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AIAA JOURNAL Density Measurements of a Turbulent Wake Using Acetone Planar Laser-Induced Fluorescence John Z. Reid,∗ Kyle P. Lynch,† and Brian S. Thurow‡ Auburn University, Auburn, Alabama 36849 Downloaded by Brian Thurow on February 28, 2013 | http://arc.aiaa.org | DOI: 10.2514/1.J051678 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 freestream Mach 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 layer near the separation point reveal the formation of lambda shocks. The density 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 density measurements and providing a new method for the evaluation of aerooptic distortion in compressible flows. density fluctuations that strongly affect the dynamics of the flow. For many applications, and aerooptics in particular, the fluctuations in density are of explicit importance and offer the most straightforward description of the relevant flow physics. As a result, aeroopticsrelated research has often focused on numerical solutions that can provide full-field density data to better understand the relationship between structures in the flow and distortions of an optical wave front passing through the flow. This is in contrast to the capabilities of the most common experimental techniques, which typically focus on qualitative flow visualization or velocity measurements. In this regard, an experimental method for performing accurate and nonintrusive measurements of density in flowfields of practical significance would be of tremendous value. This work discusses the application and accuracy of acetone planar laser-induced fluorescence (PLIF) for planar density measurements in the turbulent wake created by a hemisphere in a Mach 0.78 freestream flow and briefly addresses the relationship between the density measurements and optical wave front distortion. Nomenclature c D dV c E h K k n P P2 P∞ , P1 Sf Sf;∞ T T∞ η λ λwf ρ ρ∞ σ ϕ χ = = = = = = = = = = = = = = = = = = = = = = = speed of light hemisphere diameter collection volume laser fluence Planck’s constant Gladstone–Dale constant Boltzmann’s constant index of refraction static pressure wake pressure freestream pressure acetone fluorescence signal freestream acetone fluorescence signal static temperature freestream temperature optical collection efficiency excitation wavelength wave front wavelength density freestream density absorption cross section fluorescence quantum yield acetone mole fraction I. H II. Background A. Optical Density Measurement Techniques Introduction IGH-SPEED compressible flowfields are characterized by their turbulent nature and often contain large spatial and temporal Presented as Paper 2011-0987 at the 49th AIAA Aerospace Sciences Meeting and Exhibit, Orlando, FL, 4–7 January 2011; received 28 October 2011; revision received 11 October 2012; accepted for publication 17 October 2012; published online 18 February 2013. Copyright © 2012 by Brian Thurow. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 1533-385X/13 and $10.00 in correspondence with the CCC. *Graduate Research Assistant, Department of Aerospace Engineering. Student Member AIAA. † Graduate Research Assistant; currently Ph.D. Candidate, Delft University of Technology, The Netherlands. ‡ Associate Professor, Department of Aerospace Engineering; thurow@ auburn.edu. Optics-based flow measurement techniques are generally categorized by their use of molecular or particle seeding to interrogate the flow. The former involve elastic scattering, inelastic scattering, or fluorescence to generate a signal, whereas particle seeding techniques involve Mie or Rayleigh scattering from small particles contained in the flow. A number of issues exist with particle seeding for measuring a scalar quantity, such as density, notably the difficulty in ensuring high concentrations of uniform seeding. In contrast, molecular seeding offers the ability for excellent seeding uniformity and ensures the tracers follow the flow faithfully. Also, the binary nature of a particle measurement greatly increases the noise due to quantization, rendering a measurement of density impractical. In contrast, the far greater number density of seeding molecules reduces the quantization noise and allows a measurement of number density to correspond to the fluid density. Eckbreth [1] gives a detailed description of multiple optical methods based on molecular seeding that have potential to be adapted for density measurements in a flowfield. These methods include molecular Rayleigh scattering, Raman scattering, laser-induced fluorescence, and coherent anti-Stokes−Raman spectroscopy. For a flow of uniform gas composition molecular Rayleigh scattering is attractive as the signal is directly proportional to the gas density and incident laser energy such that flow seeding is not strictly required. Miles et al. [2] provides a detailed review of Rayleigh scattering and AIAA Early Edition / 1 Downloaded by Brian Thurow on February 28, 2013 | http://arc.aiaa.org | DOI: 10.2514/1.J051678 2 AIAA Early Edition / different methods for performing multiparameter measurements using spectral and intensity data. Recent studies using molecular Rayleigh scattering for density measurement in air are generally restricted to point measurements due