TIME RESOLVED IMAGING IN COMPRESSIBLE FLOWSUSING A CRANZ-SCHARDIN CAMERAByWilliam Brouwer

SUBMITTED IN PARTIAL FULFILLMENT OF THEREQUIREMENTS FOR THE DEGREE OFBACHELOR OF SCIENCE, HONOURSATTHE UNIVERSITY OF QUEENSLANDBRISBANE, AUSTRALIA8 NOVEMBER 1999

Exept where aknowledged in the ustomary manner, this thesis is, to thebest of my knowledge, original and has not been submitted, in whole or in part,as part of a degree at any UniversityWilliam Brouwer

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Table of ContentsTable of Contents vList of Figures viAknowledgments viiiAbstrat ix1 Introdution 12 Optial Diagnostis 32.1 The Shadow Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1.1 Theoretial Considerations . . . . . . . . . . . . . . . . . . . . 43 The Cranz Shardin Camera 93.1 Illumination and Control . . . . . . . . . . . . . . . . . . . . . . . . . 103.2 Optomehanial Features . . . . . . . . . . . . . . . . . . . . . . . . . 113.2.1 Design Criterion . . . . . . . . . . . . . . . . . . . . . . . . . 114 Light Emitting Diodes (LED's) 155 Experiment 205.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205.2 Preliminary Investigations . . . . . . . . . . . . . . . . . . . . . . . . 205.3 Diode Charaterisation . . . . . . . . . . . . . . . . . . . . . . . . . . 255.4 Preparation for Multiple Images . . . . . . . . . . . . . . . . . . . . . 265.5 Appliation to the Drummond Tube . . . . . . . . . . . . . . . . . . . 275.5.1 Single Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.5.2 Multiple Frames . . . . . . . . . . . . . . . . . . . . . . . . . . 31

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6 Conlusions 336.1 Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Bibliography 36A Ciruit Diagrams 38B Compressible Fluid Flows 39B.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 39B.2 Mah Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44B.3 The Shok Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

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List of Figures2.1 The density �eld and its �rst two derivatives, of an optially inhomo-geneous medium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Deviation of optial beam through inhomogeneous media. . . . . . . . 53.1 Generi Cranz-Shardin amera. . . . . . . . . . . . . . . . . . . . . . 103.2 Light gathering and ollimation system. Initial lenses produe the or-ret vergene for the �rst mirror whilst harnessing the LED's dispersiveemission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.3 Geometry for determining magni�ation . . . . . . . . . . . . . . . . 144.1 Struture and energeti proesses within the p-n semiondutor juntion. 164.2 Strutural features of the type T1-3/4 LED. . . . . . . . . . . . . . . 184.3 Embedding of optial �bre in an LED. . . . . . . . . . . . . . . . . . 195.1 Typial output from LED driver iruit (pulse width approx. 5�s). . 215.2 Experimental set up for a generi Cranz-Shardin sheme. . . . . . . 225.3 Shadowgraphs of density �eld surrounding soldering iron. Left: thisimage was produed with a pulse of approx. 1�s at 1amp; two density�eld lines are visible, extending from the iron. Right: the LED pulsewas approx. 20�s at 2 amps. Faintly visible in the top right handorner is a vortex. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245.4 Response of type HLMP-DG08 LED. . . . . . . . . . . . . . . . . . . 255.5 Eletrial subsystem of the Cranz Shardin Camera. . . . . . . . . . . 27vi

5.6 The small shok tunnel faility. . . . . . . . . . . . . . . . . . . . . . 295.7 Experimental set up for single frame shots; top view . . . . . . . . . . 305.8 (Following Panel) Shlieren image of ow over a ylinder. LED pulsesize approx. 8�s at 5amps. . . . . . . . . . . . . . . . . . . . . . . . . 305.9 (Following Panel) Shadowgraph image of ow over a ylinder. LEDpulse size approx. 8�s at 5amps. . . . . . . . . . . . . . . . . . . . . 315.10 Experimental layout for obtaining four images; top view. . . . . . . . 325.11 CMOS ontrol iruit output showing resolution between pulses. . . . 325.12 (Following Panel) Multiple shadowgraphs of ow over a ylinder; timeinreases as one proeeds anti-lokwise from the lower left-hand or-ner. LED pulse size approx. 8�s at 5amps, pulse separation, 200�s. . 32A.1 Analogue driver iruit. During initial testing, transistor gating ar-rangement was absent, pulsed input fed diretly into the non-invertinginput of the op-amp . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38A.2 CMOS timing ontrol iruit. The output amplitude is varied by apotentiometer. `INPUT' is tied to every driver hannel and `ENABLE'to eah individual hannel; supports up to ten. The devie resets afterounting out a spei� number of pulses depending on the hip set of`reset selet'. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38A.3 Zero orretion. Holds the analogue driver stages at zero volts wheninput terminals are open. . . . . . . . . . . . . . . . . . . . . . . . . . 38A.4 Logi swith. Produes lean input TTL trigger signal, free from jitterwhih otherwise destabilises the iruit. . . . . . . . . . . . . . . . . . 38B.1 Fluid ow in one-dimension . . . . . . . . . . . . . . . . . . . . . . . 39B.2 Portion of uid bounded by two surfaes . . . . . . . . . . . . . . . . 40B.3 Piston system for alulation of energy relation . . . . . . . . . . . . 41B.4 Pressure fores exerted on elementary partile . . . . . . . . . . . . . 42B.5 Shok wave separating regions 1 and 2 in states of equilibrium . . . . 47vii

AknowledgmentsI am greatly indebted to Tim MIntyre, Tony Gardner and Barry Allsop for their ol-letive support and servies rendered. Tim I have to thank for being my long-su�eringsupervisor. He injeted muh knowledge, suggested avenues to pursue, whilst keep-ing my (easily distrated) attention foused upon the task at hand. Tony provideda good deal of support and advie, also laying down foundations on whih I havebuilt. Barry is responsible for the design of all iruitry used within this projet. Healso intervened (heerfully) on many o

asions to alleviate problems indued by theexperimenter.In addition many individuals volunteered advie and assistane at various stages,most reently Brad Littleton and Alexis Bishop. Alexis was instrumental in assem-bling the optis for the �nal experiments performed, Brad in solving some tehnialdiÆulties.I am deeply grateful to my dear wife for her patiene and lovely ountenane whihdaily greets, enourages and strengthens me.

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AbstratA Cranz Shardin amera arrangement was devised and onstruted to obtain timeresolved shadowgraphs of ow over a ylinder. Detahed shok waves are learlyvisible as well as some three dimensional e�ets. The amera system uses a high powerAlInGaP light emitting diode (LED), the model HLMP-DG08 by Hewlett Pakard.The diode has a narrow viewing angle (60), high luminous intensity (6500md �20mA), with peak emission at 626nm and a FWHM1 of 17nm. Within the amerasystem, the LED is pulsed rapidly at high urrents, serving as both shutter and lightsoure. These pulses are separated temporally and spatially, bak-lighting the objetwhih is subsequently imaged onto the �lm plane. Generation of pulsed input to thesoures is provided by CMOS2 iruitry oupled with an analogue driver stage foreah hannel, produing high urrent gain. The maximum output of the analoguedriver stages was in the viinity of 5 amps, produing suÆient light intensity in theLED's to saturate a CCD3 amera. The light emitting diode is advantageous overlasers in this appliation for a number of reasons. Besides the obvious redution inost, LED's are responsive (�res: = 20ns) may be swithed rapidly and have a fairlygood signal to noise ratio for suh a small, inexpensive devie. The amera overallpromises to be an invaluable diagnosti tool, at least in situations where ompetingluminosity an be redued.1Full width (at) half maximum (intensity).2Complementary Metal Oxide Semiondutor.3Charge Coupled Devie. ix

