperature

crank shaft angle

In the absance of injection and flow into crevices, dm/d = 0

T

T

v

o

o

dTcuu


Single-zone Models

(2)

first term is the heat release by combustion,

final term is mass flow rate into the crevices,

conservation of mass applied to combustion chamber,

(3)

when cylinder p is high, h corresponds to that of the combustion chamber,

(during expansion stroke h is (4) that of the gases in crevices)

d

dmuh

d

dQ

d

dVp

d

dTmc

d

dQ CRv

CH )(

d

dm

d

dm CR

m

pVuh

0 / ddmCR

0 / ddmCR


Single-zone Models

if crevice volume and T assumed constant, and crevice p is equal to that of cylinder charge, mass flow rate into crevices will be,

(5)

crevice temperature is set equal to Tw ,the wall temperature, and VCR is the crevice volume

substituting eqn (5) into eqns (2) and (3) gives heat released by combustion - when heat transfer losses are specified.

w

CRCR

RT

ddpV

d

dm

/


Single-zone Models

Cylinder charge is considered as an ideal gas,

(6)

where gas constant R, is a function of mixture pressure, temperature, equivalence ratio ( ) and mass fraction of the residual gases (f ).

mRTpV

) , , ,( fpTfR


Single-zone Models

Eqns (3) to (6) are substituted into eqn (2) to obtain an eqn which relates the heat release rate to combustion chamber p and V, mass fraction of residual gases, wall T and crevice V.

The resulting eqn can be used in heat release analyses if experimentally determined p diagrams are used to predict the heat release rate.

Alternatively resulting eqn can be used as a predictive tool if heat release rate dQCH/d is specified as a function of crank shaft angle to yield mixture p and T – mass burning rate can be specified by Wiebe function or other.


Single-zone Models

If the mass flow rates into crevices are neglected, the mass of the cylinder charge is constant.

where mb and mu are the mass of burnt and unburnt gases

Mass fraction of the burnt gases can be calculated from Wiebe function.

0 d

dm

d

dm

d

dm ub


Single-zone Models

Wiebe function

(7)

o crank shaft angle at start of combustion

b combustion duration

xb mass fraction of burnt gases

3 < a <10 parameters

1 < m < 3

(a = 5 and m = 2)

1

exp1

m

b

obb a

m

mx

2

/cos1 bobb

m

mx


Single-zone Models

heat release rate will be,

C is the heat of combustion which is approx

dmb / d is obtained from eqn (7)

The burnt gases in cylinder are close to thermodynamic equilibrium, their properties are usually specified through curve fits to thermodynamic equilibrium calculations

- curve fit reduces computation time.

NO formation is not an equilibrium process - effected by the T gradients and the oxygen concentration : Zeldovich mechanism

d

dmC

d

dQ bCH

o

b

o

u uu


Single-zone Models

Single zone models do not account for combustion chamber geometry, except in a global manner through V in eqns (2), (4) and (6)

These models do not consider flame propagation phenomena and do not account for the burnt and unburnt gases in combustion chamber.

Cylinder volume change as a function of crank shaft angle can be calculated by,

AxVV c

4

2DA

22 sin cos rlrlrPQlrx


Single-zone Models


Single-zone Models

Heat transfer losses can be calculated from Nusselt-Reynolds number correlations as,

h the film heat transfer coefficient,

L characteristic dimension,

the gas thermal conductivity,

v characteristic velocity

a=0.037 , b=0.8 , c=0.3

pc Pr

cbaLh

Nu Pr Re

L Re


Single-zone Models

Instantaneous wall heat transfer is given by Woschni, during combustion-

expansion c”1 = 2.28 c”2 = 0.00324

TThAq ww

53.02.0

8.0

8.0

00326.0

TB

vvph combmot

pismot vcv "

1

motd

comb ppVp

TVcv

11

1"

2

60

2SNvpis


Single-zone Models

In addition to convective heat transfer, radiative heat transfer can also be important.

