Received: 25 September 1996/Accepted: 19 May 1997

N. J. Dam, M. Rodenburg, R. A. L. Tolboom, G. G. M. Stoffels,P. M. Huisman-Kleinherenbrink, J. J. ter MeulenUniversity of Nijmegen, Department of Molecular and Laser PhysicsToernooiveld, NL-6525 ED Nijmegen, The Netherlands

Correspondence to: N. J. Dam

We want to thank B. Timmerman (Delft University of Technology)for providing us with drawings of the flow generator and fordiscussions, and S. Stoks for his aid with the image processing. Also,we would like to thank an (anonymous) referee for providingdetailed, constructive criticism on an earlier version of thismanuscript. This research is supported by the Technology Founda-tion (STW).

Originals Experiments in Fluids 24 (1998) 93—101 ( Springer-Verlag 1998

Imaging of an underexpanded nozzle flow by UV laser Rayleigh scatteringN. J. Dam, M. Rodenburg, R. A. L. Tolboom, G. G. M. Stoffels, P. M. Huisman-Kleinherenbrink, J. J. ter Meulen

Abstract Rayleigh scattering of ultra-violet laser light isapplied as a diagnostic tool to record gas density distributionsin a supersonic nozzle flow. The output beam of a pulsed ArFexcimer laser (j\193.4 nm) is focussed into a thin light sheetradially intersecting a dry air flow emanating from a circularnozzle. An intensified CCD camera is used to record theRayleigh scattered light in a direction perpendicular to thelight sheet. Since the Rayleigh scattering intensity is directlyproportional to the local gas density, this results in two-dimensional gas density distribution maps of radial slicesthrough the flow. Images of the flow density are presentedfor stagnation pressures between 0.2 and 0.7 MPa (0.1 MPa{1 bar), showing the transition from subsonic to supersonicflow and, at higher pressures, the formation of a Mach disk.Density maps can be recorded with single laser pulses,effectively freezing the flow structure on a 20 ns time scale. Thediamond pattern, characteristic for underexpanded supersonicnozzle flows, is quantitatively monitored, with the experi-mental results being in reasonable agreement with predictionsfrom a simplified theoretical model.

1IntroductionComplete characterization of flow fields, in terms of density,temperature, pressure and flow velocity, with high spatial andtemporal resolution is one of the most alluring wishdreams inaerodynamics and combustion research (Settles 1988). Non-invasive probes are, obviously, preferred above invasive ones,and optical techniques, mainly employing lasers because oftheir unsurpassed spectral brightness, rank high among the

former (see e.g. Eckbreth 1988). Recent developments in bothhigh power tunable laser systems and intensified solid statecameras have allowed to extend the possibilities of laserdiagnostics to instantaneous, two-dimensional (2D) flow fieldcharacterization.

Laser Induced Fluorescence (LIF) has often been used as themethod of choice for flow characterization (Laufer et al. 1990;Miles et al. 1988; Gutmark et al. 1991). Yet, although LIFhas the advantage of large scattering cross section and goodmolecule specificity, it has the disadvantage of being relativelysensitive to the physical conditions within the flow, becauseof the occurrence of collisional fluorescence quenching. Thisfluorescence quenching is a main obstacle in the quantitativeinterpretation of LIF data in high pressure environments(ambient pressure and above; see e.g. Andresen et al. 1988;Brugman et al. 1993). Rayleigh and Raman scattering, onthe other hand, are relatively weak but virtually insensitiveto collisional quenching, which allows for a straightforwardinterpretation of the scattering signal strengths. Because of itsvery low scattering efficiency, Raman scattering has been littleused for flow diagnostics up to now (but new developments insolid state lasers may change this, see e.g. Varghese et al. 1996),but Rayleigh scattering has already widely been applied tocombustion (Zhao and Hiroyasu 1993; Sick 1997) and flowdiagnostics (Escoda and Long 1983; Smith et al. 1989; Miles andLempert 1990; Fourguette et al. 1991; Seasholtz and Lock 1992;Lock et al. 1992; Kampmann et al. 1993; Grunefeld et al. 1994).

