IGNITION OF A LIQUID FUEL UNDER HIGH INTENSITY RADIATION

Report Number AFOSR-TR-80-0A76

‘chnical Information

Center Accession No. ADA-086283

Final Progress Report including progress from

May 1, 1978 to September 30, 1979

Takashi Kashiwagi

Howard R. Baum

and

John A. Rockett

Center for Fire Research

National Bureau of Standards

Washington, D.C. 20234

This work is supported by the Air Force Office of Scientific Research

under Contract AFOSR-ISSA- 79-0006

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IGNITION OF A LIQUID FUEL UNDER HIGH INTENSITY

FINAL

1 May 78 - 20 Sep 79

RADIATION 6. PERFORMING ORG. REPORT NUMBER

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TAKASHI KASHIWAGI

HOWARD R BAUM

JOHN A ROCKETT

AFOSR-ISSA-79-0006

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CENTER FOR FIRE RESEARCH

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SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reverse side if necessary and Identify by block number)

RADIATIVE IGNITION MECHANISMS

LASER SUPPORTED IGNITION AND COMBUSTION

HYDROCARBON IGNITION

AIRCRAFT FUEL IGNITION

AIRCRAFT FIRES AND EXPLOSIONS

20. ABSTRACT (Continue on reverse side If necessary and identify by block number)

This report summarizes progress in the study of ignition of a liquid fuel under

high intensity radiation. It describes an experimental study of the key processes during ignition and a theoretical modeling study of part of the phenomena

during the ignition period. The experiments were conducted using a CW CO 2 laser

with incident fluxes from 1000 to 5000 W/cm^ and n-decane as the flammable

liquid. High speed photographs of ignition events showed a periodic depression

in the decane surface, probably caused by the thrust of the strong decane vapor

flux; radial outward motion of the liquid, probably caused by a surface

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SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)
UlNL.LiAabit- 1C.U SECURITY CLASSIFICATION OF THIS PAGEfHTian Data Enterad) tension, gradient was also observed. The first appearance of flame was in

the gas phase well above the surface. The proposed autoignition mechanism

of decane by the CO 2 laser is the absorption of the incident laser beam by

the vapor plume. The effect on ignition of the incident angle of the laser

beam with respect to the decane surface was studied from 90° to 30°. On

reducing the incident angle, the ignition delay time becomes longer and the

minimum incident flux for ignition increases significantly. A theoretical

model describing the flow motion in the gas phase caused by a heated surface was calculated numerically and solved anlaytically

.

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IGNITION OF A LIQUID FUEL UNDER HIGH INTENSITY RADIATION

Takashi Kashlwagi, Howard R. Baum and John A. Rockett

Abstract

This report summarizes progress in the study of ignition of a

liquid fuel under high intensity radiation; the period covered is

from May 1, 1977 to September 30, 1979. It describes an experimental study of the key processes during ignition and a theoretical

modeling study of part of the phenomena during the ignition period.

The experiments were conducted using a GW CO 2 laser with incident

fluxes from 1000 to 5000 W/cm^ and n-decane as the flammable liquid.

High speed photographs of ignition events showed a periodic depression

in the decane surface, probably caused by the thrust of the strong

decane vapor flux; radial outward motion of the liquid, probably

caused by a surface tension gradient was also observed. The first

appearance of flame was in the gas phase well above the surface.

The proposed autoignition mechanism of decane by the CO 2 laser is

the absorption of the incident laser beam by the vapor plume. The

effect on Ignition of the incident angle of the laser beam with

respect to the decane surface was studied from 90® to 30° . On

reducing the incident angle, the ignition delay time becomes longer

and the minimum incident flux for ignition increases significantly.

A theoretical model describing the flow motion in the gas phase

caused by a heated surface was calculated numerically and solved

analytically.
1 . INTRODUCTION

Laser technology has been rapidly advancing in the last several

years. Power outputs of modern lasers have Increased significantly and

these lasers can now be used as tactical weapons. A high power laser

weapon can ignite aircraft fuel by fuel tank penetration and can thus

cause a fire or explosion on the aircraft. However, the ignition of

flammable liquids by laser radiation has been little studied and is

little understood; the ignition of solids [1,2] and the vaporization of

liquids by high power lasers [3,4] have been studied. The objective of

this study is to obtain a fundamental understanding of the mechanism of

ignition of flammable liquids by a high power laser.

This paper is a final progress report of this study during the

period from May 1977 to September 1979. It describes an experimental

study of the key processes during ignition and a theoretical study of

the modeling of a part of the phenomena during the ignition period.

2 . EXPERIMENTAL APPARATUS

A schematic illustration of the experimental apparatus is provided

in figure 1. A photograph of the equipment is shown in figure 2. A

Coherent Radiation Model 41 CO 2 laser* emits an approximately 5 mm

diameter beam at 1/e intensity. Beam power can be varied from 240 to

350 watts in the fundamental mode with a Gaussian power distribution

across the beam. The incident flux distribution at the sample surface

position is measured at normal incidence prior to each ignition experiment

by traversing a water cooled calorimeter with 0.25 mm diameter sensing

*In order to adequately describe materials and experimental procedures it was occasionally necessary to identify commercial products by manufacturer's name

or label. In no Instance does such identification imply endorsement by the

National Bureau of Standards nor does it imply that the particular product

or equipment is necessarily the best available for that purpose.

2
element. The maximum value of the incident flux measured in this manner

is used as the incident radiant flux in this study.

A rotating mirror is used as a shutter to provide a step-function

irradiance and remains open through the ignition event. Ignition is defined

by the first light emission detected by an EMI 7656 photomultiplier, the

output of which is recorded by an oscillographic recorder with maximum

resolution of ± 1 msec. At the onset of flaming, a step-function-like output

of the -photomultiplier is observed. This provides an unambiguous measure

of the time of ignition. In this study, n-decane was used as the liquid fuel

and air as the environmental gas.

