Ignition of a Liquid Fuel Jet by an Electrical Discharge Propagating along the Jet.

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ABSTRACT

GRAY, PARKER BAHNSON. Ignition of a Liquid Fuel Jet by an Electrical Discharge Propagating along the Jet. (Under the direction of Dr. Alexei Saveliev.)

The desire for more efficient engines motivates the investigation of new ignition

sys-tems. Breakdown through a fluid spray occurs at lower voltages than does breakdown

through air. The reduced voltage necessary for breakdown through a fluid jet or spray

presents the possibility of using such a discharge to ignite the spray. This reduction in

voltage was first seen for a water jet but applies to other fluids as well. Increased

con-ductivity makes such a breakdown easier to achieve. Using such a breakdown mechanism

would ignite the fuel inside the spray instead of at the edge of the spray, giving it the

potential to increase the burning rate.

Exposing certain fluids to an electric field can generates spray. This spray may be used

as an atomization mechanism. The structure of this spray depends on the conductivity

and surface tension of the fluid. Lower surface tension and higher conductivity cause

the fluid to break into droplets more readily. Water and ethanol were found to produce

sprays while kerosene simply dripped. This makes ethanol a good choice for a system

using an electrospray as the atomizer. By using the electric field to produce a spray, the

same electrodes may be used both to produce the spray and to ignite it.

The proposed mechanism ignited the ethanol spray by means of a discharge through

the spray similar to that seen in water. Kerosene ignition was achieved as well. The

preliminary work shows that the ignition system presents a viable alternative to current

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c

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Ignition of a Liquid Fuel Jet by an Electrical Discharge Propagating along the Jet

by

Parker Bahnson Gray

A thesis submitted to the Graduate Faculty of North Carolina State University

in partial fulfillment of the requirements for the Degree of

Master of Science

Mechanical Engineering

Raleigh, North Carolina

2010

APPROVED BY:

Dr. Tiegang Fang Dr. Gregory Buckner

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DEDICATION

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BIOGRAPHY

The author spent his childhood in Winston-Salem, North Carolina. He attended high

school at Woodberry Forest School in Virginia. He went to college at Vanderbilt

Univer-sity in Nashville, TN, where he graduated Summa cum Laude with a degree in physics

and mathematics. While at Vanderbilt. he worked with two different groups in the

physics department. One group focused on solid state physics and was growing V O2

nanocrystals. The other group was performing preliminary work and building detectors

for BTeV, a high energy particle physics experiment that was to be built at Fermilab.

The author has always been drawn to scientific disciplines as a way of better

under-standing the world. His work at North Carolina State University has helped to further

this understanding while incorporating practical applications to the knowledge he has

gained. He has presented this work already both at the 2009 Eastern States Section

Meeting of the Combustion Institute in College Park, MD and at the 2010 IEEE

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ACKNOWLEDGEMENTS

The author would like to extend his thanks to his advisor, Dr. Saveliev, for his guidance

and help with the research. Without his ideas, none of this would have been possible.

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LIST OF TABLES

Table 2.1 Fluid Properties, Physical . . . 23

Table 2.2 Fluid Properties, Electrical . . . 23

Table 2.3 Fluid Properties, Conductivity . . . 23

Table 2.4 Slope of linear fit for current as a function of voltage, in µA_kV. . . . 45 Table 2.5 Slope of linear fit for current as a function of velocity, in _m/sµA . . . . 45 Table 2.6 Correlation coefficients for tap water with respect to voltage at jet

velocities above 3m_s. . . 52

Table 4.1 CMOS Truth Table . . . 97

Table 4.2 Resistance and Capacitance Values for Ethanol Ignition by

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LIST OF FIGURES

Figure 2.1 Calibration of the pump: jet velocity of the fluid leaving the needle vs. power setting. . . 26

Figure 2.2 Example image of the jet flow under no applied electric field used

to measure the capillary breakup time. 0.91 m

s jet velocity, or 15.4_minmL flow rate. . . 30

Figure 2.3 Length of a tap water jet as it begins to break up as a function of

the velocity of the jet. . . 31

Figure 2.4 Corona discharge currents with no fluid flow. . . 36

Figure 2.5 Current due to surface charge carried by a tap water jet as a

function of increasing voltage. . . 39

Figure 2.6 Current due to surface charge carried by a tap water jet as a

function of increasing jet velocity . . . 40

Figure 2.7 Current due to surface charge carried by a distilled water jet as a

function of increasing voltage. . . 41

Figure 2.8 Current due to surface charge carried by distilled water jet as a

function of increasing velocity. . . 42

Figure 2.9 Current due to surface charge carried by ethanol jet as a function

of increasing voltage. . . 43 Figure 2.10 Current due to surface charge carried by ethanol jet as a function

of increasing velocity. . . 44 Figure 2.11 Measured current for a kerosene jet as a function of voltage. Corona

current under no fluid flow is included to demonstrate that less

cur-rent was measured with a kerosene jet than without. . . 47

Figure 2.12 Subtraction of the corona discharge current for a pan filled with distilled water from the measured current for a distilled water jet. Demonstrates that the corona current is greater than the current carried by the jet. . . 48 Figure 2.13 Measured current from a tap water jet as a function of velocity.

Displays the limited charging rate as velocity increases. . . 50

Figure 2.14 Surface charge on a tap water jet vs velocity vs. jet velocity.

Displays the velocity at which the maximum charging rate occurs. 51

Figure 2.15 Model of the current from a fluid jet, assuming a finite charging time. . . 54

Figure 2.16 Setup for flow characterization experiments. . . 57

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Figure 2.19 Images of spray produced by a distilled water jet, 45.96 mm gap width, 0.91 m_sjet velocity, or 15.4_minmL. . . 62 Figure 2.20 Breakup time of a jet of distilled water as a function of applied

voltage, 45.95 mm gap width. . . 63

Figure 2.21 Images of spray produced by an ethanol jet, 39.49 mm gap width, 0.91 m_sjet velocity, or 15.4_minmL. . . 65 Figure 2.22 Breakup time of a jet of ethanol as a function of applied voltage,

39.49 mm gap width. . . 66

Figure 2.23 Images of spray produced by a kerosene jet, 44.94 mm gap width, 0.91 m_sjet velocity, or 15.4_minmL. . . 68 Figure 2.24 Breakup time of a jet of kerosene as a function of applied voltage,

44.94 mm gap width. . . 69

Figure 3.1 Experimental setup used to generate a discharge through a water

jet. . . 74

Figure 3.2 Voltage vs time for breakdown in distilled water at a distance of

24.3 mm. . . 76

Figure 3.3 Current vs time for breakdown in distilled water at a distance of

24.3 mm. . . 77

Figure 3.4 Voltage measurement at which electrical breakdown occurred vs

interelectrode distance for distilled water. . . 79

Figure 3.5 Voltage measurement at which electrical breakdown occurred vs

interelectrode distance for tap water. . . 80 Figure 3.6 Discharge along the surface of a tap water jet, 1.82m_s jet velocity,

