Nonconventional Technologies Review – no. 2/2009
ANALYTICAL SOLUTIONS OF LIQUID FUELS PULVERIZATION
*Carmen Violeta Iancu, Nicolae Chiorean, Vasile Bogdan, Dan Craciun
Cercetător Ştiinţific grd III, Universitatea din Oradea, e-mail: ciancu@uoradea.ro
Abstract: Pulverization studies are usually done experimentally. A complete analytical solution of the
problems referring to that drop dimension is very hard to be undertaken because of two reasons: 1. The
wavelength and the oscillation intensity is not known precisely; 2. The drops that result are obtained by
means of a complex drop granulation process. That is formed in the change space.
Keywords: fuel, pulverization, pollution
1. INTRODUCTION
The processing of the crude oil in
refineries allows easy or hard compound
fractionating, depending on its different
utilisation, such as:
- gases (butane, propane)
- petrol;
- aviation petrol;
- lamp petrol;
- diesel;
- light liquid fuels;
hard liquid fuels – fuel oil.
Liquid light fuels and liquid hard fuels are
of the utmost importance for hotbed burning
because of their low price, low evaporation
losses and because of the minimum
explosion danger. Although a series of
preparing methods are needed for bringing
them in the burning state in hotbeds, when it
comes to costs, fuel oil remains the basic fuel
for burning, whenever possible, from
technological point of view.
The base of fuel oil is formed of the black
undistilled high viscosity residue fractions. In
Romania this fuel is standardised: STAS 5180.
We must note the fact that fuel oils (hard
liquid fuels), are composed of a high variety
of hydrocarbures and mixed impurity in
different proportions and compositions,
depending on the deposit of which they are
extracted, that is, on the used crude oil and
on the basic substance processing.
By fuel it is understood any substance
that, reacting to the oxygen in the
atmosphere, transforms its chemical energy
into heat and produces burning gases at high
temperatures,
allowing
cost
efficient
utilisation of the heat in technical and
economical conditions. Thus some organic
substances are excluded from the fuel
category (alcohol and ether), which burn with
the oxygen from the air and produce heat, but
this cannot be used cost efficient from a
technical economical point of view.
Fuels are composed of hydrocarbures,
with high or low content of mineral
substances, included in their composition as
a result of the transformation process of the
organic substance at high pressures and in
the absence of oxygen.
Fuel classification:
- depending on the aggregation state,
fuels are: solid, liquid and gas;
- depending on the procurement
method, fuels are: natural, artificial and
synthetic;
- depending on quality, fuels are:
inferior, medium and superior;
- depending on the purpose of
utilisation, fuels are: technological and
energetic.
Liquid fuels used in numerous domains
are composed of complex mixtures of liquid
hydrocarbures and compounds with the
oxygen, sulfur and nitrogen.
Fuel oil is a hard liquid fuel, designed for
burning in the energetic and industrial kettles
– obtained as a residue from atmospheric
distillation of unfinished petroleum, from the
destructive distillation of the residues as well
as by mixing them with distilled fractions.
2. LIQUID FUELS MAIN
CHARACTERISTICS
PRESENTATION, WHICH
INFLUENCE THE PULVERISATION
PROCESS
The physical chemical characteristics of
the liquid fuels influence the burning process,
47 Nonconventional Technologies Review – no. 2/2009
a test tube, ceases to flow). The flow point is
important for transport and manipulation. For
fuel oil, the freezing point varies from
(5÷42)0C.
6. Ignition temperature
Ignition temperature characterises the
fuels, from the danger of ignition point of
view, during their behaviour in the ignition
process, STAS 51-70.
7. Coke number
Coke number is determined by distilling a
sample until, through vaporisation, remains
only 10% of the initial quantity. This residue is
heated in a container, until no more gases
are disengaged and only coke residue
remains. This weighted amount, represents in
percents, the initial quantity of fuel, the
Condrason number. The determining is done
on STAS 28-70. The Condrason number
generally characterises coke fuel oil capacity.