to the low-signal levels produced by the Rayleigh scattering process. Some examples include the work in [3,4] who used high-powered continuous wave lasers and relatively large collection optics to measure the signal at a point in the flow. Time-averaged planar measurements were realized through mechanical translation of the measurement system through the flow. The low-signal levels encountered in Rayleigh scattering can be circumvented for instantaneous planar imaging with the use of highenergy ultraviolet (UV) lasers and intensified cameras, such as demonstrated in [5]. An alternative is to use different gases in lieu of air to increase the Rayleigh scattering cross section. This method was employed in [6] where instantaneous planar measurements were performed by using a specially designed shear layer facility to exploit the large and small scattering cross sections of ethylene and helium, respectively. In the configuration, the observed signal is a measure of the local concentration of ethylene, which contrasts significantly with the miniscule signal from helium. Raman scattering, which typically has even lower signals than Rayleigh scattering, also has the potential to be used for planar density measurements as demonstrated in [7] for the 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 mixture fraction (e.g., [29–33]) in a variety of flows. PLIF is based on the absorption and fluorescence of laser light by tracer molecules either already present or seeded into a flow. The atomic structure of particular molecules results in unique absorption spectra, typically in the UV. Using an appropriate laser source with strong spectral overlap in an absorption band photons can be efficiently absorbed by the molecule to raise its energy level. To return to a ground or equilibrium state both short-term (fluorescence) and long-term (phosphorescence) radiative processes occur, emitting photons within separate, longer-wavelength emission spectra. PLIF-based techniques generally benefit from greater signal levels than Rayleigh scattering, which generally makes them more suitable for instantaneous measurements. Moreover, background interference from surface scattering can be better mitigated through the use of various filters to block light near the excitation wavelength. Although many PLIF techniques exploit naturally occurring species, such as those associate with combustion, full-field flow measurements, such as the planar density measurements targeted in this work, require that the entire flow be uniformly and passively seeded to ensure a direct relationship between local species concentration and flow density. Common PLIF species that have been employed for full-field measurements include nitric 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 a tracer molecule, have a lot in common with the work discussed here as many of the practical experimental issues are common to both. King et al. [29], for example, developed a method whereby one stream is seeded with NO and the other stream is seeded with acetone. Simultaneous NO/acetone PLIF, where the NO PLIF signal is suppressed upon mixing due to oxygen quenching, is then used to measure the degree of mixing present at a given location within the image. This technique was subsequently applied in [30,32] for mixture fraction measurements in axisymmetric and planar shear layers. Catrakis et al. [34], in a similar vein, used acetone PLIF imaging of one stream mixing with an unseeded stream in an effort to estimate the local concentration of acetone. Extension of these techniques to a measurement of the local flow density, where the local density is modeled as directly proportional to degree of mixing between the two streams, is possible for the incompressible mixing of two temperature matched streams of different density gases. Fitzgerald and Jumper [35], however, show that for compressible shear layers of aerooptic interest, such as that studied in this work, the relationship between local density, pressure, and mixture fraction is sufficiently complex to preclude the direct use of mixture fraction data for density measurements. REID, LYNCH, AND THUROW The technique presented herein uses the acetone PLIF technique to perform a full-field density measurement. In a similar fashion for single excitation line temperature measurements the entire flowfield is seeded with the tracer molecule such that the observed signal is only dependent on the local flow properties and not the degree of mixing or local species concentration, which is constant. Whereby temperature measurements generally assume a constant pressure within the flow to arrive at their measurement this restriction is relaxed in this work such that the uncertainty in local pressure, which can be significant in compressible flows, is absorbed into the measurement uncertainty. B. Aerooptics Application of Measurements The ability to directly measure a planar density field provides uniquely useful data for aerooptics analysis. To describe the aerooptics problem briefly the propagation of a collimated, coherent beam of light is dependent on the index of refraction of the medium through which it travels. In turbulent flowfields, density fluctuations directly lead to fluctuations in the index of refraction, causing the wave