Density Measurements of a Turbulent Wake UsingAcetone Planar Laser-Induced Fluorescence

John Z. Reid,∗ Kyle P. Lynch,† and Brian S. Thurow‡

Auburn University, Auburn, Alabama 36849

DOI: 10.2514/1.J051678

The application of a planar density measurement technique for compressible flowfields based on acetone planar

laser-induced fluorescence is presented. An error analysis indicates a minimum inherent uncertainty of ∼2.5% in

density measurements due to uncertainty in local pressure and a total experimental uncertainty of 8%, primarily

driven by shot noise due to low-signal levels. The technique is demonstrated through the visualization of the separated

shear layer and turbulent wake of a wall-mounted hemisphere at a freestreamMach number of 0.78 and a Reynolds

number of approximately 900,000. The flow is marked by a large-scale flapping motion of the wake and low-density

vortex cores, where density drops of up to 50% of the freestream density are detected. In addition, closeup images of

the shear layernear the separationpoint reveal the formationof lambda shocks. Thedensity fields are used to perform

aerooptic distortion calculations through spatial integration of the density field. A correlation is found between the

spatial scale of the distortion and the features present in the density field. These findings demonstrate the viability of

acetone planar laser-induced fluorescence for conducting planar densitymeasurements and providing a newmethod

for the evaluation of aerooptic distortion in compressible flows.

Nomenclature

c = speed of lightD = hemisphere diameterdVc = collection volumeE = laser fluenceh = Planck’s constantK = Gladstone–Dale constantk = Boltzmann’s constantn = index of refractionP = static pressureP2 = wake pressureP∞, P1 = freestream pressureSf = acetone fluorescence signalSf;∞ = freestream acetone fluorescence signalT = static temperatureT∞ = freestream temperatureη = optical collection efficiencyλ = excitation wavelengthλwf = wave front wavelengthρ = densityρ∞ = freestream densityσ = absorption cross sectionϕ = fluorescence quantum yieldχ = acetone mole fraction

I. Introduction

H IGH-SPEEDcompressible flowfields are characterized by theirturbulent nature and often contain large spatial and temporal

density fluctuations that strongly affect the dynamics of the flow. Formany applications, and aerooptics in particular, the fluctuations indensity are of explicit importance and offer the most straightforwarddescription of the relevant flow physics. As a result, aerooptics-related research has often focused on numerical solutions that canprovide full-field density data to better understand the relationshipbetween structures in the flow and distortions of an optical wave frontpassing through the flow. This is in contrast to the capabilities ofthe most common experimental techniques, which typically focuson qualitative flow visualization or velocity measurements. In thisregard, an experimental method for performing accurate and non-intrusive measurements of density in flowfields of practical signifi-cance would be of tremendous value. This work discusses theapplication and accuracy of acetone planar laser-induced fluores-cence (PLIF) for planar density measurements in the turbulent wakecreated by a hemisphere in a Mach 0.78 freestream flow and brieflyaddresses the relationship between the density measurements andoptical wave front distortion.

II. Background

A. Optical Density Measurement Techniques

Optics-based flow measurement techniques are generally catego-rized by their use of molecular or particle seeding to interrogate theflow. The former involve elastic scattering, inelastic scattering, orfluorescence to generate a signal, whereas particle seeding tech-niques involve Mie or Rayleigh scattering from small particlescontained in the flow. A number of issues exist with particle seedingfor measuring a scalar quantity, such as density, notably the difficultyin ensuring high concentrations of uniform seeding. In contrast,molecular seeding offers the ability for excellent seeding uniformityand ensures the tracers follow the flow faithfully. Also, the binarynature of a particle measurement greatly increases the noise due toquantization, rendering a measurement of density impractical. Incontrast, the far greater number density of seedingmolecules reducesthe quantization noise and allows a measurement of number densityto correspond to the fluid density.Eckbreth [1] gives a detailed description of multiple optical

methods based onmolecular seeding that have potential to be adaptedfor density measurements in a flowfield. These methods includemolecular Rayleigh scattering, Raman scattering, laser-inducedfluorescence, and coherent anti-Stokes−Raman spectroscopy. For aflow of uniform gas composition molecular Rayleigh scattering isattractive as the signal is directly proportional to the gas density andincident laser energy such that flow seeding is not strictly required.Miles et al. [2] provides a detailed review of Rayleigh scattering and

Presented as Paper 2011-0987 at the 49th AIAA Aerospace SciencesMeeting and Exhibit, Orlando, FL, 4–7 January 2011; received 28 October2011; revision received 11October 2012; accepted for publication 17October2012; published online 18 February 2013. Copyright © 2012 byBrian Thurow. Published by the American Institute of Aeronautics andAstronautics, Inc., with permission. Copies of this paper may be made forpersonal or internal use, on condition that the copier pay the $10.00 per-copyfee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers,MA 01923; include the code 1533-385X/13 and $10.00 in correspondencewith the CCC.

*Graduate Research Assistant, Department of Aerospace Engineering.Student Member AIAA.

†Graduate Research Assistant; currently Ph.D. Candidate, Delft Universityof Technology, The Netherlands.

‡Associate Professor, Department of Aerospace Engineering; thurow@auburn.edu.

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different methods for performing multiparameter measurementsusing spectral and intensity data. Recent studies using molecularRayleigh scattering for density measurement in air are generallyrestricted to point measurements due to the low-signal levelsproduced by theRayleigh scattering process. Some examples includethework in [3,4] who used high-powered continuouswave lasers andrelatively large collection optics tomeasure the signal at a point in theflow. Time-averaged planar measurements were realized throughmechanical translation of the measurement system through the flow.The low-signal levels encountered in Rayleigh scattering can becircumvented for instantaneous planar imaging with the use of high-energy ultraviolet (UV) lasers and intensified cameras, such asdemonstrated in [5]. An alternative is to use different gases in lieu ofair to increase the Rayleigh scattering cross section. This methodwasemployed in [6] where instantaneous planar measurements wereperformed by using a specially designed shear layer facility to exploitthe large and small scattering cross sections of ethylene and helium,respectively. In the configuration, the observed signal is a measure ofthe local concentration of ethylene,which contrasts significantlywiththe miniscule signal from helium. Raman scattering, which typicallyhas even lower signals than Rayleigh scattering, also has the potentialto be used for planar density measurements as demonstrated in [7] forthe imaging of helium−nitrogen flows.The technique adopted in this work is PLIF. PLIF has been used in

