Supervisor; Professor R. M. Clements ii
A bstract
The p la sm a je t, a com m only u sed ignition device, h a s b een investigated as a source of acoustic energy su itab le for sub-bottom profiling. Named th e plasm a gun, th e device discharges electrical energy in a cylindrical a rc ignited in a g a se o u s en v iro n m en t su rro u n d e d by w ater. W hen th e arc energy evaporates w ater, it produces a rapidly expanding vapor bubble th a t creates th e acoustic pressure wave.
Acoustic properties of th e device are sim ilar to sm all explosives, and to electric sparkers. M ultiple bubble oscillations, a problem of explosive-type sources, are generally less troublesom e for the plasm a gun th a n w ith the sparker sources. Some degree of frequency control of the acoustic pulse is possible if proper values are selected for the electrical circ u it co m p o n en ts a n d for th e to ta l sto red electrical energy. P eak acoustic p re ssu re s are controlled b o th by th e total electric energy an d by th e ra te it is delivered to th e arc. These quantities are determ ined by capacitance, inductance, and charging voltage. Frequency com ponents of the prim ary pressure pulse depend on th e arc discharge frequency and on th e im m ersion d ep th of the device. The bubble period depends prim arily on the am ount of energy discharged into th e water; th is in tu rn is proportional to th e total stored electrical energy.
The p lasm a gun h a s been com pared to sm all air gu n s, pingers, sp a rk e rs , a n d b o o m ers. S u b -b o tto m p ro files o b ta in e d show penetration less th a n the 1 in3 air gun b u t with more resolution.
iii
Stored energy in the plasm a gun, however, w as nearly five tim es less. Penetration w as equal and resolution better th an electric sp ark ers of the sam e energy. Penetration w as b etter and resolution poorer th a n the pinger, an d resolution poorer and penetration slightly b etter th a n the boom er source. Except for th e sparkers, w hich used th e sam e power supply, the plasm a gun h as a decided advantage in equipm ent size a n d ease of deployment.
Examiners:
Dr. R. M. Clements, Supervisor (Dept, of Physics and Astronomy)
Dr. G. B. Friedm ann, Dept. Member (Dept, of Physics and Astronomy)
Dr. A. Watton, Dept. Member (Dept, of Physics and Astronomy)
Dr. R. NjCyBden. Outside Member (Dept, of Chemirtiy)
Dr. D. M. Farm er, O utside Member (Institute of Ocean Sciences)
Dr. D. R. Topham, Outside Member (Institute of Ocean Sciences)
Dr. H. Hopkins, External Examiner (Woods Hole Oceanographic Institution)
iv
Table of Contents
A bstract ii
Table of C ontents iv
List of Figures vii
Acknowledgements x
1
Introduction
1
1.1 Underwater acoustic source review 1
1.1.1 The air gun 2
1.1.2 The electric sp a rk e r 2
1.1.3 Boomer types of sources 4
1.2 General considerations for acoustic sources 4
1.3 Plasm a je t historical review 5
1.4 Outline of rem aining ch ap ters 8
2
Preliminary experiments
10
2.1 Prototype device 10
2.2 The seagoing device 16
2.3 Single waveform p re ssu re signatures 17
3
Detailed single hydrophone measurements
20
3.1 Pressure m easurem ents in large volume
environm ents 2 0
3.2 Pressure m easurem ents in limited volume
environm ents 2 5
V
3.2.1b R esults of cavity size experim ents 2 9 3.2.2 Air flowrate effects on peak p re ssu re 2 9 3.2.3 The effect of stored electrical energy on
bubble pulse peiiod 30
3.2.4 Circuit inductance and capacitance effects
on the prim ary pulse shape 31
3 .2 .4 a The effect of m aximum cu rren t o n peak
pressure 31
3.2.4b C apacitance and inductance effects
on prim ary pulse width 35
3.2.5 Results of circuit param eters on th e
acoustic pressu re signature 37
4 F requency a n d energy m easu rem en ts 3 8
4.1 Acoustic spectral analyses 3 8
4.1.1 Frequency analyses conclusions an d
discussion 4 6
4.2 Energy analyses 47
4.2.1 Energy and efficiency resu lts 51
5 Theoretical models
52
5.1 In troduction to th e modeling 52
5.2 The first few m icroseconds 52
5.3 The first few h u n d red m icroseconds 57
5.4 The first few m illiseconds 6 3
5.4.1 D iscussion of the millisecond m odeling 6 8 5.5 D iscussion of the overall modeling 6 9
6
Seismic profiling
71
6.1 In troduction to profiling 71
6.2 C om parison sub-bottom reflection profiles 73 6.2.1 Plasm a gun records over various bottom s 73
vi
6.2.2 Air gu n (1 in3) an d plasm a g u n com parison 75 6.2.3 Com parison of plasm a gun an d sp ark er units 79 6.2.4 Com parison of th e pinger (Raytheon 7kHz)
and th e plasm a g un 8 3
6.2.5 Com parison of the plasm a gu n and th e boomer
(&G&G Uniboom®) source 86
6.3 Profiling system developm ent 8 9
7
Conclusions and recommendations
90
7.1 Conclusions 90
7.2 Recom m endations for fu rth er stu d y 92
7.2.1 Platform stability 92
7.2.2 Multiple so u rces 93
7.2.3 Reproducibility of pressure signature 93 7.2.4 S tudy of o th er physical processes 93
References
95
Appendix A Near and far radiation fields
100
vii
List of Figures
1.1 Schem atic of plasm a je t and circuitry. 6 2.1 Prototype underw ater plasm a je t. 10
2.2 Electrical circuit diagram . 11
2.3 High speed photographs of bubble growth after
u n d erw ater discharge of a 5 J plasm a jet. 12 2 .4 Video shadow graph images of the bubble growth
after underw ater discharge of a 10 J plasm a jet. 13 2.5 Video shadow graph showing shock wave a t bubble
collapse. 14
2.6 Received acoustic signal from 30 J scored
electrical energy plasm a je t. 15
2.7 C ross-section of th e plasm a gun. 17 2.8 Near, interm ediate, and far field p ressu re
sig n atu res of the plasm a gun. 18
3.1 Polar plot of sound pressure level m easured at
0.711 m. 2 2
3.2 Polar plot of sound pressure level m easu red at
0 .3 5 6 m. 22
3.3 Parallel an d coaxial sp ark cr electrodes. 2 3 3.4 P ressure signatures of sparkers an d plasm a gun. 2 4 3 .5 D eploym ent schem e for n e a r an d far field
m easu rem en ts. 2 5
viii 2 7 2 8 2 9 31 3 2 3 2 3 5 3 6 3 9 41 41 4 2 4 3 4 4 4 4 4 5 4 6 4 7 4 9 5 0 5 0 5 3 5 6 5 7 5 8 Effect of cavity size on pressure param eters.
3.7 a and 3.7 b. 3.7 c and 3.7 d.
Effects of airflow on peak pressure.
Bubble period v ersu s cube root of stored energy. Acoustic p ressu re versus discharge current. Acoustic p ressu re versus discharge cu rren t
squared.
Peak cu rren t v ersu s capacitor voltage. Pulse w idth v ersu s capacitance.
Bubble frequency versus stored energy. Normalized p ressu re versus tim e for low an d high frequency discharges.
Power sp ectra for low and high frequency discharges.
Synthesized normalized pressu re versus time. Power spectrum including bubble pulse.
A ctual far field signature.
Power spectrum for real pressure signature. P ressu re sig n atu res for different reflection tim es. Power sp e ctra of p ressu re signatures with
different reflection tim es.
Commonly used pressure signature param eters. Energy versus tim e for plasm a gun.