Chapter 1IntrodutionErnst Mah is perhaps most well known for his position regarding the inadmissabilityof a sienti� statement unless a

ompanied by empirial veri�ation. Mah pur-ported that all knowledge is a oneptual organization of sensory experiene. Thisrigorous riteria led him to rejet the notions of absolute time and spae, paving theway for Einstein's theory of relativity.During the twenty year period 1873 to 1893 Mah developed visualization teh-niques for the measurement of wave propagation and related phenomena in uidsand established governing equations for supersoni ows. A supersoni ow is onefor whih the ratio between the speed of the ow and the speed of sound in the owis greater than unity, a dimensionless parameter referred to as the Mah Number.(The reader unfamiliar with the features of ompressible ows may wish to onsultAppendix B for a brief disussion).In 1929 C Cranz and H Shardin [4℄ through simple arrangement of light souresand optis devised a amera whih aptures rapidly o

urring events. The devie hasbeen used fairly widely over the last seventy years in a number of appliations, thoughthis work draws primarily from Tsai and Bakos [16℄, Lu and Liu [10, 11℄ Stasiki etal [14, 2℄ and Germer [7℄.Tsai and Bakos based at the GASL faility used a Cranz Shardin amera toobtain time resolved shlieren images of ow over various objets of interest, within a1

2shok tunnel test environment. Images are reorded using CCD ameras oupled withLED light soures and band-pass �ltering is employed when ow luminosity beomesintrusive. Lu and Liu explore optial design onsiderations for the amera and applythem to the study of shok-bubble interations. This partiular design is perhaps moresuited to a multiple shlieren system, sine there is no real provision for `defoussing',as required in a shadowgraph sheme. In support of this statement, they obtainseveral frames of the dynamial event, bak lit by the soures, however the shok waveitself is not visible. Stasiki et al produed time resolved interferograms using a MahZehnder arrangement in onjuntion with a Cranz Shardin sheme, illuminated againby a light emitting diode. This group also developed a fully integrated high speedamera devie ontaining CCD's oupled with frame grabbing tehnology. Previously,a similar, less elaborate high speed video amera was outlined by Germer (1986).Of interest to various groups around the world are the ow properties existingwithin the SCRAMjet, or supersoni-ombustion ramjet. Features of interest inludeshok waves and assoiated thermodynami variables, whih are desribed by exatexpressions for a small sublass of possible situations (Appendix B). Generally speak-ing, real gas e�ets (e.g., visosity) and non-simple geometries ditate the use of theNavier Stokes equations, solved via omputational means. The experimentalist in-vokes non-intrusive optial tehniques to test the validity of these preditions, gainingan appreiation of the ow properties whih o

ur in reality. The objet of this exper-imental thesis lies within the realm of Optial Diagnostis, and may be summarisedas thus;To design and implement an LED illuminated Cranz Shardin amera, forthe non-intrusive study of ow properties whih evolve with time.The system is ultimately intended for the investigation of unsteady ows existing ina model SCRAMjet engine, testing onduted in the T4 shok tunnel faility, withinthe University of Queensland's Department of Mehanial Engineering.

Chapter 2Optial DiagnostisOptial methods[9, 15, 12℄ may be lassed as exploiting either moleular propertiesof the test medium (e.g., Planar Laser Indued Fluoresene (PLIF), Coherent Anti-Stokes Raman Spetrosopy (CARS) and Degenerate Four-Wave Mixing (DFWM)),or the refrative index. The three most ommon optial tehniques, Interferometry,Shlieren and Shadowgraph, fall into the latter ategory, i.e., they rely on the varianeof the speed of light with the density of the medium through whih it is passing.Expressed in terms of the index of refration, one may write;n = 1 + �� (2.1)where � is the density of the disturbed media; � is the Gladstone-Dale onstant.Equation 2.1 demonstrates the variane of the refrative index with density. Henethe path taken by penetrating light rays di�ers depending on the loal value of thedensity. As a result, inoming light is subjet to two e�ets;1. A turning of the wave fronts i.e., refration,2. A relative phase shift between di�erent rays.E�et (1) is exploited in the shlieren and shadow methods, (2) is the basis forinterferometry. Inidentally, these methods fall into a hierarhy in terms of theirrelation to the density. Interferometry is diretly proportional and therefore at the3

4top of the hierarhy. Shlieren is proportional to the �rst derivative of the density andshadowgraph to the seond derivative. These two tehniques are used for qualitativepurposes only; shlieren is used where greater sensitivity is desired and shadowgraphgenerally for higher density media.2.1 The Shadow MethodShlieren and shadowgraph tehniques are usually attributed to Toepler (1864) andDvorak (1880), respetively. However Robert Hooke (1635-1703), working from atmo-spherial refration, identi�ed the shlieren method in 1672. Also shadowgraph wasused independently by Jahannes Wiesel (1583-1662) in 1649, Robert Hooke in 1683and Jean Paul Marat (1743-93) in 1780[13℄. The shadowgraph e�et is readily ob-servable in nature under ordinary unpolarized sunlight; for example the shimmeringimage of rippling water on a wall to the rear of a �sh tank.To produe a shadowgraph image, the objet of interest is illuminated with parallellight. Penils of light after transmission form bright regions on a sreen where theyrowd together and dark regions where they diverge. At plaes where their spaingremains even, the illumination is normal. The shadow e�et thus depends on therate at whih the penils of light onverge. Convergene is measured by the rate ofhange in the deetion, whih in turn is proportional to the density gradient. Heneshadowgraph is proportional to the seond derivative of the density gradient, �gure2.1.2.1.1 Theoretial ConsiderationsThis outline follows the presentation given in Merzkirh [12℄. Consider light impingingon a ompressible ow �eld, �gure 2.2. The index of refration is a funtion of thethree spatial o-ordinates, n = n(x; y; z). Snell's law ditates that the deeted beamwill strike the sreen at Q� instead of Q and in the plane of the �lm we may measurethe displaement QQ�. The optial path length for the deeted ray is thus somewhat

5

Figure 2.1: The density �eld and its �rst two derivatives, of an optially inhomoge-neous medium.κρ

Light ScreenMedia

x

z

y

W l

Q*

Q

n = 1 +

Figure 2.2: Deviation of optial beam through inhomogeneous media.di�erent. For ontinuous hanges in the refrative index, Fermat's priniple is applied;Æ Z n(x; y; z)ds = 0whih states that the variation of optial path length along a light ray must vanish.In the usual ustom we may write the orresponding Euler Lagrange equations;dds �F�x0! = �F�x ! ; dds �F�y0! = �F�y ! ; dds �F�z0! = �F�z !where F = F (x; y; z; x0; y0; z0; s) = n(x; y; z)q(x02 + y02 + z02);ds2 = dx2 + dy2 + dz2; q(x02 + y02 + z02) = 1:

6Thus dds ndxds! = �n�x! ; dds ndyds! = �n�y! ; dds ndzds! = �n�z ! :We take the inident rays to be parallel with the z-axis. Eliminating the ar lengthparameter s, write x and y as funtions of z;d2xdz2 = 241 + dxdz!2 + dydz!235 " 1n �n�x � dxdz 1n �n�z # ;d2ydz2 = 241 + dxdz!2 + dydz!235 " 1n �n�y � dydz 1n �n�z # :Light rays pass through the inhomogeneous medium momentarily and su�er onlysmall deviations � , but have some degree of urvature. Therefore to a good ap-proximation all terms whih are �rst order derivatives of the z o-ordinate vanishand d2xdz2 = 1n �n�x = ��x(lnn); d2ydz2 = 1n �n�y = ��y (lnn):The radius of urvature for a light ray is then1R = er(lnn)where e is the unit vetor perpendiular to the light path. The integral equations forthe o-ordinates have trivial solutions and the deetions su�ered by the light at theviewing sreen, a distane l away from the exit plane of the test medium, are;(QQ�)x = l Z �� d2xdz2 dz = l Z �� 1n �n�xdz;(QQ�)y = l Z �� d2ydz2 dz = l Z �� 1n �n�y dz:The photographi �lm is sensitive to di�erenes in relative intensities. The intensityon the sreen of the deeted rays is equal to the intensity in the undisturbed ase I,divided by the Jaobian whih maps I� ! I inI�(x�; y�) =Xi Ii(x; y)����(x�;y�)�(x;y) ��� :