the past to measure local species concentration (e.g., [8–17]),temperature (e.g., [8,18–24]), velocity (e.g., [25–28]), and mixturefraction (e.g., [29–33]) in a variety of flows. PLIF is based on theabsorption and fluorescence of laser light by tracer molecules eitheralready present or seeded into a flow. The atomic structure ofparticular molecules results in unique absorption spectra, typically intheUV.Using an appropriate laser sourcewith strong spectral overlapin an absorption band photons can be efficiently absorbed by themolecule to raise its energy level. To return to a ground or equilibriumstate both short-term (fluorescence) and long-term (phosphores-cence) radiative processes occur, emitting photons within separate,longer-wavelength emission spectra. PLIF-based techniques gener-ally benefit from greater signal levels thanRayleigh scattering, whichgenerally makes them more suitable for instantaneous measure-ments. Moreover, background interference from surface scatteringcan be better mitigated through the use of various filters to block lightnear the excitation wavelength. Although many PLIF techniquesexploit naturally occurring species, such as those associate withcombustion, full-field flowmeasurements, such as the planar densitymeasurements targeted in this work, require that the entire flow beuniformly and passively seeded to ensure a direct relationshipbetween local species concentration and flow density. CommonPLIFspecies that have been employed for full-field measurements includenitric oxide (NO), iodine, and acetone.Techniques developed for the measurement of mixture fraction in

shear layers, where an entire flow stream is uniformly seeded with atracer molecule, have a lot in common with the work discussed hereas many of the practical experimental issues are common to both.King et al. [29], for example, developed a method whereby onestream is seededwithNO and the other stream is seededwith acetone.Simultaneous NO/acetone PLIF, where the NO PLIF signal issuppressed upon mixing due to oxygen quenching, is then used tomeasure the degree of mixing present at a given location within theimage. This technique was subsequently applied in [30,32] formixture fraction measurements in axisymmetric and planar shearlayers. Catrakis et al. [34], in a similar vein, used acetone PLIFimaging of one streammixing with an unseeded stream in an effort toestimate the local concentration of acetone. Extension of thesetechniques to ameasurement of the local flowdensity, where the localdensity is modeled as directly proportional to degree of mixingbetween the two streams, is possible for the incompressiblemixing oftwo temperature matched streams of different density gases.Fitzgerald and Jumper [35], however, show that for compressibleshear layers of aerooptic interest, such as that studied in this work, therelationship between local density, pressure, and mixture fraction issufficiently complex to preclude the direct use of mixture fractiondata for density measurements.

The technique presented herein uses the acetone PLIF technique toperform a full-field density measurement. In a similar fashion forsingle excitation line temperature measurements the entire flowfieldis seeded with the tracer molecule such that the observed signal isonly dependent on the local flow properties and not the degree ofmixing or local species concentration, which is constant. Wherebytemperature measurements generally assume a constant pressurewithin the flow to arrive at their measurement this restriction isrelaxed in this work such that the uncertainty in local pressure, whichcan be significant in compressible flows, is absorbed into themeasurement uncertainty.

B. Aerooptics Application of Measurements

The ability to directly measure a planar density field providesuniquely useful data for aerooptics analysis. To describe the aeroopticsproblembriefly the propagation of a collimated, coherent beamof lightis dependent on the index of refraction of themedium throughwhich ittravels. In turbulent flowfields, density fluctuations directly lead tofluctuations in the index of refraction, causing the wave front of thebeam to become abberated. The study of the interaction of fluidproperties and light propagation is termed aerooptics [36].This research field has attracted interest recently as imaging,

optical communications, and directed energy weapon systems havebecome more common. In each of these cases, degradation of theoptical wave front places a limit on the performance of these systems,particularly when used on aircraft platforms. An example is a turret-mounted laser aperture on the fuselage of an aircraft; the unsteadyturbulent flow around the turret, particularly in the shear layer andwake region, generates large density fluctuations that alter the wavefront as the beam exits the aperture [37–39]. As the beam continuestoward a target the distorted wave front causes the beam to divergeand degrade in quality. By the time the beam reaches the target it haslost its initial coherence and is less effective.Quantitatively, the distortion of an optical wave front can be

described by spatial variations in the optical path length (OPL). TheOPL is the distance that light travels in a vacuum in the same amountof time that it takes light to travel through a volume of a mediumwithan index-of-refraction value greater than or equal to unity. Consid-ered mathematically, the OPL is a three-dimensional integration ofthe index of refraction (n), as seen in Eq. (1), where z is taken as thedirection of light propagation:

OPL�x; y; t� �Zn�x; y; z; t� dz (1)

A more commonly used measure of the aerooptic distortion is theoptical path difference (OPD). The OPD is simply the differencebetween the OPL and the mean spatial OPL across the beam aperture(OPL). To convert the density field to an index-of-refraction field, theGladstone–Dale equation [Eq. (2)] is used, where the Gladstone–Dale constant K is approximately 2.27 × 10−4 m3∕kg for light at532 nm:

n�x; y; z; t� � 1� K�λwf�ρ�x; y; z; t� (2)

Thus, the distortion of an optical wave front is the integrated effect ofthe three-dimensional density field through which the beam passes.In principle, if the density field of the flow is known, the distortioncan be completely characterized and adaptive optics can be used tocorrect for the distortion.In the case of a turret, or more generally, a hemisphere, the features

characterizing the flowfield include a turbulent boundary layer,necklace−horseshoe vortex, separated shear layer, and turbulentwake. All of these features are three-dimensional in nature and, thus,affect the three-dimensional density field. Past investigations havesucceeded in using a variety of experimental methods to characterizeflows with similar structure and measure the resulting wave frontaberrations. These studies have found that in addition to compress-ibility effects the unsteady behavior of the large-scale turbulentstructures in the flow are a dominant source of distortion, particularlyin the separated shear layer. These large-scale vortical structures