The experimental chamber is 34 cm inside diameter with 40 cm depth. The

chamber is mounted on bearings and can be rotated 90 degrees by a worm gear.

The incident angle of the laser beam is varied by changing locations of two

mirrors and by the rotation of the chamber as shown in figure 1. After each

ignition test, the gas in the chamber is evacuated by a vacuum pump and

fresh air admitted.

The fuel container is fastened onto a support plate which is mounted

on the chamber wall. When the chamber rotates, the support plate tilts and

the axis of the container is along the incident laser beam. To make the

container top parallel to the horizontal decane surface, the top of the

container is cut to be horizontal when it is tilted, thus a separate container

is needed for each angle. Decane is always filled to the top of the container.

3
A square aluminum container with schlieren quality glass windows for

two sides was used when high speed motion pictures were taken to observe

the flow motion in decane near the decane surface.

3. EXPERIMENTAL RESULTS

The first series of experiments was conducted to find a container size

which did not affect ignition delay time under various experimental conditions.

The effect of the depth of the container on ignition delay time was studied

with a 5 cm diameter container under the vertical radiation mode (incident

angle Q = 90°). The depth of the container was varied from 1.2 cm to 34 cm.

Ignition delay times with various depths are shown in figure 3, which indicate

little effect of depth on ignition delay time.

Similarly, the effect of the diameter of the container on ignition

delay time was studied with a 5 cm deep container at 0 = 90° under two

different incident radiant fluxes. The diameter of the container was varied

from 2.5 cm to 10 cm. Results are shown in figure 4a at the incident radiant

flux = 4160 W/cm^ and in figure 4b at = 1670 W/cm^. At high flux,

there was no effect of the diameter of the container on ignition delay time.

But at low flux, ignition delay time became significantly longer for the

container whose diameter was less than 4 cm. Apparently the motion in the

liquid, which will be described later, causes some heat loss to the container

wall and delays the ignition. From these results, a container of 6 cm diameter

and 5 cm depth filled to the top was selected and used for all experiments

described in this report.

In ignition experiments, bursting sounds similar to those when water

droplets fall onto a heated plate were clearly heard during the ignition

period, indicating the rapid boiling of decane during the experiment. At low

4
radiant flux a large volume of decane was heated during the long ignition

delay and a large amount of decane evaporated. Under these conditions,

ignition was associated with a puff sound and the size of the flame immediately

after ignition tended to be larger than that at high incident radiant flux.

Two types of high speed motion pictures were taken to observe the

behavior of the decane surface and the onset of ignition; some were taken

from the top and others were taken from the side through the glass window.

Some enlarged frames of the former are shown in figure 5. The incident

angle of the laser beam to the surface was 30 degrees and the shape of the

container top was the cross sectional cut of a cylinder tilted at 60

degrees. The direction of the laser beam was from the left. The top

figure (5a) shows decane surface in the container before the laser

irradiates the decane. The figure (5b) shows the development of surface

waves traveling rapidly outward from the irradiated area shortly after

the laser irradiation was started. Surface waves traveled rapidly along

the surface, shown in figure (5c) , and reached the wall of the container

as shown in figure 5d. Under the low incident flux used in figure 5,

surface waves could reach the wall and be reflected. Under the high

incident flux, ignition occurred before the surface waves reached the

wall. In figure 5e, the onset of ignition was observed in the gas phase

far from the decane surface, (light area at the left above the surface)

Rapid flame spread along the plume of the decane vapor was observed

immediately after ignition as shown in figure 5f. High speed color

pictures, under the high incident flux, show a small, bright yellow rod

shape of color at the location where the incident laser beam interacted

with the plume of the decane vapor. This was a much brighter color than

the rest of the flame and it remained until the laser beam was turned

off.

5
The side view of the behavior of the decane surface is shown in

figures 6 and 7. In figure 6, the incident angle of the laser beam from

the left to the surface, 0, was 30 degrees. In figure 7, the incident

angle was 90 degrees and the pictures are negative. Both figures show

that a bubble like depression at the surface is formed shortly after the

irradiation starts and this depression grows rapidly to about 3 mm

diameter. We infer that the depression is due to vaporization thrust

and is not a bubble since: (1) if it were a bubble, then its top surface

would be irradiated in the area of peak flux and would be vaporized

immediately upon formation leaving the bubble open to collapse and, (2)

the early pictures indicate vaguely a rising plume of decane vapor above

the depression. This implies vigorous vaporization instead of bubble

formation (which implies weak vaporization)

In figures 6 and 7, about 10 msec after the irradiation starts, the

depression has started to collapse. At 9 = 30°, the depression started

to collapse from the left side from which the incident laser beam was

coming. However, at 0 = 90°, the depression collapsed symmetrically to

small bubbles. At 0 = 30°, the formation of the next depression took

about 40 msec, but at 9 = 90°, the next depression was formed rapidly

after a delay of about 10 to 15 msec. At 0 = 30°, the second depression was smaller and not as distinct as the first one and the depression tended

to be formed more distinctly at the side opposite that of the approaching

incident laser beam. Again, the second depression collapsed and this

cycle of the formation of the depression and its collapse was repeated

during the ignition period and even after ignition. At 0 = 90°, this cycle was repeated with much faster frequency than that at 0 = 30°. At 0 = 30°,

the first appearance of flame was about 10 mm above the decane surface and

about 20 mm away from the irradiated area. Flame spread from the point of

first appearance of flame upward, presumably due to buoyancy, and then spread

toward the irradiated area of the decane surface along the laser beam. The

6
observed rod shape flame is similar to that shown in figure 5. At 0 = 90°, the

first appearance of flame was above the viewing area of the picture and the

flame spread down, as is shown in figure 7.