7In terms of the small deetion � su�ered by the light rays, the o-ordinates at thesreen are x� = x+�x(x; y); y� = y +�y(x; y):To �rst order, the Taylor expansion for the mapping funtion gives������(x�; y�)�(x; y) ����� � 1 + ��x�x + ��y�y :The small quantities � are equivalent to the displaements QQ� determined earlier;�x = l tan �x = l Z 1n �n�xdz; �y = l tan �y = l Z 1n �n�y dzwhere �x,�y are the small angles of deetion. Combining equations then, the relativeintensity hange reorded by the �lm isI � I�I� = �II� = l Z �� �2�x2 + �2�y2! (lnn)dz:If the test region is enlosed by glass walls whih are plane and of uniform thikness,then na' = n�xfor small angles, so ' = nna �xwhere ' is the angle after passage through the glass and na the refrative index ofambient air. Bak substitution gives for the relative intensity hange at the sreen;�II� = lna Z �2n�x2 + �2n�y2! dz:Now n = 1 + �� and na � 1 so we have �nally�II� = �lW �2��x2 + �2��y2! (2.2)where W is the width of the test setion. The distane l is often referred to as thedefoussing and gives a measure of the strength of the optial inhomogeneity. For a

8weak e�et suh as the density gradient produed around a hot soldering iron, a largel is required sine the light is only weakly divergent. However for a strong e�et suhas a shok wave, the light diverges quikly and only a small defoussing is requiredfor good ontrast.

Chapter 3The Cranz Shardin CameraIn high speed framing ameras, rotating optomehanial omponents are used to im-age sequential events. Far more ost e�etive is the Cranz Shardin Camera (CSC),devised by the German experimentalists C Cranz and H Shardin in 1929 [4℄. Es-sentially, an array of point soures, �red in sequene, provides both the light andshutter ation required to apture images. Light pulses are separated temporally andspatially, bak-lighting the objet whih is subsequently imaged onto the �lm plane.Image separation is failitated by a geometri arrangement of lenses and light soures.The images are reorded on a single photographi �lm plane, the maximum numberof images restrited by the �lm dimensions. The distint advantage of the CranzShardin amera over onventional high speed ameras lies in it's simpliity, �gure3.1.Sine its ineption the Cranz Shardin amera has been used in various applia-tions, most notably uid dynamis, ballistis and frature mehanis. To a limitedextent it has been employed in the study of photoelastiity or the study of the hangein the optial properties of an objet when subjet to mehanial stress. Christie [3℄in England desribed the �rst appliation of the Cranz Shardin amera to photoe-lastiity in 1955, and Wells and Post [17℄ introdued the amera in the United Statesin 1957. 9

10Mirror/Lens 2

Light Sources Media Film Plane

Objectives

Mirror/Lens 1Figure 3.1: Generi Cranz-Shardin amera.3.1 Illumination and ControlTraditionally, spark gaps served as light soures and in some appliations ontinue tobe used, espeially where high light intensity is required1. However, spark gaps su�erfrom temporal jitter and are unsuitable where a high degree of preision is required. Inlater years, ruby lasers beame the preferred light soure. Lower in prie and smallerin size is the light emitting diode. The LED has a response time of several nanoseondsand if ombined with appropriate ontrol iruitry, may be pulsed at framing rates ofthe order of 106s�1 [14℄. Semiondutor manufaturers suh as Stanley and HewlettPakard produe modern LED's with very high luminous intensities (� 104md) andnarrow spetral bandwidth (� 10nm). This being said, some important distintionsbetween LED's and lasers are worth noting;� LED's are a dispersive, non-point soure� The pulsed power output of an LED is less than that of an semiondutor laserdiode (SLD) of omparable size.Nonetheless, LED's have been used quite su

essfully in various appliations, al-though there is evidene to suggest that SLD's may prove to be bene�ial where1Partiularly in frature mehanis. The amera is operated in reeted mode; that is, light isreeted o� a solid objet, as opposed to the objet being baklit.

11higher light energy and shorter light pulse duration are required [5℄. The LED is typ-ially pulsed for durations of 1-100�s at urrents of up to 5-10amps. Commeriallyavailable pulsed power supplies, produed by suh ompanies as Avteh of Canada,are generally used to ontrol and drive multiple LED's for the periods, frame ratesand urrents required. Suh supplies onsist of digital ontrol iruitry oupled withanalogue driver stages for high urrent gain.3.2 Optomehanial FeaturesThe operational priniples of the amera are rather straightforward. Essentially pointsoures are plaed within the foal plane of a lens or mirror whih ollimates thebeams. These ollimated beams (traversing slightly di�erent paths) illuminate theobjet, and are foused down by a seond lens or mirror of similar features to the �rst.An array of objetive lenses is often used for magni�ation, images produed on asingle �lm plane. Hene the Cranz Shardin amera is referred to as being a `multipleobjetive' amera. Traditionally, sheet or polaroid �lm is used as the imaging media.Charge oupled devie (CCD) ameras are superior in terms of image aquisition andmanipulation. However even expensive, high resolution models still lak the larityof onventional sheet �lm, suh as that produed by the English ompany Ilford.Related to the imaging proess are a number of fators, pertinent to good design.Considered olletively, these features present somewhat of a onundrum. After themanner of Lu and Liu [10℄ we shall treat them individually, in the proess developinga framework whih shall be followed loosely in this work. The optial elements withinthe amera are listed in table 3.1.3.2.1 Design Criterion� Due to the dispersion of the LED beam, some light will be disarded if theaperture of the ollimating optis is too small.In other words, after the beam has traversed the distane orresponding to the foal

12Element Foal Dia.Initial lens(es) fi DiMirror/lens 1 f1 D1Mirror/lens 2 f2 D2Objetives fo DoTable 3.1: Optial elements within the Cranz Shardin Camera. Mirrors are generallyused over lenses for large viewing �elds, owing to their lower ost.length of the ollimating mirror/lens 1 (ML1), the spot size may well be larger thanthe diameter of ML1. One approah to olleting the LED's emission and produingpoint soures is to insert the diodes in the virtual objet spae of small diameterlenses. Let the size of the viewing �eld be W , the distane between the soure andlens be d and between lens and ML1 be di; then standard geometrial optis relationsgive: di = �1� DiW � f1; d = fif1DifiW + f1DiThis approah produes `virtual' point soures in the foal plane of ML1, �gure 3.2.When hoosing the various parameters for these lenses one needs to keep in mind the

ML1f

d d i

1

Initial lens

Figure 3.2: Light gathering and ollimation system. Initial lenses produe the orretvergene for the �rst mirror whilst harnessing the LED's dispersive emission.angular dispersion of the LED beam. Namely, if the divergene of the beam is � thentan� � Di2d

13in order that no light be disarded.� Sine the soures are separated spatially eah image obtained is a slightly dif-ferent perspetive of the objet. It is therefore desirous to have a small angleof inidene between light soure and optial axis to minimize this e�et.If the angle of light inident on ML1 from a partiular LED is �, and the light soureis a distane d0 from the optial axis, thentan � = d0f1provides a design riterion. Inreasing the foal length and or dereasing the distanebetween the LED's minimizes the angle of inidene. Ideally the objet of interestought to be plaed in the foal plane of ML1 whih is the ommon plane for all theparallel beams, permitting the largest viewing �eld.� The number of images obtainable for a given viewing �eld is onstrained by thesize of the �lm. Therefore the magni�ation ratio is inversely proportional tothe number of images desired.Consider �gure 3.3. Suppose the objet under onsideration is plaed in the foalplane of ML2, with h the height of the objet, h0 the height of the image after anobjetive lens; then tan� = h2f2 and tan� = h02foand thus the magni�ation � = h0h = fof2If instant �lm is used then a large magni�ation ratio is desirous, sine imageenlargement will be detrimental to quality. However, owing to the relatively smallsize of the �lm, to obtain a large viewing �eld the magni�ation ratio (and numberof images) should be small.Let the minimum length of the �lm be V ; then the maximum number of imagesin this dimension is nmax of size v. Also let the separation of objetive lenses be do