There is a direct dependence between the
value of this index and the emergence of the
solid unburned at fuel oil combustion. If this
index is higher than 14% fuel oil pulverisation
by vapour is recommended.
The value of coke index for fuel oil
300/50S is higher than assort 70/40S and this
befriends the formation of deposit carbon
deposits on the diuse, deflector ambrasure or
the walls of the hotbed.
8. Burning point.
The burning point is the minimal
temperature, at which the fuel oil vapours on
the surface of the liquid, catches fire and
burns on, when ignited from an external
flame.
the wear out of the pulverisation device as
well as their transport, deposit and
manipulation.
The
physical
chemical
characteristics that influence pulverisation,
vaporisation, ignition and burning of fuels are
also named energetic characteristics.
Energetic characteristics of the liquid
fuels:
1. Volatility
Volatility is the evaporation property of the
liquid fuels that divides fuels in: light, with
high volatility (petrol), light, with reduced
volatility (petroleum), semi-fluids (diesel and
light fuel), heavy (fuel oil).
2. Viscosity
Viscosity is the basic characteristic of the
liquid fuels, similar to the electrical resistance
of a conductor. The liquid fuels are evaluated
depending on this characteristic because it
conditions
the
pumping
possibility,
pulverisation and preheating installation. The
liquid fuel viscosity descends as temperature
rises and vice-versa. There are optimal and
maximum viscosity for pumping and
pulverisation that depend on the pump type,
on debit and on the method of mechanical
pulverisation or by auxiliary fluids (vapour or
compressed air).
3. Superficial tension
Superficial tension is a physical
characteristic of the heavy fuels which, like
viscosity, conditions their pulverisation. For
fuel oil, the superficial tension is usually
lowered together with the initial diminishing of
viscosity and together with the temperature
rise.
4. Density
Density is expressed as conventional
density, that is, the ratio between the
exchange density at 200C and the water
density at 40C. The relative density value
depends on the chemical structure of the fuel.
Determining the density of the liquid fuels is
done with the areometer, with the hydrostatic
balance Mohr – Westphal and the pirometer.
The density at 200C is calculated with the
equation:
q20 = qt+cdx(t-20) [kg/m3]
where: qt - is the density at temperature
0
t[ C] in kg/m3;
cd - is the correction coefficient for fuel
dilatation.
5. Fluidity (flow capacity)
Flow capacity is characterised by the
freezing point (the highest temperature at
which a liquid sample, subjected to cooling in
Physical and chemical characteristics of
the liquid fuels:
1. Thermal power
Thermal power is one of the most
important characteristics of the liquid fuels
and represents the output heat of the
complete burning of 1 kg of fuel. The
difference between the superior and inferior
thermal power, in the case of fuel oils, is of
approx. (1500÷3000) kJ/kg and it is due to
the heat vaporisation of the water contained
in the fuel oil.
2. Specific mass
The specific mass for the burning process
indicates the quantitative component of the
fuel oil, especially the carbon and hydrogen
content. The C/H ratio for a fuel oil is between
(6÷8) %. Together with the rise of
48 Nonconventional Technologies Review – no. 2/2009
because of the air excess SO3 emerges,
which, combined with water (vaporised) from
heat gases, is transformed into sulphuric
acid. The presence of sulphur in fuel oil
creates problems during its burning in vapour
generators as follows:
- the corrosion of heat transfer areas
positioned in the path of burning gases (the
cold part of the tank, the air pre-heater);
- atmosphere pollution.
temperature, the specific mass q diminishes
as in the equation:
qsp = q15-(t-15)x0,0007 [kg/cm3],
where: q15 - is the specific mass at 150C,
[kg/cm3],
t – heating temperature, [0C];
3. The specific heat and thermal
conductivity
For establishing the thermal energy
requirement for heating, the specific heat and
the thermal conductivity coefficient must be
noted. As medium values, the specific
medium heat of fuel oil is 2,1kJ/kg0C. The
thermal conductivity coefficient is 0,5kJ/m h
0
C.