Energy v ersu s tim e for parallel sparker. Energy v ersu s tim e for coaxial sparker. Geometry of th e plasm a cavity and of the expanding arc channel.
Normalized therm al area versus time. Expanding hem ispherical vapor bubble.
lx 5.5 P ressure v ersu s time for model an d experim ent I. 62 5.6 P ressure versus time for model an d experim ent II. 62 5.7 Expanding spherical bubble and pressure pulse. 64 5.8 Sequence of shadow graph video images showing
bubble growth. 66
5.9 P ressure versus time for spherical bubble model. 67 5.10 Bubble model an d experimental p ressures. 67 6.1 Block diagram of seismic profiling system . 72 6.2 Exam ples of plasm a gun records over three
sub-bottom s. 7 4
6.3 Com parative seism ic reflection profiles,
plasm a gun and air gun 7 6
6 .4 Com parison of acoustic survey techniques. 78 6.5 Plasm a gun profile of Cadboro Bay. 81 6.6 Parallel sp ark er profile of Cadboro Bay. 82 6.7 Pinger sub-Dottom profile of Patricia Bay. 84 6.8 Plasm a gun sub-bottom profile of Patricia Bay. 85 6.9 Plasm a gun profile of Patricia Bay. 87
6 .8 Boomer profile of Patricia Bay. 88
X
ACKNOWLEDGEMENTS
I would like to tk a n k my supervisors Dr. Monty Clem ents for his assistance in the research and the preparation of th is dissertation, and for the use of his sailing vessel Sabrina, and Dr. David Topham for his guidance in the theoretical portion of th e study. Finally to m y wife, Ja n e t, very special th a n k s for putting up with this endeavor th is late in our lives.
Special th a n k s a re also due to th e R esearch A ssociates and Technicians th a t have been involved in th is research during th e p a st six years, in particular: David Ridley, Russell W arren, Gary Sheffler, Law rence P itt. David S m ith, P eter W ard, Lin S u n a n d Owen S tep h en so n . The u s e of the facilities of th e In stitu te of Ocean S c ie n c e s a n d th e P acific G eo scien ces C e n tre is g ra te fu lly acknowledged. The help accorded by Dr. T. S. Hamilton of PGC and the officers and crew of th e C. S. S. Parizeau w as particularly useful. Dr. P. R. Smy and R. F. Hafiey of the University of Alberta kindly lent th eir equipm ent an d help for th e high speed video im ages. Adelle Clements kindly gave h er editorial expertise.
The financial su p p o rt provided by th e B ritish Colum bia Science Council, the N atural Science and Engineering Research Council, Butte College, an d by th e Physics and Astronom y D epartm ent is greatly acknowledged.
CHAPTER 1
Introduction
1.1 Underwater acoustic source historical review.
One of th e first references to the u se of sound as a tool to locate objects in th e se a w as by Leonardo d a Vinci late in the fifteenth century. The development of underw ater acoustics did not proceed in e a rn e st, however, u n til naval-m ilitary estab lish m e n ts required sea detection a p p a ra tu s to u se ag a in st opposing forces early in th is cen tu ry . Com m ercial applications of th e se m ilitary devices have t_volved into sta n d a rd in stru m en ts for conventional depth sounding, b o tto m profiling, detection of su b -b o tto m geologic featu res, and com m unications [Urick 1975].
The m ajority of underw ater acoustic sources now in u se present are grouped in two broad areas—im pulsive and electromagnetic. The la tte r type re su lts from th e reaction of a m aterial object to periodic electric or m agnetic fields. While im pulsive sources, including air g u n s, w ater guns, and sp arkers are necessarily single sh o t or low repetition ra te devices, electrom agnetic devices, such as piezoelectric crystals, are able to be used repetitively. The properties of m any of th e se devices are sum m arized by B unce 11980]. Im pulsive type sources presently in use in underw ater acoustics are primarily air guns and to a le sse r ex ten t electric s p a rk e rs. B ecause of probable environm ental harm , underw ater u se of large chemical explosives is uncom m on.
A class of sources, represented by th e boomer, th e Uniboom®, a n d th e B ubble Pulser® have som e ch a ra c te ristic s of b o th th e impulsive an d continuous electromagnetic sources. The pulse shape is sim ilar to a n impulsive device b u t th e repetition, although a t a lower frequency, h a s sim ilar characteristics to th e electromagnetic sources.
CHAPTER 1. INTRODUCTION
2
B ecause this dissertation reports the study of the processes of an impulsive acoustic source, the details of repetitive sources will only be discussed peripherally. The impulsive acoustic source is prim arily used for sub-bottom profiling. Because the technique used is 1 tased on m easurem ents in the far field of the acoustic source, a d iscu ssio n of the far field is included in Appendix A. Most co m p ariso n s of the plasm a device will be m ade to air guns, electric s p a rk e rs, and to boomers. The following discussion will provide th e b ack g ro u n d for these devices.
1.1.1 The air gun
The air gun is a pneum atic acoustic source. It co n sists of an air com pressor with storage reservoir, and control system a b o a rd ship. An underw ater cham ber connected pneum atically an d electrically to the ship allows p ressu rizatio n and control to ven t a ir p ressu rized between 5 to 30 MPa. The explosive venting of the high p ressu re air re s u lts in a n in itial p re ssu re wave followed by se v e ra l b u b b le oscillations. Each succeeding oscillation h a s a sh o rter period because of energy losses to th e surroundings. The collapse of th e 1 >ubble can produce su bsequent p ressu re pulses greater th a n th e in iti;.' p ressu re pulse. Some degree of control of the shape of the p re ssu re signature of a n air gu n can bo achieved by altering th e size of th e p ressu re cham ber and the am o u n t of air pressure applied {Parkes a n d H atton i386],
1.1.2 The electric sparker.
The electric sp a rk e r is one of th e sim plest devices for producing an acoustic pulse. The system consists of a high voltage pow er supply, a sw itching circuit, an d a pair of electrodes. On firing, th e stored electrical energy is discharged between th e two electro d es th ro u g h the seawater. The discharge vaporizes the seaw ater into steam , gases, and plasm a consisting of various ions, electrons, and atom s. The rapid vaporization produces the initial acoustic pulse. As w ith th e air gun,
CHAPTER 1. INTRODUCTION
3
contraction and re-expansion of the cooling steam bubble resu lts in a series of pressure pulsations of decreasing periods. Since the sparker pro d u ces a bub b le prim arily of steam , th e ten d en cy for repeated b ub b le oscillations is som ewhat reduced com pared to th e a ir gun because m ost gas is condensed after the first contractions (air in the air g u n bubble i kes longer to be absorbed by the surrounding w ater [Kramer et al. 1968]). Peak p ressu res of the collapsing bubbles may also exceed th e prim ary pressure pulse [Kosenko et al. 1980]. Because of th e relatively poor conductivity of fresh w ater com pared to sea w ater electrical sp a rk e rs do not work reliably in fresh v/rder u n le ss the voltages used are very high. This also affects th eir shot-to-shot reproducibility in n e a r shore marine environn. 'n ts of variable salinity. An electrodeless sp ark undei .vater sound source having m any sim ilar characteristics of sp ark e rs b u t with b etter reproducibility h a s been investigated by Wright [1970].
A certain degree of control over p en etratio n a n d resolution of a sp ark ers gives them a versatility com parable to air guns when various power supply and electrode geometry com binations are used. Stored energy can be varied by changing e ith er th e value of the storage capacitors in the power supply, the charging voltage, or both. The n a tu re of the electrical d isch arg e-p ea k current, cu rre n t duration, and electrical dam p in g can be p artia lly controlled by ch an g in g th e electrical com ponents of th e total circ u it—capacitance, inductance, and resistance. The shape of the initial acoustic pulse is also affected by th e electrical p aram eters and electrode geom etries; th e period of the bubble p u lsatio n depends on th e total electrical energy stored in the circuit [Caulfield 1962].