14Objective

f f

h

2 0

ML2

φφ

h

Figure 3.3: Geometry for determining magni�ationand the size of the viewing �eld W . Now W � donmax assuming there is no overlapof images; in order for this to hold, we therefore requireW = v� and W = do�In onlusion the following relations provide riterion for the design of a CranzShardin Camera, where all symbols are as previously de�ned;� = fof2 ; tan � = d0f1 ;W = do� ; nmax = Vdo ;di = �1� DiW � f1; d = fif1DifiW + f1Di ;with tan� � Di2d

Chapter 4Light Emitting Diodes (LED's)The operational mehanism of the LED is a form of eletroluminesene [6℄. Thisphenomena is utilized, for instane, in the athode ray tube (CRT) of a viewingsreen. However within the rystal of an LED, eletrons do not reside in �xed orbitalsas in the Phosphor of a CRT but rather o

upy a owing sea of harge whih movesamongst all the atoms in the material. At the same time they maintain a spei�energy level as if attahed to an individual atom. The rystal within an LED is thefamiliar semiondutor p-n type juntion, whih onsists of two di�erent ondutiverystals, married at the juntion region. Eletrons an only assume spei� energylevels and within semiondutors the two highest levels are referred to as the valeneand ondution bands.In undoped materials, the forbidden region between the upper valene and lowerondution band is referred to as the energy gap. When impurities are added (doping)eletroni states are produed in the forbidden region. Impurities whih add eletronsto the ondution band are alled donors and produe n-type ondutivity. Impuritieswhih a

ept eletrons and reate eletron holes in the valene band are referred to asa

eptors and produe p-type material, �gure 4.1(a). A p-n juntion an be reatedin semiondutors by doping one region with atoms of the donor material and anadjaent region with a

eptor atoms. Eletrons and holes subsequently di�use inopposite diretions aross the juntion until equilibrium is reahed. As a result, a15

16potential barrier is produed, slightly less than the energy gap, spanning the juntionregion, �gure 4.1(b).

Figure 4.1: Struture and energeti proesses within the p-n semiondutor juntion.This potential barrier may be ounterated by the appliation of an external po-tential di�erene, allowing additional holes and eletrons to ow aross the juntion,�gure 4.1(). These arriers, injeted in to the juntion region, undergo a proessof annihilation (reombination with a arrier of the opposite polarity) by one of twomeans;1. A non-radiative proess in whih the energy released is in the form of phononsor heat energy2. A radiative proess in whih the energy released is in the form of photons orvisible light.

17The seond proess is of ourse the most desirous and maybe further subdivided intotwo methods of reombination in whih either;1. An eletron in the lower ondution band ombines with a hole near the topof the of the valene band. The wavelength of the light produed is then givenapproximately by the band-gap energy of the rystal. This is the `band-to-bandreombination' and is the predominant method in diret band-gap materials forexample GaAs2. A photon is produed by the reation and annihilation of a bound exiton at aniso eletroni entre. These entres assoiated with impurities in the rystal arenormally neutral but introdue a loalized potential whih subsequently attratseletrons. In p-type material injeted eletrons ongregate at the entres, andthe negatively harged entre attrats a hole from the valene band forming abound exiton. The energy of the photon reated in this annihilation of the hole-eletron pair is equal to the band gap energy minus an energy approximatelyequal to the binding energy of the entre. This is the predominant method inindiret band-gap materials suh as GaP.The photon energy an be onverted to wavelength via:� = 1240�E (nm)where �E is the energy transition in eletron volts. Lossew �rst identi�ed emissionof photons from a p-n juntion in 1923.Referring to �gure 4.2, the semiondutive die-hip is generally 0.3 to 0.5mmsquare with a thikness of 0.3mm. Most LED's emit from all faets of the die, thoughnot from below whih is generally metal oated. A die up-mirror serves to ollet theradiant energy from all faets and projet light in more or less the forward diretion.In this partiular model, the ontents are housed in a T1-3/4 type pakage. Thedome-like top of the T1-3/4 type forms an immersion lens whih ouples with the dieup to form the light beam.

18

Figure 4.2: Strutural features of the type T1-3/4 LED.Not all light emitted from the LED's p-n juntion meets the observers eye, due toloss from three di�erent mehanisms;1. Absorption within the LED material2. Fresnel loss; This fator is substantially redued by both oating the LED hipin an intermediate material, and enapsulating the LED in a plasti with indexof refration � 1:53. Critial angle loss; a small proportion of emitted photons whose angle is greaterthan the ritial angle at the emission surfae su�er total internal reetion.This loss is redued by inreasing the index of refration of the enapsulatingmaterial and a domed exit surfae.To it's advantage, an LED requires low urrent and voltage to produe useful lightoutput, the emission area is preisely de�ned in the semiondutor manufaturingproess and the devie may be swithed at high speeds. However, in omparisonwith laser diodes the LED has an emitting area whih is several orders of magnitude

19larger. This an be improved upon. Partiularly within the ommuniations industry,optial �bre is embedded diretly into the devie, just above the semiondutive die,�gure 4.3. The hip itself is imaged diretly, eliminating noise introdued by thediode asing, emulating a point soure more a

urately. As one would expet though,a signi�ant amount of light is sari�ed.

Figure 4.3: Embedding of optial �bre in an LED.

Chapter 5Experiment5.1 MotivationIt is intended to use a Cranz Shardin amera sheme in visualising unsteady owphenomena within the model SCRAMjet engine. This devie is routinely tested inthe T4 shok tunnel faility at the Department of Mehanial Engineering, Universityof Queensland. T4 is a short duration test faility; supersoni ows simulating trueoperational onditions are reated for periods of several milliseonds or less. There-fore, to image the evolution of proesses whih o

ur within this narrow window, theamera must issue a stream of light pulses whose width and temporal resolution1 areof the order of miroseonds in duration. As disussed, the LED is ideally suited tosuh a task.5.2 Preliminary InvestigationsA driver iruit was designed and onstruted by Mr B. V. Allsop to pulse an LEDfor various periods and urrents. The driver iruit onsisting of a fast op-amp andseries transistors, stepped up in power, provides urrent gain, input pulse and supply1Inrement of time between eah su

essive pulse. Frame or repetition rate (s�1) refers to thereiproal of this time and is the frequeny of the pulse train.20

21voltages provided by external soures. The output urrent is variable, dependent onthe input pulse amplitude and VCC aross the transistors, and monitored by a sensingresistor of one ohm. The voltage produed aross the resistor and displayed on theTEKTRONIX osillosope is `equal' to the urrent (V = I�1), allowing for a smallerror in the value of the resistor. The iruit also permits ontinuous operation at20-30 milliamps for purposes of alignment. Lines within the iruit are restrited inlength and twisted where possible to redue the impedane, and hene the induedvoltage spikes produed by the rapidly hanging urrent, desribed by Lenz's law:V = LdIdt . A shemati for the devie is displayed in Appendix A.1. Figure 5.1 is aplot of the output urrent pulse whih drives the LED.

−2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5

x 10−5

−1

0

1

2

3

4

5

6

Time (s)

Am

plitu

de (

V=

I)

Pulsed Output, LED Driver

Figure 5.1: Typial output from LED driver iruit (pulse width approx. 5�s).A Cranz Shardin amera arrangement was devised and a simple one soure versiononstruted on the `dane' oor2, �gure5.2, values for the essential elements listed intable 5.1.2Platform of T4 faility, level with the test setion. On the dane oor is shok tunnel instrumen-tation and optis for performing investigations; in the test setion is plaed the objet of interest.