22.5 kV, 34 mm interelectrode distance . . . 81

Figure 3.7 Average discharge energy vs interelectrode distance for distilled

water. . . 83

Figure 3.8 Average discharge energy vs interelectrode distance for tap water. 84

Figure 3.9 Frequency of electrical breakdown through a distilled water jet as

a function of applied voltage. . . 87 Figure 3.10 Frequency of electrical breakdown through a tap water jet as a

function of applied voltage. . . 88

Figure 4.1 Experimental setup for ignition of ethanol and kerosene. . . 93

Figure 4.2 Diagram of CMOS CD54HCT132E logic circuit inputs and

out-puts used to synchronize the camera and intensifier with the spark. 96

Figure 4.3 Photograph of black box used to encase experiment. The exposed

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Figure 4.4 Pulse energies for ignition of an ethanol spray vs resistance be-tween the high voltage supply and needle electrode. The pulse energy continues to decrease as the resistance increases, but may be thought of as relatively constant once the resistor is in place. . 101

Figure 4.5 Breakdown voltage vs. distance for an ethanol spray. . . 103

Figure 4.6 Effective capacitance vs. distance for the initial breakdown pulse

in ethanol ignition. Capacitances are the average value across all velocities measured for each gap width. . . 104

Figure 4.7 Effective capacitance vs. velocity for initial breakdown pulse in

ethanol ignition. Capacitances are the average value across all gap widths for each velocity. . . 105

Figure 4.8 Voltage characteristics for ethanol ignition images seen in Figure

4.8. 1.13m_s jet velocity, or 19_minmL. 21 mm gap width. . . 107

Figure 4.9 Ethanol ignition displaying the continuous discharge column

re-sponsible for ignition. Times are elapsed time after initial spark. Ignition can be seen in (e) and (f). 0.91m_s jet velocity, or 15.5_minmL. 21 mm gap width. Voltage characteristics may be seen in Figure 4.8.108 Figure 4.10 Ethanol ignition with a secondary ignition in the center of the gap.

The secondary ignition can be seen beginning in (a) and falls past the lower electrode in (c) before leaving the field of view. Times are elapsed time after trigger point. 0.91m_s jet velocity, or 15.5_minmL. 25.4 mm gap width. . . 110 Figure 4.11 Voltage characteristics for ignition of ethanol at the lowest

avail-able flow rate, 0.2_minmL, and seen in Figure 4.12. 21 mm gap width. 112 Figure 4.12 Ethanol ignition at the lowest available flow rate. Ignition begins

in (c) and (d). The flame replaces the discharge column and is all that is visible in (g) and after. 21 mm gap width. 0.05m_s jet velocity, or 0.2_minmL. . . 113 Figure 4.13 Circuit between the high voltage supply and the needle electrode

for pulse experiments. . . 116 Figure 4.14 Voltage characteristics for ignition of ethanol by a repetitive pulse

discharge, seen in Figure 4.15. Ignition was seen after the eighth pulse. 20 mm gap width. 0.68m_s jet velocity, or 11.6_minmL flow rate. 118 Figure 4.15 Ethanol ignition by a repetitive pulsed discharge. The eighth pulse

can be seen in (c), after which ignition below the bottom electrode becomes visible. 20 mm gap width, 0.68m_s jet velocity, or 11.6_minmL flow rate. . . 119 Figure 4.16 Ethanol ignition with as close to a single spark as was possible.

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Figure 4.17 Example of voltage characteristics for ignition of a kerosene jet. 0.68 m_s jet velocity, or 11.6 _minmL flow rate. 12.5 mm gap width. . . 124 Figure 4.18 Ignition of a kerosene jet. Discharge can be seen in (a) and (b),

followed by beginnings of flame in (c). The flame then falls with the jet over (d) through (h). 0.46 m_s jet velocity, or 7.8 _minmL. 19 mm gap width. . . 125

Figure A.1 Breakup time of a jet of tap water as a function of applied voltage, 31.84 mm gap width, 0.91m_s jet velocity. . . 138 Figure A.2 Breakup time of a jet of tap water as a function of applied voltage,

45.83 mm gap width, 0.91m

s jet velocity. . . 139 Figure A.3 Breakup time of a jet of tap water as a function of applied voltage,

45.83 mm gap width, 1.14m_s jet velocity. . . 140 Figure A.4 Breakup time of a jet of tap water as a function of applied voltage,

45.83 mm gap width, 1.37m_s jet velocity. . . 141

Figure A.5 Breakup time of a jet of distilled water as a function of applied

voltage, 45.96 mm gap width, 0.91m

s jet velocity. . . 142

voltage, 45.96 mm gap width, 1.14m_s jet velocity. . . 143

voltage, 45.96 mm gap width, 1.37m_s jet velocity. . . 144

Figure A.8 Breakup time of a jet of ethanol as a function of applied voltage,

s jet velocity. . . 145

Figure A.9 Breakup time of a jet of ethanol as a function of applied voltage,

39.49 mm gap width, 1.14m_s jet velocity. . . 146 Figure A.10 Breakup time of a jet of ethanol as a function of applied voltage,

39.49 mm gap width, 1.37m_s jet velocity. . . 147 Figure A.11 Breakup time of a jet of kerosene as a function of applied voltage,

s jet velocity. . . 148 Figure A.12 Breakup time of a jet of kerosene as a function of applied voltage,

44.94 mm gap width, 1.14m_s jet velocity. . . 149 Figure A.13 Breakup time of a jet of kerosene as a function of applied voltage,

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Chapter 1 Introduction

1.1 Thesis Objectives

The first research objective was to characterize the flow of a fluid jet exposed to high

voltage. Further research relied on an understanding of each fluid’s properties: the

reaction of each fluid to an electric field, the structure of the fluid jet, and the conductive

properties of that jet. The characteristics of the fluid spray needed to be known. The

length of the fluid jet under varying voltage as well as the charge carried on the surface

of the fluid were measured.

The second objective was to determine the properties of electrical breakdown through

a jet of water under the conditions that produced the fluid spray. This would provide a

basis for comparison with any later work on the discharge through a fuel jet to help to

prove that such a discharge was affected by the presence of the jet.

The main objective, then, was to discover whether a discharge through such a fluid

jet at lower electric field strengths than a discharge through air alone could ignite the

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cause of ignition. This involved finding the type and energy of the igniting discharge, as

well as whether other discharge types could be responsible for ignition. Also important

were investigating where the ignition occurred in the spray, the ignition delay time, and

what conditions were necessary to sustain a flame after an ignition.

1.2 Background

Ignition of a fluid jet by means of an electrical discharge through the jet delves into

many different fields of physics and engineering. The flow produced by the charged

needle is a type of electrospray with a higher flow rate than a classical Taylor cone-jet.

It has both characteristics of such an electrospray as well as similarities to a the simple

capillary breakup of a fluid jet. The amount of charge that the fluid holds will prove

to be important as well. The discharge along the jet or through the spray has different

characteristics than breakdown through air alone and so discharges both underwater and

through water jets must be compared to what was seen. In addition, a comparison to

spark ignition systems will help to determine what uses this new ignition system may

have.

