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CHAPTER 1

INTRODUCTION

1.1 Brief Background

Combustion of liquid fuels provide a major portion of world energy supply. In most

of the practical combustion devices like diesel engines, gas turbines, industrial boilers and

furnaces, liquid rockets, liquid fuel is mixed with the oxidiser and burned in the form of

sprays. There is also an increasing interest in spray technology in material formation,

surface coating, agricultural and medical application, spray cooling in electronic systems

and chemical processes[1]. A spray is a two phase flow involving a liquid as a dispersed

or discrete phase in the form of droplets and a gas as the continuous phase.

It can be regarded as a turbulent, chemically reacting multicomponent flow with

phase change involving thermodynamics, heat and mass transport, chemical kinetics and

fluid dynamics, therefore direct studies on spray combustion may be tedious and

inaccurate. An essential prerequisite for any understanding of spray combustion and its

application in the design of efficient and clean combustion systems is knowledge of laws

governing droplet evaporation and combustion (Fig1.1).

The varied applications of spray combustion have led to studies of both spray

combustion and associated processes such as droplet evaporation and combustion.

Objectives have been to establish design criteria for efficient and stable combustors,

determination of heat transfer rates to combustion chamber surfaces, and to examine the

formation of pollutants such as NOX, CO, CO2 , unburned hydrocarbons and soot.

While many studies are purely experimental, an underlying theme has always been

to develop predictive models for spray processes in order to reduce the cost of

development by cut and try methods. Spray combustion may be steady, unidimensional in

liquid rocket engines; steady, two dimensional in gas turbine; steady, three dimensional in

industrial boilers and an unsteady, three dimensional phenomenon in diesel engines [2],

(Table 1.1).

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These combustion systems utilise liquid fuel sprays in order to increase the fuel

surface area and thus increase the vaporisation and combustion rates. The droplet

mass burning rate is also increased manifold assuming that a single large drop and one

million drops burn under the same ambient conditions. Thus the motivation for spray

and intimately associated droplet vaporisation and combustion is understandable [3].

Once liquid fuel is injected into a combustion chamber, it undergoes atomisation

which causes the liquid to break up into a large number of droplets of various sizes

and velocities.

Depending upon the spray density and ambient conditions, some of the droplets

may continue to shatter, and some may recombine in droplet collisions. Vaporisation

takes place during this time and the fuel vapour produced mixes with the surrounding

gas and then either due to high ambient oxidiser temperature or because of an existing

flame front or due the presence of ignition source, combustion of air-fuel mixture

occurs. The hot products of combustion mix with the vapour and droplets. If enough

residence time is provided, the entire amount of fuel will be converted to combustion

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products. Carbon produced in the combustion process may either continue to oxidise

to produce final gaseous products or may agglomerate to form exhaust particulates.

To simplify the problem, spray can be divided into three zones; the spray

formation region, the vaporisation region and the combustion region. At the end of

spray formation region, one would like to know the droplet size, velocity and number

distribution, air velocity and temperature and droplet temperatures. In some sprays,

the breakup region will overlap the vaporisation region. To follow the process through

vaporisation region, a model is needed for air motion including turbulence and the

interaction of air and droplet momentum. To follow droplet motion, droplet drag

coefficients and droplet vaporisation models are needed.

Understanding the ignition process is necessary for establishing the onset of

burning process. Then droplet burning rate relationships are needed. If emissions are

to be predicted, models for reaction kinetics are required.

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Radiation from carbon particles formed in diffusion flames is an important

component in the energy balance and in the diffusion flame temperature prediction.

Convective heat losses may also play a role and are tied to the general problem of

prediction of mixing, recirculation of products and turbulence.

Additional factor prevalent in diesel type combustion is the presence of high

pressures which may cause droplets to approach their critical point, causing droplet

breakup and a shift in the vaporisation and burning rates. In some engines including

oil burners, residual fuels are used which may breakdown or crack in the liquid

droplet phase causing different burning rates and the formation of residual carbon

shells. In addition to these combustion effects, diesel engines have a very dense

spray in which droplet interaction and local cooling by vaporisation are important.

For small engines and for cold starting conditions, spray typically hits the piston

surface, causing droplets to wet the surface which changes the vaporisation and

mixing mechanisms. Finally, combustion in an enclosure such as in engine cylinder

may also cause combustion induced motion.