22

Objective lensFilm plane

f

f

1

2

ML2

ML1

d i

d

W

Lens plane

LED plane

Test Section

Figure 5.2: Experimental set up for a generi Cranz-Shardin sheme.A single LED (initially a type HLMP-DL08, Hewlett Pakard) was plaed withinthe virtual objet spae of a onverging lens, reating a virtual point soure in thefoal plane a large onvex mirror. `Parallel' light from the mirror illuminated the testsetion of the shok tunnel and a real image produed in the �lm plane of a amera.In all tests whih followed, apart from ontinuous operation at 20-30 milliamps, theLED was pulsed for periods between 1 and 20 �s, for urrents of up to 5 amps. Severalfators beame immediately obvious;1. The intensity and dispersive nature of the LED were not very ompetitive withthe abundant sunlight, the beam virtually invisible on a piee of white paperplaed quite near the soure.2. The optial and mehanial axis of the LED are somewhat di�erent. Thisoupled with (1) made the LED very awkward to align. Essentially alignmentwas a proess of tweaking the diode and then observing it's position in the �lm

23Element Parameter(s) Value(s)Initial lens fi; Di; d; di +50mm,25mm;43mm,2130mmML1, mirror f1; D1 +2440mm,200mmML2, mirror f2; D2 +3000mm,200mmObjetive lens fo; Do +300mm,50mmViewing Field W 200mmImaging Media 3000ISO �lm, PolaroidLED HLMP-DL08Table 5.1: Elements of Cranz Shardin amera, for initial testing in the T4 shoktunnel faility.plane, requiring an inordinate amount of patiene.3. Spae restritions near the test setion neessitated the use of a 45 degree mir-ror. The optimal position for the mirror still ontributed to the sari�e of asigni�ant amount of light.4. The beam pro�le resembled a series of onentri rings. Spatial �ltering bymeans of a simple pinhole was observed to disard too muh of the light andultimately this LED was replaed by the type HLMP-DG08. Features of bothdiodes are summarized in table 5.2.Devie HLMP-DL08 HLMP-DG08�1=2 60 60� 590nm 626nmFWHM 17nm 17nmLum. Intensity �20mA 9300md 6500mdJuntion Temp. 1300 1300Response Time (�res:) 20ns 20nsTable 5.2: Charateristis of two Hewlett Pakard AlInGaP LED Lamps. �1=2 is thehalf angle of dispersion.Further tests were performed under low light onditions at di�erent loationswith the aim of obtaining a shadowgraph of the density �eld surrounding a hot sol-dering iron; at this point an alignment laser was introdued. In all instanes Polaroid

243000ISO �lm was used. The �lm is ontained in a pak, mounted on the bak ofamera bellows and exposed by opening and losing a manual shutter.The LED was onsiderably easier to align and yielded a shadowgraph faintlyobservable to the eye when plaed in the �lm plane. However, all pitures taken werewashed out by sunlight, even though light impinging on the amera was availableonly via a small aperture.An exellent dark room for test work was found in the Parnell building and onemore the generi system depited above built. The light soures, ollimating lens andobjet were plaed in a rude optis box to restrit stray reetions et. Initially anattempt was made to obtain a shadowgraph of a andle ame however as expeted theluminosity washed out the �lm. A little more enouraging were the results obtainedfrom a low power 7 watt soldering iron; for the �rst time faint shadowgraph imageswere obtained. Figure 5.3 displays two of the images, whih were for various urrentvalues and pulse widths.200 400 600

100

200

300

400

500

200 400 600

100

200

300

400

500

600Figure 5.3: Shadowgraphs of density �eld surrounding soldering iron. Left: this imagewas produed with a pulse of approx. 1�s at 1amp; two density �eld lines are visible,extending from the iron. Right: the LED pulse was approx. 20�s at 2 amps. Faintlyvisible in the top right hand orner is a vortex.The �eld of view was 50 millimetres in diameter, reated by an aperture illu-minated by a parallel beam of 100 millimetres diameter. Even with this signi�antamount of light disarded, there was enough intensity from the LED's to illuminatethe objet and expose the �lm; this gives one hope that the multiple soure systemwill work with a large viewing �eld, provided objet luminosity an be dealt with. In

25further support of this statement, the pulsed output at 5 amps, 1 �s was suÆientlypowerful to saturate the �lm ompletely.5.3 Diode CharaterisationThroughout the ourse of investigations, it was apparent that the high speed �lm(3000ISO) was not neessary; the LED produed ample intensity. Using a �lm oflower speed will drastially redue the e�ets of extraneous light. The literaturesuggests that the pulsed output of the diode is in the viinity of 1 watt [2℄. Figure5.4 gives a measure of the LED output vs input urrent. The plot was obtainedby mounting an LED against a photodiode and monitoring the output of the diodeon hannel 1 of a CRO, as the urrent amplitude of the driver iruit was varied(displayed on hannel 2).

1 2 3 4 5 6 760

70

80

90

100

110

120

130

LED current (Amps)

Pho

todi

ode

outp

ut (

A.U

.)

LED output

pulse width: 10^-6 sec.

Figure 5.4: Response of type HLMP-DG08 LED.The output apparently reahes a maximum in the region 6-7 Amps, at whih pointsaturation e�ets inhibit further gains. Driving with muh above 7 Amps proves

26destrutive even for short durations, a result of ohmi heating; even in ontinuousoperation the juntion temperature is in the viinity of 1300.The larity of images obtained by suh methods as shlieren and shadowgraphrelies on the light soure being point-like, ritial for produing a well ollimatedbeam. The LED only rudely emulates a point soure and this was manifest in theresults. However as mentioned previously the LED semiondutive die is quite small,so if properly harnessed may prove quite reliable.5.4 Preparation for Multiple ImagesTo ontrol a multiple soure system, a CMOS digital iruit was built by the author,again devised by Mr Allsop. Appendix A.2 displays a shemati for this devie; �gure5.5 is a ow diagram for the entire eletroni subsystem of the Cranz Shardin amera.The ontrol iruit is a single unit, omposed mainly of the type HCT4017 ounter-divider. It is apable of supporting up to ten hannels (light soures). Referring to the�gure, an input TTL signal triggers the devie. A subiruit ontrols the trigger delay,this period spei�ed by a seleted pin on the 4017; delays are available in inrements of50�s up till 4.95ms. In the usual fashion, a rystal osillator provides the `heartbeat'for the iruit, in this ase set to 1 MHz. Depending on the pin-out of this partiularhip, other time bases are available. One the trigger delay has ounted out a spei�number of pulses, this triggers the frame rate subiruit. Again, the frame rate (timebetween pulses) is adjustable via seleted pins. This then issues a stream of pulses tothe `input' terminals of all hannels. In the urrent measurements 4 hannels are used,hene four pulses are issued. The pulse width is determined by the RC ombinationon a monostable. The frame rate iruit triggers `reset selet' whose outputs go tothe `enable' ports of eah individual hannel. Note from the diagram the temporalresolution of eah of these pulses. The enable and input terminals are added at theanalogue driver iruits, and hene eah LED pulses only when the analogue driverreeives two aÆrmative logi signals. The full driver iruit is idential to that used

271 MHzXtalOscillator

TriggerDelay

LED driver(s)

Frame Rate

ResetSelect

Pulse Width

Q0

Q1

Q2

Q3

990 10-

µs

4950 µs50-

1-100 µs INPUT, all

ENABLE, ch1

ENABLE, ch2

ENABLE, ch3

ENABLE, ch4

CMOS timing control

channels

Trigger

Figure 5.5: Eletrial subsystem of the Cranz Shardin Camera.for testing, apart from the transistor gating arrangement and additional op-amp,Appendix A.3. Also, a logi trigger was built to eliminate jitter assoiated with astandard push button swith, Appendix A.4.5.5 Appliation to the Drummond TubeOwing to unfavourable onditions presented by the T4 environment, it was deidedto test the ompleted amera system in the small shok tunnel faility [8, 1℄.Although being somewhat smaller and more limited in it's operating range, itdoes permit ten or more tests a day, as opposed to approximately four on T4. Ithas the added advantage of being able to be isolated from sunlight and su�ers littlefrom vibration or reoil. The plant was originally aquired from the DSTO and has