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generate low-pressure wells at their core, causing a change in densitythroughout the structure. However, the experimental techniquescurrently in use do not directly measure the density field but insteadrely on a combination of velocity measurements and wave frontsensors to analyze optical distortions [37,38]. The techniquedescribed herein directly measures the density field, providing aunique ability to investigate aerooptic distortion by its fundamentalmechanisms. In addition, by obtaining the density field, the aeroopticdistortion for any wave front type, size, wavelength, and orientation/path through the medium can be approximated. This is in contrast totraditional wave front measurement techniques using aMalley probe[36] or a Shack–Hartmann wave front sensor where parameters, suchas beam size, wave front wavelength, and propagation angle have tobe set for each experiment.Besides the utility of the measurement for aerooptics applications,

the density field provides further insight into the structures andtopology of the flow.Byobtaining densitydata and coupling themwithvelocity data flow characteristics causing density fluctuations can bebetter understood.These densityvalues can be usedas avalidation for avariety of models, such as the weakly compressible model [35] andcomputational fluid dynamics (CFD) solutions for separated flows.This study presents the application of acetone PLIF for planar

density measurements in the wake of a hemisphere placed in a Mach0.78 freestream flow. The implementation of established acetoneabsorption cross-sectional data and a fluorescence quantum yieldmodel is used to convert raw image intensity data to a density field. Anoverviewof themodel and conversionprocedure isgiven toprovide thereader with an uncertainty estimate in the data. Next, an experimentaltest of the technique is performed, and results are shown at multiplelocationswithin the flow todemonstrate theviability anduniquenessofthe technique and the utility of the method for aerooptic analysis.

III. Adapting Acetone Planar Laser-InducedFluorescence for Density Measurements

Acetonewas chosen as the tracer molecule in this study because ofthe favorable characteristics it possesses, including low cost, high-vapor pressure, safe handling properties, and a broadband absorptionspectrum that peaks from 260 to 290 nm [18,19,21,40,41]. Thus,acetone can be efficiently excited by using the fourth-harmonicoutput of Nd:YAG laser systems at 266 nm. The fluorescenceemission spectrum of acetone is also broadband and peaks from 445to 480 nm; a range of wavelengths that are efficiently detected bycharge-coupled device (CCD) sensors. The captured signal can bemapped to a density value, allowing a planar density field to bemeasured from an acetone PLIF image. This section details themapping from signal values to densitymeasurements and provides anuncertainty estimate.

A. Fluorescence Signal Equation

The acetone fluorescence signal is quantified by Eq. (3) [18],where the majority of the terms are constant parameters throughoutthe flow: Planck’s constant, h; Boltzmann’s constant, k; the speed oflight, c; excitation wavelength, λ; collection volume, dVc; andacetone mole fraction, χ. Note that maintaining a constant acetonemole fraction throughout the flow is an essential feature of the presenttechnique in contrast to other applications of acetone PLIF as apassive scalar tracer for concentration or mixing measurements:

Sf �E

hc∕ληdVc

�χP

kT

�σ�λ; T�ϕ�λ; T; P;

Xi

χi� (3)

The variable terms remaining are the laser fluenceE, optical collectionefficiency η, static pressure P, static temperature T, absorption crosssection σ, and fluorescence quantum yield ϕ. Eliminating thevariations in many of these parameters is the focus of a number ofimage processing steps. In order of execution, these steps include:average dark image subtraction, vignetting correction, high-intensitypixel filtering, laser sheet nonuniformity correction, freestreamintensity normalization, and a 3 × 3 moving average spatial filtering.

The average dark image subtraction eliminates ambient andreflected light present in each image, so that the measured signalcontains aminimal number of contributions beside the useful acetonefluorescence. Following this, a vignetting correction is applied toaccount for the change in optical collection efficiency due to thereduced collection angle for object points located off of the opticalaxis. This correction procedure uses a set of coefficients calculatedusing the cos4 law [42]. Next, a filtering of high-intensity pixelseliminates traces of a small amount of residual particle scatteringobserved in the images. This filter uses a threshold intensity value, setto 1800 counts (over three times themean signal level). If the intensityvalue of anypixel is greater than the threshold value then the pixel andits 12 neighboring pixels, arranged in a diamond pattern around thecentral high-intensity pixel, are set to the mean value of the 11 × 11region of surrounding pixels, excluding the pixels to be modified.After this, a laser sheet nonuniformity correctionmodeled after the

technique outlined in [6] accounts for the approximately Gaussianenergy profile of the laser sheet throughout the test section. In thistechnique the laser sheet ismodeled as a radial fan propagating from avirtual point contained outside of the field of view (FOV) of theimage. Points in the image are then mapped to an �r; θ� coordinatesystem, where it is assumed that variations in the θ direction areassociated with the nonuniformity of the incident laser beam, andvariations in the r direction are due to the energy of the beamspreading out radially in a 1∕r fashion. To estimate the nonuniformdistribution of energy in in the θ direction, which can vary from pulseto pulse, we used an in situ calibration method similar in [29]. Weassumed that the density, and, therefore, fluorescent signal in thefreestream is a constant value such that any variations in imageintensity can be attributed to variations in the incident laser flux. Aset of correction coefficients based on the distribution are calculatedand then applied to the entire image. Additionally, losses due toabsorptionwere estimated fromBeer’s law to be less than 3%over thepath length of the image due to the relatively low concentration ofacetone contained in the flow. This loss was not accounted for in thiswork. A 3 × 3moving average (i.e., low-pass) filter is then applied toeach image to reduce the effects of image noise (readout noise, shotnoise, etc.).Once the previous image processing steps are complete, E and η

can be considered as constant throughout the image andEq. (3) can besimplified to Eq. (4), where C accounts for the constant factorsthroughout the image:

Sf � CP

Tσ�T�ϕ�T; P� (4)

The image processing and in situ calibration procedure ends with anormalization of the image intensity to the average freestreamintensity value (assumed to be a constant value) allowing the constantfactors to cancel and the remaining equation to be rewritten in theform of a ratio as shown in Eq. (5):