Different fluid dynamics and transport phenomena can occur in various ways

with sprays. On the scale of an individual droplet size in a spray, boundary layers

and wakes develop because of the relative motion between the droplet surface and

ambient gas. Other complicated and coupled fluid dynamic factors are; shear driven

internal ciculation of the liquid in the droplet, Stefan flow due to vaporisation, flow

modifications due to closely neighbouring droplets in the spray, droplet distortion

and shattering etc. Complexities on a larger scale include integrated exchanges of

mass, momentum and energy of many droplets in some sub volume of interest with

the gas flow.

The applications in which the mass vaporisation rate is large where ambient

gas is at a very high temperature (1000 K or more), physical behaviour is modified,

coupling between two phases becomes stronger and droplet lifetime ( time taken by

the droplet to vaporise completely ) becomes as short as some of the characteristic

times, like droplet heating time. Liquid and gas phases exhibit different magnitudes

of scales, liquid phase mass diffusion is slower than liquid phase heat diffusion and

extremely slow compared with momentum diffusion in the liquid phase or heat,

momentum diffusion in the gas phase. Mass diffusion plays a vital role in the

vaporisation process for a multicomponent fuel. At first, early in the droplet lifetime,

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the more volatile substance will vaporise from the droplet surface leaving only the

less volatile material that vaporises more slowly. More volatile material still exists in

the droplet interior and tends to diffuse towards the surface because of the

concentration gradients created by prior vaporisation. This diffusion is balanced by

the counter diffusion of the less volatile fuel component towards the droplet interior,

and as a result of this process, different components posses different vaporisation

rates which can vary significantly during the lifetime. There is also a disparity in

scales regarding droplet diameters involved in a spray, varying from a few tens of

microns to a few hundreds of microns in diameter, whereas combustor or flow

chamber dimensions can be several orders of magnitude larger.

The submillimeter scales associated with spray problem have made detailed

experimental measurements very difficult and experiments have been successful

primarily in resolving global characteristics of spray.

Modern nonintrusive laser diagnostics have made resolution possible on a scale

of less than 100 microns, as a result more experimental information has started to

come lately. Nevertheless theory and computation have led experiments in analysing

complex spray systems [4].

1.2 Experimental Methodology and Related Aspects

Experimental study of droplet combustion has broadly employed the

following

methods:

(i) A single droplet suspended at the end of a thin quartz fiber

(ii) A freely falling single droplet or droplet stream

(iii) A porous sphere with liquid fuel being fed to its interior at such a rate that

the surface is just wetted to support the combustion

The suspended droplet experiment can be easily set up and performed.

Furthermore, since the droplet is stationed, detailed cine-microphotography can be

taken of its burning sequence. Because of the thickness of the suspended fiber and its

thickened end, it is difficult to suspend a droplet much smaller than 1mm in

diameter, which is much larger than typical droplet sizes within sprays. This should

not be of serious concern if the size dependence of the phenomenon of interest is

known. However, the suspension fiber also distorts the droplet shape from spherical,

the distortion is especially severe towards the end of the droplet lifetime when the

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droplet size becomes comparable with the suspension fiber and its thickened end.

There is also heat transfer from the flame to the suspension fiber at the point they

intercept.

The amount of heat conducted away from the droplet represents a loss,

although the amount conducted towards the droplet can enhance the vaporisation rate

because heat transfer through the fiber is more efficient than that through the gas

medium between the flame and the droplet surface[5]. Okajima and Kumagai [6]

have shown that the net effect is a slight reduction in the burning rate.

The suspension technique is also limited to fuels which are relatively non

volatile, because otherwise much vaporisation would have occurred during the

period involved with suspending the droplet, charging the chamber with the proper

environment, and applying the ignition stimulus. The problem is particularly severe

for multicomponent fuels whose composition can be altered from a prepared value

by an extent which is not known because of preferential vaporisation of components

with different volatilities.

Free droplet experiments offer the advantages of small sizes, non-interference

from suspension fiber, and the capability of using volatile fuels. However, the

experimental methodology is generally more complex and delicate. Furthermore,

since the droplets are not stationary, it is usually more involved to obtain detailed

photography. Their free fall motion, together with their continuously diminishing

size, also implies that the intensity of forced convection continuously changes.

The porous sphere experiment is truly steady state one and therefore most

closely conforms to the assumption of the 2d law− . This experiment allows detailed

probing of the flame structure. Its main drawbacks are the excessively large size and

the preclusion of observing certain transient aspects, which are inherently present

during droplet combustion.

