Lefebvre A.H., Ballal D.R. Gas Turbine Combustion: Alternative Fuels and Emissions

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220 Gas Turbine Combustion: Alternative Fuels and Emissions, Third Edition

67. Foster, H. H., “Effect of Spark Repetition Rate on the Ignition Limits of a Single

Tubular Combustor,” NACA RM E51J18, 1951.

68. Armstrong, J. C., and Wilsted, H. D., “Investigation of Several Techniques for

Improving Altitude-Starting Limits of Turbojet Engines,” NACA RM E52103,

National Advisory Committee for Aeronautics, Washington DC, 1952.

69. Ballal, D. R., and Lefebvre, A. H., “Ignition and Flame Quenching in Flowing

Gaseous Mixtures,” Proceedings of the Royal Society London Series A, Vol. 357,

No. 1689, pp. 163–81, 1977.

70. Foster, H. H., and Straight, D. M., “Effect of Fuel Volatility Characteristics on

Ignition Energy Requirements in a Turbojet Combustor,” NACA RM E52J21,

1953.

71. Foster, H. H., “Ignition Energy Requirements in a Single Tubular Combustor,”

NACA RM E51A24, National Advisory Committee for Aeronautics, Washington

DC, 1951.

72. Lefebvre, A. H., and Halls, G. A., “Mechanism of Ignition in Gas Turbire

Combustion Chambers,” unpublished Rolls-Royce Report No. 32, 1957.

73. Odgers, J., White, I., and Kretschmer, D., “The Experimental Behavior

of Premixed Flames in Tubes—The Effect of Diluent Gases,” ASME Paper

79-GT-168, American Society of Mechanical Engineers, New York, NY, 1979.

221

Fuel Injection

6.1 Basic Processes in Atomization

6.1.1 introduction

The atomization process is essentially one in which bulk fuel is converted

into small drops. It represents a disruption of the consolidating inuence of

surface tension by the action of internal and external forces. In the absence

of such disruptive forces, surface tension tends to pull the liquid into the form

of a sphere, which has the minimum surface energy. Liquid viscosity has

an adverse effect on atomization because it opposes any change in system

geometry. On the other hand, aerodynamic forces acting on the liquid sur-

face promote the disruption process by applying an external distorting force

to the bulk liquid. Breakup occurs when the magnitude of the disruptive force

just exceeds the consolidating surface tension force.

The atomization process is generally regarded as comprising two separate

processes—primary atomization, in which the fuel stream is broken up into

shreds and ligaments, and secondary atomization, in which the large drops

and globules produced in primary atomization are further disintegrated into

smaller droplets. These processes together determine the detailed character-

istics of the fuel spray in regard to droplet velocities and drop-size distribu-

tions. In practice, they are markedly affected by the internal geometry of the

atomizer, the properties of the gaseous medium into which the fuel stream is

discharged, and the physical properties of the fuel itself.

In the following, we shall discuss the various mechanisms whereby a jet or

sheet of fuel issuing from an atomizer is broken down into drops. A distinc-

tion is made between the two basic mechanisms of atomization—classical

and prompt. Almost all the theoretical and experimental studies carried out

in the past have been devoted to the various classical mechanisms of jet and

sheet breakup, but it is now becoming increasingly recognized that for many

practical atomizers, the prompt mechanism is the primary mode of atomiza-

tion over much of their normal operating range.

The process of jet disintegration is of great importance for the design of

plain-orice pressure nozzles and plain-jet airblast atomizers, whereas the

222 Gas Turbine Combustion: Alternative Fuels and Emissions, Third Edition

mechanism of sheet breakup has direct relevance to the performance of

pressure-swirl and prelming airblast atomizers. In view of their impor-

tance to both jet and sheet disintegration, the various mechanisms of drop

breakup are considered rst.

6.1.2 Breakup of Drops

The atomization process usually involves several interacting mechanisms,

including the splitting up of the larger drops during the nal stages of disin-

tegration. A parameter of prime importance is the Weber number, We, which

is the ratio of the disruptive aerodynamic force, represented by

0.5U

, to

the consolidating surface tension force,

σ D

. The higher the Weber number,

the larger the deforming external pressure forces, compared with the restor-

ing surface tension forces.