SfSf;∞

�PT σ�T�ϕ�T; P�

P∞T∞

σ�T∞�ϕ�T∞; P∞�� ρσ�T�ϕ�T; ρRT�

ρ∞σ�T∞�ϕ�T∞; ρ∞RT∞�

�ρσ

�PρR

�ϕ

�PρR ; P

�

ρ∞σ

�P∞ρ∞R

�ϕ

�P∞ρ∞R

; P∞

� (5)

Formalized as such, we see that the signal is directly proportional tothe local flow density with a modest dependence on the localtemperature and pressure in the fluorescence quantum yield andabsorption cross section. Thus, in the absence of an independentmeasurement, variations in the local pressure and temperature willpresent themselves as an uncertainty in the estimation of density. Byassuming ideal gas behavior the equation of state allows Eq. (5) to berewritten to eliminate one of the redundant parameters. For ourpurposes the last expression given in terms of ρ and p is the mostuseful, as we have measurements of the total and static pressuresavailable within the test section such that we can estimate the

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expected variations in local pressure. To quantify this uncertainty thebehavior of fluorescence quantum yield and absorption cross sectionwith variations in pressure and density were investigated.

B. Fluorescence Yield and Absorption Cross-Sectional Model

The photophysics and physical qualities of acetone vapor havebeenwell characterized in [41], in particular, theweak dependence offluorescence signal on pressure and temperature (relative to othercommonly used tracers) and the quenching of the long lifetimephosphorescence signal by oxygen were reported. Further work in[19] established a physically-based model for the fluorescencequantum yield and absorption cross section as a function oftemperature, pressure, excitation wavelength, and gas composition.This model is based on a multistep decay process that takes intoaccount the multiple decay probabilities that exist for polyatomicmolecules, such as fluorescence, vibrational relaxation, and inter-system crossing. Bryant et al. [43], Tran et al. [44] and Hartwig [45]extended the model of Thurber to wider pressure and temperatureranges and tested the model accuracy.In this study, the model of Thurber et al. [19] was used with inputs

corresponding to the experimental conditions tested in this work.Oxygen effects were taken into account, and the excitationwavelength was set to 266 nm. The acetone mole fraction was set to3%within the assumption of small acetone mole fraction used by themodel. With these parameters set pressure and temperature could beinput to the model, and both the fluorescence quantum yield andabsorption cross section would be returned.In the absence of an independent measure of pressure at each point

in the flow the uncertainty in the values of fluorescence quantumyield and absorption cross section must be included in the mea-surement uncertainty. Toquantify this variation the range of pressuresencountered in the flow were considered. Because the primaryconcern is to measure density variations in the turbulent shear layerand wake produced by the hemisphere the bounds are placed at thelowest pressures (wake) and highest pressures (freestream) expectedin the region. It is assumed that the pressure drops associated withthe vortex cores in the shear layer and wake, although significantin a local sense, would still remain within the bounds set by theseextremes. During each test run the freestream static pressure andwake static pressure are measured in order to set the physical valuesof these pressure bounds.Normalized signal versus normalized density curves are created

for each pressure bound through the use of Eq. (5). Values for thefluorescent quantum yield and absorption cross section were takendirectly from Thurber’s model as described above. A sample curve isshown in Fig. 1, where the effect of pressure on the expected signal

can be observed. The effect of temperature is also implicitly includedin these curves through the equation of state. An average of the twocurves is created and used as the reference curve for converting thenormalized signal to normalized density. Note that the relationshipbetween normalized signal and normalized density is nearlyproportional but cannot be considered linear due to the effects ofpressure and temperature.

C. Measurement Uncertainty

The density measurement uncertainty due to the pressureuncertainty is relatively small and is estimated to be less than 2.5%over the density range encountered in this flow. As can be seen inFig. 1, for a density ratio of approximately 0.65, the uncertainty dueto pressure variations vanishes as the relative changes in fluorescencequantum yield and absorption cross section cancel out. Using theaverage of the two curvesminimizes error, because the average curvelies exactly between the curves for the two pressure bounds. Thus, theaverage curve can be considered as representative of the averagepressure condition. A consequence of this choice is a bias errordepending on local pressure values. At normalized signal valuesbelow 0.65 the average curve undercalculates the density values inthe freestream region and overcalculates the density values in thewake region. The opposite situation occurs for normalized signalvalues above 0.65. This bias error could be minimized by allowingthe pressure to vary depending on the region of the image beinganalyzed; however, this was not pursued herein.Total uncertainty in the density measurement is a summation of

the uncertainties due to pressure and the measurement of thefluorescence signal. The accuracy by which the fluorescence signalcan bemeasured depends onmultiple factors, including the quality ofthe image sensor (quantum efficiency, read noise, dark noise,dynamic range, etc.), shot noise, and the calibration procedure used toaccount for vignetting and laser sheet nonuniformity. The combinedeffect of these noise sources was estimated by observing the signallevel in the freestream region of the flow, where density fluctuationsshould be vanishingly small. Under this assumption any variations(quantified in terms of the standard deviation) in signal in thefreestream are treated as an estimate of measurement uncertainty.Both raw and postprocessed images displayed an approximately 7%pixel-to-pixel variation in intensity and signal ratio, respectively, inthe freestream with a spatial resolution of ∼33 μm∕pixel. Low-passfiltering the images with a 3 × 3 pixel-averaging filter reduced thisuncertainty to ∼2.5% at the expense of reduced spatial resolution (tonominally 100 μm). The standard deviation is lowest near thecenterline of the laser sheet and increases as laser energy decreasestoward the edges, indicating the low-signal levels are the primarydriver of the uncertainty.In summary, the overall uncertainty of the density measurement,

accounting for the uncertainty of the conversion from normalizedsignal to normalized density and themeasurement of the fluorescencesignal, is estimated via a summation of squared errors to be approxi-mately 8% without low-pass filtering and 3.5% with low-passfiltering.