front of the beam to become abberated. The study of the interaction of fluid properties and light propagation is termed aerooptics [36]. This research field has attracted interest recently as imaging, optical communications, and directed energy weapon systems have become more common. In each of these cases, degradation of the optical wave front places a limit on the performance of these systems, particularly when used on aircraft platforms. An example is a turretmounted laser aperture on the fuselage of an aircraft; the unsteady turbulent flow around the turret, particularly in the shear layer and wake region, generates large density fluctuations that alter the wave front as the beam exits the aperture [37–39]. As the beam continues toward a target the distorted wave front causes the beam to diverge and degrade in quality. By the time the beam reaches the target it has lost 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). The OPL is the distance that light travels in a vacuum in the same amount of time that it takes light to travel through a volume of a medium with an index-of-refraction value greater than or equal to unity. Considered mathematically, the OPL is a three-dimensional integration of the index of refraction (n), as seen in Eq. (1), where z is taken as the direction of light propagation: Z OPLx; y; t nx; y; z; t dz (1) A more commonly used measure of the aerooptic distortion is the optical path difference (OPD). The OPD is simply the difference between the OPL and the mean spatial OPL across the beam aperture (OPL). To convert the density field to an index-of-refraction field, the Gladstone–Dale equation [Eq. (2)] is used, where the Gladstone– Dale constant K is approximately 2.27 × 10−4 m3 ∕kg for light at 532 nm: nx; y; z; t 1 Kλwf ρx; y; z; t (2) Thus, the distortion of an optical wave front is the integrated effect of the three-dimensional density field through which the beam passes. In principle, if the density field of the flow is known, the distortion can be completely characterized and adaptive optics can be used to correct 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 turbulent wake. All of these features are three-dimensional in nature and, thus, affect the three-dimensional density field. Past investigations have succeeded in using a variety of experimental methods to characterize flows with similar structure and measure the resulting wave front aberrations. These studies have found that in addition to compressibility effects the unsteady behavior of the large-scale turbulent structures in the flow are a dominant source of distortion, particularly in the separated shear layer. These large-scale vortical structures Downloaded by Brian Thurow on February 28, 2013 | http://arc.aiaa.org | DOI: 10.2514/1.J051678 AIAA Early Edition / generate low-pressure wells at their core, causing a change in density throughout the structure. However, the experimental techniques currently in use do not directly measure the density field but instead rely on a combination of velocity measurements and wave front sensors to analyze optical distortions [37,38]. The technique described herein directly measures the density field, providing a unique ability to investigate aerooptic distortion by its fundamental mechanisms. In addition, by obtaining the density field, the aerooptic distortion for any wave front type, size, wavelength, and orientation/ path through the medium can be approximated. This is in contrast to traditional wave front measurement techniques using a Malley probe [36] or a Shack–Hartmann wave front sensor where parameters, such as beam size, wave front wavelength, and propagation angle have to be set for each experiment. Besides the utility of the measurement for aerooptics applications, the density field provides further insight into the structures and topology of the flow. By obtaining density data and coupling them with velocity data flow characteristics causing density fluctuations can be better understood. These density values can be used as a validation for a variety of models, such as the weakly compressible model [35] and computational 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 Mach 0.78 freestream flow. The implementation of established acetone absorption cross-sectional data and a fluorescence quantum yield model is used to convert raw image intensity data to a density field. An overview of the model and conversion procedure is given to provide the reader with an uncertainty estimate in the data. Next, an experimental test of the technique is performed, and results are shown at multiple locations within the flow to demonstrate the viability and uniqueness of the technique and the utility of the method for aerooptic analysis. III. Adapting Acetone Planar Laser-Induced Fluorescence for Density Measurements Acetone was chosen as the tracer molecule in this study because of the favorable characteristics it possesses, including low cost, highvapor pressure, safe handling properties, and a broadband absorption spectrum that peaks from 260 to 290 nm [18,19,21,40,41]. Thus, acetone can be efficiently excited by using the fourth-harmonic output of Nd:YAG laser systems at 266 nm. The fluorescence emission spectrum of acetone is also broadband and peaks from 445 to 480 nm; a range