4. Purity
This characteristic refers to ash and
humidity. Differing from the solid fuels, the
liquid fuels are very pure, the humidity and
ash content being very low. Hence, the ash
content is 0,2% for the light fuel and 0,3% for
heavy fuels;
5. Mass heat
Mass heat of the liquid fuels is
determined by:
c = 1,74 + 0,0025 x tcomb[kJ/kg K]
where: tcomb - is the fuel temperature [0C];
6. The raisin and bitumen compounds
The raisin and bitumen compounds are
formed of the heaviest and most carbon rich
hydrocarbures resulted from the distillation
process and can reach percents of approx.
(28÷30)%, thus inculcating the fuel oil with
the next characteristics: black colour and high
viscosity. For the very viscous fuel oils, a part
of these components can be distributed in
solid form and can deposit on the bottom of
tanks. These are presented with a risk of
dishing the diuse;
7. Metal content
The metal content (vanadium, sodium,
nickel) varies, depending on the origin of the
crude petroleum and on the refining scheme.
The sodium and vanadium compounds
generate corrosion phenomena at high
temperatures and lead to the formation of
deposits.
8. Sulphur content
Fuel oil contains organically linked
sulphur and the quantity of sulphur depends
on the fuel oil provenience and on the
processing method. From chemical point of
view, this component is neutral and does not
act through corrosion on the metal parts with
which it comes in contact. Through burning,
the sulphur is transformed in SO2, and
3. THE THEORY OF LIQUID FUEL
LOAD DECOMPOSITION.
PULVERISATION PROCEDURES
The phenomenon of liquid fuel load
decomposition has constituted the object of a
series of theoretical and experimental
researches in the last hundred years. The
first analysis of load instability has been
carried out by Rayleigh (1878). Later on,
physicists and engineers developed the
theory and carried out experiments for
comparing the theoretical and experimental
data.
In the study of jet decomposition Rayleigh
used the method of the little oscillations. He
studied the ideal liquid jet, which decomposes
because of the rotary symmetrical oscillations
or symmetrical spiral. The jet separates when
the length of the oscillation wave surpasses
the
length
of
the
undisturbed
jet
circumference. On first approximation the
length of the wave with maximum amplitude
lopt is:
l opt = 2 ⋅ a ⋅ π ⋅ 2 (1)
and the optimum
stimulation in time is:
μ opt =
σ
6 ⋅ a 3 ⋅ q1
speed
of
(2)
The notes have the following significance:
σ[kg/m] represents the superficial tension,
q1[kg/m3] represents the liquid specific mass
and a[m] represents the gap radius diuse.
Equation (1) shows us that the
wavelength, which leads to separation,
depends only on the load radius and not on
the other physical parameters of the liquid in
the environment where the injection is done.
The experimental researches of Haenlein
have showed non-viscous or viscous liquid jet
decomposition phenomena, liquid that
emerged from the same diuse. The
49 growth
Nonconventional Technologies Review – no. 2/2009
remains constant and the spiral symmetrical
load obtained may be considered as an
elastic bar subjected to compressing and
bending. From equations on the theory of
elasticity result the equations for the force
and moment equilibrium, which act on the
bent part of the load. The deviation δ1 of the
curved axis in report with the straight one is
taken under the form:
decomposition form depended on the spray
speed and on the physical characteristics of
the liquid, such as:: superficial tension σ,
density ρ and dynamic viscosity η.
This research determined Weber A. to
study jet decomposition of the non-viscous
and viscous liquid from a theoretical point of
view.
He
analytically
determined
decomposition conditions and length of the
compact portion of a jet of viscous liquid, also
applying Weber theory of the little oscillations
that he first researched for the case of a liquid
jet which is decomposed due to the rotary
symmetrical oscillations without the influence
of air (the jet is fixed or in an environment
with very low pressure).