IV. Experimental Arrangement

The technique was applied to measure the density field of theseparated shear layer and turbulent wake of a wall-mountedhemisphere located in a transonic freestream flow. These conditionsand geometry produce a canonical flowfield of general academicinterest, aswell as practical interest due to the geometrical similaritiesto turrets being considered for various applications. To facilitate theseexperiments a small-scale transonic wind tunnel was designed andconstructed with the capacity for a small diameter hemisphere to bemounted to the upper wall of the test section. The general flowfeatures of a wall-mounted hemisphere, and other bluff bodies arewell established in literature [37,38,46,47]. These features include aflat-plate turbulent boundary layer upstream of the hemisphere,followed by a horseshoe and necklace vortex system that is created atthe upstream junction of the hemisphere and the wall. This vorticalsystem wraps around the base of the hemisphere and travels

Fig. 1 Normalized signal versus normalized density. Themaximumandminimum pressure curves are calculated by the absorption cross section/fluorescence yield model and are shown with markers.

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downstream to the wake region. Along the top of the hemisphere aseparated shear layer forms and comprises both small- and large-scale vortical motions. These vortical motions evolve into theturbulent wake downstream of the hemisphere. The shear layer andturbulent wake are the primary areas of interest due to the intensedensity fluctuations that exist in these regions.

A. Transonic Wind Tunnel and Model Geometry

To facilitate experiments at transonic conditions a new nozzle, testsection, and diffuser were designed and constructed to interface withthe stagnation chamber and exit piping of an existing supersonicwindtunnel. By using existing air storage and compressor infrastructurethe costs for the new transonic wind tunnel were greatly reduced. Thetunnel is a blowdown design using regulated compressed air andexhausting into ambient conditions downstream of the diffuser. Thecompressed air source is a 650 cfm compressor and desiccate dryercapable of providing dry air at pressures up to 125 psig, which isstored in two large tanks that are connected to a stagnation chamberusing large-diameter-compressed air lines. A pressure regulator isused tomaintain roughly constant pressure in the stagnation chamber,while the storage pressure decreases. The stagnation chamber isattached to a three-dimensional smooth contour nozzle followed bythe test section and then the diffuser. Run times are on the orderof 25 s.A basic schematic of the test section is presented in Fig. 2. The test

section has a constant cross-sectional area of 4 in: × 4 in: and doesnot incorporate corrections for boundary-layer growth. It is a fixed-wall design to enable optical access of three sides of the test sectionusing UV-fused silica windows. The bottom window has anantireflective coating to reduce reflective losses for UV light enteringthe test section. The test section does not contain porous walls liketraditional transonic facilities, so that schlieren photography wasused to ensure transient shock waves were weak enough as to not bereflected back into the region of interest.Downstream of the test section is a plate with a small converging-

diverging profile whose purpose is to create a choked flow conditionafter the test section but prior to the diffuser. By modifying the arearatio at the choke location a range of Mach numbers can be enforcedin the test section. For the tests conducted in this study the Machnumber is set to 0.78 as determined through pressure measurements.This design was chosen due to the limited control available with theexisting regulators and valves, and it allows for small variations ininlet pressure without affecting the freestream Mach number. Thestagnation and storage pressures are monitored and recorded overthe course of each run in addition to the freestream pressure (P1) and

the wake pressure (P2). These measurements are performed usingOmega PX209 transducers.Themodel is a 1-in.-diamhemisphere that ismounted to the ceiling

of the wind tunnel, approximately 4 in. downstream from the end ofthe nozzle contour. This diameter results in a blockage ratio of ∼5%and is small enough to avoid choking the tunnel flow at this location.Freestream turbulence levels were not measured directly but found tobe lower than the resolution of PIV measurements (not shown),which are estimated to be about 1–2% of the freestream velocity. Thehemisphere is constructed of aluminum and is anodized black.During testing some fluorescence of the hemisphere surface wasencountered but was of a low enough intensity to prevent saturatingthe CCD detector.

B. Acetone Seeding

Acetone is seeded by injection into the high-pressure air supplyline far upstream (∼30 ft) of the stagnation chamber and test sectionto allowmixing and evaporation to occur over a larger distance than ifdirectly injected into the stagnation chamber. The seeding system isschematically presented in Fig. 3. A small pressure vessel is filledwith liquid acetone and is pressurized by a nitrogen tank to approxi-mately 30 psi greater than the initial compressed air storage pressure.The pressure forces the liquid acetone through a submerged exit pipe,out of the pressure vessel, and through a spray nozzle inside ofthe compressed air supply pipe. Uniform seeding was verified byimaging the flow without the model installed, where no signs ofpatchy or inhomogeneous seedingwere apparent. Also, to ensure thatthe acetone was completely evaporated and no particles remained, ascattering test was also conducted using the laser at 532 nm. In thesetests a small number of particles were observed with and withoutacetone seeding and believed to be due to contaminants (dust, oil,etc.) in the air supply system. The introduction of acetone, however,did not result in a discernible increase in the number of particles thatcould be identified in the visible wavelength images. A significantlysmaller number of particles are observed in the PLIF images as thescattered UV light does not transmit through the camera lens, whichis not UV grade. Still, we do note that some particle-like features canbe observed in the PLIF images. It is not clearwhat the source of thesefeatures are but speculate that it could be small oil droplets orcontaminant particles that also exhibit fluorescence. The potential fora stray droplet of acetone that did not evaporate or recently formed isalso a possibility; however, these occurrences are relatively sparseand effectively filtered out by the image processing. The amount ofacetone seeded during a given run is estimated to be between 2–3%by mass. This was determined by observing the amount of liquid

Fig. 2 Schematic of wind tunnel test section and optical configuration.