28undergone refurbishment inluding various hanges to the plumbing. Pitured in�gure 5.6 is a shemati of the faility. The driver tube is separated from the test orshok tube by an aluminium diaphragm. When the driver setion is �lled with gas(e.g., helium) at the appropriate pressure the diaphragm is ruptured by a sharp rod.The resultant shok travels down the tube �lled with the test gas at speeds in theviinity of 2km/s. After bursting a small ellophane diaphragm near the Mah nozzle,the shok expands through the nozzle, over the test objet and is �nally spent in thedump tank. The test setion is 300mm in length and about 460mm in diameter. Thespeed of the shok is governed by a number of fators, largely the pressure and natureof the driver and test gases. The entire proess, from the emission of the shok toits arrival in the dump tank, takes plae within several milliseonds; the atual testduration lasts for several hundred miroseonds.5.5.1 Single FramesUsing the reently �nished pulsed supply, omprised of ontrol and driver iruits, asingle soure shlieren and shadowgraph system was assembled near the test setionof the shok tube, �gure 5.7. Note the insertion of the knife edge. This is the distin-guishing feature of the shlieren tehnique. Light deeted by optial inhomogeneities(e.g., shok waves) is foused to a di�erent point and may be seletively bloked bythe knife edge, it's absene deteted in the �lm plane. Shadowgraph however pro-dues ontrast through defoussing, disussed previously. Experimentally then theproess by whih shoks are imaged in either ase may be summarized as follows;1. Shlieren The objet is foused onto the imaging media (in this ase a CCD).Contrast is produed by obstrution of the deeted light. Shlieren is propor-tional to the �rst derivative of the density �eld.2. Shadowgraph A plane in front of the objet is foused onto the imaging me-dia, the distane between plane and objet orresponding to the defoussingdistane. Shadowgraph is proportional to the seond derivative of density.

29

Figure 5.6: The small shok tunnel faility.

30f=+400 mm

Knife Edge

CCD

Trigger

Pulsed Supply

Incoming Shock

To Dump Tank

Mach Nozzle

LE

D

Aperture

Cylinder

TTLArrangement for Schlieren

f=+400 mm

Figure 5.7: Experimental set up for single frame shots; top viewUsing a light pulse width of about 8 �s single shlieren and shadowgraph imagesof a ylinder were obtained. The pulsed power supply reeives a trigger signal froma pressure transduer plaed near the Mah nozzle of the shok tube; the triggerdelay3 in this ase was about 420�s. The trigger delay allows for the �nite timetaken by the shok to traverse the Mah nozzle before entering the test setion. Inthe shlieren image, the shok appears as a thin dark band detahed some distanefrom the ylinder. The shok ompresses the ow (Appendix B) and therefore thedensity pro�le resembles a step funtion. Reall �gure 2.1; shlieren is proportionalto the �rst derivative of the density and hene the light intensity pro�le orrespondsto a single urve, �gure 5.8. The signal to noise appears quite good, although ridgesvisible to the naked eye on the top of the LED are apparent in the bakground. Thisis due to an aperture positioned in front of the LED in the foal plane of the �rst lens;3Time between reeipt of trigger signal and emission of �rst light pulse.Figure 5.8: (Following Panel) Shlieren image of ow over a ylinder. LED pulse sizeapprox. 8�s at 5amps.

31the very tip of the devie ats as the point soure. Figure 5.9 displays a shadowgraphimage, in whih the shok appears as a light and dark region, owing to the dependeneon the seond derivative of the density; the seond derivative of a step funtion is apositive and negative urve either side of the disontinuity.The ylinder is �nite in length, therefore the shok `folds' around the edges, to adegree. These `edge e�ets' may be responsible for the extra shok visible near theextremities of the ow.5.5.2 Multiple FramesMultiple images were obtained in due ourse, the experimental on�guration as per�gure 5.10. The LED's had their dome lenses removed, the semiondutor hipsserving as point soures. The soures were arranged in a square array and plaed aninh apart, governed by the diameters of the �nal lenses. Figure 5.11 is a plot of theoutput pulse train from the CMOS ontrol iruit, showing the temporal resolutionbetween pulses. Colour images of the ow are displayed in �gure 5.12. Note theobvious distortion, due to the large angle of inidene between the light beams andoptial axis, introduing spherial aberration. Also the images aptured by a KodakCCD amera appear saturated, despite the modi�ed LED's being quite dispersive.These results are very enouraging; there is ertainly adequate intensity developed bythe LED's for this small system and if ertain parameters are optimized then sharpimages will result.Figure 5.9: (Following Panel) Shadowgraph image of ow over a ylinder. LED pulsesize approx. 8�s at 5amps.

32f=+80 mm

CCD

Trigger

Pulsed Supply

TTLIncoming Shock

To Dump Tank

to LED’s

Arrangement, 4 source system

f=+100 mmd=12.7 mm

f=+300 mm

Figure 5.10: Experimental layout for obtaining four images; top view.

−0.5 0 0.5 1 1.5 2 2.5 3 3.5

x 10−4

−0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Time (s)

Am

plitu

de (

V)

CMOS Output

Figure 5.11: CMOS ontrol iruit output showing resolution between pulses.Figure 5.12: (Following Panel) Multiple shadowgraphs of ow over a ylinder; timeinreases as one proeeds anti-lokwise from the lower left-hand orner. LED pulsesize approx. 8�s at 5amps, pulse separation, 200�s.

Chapter 6ConlusionsA Cranz Shardin amera sheme was used su

essfully to image shok waves in super-soni ows, where the e�ets of external light an be redued. Multiple shadowgraphsas well as single shlieren and shadowgraph images have been obtained. The lightemitting diode has proved advantageous over lasers in this appliation owing to itslower ost, ompatness and ability to be pulsed rapidly and repeatedly; framing ratesof the order of 106s�1 are ahievable. The diode was quite rugged, able to withstandurrents in the viinity of 5 amps for up to several hundred miroseonds, produingsuÆient intensity to saturate the 3000ISO Polaroid �lm. As a result a CCD amerawas used preferentially over �lm, whih also su�ered saturation e�ets. The optialsystem used departs somewhat from Lu and Liu's sheme. Initial lenses weren't ne-essary for harnessing the light; for this small viewing �eld the dispersive LED hipitself produed ample intensity. In the literature, usually a �nal, single objetive lensarray is used to produe magni�ation. This simple sheme allows diret imagingonto a �lm plane. However the optial beams are not parallel, a strong requisite forgood ontrast in a shadowgraph system. On the other hand, using multiple lensesto keep the beams ollimated and redue the image size to suit the CCD apertureintrodues signi�ant distortion. When hoosing the imaging media, one needs totake into a

ount the following; 33

341. If using �lm, a lower ISO is required in onjuntion with a system of stops,�lters, shutters et to restrit exess light, or,2. If a CCD is used, a fousing lens with larger numerial aperture is needed.This would permit a wider viewing �eld, alleviating distortion introdued whentrying to image a large �eld down through a relatively small aperture.It is interesting to note in the literature that the Cranz Shardin amera is gener-ally used to obtain bak-lit images of rapidly o

urring events, and not shadowgraphsper se. The diÆulty in obtaining undistorted, multiple shadowgraphs lies in at-tempting to keep the optial beams ollimated, beams whih are divergent owing tothe di�erent optial paths traversed. The devie is perhaps best suited to a shlierensheme, where the ollimation of the �nal beam is not so ruial and ontrast isprodued more easily.6.1 Further WorkThe fully integrated LED pulsed supply has been developed to the point where itmay be assembled in a proper instrument ase. To that end, PCB artwork needs tobe reated from the iruit diagrams.The signal to noise of the LED's was quite reasonable, further improved by removalof the dome lenses. The semiondutor hips themselves emulated point soures well,although a signi�ant amount of light was sari�ed. Bretthaur et al use optial �breto ouple the light soures to the optis. The bene�ts are two-fold:1. LED's an be mounted at the iruit itself, alleviating pulse distortion reatedby indued voltages.2. The �bre ould be positioned just above the die hip, harnessing most of thedispersive emission. It has been observed that imaging the hip diretly removesnoise introdued by imperfetions on the surfae of the diode.