of wavelengths that are efficiently detected by charge-coupled device (CCD) sensors. The captured signal can be mapped to a density value, allowing a planar density field to be measured from an acetone PLIF image. This section details the mapping from signal values to density measurements and provides an uncertainty estimate. A. Fluorescence Signal Equation The acetone fluorescence signal is quantified by Eq. (3) [18], where the majority of the terms are constant parameters throughout the flow: Planck’s constant, h; Boltzmann’s constant, k; the speed of light, c; excitation wavelength, λ; collection volume, dV c ; and acetone mole fraction, χ. Note that maintaining a constant acetone mole fraction throughout the flow is an essential feature of the present technique in contrast to other applications of acetone PLIF as a passive scalar tracer for concentration or mixing measurements: X E χP Sf ηdV c σλ; Tϕλ; T; P; χi (3) hc∕λ kT i The variable terms remaining are the laser fluence E, optical collection efficiency η, static pressure P, static temperature T, absorption cross section σ, and fluorescence quantum yield ϕ. Eliminating the variations in many of these parameters is the focus of a number of image processing steps. In order of execution, these steps include: average dark image subtraction, vignetting correction, high-intensity pixel filtering, laser sheet nonuniformity correction, freestream intensity normalization, and a 3 × 3 moving average spatial filtering. 3 REID, LYNCH, AND THUROW The average dark image subtraction eliminates ambient and reflected light present in each image, so that the measured signal contains a minimal number of contributions beside the useful acetone fluorescence. Following this, a vignetting correction is applied to account for the change in optical collection efficiency due to the reduced collection angle for object points located off of the optical axis. This correction procedure uses a set of coefficients calculated using the cos4 law [42]. Next, a filtering of high-intensity pixels eliminates traces of a small amount of residual particle scattering observed in the images. This filter uses a threshold intensity value, set to 1800 counts (over three times the mean signal level). If the intensity value of any pixel is greater than the threshold value then the pixel and its 12 neighboring pixels, arranged in a diamond pattern around the central high-intensity pixel, are set to the mean value of the 11 × 11 region of surrounding pixels, excluding the pixels to be modified. After this, a laser sheet nonuniformity correction modeled after the technique outlined in [6] accounts for the approximately Gaussian energy profile of the laser sheet throughout the test section. In this technique the laser sheet is modeled as a radial fan propagating from a virtual point contained outside of the field of view (FOV) of the image. Points in the image are then mapped to an r; θ coordinate system, where it is assumed that variations in the θ direction are associated with the nonuniformity of the incident laser beam, and variations in the r direction are due to the energy of the beam spreading out radially in a 1∕r fashion. To estimate the nonuniform distribution of energy in in the θ direction, which can vary from pulse to pulse, we used an in situ calibration method similar in [29]. We assumed that the density, and, therefore, fluorescent signal in the freestream is a constant value such that any variations in image intensity can be attributed to variations in the incident laser flux. A set of correction coefficients based on the distribution are calculated and then applied to the entire image. Additionally, losses due to absorption were estimated from Beer’s law to be less than 3% over the path length of the image due to the relatively low concentration of acetone contained in the flow. This loss was not accounted for in this work. A 3 × 3 moving average (i.e., low-pass) filter is then applied to each image to reduce the effects of image noise (readout noise, shot noise, etc.). Once the previous image processing steps are complete, E and η can be considered as constant throughout the image and Eq. (3) can be simplified to Eq. (4), where C accounts for the constant factors throughout the image: Sf C P σTϕT; P T (4) The image processing and in situ calibration procedure ends with a normalization of the image intensity to the average freestream intensity value (assumed to be a constant value) allowing the constant factors to cancel and the remaining equation to be rewritten in the form of a ratio as shown in Eq. (5): P Sf σTϕT; P ρσTϕT; ρRT P∞ T Sf;∞ T σT ∞ ϕT ∞ ; P∞ ρ∞ σT ∞ ϕT ∞ ; ρ∞ RT ∞ ∞ P P ρσ ρR ;P ϕ ρR ρ∞ σ ρP∞∞R ϕ ρP∞∞R ; P∞ (5) Formalized as such, we see that the signal is directly proportional to the local flow density with a modest dependence on the local temperature and pressure in the fluorescence quantum yield and absorption cross section. Thus, in the absence of an independent measurement, variations in the local pressure and temperature will present themselves as an uncertainty in the estimation of density. By assuming ideal gas behavior the equation of state allows Eq. (5) to be rewritten to eliminate one of the redundant parameters. For our purposes the last expression given in terms