As a result the following formulae have
been obtained:
- for the optimum length that is
decomposed:
l opt
⎛
δ1 = δ ⋅ e
*
μ2 + μ ⋅
1
8 ⋅ ql ⋅ a
σ
3
+
6 ⋅ ηi ⋅ a
μ2 + μ ⋅
3⋅ n
ρ⋅a
3
⋅ ζ2 =
σ
2⋅ρ⋅a
3
(
)
⋅ 1 − ζ2 ⋅ ζ2 +
(4)
σ
ρg ⋅ w 2
2 ⋅ ρ ⋅ a2
⋅ ζ 3 ⋅ f 0 (ζ )(5)
Here ζ1 = ζ. was put in the hypothesis that
w speed is low compared to the speed of
sound ws.
In the equation (5), f0(ζ),. has the next
significance:
f 0 (ζ ) =
1,2 ⋅ ρ ⋅ a
μ=
( ) ≥ 0, (6),
( )
− i ⋅ H10 ⋅ i ⋅ ζ
H11 ⋅ i ⋅ ζ
⋅ cos ζ ⋅
χ
a
(7 )
2
⋅
η⋅ ζ2
ρ⋅a2
+μ
10 η
η⋅ζ
⋅
+ 3⋅
+μ
3 ρ⋅a2
ρ⋅a2
2
=
ρ l ⋅ w 2r
ρ⋅a2
1
f 0 (ζ 1 ) +
1
⋅ ζ ⋅ f1 (ζ ) −
2⋅a
a3 ⋅ρ
⋅ ζ 2 (8)
(9)
ζ1
1−ζ 2
η
⋅ 2 ⋅ a ⋅ ρ ⋅ σ ⋅ G (ζ , η' η )(10 )
where: G(ζ, η’/η) – is a transcendental
complicated function;
η’/η. – viscosity report;
η’ – the dynamical viscosity of the
surrounding liquid.
From equation (10) is deduced that
although non-dimensioned amplitude speed
of growth depends on the superficial tension
σ, density ρ, and the a lane radius, as well as
wher: H0(1) and H1(1) are the Hankel
functions after Janhnke-Emde.
In the view formation analysis, Weber
studied the curving of the axial line of the load
under the influence of aerodynamic forces. In
this case, the transversal section of the load
50
χ⎞
⎟
w⎠
The terms which produce, respectively
prevent decomposition are on the right. For
liquids without viscosity, on the left remains
only μ2; these are the maximum values of μ
for a certain determined right part.
Tomotika has proposed the newest
decomposition theory of the liquid load, very
useful for the comparison of the experimental
data. Because Tomotika saw about the
injection of one fluid into another at relatively
low speeds, the report between the viscosity
parameters and load speed equalling zero
has been considered to be important. In the
absence of relatively high speeds, the linear
hydrodynamic
equations
(which
are
expressed by Bessel functions of the first
order of imaginary substantiation) of the
current function can be precisely solved.
Using the edge conditions and neglecting the
inertia forces the next equation has been
deduced for the stimulation wavelength,
which grows the fastest:
Using time integral for the hydrodynamic
potential of the airflow speed which surrounds
the liquid load, Weber has also studied, from
a theoretical point of view, the liquid jet which
moves into air, that is, its drop decomposition
under the action of superficial forces
appeared by means of environment action.
The results of this formal linear analysis lead
to the next equation for load decomposition
under the influence of superficial tension and
exterior environment forces.
3⋅
η⋅ζ2
where: f 1 (ζ ) =
- for the stimulation growth speed in time:
μ opt =
⎝
The
final
equation,
obtained
by
substituting equation (7) in elasticity
equations is written as follows:
⎞
9 ⋅ η l2
⎟ (3)
2 ⋅ σ ⋅ ql ⋅ a ⎟
⎠
⎛
= 2 ⋅ π ⋅ a ⋅ 2⎜1 +
⎜
⎝
μ ⋅⎜ τ +
Nonconventional Technologies Review – no. 2/2009
• Pulverisation installations with two
pumping degrees and fuel return.
the viscosity η, non-dimensional wavelength
(λ/2a=π/3), corresponding to the stimulation
with the maximum growth speed, does not
depend on the superficial tension, density
and load radius.