The value of all these techniques is twofold. On theone hand, they are non-intrusive, that is, they do notperturb the flow to which they are applied. This is of specialimportance in the case of supersonic flows, where conven-tional mechanical probes perturb the flow significantly.Furthermore, the above-mentioned optical techniques areable to instantaneously provide data on two-dimensionaldensity distributions in a flow, in contrast to the moreconventional flow diagnostic techniques like Schlieren orshadowgraphy, which provide data integrated along a line-of-sight.

In this paper we exploit both these advantages in whatappears to be a first application of molecular Rayleighscattering to 2D density measurements in an underexpandednozzle flow. Molecular Rayleigh scattering is elastic lightscattering off individual molecules. It is the result of thenon-resonant interaction between the molecule and theincident light and, as compared to fluorescence, it is a relativelyweak process. The total radiation power, Ps, scattered from

93

Laser sheetCylindrical

optics

IntensifiedCCD camera

Excimerlaser

Nozzle

Rayleighscattering

Fig. 1. Schematic view of the experimental setup used to recordRayleigh scattering images. The nozzle flow is directed verticallyupwards, and is intersected by a light sheet of 22]0.5 mm2 crosssection, derived from an ArF excimer laser. Rayleigh scattered light isdetected under right angles with both the flow axis and the laser beampropagation direction

c

Fig. 2a–d. Rayleigh scattering images of the laser light sheetin ambient air directly above the nozzle, both without (a) and with (c)flow present (300 kPa dry air). b Laser intensity distribution abovethe nozzle opening (derived from a vertical cross section through thecentre of image a). d Density distribution derived by dividing imagec by image a; in this ratio the inhomogeneities in laser beamprofile and detection system cancel, so that each pixel valuedirectly gives the relative density with respect to ambient airdensityFig. 3a–h. Rayleigh scattering images of dry air flows for differentsettling chamber pressures (averages over 250 laser shots). The imagesare 26 mm high; the flow goes from bottom to top and the nozzleexit is situated 0.3 mm below the lower edge of each image. All imagesare normalized to the ambient air scattering intensity and showrelative density variations with respect to ambient air density. Thefalse colour scale is the same for all images; isochores are superposed.The high intensity ‘fog’ scattering lobes have been truncated.Parameters for the individual plots (notation: (po; oi; Do), with po thestagnation pressure in kPa, oi the relative density value of theinnermost contour and Do the relative density step between contours).a (200; 1.0, 0.05); b (250; 1.0, 0.05); c (300; 0.8, 0.1); d (350; 1.0, 0.2);e (400; 0.8, 0.2); f (500; 0.6, 0.2); h (700; 0.6, 0.2)

a small volume element dV in a dilute gas with number densityo can be written as

dPsdX

\odpsdX

Io dV (1)

in which dps/dX denotes the differential cross section for

Rayleigh scattering and Io

the local incident light intensity. Theformer can be written in terms of macroscopic properties ofthe medium as (Boyd 1992)

dpsdX

\(n[1)24n2o2c4

u4 sin2 h (2)

in which n denotes the local refractive index of the medium,u is the angular frequency of the incident radiation and c thevelocity of light in vacuum. The scattering is detected ina direction h with respect to the polarisation of the incidentlight (h\90° in our case). Since (n[1) is proportional to thelocal number density, the differential cross section itself isindependent of o. From Eqs. (1,2) it follows that the Rayleighscattering yield is proportional to u4 (which is a strongargument for the use of ultra-violet (UV) lasers), and to thelocal scatterer density.

In this paper we present two-dimensional images of thedensity in a plane containing the axis of a cylindricallysymmetric underexpanded nozzle flow, using UV laserRayleigh scattering. The general structure of such flows is wellknown (see e.g. Lanen 1990; Timmerman and Watt 1995; andalso the shadowgraphs in Van Dyke 1982), so we will empha-size the technical aspects in this paper. The results arecompared with predictions from a simplified theoretical modelof the flow.