of ρ and p is the most useful, as we have measurements of the total and static pressures available within the test section such that we can estimate the 4 AIAA Early Edition / expected variations in local pressure. To quantify this uncertainty the behavior of fluorescence quantum yield and absorption cross section with variations in pressure and density were investigated. Downloaded by Brian Thurow on February 28, 2013 | http://arc.aiaa.org | DOI: 10.2514/1.J051678 B. Fluorescence Yield and Absorption Cross-Sectional Model The photophysics and physical qualities of acetone vapor have been well characterized in [41], in particular, the weak dependence of fluorescence signal on pressure and temperature (relative to other commonly used tracers) and the quenching of the long lifetime phosphorescence signal by oxygen were reported. Further work in [19] established a physically-based model for the fluorescence quantum yield and absorption cross section as a function of temperature, pressure, excitation wavelength, and gas composition. This model is based on a multistep decay process that takes into account the multiple decay probabilities that exist for polyatomic molecules, such as fluorescence, vibrational relaxation, and intersystem crossing. Bryant et al. [43], Tran et al. [44] and Hartwig [45] extended the model of Thurber to wider pressure and temperature ranges 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 excitation wavelength was set to 266 nm. The acetone mole fraction was set to 3% within the assumption of small acetone mole fraction used by the model. With these parameters set pressure and temperature could be input to the model, and both the fluorescence quantum yield and absorption 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 quantum yield and absorption cross section must be included in the measurement uncertainty. To quantify this variation the range of pressures encountered in the flow were considered. Because the primary concern is to measure density variations in the turbulent shear layer and wake produced by the hemisphere the bounds are placed at the lowest pressures (wake) and highest pressures (freestream) expected in the region. It is assumed that the pressure drops associated with the vortex cores in the shear layer and wake, although significant in a local sense, would still remain within the bounds set by these extremes. During each test run the freestream static pressure and wake static pressure are measured in order to set the physical values of these pressure bounds. Normalized signal versus normalized density curves are created for each pressure bound through the use of Eq. (5). Values for the fluorescent quantum yield and absorption cross section were taken directly from Thurber’s model as described above. A sample curve is shown in Fig. 1, where the effect of pressure on the expected signal REID, LYNCH, AND THUROW can be observed. The effect of temperature is also implicitly included in these curves through the equation of state. An average of the two curves is created and used as the reference curve for converting the normalized signal to normalized density. Note that the relationship between normalized signal and normalized density is nearly proportional but cannot be considered linear due to the effects of pressure and temperature. C. Measurement Uncertainty The density measurement uncertainty due to the pressure uncertainty is relatively small and is estimated to be less than 2.5% over the density range encountered in this flow. As can be seen in Fig. 1, for a density ratio of approximately 0.65, the uncertainty due to pressure variations vanishes as the relative changes in fluorescence quantum yield and absorption cross section cancel out. Using the average of the two curves minimizes error, because the average curve lies exactly between the curves for the two pressure bounds. Thus, the average curve can be considered as representative of the average pressure condition. A consequence of this choice is a bias error depending on local pressure values. At normalized signal values below 0.65 the average curve undercalculates the density values in the freestream region and overcalculates the density values in the wake region. The opposite situation occurs for normalized signal values above 0.65. This bias error could be minimized by allowing the pressure to vary depending on the region of the image being analyzed; 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 the fluorescence signal. The accuracy by which the fluorescence signal can be measured depends on multiple factors, including the quality of the image sensor (quantum efficiency, read noise, dark noise, dynamic range, etc.), shot noise, and the calibration procedure used to account for vignetting and laser sheet nonuniformity. The combined effect of these noise sources was estimated by observing the signal level in the freestream region of the flow, where density fluctuations should be vanishingly small. Under this assumption any variations (quantified in terms of the standard deviation) in signal in the freestream 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, in the freestream with a spatial resolution of ∼33 μm∕pixel. Low-pass filtering the images with a 3 × 3 pixel-averaging filter reduced this