4. BASIC CHARACTERISTIC OF
THE PULVERISED LIQUID JET
The characteristics of the pulverised liquid
jet are different through the following
elements:
• Pulverisation
filigree
which
is
characterised by the average diameter of the
particles:
- arithmetical average diameter:
k
d m1 =
Fig.1. The non-dimensional wavelength
dependence on the viscosity report (after
Tomotika’s theory)
i =1
⋅ di
i
k
∑n
i =1
[m](11)
i
where: di – the average diameter of drops
on the interval;
ni – the number of drops with dI diameter,
in an interval;
k – number of intervals.
- the average surface diameter:
Because the analytical solving of the
function G(ζ, η’/η) is complicated, the
numerical method has been employed. The
results of equation (10) are given in a
graphical form. Fig.1 presents the relation
between non-dimensional wavelength λ/2a
corresponding to the stimulation which grows
the fastest, and the report η’/η; this relation
has been obtained from Tomotika’s
determined equation.
From the figure results that Tomotika’s
analysis gives minimal wavelengths if the
viscosity are almost equal and maximum
lengths, tending to infinite, in the case when
viscosity report is indefinitely big or null. This
characteristic of the wavelength for different
reports η’/η, corresponds qualitatively with
Rayleigh’s (at the limit) and Weber’s theory
for η’/η.
It results that even if all theories of load
decomposition are based of the capillary load
of Rayleigh, Weber was the only one to have
succeeded in obtaining the theory where the
influence of viscosity report, the superficial
tension and densities are taken into account.
Applying these theories, respectively their
rightness may be clarified only to the extent
that the experimental data confirms them.
The
preheating
and
pulverisation
installations of liquid fuels are divided in two
categories:
• Pulverisation installations with a
pumping degree;
k
d m2 =
∑n
i =1
⋅ d i2
i
[m](12)
k
∑n
i =1
i
- volume average diameter:
k
∑n
i =1
d m3 = 3
i
⋅ d i3
k
∑n
i =1
[m](13)
i
- average Sauter diameter (drop average
diameter in an homogenous cloud, with the
same surface and the same number of drops
ast the studied drop cloud):
k
d mS =
∑n
i =1
k
i
∑n
i =1
i
⋅ d 3i
⋅d
[m](14)
2
i
- the average Vitman diameter (the
average diameter of the drops in an
homogenous cloud with the same number of
drops and the same mass as the studied jet):
51 ∑n
Nonconventional Technologies Review – no. 2/2009
k
d mV 1 =
∑n
i =1
k
i
∑n
i =1
i
⋅ d 4i
⋅d
container pulverisators
appropriate.
[m](15)
d mS =
585 ⋅ σ C
wreal ⋅ ρ c
⎛ ηc
+ 597 ⋅ ⎜
⎜ ρ ⋅σ
c
c
⎝
⎞
⎟
⎟
⎠
0 , 45
1, 5
⎛
G ⋅ρ ⎞
⋅ ⎜⎜1000 ⋅ c a ⎟⎟
Ga ⋅ ρ c ⎠
⎝
[μm](16)
• Pulverisation (dispersion) angle is the
solid angle inside which the fuel drops are
found, being the measure of the tangential
and axial component of the speed of liquid
fuel drops.
The pulverisation angle results from:
tgθ
= 3,05 ⋅ 10 − 2
tgθ 0
⎞n
⎟
⎟
⎠
⎞
⎟⎟
⎠
−0 , 4
(18)
5. CONCLUSIONS
The constitution of the complex
pulverisation laws of the fluids was not
possible in analytical mode until now.
Applying analytical mathematics is generally
limited to the problem determination, thus to
settling the differential equations and to the
contour conditions. The solving of equation is
possible only in some special cases and with
a series of simplifying hypothesis. That’s why,
pulverisation studies are generally conducted
experimentally. But this research too is
marked by great difficulty, mostly conditioned
by formed drop smallness and by its relative
high speed. The introduction of tests on
models brings about major facilitation in the
experimental
research,
allowing
the
possibility of using bigger dimensions and
lower speeds; beside this, the similitude
allows
result
generalisation
of
the
measurements for dynamically alike systems.