All combustion experiments conducted under the influence of gravity are

complicated by buoyancy. For droplet combustion the effects are manifested in two

ways. First, the burning rate is increased because of the enhanced transport rates.

Second, the flame is usually so severely distorted from spherical symmetry that it is

not meaningful to identify a flame “diameter”. The distortion increases with the

droplet size and therefore is particularly serious for experiments using suspended

droplet and porous sphere techniques.

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Two techniques have been employed at minimising or eliminating buoyancy,

Kumagai and his associates [6,7] conducted single droplet experiment in a freely

falling chamber or “drop tower”. By further impulsively pulling the suspension fiber

upward as free fall starts, a gravity free unsuspended droplet can be obtained. This is

probably the most desired technique to study spherically symmetric droplet

combustion. The experiment however, is an extremely sophisticated one in that

degree of precision and synchronisation is required, especially the procedure

involved with freeing the droplet from the suspension fiber. The experiment also

needs a high droplet tower with at least one second of free fall, in order to allow for

the time to consume a droplet with initial diameter of the order of 1mm.

Drop Towers

Drop towers provide easier access to a microgravity (μg) environment and

many facilities of this type have been developed by individual workers.

These facilities generally involve test times less than 1s, which require free fall

distances less than 5m. The capabilities of drop towers to sustain low gravity

conditions varies with specific design, but it is not difficult to achieve values smaller

than 10-3g. Longer test times require more sophisticated facilities with drop towers

at NASA Lewis and elsewhere in the United States and Europe providing 2-5s at μg

down to 10-4 – 10-6 g and a new facility in Japan providing 10s test times at similar

conditions [8]. A number of experimental studies are being carried out at NASA’s

Microgravity Combustion Programme [9]. A disadvantage of most free fall facilities

having longer test times, however, is that the test apparatus is subjected to a

considerable shock load, of the order of 100g at the end of a drop test. The 10s drop

tower in Japan is an exception, however, and has relatively modest deceleration

rates. Thus, at the current time, an interesting array of test facilities and

instrumentation are available for microgravity combustion tests in drop towers with

more advanced laser diagnostics in the offing.

A frustrating feature of these facilities, however, is that 2-10s is a very short

time to develop combustion processes and to achieve the steady state conditions for

combustion experiments that are easiest to interpret. This has prompted the

development of aircraft and space facilities in spite of their costs and more limited

availability.

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Droplet Combustion Under Near Zero Gravity (Microgravity) Conditions

The absence of gravity simplifies the study of the controlling mechanisms in

combustion because of the absence of buoyancy. This helps in the verification of

theoretical models. From the fire safety point of view, there is a lack of knowledge

about the combustion behavior of materials in a low gravity environment.

In recent years, the subject of microgravity droplet combustion has gained

importance because of the opportunities offered by it in studying complex natural

phenomenon like fire hazards which cannot be studied successfully on the ground in

the presence of gravity.

While sophisticated tools have been developed for combustion research, truly

significant progress has been hindered by the lack of “clean” and well defined

combustion and flame phenomena through which individual processes can be

isolated and studied in depth. A major cause of difficulty has been buoyancy.

It is therefore not unrealistic to anticipate that the current interest in

microgravity combustion if sustained, could usher in the fifth period of combustion

research, during which many of the fundamental issues of combustion and fire safety

are finally resolved in a rigorous manner.

Microgravity offers new opportunity for fundamental studies of combustion

phenomena, there now is ample evidence that our current understanding of fire and

explosion hazards at normal gravity has questionable relevance at microgravity

conditions. These microgravity experimental results show the following

inadequacies of the 2d law− :

During a short initial period, the droplet size hardly changes. This is caused by

droplet heating. The instantaneous flame to droplet radius ratio /f lr r or /F D is not

a constant but varies with time (Fig 1.2). This is caused by fuel vapour accumulation.

The experimental value of /F D is smaller than the theoretical value. This is due to

variable property effects.

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1.3 Isolated, Spherically Symmetric, Steady State Liquid Droplet Combustion

Since early 1950s, it has been recognised that symmetrical burning of an

isolated droplet (relative velocity between the droplet surface and the surrounding

gas is zero or 0gRe = ) represents an ideal situation in which to study the complex

coupling of chemical reactions and two phase flow with phase change. The

simplified geometry of the combustion environment along with certain simplifying

assumptions concerning physical and chemical processes permits mathematical

simplification of the problem and leads to simple description of the combustion

process.