2ExperimentalA schematic view of the experimental setup is shown in Fig. 1.The nozzle used in these experiments is an accurate copy of theone used by Timmerman and Watt (1995) in their holographicstudy of nozzle flows, except for the exit tube diameter. Inbrief, the axisymmetrical flow generator consists of a smallsettling chamber which smoothly tapers into a circular outlettube of 5 mm inner diameter (was 6.5 mm in the original

design) and 60 mm length. It was fed by dry air obtained fromgas bottles, without additional filtering. Dry air (\25 ppmvH

2O) was used in order to avoid water condensation (‘fog’

formation) which would create undesired Rayleigh scatterers.(Although this has actually been used to advantage byFourguette et al. 1991). A small pitot tube (outer diameter2 mm), connected to a mechanical manometer (accuracy^20 kPa) was used to monitor the settling chamber pressure.During each run the stagnation pressure was manually keptconstant to within ^10 kPa.

An excimer laser (Lambda Physik COMPEX 350T, used inbroad-band mode), operated at ArF (j\193.4^0.5 nm), wasused to irradiate the flow. This laser provides 18 ns pulsesof about 90 mJ/pulse available to the experiment (at 10 Hzrepetition frequency). The laser beam has a rectangular crosssection of about 25]3 mm2, which, by using two cylindricallenses and a slit diaphragm, was transformed into a light sheetof about 22 mm high and 0.5 mm thick at the position of theflow axis.

The nozzle flow was directed vertically upwards, parallel tothe height of the laser light sheet. Scattered light was collectedin a direction perpendicular to the light sheet by an intensifiedslow-scan CCD camera (Princeton Instr. ICCD 576, 576]384pixels of 22]22 lm each) equipped with a bellows and anf\105 mm UV Nikkor objective. A 26 mm high region directlyabove the nozzle exit was imaged onto the CCD chip, resultingin a nominal spatial resolution of about 45 lm/pixel. Theactual resolution is limited by the image intensifier (an 18 mmdiameter multi-channel plate), and is estimated at about100 lm. A Peltier element kept the CCD chip at a constanttemperature of [30 °C, resulting in a dark count of 19^2 s~1(average^1p). Typical pixel values (single laser shots) amountto 3500, so that the accuracy of the data is photon shot noiselimited. The dynamic range of the detection system amounts to16 bits (single shot). The image intensifier was used with a gateof 20 ns.

94

95

1 In fact, we make the assumption here that the composition of the flowis the same as that of the surrounding air.

3Results

3.1Flow structureFigure 2a shows a Rayleigh scattering image of the laser beamin ambient air above the nozzle exit (no flow present). FromEq. (1) it follows that each pixel value, S, is proportional to thelocal laser power, that is,

Saa(x, y)\)(x, y) oaadpsdX

Io(x, y) dV (3)

in which the subscript aa stands for ambient air and ) isa proportionality factor including the collection efficiency ofthe optics and local variations in the sensitivity of the detectionsystem (notably the image intensifier). Since a uniform densitymay be assumed for ambient air, the intensity variations in thisimage (Fig. 2a) directly represent the laser intensity distribu-tion and local variations in the detection sensitivity. The laserlight intensity is seen to be concentrated in (but not limited to)an about 22 mm high band and to decline fairly steeply at theupper edge. A vertical cross section through the image showsthe intensity distribution in more detail (Fig. 2b). The intensitydip at about 15 mm above the nozzle is due to the particulari-ties of the excimer laser optics. Figure 2c shows the sameregion as in Fig. 2a, but with a dry air flow emanating from thenozzle (stagnation pressure 300 kPa). The density variationsintroduced by the supersonic flow are clearly visible in thecentral part of the figure. Since both the ambient air image (Fig.2a) and the flow image (Fig. 2c) reflect spatial inhomogeneitiesin the detection system and the laser beam profile in the sameway, the former can be used to normalize the latter. Toillustrate this, Fig. 2d shows the density in the flow relative toambient air density,1 that is,

T(x, y)$%&\o&-08

(x, y)oaa

PS&-08

(x, y)Saa(x, y)

(4)

Rayleigh scattering images of a dry air flow for several valuesof the settling chamber pressure are presented in Fig. 3. Theseimages represent relative densities (relative to ambient airdensity) in a plane containing the flow axis, averaged over 250laser shots (25 s measurement time). They are corrected forspatial inhomogeneities in the detection system and laser beamprofile by scaling them with respect to an ambient air imagerecorded without flow, as discussed above (Eq. (4)); the shotnoise limit in these images corresponds to about 1% in thehigh intensity regions. Scaling factors were used to enhancecontrast in the individual images. Density contour plotsderived from these images are superposed on the false colourimages.