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acetone present in the small pressure vessel prior to and after each runand calculating the tunnel mass flow rate based on pressure andvelocity measurements.Toward the end of test runs local condensation of acetone occurred

in the flow particularly in the separated shear layer behind thehemisphere. Similar to the particle detection method condensationwas detected by direct imaging of light scattered by condensedparticles when illuminated with a 532 nm laser sheet. The onset ofcondensation is believed to be caused by the gradual decrease instagnation temperature experienced throughout the run as the storagepressure decreases, leading to lower temperatures in the test section.Another contributor is the slight variation in the acetone molefraction throughout the run that is caused by the increasing pressuredifferential between the nitrogen tank and the compressed air supplyline pipe (i.e., storage pressure) as the storage pressure drops. Notethat only the mole fraction is modified, and the uniformity of theacetone seeding remains. For the purposes of data analysis the timeframe of the condensation process during the run was identified. Thedensity images acquired during this time frame of condensation werecompared to those obtained during the test run when condensationwas considered minimal (single, average, and standard deviationimages were compared). It is interesting to note that the condensationof acetone could not be detected through direct inspection of theacetone PLIF images indicating that the condensed particles are quitesmall with fluorescence characteristics virtually the same as thoseencountered in the gas phase. This trend is not expected to hold truefor larger particle sizes but suggests that small amounts of conden-sation can be tolerated in the application of acetone PLIF in otherfacilities. Based upon these conclusions all acetone PLIF densityimageswere deemed valid andwere used for statistical analysis of theflowfield.

C. Optical Configuration

A new wave Solo 200XT PIV laser was used to produce UV lightby converting both pulses of the 532 nm output to 266 nm using aKDP nonlinear crystal. The resulting combined pulse energy wasapproximately 38 mJ∕pulse at 266 nm. Harmonic conversion effi-ciency was improved by delaying one pulse relative to the other. Inthese experiments the two pulses were separated by 100 ns overwhich time the flowwouldmove less than 1 pixel. As shown in Fig. 2the laser sheet is formed using a combination of spherical andcylindrical lenses, creating a beam roughly 1.5 in. wide and approxi-mately 1 mm thick. The beam is steered at a 45 deg angle into the test

section to increase the width of the shear layer region illuminated bythe most intense portion of the beam. All optics are mounted onto atranslating stage, allowing multiple planes to be imaged.Imaging is performed using a SensicamQECCD camera (actively

cooled, 1376 × 1040 pixel resolution, 6.45 μm pixel size) at 7 Hz. A25 mm focal length lens is used with an f-number of 1.6. The imagesare acquired without any hardware binning. Images were obtainedwithin thewake region of the flowfield, using a FOVof 1.8 × 1.3 in:,corresponding to a location 0.16–1.96 diameters downstream of thecenter of the hemisphere. In addition, to better understand the three-dimensional characteristics of the overall flowfield, a small set ofimages was acquired for planes (streamwise–transverse) parallel tothe centerline but shifted off of the centerline axis by D∕8, D∕4,3D∕8, D∕2, and 5D∕8. The FOV for this additional set of imageswas 1.25 0 0 × 0.95 0 0, corresponding to a streamwise location of−0.14–0.86 diameters relative to the center of the hemisphere.

V. Results

A. Wake Region Density Fields

A total of 344 density measurements along the centerline of thehemisphere were obtained over the course of 5 experimental runs. Inaddition, between 15 and 25 images were acquired at each of the 5off-axis planes. Examples are shown herein of the centerline and oneoff-axis case. Figure 4 presents a set of four normalized density fieldsalong the centerline of the hemisphere. The flow direction is from leftto right, and portions of the images have been masked, whichcorrespond to regions of low-laser energy and resulting low-signal-to-noise ratio (generally less than 10). In these images, the constantfreestream density values and notable lack of any intensity biaseswithin the freestream region indicate the effectiveness and strength ofthe uniform seeding, as well as the image processing steps used tocorrect for variations in the laser sheet intensity across the imagingregion.To illustrate the quantitative accuracy of the images, Fig. 5 shows

two horizontal density profiles taken from the postprocessed imagedata displayed in Fig. 4a. The first profile was taken at a verticallocation of y∕D � 1.24 and was chosen to represent the freestreamflow. The density measured in this region is roughly uniform with amean value that is slightly greater than the estimated freestreamdensity andwith a standard deviation of 2.9%of the freestream value.The mean density is seen to decrease slightly, and the fluctuationsincrease slightly near the edges of the laser sheet due to the lowersignal levels associated with this region of the image. The observedmean and fluctuating values in the freestream are in line with theuncertainty analysis discussed earlier, lending confidence to thequantitative accuracy of the measurements. The second profile wastaken at y∕D � 0.44 and corresponds to a slice through the center ofthe vortex-like structure located at x∕D ∼ 0.5 in Fig. 4a. As can beseen, the magnitude of density fluctuations visualized in the image issignificantly larger than the estimated measurement uncertainty. Thedensity in the vortex core is seen to drop significantly relative to itssurroundings with a minimum density of approximately 45% tothat of the freestream with the overall wake having a density on theorder of 70–80% to that of the freestream. High-spatial frequencyfluctuations associated with measurement noise (primarily shotnoise) are of similar magnitude to that of the freestream.All images present in Fig. 4 exhibit a range of structures and

interactions. This wide variety of fluid behavior is a testament to therich complexity of the hemispherical flowfield, as well as the noveltyof the measurement technique for measuring the structure andtopology quantitatively and with high-spatial resolution. It should benoted that the images in Fig. 4 have been chosen for their clarity butare not exceptional.The two most notable features present in these images is the large-

scale motions of the wake region and the presence of low-densitycores in the shear-layer region separating the freestream from thewake. The large-scale motion of the wake region is most prevalent inFig. 4d, where the low-density wake, with a density of 80–90% of thefreestream, is separated from the high-density freestream by a sharpinterface. The interface between wake and freestream fluid exhibits

Fig. 3 Schematic of acetone seeding system that uses pressurizednitrogen to inject acetone upstream within a compressed air supply line.