uncertainty to ∼2.5% at the expense of reduced spatial resolution (to nominally 100 μm). The standard deviation is lowest near the centerline of the laser sheet and increases as laser energy decreases toward the edges, indicating the low-signal levels are the primary driver of the uncertainty. In summary, the overall uncertainty of the density measurement, accounting for the uncertainty of the conversion from normalized signal to normalized density and the measurement of the fluorescence signal, is estimated via a summation of squared errors to be approximately 8% without low-pass filtering and 3.5% with low-pass filtering. IV. Fig. 1 Normalized signal versus normalized density. The maximum and minimum pressure curves are calculated by the absorption cross section/ fluorescence yield model and are shown with markers. Experimental Arrangement The technique was applied to measure the density field of the separated shear layer and turbulent wake of a wall-mounted hemisphere located in a transonic freestream flow. These conditions and geometry produce a canonical flowfield of general academic interest, as well as practical interest due to the geometrical similarities to turrets being considered for various applications. To facilitate these experiments a small-scale transonic wind tunnel was designed and constructed with the capacity for a small diameter hemisphere to be mounted to the upper wall of the test section. The general flow features of a wall-mounted hemisphere, and other bluff bodies are well established in literature [37,38,46,47]. These features include a flat-plate turbulent boundary layer upstream of the hemisphere, followed by a horseshoe and necklace vortex system that is created at the upstream junction of the hemisphere and the wall. This vortical system wraps around the base of the hemisphere and travels AIAA Early Edition / downstream to the wake region. Along the top of the hemisphere a separated shear layer forms and comprises both small- and largescale vortical motions. These vortical motions evolve into the turbulent wake downstream of the hemisphere. The shear layer and turbulent wake are the primary areas of interest due to the intense density fluctuations that exist in these regions. Downloaded by Brian Thurow on February 28, 2013 | http://arc.aiaa.org | DOI: 10.2514/1.J051678 A. Transonic Wind Tunnel and Model Geometry To facilitate experiments at transonic conditions a new nozzle, test section, and diffuser were designed and constructed to interface with the stagnation chamber and exit piping of an existing supersonic wind tunnel. By using existing air storage and compressor infrastructure the costs for the new transonic wind tunnel were greatly reduced. The tunnel is a blowdown design using regulated compressed air and exhausting into ambient conditions downstream of the diffuser. The compressed air source is a 650 cfm compressor and desiccate dryer capable of providing dry air at pressures up to 125 psig, which is stored in two large tanks that are connected to a stagnation chamber using large-diameter-compressed air lines. A pressure regulator is used to maintain roughly constant pressure in the stagnation chamber, while the storage pressure decreases. The stagnation chamber is attached to a three-dimensional smooth contour nozzle followed by the test section and then the diffuser. Run times are on the order of 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 does not incorporate corrections for boundary-layer growth. It is a fixedwall design to enable optical access of three sides of the test section using UV-fused silica windows. The bottom window has an antireflective coating to reduce reflective losses for UV light entering the test section. The test section does not contain porous walls like traditional transonic facilities, so that schlieren photography was used to ensure transient shock waves were weak enough as to not be reflected back into the region of interest. Downstream of the test section is a plate with a small convergingdiverging profile whose purpose is to create a choked flow condition after the test section but prior to the diffuser. By modifying the area ratio at the choke location a range of Mach numbers can be enforced in the test section. For the tests conducted in this study the Mach number is set to 0.78 as determined through pressure measurements. This design was chosen due to the limited control available with the existing regulators and valves, and it allows for small variations in inlet pressure without affecting the freestream Mach number. The stagnation and storage pressures are monitored and recorded over the course of each run in addition to the freestream pressure (P1 ) and Fig. 2 REID, LYNCH, AND THUROW 5 the wake pressure (P2 ). These measurements are performed using Omega PX209 transducers. The model is a 1-in.