Annand’s eqn for heat transfer

N engine speed [rpm]

A area exposed for heat transfer

a,b,c constants

thermal conductivity of gas

D engine bore diameter

T gas temperature

Tw wall temperature

44 Re 6

ww

bL TTcTTD

a

N

A

d

dQ


Multi-zone Models

They account for combustion chamber geometry and for the presence of burnt and unburnt gases

Cylinder mixture is divided into burnt and unburnt zones, which are seperated from each other be a surface of discontinuity – an infinitesimally thin flame that propagates into the unburnt gases.

Composition and temperature of the burnt and unburnt gases are different, the pressure is uniform throughout the combustion chamber.

The assumption of uniform T in unburnt gases is reasonable, but in burnt gases there is significant T gradients - due to differences between first burning then compressing the burnt gas (compared to first compressing and then burning the fresh charge)

Multi-zone models do not consider the flame structure – but may account for quenching.


Multi-zone Models

Unburned gas

Flame front

Piston

Propagation

Burned gas


Assumptions

Assumptions made are,

uniform pressure throughout the combustion chamber

uniform temperature in the burnt and unburnt gases

no heat transfer between unburnt and burnt gases at flame front

unburnt gases frozen and burnt gases in chemical equilibrium


Governing Equations

bbuu umumU

mmm bu

T

T

v

o

o

dTcuu

b

o

T

T

bv

o

bb dTcuu ,u

o

T

T

uv

o

uu dTcuu ,

d

dm

d

dm

d

dm

d

dm

d

dm CRbCRubu ,,


Governing Equations

mVVV bu

uuuu TRmpV bbbb TRmpV

d

dmh

d

dmh

d

dQ

d

dVp

d

umd CRu

u

Ru

uuuuu ,,

d

dmh

d

dmh

d

dQ

d

dVp

d

umd CRb

b

Rb

ubbbb ,,


Governing Equations

Here, subscripts

b and u burnt and unburnt

R chemical reaction

CR flow into crevice volume

so last two terms denote the heat fluxes associated with chemical reactions and heat fluxes associated with flow into crevices respectively.

Also,

which is the combustion rate or the mass burning rate.

d

dm

d

dm

d

dmcRbRu

,,


Leakage and Flow into Crevices

In the absence of leakage and flow into crevices,

If there is leakage,

d

dm

dθ

dmuu,R

d

dm

dθ

dmbb,R

d

dm

d

dm

dθ

dm CRbCRu ,,

d

dm

d

dm

dθ

dm RbCRbb ,,

d

dm

d

dm

dθ

dm RuCRuu ,,


Governing Equations

So, arranging eqns,

here,

is the specific enthalpy of unburnt gases if

and the specific enthalpy of burnt gases if

u

uuu

m

Vpuh

d

dmhu

d

dmuh

d

dQ

d

dVp

d

dTcm

CRu

u

Ru

uuuuu

uvu

,,

,

d

dmhu

d

dmuh

d

dQ

d

dVp

d

dTcm

CRb

b

Rb

bbbbb

bvb

,,

,

b

bbb

m

Vpuh

h 0 /, ddm CRu

0 /, ddm CRb


Governing Equations

Leakage of burnt and unburnt gases can be calculated by,

Combustion chamber pressure is obtained by adding state eqns,

The gas constant is a function of equivalence ratio, residual gas mass fraction, pressure and temperature (Tu for Ru and Tb for Rb).

w

CRCR

RT

ddpV

d

dm

/

bbbuuubu TRmTRmVVp


Governing Equations

Mass fraction of burnt and unburnt gases,

differentiating the above eqn for xb w.r.t. crank shaft angle gives,

or

m

mx u

u m

mx b

b

d

dm

d

dm

d

dxm

d

dmx

d

dm CRbcbb

b ,

d

dxm

d

dmx

d

dm

d

dm bb

CRbc ,


Governing Equations

The first order O.D.E. for mu, mb, Vb, Tu, Tb, mc and p are obtained.

Vu can be calculated by knowing Vb

This system of eqns is not closed - more unknowns than the number of eqns.

Closure can be achieved by specifying mass burning rate,

and the geometry of the flame front.

Flame front is usually assumed to propagate spherically from the spark plug, and the mass burning rate (or turbulent flame speed) is either specified or calculated by phenomenological models.