35The system ould be applied to the T4 environment as originally intended if perhapsa kerr ell1 and band pass �lter were introdued. Tsai et al use spetral �lteringto eliminate the e�ets of ow luminosity, whih works well owing to the narrowbandwidth of the diode's emission. The kerr ell ould be triggered and held open forthe duration of the test, eliminating the need to open and lose the polaroid shuttermanually. However, it may be that using lower speed �lm will eliminate the need fora shutter. Tsai's group use a Cranz Shardin sheme to produe multiple shlierenimages; it might be prudent to examine the use of knife edges for ontrast.

1A high speed eletro-opti shutter

Bibliography[1℄ J.M. Austin, P. A. Jaobs, M. C. Kong, P. Barker, B. N. Littleton, and R. Gam-mie. The small shok tunnel faility at UQ. Tehnial Report 2, Department ofMehanial Engineering, July 1997.[2℄ B. Bretthauer, G. E. A. Meier, and B. Stasiki. An eletroni ranz-shardinamera. Review of Sienti� Instruments, 62(2):364{368, 1991.[3℄ D. G. Christie. A multiple spark amera for dynami stress analysis. Jnl. Phot.Si., 3:153{159, 1955.[4℄ C. Cranz and H. Shardin. Kinematographi auf ruhendem �lm und mit extremhoher bildfrequenz. Zs. Physik, 56:147{183, 1929.[5℄ L. A. Cross. Proeedings of the SPIE{The International Soiety for Optial En-gineering, 981:272, 1989.[6℄ S. Gage et al. Optoeletronis/Fibre Optis Appliations Manual. MGraw Hill,2 edition, 1981.[7℄ R. Germer. High speed video tehniques with

d-ameras. Proeedings of theSPIE{The International Soiety for Optial Engineering, 674(2):631{637, 1986.[8℄ K. Hannemann, P. A. Jaobs, J. M. Austin, A. Thomas, and T. MIntyre. Tran-sient and steady-state ow in a small shok tube. Proeedings of the 21st Inter-national Symposium on Shok Waves, 1998.36

37[9℄ H. W. Liepmann and A. Roshko. Elements of Gas Dynamis. John Wiley &Sons, In., 1957.[10℄ F. K. Lu and X. Liu. Optial design of ranz-shardin ameras. Optial Engi-neering, 36(7):1935{1941, 1997.[11℄ F. K. Lu, X. Zhang, and X. Liu. Visualisation of on�ned shok-bubble in-terations. Proeedings of the 21st International Symposium on Shok Waves,1998.[12℄ W. Merzkirh. Flow visualization. Aademi Press, New York, 1974.[13℄ J. Rienitz. Optial inhomogeneities: Shlieren and shadowgraph methods in theseventeenth and eighteenth enturies. Endeavour, 21(2):77{81, 1997.[14℄ B. Stasiki and G. E. A. Meier. A omputer ontrolled ultra high-speed videoamera system. Proeedings of the SPIE{The International Soiety for OptialEngineering, 2513:196{208, 1995.[15℄ A. M. Thomas, T. J. MIntyre, A. I. Bishop, and H. Rubinsztein-Dunlop. Planarlaser indued uroesene for studies of shok tube and tunnel ows. Proeedingsof the 21st International Symposium on Shok Waves, 1998.[16℄ C. Y. Tsai and R. J. Bakos. Shok tunnel ow visualisation with a high speedshlieren and laser holographi interferometry system. 20 th AIAA AdvanedMeasurement and Ground Testing Tehnology Conferene, 1998.[17℄ A. A. Wells and D. Post. The dynami stress distribution surrounding a runningrak{a photoelasti analysis. Pro. SESA, 16(1):69{92, 1957.

Appendix ACiruit DiagramsFigure A.1: Analogue driver iruit. During initial testing, transistor gating arrange-ment was absent, pulsed input fed diretly into the non-inverting input of the op-ampFigure A.2: CMOS timing ontrol iruit. The output amplitude is varied by a poten-tiometer. `INPUT' is tied to every driver hannel and `ENABLE' to eah individualhannel; supports up to ten. The devie resets after ounting out a spei� numberof pulses depending on the hip set of `reset selet'.Figure A.3: Zero orretion. Holds the analogue driver stages at zero volts wheninput terminals are open.Figure A.4: Logi swith. Produes lean input TTL trigger signal, free from jitterwhih otherwise destabilises the iruit.

38

Appendix BCompressible Fluid FlowsB.1 Governing EquationsThe disussion of this hapter is similar to the treatment given in Leipmann andRoshko's Elements of Gasdynamis.Vital to the understanding of phenomena whih o

ur in high speed ompressibleows are the governing equations. It is suÆient for the sope of this work to onsiderfritionless, ompressible uid ow in one dimension only, �gure B.1

x

u

AFigure B.1: Fluid ow in one-dimensionThe ross-setional area A and veloity u have some funtional dependene on xfrom whih we may determine ow parameters in a region (2) given those in (1) usingequations of ontinuity, energy and momentum. These relations are easily extendedto two-dimensional supersoni ows. 39

40The most general statement of the ontinuity equation may be derived from �gureB.2.1

2

AA

x

∆ x

uρ

ρu A + ddx

(ρu A )∆

Figure B.2: Portion of uid bounded by two surfaesThe mass between surfaes 1 and 2 is �A�x, inreasing at the rate ��t(�A�x),whih negleting the presene of a soure must be equivalent to the net inow, viz� ��x(�uA)�x = ��t(�A�x)Now �x is independent of time, therefore the equation of ontinuity for a non-steady ow follows; ��x(�uA) + ��t(�A) = 0: (B.1)The �rst law of thermodynamis is ommonly written in the form�E = �Q +�W (B.2)That is,There exists a variable of state, the internal energy E whih under-goes an inremental hange �E when going from equilibrium state A toequilibrium state B, given by the sum of the ow of heat �Q into andwork �W done on the system.

41

2

q

p2

u2

p1

u1

ρ ρ1 2

1 1

2Figure B.3: Piston system for alulation of energy relationConsider the system of �gure B.3 whih ontains uid bounded by two pistonswith surfae(s) 1 and 2.The pistons su�er a displaement and in addition heat may ow into the system.In onsidering the work done on the portion of uid assume that the volume displaedat 1 is a spei� volume v1 orresponding to unit mass. Likewise at 2 a volume v2 isdisplaed. Hene the work done on the system by the pistons is�W = p1v1 � p2v2Denote the loal energy as (e+ 12u2) where e is the internal energy and u is the veloityof the piston. Then the inrease in energy is�E = (e+ 12u2)2 � (e+ 12u2)1:Equating then and inluding the e�et of heat ow into the system (denote �Qas q)we have for steady ows;q + p1v1 � p2v2 = (e+ 12u2)2 � (e+ 12u2)1 (B.3)For a owing uid the basi thermodynami quantity is the enthalpy h ratherthan internal energy, where h = e + pv; so we may further simplify Eq. (B.3) by