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relatively large flapping motions with the freestream fluid nearlytouching the wall at x∕d � 0.9 and the low-speed wake fluidprotruding well out into the freestream at x∕d � 1.6.Although the interface between the freestream and wake is

generally quite sharp it also contains several vortex-like structures asindicated by relatively large drops in local density (up to 50%) that arecircular in shape. These vortices are clearly seen in Figs. 4a and 4band tend to bemore distinct (i.e., smaller with largermagnitude dropsin density) near the separation point. Further downstream in the shearlayer the vortex cores are generally larger with a reduction in themagnitude of the density drop. It is worth noting that the density dropwithin the shear layer can be significantly greater than that observed

in the wake; a phenomena noted in [36] and attributed to the low-pressure wells that form at the center of regions of high vorticity.The average density was calculated based on a set of 344 images

and is presented in Fig. 6a. Note that low-density vortex cores orstructures cannot be seen in the image due to the highly unsteadynature of the flow. Rather, a smooth variation in the density field isobserved with the region closest to the hemisphere exhibiting thelargest decrease in density. The average density field recovers rapidlyto the freestream value within 1.0–1.5 diameters of the separationpoint. The standard deviation of the same set of 344 images is shownin Fig. 6b, providing an indication of the location and magnitude ofdensity fluctuations. The most significant fluctuations occur withinthe shear layer being shed at the top of the hemisphere with peakmagnitudes of 12% occurring approximately 1 diameter downstreamof the separation point. This should be contrasted with the peakdensity fluctuations on the order of 50% for the low-density vortexcores observed in the instantaneous images of Fig. 4. Thus, thestatistical data mask the separate contributions of the large-scalewake motion and small vortices contained in the shear layer. Inaddition, the magnitude of fluctuations observed in the freestream isapproximately 2–3% of the freestream value, which is in accordancewith the estimated measurement uncertainty. The magnitudeincreases near the edges of the laser sheet, where the incident lasersheet intensity is relatively low-producing lower signal to noiseratios.In addition to data acquired along the centerline of the hemisphere

a small number of additional images were acquired along planesoffset from the centerline to assess the general three-dimensionalityof the flowfield. In Fig. 7a an image is shown of a plane located one-quarter of a diameter from the centerline plane. In this single imagethe wake structure appears to have a smaller overall scale than thecenterline images; this is confirmed in average images, which show areduction in the extent of the separated region but are not shownfor sake of brevity. In general, the large-scale motion of the wake

Fig. 5 Density profiles taken from Fig. 4a at y∕D � 1.24 (freestream)and y∕D � 0.44 (center of free shear layer).

a) b)

c) d)

Fig. 4 Set of four normalized density fields of the centerline plane andwake region. Dashed lines in a) indicate locationwhere profiles are shown in Fig. 5.

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is subdued, and the shear layer appears to contain a higherconcentration of small vortex cores. Figure 7b shows a plane locatedone-half of a diameter from the centerline plane. The large-scalemotion of the wake is again noticeably smaller than the centerlinecase, and freestream fluid appears to protrude down through thewakeregion. In this case the presence of distinct vortex cores is notobserved as the laser sheet is no longer oriented perpendicular to thethree-dimensional shear layer.Although not the focus of this investigation the level of detail

provided in the images suggests their suitability for the application ofestablished turbulence analysis tools, such as the spatial correlation,intermittency, and fractal analysis, to provide corroborating data thatmore fully elucidate the flowfield in concert with other nonintrusivemeasurement techniques, such as particle image velocimetry.

B. Separation Region Density Fields

In addition to views at off-centerline planes a closer look was alsotaken at the apex of the hemisphere, where a shear layer developsafter the boundary layer attached to the model separates. Figure 8shows two representative images of this closeup region. Again,the freestream region is uniform with no discernable bias. Cleardelineation can be seen between the freestream fluid and the growingshear layer. A prominent feature in both the images shown here, aswell as a majority of the images acquired, is the presence of a stronglambda-type shock located at the same position as the shear-layerseparation point. This same shock structurewas observed in schlierenimaging acquired during tunnel qualification.In the data acquired for this study large differenceswere seen in the

early development of the shear layer. Figure 8a is an example of early

a) b)

Fig. 6 Planar density field statistics. a) Ensemble average normalized density field (ρ∕ρ∞) and b) percentage density fluctuations, �ρ∕ρ∞� 0, for thecenterline plane.

a) b)Fig. 7 Pair of normalized density fields from a) plane located one-quarter of a diameter from the centerline, and b) plane located one-half of a diameterfrom the centerline.

a) b)Fig. 8 Pair of normalized density fields of a closeup region near the apex of the hemisphere. The colormap for both images is equal and identical to Fig. 4.

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shear layer growth, which appears to only consist of a large-scaleseparated region, whereas Fig. 8b presents an alternate mode offormation, where structure also appears to exist withinmore coherentstructures that contain stronger density drops indicative of vorticalmotion.

C. Wave Front Distortion Measurements

Using the density values and the Gladstone–Dale relation,[Eq. (2)], the index-of-refraction field can be calculated in astraightforwardmanner. This permits the use of numerical integrationto yield the OPL directly from the density data as shown in Eq. (1),wherevariations inOPL across the beam aperture represent distortionof the beam. Wave front distortion is typically represented by theoptical path difference, (OPD):

OPD � OPL − OPL (6)

whereOPL is the spatial average of theOPL across the aperture of thebeam. In this section we present some representative wave frontdistortion calculations to illustrate the potential for density measure-ments to be used for aerooptic analysis. A more comprehensiveanalysis of the data is beyond the scope of this paper.The distortion of a wave front passing through the turbulent wake

was determined by the numerical integration of the density fieldalong a path originating at the center of the hemisphere. The wavefront diameter was modeled as approximately one-third of thehemisphere diameter with the beam aperture discretized into 100equally spaced light rays. Each of the rays was propagated from adistance at the center of the hemisphere into the freestream at an angle

of 34 deg from thewall as illustrated in Fig. 9.Within the hemispherethe index-of-refractionvalue is set uniformly to unity. TheOPL alongeach light ray was determined through numerical integration ofthe index of refraction along this path, where it is assumed thatdeflections of the ray are small in comparison to the index-of-refraction gradients. The average OPL of all 100 rays is then used todetermineOPL and OPD as given in Eq. (6). The uncertainty in OPLfor each ray is estimated to be approximately 0.006 μm. This valuewas calculated using Eq. (1) to propagate the uncertainty in density toindex of refraction and the central limit theorem to estimate theuncertainty in the OPL upon integration. This value is representativeof the local, small-scale fluctuations observed in the calculatedOPDs, whereas the large-scale fluctuations are observed to be on theorder of 1.0 μm, indicating that the calculated wave fronts are highquality.Figure 9 presents two examples of this procedure. In Figs. 9a and

9c the integration region is identified, and a local coordinate system isdefined with respect to the region. In Figs. 9b and 9d the respectivevalues of theOPD for each wave front are given. These two exampleshave been chosen as being representative of the influences that bothlarge- (on the order of the hemisphere diameter) and small-scalestructures have on the resulting wave front. In Fig. 9a the shear layergrows with downstream location and is host to a number of small-scale eddies that also develop in extent. However, the densityfluctuations within the eddies are relatively small as compared toobservations in other images. The main density fluctuations withinthe image are associated with the interface between the wake regionand the freestream. In this case the wake is growing in thedownstream direction, and the interface is inclined relative to thefreestream direction such that there is a relatively steep gradient in

a) b)

d)c)

Fig. 9 Two examples of wavefront calculations. a) and c) show the density field and region of integration; b) and d) show, respectively, the associatedvalues of the OPD.