CHAPTER 1. INTRODUCTION
4
1.1.3 Boomer types of acoustic sources.
These devices, som etim es called p u lsed electrom agnetic, operate on Lenz' law, i.e. th a t a changing m agnetic field will induce cu rren ts in su rro u n d in g con d u cto rs th a t will oppose th e in d u cin g change. When current in a coil adjacent to a conducting disk (or p air of disks) forces th e d isk s away from the coil, th e rap id ity of th e m ovem ent creates a p ressu re wave in the su rro u n d in g w ater. The sh ap e of the p ressu re p u lse is controlled by th e sizes of th e d isk s, th e p eak cu rren t, and th e c u rre n t duration. B ecause of its m echanical an d electric a stability, boom er p re ssu re tra c e s are very reproducible. Boomer sources are directional, the p ressu re p u lse is confined w ithin a cone of approxim ately 60° w ith h ig h e r freq u en cy co m p o n en ts limited to only 10°. In m oderate se a s th is directionality lim its th e contoJ of th e position of the a rea insonified by th e device (the footprint). In ten sity of the p ressu re p u lse is lim ited by cavitation effects from the plates returning to th e ir equilibrium positions. A loosely fitting Texible m em brane to reduce th e cavitation covers th e outer surface of the conducting disk in the Uniboom® device.
1.2 General considerations for acoustic sources.
An ideal acoustic source would have a very fa st rising p re ssu re pulse. This pressure signature would th e n contain a very wide b an d of acoustic frequencies which could be used w ith various com binations of filtering to stu d y different sizes of objects a n d to probe to different d ep th s. The reso lu tio n of a n a c o u stic so u rce d ep e n d s u p o n its effective operating frequency, the higher th e frequency th e b e tte r the resolution. B ecause w ater and e a rth m a te ria ls a tte n u a te aco u stic energy approxim ately as th e sq u are of th e frequency (Urick 1975], lower freq u en cy so u rc e s (poor resolvers) provide b e tte r p en e tratio n . Real acoustic so u rc e s c a n only ap p ro x im a te th e ch a ra cte ristics of a n ideal source, a n d a re alw ays a com prom ise between resolution and penetration. Repeated p re ssu re p u lses d u e to the collapses a n d expansions of g as b u b b le s a re to be avoided if
CHAPTER 1. INTRODUCTION 5
possible to prevent further confusion of the acoustic signature [Parkes and H atton 1986].
A ttem pts to elim inate b u b b le o scilla tio n s from explosive type devices depend on the d estru ctio n of th e bubble. Devices have been added to air guns th a t reinflate th e collapsing bubble, preventing it from collapsing. Bubble oscillation c a n be reduced for a irg u n s and sp ark e rs by towing them slightly subm erged so the b u b b les b reak w hen they pierce the w ater surface. U nw anted bubble p u lsatio n s can also be ameliorated by arrays of individual devices operated a t different energies. B ecause the tim e betw een th e prim ary p ressu re p u lse and the bubble pulse depends on th e energy deposited into the w ater, the bubble pulses from different individual so u rces w ithin an a rra y will occur at differing tim es, b u t th e p rim ary p u lses will all begin a t the sam e time if triggering is sim u ltan eo u s. U nder these conditions, the prim ary pulses will add constructively w hereas the bubble p u lse s will not. M athem atical te c h n iq u e s e x ist to deconvolve th e p rim ary p ressu re p u lse from the bubble p u lse if th e sh ap e of th e p re ssu re signature is accurately known. U nfortunately individual airg u n s and sparkers produce varying sig n atu res because the bubbles produced by them do n o t have the sam e geom etric shape. The pulse sh ap in g th a t resu lts from using arrays does w aste potentially useful energy, b u t it is expedient.
1.3 Plasma jet historical review.
The following se ctio n is in c lu d e d to give th e re a d e r som e perspective of the operation of th e p la sm a je t, som e of th e stu d ies of its operation, and some of th e u s e s th a t have been found for th e device.
T he origin a n d th e in v e n to rs o f th e p u lse d p la sm a j e t are som ew hat in dispute. A lthough several U. S. p a te n ts were issu ed between 1959 and 1971 for sp a rk igniters th a t u se the concept of a c en tral electrode recessed below th e su rface of th e plug, th e first published account of the u se of th e p la sm a je t a s a device to en h an ce
CHAPTER 1. INTRODUCTION
6
com bustion w as given by Topham , et al. 11975). (W aterston [1973J used a sim ilar device in ignition stu d ies for h is doctoral dissertation, b u t his work rem ains unpublished).
During th e p a st fifteen years, th e plasm a je t a s an ignition source in internal com bustion engines fueled by gaseous a n d liquid fuels h as held the in te re st of m any investigators. M uch of th is work h a s been sum m arized by Clem ents (1984). These stu d ies have generally been directed tow ard th e en h an ce d co m b u stio n of le a n e r th a n norm al m ixtures of fuel and air w ith the hope th a t m ore efficient, faster, and clean er b u rn in g w ould re s u lt. The ig nition of g a se s in hostile environm ents of tem perature and p ressu re h as also been investigated. The plasm a je t w as studied a s a source to ignite u n a tte n d e d furnaces in a n arctic environm ent by Cote et al. [1986] a n d by Pearce et al. [1990], and to reignite a je t engine in a sim ulated situ atio n of flameout by Cheriyan et al. [1990]. A lthough the plasm a je t devices used by each of the various experim enters are slightly different the essential details are show n in Figure 1.1.
Trigger Circuit
Discharge Circuit
Figure 1.1: Schem atic of plasm a je t an d circuitry.
The discharge circuit co n sists of two se p arate sections: a trigger circuit and a storage circuit. In firing, th e trigger circu it sw itches a small charged capacitor acro ss a p u lse tran sfo rm er producing a high voltage across th e the cavity of th e p lasm a je t (between th e central and the end plate electrodes). T his c a u se s th e g a se s in th e cavity to
End Plate Electrode ” (grounded) — Plasm a Cavity •Insulator
CHAPTER 1. INTRODUCTION
7
ionize creating a conductive p ath . The storage circuit containing up to several h u n d re d jo u le s of electrical energy c a n then discharge c u rre n ts u p to th o u s a n d s of am peres. The trigger circuit and the storage circuit are isolated from each other by either an inductor or a b an k of diodes.
When a large am ount of electrical energy is supplied to a plasm a in a blind cavity in a sh o rt period of time, a je t of plasm a is ejected from the open end of the cavity. This plasm a contains ions, electrons, and n e u tra l atom s and m olecules. T em p eratu res of th e plasm a on th e order of 104 K have been m easured by several investigators [Topham 1972a, b]. The highly energetic and che.-iically active n atu re of the discharge h a s been detailed in com bustion stu d ies relating to shock heating and turbulence T o p h am et al. 1986) and the effect th a t free rad icals an d chem istry play in th e process h a s also been reported. [Weinberg et al. 1978], [Clements et al. 1984] and [Ridley et al. 1985].
Topham e t al. [1975] were the first to extensively study the n atu re of the discharge in a gaseous environm ent in and n ear the cavity of the plasm a jet. They investigated the sh ap e of th e discharge using both fram ing and strea k photography, m easured p re ssu re s on and off axis, and calculated electron d en sity a n d gas te m p eratu re. Smy et al. [1982] m easured plasm a j e t exit velocities of the order of 5 x 103 m / s and showed th a t there were thin bo u n d aries (< 1 mm) of th e Jet. The large s h e a r forces th a t developed re s u lt in large instabilities th a t p ro d u ced c o n sid era b le tu rb u le n c e . T he tu rb u le n t do w n stream stru ctu re of th e plasm a je t ex h a u st investigated in more detail by Smy et al. [1987] w as found to be sim ilar to th e aerodynam ic shock stru c tu re ch aracteristic of highly under-expanded Jet flow detailed by Adamson an d Nicholls [1959].