Initially, these studies provided a fundamental foundation upon which to

develop more applied, empirical descriptions of spray combustion. The combustion

of a single isolated liquid droplet in an infinite oxidising medium is shown

schematically in (Fig 1.1).

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Important assumptions of steady state droplet combustion model are:

An isolated, single component, spherical liquid fuel droplet burns in a quiescent

infinite oxidising medium surrounded by a spherically symmetric flame. There are

no effects of buoyancy, natural or forced convection. The droplet is at its boiling

point temperature, vaporising with a steady rate, obeying the 2d law− .

The fuel is a pure liquid with zero solubility for gases. Phase equilibrium

prevails at the liquid-vapour interface.

The ambient pressure is uniform and subcritical.

The gas phase is asuumed quasi-steady and is divided in two zones. The inner

zone between the droplet surface and flame consists of only fuel vapour while the

outer zone consists of oxidiser and combustion products.

Fuel and oxidiser react instantaneously in stoichiometric proportions at the

flame. Chemical kinetics is assumed to be infinitely fast, resulting in the flame being

represented as an infinitesimally thin sheet.

The gas phase Lewis number gLe is assumed unity.

Conduction is the only mode of heat transport. Radiation heat transfer is assumed

negligible.

Thermodynamic and transport properties are treated as constants. Ideal gas

relations can be used for the gas phase.

In this spherically symmetric geometrical configuration (Fig1.1), fuel vaporises

at the droplet surface and diffuses outward while oxidiser diffuses inward from the

ambient environment. The fuel and oxidiser react stoichiometrically, resulting in a

zone of intense reaction (a non premixed flame). Heat is transported via conduction

and radiation outward from the flame to ambient atmosphere (infinity) and inward

back to the droplet surface. The heat deposited at the droplet surface is balanced by

the evaporation process at the vapour/liquid interface. The “classical” 2d law− for

droplet combustion was first formulated in the 1950s by assuming that gas phase

chemical reaction is infinitely fast with respect to gas phase transport, thus confining

chemical reaction to an infinitesimally thin sheet.

The 2d law− theory predicts that the burning constant bk , instantaneous flame

to droplet diameter ratio /F D and flame temperature fT remain constant

throughout the droplet burning lifetime and are described by the following equations:

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( ) [ ]2 8ln 1g

b Tpg l

dk D Bdt C

λρ

≡ − = + (1.1)

[ ][ ]ln 1

ln ( 1) /TBF

D ν ν+

=+

(1.2)

[ 1](1 )f T b

pg

LT B TC

νν

= − ++

(1.3)

where, bk → burning constant

D → instantaneous droplet diameter

gλ → thermal conductivity of the gas

pgC → specific heat of the gas

lρ → liquid density

TB → heat transfer number

F → instataneous flame diameter

ν → (A/F)stoich on mass basis

fT → flame temperature

T∞→ ambient temperature

bT → droplet boiling point temperature

L→ latent heat of vaporisation

chΔ → heat of combustion of liquid fuel

The heat transfer number BT , is a non dimensional thermodynamic parameter

given by:

( )c

pg b

T

h C T TB

Lν ∞Δ

+ −= (1.4)

Equations (1.1) and (1.3) reproduce experimental observations to varying

degrees of success. For single component droplets, the burning constant does not

vary in many cases over most of the droplet lifetime. Also, the qualitative predictions

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are quite correct as experiments show that burning constant increases with increasing

/g pgCλ and decreases with increasinglρ . Quantitative agreement between

experiment and equation (1.1) can also be achieved, provided that appropriate

selections of transport properties are made. The flame temperature predicted by

equation (1.3) is essentially the adiabatic flame temperature of the given fuel

oxidiser system assuming no dissociation or infinitesimally thin flame thickness.

Quantitative agreement in this case can be obtained by assuming a suitably enhanced

specific heat to account for deficiencies.

The /F D ratio which varies throughout the combustion lifetime is vastly over-

predicted under all circumstances by equation (1.2). It can be said that the

quantitative agreement is much worse for the flame position than for the burning

constant.

1.4 Advanced Approaches Isolated, Spherically Symmetric, Unsteady Liquid Droplet Combustion (Droplet Heating and Fuel Accumulation Effects)

By accounting for transient heating of the liquid droplet Fig1.3(a), it is possible

to explain the experimentally observed initial period during which the droplet

burning rate is low even with infinitely fast chemistry. An energy balance at the

droplet surface shows that heat conducted to the surface from the gas phase balances

with heat lost by conduction into the liquid interior and heat lost from the surface

due to vaporisation.