1.2.1 Classical Spark Ignition and Motivations for New Ignition

Systems

Classical spark ignition has been widely studied and remains one of the most popular

ignition systems. It relies on the use of a spark plug, generally placed in the side of

the combustion chamber, to generate a spark of sufficient energy to thermally ignite the

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that energy is not wasted. The minimum ignition energy also depends on the size of the

fuel droplets and is lower at higher equivalence ratios. The energy required is higher for a

longer interelectrode distance because the heating energy is spread over a larger volume.

In the case of kerosene-air mixtures and as a useful order of magnitude estimate for other

fuels, the minimum ignition energy is on the order of 5 to 10 mJ [1, 2].

The goal with a new ignition system, then, is the ability to ignite the mixture in the

center of the combustion chamber in order to increase the probability of ignition and

reduce the burning time. Unfortunately, the turbulent conditions present in real engines

may spread the budding flame kernel away from the areas in which the fuel/air ratio is

close enough to stoichiometric to allow for a successful ignition. By igniting at the center

of the chamber, there is a greater chance that the flame kernel will begin in an area

where the air/fuel ratio is favorable to its continued development, increasing the chance

that the flame will survive. Once ignition is successfully achieved, the flame will spread

outward from the kernel at a finite rate. Ignition from the center of the chamber will

maximize the surface area of this expanding flame such that the total burn time is at

a minimum, increasing the efficiency of the engine by reducing losses due to the second

law of thermodynamics [3].

Ignition by a discharge through an electrospray has the potential to cause ignition in

the center of the chamber from a discharge that spreads through the fuel spray [4, 5]. It

also has the advantage that it does not require a separate atomization system. It may

also allow for decreased total burn times by igniting in the center of the spray, maximizing

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1.2.2 Capillary Instability of a Fluid Jet

The work done by Lord Rayleigh remains a central source on the instability of a fluid

jet flowing out of a capillary. Rayleigh’s work indicates that the time before a fluid jet

falling under gravity breaks up is determined by instability modes in the jet that alter

the surface shape of the jet and eventually pinch it apart. If these instability modes

have a wavelength less than the circumference of the jet, then the jet will remain stable;

wavelengths greater than the circumference of the jet will decrease the surface area of

the jet. This happens during the thin parts of the jet surface’s sinusoidal shape, where

the curved shape is caused by the instabilities. This will result in the jet’s breaking into

droplets once the surface area has been reduced enough that surface tension no longer

holds the jet together. The greatest instability occurs when the wavelength is equal to 1.5

times the circumference, and the instability grows in time at a rate that can be described

byexp(qt) [6, 7]. Ashgriz simplified his equations to find that:

r = 1 +δ0exp(ωt−ikz) (1.1)

ω =

I1(k)

I0(k)

(1−k2)k

1/2

(1.2)

k = 2πRinnerλ−1 is the wavenumber, δ0 is the magnitude of the initial disturbance due

to the instability, r is the ratio of the radius of the jet to its undisturbed radius, and I0

and I1 are Bessel functions [8]. From here he found that the breakup time, tb, is equal

to:

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R =

1−1

2δ

2 0

1/2

(1.4)

Applying these to the 0.6 mm inner diameter and 0.9 mm outer diameter needle used,

assuming the maximum instability mode ofλ= 1.5∗circumf erence and that the initial

magnitude of the instability is equal to:

δ0 =

Router Rinner

−1 (1.5)

the predicted breakup time is 5.64 s. This will be compared to the measured breakup

time in Section 2.3. Note that increasing the initial disturbance from a 0.9 mm radius to

a 1.0 mm radius decreases the breakup time by a factor of 2 to 2.47 s, showing that even

a slight deviation from this estimated initial disturbance can have a very large effect on

the predicted breakup time.

1.2.3 Electrosprays and Taylor Cones

When a fluid droplet is sufficiently electrically charged, the repulsive internal electrical

forces between the charges on the fluid will exert an outward pressure that will overwhelm

the inward pressure of the surface tension, breaking apart the droplet. This will occur

when:

q >

q

16πa3

0σ (1.6)

whereq is the total charge contained in the droplet,a0 is the droplet radius, andσ is the

surface tension [9]. When the droplet is at the exit of a capillary and electrical forces pull

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to induce at least charge q above, this breakup will take the form of a jet of fluid off of

the droplet. In this case, the fluid droplet outside the capillary’s aperture will take on a

conic shape, a so-called Taylor cone, with the jet of fluid exiting from the tip of the cone

[10]. Taylor discovered that this jet mechanism was true for conducting fluids, whereas

nonconducting fluids were drawn out of the capillary as single droplets. In subsequent

years, de la Mora further examined the effect of conductivity on the structure of such

Taylor cones. He discovered that the charge carried out of the jet in a particular time,

which can be thought of as a current, becomes independent of voltage at higher voltages

in fluids with conductivities greater than 100_cmS . This is due to the face that while

the charge per volume continues to increase with voltage, the expelled volume seems

to decrease. This occurs as the emitted jet becomes progressively narrower at higher

voltages [11]. De la Mora determined that the current can be described as follows:

I =f(x)pσKQ/ (1.7)

where I is the current, f(x) is an empirical function determined by their experiments,

K is the conductivity, Q is the flow rate, and is the dielectric constant. Cherney

expanded on this work and found that the density and viscosity have little effect on the

structure of the cone-jet so long as they are large compared to the capillary and meniscus

surface tension forces. Density affects velocity and surface charge but not jet radius, and

viscosity only affects velocity inside the capillary [12]. In other words, the properties that

determine the shape of the cone-jet are only the electrical properties and surface tension.

Once the initial jet has formed, various instabilities in addition to the capillary

insta-bility assert themselves. One possiinsta-bility is that the breakup takes the form of a simple

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instability. In the case of high surface charge, however, this is a different mechanism

than the capillary instability. The droplets’ charge is sufficiently high, as described in

equation 1.6, for them to then break up further into smaller droplets. This breakup mode

reaches a limit with fluids of very low conductivities, such as kerosene. Such

nonconduc-tive fluids simply drip rather than forming a jet. The droplets they form are smaller than

the capillary from which the fluid flows. The electrical forces have difficulty drawing the

fluid out of the capillary, resulting in very low flow rates [13]. The lack of charge mobility

due to effectively zero conductivity is what prevents forming and sustaining a jet driven

by the flow of charge out of the meniscus. A second possibility is that the jet will begin

to develop ”kinks” or potentially even swirl around its axis with a progressively larger

radius. In a third breakup mode, the jet emits smaller jets off of it in a Christmas-tree

like pattern. These smaller jets then break into tiny droplets [14]. The third pattern was

confirmed for ethanol by Dunn, who also discovered that increasing the surface charge

will increase the number of tiny jets off of the main jet. Further down the spray, the

charge present on the droplets formed by these jets resembles a Fermi-Dirac distribution

[15]. Such a distribution implies that each droplet can be thought of as having energy

lev-els that are open to ions. The addition of each ion, then, occupies one of the energy levlev-els

and makes the addition of another ion to that droplet less favorable than to a different

droplet that does not yet have that energy level filled. It also implies that the droplets

should all be roughly the same size in order to minimize the energy and maximize the

entropy of the system. This will prove to be important in the use of electrosprays as an

atomization method for combustion.