The detailed developm ent of the arc discharge within th e plasm a je t cavity linking the energy an d m om entum of th e ejected fluid to the electrical in p u t p aram eters an d th e cavity size is being investigated by Topham [1990], In th is a n a ly sis th e a rc p ro cess is th a t of a q uasi-steady su p erso n ic Je t driven by a variable stagnation p ressu re
CHAPTER 1. INTRODUCTION
8
which is sim ilar in tem poral sh ap e to the c u rre n t in p u t waveform. The model sim u lates an expanding rad ial electric arc ru n n in g the length of th e cavity actin g a s a ra d ia l p isto n th a t produces th e n ecessary driving p ressu re. T opham 's model is based on h is earlier w orks [Topham 1971 a n d 1972a, b] an d on th e work of Cowley [1974]. Both studies model a more general class of cylindrical electric arcs a n d th e m athem atical tech n iq u es th a t characterize them . The theoretical developm ent of th e very early stages of the pressure pulse of the p lasm a je t discharging underw ater in th is dissertation is based on these analyses.
1.4 Outline of remaining chapters.
Three objectives guided the work in th is dissertation:
1. To investigate the relevant physics involved in discharging the pu lsed plasm a je t u n d erw ater and th e acoustic pulse th a t it develops.
2. To develop a theoretical model w hich describes the physics as closely a s possible.
3. To u s e a device th a t evolved from th e initial experim ents and describe its perform ance as a n underw ater acoustic source. E x p erim en ts were carrie d o u t in lab o rato ries, from docks and piers, a n d abo ard ship to determ ine th e b asic physics of the device. Most of th e p h y sics w as initially d eterm in ed from th e ac o u stic p ressu re signature, which could only be separated from the m ultitude of aco u stic reflections p re s e n t in sm all enclosed environm ents by m aking m easurem ents aboard ships.
P relim inary experim ents involved adapting th e traditional plasm a je t igniter to discharge reliably u n d erw ater an d studying the process u sin g h ig h sp eed im aging m e th o d s. P re ssu re sig n a tu re s w ere originally m easu red in sm all volum e acoustical ta n k s, b u t reflection p ro b lem s in d ic a te d m e a s u re m e n ts s h o u ld b e m ade in la rg e r environm ents. M easurem ents m ade a t the dock of the Royal Victoria Yacht C lub yielded positive p relim in ary re s u lts . These led to th e
CHAPTER i . INTRODUCTION 9
construction of a device th a t w as u sed as a n acoustic source during a geophysical c ru ise ab o a rd th e CSS Parizeau along inlets in the m ainland coast of B ritish Colum bia. The acoustic performance of the device, now nam ed the p la sm a gun, was by this time deemed to be of sufficient value th a t p a te n ts for th e concepts were applied for. (See P aten ts [1988])
Physical processes th a t related th e stored electrical energy, the arc processes in th e p la sm a cavity, the development of the acoustic p ressu re pulse in th e w ater, an d th e extent th a t the p ressu re pulse could be controlled were poorly understood during this prelim inary experim ental period. It w as determ ined th a t to develop the plasm a gun a s an acoustic source, detailed m easurem ents of the effects of electrical circuit p a ram ete rs an d plasm a cavity geometry had on the p re s s u re s ig n a tu re w o u ld be n e c e ssa ry . N ear field p re s s u re m easu rem en ts were co n d u cted in a larger acoustical facility (2.4 m diam eter by 2.4 m height) a n d a t th e dock of the Institute of Ocean Sciences, Sidney, B. C. B oth n e a r and far field sig n atu res were m easu red in Cadboro B ay a n d H aro S trait from the sailing vessel
Sabrina.
A th e o re tic a l m odel re la tin g th e p re ssu re sig n a tu re to the electrical p a ram ete rs a n d sto re d energy th a t produced reasonable re su lts w as developed u s in g previous work on cylindrical electrical arcs, classical acoustics, therm odynam ics, and oscillations of bubble cavities in fluids. This m odel can estim ate the pressure signature and p arts of its acoustic spectrum .
Finally, a packaged p lasm a gun was designed and built for use as a sub-bottom profiler. The sy stem w as tested extensively u sin g single an d m u lti-elem en t h y d ro p h o n e s d etecto rs a n d graphic reco rd ers commonly employed for shallow high resolution m arine geophysical surveys.
CHAPTER 2 . PRELIMINARY EXPERIMENTS 10
CHAPTER 2
Prelim inary experim ents
2.1 The prototype device.
The p lasm a je t operates in a gaseous environm ent, a n d th u s to operate u n d erw ate r, gas m u st be supplied to th e p lasm a cavity. F low rates of a few m illilitres p er second are required to produce reliable firing. Initially a stan d ard ignition plasm a je t w as altered to allow airflow into th e p lasm a cavity. Later, a som ew hat m ore sophisticated ap p a ra tu s w as designed from sta n d ard plastic plum bing pipe th a t allowed the plasm a je t to be operated approximately one
Electrical In Air In Electrical In Plastic Plumbing Pipe V . End Plate Electrode' Connector Plasma Cavity Insulator Central Electrode Plasma Jet
CHAPTER 2 . PRELIMINARY EXPERIMENTS
m etre below the w ater surface. Figure 2.1 shows the basic features of th e firs t u n d e rw a te r p la sm a Je t u se d in a re a so n ab ly open environm ent. In th is device air w as supplied to the plasm a cavity by pressurizing th e entire piping system to a few hundred kilopascals. The a n n u la r space betw een the ce n tral electrode and th e in su lato r provided the conduit for the air to p ass into the plasm a cavity and th en into th e su rrounding water. Power w as supplied to th e plasm a je t by a m etal conductor passing coaxially down the inner length of the plastic tu b in g w here it w as connected to the central electrode. The end plate electrode w as connected by a re tu rn cable (not shown) to the power supply. A block circuit diagram of the electrical system is shown in Figure 2.2. Trigger Power Supply 0 - 2 kVDC
T
I I 5 I4
Current I Breakdown Pulse C. D. Pulse Generator Pulse Transformer Storage-JjP
.
Capacitors
/"pS Stored Energy
Rojowski Coil
SHIPBOARD || PLASMA GUN
Jet
Figure 2.2: Electrical circuit diagram.
High speed photographic experim ents were conducted u sin g a Fastax® high speed 16 m m cam era to determ ine the n a tu re of the plasm a discharge into the water. The m aximum frame rate possible w ith th e cam era w as approxim ately two fram es per m illisecond. Figure 2.3 shows the re su lts of the underw ater discharge using a total stored electrical energy of 5 joules.
CHAPTER 2. PRELIMINARY EXPERIMENTS
12
b
Figure 2.3: High sp e ed photographs of bubble growth after underw ater discharge of a 5 J plasm a jet. Figure 2.3 a is an uncertain time after discharge. Each succeeding photo is 0.5 m s later.