Wiebe function described for single-zone models gives mass burning rate,

d

dmc

1

exp1

m

b

obb a

m

mx


Mass Burning Rate

Spherical flame front assumption - leads to large underpredictions of flame surface area, as this assumptions constrains flame surface area-to-volume ratio to be absolute minimum and flame is trancated by combustion chamber walls.

Interaction of flame front with combustion generated flow field may result in highly curved flames, aerodynamic and geometrical strechings and flame quenching.

Combustion can be approached by

phenomenological models that calculate mass burning rate from physical considerations,

specifying turbulent flame speed for the calculation of the amount of fuel burnt

specifying the mass burning rate.


Mass Burning Rate

Some models attempt to predict the burning rate from fundamental physical quantities such as turbulence intensity, integral length scale, Kolmogorov eddy size, kinetics of fuel-air oxidation process.

The purpouse is to predict ignition delay and combustion rate as a function of engine design and operating conditions.

The burning process can be modeled as a flame of surface area Af - usually assumed to be a sphere propogating through the unburnt gas mixture of density u with a turbulent flame speed ST such that,

Tfub SA

d

dm


Mass Burning Rate

Experiments show that ST is proportional to the turbulent intensity, u’

Some researchers assumed that ST is proportional to the laminar flame speed SL with a proportionality constant that is a function of u’ - in this approach effects of turbulent length scale on ST are not included.

Turbulent length scale is very important during ignition and extinction - where quenching due to velocity gradients is important.

If

where g is a function of engine speed, the resulting model is unable to predict combustion duration as a function of the ignition delay time and equivalence ratio.

LT SgS


Calculation of the Mass Burning Rate

Blizard - Keck Model

BK model considers the effect of u’ (turbulence intensity), SL (laminar flame speed) and (turbulence length scale) on burning rate and assumes that large eddies entrain the fresh mixture, whereas small eddies burn in a laminar maner with a characteristic time,

and mass entrainment of fresh mixture into flame front is,

where ue is the entrainment velocity

BK model assumes that ent. velocity is proportional to inlet gas speed and that is proportional to valve lift.

It is an algebraic model.

Lb S/

efue uA

dt

dm



Algebraic Models

These models use conservation equations for the turbulence kinetic energy to calculate entrainment velocity, but specify turbulent length scale algebraically (or from equilibrium considerations)

Poulos and Heywood,

calculated from the mean flow (K) and turbulence kinetic energy (k) conservation equations.

'uSu Le

m

mKP

Vm

dt

dK exh

2

2

intint

2/1

3

2'

ku

m

mkmP

dt

dk exh

2/1

2

m

kKLCP

L

mk2/3

3/2



Here is the length scale of energy containing eddies, is the mean flow rate, is the dissipation of turbulence kinetic energy, L is a length scale, C is a constant.

int and exh indicate flow into and out of the cylinder

Length scale is assumed to be equal to L,

where D is the cylinder diameter.

Turbulent flow field is assumed homogeneous and isotropic (as flame generated turbulence is neglected).

4/ 2D

VL

m



Combustion process is modelled as the entrainment of the unburnt mixture by the flame and combustion within the flame,

where f is the residual mass fraction.

Lfue SuA

dt

dm '

b

beb mm

dt

dm

L

bS

1062.4706.4 2

,

ff

p

p

T

T

S

S

refref

u

refL

L

2/1

'15

LuL


Specification of the Turbulent Flame Speed

Turbulent flame speed can be specified as a function of turbulence intensity, laminar flame speed, and engine rpm.

These models assume that flame propogates spherically through the combustion chamber.

Turbulent flame speed,

during flame development, until flame radius reaches approx 0.03 m

expansion velocity can be obtained by,

LL

T

S

u

S

S '01.41

2/1

03.0

'01.41

f

LtdevelopmenflameL

TR

S

u

S

S

1b

u

L

T

S

S


This eqn is physically explained by,

f is the turbulence enhancement factor which is proportional to engine speed, n in [rpm]

Hiroyashu and Kadota model

Rubin and McLean model

LT SfS

nf 00197.01

nf 002.01

L

B

T SAS Re



Andrews model

where is the Taylor microscale

Re fS

S

L

T

' Re

u



Mass Burning Rate

Mass fraction of burnt gas is specified - by models like Wiebe function

Tfuc SA

d

dm

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