Initially, when the droplet temperature is low, much of the heat supplied to the

surface is conducted inward, resulting in a lower rate of vaporisation. As a result

there exists a temperature gradient within the droplet. Once the droplet heats up

towards the liquid boiling point, little heat is conduced into the liquid interior and the

vaporisation rate reaches its quasi-steady value.

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Accounting for the accumulation of fuel vapour between the liquid droplet and

the flame reproduces the observed variation in the flame position with time

Fig1.3(b). In the 2d law− formulation, it is implicitly assumed that the rate of

vaporisation at the droplet surface is directly equal to the rate of consumption of fuel

at the flame sheet.

Due to initial loss of temperature at the droplet surface because of droplet

heating, only a small mass of fuel is evaporated from the droplet surface and as a

result the flame must be close to the droplet surface to achieve stoichiometric

combustion of fuel and oxidiser. But as the droplet heating period ends and more

surface evaporation of fuel starts and moreover due to close proximity of the flame,

there is an abundance of fuel vapour resulting in its accumulation between droplet

surface and flame which pushes the flame outwards or away from the droplet

surface.

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The following conclusions can be made regarding spherically symmetric,

unsteady droplet burning for a single component fuel in an environment, whose

pressure is also sufficiently below the critical pressure of the fuel:

Droplet heating proceeds fairly rapidly during the droplet lifetime.

The period of heating subsequently to ignition is expected to be not too sensitive to

fuel volatility.

Droplet heating only slightly prolongs the total burning time of the droplet.

The flame diameter is not constant but varies with time. It increases first and

then decreases.Whereas /F D ratio increases throughout the droplet burning history,

unlike the quasi-steady theory, where it has a constant value. This is caused by fuel

vapour accumulation.

The experimental /F D value is much smaller than the theoretical (quasi-

steady value). This is caused by variable property effect.

The droplet temperature distribution may remain non uniform and temporally

varying throughout the lifetime.

The existence of the fuel vapour accumulation process implies that overall mass

conservation for the fuel vapour should read, vaporisation rate at droplet surface =

consumption rate at flame + accumulation rate in inner region. For above formula,

the last term is absent in the 2d law− .

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1.5 Variable Properties

In advanced approaches related to droplet combustion modelling,

thermodynamic and transport properties are not treated as constant as assumed in

simplified theories.

In most of these studies, thermophysical properties are strong functions of

temperature, concentration and pressure.

Actually 2d law− assumes a non convective, steady state spherical combustion

together with constant properties assumption. In an actual combustion chamber,

temperature may vary from a few hundred degrees to a few thousand degrees in the

gas surrounding the droplet. Pressure may vary from atmospheric to many times the

critical pressure of the fuel (depending upon the engine). Fuels used may be

multicomponent in nature.

These variations are bound to affect the thermophysical properties, which must

be evaluated as a function of temperature, pressure and concentration as the situation

suggests. Only then the modelling results obtained will be closer to the experimental

observations under the same burning conditions.

The spherically symmetric diffusion controlled combustion model is usually

broken up into two regions, the inflame zone (between the droplet surface and flame)

and the post flame zone ( between the flame surface and ambient atmosphere ).

Hubbard et al. [10] numerically integrated the governing equations of energy (in

both liquid and gas phases) and mass, momentum and species equations in gas

phase, for a diffusion controlled droplet combustion model. These authors used

different empirical relations for calculating the thermophysical properties and came

to the conclusion that one can use the arithmetic mean or empirical results of

Sparrow and Gregg (popularly known as Sparrow’s one third rule).

1.6 Multicomponent Droplet Vaporisation / Combustion

A liquid composed of a multitude of chemical species is called a

multicomponent (MC) liquid. The overwhelming majority of liquids used for power

production are MC liquids; these include gasoline, diesel fuel and kerosene. When

used in combustion chambers, these liquids are atomised into fine sprays in order to

increase the surface area per volume, so as to promote evaporation. Typically, the

modelling of MC fuel evaporating drops has been performed either with single

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component species surrogates or with mixtures of two chemical species to represent

the MC fuel.

Much of the earlier studies on droplet combustion used pure fuels.