-diam hemisphere that is mounted to the ceiling of the wind tunnel, approximately 4 in. downstream from the end of the 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 to be lower than the resolution of PIV measurements (not shown), which are estimated to be about 1–2% of the freestream velocity. The hemisphere is constructed of aluminum and is anodized black. During testing some fluorescence of the hemisphere surface was encountered but was of a low enough intensity to prevent saturating the CCD detector. B. Acetone Seeding Acetone is seeded by injection into the high-pressure air supply line far upstream (∼30 ft) of the stagnation chamber and test section to allow mixing and evaporation to occur over a larger distance than if directly injected into the stagnation chamber. The seeding system is schematically presented in Fig. 3. A small pressure vessel is filled with liquid acetone and is pressurized by a nitrogen tank to approximately 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 of the compressed air supply pipe. Uniform seeding was verified by imaging the flow without the model installed, where no signs of patchy or inhomogeneous seeding were apparent. Also, to ensure that the acetone was completely evaporated and no particles remained, a scattering test was also conducted using the laser at 532 nm. In these tests a small number of particles were observed with and without acetone 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 that could be identified in the visible wavelength images. A significantly smaller number of particles are observed in the PLIF images as the scattered UV light does not transmit through the camera lens, which is not UV grade. Still, we do note that some particle-like features can be observed in the PLIF images. It is not clear what the source of these features are but speculate that it could be small oil droplets or contaminant particles that also exhibit fluorescence. The potential for a stray droplet of acetone that did not evaporate or recently formed is also a possibility; however, these occurrences are relatively sparse and effectively filtered out by the image processing. The amount of acetone seeded during a given run is estimated to be between 2–3% by mass. This was determined by observing the amount of liquid Schematic of wind tunnel test section and optical configuration. 6 AIAA Early Edition / REID, LYNCH, AND THUROW section to increase the width of the shear layer region illuminated by the most intense portion of the beam. All optics are mounted onto a translating stage, allowing multiple planes to be imaged. Imaging is performed using a Sensicam QE CCD camera (actively cooled, 1376 × 1040 pixel resolution, 6.45 μm pixel size) at 7 Hz. A 25 mm focal length lens is used with an f-number of 1.6. The images are acquired without any hardware binning. Images were obtained within the wake region of the flowfield, using a FOVof 1.8 × 1.3 in:, corresponding to a location 0.16–1.96 diameters downstream of the center of the hemisphere. In addition, to better understand the threedimensional characteristics of the overall flowfield, a small set of images was acquired for planes (streamwise–transverse) parallel to the 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 images was 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 Downloaded by Brian Thurow on February 28, 2013 | http://arc.aiaa.org | DOI: 10.2514/1.J051678 A. Wake Region Density Fields Fig. 3 Schematic of acetone seeding system that uses pressurized nitrogen to inject acetone upstream within a compressed air supply line. acetone present in the small pressure vessel prior to and after each run and calculating the tunnel mass flow rate based on pressure and velocity measurements. Toward the end of test runs local condensation of acetone occurred in the flow particularly in the separated shear layer behind the hemisphere. Similar to the particle detection method condensation was detected by direct imaging of light scattered by condensed particles when illuminated with a 532 nm laser sheet. The onset of condensation is believed to be caused by the gradual decrease in stagnation temperature experienced throughout the run as the storage pressure decreases, leading to lower temperatures in the test section. Another contributor is the slight variation in the acetone mole fraction throughout the run that is caused by the increasing pressure differential between the nitrogen tank and the compressed air supply line pipe (i.e., storage pressure) as the storage pressure drops. Note that only the mole fraction is modified, and the uniformity of the acetone seeding remains. For the purposes of data analysis the time frame of the condensation process during the run was identified. The density images acquired during this time frame of condensation were compared to those obtained during the test run when condensation was considered minimal (single, average, and standard deviation images were compared). It is interesting to note that the condensation of acetone could not be detected through direct inspection of the acetone PLIF images indicating that the condensed particles are quite small with fluorescence characteristics virtually the same as those encountered in the gas phase. This trend is not expected to hold true for larger particle sizes but suggests that small amounts of condensation can be tolerated in the application of acetone PLIF in other facilities. Based upon these conclusions all acetone PLIF density images were deemed valid and were used for statistical analysis of the flowfield. C. Optical Configuration A new wave Solo 200XT PIV laser was used to produce UV light by converting both pulses of the 532 nm output to 266 nm using a KDP nonlinear