The development of a periodical pattern of density fluctu-ations with increasing settling chamber pressure po is veryevident in Fig. 3. Both the distance between density extremaand the contrast between high and low density regions is seento increase with increasing p

o. The very intense lobes develop-

ing around the flow boundary for poP350 kPa (Fig. 3d—h) are

attributed to Rayleigh scattering from small ice particles orwater droplets formed by water vapour condensing in theambient air entrained by the flow (see also Fourguette et al.1991; Chuech et al. 1989). Note that this condensation onlyoccurs at the jet boundary, since we use dry air for the flowitself. In the core of the jet, therefore, the Rayleigh scatteringintensity is a proper measure for the local molecular numberdensity.

In Fig. 4 the relative density, T(x, y) of Eq. (4), on the axis ofthe flows presented in Fig. 3, is plotted as a function of heightabove the nozzle exit. All density values are averages overa 0.3 mm (7 pixel columns) wide strip centered on the flowaxis. The relative ambient air density is also incorporated inFig. 4 (thin lines); it is obtained from an average over 0.5 mm(11 pixel columns) at the right edge of each image in Fig. 3.Ideally, the latter curves should be straight lines at o/o

aa\1. In

Fig. 4, however, they all lie about 2% above this value. Thisindicates that the influence of the flow on the ambient airdensity extends to the edge of the field of view of the camera(the images of Fig. 3 are 17.5 mm wide).

The distances between successive density maxima, asderived from Fig. 4, are plotted in Fig. 5 for those values of pofor which repetitive maxima were observed. Included are alsothe model predictions (open symbols), discussed below.

Because of the relatively large Rayleigh scattering crosssections in the UV spectral range, Rayleigh scattering imagescan also be obtained with single laser shots. As an example,three single shot images of the dry air flow at p

o\300 kPa are

presented in Fig. 6. These images represent relative densityvariations (as those of Fig. 3), frozen on a time scale of theduration of the laser pulse (18 ns), which, for all practicalpurposes, can be considered as instantaneous. Interestingly,these frozen images indicate that the instantaneous structureof the flow may vary quite considerably around its averagestructure of Fig. 3c. Although Fig. 6b resembles the averagestructure of Fig. 3c quite well, the other two images showa somewhat helical structure, especially in the downstream partof the flow.

4Discussion

4.1Flow featuresThe prominent feature in the cross sections of the flows of Fig.3b—f is the pattern of alternating low and high density regions.These compression-rarefaction ‘diamonds’ (i.e. the highdensity regions with a somewhat angular outline) are charac-teristic for underexpanded nozzle flows. Our results aresomewhat intermediate between, on the one hand, those ofLanen (1990) and Timmerman and Watt (1995), obtainedusing holographic methods and showing diamond-like featureswith rather rounded outline, and, on the other hand, shadow-graphs like, for instance, those published by Van Dyke (1982),which show very sharply delimited lozenge-like features. In ourmeasurements, the angular structure of the high densityregions is most pronounced close to the nozzle and it becomesmore distinct with increasing stagnation pressure. Also, the

96

Fig. 4a–h. Fat lines: Number density on the axis of the flow, relative to that of ambient air, for different settling chamber pressures (as inthe previous figure) as a function of the distance z downstream of the nozzle exit plane. The thin lines show the measured number densityof the air adjacent to the jet. The glitch in some of the ambient air curves near z\3 mm is due to a spurious reflection. In h the derivativeof the density curve is inserted, showing a sharp spike (0.26 mm wide) at the position of the Mach disk

diamonds are slightly asymmetrical, as can very well be seen inthe first (most upstream) diamonds of Figs. 3c—e. Generally,the upstream side of each diamond is more sharply delimitedthan the downstream side. This is in agreement with expecta-

tions, since the upstream boundary is a shock wave, whereasthe downstream boundary is an expansion fan. Because thewhole pattern is the result of multiple reflections of shockwaves and expansion fans off the flow boundary, and because

97

Fig. 5. Distances between subsequent density maxima in theflow for different settling chamber pressures. Solid symbols:measured distances; open symbols: model predictions (see text)

the pattern starts with a relatively ill defined expansion fan (ascompared to a shock wave), the outline of the diamonds fadeswith increasing height above the nozzle exit. As a result, theupstream diamonds are most clearly angular whereas thedownstream ones show a more rounded outline.