Multicomponent effects were not considered to be serious for the reason that the

requirements of combustor efficiency and emission were generally not stringent.

However, recent developments in engine design and fuel formulation indicate that

multicomponent effects will become progressively more important in the utilisation

of liquid fuels. Combustion processes within engine will be more tightly controlled

to further improve efficiency and reduce emissions.

The synthetic fuels derived from coal tar, sand and oil shale will have more

complex composition as well as higher and wider boiling point ranges.

There also exists considerable interest in the utilisation of such hybrid fuels as

water/oil emulsions, alcohol/oil solutions and emulsions, and coal/oil mixtures. The

widely different physical and chemical properties of the constituents of these hybrid

fuels necessitate consideration of multicomponent effects in an essential way.

To understand heterogeneous multicomponent fuel combustion either as a

droplet or in some other form (e.g. pool burning), the following factors have to be

considered:

The relative concentrations and volatility of the liquid constituents, as would be

expected. The miscibility of the liquid constituents. This controls the phase change

characteristics. The internal circulation which influences the rate with which the

liquid components can be brought to the surface where vaporisation takes place.

There are various other complications that occur when a multicomponent liquid

is considered. Different components vaporise at different rates, creating

concentration gradients in the liquid phase and causing liquid phase mass diffusion.

The theory requires the coupled solutions of liquid phase species continuity and heat

diffusion equations, and multicomponent phase equilibrium relations (typically

Roult’s law). Liquid phase mass diffusion is much slower than liquid phase heat

diffusion so that thin diffusion layers can occur near the surface, especially at high

ambient temperatures at which the surface regression rate is large. The more volatile

substances tend to vaporise faster at first until their surface concentration values are

diminished (Fig 1.4) and further vaporisation of those quantities becomes liquid

phase mass diffusion controlled [11].

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Mass diffusion the liquid phase is of primary importance in the vaporisation

process for a multicomponent fuel. Therefore for studying multicomponent droplet

evaporation / combustion, a detailed liquid phase analysis is a prior step.

1.7 Supercritical Droplet Vaporisation / Combustion

In some applications like diesel engines, liquid rockets and gas turbine engines,

fuel droplets are subjected to temperatures and pressures beyond their critical point

during the combustion process. This phenomenon is shown in the phase diagram

(Fig1.5). This gives rise to a number of interesting phenomena at the critical

point. Of particular importance in the study are the changes in the specific heat ( )pc

of the fuel, which goes to infinity, and the latent heat of vaporisation which goes to

zero at the critical point. In many liquid fueled engines and combustors, the liquid

fuel droplets undergo a supercritical phase transition prior to combustion.

The droplets pass from a subcritical liquid state to a supercritical fluid state,

accompanied by mass transfer. However, current combustion models of such

systems describe the transition by subcritical means. High pressures and supercritical

conditions in diesel engines, jet engines, and liquid rocket engines present a

challenge to the modelling and the fundamental understanding of the mechanism

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controlling the mixing and combustion behaviour of these devices. Accordingly,

there has been re-emergence of investigations to provide a detailed description of the

fundamental phenomenon inherent in these conditions.

Unresolved and controversial topics of interest include prediction of phase

equilibrium at high and supercritical pressure including the choice of a proper

equation of state. Present study has employed Redlich-Kwong equation of state

given below as equation (1.5):

0.5( )uR T aP

v b v v b T= −

− + (1.5)

Where uR , T and v are the universal gas constant, absolute temperature and

molar volume respectively and ,a b are constants; definition of critical interface;

importance of liquid diffusion; significance of transport property singularities in the

neighborhood of critical mixing conditions; influence of convection and 2d law−

behaviour at supercritical conditions. There are key challenges associated with

operation at near critical and supercritical conditions in order to increase efficiency

and combustion rate processes. The distinction between liquids and gases disappears

at high pressures above the thermodynamic critical point which has a strong non

linear dependence on the composition.

This introduces some crucial phenomena that were neglected decades ago when

the composition distinction between the original liquid and its surrounding gases in

the combustor were neglected. Also, the reduced surface tension can cause a new

mechanism to be the rate controlling factor for energy conversion.

High pressure and supercritical ambient conditions have a considerable

influence on the mechanisms controlling engine behaviour and performance. Most of

these effects are related to droplet behaviour. When liquid is injected into a

combustion chamber that is filled with a gas at supercritical thermodynamic

conditions, all aspects of the combustion process from atomisation to chemical

reaction can be expected to depart significantly from the better known subcritical

patterns. Studies in the past have investigated how and to what extent supercritical

conditions may affect various aspects of the combustion of an isolated droplet in a

quiescent environment. Detailed reviews on the subject are contributed by Givler

and Abraham [12], and recently by Kuo [13].