42this introdution and further if the proess is adiabati, i.e. q = 0, then the adiabatienergy equation results; h2 + 12u22 = h1 + 12u21 (B.4)This expression, sine derived from the �rst law of thermodynamis, relates on-ditions at two equilibrium states and is valid even if there are visous stresses, heattransfer et between surfaes 1 and 2 so long as the states are in equilibrium.Tantamount to the momentum relation is Euler's equation. If one begins fromNewton's law F = ma, within a ow the a

eleration is the result of two e�ets;1. Convetive e�ets, whereby the time rate of hange of veloity is proportionalto the produt of the veloity and veloity gradient in the uid,u�u�x2. Non-steady or non-stationary properties of the ow,�u�t :The total a

eleration is then, in general,ax = u�u�x + �u�t :Figure B.4 illustrates the pressures su�ered by a partile of elementary shape.pA

pA

x

+dxd (pA)∆ x

∆Figure B.4: Pressure fores exerted on elementary partile

43The resultant fore per unit mass may be extended to a partile of arbitrary shapeby appliation of Gauss' theorem and is given byfx = �1� �p�x:This alulation ignores visosity and shear e�ets and is appliable to a ow wherethese e�ets are negligible. From Newton's law written in terms of the fore per unitmass, one may thus write, u�u�x + �u�t = �1� �p�x (B.5)whih is referred to as Euler's equation in one dimension.The momentum equation is obtained by ombination of the Euler and ontinu-ity equations. It is onvenient for the desription of ows through a spae de�nedby ertain �xed surfaes, desribing the hange of momentum within this `ontrolvolume'.Multiplying Euler's equation by �A and the ontinuity equation by u gives�A�u�t + �uA�u�x = �A�p�xand u ��t(�A) + u ��x(�uA) = 0respetively. Equating;��t (�uA) + ��x (�u2A) = �A�p�x = � ��x (�A) + p�A�x (B.6)whih is the momentum equation in one dimension. Integrating with respet to x;��t Z 21 (�uA)dx+ (�2u22A2 � �1u21A1) = (p1A1 � p2A2) + �m(A2 � A1)where the last term is obtained by de�ning a mean pressure �m between surfae 1and 2.The LHS is the rate of hange of momentum in the ontrol volume and has on-tributions from non-stationary hanges within and the inward ux of momentum.

44Again, this equation is independent of fritional fores within the ontrol volumegranted that dissipative mehanisms are absent from the referene surfaes 1 and 2.For a steady ow in a dut of onstant area, the momentum equation redues to�2u22 � �1u21 = p1 � p2 (B.7)A useful result obtainable from the di�erential form of the energy and Eulerequation is that an adiabati, non-visous, non onduting ow is isentropi. For aperfet gas this leads to the relationsppo = ( ��o ) = ( TTo ) (�1) (B.8)where the subsript o denotes stagnation onditions or onditions within a suÆientlylarge reservoir where the veloity may be onsidered to be negligible.B.2 Mah NumberThe speed of sound, a, within a uid is related to the ompressibility bya2 = �p��!s ;whih is the speed small disturbanes propagate at through the uid. The produtionof a sound wave is essentially an isentropi proess and from Eq. (B.8) we maydetermine a2 = p� = RT: (B.9)This is a useful uid parameter when ompared with the ow speed whih as previ-ously mentioned is referred to as the Mah number;M = ua (B.10)The value of M determines whih of three regimes a uid ow may be lassi�ed as;� If M > 1, the ow is supersoni

45� If M = 1, the ow is transoni� If M < 1, the ow is subsoni.Now from ontinuity we may writed�� + duu + dAA = 0 (B.11)and from the Euler equation (for a steady ow);u du = �d�� = �dpd�:d�� = �a2:d�� :Introduing M = ua this last result may be expressed asu du = � u2M2 :d��or �duu M2 = d�� (B.12)Substituting Eq. (B.13) into (B.12) and performing some algebrai manipulationgives the area veloity relation; duu = � dA=A1�M2 : (B.13)This has two interesting onsequenes;1. For subsoni ows (M < 1) a derease in area is a

ompanied by an inrease inow veloity2. For supersoni ows (M > 1) an inrease in area is assoiated with an inreasein ow veloity.For soni speeds (M = 1) the relation an only be �nite for dA=A = 0 i.e. thereexists a throat at this point in the ow.The energy equation for an adiabati, perfet gas ow,

46u22 + pT = pTo (B.14)an be used to express the relation between veloity, the reservoir and generalspeed of sound as u22 + a2 � 1 = a2o � 1 : (B.15)The isentropi relations (B.8) then give for the following thermodynami variables;pop = �1 + �12 M2�

�1�o� = �1 + �12 M2� 1�1 9>=>; (B.16)The values of �o and po are loally onstant and only entirely onstant throughoutan isentropi ow. A useful point at whih the energy equation may be evaluated iswhere M = 1 i.e. at a throat. Quantities in this region are soni variables denotedwith supersript *. The energy equation in terms of the soni variables may be writtenu22 + a2 � 1 = 12 + 1 � 1a�2; (B.17)using the fat that M = 1 therefore u� = a�.Related to the Mah number is the speed ratio,M� = u=a�. M� is easily expressedas a funtion of M by dividing Eq. (B.17) by u2;M�2 = + 12M2 � ( � 1) (B.18)B.3 The Shok RelationsIt has been determined that regardless of intermediate non-equilibrium proesses, therelationship between equilibrium regions 1 and 2 for onstant-area adiabati ow aregiven by �1u1 = �2u2p1 + �1u21 = p2 + �2u22h1 + 12u21 = h2 + 12u22 9>>>>=>>>>; (B.19)

47In supersoni, ompressible ows the region of dissipation is a disontinuity re-ferred to as a shok wave. It is typially several atomi distanes thik allowingnon-equilibrium ollisional proesses to take plae. Regions of equilibrium may bebrought arbitrarily lose to the disturbane and the equations (B.19) give the rela-tionship between regions 1 and 2, �gure B.52u u1

Figure B.5: Shok wave separating regions 1 and 2 in states of equilibriumThese equations are analytially solvable for a perfet gas and an expression maybe determined in terms of the value of the Mah number M1 ahead of the shok.Dividing the momentum equation by the ontinuity ondition gives for the veloitydi�erene u1 � u2 = p2�2u2 � p1�1u1 = a22u2 � a21u1 (B.20)using a2 = p=� for a perfet gas. This expression may be further simpli�ed byemploying Eq (B.17), whih gives the Prandtl or Meyer relation;u1u2 = a�2 (B.21)i.e. M�2 = 1=M�1 (B.22)So intuitively, the shok wave represents a boundary between supersoni and subsoniveloity regimes. It remains to be seen whih regime orresponds to whih region,before or after the shok. From the orrespondene between M� and M given in Eq.(B.18) one may determine the relationship between Mah numbers;M22 = 1 + �12 M21M21 � �12 (B.23)

48Using ontinuity, Eq. (B.18) and the ratio between veloities u1=u2 = M�21 , therelation between densities is �2�1 = u1u2 = ( + 1)M21( � 1)M21 + 2 : (B.24)By substituting this expression into the momentum equation in onjuntion witha21 = p1=�1, the pressure jump or shok strength may be determined to be;p2 � p1p1 = �p1p1 = 2

+ 1(M21 � 1): (B.25)Finally, the veloity ratio in onjuntion with the energy equation gives for the tem-perature ratio T2T1 = 1 + 2( � 1)( + 1)2 M21 + 1M21 (M21 � 1): (B.26)Now (negleting the details) the entropy an be approximately written ass2 � s1R = 2( + 1)2 (M21 � 1)33 : (B.27)Sine the hange in entropy is a positive quantity for an adiabati ow, M1 mustalways be greater than or equal to 1. In other words, the jump in veloity betweenregions 1 and 2 is always from supersoni to subsoni. The orresponding jumps intemperature, pressure and density are always to higher values, therefore the shok issaid to ompress the ow.The visualization of shok waves and other features of ompressible ows lieswithin the realm of optial diagnosti tehniques.