The shadowgraphs show much sharper boundaries anda more angular structure than the somewhat rounded featuresobtained from holographic and Rayleigh measurements.Probably, the reason for these differences has to be sought inthe particularities of the different visualisation techniques.Holography (combined with tomographic reconstruction) andour Rayleigh scattering images provide the local, absolutenumber density in the flow. Shadowgraphy, on the other hand,is sensitive to the second derivative of the density (via therefractive index) and provides integrated data along a line-of-sight through the flow. Thus, shadowgraphy is much moresensitive to density gradients (because of the derivativesensitivity) and to planes of maximum or minimum densitythat contain the line-of-sight (because of the integration),explaining both the sharp boundaries of the diamonds (shockand expansion waves) as well as the partitioning of thediamond itself (plane of maximum density) (Van Dyke 1982;see also the comparison in Lanen (1990)).

The oscillating behaviour of the on-axis flow density withheight above the nozzle exit that is to be expected from Figs.3b—g is clearly borne out by the on-axis density curves of Fig. 4.The on-axis density of the subsonic flow of Fig. 3a is aboutconstant, but all supersonic jets show an oscillating on-axisdensity. In many cases, the rising slopes (upstream diamondboundaries) are steeper than the subsequent falling ones, asdiscussed above.

The formation and growth of a Mach disk can be seen in theflows with p

oP450 kPa (Figs. 3f—h). At sufficiently high

stagnation pressure a Mach disk is expected to close thesupersonic part of the jet downstream of the first densityminimum. Downstream of the Mach disk the flow wouldbe subsonic, but this central, subsonic core would still besurrounded by the supersonic flow that passes along the Mach

disk (see e.g. the very illustrative photographs in Yip et al.1989). This is exactly what is seen to happen in Figs. 3f—h. Atpo\450 kPa a narrow Mach disk forms on the flow axis at the

end of the first density minimum. The first diamond in thepattern, that still persists in the supersonic flow passing aroundthis Mach disk, is penetrated in its core by the (relatively lowdensity) subsonic flow downstream of the Mach disk. As thestagnation pressure rises, the Mach disk increases in diameterand the splitting of the first diamond becomes ever moreconspicuous. Interestingly, the supersonic flow around the jetcore appears to close down over the subsonic core in thedownstream part of the flow, giving rise to a well developedsecond diamond in Figs. 3f, g. Unfortunately, the high intensitylobes at the jet boundary tend to swamp the downstream jetstructure in these cases. At the highest stagnation pressureused in the present study, p

o\700 kPa, the first diamond is

almost completely wedged apart by the subsonic core followingthe Mach disk, but still the supersonic ‘slip stream’ can be seen,albeit in this case mainly because it prevents ambient airpenetration and is therefore free of fog scattering. At thisstagnation pressure the Mach disk is 0.26 mm thick (full widthat half maximum of the spike in the derivative of Fig. 4h).

The power of the UV laser Rayleigh scattering method is welldemonstrated by the single shot images of Fig. 6. Since theread-out time of our slow-scan camera system puts a lowerlimit of about 300 ms to the time interval between two singleshot images, it is at present not possible to be more specificabout the time evolution of the helical structure that is visiblein especially the downstream parts of Figs. 6a and c. Thislimitation may be overcome by the use of video-rate CCDcameras or slow-scan systems with streak-mode option, incombination with higher repetition rate laser systems. Yet, thehelicity evident in Figs. 6a and c, together with the near perfectsymmetry of the averaged Fig. 3c, seem to point towardsa corkscrew motion of the flow, which is somewhat unexpectedfor a symmetrical, smooth (albeit drilled) nozzle. It should,however, be noted that similar indications were already foundby Timmerman and Watt (1995).