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1.8 Extension to Convective Environment

A simplified approach involves the extension of spherically symmetric model

to forced convective situation using empirical relations which are a function of gas

phase Nusselt, Reynolds and Prandtl numbers [2]. Lefebvre [14] has given an

equation for mass burning rate using these empirical relations.

Another expression for burning rate is provided by Turns [15]. One commonly

used emperical result is Ranz and Marshall correlation that corrects the spherically

symmetric vaporisation rate for forced convective environment [4].

As evident from preceding discussion, vaporising droplet is a challenging

multidisciplinary issue. In general there is a relative motion between the droplet and

ambient gas. The Reynolds number based on relative velocity, droplet diameter, and

gas phase properties is an important descriptor of the gaseous flow field, apart from

internal liquid circulation.

These flow features have a direct impact on the exchanges of mass, momentum

and energy between the gas and liquid phases. Apart from these issues, there is a

problem of continuously changing droplet radius.

Important assumptions invoked in droplet modelling studies which simplify the

problem but at the same time preserve the essential physics are as follows:

A single, isolated liquid fuel droplet vaporises in a quiescent infinite oxidising

medium; system is spherically symmetric with no effects of buoyancy, free or forced

convection (relative velocity between the droplet surface and ambient gas is

negligible implying 0gRe = and Weber number (We) is less than 1);

Droplet processes are diffusion controlled with the consideration of only

ordinary diffusion; pressure is uniform and constant (less than critical pressure of the

fuel); fuel vapour and oxidiser react instantaneously in stoichiometric proportions at

the flame, infinitely fast chemical kinetics is considered resulting in the flame being

represented as an infinitely thin sheet; conduction is the only mode of heat transport

and radiation heat transport is neglected; droplet is at its boiling point temperature

and droplet heating is ignored; liquid droplet is made up of single chemical species

(single component fuel with a definite boiling point); products of combustion are not

absorbed in the liquid; all gas phase processes are assumed to be occurring in a

quasi-steady manner; gas phase mixture behaves as an ideal gas; phase equilibrium

is stated at the droplet-gas interface; kinetic energy and viscous dissipation effects

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are negligible; Soret and Dufour effects are neglected; gas phase thermophysical and

transport properties and the product of density and mass diffusivity are constant; gas

phase Lewis number is unity.

Above assumptions can be relaxed depending upon the prevailing ambient

pressure and temperature, liquid and gas phase composition and fluid dynamical

aspects of the problem.

1.9 Objective of the Present Study

As evident from the preceding discussion, droplet modelling is fundamental for

understanding spray combustion phenomena and plays a vital role in spray

calculations.

The aim of the present work is to quantify the effects of different type of fuels,

ambient pressure and temperature, ambient gas phase composition, convection and

droplet sizes on important combustion parameters like flame temperature, flame

location and its movement (governed by flame diameter, /F D ratio, flame stand off

distance), droplet temperature, mass burning rate, vaporisation / burning constant,

droplet lifetime, and on emission characteristics of important combustion products

around the burning droplet by developing simple but realistic droplet sub models

represented by computer programmes that can be successfully incorporated in spray

codes.

1.10 Organisation of Thesis

The present work is divided into six chapters. Practical relevance of Droplet

Combustion and its different aspects are introduced in the first chapter. The second

chapter of Literature Review deals with the current understanding of the subject,

potential areas which may require further research and motivation for the present

study. Development of different droplet submodels with important assumptions and

solution technique is discussed in chapter 3 of Problem Formulation and Solution

Technique. Chapter 4 deals with the determination of thermodynamic and transport

properties of fuels chosen for the present study. In chapter 5, results of this study are

presented and discussed in light of the existing experimental and modelling data for

the same conditions. They include variation of basic parameters in the gas phase for

a spherical droplet, forced convection and droplet heating effects and general

behaviour of emissions for a burning droplet. Remaining results include the effects

of variation of ambient pressure ,P∞ ambient temperature ,T∞ ambient gas

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composition , ,oY ∞ droplet size and fuels on important combustion characteristics of

single droplets.

Conclusions/contributions of the study with further scope for future work is

discussed in chapter 6.