CHAPTER 2. PRELIMINARY EXPERIMENTS 1 3
The m ajor discovery from th is p a r t of th e s tu d y w as th e appearance of the bubble seen in photographs 2.3a, b, and c. Bubbles of th is type are associated with m ost types of impulsive und erw ater aco u stic sources, e.g. chem ical explosives, airg u n s. an d sp a rk e rs [Sheriff an d G eldart 1982]. These photographs initially led to th e belief th a t the plasm a plum e, shown in Figure 2.3d, e, and f, issuing from the plasm a cavity after the bubble developm ent destroyed th e collapsing bubble prior to its complete collapse [Smith, et al. 1987]. A sim ilar set of images ta k en a t the University of Alberta w ith th e Spin Physics® high speed video system using shadowgraph optics shown in Figure 2.4 tends to confirm this idea. While this may be tru e for some plasm a discharges it is not generally the case. Figure 2.5 show s the
Figure 2.4: Video shadowgraph images of the bubble growth after underw ater discharge of a 10 J plasm a jet. Image U is a t tim e 0, each succeeding image is 0.5 m s later.
CHAPTER 2. PRELIMINARY EXPERIMENTS 1 4
shock wave resulting w hen a bubble collapsed before it was destroyed. This figure is a videograph tak en with the Spin Physics® system , using shadow graph optics a t a fram ing rate of 4 fram es per millisecond with exposure tim e of 2 00 nanoseconds. Sub-m icrosecond exposures are required to freeze th e m otion of the shock wave.
Shadow graph im aging allows the imaging of objects th a t have a large difference in refractive index with resp ect to th e background field. It is useful in the im aging of shock fronts, flow fields, and in gas or vapor b u bbles im m ersed in fluids. It m ay be show n [Goldstein, 1970] th a t th e change in in te r sity between two p o in ts in a n image field is proportional to th e second derivative of th e refractive index with respect to distance in th e plane perpendicular to the illum ination axis.
«• • ►-*>
Figure 2.5: Video shadow graph showing shock wave a t bubble collapse.
CHAPTER 2 . PRELIMINARY EXPERIMENTS 1 5
P ressure m easurem ents conducted In small te st tanks (less th a n 1 m 3 volume) in th e laboratory yielded no clear resu lts as to the nature of th e p re ssu re p u lse p roduced by the plasm a je t discharge. The pressure m e asu rem e n ts were confused by the m any nearby reflecting surfaces of th e sm all ta n k environm ent. To overcome the problem of the reflections, the device w as se t up on a pier a t the Royal Victoria Y acht C lub. An A tlantic R esearch LC-10 hydrophone (sensitivity 25,000 P a/V , 0 to 30 kHz) w as deployed on a n adjacent pier a t a distance of 11 m. The p lasm r je t and the hydrophone were immersed
1 m in w ater of depth of approximately 5 m. Figure 2.6 is a copy of an oscillogram recorded by th e Tektronics 7D20 digitizing oscilloscope of th e p ressu re pulse received by the hydrophone.
Figure 2.6: Received acoustic signal from 30 J stored electrical energy plasm a jet. Horizontal scale: 100 ps/div, vertical scale 5 mV/div.
CHAPTER 2. PRELIMINARY EXPERIMENTS
16
At th is time in the study of the underw ater discharge of the plasm a jet (Summr.- 191'<P\ it was felt th a t sufficient knowledge had been gained tc a p p ; C an ad ian and United States p a te n ts for th e device [see P. " . > lfr^sj. km addition, an opportunity aro se to take p a rt in a geof vsical re se arc h cru ise sponsored by th e Pacific G eosciences Centre of Sidney, B.C. aboard the CSS Parizeau.
2.2 The seagoing device.
For th e cru ise aboard the P arizeau the device w as com pletely redesigned to allow it to be deployed from the large ship and to be self-contained electrically. It stored 150 J of electric energy and could be ch arg ed a n d discharged twice per m in u te. A fu rth e r co n strain t, b ecau se of tim e considerations, w as th a t th e device be fabricated from off-the-shelf materials. Figure 2.7 shows the essentials of th e newly evolved system the plasma gun.
CHAPTER 2. PRELIMINARY EXPERIMENTS
Air lin e----Water tight connector Capacitor bank Trigger Electronics ► Power supply High voltage connector Spark gap— Electrode — Insulator'
End plate electrode
Plasma cavity
-►
0.30 metre
Figure 2.7: Cross-section of the plasma gun.
2.3 Single waveform pressure signatures.
During the Parizeau cruise pressure waveforms were m easured in both the n e a r and far field environm ents. (A discussion of the n e a r field and far field is given in Appendix A). Figure 2.8 show s th e pressure traces m easured at three w ater depths: 15, 1.5, and 0.3 m. At 15 m, th e p ressu re signature is th a t in the n ear field (no surface reflection), a t d ep th 0.3 m is th a t in the far field (strong su rface reflection), an d a t 1.5 n. it is between the n ear and far fields . There is evidence of a bubble pulse on the n ear field pressure signature (15 m depth) a t approxim ately 5 m s. The other signatures tak en a t lesser depths (hence pressure) probably would not have shown a bubble pulse
CHAPTER 2. PRELIMINARY EXPERIMENTS 1 8
on this time scale. Acoustic p ressu re signatures were detected with a single EDO Model 6194 hydrophone with a 0-50 kHz p assb an d using a lOOx pream plifier an d recorded u sin g a digitizing oscilloscope in conjunction with a PDP 1120 com puter.
■0.3 m depth
1.5 m depth 0.20 kP a
15 m depth
5 ms
Figure 2.8: Near, interm ediate, and far field pressure signatures of the plasm a gun.
The prim ary acoustic source device aboard for th e Parizeau cruise was a Bolt PAR® 1 cubic inch (1.6 x 10‘5 m 3) air gun. Figure 2.9 shows the p ressu re signatures of both the air gun and the plasm a gun u n d er sim ilar conditions. B oth acoustic sig n a tu re s were detected with th e sam e system as th a t of Figure 2.8. The hydrophone w as located 24 m below th e su rfa ce directly u n d e r th e so u rce. To suppress th e bubble pulse b o th devices were im m ersed to a depth of approxim ately 0.3 m. Note th e absence of the p ressu re precursors in the plasm a gun. In the air g u n these precursors are caused by the valve m echanism s th a t vent th e high pressu re air into the w ater. The electrical energy sto red in th e cap acito rs of th e p la sm a g u n w as approxim ately 150 J and th e energy stored in the air g un is calculated to be 700 J , assu m in g an average between adiabatic an d isotherm al
CHAPTER 2 . PRELIMINARY EXPERIMENTS 1 9
expansions. Previous m easu rem en ts on plasm a je ts in air [Smy et al. 1983], show th e am ount of energy deposited as therm al energy in the cavity th a t su b seq u en tly h e a t a n d expands the gas is 8-10% of th e sto red electrical energy o r approxim ately 12-15 J for th e p la sm a source. The energy available to th e air gun cham ber is therefore nearly 50 tim es greater th a n th a t available to the plasm a gun cavity.
Plasma Gun
11 vit 3 CO CO V l - l Cu Time (ms)Airgun
3 5 1 2 4 0 Time (ms)Figure 2.9: P ressure signatures of air gun and plasm a gun at im m ersion depths of 0.3 m.
More d e ta ils of th e s e exp erim en ts, p articu larly a s re la ted to seism ic profiling are found in Pitt e t al. (1988]. After the prelim inary experim ents were com pleted, it w as deem ed necessary to determ ine the fu n d am en tal physics of th e device. The effects of cavity volum es, cavity airflow rate s, and th e effects of electrical circuit p aram eters on th e p re ssu re sig n a tu re w ere m easu red u sin g single hydrophones in b o th th e n e a r a n d far fields (including th e surface reflection) an d studied in detail.