Taylor cone-jets have been applied to textiles as a means of spinning highly viscous

polymers into threads. In modeling such spinning, Koombhongse and Yarin [16] derived

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resulting jet. For fluids where viscosity is a factor, the bending (or kink) perturbations

will grow much faster than the capillary instabilities if:

πµ2

ρλ2_ln(L/a

0)

>>1 (1.8)

where λ is the charge per unit length, L is the length of the jet before breakup, µis the

viscosity, and a0 is the radius of the jet. In all fluids used in the experiments herein,

surface tension will prove to be much more important than viscosity. For such a case,

the electrical repulsive forces will overwhelm the surface tension if:

λ2ln(L/a0)> πa0σ (1.9)

Here again one sees the same sort of relationship as in Equation 1.6 for the Rayleigh

instability of a charged droplet, this time derived for a cylinder of fluid instead of a

droplet. As before, the maximum charge is merely a function of the jet size and the

surface tension.

The length before breakup of a charged jet depends on both the stress due to the

mutual repulsion of charges on its surface and also a second stress from the presence of

the electric field produced by the charging electrode. According to Panofsky, this field

exerts stresses on the liquid both parallel and transverse to the field that are equal to:

0E2/2 (1.10)

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An external electric field exerts a volume force on a dielectric such that:

F =ρeE−

0

2∇+

0

2∇

E2d

dρρ

(1.11)

where ρe is the charge density in the volume. The Clausius-Mossotti relation provides a

relationship between and ρ:

−1

+ 2 =

N0ρα

3M (1.12)

whereN0 is Avogadro’s number, M is the molecular weight, and α is the polarizeability.

This can be used to find d_dρ, such that:

d

dρ =

N0α

9M (+ 2)

2

(1.13)

Panofsky used this relation to derive the pressure difference between two regions of

a dielectric liquid, but the same principle applies for the total volume force [17]. This

leads equation 1.11 to become:

F =ρeE−

0

2∇+

0

2∇

E2(+ 2)(−1)

3

(1.14)

The first term describes the force on the charge carried by the jet. The second can

be thought of as acting outward from the center of the jet along the surface of the jet.

It exists where changes from the value of the fluid to the value of air and so acts in

the opposite direction of the surface tension. The third term depends on the change in

the electric field. Some simplification of this term will aid in understanding the jet. If

we look at the component of the force purely down the axis of the jet and assume thatρ

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equation becomes:

F =ρeE+

0

6(+ 2)(−1)∇(E

2₎ _(1.15)

The first term will generally be a repulsive force downward from the charging electrode

and will simply increase the velocity of the jet. This increase in velocity, of course, will

result in a decrease in the jet’s radius as it falls and thus will facilitate breakup. Keeping

in mind that this ignores the boundary layer between the fluid and air, the second term

describes the stress on the jet due to the external electric field. The more pronounced

the inhomogeneities in the electric field, the greater this force becomes.

According to calculations by Thong and Weinberg [18], the enhanced electric field

strength about a small tip charged to a particular voltage is equal to:

E =

√

2V0

rln(4z0/r)

(1.16)

where z0 is the interelectrode distance and V0 is the applied voltage. The smaller the

needle and larger the ratio between the interelectrode distance and needle radius, the

greater the electric field enhancement around the needle tip. A strong localized electric

field about the needle tip will increase the field gradient as the jet flows away from the

needle tip, increasing the stress on the jet and facilitating breakup into droplets.

1.2.4 Jet Surface Charge: A Simple Model

The jet used in experiments differs somewhat from the electrospray jets described in

Section 1.2.3 in that the flow rate is much higher. For such a jet, one simple model that

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null at the center of the jet. The jet is modeled as an infinitely long cylinder, allowing

edge effects to be ignored. Starting with Gauss’s law, as well as the definition of electric

potential:

Z Z

E·dA= q

0

(1.17)

−∇V =E (1.18)

where V is the electric potential and A is the area. From here, it follows that:

E = q

0A

= q

2π0rl

(1.19)

wherer is the radius of the cylinder and l is its length. The linear charge densityλ may

be defined here as q/l. The potentialV may be found by integrating with respect to the

radius r, the only direction in which the field will vary:

V =−

Z

E·dr =−

Z _λ

2π0r

=− λ

2π0

[ln(r)−ln(r0)] (1.20)

If we set the potential V = 0 at r0 → ∞,, then the linear charge density is found to be:

λ = −2π0V0

ln(rs)

(1.21)

where V0 is the potential at the surface, v is the jet velocity, and rs is the radius of the

surface of the cylinder. The surface charge will thus approach a singularity as r → 0.

Because this cylinder is moving as the surface of the fluid jet, a current may be defined

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I =λv= −2π0V0v

ln(rs)

(1.22)

This current is what is largely looked at experimentally. Plugging in values forπ,0, and

rs = 0.0003m, this equation reduces to:

I =

6.85∗10−12 A∗s

V ∗m

∗V0∗v =

0.00685 µA∗s

kV ∗m

∗V0 ∗v (1.23)

This model will be compared to measured values in Section 2.4.

1.2.5 Electrospraying as an Atomizer

Based on the work of Dunn and Snarski [15] described in Section 1.2.3, one may conclude

that electrospraying would be a convenient way to produce an atomized spray. This is

indeed the case, and electrospraying has been studied for applications in combustion

systems. It has been found that such a spray produces somewhat evenly sized droplets

far downstream, once the droplets reach a form of electrostatic equilibrium. The spacing

between the droplets is due to the field produced by the charge on the droplets. The

rate of acceleration of the expansion of the area containing the droplets will decrease as

the spray travels farther downstream [19]. Increasing the applied electric field strength

will thus increase the spreading distance of the charged spray [20]. Gomez and Tang

found that larger charged droplets break up more readily than smaller droplets, even

when the charge-to-volume ratio of the larger droplets is lower than that of the smaller

droplets [21]. Droplet size should thus asymptotically approach a minimum such that,

given sufficient time, the droplets should be about the same size. Together, these findings

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The conductivity of the fluid is important in producing a useful atomized spray for

much the same reason as it matters in producing a Taylor cone-jet. The ability to produce

a jet seems essential in that it helps to initiate further breakup into smaller droplets.

Without a jet, the fluid will simply drip as single droplets and will not spread outward.

This presents a problem considering that the majority of widely used hydrocarbon fuels

are nonconductive, minimizing the effect that electric forces have on them. One solution

to this problem is to add an anti-static additive to the fuel [18]. This will increase its

conductivity such that normal electrospraying becomes possible, but it unfortunately can

also limit the choice of fuel and increase the cost of that fuel. A second popular solution

is to take advantage of the enhancement to electric field strength about a sharp tip

described in equation 1.16. The placement of a sharp nonconductive tip, such as a glass

filament, results in an enhanced charging rate of the nonconductive fluids and dispenses

with the need for any additives [20, 22, 23]. For such a setup, using a smaller aperture

and higher flow rate results in more charge being added to each volume of liquid, leading

to better atomization [20].