4.2Model predictionsTo our knowledge, the Rayleigh scattering measurementspresented above represent a first application of the techniqueto the visualisation of the diamond pattern in a supersonicflow. It would therefore be of interest to compare the resultsboth with calculations and with holographic measurements onthe same flow generator. Although both are in progress, thesedata are not available yet (Timmerman, pers. comm.). For themoment, therefore, we compare our measurements to a simplemodel (hand calculator scale) to at least obtain order ofmagnitude estimates of what might be expected theoretically.

The difference between background pressure and exitpressure of the underexpanded jet gives rise to expansion fansat the nozzle exit. The diamond pattern observed in the free jetstream is a result of multiple reflections of these expansion fansfrom the free (background) pressure boundary. Upon eachreflection, expansion fans turn into oblique shock waves andvice versa. We have approximated each of these expansion fansand oblique shock waves by discrete waves, equivalent tothe former in terms of velocity vector and changes of flow

98

Fig. 6a–c. Rayleigh scattering images of the flow at 300 kPa settling chamber pressure, each recorded with a single shot of the excimerlaser. These images reveal the flow structure frozen on a nanosecond time scaleFig. 7. Calculated flow structure for po\300 kPa. Thick lines delimit the flow boundary, the thin lines indicate shock and expansionwaves; predicted density maxima are indicated by black dots. Overlaid is the measured flow structure from Fig. 3c

99

Table 1. Observed and calculated values for the flow density relativeto that of ambient air (o

&-08/oaa), for the first minimum and the first

(complete) maximum in the diamond pattern. For po\200 kPa theflow was still subsonic (in the experiment); for po\400 kPa the modelcalculations predict a Mach disk

o&-08

/oaa 200 kPa 250 kPa 300 kPa 350 kPa 400 kPamin max min max min max min max min max

Observed — — 1.25 1.41 1.00 1.68 0.86 2.04 0.73 2.26Calculated 1.19 1.26 1.12 1.56 1.04 1.87 0.96 2.23 — —

parameters on both sides of the wave. The directions andstrengths of the discrete waves are calculated from theboundary conditions on velocity and pressure (Zucrow andHoffman 1976). It turns out that the strength of such a discretewave in a symmetric flow remains unchanged when this waveis intersected by another one. Although the expansion fans areassumed to be isentropic, non-isentropic shock equations areused for the shock waves, resulting in a slight decrease instrength of the discrete waves upon reflection from the freepressure boundary. Consequently, the diamond pattern grad-ually fades downstream.

In our calculations we assumed a planar, inviscid flow. Forthe central plane of an axisymmetric flow the planar approxi-mation is expected to be fairly good, when any effects ofintersecting expansion fans and/or shock waves can beneglected. The neglect of interference effects, however, is lesscritical for real planar flows than for axisymmetric ones, sincein the latter case out-of-plane waves interfere in the axialregion, too.

Results for the first 25 mm (5 maxima) of the flow fora stagnation pressure po of 300 kPa are shown in Fig. 7. The gasdensity o

&-08is calculated from the ideal gas law, assuming the

stagnation temperature to be equal to ambient. Results fora range of values for p

oare given in Table 1 (relative densities

in the first minimum and subsequent maximum) and Fig. 5(distance between successive maxima). No diamond patternis expected for p

o\1.89p

aaand for p

o[3.51p

aaa Mach disk

occurs at the end of the first minimum.In spite of the approximations of the model the measured

pattern is generally well reproduced by the calculations. Bothshow the same structure and the same trends upon an increaseof the reservoir pressure. The measured distances betweensubsequent density maxima fairly closely correspond to themodel predictions, and show the same decrease with increas-ing downstream distance in the flow. Clearly, however, thetheoretical results reproduce the experiments best if thecalculations assume a stagnation pressure that is about 25 kPalower than the measured one. There are two probable causesfor this decrepancy. On the experimental side, the pitot tubemeasurements probably contain a relatively large dynamiccomponent (the settling chamber of our nozzle is of finite size),and may therefore give too high readings. Also, our modelcannot account for friction losses in the nozzle exit tube. Thesetwo effects should explain a large part of the discrepanciesbetween model calculations and experiments at low pressure.A similar conclusion can be drawn with respect to thecalculated densities. With increasing stagnation pressure thestrength of the shock waves increases and so does the contrastbetween density maxima and minima. Minimum densities fallbelow ambient for p