It is interesting to analyze the mechanism of the formation of the

depression more closely. Since the depression distance caused by photon pressure

with the flux range used in this study is at most 0.1 ram compared to the

observed 3 mm, the effect of photon pressure on the formation of the depression

is negligible. Vigorous vaporization of decane by the incident flux used

in this study can produce a significant momentum flux leaving the surface

which in turn presses down on that surface. The momentum of the decane

vapor leaving the surface should be balanced with the surface tension force

caused by the area increase and the hydrostatic force. The velocity of

decane vapor leaving the surface can be estimated from this balance.

+ pgh = PgVg2 (1)

where r is the surface tension, 23.4 g/sec^ for decane [5], R is the radius

of the depression, 3 mm, p liquid decane density, 0.73 g/cm^, h distance of the

surface depression, 3 mm, and pg density of decane vapor at boiling temperature

174°C [6], 0.00423 g/cm^. Then, the velocity of decane vapor leaving the

surface vg is approximately

Vg ^ 300 cm/sec

From close examination of the pictures in figures 6 and 7, the speed of the

rising plume is at least this order of magnitude. The amount of the energy

required to produce this rate of vaporization of decane is estimated by

7
where Q is latent of heat of vaporization of decane, 263 j/g [5]. Then,

using the same values for p and V as above, the endothermic flux for

vaporization is about 330 W/cm^ which is well below the incident radiant flux.

Therefore, the incident radiant flux in this study is high enough to provide

the estimated amount of vaporization needed to cause the observed depression

on the decane surface. Therefore, it is reasonable to consider that the

surface depression observed during the ignition period is in fact caused by

the momentum of decane vapor leaving the decane surface. A further confirmation that the vigorous vaporization causes the depression of the decane

surface by its momentum was attempted by taking high speed schlieren pictures

during the ignition period. Preliminary study of these indicates that the

vaporization of decane in the present experimental condition behaves like an

explosion and it appears to throw off not only decane vapor but also fragments

of liquid decane, as shown in figure 8. However, further study with more

high speed schlieren pictures is necessary to confirm this mechanism.

The boiling temperature of decane is 174“C [6] and the gas phase

temperature near the surface could rise to this temperature by conduction/

convection from the decane surface. However, this is too low a temperature

to initiate a gas phase chemical reaction and to attain a runaway condition

(roughly 600°C is required for ignition [7]). From the observation of the

location of the first appearance of flame in figures 5 and 6, it is apparent

that the absorption of the laser beam by the decane vapor is the key heating

mechanism in the gas phase causing ignition. This was confirmed by the

ignition of vapor from decane heated on an electrical hot plate by passing

the laser beam through the vapor parallel to but above the liquid decane

surface.

8
To absorb enough energy from the laser beam to heat the gas phase to

ignition, a sufficient amount of decane vapor is required at the location

of the first appearance of flame. Judging from the distance between the

irradiated area and the ignition location shown in figure 6, the transport

process of decane vapor from the surface to the location of the first appearance of flame may well be the key factor for ignition under low incident

laser angles. As described above, decane vapor/decane fragments are released

from the decane surface with significant inertia into the gas phase. It

appears in figure 8 that this explosion like vaporization could distribute

a sufficient amount of momentum for decane vapor/ fragments to go in all

directions. However, in figure 6, the release of decane vapor appears

directly upward rather than in all directions (although the pictures are

direct rather than schlieren) . Since the density of decane vapor at its

boiling temperature is much greater than that of air, decane vapor will

tend to sink back to the decane surface. After decane vapor is released

into the gas phase by the jet-like flow, cooled decane vapor starts to fall

and may intersect the laser beam. The direction of the release of decane

vapor/fragments is presently not conclusive. Further study is necessary to

clarify the transport process of decane vapor/ fragments from the irradiation

surface to the location of the first appearance of flame.

The periodic collapse of the depression on the decane surface can be

explained as follows; After the release of decane vapor/fragments into the

gas phase, they start to absorb the incident laser energy, which reduces the

laser flux reaching the decane surface. This reduction in the laser flux

is significant for polymeric solids [8,9] and can be significant for decane.

This reduces the amount of vaporization, which reduces the amount of depression.

9
The reduction in the amount of vaporization decreases the amount of decane

vapor in the gas phase and the absorption of the laser energy decreases.

More laser flux reaches the decane surface causing more vaporization and

this cycle repeats periodically. Also, there may well be some effect of

the flow motion in the decane caused by surface tension, and the collapse

of the surface depression. The rapid outward radial movement shown in

figure 5 was generated by surface waves and thereby the surface tension

gradient caused by the steep temperature gradient along the radial direction

[10,11]. This movement was confirmed by the rapid radial outward displacement of a small chip of plastic foam floating on the decane surface near

the irradiated area. This flow removes part of the absorbed energy of the

incident laser beam from the irradiated area. It also induces a convective

upward flow from below to the irradiated area, satisfying the conservation

of the mass. Therefore, the flow motion driven by a surface tension gradient

can modify the amount of available energy for vaporization and the behavior

of the surface depression.

The absorption characteristic of liquid decane in the region of the

laser lines was determined by measurement of the absorption coefficient.

Linear absorbance (log I^/I) was measured with a Perkin-Elmer Model 180

Infrared Photometer using a variable length cell from wavenumber 1100 to

800 cm ^ . Results are shown in figure 9 with various thicknesses of the

cell. Absorption coefficients of liquid decane can be calculated as:

K

2.30

I log Y

Io

( 2 )

10
where I is the thickness of the cell. However, figure 9 shows that the

absorbance of the decane too sensitive to the wavenumber. Therefore, to

obtain the absorption coefficient of decane, the fine structure of the emission

spectrum of the CO 2 laser cannot be neglected. Then, the spectral average

extinction coefficient becomes

K =

y; J^a)^

(3)

the fine line structure of the emission spectrum of the CO 2 laser is shown

in figure 10. Since the width of the laser lines is much narrower than

those of the absorption bands, equation (3) can be written as

Using data from figure 9 and 10, the calculated absorption coefficient of

liquid decane is 16 cm ^ which is much smaller than about 90 cm ^ for solid

polystyrene [1]. Therefore, the laser beam can penetrate further into the

decane. At 3 mm depth in the decane, the radiant flux is about 20 W/cm^.