For more conductive fuels, such as ethanol and butanol, no further enhancement of the

spraying needle is necessary. Ethanol has already been seen in Section 1.2.3 to produce

an electrospray. Butanol can be used in much the same way, producing a spray similar

to that of ethanol in a Taylor cone-jet setup [24]. The spray produced is unfortunately

not entirely evenly sized, but effective atomization can still be achieved in this way. In

much the same way, hydrocarbon electrosprays were found to be not perfectly evenly

sized either. At the center of the spray are larger droplets with a smaller charge to mass

ratio, while smaller droplets with a higher charge to mass ratio spread out to the edges

[20]. The variation in droplet size should not be overstated, however.

(27)

version of the electrosprays described in the literature. Many of the instabilities that

exist are very similar to those in Taylor cone-jets, but simply on a larger scale. This

facilitated the investigation of a surface discharge along or through these sprays of the

type described in Section 1.2.8.

The presence of charge in the fuel has an effect on the flame shape and burning speed.

Positive charge on a fuel droplet serves to hold the flame together into more of a spherical

shape, counteracting the buoyancy of the heated products [25]. The downward force on

the charged particles from the field produced by the anode is the dominant effect in

this case. The addition of negative charge, on the other had, causes the flame to be

more turbulent than an uncharged flame [26]. This may be due to the positive charge

affecting the soot primarily, effectively only adding a charge to the products [25]. The

excess negative charge, on the other hand, is not as easily cast aside and so affects the

flame shape itself. One beneficial effect of excess negative charge, however, is that it

seems to result in reduced NOx production as the excess electrons are released when the

droplets evaporate [23]. The electrons here may simply act as a competitive oxidizing

agent, reducing the probability that a given nitrogen molecule will react with an oxygen

radical by taking its place.

1.2.6 Overview of Relevant Discharge Types

The Townsend discharge occurs silently and invisibly in the majority of situations. It is

a low power, low current discharge that occurs at electric field strengths that are too low

to cause a self-sustained discharge in the gas. According to Fridman and Kennedy [27],

(28)

i= i0exp(αd)

1−γ[exp(αd)−1] (1.24)

where d is the gap distance, dne_dx =αne where ne is the free electron number density and

α describes the rate of electron formation, and γ is a function of α such that:

αd =ln

1

γ + 1

(1.25)

The Townsend discharge thus occurs when the denominator in Equation 1.24 is

nonzero, meaning when the electron formation rate is sufficiently low. The value ofα as

a function of the reduced electric fieldE/phas been determined for many substances. It

can be calculated using the equation:

α

p =Aexp

− B

E/p

(1.26)

and experimentally determined values ofA and B. Values of A and B are 15_cm_·1_torr and 365_cmV_·_torr for air, and 13_cm_·1_torr and 290_cmV_·_torr for water vapor. These equations describe the beginnings of an electron avalanche, but below the field strength at which a streamer

could form. It should be noted that they ignore electron recombination with gases, but a

recombination rateβmay be added to reduceαsuch that dne_dx = (α−β)ne[27]. Streamers

will begin to form once the space charge left behind by such an avalanche is sufficiently

high (generating a potential equal to that of the anode) to sustain itself to the cathode

[28]. A spark is formed when a streamer reaches the cathode. The cathode, acting as an

electron reservoir, provides electrons that begin the propagation of a negatively charged

spark in the opposite direction, along the now positively charged path left behind by the

(29)

own space charge and by the attractive field left behind by the original streamer, causing

it to move at much higher speeds than the streamer did [27].

Electrical breakdown in an aerosol operates under similar principles to one in the gas

phase, except that charge attachment to and ionization of the aerosol particles must be

taken into account as well. Following the work of Karachevtsev and Fridman [27, 29, 30],

the electron formation rate in such a plasma depends not only on the simple electron

formation and recombination rates with molecules in the gap, but also on collisions

between electron or ions and the aerosol particles that may produce or absorb an electron.

Collisions between aerosol particles and photons emitted by electron-molecule collisions

(or emitted by absorbed electrons) may result in additional electrons as well. In the case

of a plasma in an aerosol, the Townsend limit becomes:

γef f

exp[α−β]d−1 + β

α−β[exp(α−β)d−1]

= 1 (1.27)

where α and β are the Townsend coefficients of detachment and attachment discussed

above, d is the gap distance, and γef f takes into account the production of electrons

from secondary collisions, primarily with the aerosol. Because α > β always, increasing

γef f will result in a decrease in the breakdown voltage. The only difference from the

Townsend discharge in a gas, then, is in the γef f term:

γef f =γikexp

−naσiad

νi

2νi d

+γia

1−exp

−naσiad

νi

2νi d

+γνk

µ(1−ν)

ki

+γνa µν

ki

(1.28)

where γik is the probability that a collision between an ion and aerosol will produce an

(30)

and aerosol,νi _{is the ion RMS velocity,}_νi

dis the ion drift velocity,γikis the probability of

a collision between an ion and the cathode producing an electron, γνk is the probability

that a collision between a photon and the cathode will produce an electron, µ is the

probability of emitting a photon in an electron-molecule collision, ν is the probability

that that photon collides with an aerosol, ki is the probability that an ion will form in a

collision between an electron and a gas molecule, andγνais the probability that a collision

between a photon and aerosol will produce an electron. The third term assumes that all

photons that do not collide with an aerosol reach the cathode, whereas the cross-sectional

area of the cathode is very small compared to the total area toward which the photons

can travel. Thus, the term may be ignored. The fourth term will increase as the ratio

of the aerosol’s area to the total photon flux’s travel area increases. In the setup used,

the total volume of all aerosols remains constant, so this term will increase as the size

of each particle decreases. The second term will increase in the same manner, as more

ions collide with the aerosols, but this will in turn decrease the first term. Considering

that the first term, concerning electron formation at the cathode, is likely already small

due to ions being lost to drift away from the cathode (and this drift is increased by the

presence of positive charge on the aerosols), the first term may be considered to be very

small.

The space charge of the charged aerosols will increase the effective electric field in

the gap, which will increase the effective electron formation rate and thus α. It will

increase the recombination rate β as well, but because β depends on a second collision

with non-unity probability by the newly formed electron, α will increase more than β

and the charge on the aerosols will, again, result in an increased electron production rate.

This, in turn, will decrease the voltage for the Townsend limit. The field produced by

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odds of a collision in the second term and also the odds that that collision will produce an

electron due to the higher available energy. The result is that, though uncharged aerosols

often increase the breakdown voltage due to the reduced probability that charges will

traverse the gap, charged aerosols result in a decrease in the breakdown voltage as a

result of increased electron formation.

1.2.7 Electrical Discharges in Water

Electrical discharges in water, in particular underwater discharges, have become the

subject of much research in recent years. Water purification has been the main goal of

many of these studies, utilizing the UV radiation and radical species generated by the

breakdown to decompose contaminants [31, 32, 33, 34]. The field at which breakdown

occurs in water is about 30 times the breakdown field in air, however. This is in large

part due to the low probability of an electron avalanche on account of the much shorter

mean free path available to electrons in a liquid. In addition, the high dielectric constant

of water decreases the intensity of localized electric fields, further limiting electron energy

gain. The mechanism behind the breakdown in water is thus still not entirely understood,

but the dominant theory is that it is actually the end result of discharges in small gas

bubbles within the discharge path [35]. These bubbles may be pre-existing gas pockets

within the liquid or may be formed when the pre-breakdown current in the liquid heats

and vaporizes some of the liquid. The bubbles then grow as the current continues to heat

the liquid until they are large enough for a breakdown avalanche to form in the gas [36].