CHAPTER 3. DETAILED SINGLE HYDROPHONE MEASUREMENTS
2 0
CHAPTER 3
Detailed single hydrophone m easurem ents
3.1 Pressure measurements in large volume environments.
The first m ethod to m easure th e p ressu re pulse from th e plasm a gun in the n e a r field w as to sling th e device w itn ropes an d to deploy it from the dock a t th e In stitu te of Ocean Sciences in Sidney. B ritish Colum bia. The w eight of th e device, inability to m aintain proper orientation, and the com bined effects of tides and bottom reflections all com bined to produce resu lts th a t were less th a n satisfactory. Next a 2.5 m long m etal tu b e b e n t a t a right angle n ear th e end w as fashioned to fit the end of the p lasm a gun. Lowered into the w ater approxim ately two m etres, the right angle b end allowed the horizontal orientation of th e cavity end of th e device to be directed toward the receiving hydrophone. A lthough th e re su lts obtained were superior to the previous attem pts, confusion of th e p ressu re pulse by bottom and surface reflections continued to be a problem. M aintaining the plasm a gun an d the hydrophone a t th e sam e depth w as also difficult.
If the p lasm a gun could be show n to be omnidirectional, or nearly so, problem s involving th e o rien ta tio n of th e plasm a g u n an d th e hydrophone could be sim plified a g reat deal. The directivity of th e plasm a gun w as m easured in the acoustic te s t ta n k (2.4 m diam eter and 2 .4 m height) a t th e Institute of O cean Sciences. Another plasm a gun sim ilar to th a t show n in Figure 2.1 b u t fabricated of m etal to lessen electrical interference w as positioned a t th e geometric cen ter
CHAPTER 3 . DETAILED SINGLE HYDROPHONE MEASUREMENTS
2 1
of the tan k . Two EDO 6166 calibrated hydrophones (-207 ± 2 dB re XV/|iPa, 0 to 100 kHz ), one fixed a t a know n distance from center, th e o th er movable both in the radial and polar directions were deployed in the sam e horizontal plane as the plasm a gun. Circuit p aram eters for th e experim ent were C = 300 pF, L = 51 pH, V= 800 V, stored energy 96 J . Because there is some sh o t to shot variation in the p ressu re sig n atu re of th e plasm a gun, the ratio of the maximum p ressu re of th e movable hydrophone to the maxim um p ressu re of the fixed hydrophone w as used to m onitor any abnorm al pressure signatures during the m easurem ent. Sound pressure levels (SPL = 20 log P /P 0. P0 = 1 uPa) w ere th en calculated u sin g eight averaged p re ssu re v alu es for each position. The positions of the receiving h y d ro p h o n es were arran g ed so wall, bottom , and surface reflections did n o t confuse the the prim ary p ressu re pulse u ntil well after the m axim um p ressu re was reached. M easurem ents were made in th e polar direction from -10° through 190°, 0° being straig h t in front of th e plasm a gun. Symmetry of the plasm a gun stru ctu re about the 0 —180° axis allowed p ressu re values from 190° to 360° to be assu m ed from th is sym m etry. Figure 3.1 show s th e re su lts of the p re s s u re m e a su re m e n ts w hen th e m ovable hydrophone w as a t a d istance of 0.711 m from th e plasm a gun tip. Figure 3.2 shows the resu lts of a sim ilar set of m easurem ents with th e movable hydrophone at a d istan ce of 0.356 m from the plasm a gun. Note the significant n otch in th e p ressu re p a tte rn directly behind th e body of th e plasm a gun device, caused by th e plasm a gun stru ctu re shadow. At the larger distance th e notch is not apparent.
Figures 3.1 a n d 3.2 show th a t the device is nearly omnidirectional a t le ast a t distances greater th a n 0.711 m. It was now possible to
CHAPTER 3. DETAILED SINGLE HYDROPHONE MEASUREMENTS o* 30* 330* .60° 300° 270* 240° 120° 210° 150*
Figure 3.1: Polar plot of sound pressure level (dB re l^iPa at 1 m) m easured a t 0.71 lm .
0°
180*
Figure 3.2: Polar plot of sound pressure level (dB re IpPa a t 1 m) m easured a t 0.356 m.
CHAPTER 3. DETAILED SINGLE HYDROPHONE MEASUREMENTS
2 3
m easure th e p ressu re sig n a tu re of the plasm a gu n w ithout knowing the exact position of th e receiving hydrophone, as long as it w as a t a reasonable distance from th e source. The actual distance could be d eterm in ed from th e oscilloscope trac e by m e a su rin g th e tim e between the firing signal an d the arrival of the acoustic signal.
In Haro S trait a series of open ocean experim ents in w ater deep enough (25 m) to prevent bottom reflections interfering w ith resu lts were undertaken using a plasm a gun sim ilar to Figure 2.7. Here both n ea r and far field p re ssu re signatures were m easured w hich allowed peak p ressu res, total ra d ia ted acoustic energy, an d efficiency to be ascertain ed . Plasm a g u n , coaxial, and parallel sp a rk e r p re ssu re sig n atu res were m e asu red and com pared (these sp a rk er designs are u sed in C hina by th e Beijing Electrical Engineering In stitu te [Sun 1988j). D im ensions of th e parallel and coaxial sparker electrodes are show n in Figure 3.3. The sparker electrodes were designed to replace the plasm a gun electrodes directly so the sam e power su p p ly and electronics system could be used for all three devices.
nm
Figure 3.3: Parallel and coaxial sparker electrodes.
Insulators
CHAPTER 3 . DETAILED SINGLE HYDROPHONE MEASUREMENTS
Parallel
Coaxial
Plasma Gun
Figure 3.4: P ressure signatures of sparkers, and plasm a gun. Near (left) an d far field (right), each trace is 20 m s long.
CHAPTER 3. DETAILED SINGLE HYDROPHONE MEASUREMENTS
2 5
Figure 3.4 show s pressure signatures m easured from parallel and coaxial sp ark ers. and a plasm a gun obtained in the near and the far field. These p ressu re signals were collected u sin g a Tektronic 7D20 digital oscilloscope an d recorded on a PDP 1120 com puter. The deploym ent schem e for the near and far field sig n atu res are shown in F igure 3.5. In b o th c ases th e d e p th of th e h y d ro p h o n e w as approxim ately ten m etres.
Near Field
Deployment Far Field
4 m
Omnidirectional Hydrophone
Deployment
Figure 3.5: Deployment schem e for n ea r and far field pressure signatures.
3.2 Pressure measurements in limited volume environments.
W ith the com pletion of m easurem ents in th e open ocean, enough experience a n d confidence in se p a ra tin g reflections from p rim ary signals allowed a n extensive series of d a ta gathering in the laboratory to begin. A 2.4 m diam eter by 2 .4 m high acoustic ta n k w as c o n stru c te d in th e Plasm a Physics la b o ra to ry to allow n e a r field p ressu re signature m easurem ent (design criteria for th e ta n k followed those given by Levin [1974]). The sam e d a ta collection system a s used aboard th e S a b rin a w as u sed for th e se experim ents. E xperim ents
CHAPTER 3. DETAILED SINGLE HYDROPHONE MEASUREMENTS
2 6
w ere designed to determ ine th e effects of cavity diam eter, cavity length, air flow, stored energy, c u r r e n t d isch arg e tim e, an d p eak cu rren t upon various portions of the p ressu re signatures.
3.2.1a* Cavity size experiments.