With a smaller value of absorption coefficient for decane than that for

solid polystyrene, the laser beam heats a larger volume of decane than

of polystyrene. This is one of the reasons why decane requires a higher

external radiant flux for ignition and its ignition delay time is longer

than that of polystyrene at the same external radiant flux.

11
The relationship between the ignition delay time and the incident

radiant flux was studied with various incident angles. Results are shown

in figures 11a, b, and c. Although the relationship was measured at 9 = 75°

and 60°, there was little difference among 0 = 90°, 0 = 75° and 0 = 60°.

Results at 9 = 75° and 60° are not Included since the plots are similar to

figures 11 a-c. Roughly, when the incident radiant flux was below 2500 W/cm^,

Ignition delay time increased significantly with a further decrease in the

incident radiant flux. A peculiar trend was noted. Ignition delay time

appeared to increase slightly with the incident radiant flux for extremely

high flux. This was observed at all five incident angles studied in this

work. At present, it is not clear what mechanism causes this trend.

The effect of the incident laser beam angle on ignition delay time and

the minimum incident radiant flux for ignition, is clearly shown in

figures 11 and 12. When the incident radiant flux is above roughly 2500 W/cm^,

the effect of the incident laser beam angle on ignition delay time is not

great. Ignition delay times at 0 = 30° are roughly 40% longer than those at

0 = 90°. However, for incident radiant fluxes below 2500 W/cm^, this angle

effect becomes significant with a large increase of ignition delay time

found at the shallower incident beam angles. Also, the minimum incident

radiant flux for ignition increases with a decrease in the incident laser

angle. At 9 = 90° and 75°, I . 1000 W/cm^. However, at 0 = 60°, I . min min

1400 W/cm^ and at 0 = 45°, I . 1800 W/cm^ and finally at 9 = 30°, I . ’ min min

2000 W/cm^.

These trends of ignition delay time and the minimum incident radiant

flux for ignition under various incident laser angles can be explained by:

12
1) the change of incident radiant flux distribution with incident angle of

the laser beam to the decane surface; 2) the change of the absorption path

length of the incident laser beam through the plume of decane vapor; 3) the

change of the surface reflectance for the incident laser beam.

In the first mechanism, the actual incident radiant flux to the decane

surface varies with the incident angle of the laser beam. At 6 = 90°, the

shape of the laser beam on the decane surface is equal to the normal radiant

flux measured by the flux meter. However, at angles other than 6 = 90°, the

shape of the laser beam on the decane surface is ellipsoidal and the Irradiated

area increases with a decrease in the incident angle. This reduces the actual

incident radiant flux per unit area. The relationship between the normal

incident flux, I^, and the actual incident flux, I, is

I = I sin 6 o

If this were the controlling mechanistic effect of the incident angle on the

ignition, then for an I^ = 1000 W/cm^ at 90°, should be 1150 W/cm^,

1400 W/cm^ and 2000 W/cm^ at 0 = 60°, 45° and 30° respectively. These values

are roughly 25% less than the measured results except at 0 = 30. At 0 = 30°,

the predicted and measured values agree. Nevertheless, the predicted trend,

in which the minimum externa] normal radiant flux for ignition increases with

decreasing incident angle, agrees with the observed one. However, the sin 0

correction does not explain the observed relationship between the ignition

delay time and the actual incident flux, I. For example, in figure 12, the

ignition delay time for an I^ = 3000 W/cm^ and 0 = 30° is about 90 msec.

The actual incident flux I with sin 30° would be 1500 W/cm^. However, the

ignition delay time at I^ = 1500 W/cm^ and 0 = 90° is about 240 msec. Therefore,

13
the effect of the change in the incident radiant flux with the change in

the incident angle can not explain completely the observed effects of the

incident angles on ignition. However, this effect does describe fairly well

the trend of the minimum radiant flux on ignition, in which the controlling

process is apparently the heating of decane.

In the second mechanism, the interaction between the incident laser

beam and decane vapor varies significantly with the incident angle of the

laser beam. At 9 = 90°, the direction of the jet like rising plume is the

same as the incident laser beam and the interaction volume can be very large.

However, decreasing the incident laser angle reduces the interaction volume

significantly. Therefore, changing incident laser angle varies; 1) the total

energy absorbed from the laser beam by decane vapor; 2) the rate of fuel

vaporization due to the change in transmitted flux; 3) the residential flow

time of decane vapor through the laser beam heated path. The net result of

these changes on ignition varies for the same incident angle, depending on

the energy flux in the laser beam. Under high incident flux and near

vertical irradiation, the rate of vaporization is initially high. Due to

the high fuel content of the jet like short plume, it absorbs strongly the

laser energy and its temperature increases rapidly to ignition. Under high

incident flux and oblique irradiation, the rate of vaporization is initially

high. The interaction volume between the incident laser beam and the jet

like short |)lume does not differ significantly from the near vertical

irradiation and ignition occurs quickly due to the strong absorption of the

laser beam.

At low incident radiant flux, the amount of decane vaporized becomes

less and the concentration of decane vapor in the jet like plume becomes less.