Even in bubbles within the water, however, the cause of breakdown does not seem

to be a pure gas-phase electron avalanche. In de Baerdemaeker’s study of underwater

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a large gas bubble intentionally placed in the discharge path in water, the majority of

the voltage drop occurred in the bubble. This, along with the fact that the presence

of a large bubble reduced the breakdown field strength by up to 2 orders of magnitude,

lends credence to the idea that water discharges are still predominantly gas phase

dis-charges. Gershman also discovered that charge accumulates along the surface of the gas

bubble while voltage is applied to the system. A second discharge caused by this charge

propagates back in the opposite direction across the bubble’s surface after the voltage is

turned off. The reduction in the field strength necessary for breakdown makes the whole

process similar to a dielectric barrier discharge [31]. These findings were later seen by

Bruggeman in studying bubble discharges in capillaries. He observed that the breakdown

electric field decreases as the length of the bubbles in the capillary increases. The

break-down field in the bubbles was lower than that in air, confirming that a dielectric barrier

discharge along the surface is a likely mechanism [38].

For underwater discharges, the effect of conductivity seems to be to increase the

breakdown voltage. This happens in part because the more conductive water provides a

path for current to flow in the absence of breakdown, making the buildup of higher charge

concentrations and localized fields more difficult. According to Sunka, it also is due to

the fact that the ions dissolved in the water act similar to the free charge in a conductor,

counteracting some of the electric field due to the localized space charge at the heads

of streamers [28]. Clements discovered, however, that higher conductivity results in an

increase in the number of long magenta streamers. The difference here may be due to

the fact that Clements discovered that a positive applied voltage results in much more

and longer streamers than a negative applied voltage [36]. It will be shown in Section 3.2

that conductivity does decrease the breakdown voltage in the discharge along the surface

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findings. It must be stated, however, that the fact that increased conductivity decreases

breakdown voltage in the fluid jet case does not necessarily indicate that the same is true

for underwater discharges. In fact, the fluid jet does not provide a direct contiguous link

between the needle and ground electrodes in the experiments described herein, meaning

that the reduction in effective voltage due to current through the conductive fluid is not

applicable in the fluid jet case. The increased streamer production still applies, then, but

the detrimental effects on the voltage do not. This makes conductivity a net benefit for

the surface discharge along such a jet.

1.2.8 Discharge through a Fluid Jet

In studying the mechanism behind lightning in 1931, Macky discovered that water

droplets traveling through an electric field are elongated by the field. Tiny filaments,

very much like Taylor cone-jets, propagate from each end of the elongated droplet and

facilitate a discharge through the drop between the two electrodes forming the field. A

high enough electric field will virtually always result in a spark though the falling drop,

and the interelectrode voltage decreases as the drops become larger [39]. Water drops

were once again found to facilitate a discharge along a long path, guided by the stream of

drops, by Takaki in 2008. His experiment used highly conductive tap water that traveled

between two high voltage electrodes, resulting in a surface discharge along the water

droplets that then hopped between the droplets to traverse a 50 cm gap [40]. In both

cases, it is clear that the water provides a means of reducing the breakdown voltage

between the electrodes and helps to provide a path for the breakdown that occurs.

Shmelev [32, 41] studied the properties of a discharge through a contiguous jet of

(34)

from the needle through a grounded ring electrode. Once the capacitor charged to a

sufficiently high voltage, a discharge propagated along the surface of the water jet and

the resulting shock blew the jet into small droplets. The discharge then repeated and

blew apart the jet again once the contiguous jet had reformed the connection between

the two electrodes. In this case, the charging time of the capacitor was much less than

the travel time of the water between the electrodes, making the jet formation the cause

of the periodicity. It should be noted that the voltage used Shmelev’s his setup to charge

the needle was negative, unlike the positive voltage used for the experiments in Chapters

3-4.

Shmelev found three different discharge modes for the jet: a glow discharge mode,

a surface discharge, and an arc discharge. The important one to consider will be the

surface discharge, which resembles a dielectric barrier discharge. In such a discharge,

imperfections in the surface of the dielectric, such as the instabilities in the fluid jet

discussed in Section 1.2.2, locally enhance the electric field and cause the breakdown

voltage along the surface of the dielectric to be greatly reduced as compared to the

breakdown voltage in air [27]. The avalanche that results in this discharge still occurs in

the gas next to the dielectric, but it is aided by the localized field enhancements caused

by the presence of the dielectric. This low power surface discharge dissipates little of its

(35)

Chapter 2 Flow Characterization

2.1 Introduction

A fluid jet will behave differently when subjected to electrical forces than when simply

falling downward. This behavior resembles that described for Taylor cone-jets in Section

1.2.3. Depending on the fluid’s properties, it may produce a simple jet similar to how it

would behave under no electrical forces, may develop a spiraling jet that eventually breaks

up into droplets, or may simply break into a spray with a conic shape. The behavior of

conductive tap water, much less conductive distilled water, ethanol, and kerosene with

no anti-static additives will be examined. These fluids will pass through a needle that

is positively charged to several kilovolts and then travel downward through a grounded

ring. This will allow a qualitative comparison of these macroscopic, pump-driven jets to

the characteristics of Taylor cone-jets that are driven almost entirely by electrical forces.

Such a comparison will demonstrate how experiments performed on the discharge and

on ignition in Chapters 3-4 should apply to smaller scale jets and electrosprays.

(36)

Table 2.1: Fluid Properties, Physical

Fluid Density (_ccg) Viscosity (cP) Surface Tension (dyne_cm )

Water 1.027 0.911 73.56

Ethanol 0.787 1.057 23.39

n-Dodecane 0.745 1.390 24.94

n-Tridecane 0.754 1.718 25.5

n-Tetradecane 0.758 2.110 26.68

n-Pentadecane 0.765 2.558 26.68

Table 2.2: Fluid Properties, Electrical

Fluid Dipole Moment (Debye) Dielectric Constant Ionization Energy (eV)

Water 1.85 79.99 10.47

Ethanol 1.69 25.02 12.612

n-Dodecane 0 – 9.75

n-Tridecane 0 – 9.72

n-Tetradecane 0 – 9.72

n-Pentadecane 0 – 9.68

Kerosene – 2.086 –

Table 2.3: Fluid Properties, Conductivity

Fluid Conductivity (_cmµS)

Tap Water 213+11

Distilled Water 1.3+0.2

Ethanol 0.09+0.01

(37)

n-alkanes listed are included as representative of the major constituents of kerosene. The

majority of these data are from the Chemical Properties Handbook [42]. The n-alkane

ionization energies are from experimental data obtained by Zhou et al. [43]. Water and

ethanol ionization energies are from Lange’s Handbook of Chemistry [44]. Dielectric

constants were experimentally determined for ethanol and water by Mohsen-Nia et al.