To determ ine the extent to w hich th e plasm a g u n could be tu n e d by altering th e size of the plasm a cavity, the prim ary pulse w idth (the tim e th a t the positive going p re ssu re p u lse is g reater th a n am b ien t pressure), the bubble pulse period, a n d the m axim um p ressu re w as determ ined for four different cavity diam eters and seven cavity lengths betw een 4 and 10 mm. These p aram ete rs are detailed Figure 3.6, a sketch of a typical plasm a gun p ressu re signature. The range of cavity d im ensions w as dictated by th e crite rio n of reliable d isc h arg e s (shorter or longer lengths and larger diam eters re su lt in in co n sisten t firing). A calibrated hydrophone placed 130 m m directly ahead of the plasm a gun cavity end was used to m easure the p ressu re sig n atu res. Eight discharges were collected and averaged for each d ata point. The re su lts for th e cases of 96 J of sto red energy (circuit com ponent values: C = 300 pF, L = 51 jiH, Voltage 800 V) are shown in Figures 3.7 a, b, c, and d. Bubble Period Primary Pulse - i Width Time
CHAPTER 3. DETAILED SINGLE HYDROPHONE MEASUREMENTS
Pressure, Bubble Period, end Pulse Width v s Cavity Length for 1.6 mm Diameter
6 8 10
Cavity Length (mm)
Pressure, Bubble Period, and Pulse Width vs Cavity Length for 3.2 mm Diameter
6
2
0
2 4 6 8 1 0 1 2
Cavity Length (mm)
♦ P u ls e W id th (x 1 0 0 1* ) + P r| m ar y P ul 8e (x 10 0 ^ s) ♦ B u b b le P er io d (m e) « B u b b le P er io d (ms ) x P re ss u re (x 10 0 k P s) x P re ss u re (x 10 0 kP s)
CHAPTER 3. DETAILED SINGLE HYDROPHONE MEASUREMENTS
Pressure, Bubble Period, end Pulse Width vs Cavity Length for 4.8 mm Diameter
6
-6
2 4 8 10 1 2
Cavity Length (mm)
Pressure, Bubble Period, and Pulse Width vs Cavity Length for 6.4 mm Diameter
2
-2 4 6 8 10 12
Length (mm)
CHAPTER 3. DETAILED SINGLE HYDROPHONE MEASUREMENTS
2 9
3.2.1b. Results of cavity size on pressure parameters.
The experim ental d a ta show th e cavity dim ensions have very little effect upon the p ressu re param eters. Peak p ressu re, which seem s to be m ost affected by cavity length does n o t appear to be dependent on the cavity diam eter. The prim ary pulse w idth rem ains almost constant th ro u g h o u t all d im en sio n al v a ria tio n s. S im ilar experim ents for voltages of 600 an d 1 0 0 0 volts for the sam e cavity sizes also showed little effect on the p ressu re param eters.
3.2.2. Air flowrate effects on peak pressure.
The effects of air flow on th e p eak p re ssu re produced by the p lasm a g u n were determ ined by m easu rin g flows with a sta n d ard rotom eter w hich w as calibrated by ca p tu rin g th e air passing through the plasm a cavity in a large graduated cylinder. A 3.2 mm diam eter by 8 m m length cavity, capacitance 300 |iF, and inductance 51 |iH was m aintained throughout th e experim ent. R esults of the study for three values of capacitor voltage are shown in Figure 3.8. Results show th a t
300 B 600 V • 800 V ■ 1000 V o ~t » 1 i » i » '"l" »...r 0 2 4 6 8 10 Flowrate (mL/s)
CHAPTER 3. DETAILED SINGLE HYDROPHONE MEASUREMENTS
3 0
m aximum pressure produced by th e plasm a gun is achieved w hen the airflow is m aintained a t a m inim um value. Air flows less th a n 1 m L /s resu lt in inconsistent operation. The effect of air flow on p ressu re is not a strong function. The probable effect of increasing airflow is due prim arily to the poor acoustic coupling of the discharge into aerated w ater [Albers 1965] and secondarily to changing the effective cavity size because larger air b u b b les are produced a t the cavity exit. The deviations from a stra ig h t line tre n d are likely a m easure of the experim ental error.
Helium gas instead of air w as tested in th e plasm a g u n w ith no significant differences noted.
3.2.3. The effect of stored electrical energy on bubble pulse period.
Underwater explosions have been studied in great detail by m any ex p erim e n ta lists. Cole [1948] found th e b u b b le period to be proportional to th e one th ird power of th e weight of th e explosive. A ssum ing th e explosive energy to be proportional to its weight, the bubble period would then also be proportional to the cube root of the explosive energy. U sing differing c a p a c ita n c e s, voltages, an d inductances, m any experim ents were conducted studying discharges of stored energy between a few J o u le s and m any hu n d red s of Jo u les. Figure 3.9 shows th a t the bubble period produced by the plasm a gun and the cube root of th e stored energy are in a linear relationship (similar to explosives). E ach d a ta point represents an average of eight individual m easurem ents.
CHAPTER 3 . DETAILED SINGLE HYDROPHONE MEASUREMENTS 31 7 • 4 - A .o 3 2 2 3 4 5 6 7 8 (Energy) 1/3 ( j) 1/3
Figure 3.9: Bubble period versus cube root of stored energy. 3.2 .4 C irc u it in d u c tan c e an d capacitance effects on th e prim ary
p u lse shape.
3.2.4 a. T h e effect of m axim um current on peak pressure.
The effect of th e m axim um current in the discharge circuit upon th e p eak a c o u stic p re ssu re was stu d ied for a variety of charging voltages a n d cap acitan ces. All of the experim ents were conducted with a cavity diam eter of 3.2 mm and length between 6 and 8 mm and a circu it in d u c ta n c e of eith er 13 or 51 pH. R esults are shown in Figure 3.1 0 . A polynomial fit to the data of Figure 3.10 by a standard graphics package yielded a best fitting line with a quadratic function. Figure 3.11 show s the sam e data with the p ressu re plotted versus the s q u a re o f th e c u r r e n t (w ithout c a p a c ita n c e a n d in d u c ta n c e differentiation). Since th e square of the cu rre n t would be proportional to the pow er delivered to th e device if the resistan ce of the arc were co n stan t, th e nearly lin ear relationship between th e pressure and the sq u are of th e c u rre n t indicate th a t even w ith a variable arc resistance th e peak p re s s u re depends on an average power delivered to the arc.
CHAPTER 3. DETAILED SINGLE HYDROPHONE MEASUREMENTS S 3 m m e a. 300 -200 -100 -2 0 0 t r 1 2 0 0 1 7 0 0 Peak Current (A)
2200 100 jiF 51 jiH 200 jiF 51 nH 300 jiF 51 jiH 100 jiF 13 200 |iF13jiH 300 (iF 13 400 nF 13 jiH
Figure 3.10: Acoustic pressure versus discharge current.
400 300 -m a. w k 9 M M • k 0. 200 -□ -□ 100 -1x10 6 2x10 6 3 x 1 0 6 4 x 1 0 6 0 2 Peak Current Squared (A )
Figure 3 J I: Acoustic pressure versus discharge c u rren t squared.
CHAPTER 3. DETAILED SINGLE HYDROPHONE MEASUREMENTS
3 3
The electrical circuit of the plasm a gun is essentially a series RLC circuit (see Figure 2.2) with a resistance th a t changes during the arc discharge. B ecause the values of the circuit param eters used in the plasm a gu n are near the conditions th a t result in critical damping, i.e. a circu it taking th e longest tim e to decay to zero, slight changes in re s is ta n c e can p ro d u ce eith er a n overdam ped or u n d erd am p ed discharge. Usually, the system behaves as an overdamped circuit, b u t occasionally an underdam ped oscillation occurs. When it occurs, the u n d erd am p ed discharge commonly only oscillates for one-half cycle, b ecau se th e voltage across the arc is insufficient during th e negative p a r t of th e first half-cycle to m aintain th e discharge: th e arc is extinguished.
Both th e d istributed capacitance and inductance in th e circuitry an d transm ission lines of the plasm a gun's series RLC circuit are small com pared to the storage capacitance and the blocking inductor. The two series arcs—the plasm a cavity arc and secondary spark gap arc. (see Figure 2.2)—fix the resistance. Thus the storage capacitance and th e blocking inductance can be altered som ewhat to affect th e current sh ap e an d thence the prim ary pressure signature.