14
At near vertical incident laser angles the absorbed energy from the incident

laser beam is spread over the longer height of the jet like plume and the

local absorbed intensity is correspondingly less. Although the local

absorption is less, the total absorption may actually be more and the flux

transmitted through the plume becomes less and the amount of decane vaporizing

may be further reduced. Therefore, imder low incident radiant flux, the

large Interaction volume at near vertical irradiation angles tends to delay

ignition. At oblique incident laser angles, the incident flux to the decane

surface through the smaller interaction volume does not decrease as much as

at near vertical Incident laser angles, thus the vaporization rate decreases

less with time than for near vertical irradiation. This tends to favor

early ignition, but the residential flow time of decane vapor through the

heated gas layer by the absorption becomes less. For nearly vertical incident

angles, the time for decane vapor to flow through the absorptively heated

gas layer is long and eventually it becomes hot enough to trigger the

ignition. For oblique incident laser angles decane vapor cuts diagonally

across the heated gas layer and is heated only for a brief time. The long

ignition delays for low incident flux and oblique incident angles reflect

the long heating time required to raise the fuel vaporization rate sufficiently

that there will be enough decane vapor in the plume to absorb laser energy

and reach the high temperature before passing otit of interattion volume.

This mechanism introduces another parameter, the size of the laser beam,

which was not varied in this study due to the lack of the laser power to

maintain the same flux density over a larger area. If the size of the

laser beam becomes larger, the irradiated area of the decane surface becomes

larger and the pltime of decane vapor becomes wider. The larger beam and

15
wider plume produce a larger interaction volume. Then, the residence time

of a combustible mixture of gases moving through the interaction zone increases.

Absorption of the laser beam energy increases with the longer residence time.

Since the important condition for ignition is that the residence time must

be longer than the gas phase chemical reaction time, the larger beam would

reduce the minimum external radiant flux for ignition.

The third effect, the change in surface reflectance, is estimated by

using Fresnel's equation with Snell's law. Although this estimation is only

qualitative, it can show the trend of the effect of the incident angle on

reflectance. The reflectance, R, against the decane surface, of the laser

beam which has a polarization direction parallel to the plane of the incidence,

can be written as: [12]

index of the transmitted medium, decane. Although the value of the refractive

index of decane at the visible wavelength is available and is 1.4, its value at

the CO 2 laser wavelength ( 10.6 pm) is not available. From the study of Dalzell and

Sarof im [13] , it is expected that the value of refractive index at around

10.6 pm is larger than that at the visible wavelengths. Therefore, values of

(5)

where 0^ is the incident angle of the laser beam with respect to vertical

line and 9^ is the transmitted angle. Therefore, the previously discussed

0 is 0 = 90° - e.. By Snell's law,

1

n. sin 0. = n^ sin 0

i It t ( 6 )

where n^ is refractive index of the incident medium, air, and n^ is refractive

16
reflectance at various incident angles were calculated with two different

values of n^, 1.4 and 2.8, using equations (5) and (6). Results are shown

in figure 13. It shows that the qualitative trend of reflectance with the

incident laser angle does not change with the value of refractive index.

Reflectance decreases gradually with a decrease in the incident angle until

about 20° for n^ = 1.4 and about 15° for n^ = 2.8. Then, reflectance increases

sharply with a further decrease in the incident angle. Therefore, for the

values of the incident angle used in this study (0 > 30°) , the calculation shows

S qualitatively that more energy from the incident laser beam is transmitted

into the decane with a decrease in the incident angle. This means that, if

this mechanism controls the ignition processes, ignition delay time should

decrease with a decrease in the incident angle. This trend is opposite from the

one observed.

Ignition delay time was plotted against incident radiant flux in log-log

coordinates to find any characteristic relationship between them. The plot

is shown in figure 14. The relationship can be roughly expressed by the

straight line, although the line shifts slightly at different incident laser

angles. Also, near the minimum incident radiant flux for ignition, the

relationship bends sharply upward deviating from the straight line. However,

the slope of the straight line is fairly uniform from 9 = 90° to 9 = 30°

and is about -1.6. This can be expressed as:

T T ^

I

O

This relationship can be used for rough prediction of the trend of ignition

delay time with given incident radiant flux. The logarithmic plot between

sin 9 and ignition delay was not linearly correlated as well as the above

log-log relationship.

17
4 . THEORETICAL STUDY

A simplified theoretical model to describe the development of a

plume in the gas phase was developed as a first step; hopefully, this

will be extended to a more complete model which will be able to predict

qualitatively the trends of ignition delay time and the minimum external

radiant flux for ignition against various parameters such as flux,

incident laser angle and laser beam diameter. As the key processes of

the ignition mechanism are clarified experimentally, these will be added

to improve the theoretical model. The model which is discussed in this

section is a foundation for a more complete model and it emphasizes the

gas phase. However, a similar approach can be extended to calculate the

flow motion in the liquid phase. Two different approaches were used in

this study, one is numerical and the other is analytical.

4.1 Numerical Study

A schematic illustration of the model is given in figure 15. The

base is considered to be a solid and there is no motion inside of the

solid. The enclosure is included artificially to define the boundary

conditions. In the calculation, the enclosure is taken to be large

enough so that the rising plume and the associated flow do not touch its

walls. The flow is assumed to be axisymmetric and a cylindrical coordinate

system with its origin at the center of a hot spot is used. The fluid

is initially motionless and at a uniform temperature T^. The enclosure

walls are also at this temperature, except for a small centrally located

circular spot on the base of radius whose temperature increases with

time as specified up to a temperature Tw. The temperature difference

initiates and sustains a natural convection flow within the enclosure.

The Boussinesq approximation is used; in this approximation density p

18
is assumed constant except for the generation of buoyancy forces. No

chemical reaction and no mass addition are considered. Fluid properties

are taken as constant; these include kinematic viscosity v, thermal

diffusively a, and volume expansion coefficient 3. We introduce the

following dimensionless quantities: time, t = (a/H^)t; initial and

radial coordinates, X = x/H and R = r/H; vertical and radial components

of velocity, U = (H/a)u and V = (H/a)v; and temperature 9=(T-T^) / (TwVIntroducing vorticity SI and the stream function j4, the governing

equations in dimensionless form are:

19
Equation (7) contains the Prandtl number Pr = v/a and the Groshof number

Gr = gB(Tw-To)H^/v^ . The initial conditions are for x<0

= 0 = 0 0<X<1 and 0<R<Rw ( 10)

The boundary conditions for t> 0 are:

d

&

Ml Isl

-/

0.S

6-^0

dX

5 = 12 ^

Jvr 2=^’/

X~ Oj X -X'c,

jvr X'-'-O / JX; XXXk/

S -X X-/, MIX

( 11)

^

^ -r: 0—-O rfor /\ " y

The above equations are numerically solved using Torrance’s computational

programming [14,15]. The detailed calculation scheme is well described in

these references.