The critical condition for drop breakup is achieved when the aerodynamic

drag is just equal to the surface tension force, i.e.,

CDUD,

DAR

πρπσ405

(

)

(6.1)

where C

is the drag coefcient of the drop.

Rearranging these terms provides the dimensionless group

crit

/UD C

8σ

(

)

= ,

(6.2)

where subscript “crit” denotes that a critical condition has been reached.

As the rst term in Equation 6.2 is the Weber number, the equation may be

written as

We /

crit D

= 8 C .

(6.3)

For low-viscosity fuels, experimental data on C

indicate an average value

for 8/C

of around 12, i.e.,

crit

= 12.

(6.4)

For a relative velocity, U

, the maximum stable drop size is obtained from

Equation 6.2 as

max

.= 12

σρ

(6.5)

This equation has some practical signicance because in many calculations

on spray evaporation times it is only necessary to know the diameter of the

largest drop in the spray.

Fuel Injection 223

To account for the inuence of liquid viscosity on drop breakup, Hinze

[1] used a dimensionless group known as Ohnesorge number, Oh, which is

dened as

Oh We=

(

)

05.

Re,

(6.6)

where

(

)

ρσUD

and

Re =

(

)

ρµ

LR L

Substituting for We and Re in Equation 6.6 gives

(

)

µρσD

05.

(6.7)

According to Brodkey [2], the effect of viscosity on the critical Weber number

can be expressed as

We We Oh

crit crit

=+14

16.

(6.8)

where

crit

is the critical Weber number for zero viscosity.

6.1.2.1 Drop Breakup in Turbulent Flow Fields

The foregoing discussion is based on the assumption of a high relative

velocity between the fuel drop and the surrounding air. However, in many

practical situations, a high relative velocity may not exist due to the drops

becoming airborne shortly after leaving the nozzle. It is then more logical

to assume that the dynamic pressure forces of the turbulent motion of the air-

stream determine the size of the largest drop. The critical Weber number thus

becomes

crit A

=ρ σuD

max

(6.9)

where

is the RMS value of the velocity uctuations.

According to Sevik and Park [3],

crit

= 1.04. Hence

max

..= 104

σρ

(6.10)

6.2 Classical Mechanism of Jet and Sheet Breakup

This mechanism relies on the creation of small disturbances, either within

or on the surface of a fuel jet or sheet, which promote the formation of waves

that eventually lead to disintegration into ligaments and then drops. To

224 Gas Turbine Combustion: Alternative Fuels and Emissions, Third Edition

understand the role of viscosity in classical atomization, it is important

to recognize that the primary and secondary atomization processes both

require a nite amount of time for the instabilities, which are an essential

prerequisite for breakup to develop. If, for any reason, this time is length-

ened, the various breakup processes will take place further downstream

from the nozzle under conditions that are less conducive to atomization. In

particular, the relative velocity between air and fuel will be lower, resulting

in larger drops. An increase in fuel viscosity is one parameter that extends

the breakup time. Thus, when atomization proceeds by the classical mecha-

nism, an increase in fuel viscosity is always accompanied by an increase in

mean drop size.

6.2.1 Breakup of Fuel Jets

Rayleigh [4] was among the rst to theoretically study the breakup of liquid

jets. He considered the simple situation of a laminar jet issuing from a circu-

lar orice and postulated a mechanism for breakup, which is illustrated in

Figure 6.1. According to Rayleigh, the growth of small disturbances leads to

breakup when the fastest growing disturbance attains a wavelength, λ

opt

, of

4.51d, where d is the initial jet diameter. After breakup, the cylinder of length

4.51d becomes a spherical drop, so that

451

.()(),dd D×=π4 π6//

(6.11)

Oscillation of jet

causes formation

of neck

Neck breaks due

to surface tension

Drop becomes

spherical

“Satellite”

drop (not

always present)

Neck thins

Jet issues

from orifice

Figure 6.1

Breakup of a plain circular jet.

Fuel Injection 225

hence D, the drop diameter, is obtained as

Dd= 189..

(6.12)

Weber [5] later extended Rayleigh’s work to include the effect of viscosity on

the disintegration of jets into drops. We have

opt

Oh=+

(

)

44413

(6.13)

Note that the value for the constant in this expression of 4.44 corresponds

closely to Rayleigh’s value of 4.51. For low values of Oh, it leads to a drop

diameter, D, of 1.88d as opposed to Rayleigh’s 1.89d. The effect of an increase

in viscosity is to raise Oh, thereby increasing the optimum wavelength for

jet breakup.