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density across the beam aperture. Because of this, we consider thisimage to be dominated by the large-scale motion of the wake asopposed to the steep density drops associated with vortex cores. Theeffect of this flow pattern on the wave front in shown in Fig. 9b. Thegeneral trend of the wave front is a tilted wave front where OPDdecreases with increasing x 0. This behavior is due to the increasinglength of low-density (i.e., low index of refraction and shorter OPL)fluid through which the beam must pass to get to the freestream. Assuch, the distortion of the wave front is seen to be dominated by thelarge-scale wake motion. We point out that a real beam passingthrough this flow would be deflected in the −x 0’ direction due to thetilt in the wave front.In contrast, Fig. 9c was chosen as it exhibits an intense eddy

marked by a significant drop in density at the eddy core. The low-densitywake is oriented roughly horizontal relative to the freestream,producing a milder density gradient associate with the wake acrossthe beam aperture. Thus, the effect of the intense eddy in the shearlayer should have a more pronounced effect on the wave frontdistortion than the wake. The resulting wave front shown in Fig. 9d,however, does not exhibit a strong feature that can clearly beassociated with the intense eddy contained in the shear layer. Rather,the distorted wave front is relatively flat in comparison to Fig. 9b dueto the horizontal inclination of the large wake region. In addition, theeffect of the eddy is somewhat counteracted by a high-density regionof fluid positioned slightly upstream.By examining the full set of images acquired along the centerline

similar trends were observed. The dominant source of fluctuations inOPD can be associated with the large-scale motions of the wakeregion with the contributions of individual eddies contained in theshear layer, even intense ones, having a lesser effect on thewave frontdistortion. This follows from intuition, and because the calculation ofthe OPL is an integration themagnitude of fluctuations in density canat times be a smaller driver than the spatial extent of the fluctuation.We caution that these observations are constrained to the parameters(beam size, direction or propagation, and Mach number) chosen forthis example and limited by the number of images actually acquired.The main point is that this example simply serves to highlight the

type of analysis that can be performed using direct measurements ofthe density. The results found here were for a particular beam sizepointed in a particular direction. Using the same set of data similaranalysis could be performed for beams with different characteristics.We also note that this technique can also be extended to perform astatistical analysis of thewave front distortions, enabling parameters,such as the OPD ensemble average and standard deviation, to bedetermined. Because the wave front is calculated after the run iscomplete it is also possible to develop optimization routines tomodify the beam aperture and angle in concert with the integrationapproach to reduce the effects of aerooptical distortion in a way thatwould be difficult with direct optical measurements.

VI. Conclusions

A technique has been demonstrated for measuring density in ahigh-speed, compressible flowfield through the use of acetone planarlaser-induced fluorescence (PLIF). Key aspects of the present imple-mentation of the technique include uniform seeding of acetone vaporthroughout the flow, an in situ calibration procedure based on theuniform properties of the freestream, and themodeling of uncertaintyin the fluorescence signal due to uncertainty in the local pressure. Theuncertainty due to pressure is estimated to be 2.5% with the overalluncertainty estimated to be approximately 8% without low-passfiltering and 3.5% with low-pass filtering. Thus, the most significantimprovements are expected to come through increased signal-to-noise ratio (SNR) of the images. This can be realized through the useof higher energy laser pulses, spatial beam shaping tomore uniformlydistribute the energy contained in the incident pulse, and the use ofmore sensitive cameras with high-dynamic range.The utility of the technique was demonstrated through the visuali-

zation of the density field in thewake region and separated shear layergenerated by a wall-mounted hemisphere. The resulting densityfields revealed highly complex, intermittent, and three-dimensional

structures in the wake. Prominent features included a sharp interfacebetween the low-density wake and the higher density freestream, theposition of which exhibited a large-scale flapping type of motion.This interfacewas also populated by a number of small diameter, low-density structures that provide for a smoother transition between thefreestream and wake region. These smaller structures are believed tobe associated with pressure wells at the core of strong vorticalmotions. The drop in density at the core of these vortices can be quitesignificant, dropping to 50% of the freestream value in some cases.Finally, near the separation point, distinct lambda-type shockstructures appeared to be a dominant feature throughout the testing.Overall, this technique was very effective at visualizing the densityfield and providing accurate density data.The density measurements were also used to calculate the aerooptic

distortion in the wake by performing a direct integration of the index-of-refraction field. The main weakness to this method is that it has notbeen verified with traditional wave front measurement techniques,such as a Shack–Hartmann wave front sensor or a Malley probe;however, it demonstrates the utility of direct density measurements forthe estimation and analysis of aerooptic effects. A significant advan-tage for the use of planar density data is the ability to simulate varyingbeam parameters, such as aperture and size using a single image.

Acknowledgments

An Air Force Office of Scientific Research (AFOSR) YoungInvestigator Program Grant (FA9550-08-1-0150) funded this work.The authors would like to thank Abhishek Bichal and Tim Fahringerfor assistance with experiments, Andy Weldon for continued assis-tancewithmachiningwork, andDavidWall for designing the transonicfacility and assisting with its construction. The authors would also liketo thank Anwar Ahmed from Auburn University for the use of a newwave Solo 200XT Particle Image Velocimetry (PIV) laser.

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