The enlarged results near the heat source are shown in figures (16) and

(17) for two differente times. G = 3.6 x 10^ is derived from H = 2.5 cm

r

“ o and Tw = 447 ®K. The physical time scales corresponding to t = 2.1 x 10

20
and T = 7.0 X 10 ^ are about 60 msec and 210 msec, respectively. Since the

enclosure boundary is at X =* 1 and R = 1, the effect of the enclosure on the

early development is negligible. At r = 2.1 x 10 heat transfer from the

heated area to the surrounding gas phase is limited to near the source. Since

thermal diffusion is the dominant transport process, the distance traveled by

the energy at this time is about the same axially and radially. The sharp

temperature gradient near the edge of the heated area is due to the room

temperature boundary condition at the surface next to the heated area. The

vorticity distribution indicates the initiation of strong vorticity near

and over the edge of the heated area. Near the surface, the gradient of

vorticity becomes steep due to the shear caused by the induced flow from the

surroundings toward the heated plate. This steep gradient could reduce the

accuracy of the calculation of vorticity near the surface unless the step

size near the surface is very fine. The stream function clearly shows the

flow pattern, in which hot air starts to rise and the surrounding air flows

radially in toward the heated area. The effect of the heat input extends a

greater distance in the flow pattern than in the temperature distribution due

to the irrotational flow characteristic far from the heated area.

At T = 7.0 X 10 buoyancy starts to push the thermal wave further upward

than does thermal diffusion and the temperature distribution is more elongated

upwards than radially. The strong vorticity moves slightly more toward the

center, where the shear becomes strong at the edge of the rising plume. The

wall boundary grows further radially. The stream function distribution also

shows enlargement of the flow motion. It is interesting to note that the

stream lines are centered further away from the heated area than the center

of the vorticity distribution. It indicates that, if decane vapor follows the

21
flow pattern, it can spread radially and it might be possible by this means

to absorb enough energy from the incident laser beam to ignite. However, firm

conclusions can only be derived from the future model including the liquid

motion, vaporization and species equations in the gas phase.

This model is basically the same as that of the numerical study. In

this model, there is no enclosure and the gas phase is considered to be

semi-inf inite. Two-dimensional cartesian coordinates are used in this model

for the simplification because of the possibility of extending it to more

realistic three-dimensional coordinates.

Dimensionless variables are defined as follows:

4.2 Analytical Study

U = u/uo. V = v/uo

X = x/L Y = y/L

T = t/To T-To

Tw-To ( 12 )

V uo

With Pr = 1, the governing equations become

{/>'/-

22
where G r = geL^(;^-To)

Initial conditions are

= “V=0 = J2 = S= O

Boundary conditions for t > 0 are

for all X and Y,

'=^ {> fZ Z- 'A;',

XT. -' ^

<2l ^

" ^

py " ^

o?/T

d = ^

O 'jet dX- X

aJt Y^O , /X/ >Xz

CLt Yo . A/< /z I

(17)

The order of the time dependency of each variable is analyzed to estimate

the dominant terms for equations (13)-(15). Since the distance traveled by

thermal diffusion, which initiates the flow motion, is roughly proportional

to the square root of time

X^O (ST)

Since the surface temperature does not change with time, 6 ^O(l)

In equation (13) , the order of time dependency of the following two terms

should be same because they are source and inertia terms.

an' 39

3t

^

3x

23
This can be satisfied if JWO (vt) •

Similarily, equation (16) indicates

U — V~0 (t) ^ ^

0

Substitute these order of time dependencies into equations (13)-(15),

24
Therefore, all terms are same order with time except the convection terms.

The ratio of the time dependency of the convection terms to the other terms

is Therefore, if our interest is early time during the initiation

of the plume, the convection terms can be neglected in this calculation.

With T = t/xo, we can estimate the time scale in which this calculation is

reasonably accurate. Since l/ and V have a Grashof number dependence, the

value of To must be evaluated on this basis instead of the one defined in

equation (12)

With the values of L = 0.5 cm and Tw = 447®K, To is about 40 msec. With

the ratio of 0(x^'^), the calculation is quantitatively accurate up to 20 msec

(T = 0.5) and qualitatively accurate from 20 msec to 200 msec (x-^l)

The governing equations for the early time calculation are then

25
These equations with the boundary conditions described in equations (17) are

linear and may be solved analytically. Another advantage of this approach

is that the analytical procedure used here can be easily extended to the

three dimensional case which might be difficult with the numerical calculation

due to the requirement of large core size.

At first, equations (18)-(20) are converted by the Laplace transformation.

The n, ^and 0 are variables of and 9 after the Laplace transformation

respectively.

where P is a variable for Laplace transformation. Then, the above equations

are further converted by Fourier transformation with respect to the X coordinate.

( 21)

( 22 )

(23)

The fi, ^ and 6 are variables of n, j|; and 0 after the Fourier transformation

respectively.

/

( 26 )

(25)

26
where ^ is a variable for the Fourier transformation.

Boundary conditions described in equation (17) are also converted as

follows by Laplace transformation and Fourier transformation;

Similarly, solutions of equations (24) and (25) with equation (27) are

27
The solution of the energy equation, equation (28), can be converted

back by the Laplace transforaation inversion [16].

/

Using the contour integral, vorticity of equation (29) and stream

function of equation (30) are converted back by the Laplace transformation

inversion. Details of this inversion are described in Appendix A.