Weber also examined the effect of increasing jet velocity on drop size. He

found that raising the jet velocity from 0 to 15 m/s reduced λ

opt

from 4.44d to

2.8d, which produced a reduction in D from 1.88d to 1.61d. Thus, the effect

of increasing the relative velocity between the fuel jet and the surrounding

air is to reduce the optimum wavelength for jet breakup, which results in a

smaller drop size.

At even higher velocities, the atomization process is enhanced by the effect

of relative motion between the surface of the jet and the surrounding air [6].

This aerodynamic interaction causes irregularities in the previously smooth

surface, which become amplied and eventually detach themselves from

the jet surface, as illustrated in the detailed photograph of Figure 6.2, which

was obtained for a water jet by Taylor and Hoyt [7]. The ligaments formed

in this manner subsequently disintegrate into drops, and as the jet veloc-

ity increases, the diameter of the ligaments decreases. When they collapse,

smaller droplets are formed, in accordance with Rayleigh’s theory.

Figure 6.2

High-speed photograph of water jet showing surface wave instabilities and drop formation.

(From Taylor, J.J. and Hoyt, J.W., Journal of Experimental Fluids, 1, 113–20, 1983. With permission

from Springer Science+Business Media.)

226 Gas Turbine Combustion: Alternative Fuels and Emissions, Third Edition

Thus, the various modes of atomization may be classied into four main

groups according to the magnitude of the relative velocity between the jet

and the surrounding air:

1. At low velocities, the growth of axisymmetric oscillations on the

jet surface causes the jet to disintegrate into drops of fairly uniform

size. This is the Rayleigh mechanism of breakup. Drop diameters are

roughly twice the initial jet diameter.

2. With an increase in jet velocity, the basic mechanism of breakup

remains the same, but the interaction between the jet and the sur-

rounding air reduces the optimum wavelength for jet breakup,

which results in a smaller drop size. Drop diameters are about the

same as the jet diameter.

3. With a further increase in jet velocity, droplets are produced by the

unstable growth of small waves on the jet surface caused by interac-

tion between the jet and the surrounding air. These waves become

detached from the jet surface to form ligaments that disintegrate

into drops. Drop diameters are much smaller than the initial jet

diameter.

4. At very high jet velocities, atomization occurs rapidly and is com-

plete within a short distance from the nozzle. Mean drop diameters

are usually less than 80 µm.

Modes 1 to 3 follow the classical mechanisms of atomization, and drop

sizes are very dependent on fuel viscosity, ambient air density, and initial

jet diameter. Mode 4 corresponds to prompt atomization, and drop sizes are

strongly dependent on surface tension, but are fairly insensitive to variations

in viscosity, ambient air density, and initial jet diameter.

6.2.2 Breakup of Fuel Sheets

Most atomizers discharge fuel in the form of a conical sheet. In pressure-swirl

and prelming airblast atomizers, conical sheets are generated when fuel

issues from an orice with a tangential velocity component resulting from

its passage through a number of tangential or helical slots. With pressure-

swirl atomizers, the relative velocity required for atomization is achieved by

injecting the conical sheet of fuel at high velocity into slow-moving air or gas,

whereas in airblast atomizers, one or more high-velocity airstreams (usually

swirling) impinge on a slow-moving, conical sheet of fuel.

The basic mechanisms of sheet integration are broadly the same as those

responsible for jet breakup, as discussed above. According to Fraser et al.

[8], if the relative velocity between the fuel sheet and the surrounding air

is fairly low, a wave motion is generated on the sheet, which causes rings of

Fuel Injection 227

fuel to break away from its leading edge. The volume of fuel contained in the

rings can be estimated as the volume of a ribbon cut out of the sheet with a

thickness equal to that of the sheet at the breakup distance and a width equal

to one-half wavelength of the oscillation (λ

opt

/2). These cylindrical ligaments

then disintegrate into drops of uniform size according to the Rayleigh mech-

anism, as illustrated in Figure 6.3.