Although Rayleigh, Weber and Tomotika
established a series of equations (1 - 10),
which express more or less the pulverisation
process, still, none of them led the problem to
its practical appliance solving and also they
[%](17)
where: r – drop average mass, which
surpass d diameter d (%);
d – drop current diameter;
dm – drop average diameter;
n – particle distribution exponent: n=2.
• Spatial distribution of the liquid flow is
defined as being the pulverised liquid quantity
which is brought on the surface unit in a time
span and is characterised by: maximum
spread area, jet dispersion and pulverisation
angle.
• Jet dispersion is characterised by the
fuel quantity on the area unit supplied in a
time span, perpendicular on the jet axis. Jet
dispersion depends on the pulvetisator type.
The characteristic dispersion curves are
presented in fig.2. Different dispersions are
observed for pulverisators with or without
turbine. For the burning devices, turbine
52 ⎛ D − dl
⋅ ⎜⎜ c
⎝ dd
where: θ, θ0 – real and theoretical
pulverization angles.
R = 1000 ⋅ e
most
Fig.2 Fuel drop dispersion in a drop jet: a
– pulverisator without return; b - turbine
container pulverisator and return.
where: σc – superficial tension of fuel:
σc=(19÷73);
ρc – fuel density: ρc=(0,7÷1.2)g/cm3;
wreal – relative speed between fuel and
pulverization agent;
Gc – fuel debit (ks/s);
Ga – pulverization avent debit (kg/s);
Ηc
–
fuel
dynamic
viscosity:
2
ηc=(0,01÷0,03)Ns/cm
• Pulverisation uniformity is marked out
through drop distribution in a Rosin –
Rommler – Benret (R – R – B) granule-metric
curve.
The drop distribution law in pulverised
liquid fuel jet has the expression:
⎛ d
− ⎜⎜
⎝ dm
the
3
i
The average diameter may be calculated
with the equation that depends on the type of
pulverisator.
Thus,
for
pneumatic
pulverisators, the Sauter diameter is
calculated with Nukiyoma – Tanasam
relation:
are
Nonconventional Technologies Review – no. 2/2009
decomposition, another reunion and so forth.
At a very low drop density, clashes and
reunion do not take place anymore; there is
only the liquid mass division into drops. In the
decomposition space that follows the change
space, new drop decomposition that reached
a limited volume takes place.
From the reasons presented above, the
possibility of a complete analytical solving of
the problem is ruled out. The only and, at the
same time, the most certain way is the one
starting from the jet instability equation (5),
concordant to the similitude theory for
deducing the resemblance criteria which
characterise the pulverisation process.
did not determine the technical interest of
medium and maximum dimension drops.
A complete analytical solution of the
problem referring to drop dimension presents
considerable impediments for two reasons:
a) we do not know precisely the
wavelengths and oscillation intensity which
exists inside the jet and which depend on the
initial conditions of the liquid flow inside the
injector, on the injector design, on the
processing and state of the adjuster surface,
etc;
b) the drops that emerge are the result of
a complex drop granulation process and they
are formed in the change space. Troesch
shows that the pulverisation space is
composed of the abridgement space, change
space and decomposition space. The
abridgement space is the space where the
output jet in the secondary environment forms
a liked mass. The change space follows after
the abridgement space. Liquid masses that
deviate from the jet are decomposed into
drops. At a high drop density, often a drop
reunion
takes
place,
a
repeated
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[1] Ungureanu C., Pănoiu N., Ionel I.:
“Combustibili.
Instalaţii
de
ardere.
Cazane”, Editura Pedagogică Timişoara,
1998.
[2] Pănoiu N.: “Cazane de abur”, Editura
Didactică şi Pedagogică Bucureşti, 1982.
53