28
where ^ is the homogenous solution and the particular solution.

The next step is the Fourier transformation inversion of solutions

described in equations (31)-(33) . For example.

-^r/ c 01^'i

J-lk?

Then, equation (34) becomes

(34)

where

(35)

29
Defining

Similarly, vorticity becomes

Also, homogenous and particular solutions for the stream function become

30
At present, the integration of equations (37) -(40) has not been completed.

There is some chance that these may be integrated analytically. Even if

numerical integration is required, these are single integrals and can be carried

out without any difficulty and with small computation time. These solutions

will reflect the effects from the two source terms with sin (Xj 0 and sin

(X 2 ?) or cos (Xj C) and cos (X 2 C) describing the disturbance generated

around the edges of the heated base. The Xj and X 2 express the distance fro m

the sources to the observation point. Values of all terms except ^ decreases

31

W
very rapidly away from these sources and this makes the number ical

integration easy without integrating far out in the field.

5. SUMMARY

The ignition mechanism of n-decane was studied experimentally by

using a CW CO2 laser as an external radiant source; a simplified theoretical

model to describe the developmen of a plume in the gas phase was developed

as a first step.

From the experimental study of the effect of the container size on

ignition delay time, it was concluded that a container with 6 cm diameter

and 5 cm depth is sufficient to avoid any significant effect of the wall

on ignition for a beam of the diameter used in these experiments.

High speed motion picutres show the periodic appearance and collapse

of a bubble-like, half spherical surface depression near the surface. The

depression is probably formed by the momentum of decane vapor leaving the

decane surface and its collapse is caused by the absorption of the laser

beam by the decane vapor in the gas phase reducing the energy availabe

to vaporize liquid decane. Further studies are necessary to confirm these

proposed mechanisms and to clarify the transport processes of decane

vapor/droplets from the surface to the location in the gas phase where

the first appearance of flame is observed.

32
The effect on ignition delay time of incidence angle of the laser

beam on the decane surface is significant at low incident radiant flux.

A decrease in the incident angle tends to increase ignition delay time

and the minimum incident radiant flux for ignition. However, when the

incident flux is above 2500 W/cm^, this effect is not significant for

the range of incident angles studied in this work.

It is concluded that the key mechanism in the ignition of decane

by a CO2 laser is the absorption of the laser beam energy by the decane

vapor in the gas phase. The characteristic relationship between ignition

delay time and incident radiant flux can be expressed by t ~ from

0 = 90® to 0 = 30®.

The theoretical model to describe the development of a plume in the

gas phase caused by a heated surface was solved numerically and analytically.

Further improvements including the addition of liquid vaporization, mass

addition into the gas phase, species equations, absorption of laser beam

energy and chemical reaction are necessary to complete the model. These

will be carried out step-by-step with the numerically solved model. The

analytical solution for the early time behavior is derived by using the

Laplace transformation with respect to time and the Fourier transformation

with respect lateral coordinates. However, further numerical calculation

of the solution in the integral formual is necessary to complete the

analytical model.

33
6 . REFERENCES

[1] Ohlemiller, T. J. and Summerfield, M. , "Radiative Ignition of Polymeric

Materials in Oxygen/Nitrogen Mixtures", Thirteenth Symposium (International)

on Combustion, Combustion Institute, 1971, pp, 1087-1094.

[2] Stegman, R. L. , Schriempf, J, T., and Hettche, L. R. , "Experimental

Studies of Laser - Supported Absorption Waves with 5 ms Pulses of

10. 6y Radiation", J. Appl. Phys., Vol. 44, 1973, pp. 3675-3681.

[3] Chien, K. Y., "Vaporization of Liquid-Air Droplets by High-Power Laser

Beams", AIAA J. , 1975, pp. 1647-1652.

[4] Emmony, D. C. , "High Speed Study of Laser-Liquid Interaction", J. Photo.

Sci., 1977, pp. 41-44.

[5] Handbook of Tables for Applied Engineering Science, CRC Press, Cleveland,

Ohio, 1973.

[6] Weast, R. C. , Handbook of Chemistry and Physics, The Chemical Rubber

Company, 1969.

[7] Kashlwagi, T., "Effect of Sample Orientation on Radiative Ignition of

Solid Fuel", to be submitted to Combustion and Flame.

[8] Kashiwagi, T., "Experimental Observation of Radiative Ignition

Mechanisms", Combustion and Flame, 34, 231 (1979).

34
[9]

Kashiwagi, T., "Effect of Attenuation of Radiation on Surface

Temperature for Radiative Ignition", accepted for publication in

Combustion Science and Technology.

[10] MacKinven, R. , Hansel, J. G. and Classman, I., "Influence of Laboratory

Parameters on Flame Spread Across Liquid Fuels", Comb. Scl. Tech. 1, 1979,

pp. 293. ’

[11] Murad, R. J. , Lamendola, J. , Isoda, H. and Summerfield, M. , "A Study of

Some Factors Influencing the Ignition of a Liquid Pool", Comb. Flame, 15,

1979, pp. 293.

[12] Jackson, J. D. , "Classical Electrodynamics'.', John Wiley and Sons, Inc.,

New York, Chap. 7, 1962.

[13] Dalzell, W. H. and Sarofim, A. F. , "Optical Constants of Soot and Thin

Application to Heat-Flux Calculations", J. Heat Transfer, 91, 100 (1961).

[14] Torrance, K. E. , "Comparison of Finite-Difference Computations of

Natural Convection", J. Research of National Bureau of Standards, B.

Mathematical Sciences, 72B, 281 (1968).

[15] Torrance, K. E. and Rockett, J. A., "Numerical Study of Natural Convection

in an Enclosure with Localized Heating from Below - Creeping Flow to the

Onset of Laminar Instability", J. Fluid Mech. , 36, 33 (1969).