With a continuous increase in relative velocity, sheet breakup occurs closer

to the nozzle. Also, the optimum wavelength for breakup becomes smaller

and ligament and drop diameters are reduced accordingly. Finally, at very

high relative velocities, atomization starts at the nozzle exit and the mode of

sheet disintegration changes from classical to prompt.

6.3 Prompt Atomization

In situations where breakup takes place very rapidly, for example, when

high-velocity air jets impinge on a fuel jet or sheet at an appreciable angle,

or when fuel is discharged at very high velocity into stagnant or slow-

moving air, the atomization process may be described as “prompt” [9].

Under these conditions, the jet or sheet has no time to develop a wavy

structure, but is immediately torn into fragments by its vigorous interaction

with the surrounding air. An essential feature of this mode of atomization

is that the rapid and violent disruption of the fuel ensures that the ensuing

drop sizes are largely independent of the initial fuel dimension (jet diam-

eter or sheet thickness). Furthermore, drop sizes must also be independent

of viscosity, which cannot slow down a process that, by denition, occurs

instantaneously.

λ*

Figure 6.3

Successive stages in the idealized breakup of a fuel sheet. (From Fraser, R.P., Eisenklam, P.,

Dombrowski, N., and Hasson, D., AIChE Journal, 8(5), 672–80, 1962. Reproduced with

permission from John Wiley & Sons, Inc.)

228 Gas Turbine Combustion: Alternative Fuels and Emissions, Third Edition

6.4 Classical or Prompt?

As a generalization, it can be stated that for low Weber numbers (correspond-

ing to low atomizing pressures or low atomizing air velocities), the classical

mechanism is dominant, whereas when Weber numbers are high (corre-

sponding to high atomizing pressures or high atomizing air velocities), the

prompt mechanism is dominant. For any given atomizer, whether it is air-

blast or pressure-swirl, the mechanism of fuel breakup may change from one

mode to another with changes in atomizer operating conditions. Consider,

for example, airblast atomizers of the plain-jet or prelming types. At low

atomizing air velocities, these devices function mainly as pressure atomiz-

ers. With an increase in air velocity, they start to perform as airblast atom-

izers, with atomization taking place via the classical mechanism sequence of

wave formation: wave breakup → ligament formation → ligament breakup

→ drops. As air velocities rise even further, the prompt mechanism starts to

intervene in the atomization process. Finally, a velocity is reached above the

point at which the prompt mechanism is dominant.

This change in the mechanism of breakup with change in atomizer operat-

ing conditions would be of academic interest only were it not for the marked

differences exhibited by these two modes of atomization in regard to the

inuence on mean drop size of fuel viscosity, initial jet or sheet dimensions,

and atomizing air pressure [9,10]. Increasing the angle at which the atomizing

air impinges on the fuel stream promotes the changeover from classical to

prompt atomization. As mentioned above, a key parameter in determining

which of these two different atomization modes will dominate at any given

operating condition is the Weber number. For both pressure and airblast atom-

izers, prompt atomization is promoted by an increase in the Weber number.

6.5 Drop-Size Distributions

Due to the random and chaotic nature of the atomization process, the threads

and ligaments formed by the various mechanisms of jet and sheet disinte-

gration vary widely in diameter, and their subsequent breakup yields a cor-

respondingly wide range of drop sizes. Most practical atomizers produce

droplets in the size range from a few microns up to several hundred microns.

Thus, in addition to mean drop size, another parameter of importance in the

denition of a spray is the distribution of drop sizes it contains.

6.5.1 graphical representation of Drop-Size Distributions

A simple method of illustrating the distribution of drop sizes in a spray is

to plot a histogram where each ordinate represents the number of droplets

Fuel Injection 229

whose dimensions fall between the limits D − ΔD/2 and D + ΔD/2. A typi-

cal histogram of this type is shown in Figure 6.4, in which ΔD = 17 µm. As

ΔD is made smaller, the histogram assumes the form of a frequency dis-

tribution curve, as shown in Figure 6.5, provided that it is based on a suf-

ciently large sample. Figure 6.6 illustrates the use of this type of curve to

160

240

Number of drops

320

400

34 68

Drop diameter, µm

102 136 170 204

∆D

Figure 6.4

Typical drop-size histogram.

Drop diameter, D

f(D)

f(D

)

f (D) or f(D

)

Figure 6.5

Drop-size frequency distribution curves based on number and volume.