[45] and for kerosene by El-Sharkawy et al. [46]. Fluid conductivities were measured

using an Oakton CON400 Series conductivity meter.

2.2 Calibration of the Pump

2.2.1 Procedures

The pump used in all experiments, an Ismatec Reglo-z, gave no indication of the fluid

flow rate but rather simply displayed a power setting as a percentage of its maximum

power. This meant that a calibration had to be performed to correlate the fluid flow

rate with the displayed power setting. A simple function describing this correlation was

found and used for all subsequent analysis.

The procedure for determining the fluid flow rate involved much the same setup that

will be used for all experiments, in particular the flow characterization under no applied

voltage described in Section 2.3. The pump input was connected to a fluid source bottle.

Its output fed into a tube leading to the 0.6 mm inner diameter and 0.9 mm outer

diameter source needle that was used for all experiments. The pump calibration was

performed using tap water. The fluid flowed out of the needle into a large graduated

cylinder, and the time required to feed a particular volume into the graduated cylinder

(38)

for the measurements to be taken in a practical amount of time for lower pump settings

while increasing precision at higher settings. The lower amount of water used to calibrate

at the lower end contributed to the greater variance of points at lower settings, as the

exact time elapsed to feed the fluid into the cylinder was harder to determine. This is

because the water adheres to the sides of the cylinder and a few drops on the sides of the

cylinder rather than in the pool of fluid at the bottom can change the measured time by

several seconds at such low flow rates. Also, the water level in the cylinder passes the

line indicating the amount of water measured much more slowly at low flow rates than at

higher flow rates; the slow movement of the water level made precise time measurements

more difficult with the equipment available.

2.2.2 Results

Figure 2.1 shows the jet velocity vs the pump power setting, where the jet velocity is

determined by:

v = Q

A =

4V

πd2_t (2.1)

Where v is the jet velocity, Q is the flow rate, A is the area of the needle aperture, V is

the volume collected, d is the inner diameter of the needle, and t is the time over which

the volume V was collected.

The relationship between the pump power setting and jet velocity is assumed to be

linear, with the y-intercept assumed to be zero because no fluid will flow when the pump is

turned off. The slope B, its uncertaintyσB, and the uncertainty in each point (assuming

that each point has the same uncertainty) σy may be found by using the equations:

B =

PN

i=1(xiyi) PN

(39)

0 10 20 30 40 50 60 70 80 0

0.5 1 1.5 2 2.5 3 3.5

Pump Power Setting

Jet Velocity, m/s

Figure 2.1: Calibration of the pump: jet velocity of the fluid leaving the needle vs.

(40)

σy = v u u t 1

N −1

N

X

i=1

(yi−Bxi)2 (2.3)

σB =

σy

q PN

i=1x2i

(2.4)

where xi and yi in this case are the pump power setting and jet velocity at that power

setting, respectively, and N is the total number of measurements, in this case 24 [47].

The slope of the fit seen in Figure 2.1 of the jet velocity vs power setting is thus

0.0456+0.0006m_s, and the uncertaintyσy in each point is 0.13 m_s. As can be seen from the

graph, this is likely an overestimate of the actual uncertainty due to the lower precision

of measurements at lower flow rates. The real imprecision in the pump’s flow rate should

be much lower than reported.

2.3 Spray Characterization Under No Voltage

2.3.1 Procedures

To measure the breakup time due to the capillary instability under no electric field, a

similar setup was used as to calibrate the pump. Tap water flowed from the Ismatec

Reglo-z pump to the 0.6 mm diameter stainless steel needle. The water traveled directly

down from the needle into the collection pan.

An Allied Vision Technologies Stingray camera was used to observe the spray. This

camera allowed for 1 megapixel images at exposure times of a few tens of microseconds.

This allowed the viewing of the jet at a high enough shutter speed that individual drops

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To find a quantitative description of the flow, the vertical length of the jet was

mea-sured. This vertical length is the distance directly down from the needle tip to the point

at which the jet begins to break up into droplets. These measurements were made by

counting the pixels in the images of the jet. To calibrate the length scale, a ruler was

placed behind the needle in the field of view of the camera. The ruler was only about a

centimeter behind the needle while the lens’s focal distance is 1 meter, so the ruler can

be said to be effectively in the same plane as the needle and jet. The number of pixels

that corresponded to one millimeter could then be counted.

Multiple images, such as the image for a jet speed of 0.91 m_s seen in Figure 2.2, were

taken for each flow rate. The sets of images were constructed by setting the camera to

record 12-22 images in sequence. What this involved was the camera being set to run at

15 fps and save every other image. The total saved images, then, numbered 12-22 and

all but two of the 41 flow rates measured had 17 images taken for them.

2.3.2 Results

Beginning at a flow velocity of 0.82 m/s, the jet breakup length depends linearly on the jet

velocity. Each jet length plotted in Figure 2.3 is the average length of all measurements

made at that velocity. The length is assumed to be normally distributed, such that the

uncertainty σx in the average length ¯x across N measurements is equal to:

σx=

v u u t

1

N(N−1)

N

X

i=1

(xi−x)¯ 2 (2.5)

This may be used to find a linear fity =A+Bxthat weights each point by its uncertainty

(42)

A =

P

(wx2₎P

(wy)−P

(wx)P

(wxy)

P

wP

(wx2₎₋_[P

(wx)]2 (2.6)

σA =

s

P

(wx2₎ P

wP

(wx2₎₋_[P

(wx)]2 (2.7)

B =

P

wP

(wxy)−P

(wx)P

(wy)

P

wP

(wx2₎₋_[P

(wx)]2 (2.8)

σB =

s

P

w

P

wP

(wx2₎₋_[P

(wx)]2 (2.9)

whereσAandσB are the uncertainties in A and B, respectively [47]. The slope of this

lin-ear relationship is 39.67+0.39mm_m/s, and it crosses the y-axis at a length of 9.30+0.56mm.

This slope is actually a time value of 39.67 ms, which is the breakup time of the jet.

The fact that the breakup length depends linearly on the jet velocity indicates that the

breakup time is constant, as would be expected if it is due to the instability modes

de-scribed in Section 1.2.2. The length increase is only due to the longer distance that the

jet travels in the breakup time. When the breakup time was calculated using Equations

1.2 through 1.5 and assuming that the initial disturbed amplitude of the jet was equal

to the outer diameter of the needle, the breakup time was calculated to be 5.64 s. This

overestimated the breakup time by a factor of about 15 by underestimating the initial

disturbance amplitude. Solving for the initial disturbed amplitude using the

experimen-tally determined breakup time yields an initial disturbed diameter of 1.34 mm, which is

1.5 times the outer diameter of the needle.

At velocities less than 0.82m_s, if we consider the breakup to be because of instabilities

(43)

(44)

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 0

10 20 30 40 50 60 70 80 90

Jet velocity, m/s

Jet Length at Breakup, mm

(45)

greater. This is the transition region from the flow simply falling out of the needle in

droplets at lower flow rates to the formation of a jet at higher flow rates. The initial

disturbance amplitude, then, must be higher. One may think of this phenomenon as a

string of droplets coming out of the needle that are close enough together that they form

a contiguous jet. At higher velocities, this effect is smoothed out more because the fluid

has less time next to the needle for its surface tension to cause it to begin to form into

a droplet.