oP350 kPa, in experiment as well as in

theory.The simple model that we have used does not allow to

continue the calculations after a Mach disk has occurred. Thedistance z

Mof the Mach disk from the nozzle exit plane can be

calculated from (e.g. Miller 1988)

zM\0.67d Jpo/paa (5)

with d the nozzle diameter. For po\700 kPa we find a well

developed Mach disk at z%91M

\7.8 mm, whereas Eq. (5) would

predict it at z#!-#M

\8.8 mm. This, again, points to our measuredstagnation pressures being larger than the actual nozzle exitpressure. Experimentally, birth and growth of a Mach diskwith increasing stagnation pressure are seen to form part ofa continuous process, in which the central part of the flow isaffected first and grows outwards into the still supersonic outerpart of the flow as the stagnation pressure rises.

Although the agreement between model calculations andexperiment is reasonable, there are also some differences,notably in the predicted densities, as can be seen from Table 1.Certainly, the simplicity of the model will have something to dowith this, but there are also a number of experimental pitfallsthat must be taken into account. Systematic errors that mayplay a role in our experiments include (i) gas compositiondifferences between flow and ambient air, (ii) dust particles inflow or ambient air, (iii) a contribution of O

2LIF to the signal

and (iv) inaccuracies in the stagnation pressure measurements.As to the first of these points, the Rayleigh scattering intensityof ambient air images has been used to normalize the flowimages, implicitly assuming the same composition of flow andambient air. Since we used dry air to power the flow, and thewater vapour concentration in ambient air typically amountsto only 1—2% (at 300 K) this is not expected to influence theresults to any significant degree. A more serious problemmight have been dust particles in the ambient air. They wouldhave resulted in a relatively too intense ambient air Rayleighscattering image, which would require an overall multiplica-tion factor to correct for it. Since, however, the measuredminimum density values correspond well to model expecta-tions, we do not think that dust particles play a significant rolein the present experiments. Oxygen fluorescence, induced byexcitation in the Schumann—Runge bands (see e.g. Lee andHanson 1986), does occur, as has been established in separateexperiments in which the scattered light was spectrallydispersed (not shown), but has been minimized by utilising theexcimer laser in broad-band mode. Moreover, the O

2fluores-

cence signal was always found to be about two orders ofmagnitude less intense than the Rayleigh scattering contribu-tion.

The most probable reason for the difference between modelpredictions and measurements is to be found in the stagnationpressure measurements and, on the model calculation side, theplanar flow approximation and the neglect of frictional lossesin the relatively long channel between settling chamber andnozzle exit. For the same reason, the range of stagnationpressures for which more than one maximum is observed inthe measurements is larger than in the calculations.

100

5ConclusionUV laser Rayleigh scattering is shown to be a very useful,non-intrusive tool for 2D density mapping of compressibleflows. The experimental setup is straightforward, and datacollection and display is a matter of seconds, using state of theart UV laser systems and CCD cameras. The method directlyprovides local, absolute densities in a plane intersecting theflow, in contrast to many line-of-sight techniques. Moreover,single shot measurements allow to freeze the flow structure ona nanosecond time scale.

We have presented cross sections of the structure of anaxisymmetrical dry air flow, showing details of the evolution ofthe diamond pattern with increasing stagnation pressure andthe eventual development of a Mach disk. The angular outlineof the high density regions is seen to become more pronouncedwith increasing stagnation pressure but to fade with increasingdistance from the nozzle exit. For stagnation pressures above400 kPa a Mach disk is seen to form, initially only in the core ofthe flow but growing outwards with increasing stagnationpressure. Strong scattering is observed at the boundary of thenozzle flow with the ambient air, which is attributed to ‘fog’formation by water vapour condensing in the ambient air thatis entrained by the flow.

More extensive measurements on Rayleigh scattering from freeand obstructed flows, as well as a comparison of the Rayleighscattering data with data obtained from tomographic holographyand to results of more realistic calculations are in progress.

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