[16] Carslaw, H. S. and Jaeger, J. C., "Conduction of Heat in Solids", Oxford

Univ. Press, 496 (1965).

35
LIST OF FIGURES

1. Schematic illustration of experimental apparatus.

2. Picture of experimental apparatus

A - CO2 laser, B - mirror, C - mirror, D - chamber, E - safety shield

3. The effect of the container depth on ignition delay time.

4. The effect of the container diameter on ignition delay time.

(a) I^ = 4170 ± 100 W/cm2, (b) I^ = 1670 ± 80 W/cm^

5. High speed motion pictures

I = 2200 W/cm^, 0 = 30®

0

(a) before laser irradiation, (b) 28 msec after laser irradiaion,

(c) 72 msec, (d) 117 msec, (e) 340 msec, shortly after ignition,

(f) 370 msec

6. High speed motion pictures. I^ = 3000 W/cm^, 6 = 30®

7. High speed motion pictures (negative). I^ = 2000 W/cm^, 0 = 90®

8. High speed schlieren pictures. I^ = 2600 W/cm^, 0 = 90®.

knife edge is horizontal direction.

9. Spectra of linear absorbance of decane

(a) cell only, (b) Z = 0.1, (c) Z = 0.25, (d) Z = 0.5, (e) Z =* 0.75

and (f) Z - 1.0 mm.

10. Emission spectra of the CO2 laser.

11. The relationship between incident radiant flux and ignition delay

time under various incident angles, (a) 0 = 90®, (b) 0 = 45®, (c)

0 = 30®.

36
12. The relationship between incident angle and ignition delay time under

various incident radiant fluxes.

13. The calculated relationship between reflectance and incident angle.

14. The logarithmic relationship between ignition delay time and incident

radiant flux.

15. A schematic illustration of the theoretical model.

16. Computational results of early development of plume at r = 2.1 x 10

Gr = 3.6 X 10^, Pr = 0.7. (a) temperature, (b) vorticity and (c) stream

function.

17. Computational results of early development of plume at x = 7.0 x 10

Gr = 3.6 X 10^, Pr = 0.7. (a) temperature, (b) vorticity and (c) stream

function.

37
. . . f -4 i.’abioni .Jels^ :

r -•^rUiani. ‘ I

-•\ 'j i. tNv, .. :t-'-

,St

} *

• ;x' MT-tbi^fn na ti> 3D - f ' v-. i .'^Mnno!36lo-r fj'iT Ll

iJuS a

-

.X'. i l 3 XiBihS »

. I>I

. ...,•. ,i iAi v.'iv .i“»bu<a ’. ; 1191094,1 x- - lo oliJjrra.rfa'e A

X 1

I • I V. i.. . J£ fis-iyfn ic IM.-- •. :I*»v»b - r;ilve>i ifinoi'ifiJuq^oO

.'ot:

\-

• y 1 r. o-ir (*) ,K.O - i*? '=' d.C -t -4

ei

.t'l

.nol 33 Ki?’i

I f f

» '• iM » r ' ^ - «

jv i lo ;ir2 vriii-.fi •Jlo«- - '.i«o ? ie:)b >rroD r|

» - » >•'• ti'ooi ri..a;|^ ( 3 ) ;• ft ( 4) ,eiu3*ii 5H:«r»3 («) •' U t X ^ .t • iO

. 1 , 0 .' u ;

,1 » 'u«{|4tlwa;4 vt

... 1

O'

:x ton*

i- ’» ,•

« nf 40C«nO.

U.:

I- lj»»«r,. "L.

<»<. V4MC ’ V *fwl 4tDl,t

«'*#r

i.xi:
APPENDIX A

The calculation of the Laplace transformation inversion for vorticity

and stream function is described in this appendix.

From equation (29)

,

/

The first term in the above bracket is defined as

After the contour integral, which has a branch cut along the negative real

coordinate from the origin, equation (A-3) becomes

/

/f/(e i-c „ J -

e

t

A1
A2
Equation (32) can be derived by substituting equations (A-A) , (A-5) and

(A-6) into equation (A-1),

For stream function, from equation (30),
After the contour integral which is same contour as that of the vorticity,

A4
After the contour integral

A5
Equations (A-8) , (A-9) and (A-10) are substituted to equation (A“7) and

equation (33) Is derived.
Fig. 1



lo

=

4740

1

100

w/cm

DIAMETER

;5

cm

O

CN* • •

o

• •

i.

laasui) 3111111 AV130 N0I1IN9I

two

Fig. 3

=

4170

+

100

w/cm

Eo

m

• •

CO

• •

— ca

|33SUI| anil AV13Q N0I1IN9I

Fig. 4A

DIAMETER

(cmj
I

Fig. 4B
(f)

I

ime

3 cm

w.

Fig 6-Pt. 1

Time

Fig. 6-Pt. 2

Fig 7

Fig. 8 1

CO

= 0.6 -

1200

WAVELENGTH (M)

9 10 . 11 12 13

T

1100 1000 900 800

WAVENUMBER (cm-1)

700

Fig. 9
O Q o O o

OO CD ? CM

indino JO JIV3S AdVdiiaw

Fig. 10

luilYl

H19N313AVM
480

400 -

360 - - 320 h

a>

COE_ UJ 280 -

< 240

LUO

s 200

ca

160

120

80

40 h

0

INCIDENT ANGLE 90°

e= 90°

:•

• * • •

• -i.

••• •»

J I I L J L

1000 1400 1800 2200 2600 3000 3400 3800 4200 4600 INCIDENT RADIANT FLUX iW/cm^)

Fig. IIA

INCIDENT RADIANT FLUX (W/cm^)

Fig. lie

Fig. 13
IGNITION

DELAY

TIME

(msec)

Fig 14

X

Fig. 16A
CO CM

Fig. 16B

X

Fig. 17A
17B
CO

I

LO

CO

CM

LU <

V

Vs

V

VK cs CO CM

Fig. 17C