In order to yield results that were not heavily affected by the transition region in the

flow, the majority of later measurements were taken at jet velocities greater than 0.82m_s.

2.4 Surface Charge on the Fluid Jet

2.4.1 Procedures

Measuring the surface charge carried by the fluid jet required measuring the current

flowing from the collection pan to ground. The basic setup was largely the same as

described in Section 2.3.1, with a few changes. The collection pan had the dimensions

of 30.48 cm long, 17.78 cm wide, and 7.62 cm tall. The pan was placed on top of either

a 0.75 cm thick sheet of nylon, electrically isolating it from the grounded optical table

surface. Given that the measured voltages were all less than 1 V and thus insufficient

to produce any sort of appreciable discharge, the fact that the sheet of nylon did not

cover the entirety of the gap between the pan and grounded table should not reduce the

measured current. A resistor connected the pan to ground, and the voltage across this

resistor was measured using a Extech Multimeter 420 so that the current carried by the

(46)

did not survive its use in preliminary ignition trials, so it was later replaced with a 1 MΩ

resistor.

Measurements were made for tap water, distilled water, ethanol, and kerosene. The

pan was half-filled with tap water for the ethanol measurements as a safety precaution

against accidental ignition. For the other fluids, the pan was filled with just a thin layer

of the fluid that ran into it before measurements were taken. As a control condition,

the current was measured with no fluid flow as well. The conditions for no fluid flow

were for the empty pan, the empty pan with a screen on top, the pan half filled with

either tap water or distilled water, the pan bottom coated with a layer of kerosene, and

the pan bottom coated with a layer of kerosene with the screen over the top of the

pan. The screen was present in kerosene ignition experiments in order to prevent a pool

fire. Measurements were taken with the needle mount charged from 1 - 9 kV. At higher

voltages, the discharge became less stable and so made the voltage across the resistor too

erratic to measure. Three sets of such data were taken for each fluid so as to compare

different flow rates. To measure the effect of flow rate more closely, the flow rate was

varied while the voltage was held constant at 3 kV, 5 kV, and 7 kV for each fluid as

well. The flow rates corresponded to jet velocities of between 0.684m_s and 1.64m_s for

these experiments.

Further investigation was performed to find whether there existed a limit to the

charging mechanism. The measurements made for tap water were further extended at 3

kV, 5 kV, and 7 kV far past the highest velocities used for the other fluids. The highest

velocity used in these trials was 3.88m_s, which is near the pump’s upper limit. Another

set of trials were taken with the velocity held constant, as before, but again with much

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2.4.2 Results: No Fluid Flow

With no fluid flow, a measurable current out of the pan started at just above 6 kV. This

is the result of a corona discharge, beginning in the enhanced field region surrounding

the needle and ending at the pan. The magnitude of this discharge increases with voltage

and was measured between 6 kV and 10 kV. Many of the voltages for which no current

could be measured are omitted from any plots for the sake of clarity, as seen in Figure

2.4. The uncertainty in all voltmeter measurements was assumed to be either + 0.002 V

or 5%, whichever is greater. This uncertainty in voltage propagates through for current

such that:

I = V

R →δI =

∂ ∂V V R

δV = 1

RδV (2.10)

where r is the radius of the needle, v is the jet velocity, I is the current, V is the measured

voltage on the voltmeter, and R is the resistor across which voltage measurements were

taken.

It is immediately clear that the presence of water in the pan, whether more conductive

tap water or distilled water, greatly reduces the discharge current and increases the

minimum voltage necessary to initiate such a discharge to a measurable level. The

insulating effects of the water required that the voltage increase from 6.3 kV to 7.6 kV,

an increase of 23%, before a measurable discharge began. It is unclear, then, whether

any current flowed through the water at all. The pan was only filled halfway with water,

meaning that the conductive sides remained exposed. This would greatly reduce the

ground electrode’s surface area, decreasing it by 71% from 1276 cm2 _{to 367} _cm2_{. That}

no charge flowed into the water does not seem likely considering that the difference in

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the effective electric field toward the parts of the pan that contained the water, reducing

the total measured discharge current while not eliminating charge flow into the pan. One

must also consider that, with much of the pan covered by a dielectric, the other grounds

surrounding the needle may become more significant. These grounds include the stage

and the optical table. Current continues to flow, but less of it goes to the pan.

The pan filled with tap water registered a slightly higher discharge current than the

pan filled with distilled water, indicating that the conductivity of the fluid in the pan

may play a small role. The uncertainties in the measurements for distilled water and

tap water overlap, however, so these results may be misleading. Assuming they are

indicative of a trend, however, indicates that greater conductivity seems to facilitate the

discharge by reducing the impact of covering so much of the pan’s surface area. There

was less current with a thin layer of kerosene in the bottom of the pan (simulating the

small amount of kerosene present during other experiments) than for the empty pan as

well. The exposed surface of the pan was roughly double with the kerosene layer what

it was with the pan half-filled with water, so the simplest explanation here must be that

the decrease in exposed surface area was the dominant cause of the decrease in current.

In this vein, it can be stated that the reduction in surface area depends on both the

thickness of the layer of insulating fluid in the pan and the conductivity of that fluid.

Extrapolating from Figure 2.4, one can see that at higher voltages the conductivity will

begin to have a larger effect, as the corona discharge through the kerosene looks as if

it will soon converge with and become less than that of the tap water. The effect of

the dielectric constant of the fluid on the magnitude of the discharge current cannot be

determined from these data.

As is to be expected in a discharge at constant voltage, the greatest factor is the

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6 6.5 7 7.5 8 8.5 9 9.5 10 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7

Applied Voltage, kV

Corona Discharge Current, uA

Empty Pan

Empty Pan with Screen Empty Pan with Kerosene Layer

Empty Pan with Kerosene Layer and Screen Pan Filled with Tap Water

Pan Filled with Distilled Water

Ignition of a Liquid Fuel Jet by an Electrical Discharge Propagating along the Jet.

ABSTRACT

DEDICATION

BIOGRAPHY

ACKNOWLEDGEMENTS

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

Chapter 1

Introduction

1.1

Thesis Objectives

1.2

Background

1.2.1

Classical Spark Ignition and Motivations for New Ignition

Systems

1.2.2

Capillary Instability of a Fluid Jet

1.2.3

Electrosprays and Taylor Cones

1.2.4

Jet Surface Charge: A Simple Model

1.2.5

Electrospraying as an Atomizer

1.2.6

Overview of Relevant Discharge Types

1.2.7

Electrical Discharges in Water

1.2.8

Discharge through a Fluid Jet

Chapter 2

Flow Characterization

2.1

Introduction

2.2

Calibration of the Pump

2.2.1

Procedures

2.2.2

Results

2.3

Spray Characterization Under No Voltage

2.3.1

Procedures

2.3.2

Results

2.4

Surface Charge on the Fluid Jet

2.4.1

Procedures

2.4.2

Results: No Fluid Flow