S tu d ies involving sim ilar electrical system s used with underw ater sp a rk e r sources [Caulfield 1962] have shown th a t particularly a t the leading edge the p ressu re signature follows the shape of the electrical c u rre n t pulse producing the underw ater arc. Although th e plasm a g u n arc is initially established in a gaseous environm ent while the sp a rk e r arc is in a liquid environm ent, enough sim ilarities exist b etw een th e two sy stem s—p artic u larly la te r in th e d isc h arg e—to w arra n t a study of how the primary pressure signature is influenced by th e shape of c u rren t discharge.
C u rre n t in a series RLC circuit in b o th the overdam ped and underdam ped discharges is [Davie 1964]
CHAPTER 3. DETAILED SINGLE HYDROPHONE MEASUREMENTS 3 4 Rt I = -^7- e 2L sinho)t (3.1) d)L
Equation (3.1) is valid only if care is taken ab o u t th e real and im aginary n a tu re of th e frequency, to, a n d th e identity sinh(icot) = i sin(o)t) is used, where
i = r - 1
I = C urrent, V = initial capacitor voltage R = Average total resistance
L = Total Inductance
“ = 2L
C = Total capacitance t = time
The capacitance an d the in d u ctan ce b o th influence the shape of the current pulse.
Experim entation w ith th e circuit p aram eters confirm capacitance and inductance have strong effects on both th e am plitude and duration of th e c u rre n t p u lse . Figure 3 .1 2 show s th e re s u lts of several mec su rem e n ts of p eak c u rre n t v e rsu s voltage for several v alues of cap acitan ce an d in d u c ta n c e . C h an g in g the in d u c ta n c e is a more convenient m ethod to alter the peak cu rre n t b ecau se the total energy stored is n o t altered when the ind u ctan ce is changed.
CHAPTER 3. DETAILED SINGLE HYDROPHONE MEASUREMENTS 3 5 5000 4000 3000 -2 0 0 0 -1000 -T T T T T ■ 200 pF 51 nH • 400 pF 51 pH ■ 200 pF 13 pH • 400 pF 13 pH 500 1000 1500 20 0 0 Capacitor Voltage (V) 25 0 0
Figure 3.12: Peak c u rren t versus capacitor voltage.
3 .2 .4 b. C ap ac itan ce an d in d u c ta n c e effects on prim ary p ressu re pu lse w idth.
The frequency of a n RLC circuit is controlled by its resistance, inductance and capacitance. If the prim ary pressure pulse w idth can be influenced by th e d isch arg e c u rre n t sh ap e, the m ost dram atic effect w ould be by controlling th e c u rre n t period. In general the period of a n RLC circuit is given by
T = 2jc 4L2C \ l / 2
v4 L - R C y (3.2)
A nalysis of (3.2) show s t h a t for fixed resistan ce the in d u ctan ce is m ore im p o rta n t th a n th e cap acitan ce in determ ining th e period. V alues of in d u ctan ce ( te n s of m icrohemys), capacitance (hundreds of m icrofarads) an d arc resistan c e (several te n th s of an ohm) in a typical p la sm a g u n r e s u lt in a circu it close to the b o u n d a ry of
CHAPTER 3. DETAILED SINGLE HYDROPHONE MEASUREMENTS
3 6
underdam ped and dam ped oscillation 'Scott 1959]. Figure 3.13 shows the effect of capacitance u p o n th e prim ary p ressu re pulse width with co n stan t inductance of 13 an d 51 pH. The values shown are averages for several voltages. S ta n d a rd deviation from th e averages w as a m aximum of six percent. The resu lts show th a t some reduction in the p rim ary p u ls e w idth c a n be a tta in e d by decreasin g e ith er th e capacitance or the ind u ctan ce of th e circuit. Changing the value of the in d u ctan ce does n o t a lte r th e stored energy in the circuit (1 / 2 CV2). Again it m ay be desirab le to alter the prim ary pulse width w ithout affecting th e bub b le period of th e p ressu re signature. In general th e b u b b le period is responsible for one of th e dom inant frequencies of the pressu re signature.
700 g £ 600 -5 J! £ £* 500 -I CL ■ 51 pH • 13 pH 400 200 3 0 0 400 500 0 100 Capacitance (pF)
Figure 3.13: Pulse w idth versus capacitance.
D ecreasing e ith er th e c a p ac itan c e o r in d u ctan ce to values low enough to force th e circu it into underdam ped oscillation beyond the first half cycle com plicates the p ressu re signature. Restriking of the arc creates a series of sm aller p ressu re p u lses superposed upon the trailing edge of th e p rim ary p re ssu re pulse. T his m akes p ressu re
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conditions undesirable for use as an acoustic source.
Neither capacitance nor inductance values change the trailing edge of th e prim ary p u lse contour significantly. Its sh ap e resem bles an exponential decay probably because of tran sfer of h e a t energy to the surrounding w ater.
3.2.5 Results of circuit parameters on the acoustic pressure
signature.
The exp erim en tal d a ta dealing with th e circ u it p aram eters are sum m arized a s follows:
1. T h e p e a k p re ssu re . The peak pressure of the primary acoustic pulse depends upon the square of the peak current. C urrent am plitude can be altered by either increasing the capacitance, d e c re a s in g in d u c ta n c e , or by in c re a s in g voltage. For c o n s t a n t e n e rg y th e m o st e ffic ie n t m e th o d is to decrease inductance.
2. T h e w id th o f th e p rim a ry a c o u stic p u ls e . This depends most strongly on the circuit inductance b u t it is also influenced by th e capacitance. The leading edge of th e acoustic pulse follow s th e rise tim e of th e c u r r e n t p u lse reaso n ab ly closely. Rise tim es of the c u rre n t p u lse can be controlled q u ite effectively by varying th e in d u c ta n c e of th e circuit, p a rtic u la rly if c o n sta n t energy a n d h en ce c o n s ta n t bubble p erio d is d e sire d . The tra ilin g edge a p p e a rs to be re la te d to th e cooling by th e s u rro u n d in g w ater of the gases w ithin the bubble.
CHAPTER 4. FREQUENCY AND ENERGY MEASUREMENTS 3 8
Chapter 4
Frequency and Energy M easurements
4.1 Acoustic spectral analyses.
B ecause the Society of Exploration Geophysicists [Johnston et al. 1988] recom m ends th a t the surface reflection be included in th e m easu rem en t of p ressu re signatures, m easu rem en ts a t sea should allow the b est opportunity to m easure the far field signature (which includes the surface reflection). The technical problem s in m a in ta in in g a c o n s ta n t im m ersion d epth from a sm all b o at, particularly in m oderate seas, m ade these m easurem ents extremely difficult. Immersion depth uniquely determ ines the am ount of time after the beginning of the p ressu re pulse th a t the reflected p u lse beg in s to com bine to produce th e outgoing far-field p re s s u re sig n a tu re. B ecause th is am o u n t of tim e affects th e p re s s u re waveform so strongly, th e frequency dom ain of th e p re s s u re signature is also heavily affected.
To se p a ra te circuit param eter changes from those of source m otion a s they affect the p re ssu re sig n a tu re a n d to m a in ta in conditions a s sim ilar as possible between p ressu re m easu rem en ts u sin g different electrical circuit values, it w as decided to m easu re th e p re ssu re signature in the n ea r field where more control could be exercised. The d a ta from these m easurem ents could th e n be processed to sim ulate th e proper tim ing of th e surface reflection. M ost m easu rem en ts were carried o u t in th e acoustic testin g ta n k