crystal. The resulting combined pulse energy was approximately 38 mJ∕pulse at 266 nm. Harmonic conversion efficiency was improved by delaying one pulse relative to the other. In these experiments the two pulses were separated by 100 ns over which time the flow would move less than 1 pixel. As shown in Fig. 2 the laser sheet is formed using a combination of spherical and cylindrical lenses, creating a beam roughly 1.5 in. wide and approximately 1 mm thick. The beam is steered at a 45 deg angle into the test A total of 344 density measurements along the centerline of the hemisphere were obtained over the course of 5 experimental runs. In addition, between 15 and 25 images were acquired at each of the 5 off-axis planes. Examples are shown herein of the centerline and one off-axis case. Figure 4 presents a set of four normalized density fields along the centerline of the hemisphere. The flow direction is from left to right, and portions of the images have been masked, which correspond to regions of low-laser energy and resulting low-signalto-noise ratio (generally less than 10). In these images, the constant freestream density values and notable lack of any intensity biases within the freestream region indicate the effectiveness and strength of the uniform seeding, as well as the image processing steps used to correct for variations in the laser sheet intensity across the imaging region. To illustrate the quantitative accuracy of the images, Fig. 5 shows two horizontal density profiles taken from the postprocessed image data displayed in Fig. 4a. The first profile was taken at a vertical location of y∕D 1.24 and was chosen to represent the freestream flow. The density measured in this region is roughly uniform with a mean value that is slightly greater than the estimated freestream density and with a standard deviation of 2.9% of the freestream value. The mean density is seen to decrease slightly, and the fluctuations increase slightly near the edges of the laser sheet due to the lower signal levels associated with this region of the image. The observed mean and fluctuating values in the freestream are in line with the uncertainty analysis discussed earlier, lending confidence to the quantitative accuracy of the measurements. The second profile was taken at y∕D 0.44 and corresponds to a slice through the center of the vortex-like structure located at x∕D ∼ 0.5 in Fig. 4a. As can be seen, the magnitude of density fluctuations visualized in the image is significantly larger than the estimated measurement uncertainty. The density in the vortex core is seen to drop significantly relative to its surroundings with a minimum density of approximately 45% to that of the freestream with the overall wake having a density on the order of 70–80% to that of the freestream. High-spatial frequency fluctuations associated with measurement noise (primarily shot noise) 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 the rich complexity of the hemispherical flowfield, as well as the novelty of the measurement technique for measuring the structure and topology quantitatively and with high-spatial resolution. It should be noted that the images in Fig. 4 have been chosen for their clarity but are not exceptional. The two most notable features present in these images is the largescale motions of the wake region and the presence of low-density cores in the shear-layer region separating the freestream from the wake. The large-scale motion of the wake region is most prevalent in Fig. 4d, where the low-density wake, with a density of 80–90% of the freestream, is separated from the high-density freestream by a sharp interface. The interface between wake and freestream fluid exhibits AIAA Early Edition / Downloaded by Brian Thurow on February 28, 2013 | http://arc.aiaa.org | DOI: 10.2514/1.J051678 a) c) Fig. 4 REID, LYNCH, AND THUROW 7 b) d) Set of four normalized density fields of the centerline plane and wake region. Dashed lines in a) indicate location where profiles are shown in Fig. 5. relatively large flapping motions with the freestream fluid nearly touching the wall at x∕d 0.9 and the low-speed wake fluid protruding 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 as indicated by relatively large drops in local density (up to 50%) that are circular in shape. These vortices are clearly seen in Figs. 4a and 4b and tend to be more distinct (i.e., smaller with larger magnitude drops in density) near the separation point. Further downstream in the shear layer the vortex cores are generally larger with a reduction in the magnitude of the density drop. It is worth noting that the density drop within the shear layer can be significantly greater than that observed Fig. 5 Density profiles taken from Fig. 4a at y∕D 1.24 (freestream) and y∕D 0.44 (center of free shear layer). in the wake; a phenomena noted in [36] and attributed to the lowpressure 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 or structures cannot be seen in the image due to the highly unsteady nature of the flow. Rather, a smooth variation in the density field is observed with the region closest to the hemisphere exhibiting the largest decrease in density. The average density field recovers rapidly to the freestream value within 1.0–1.5 diameters of the separation point. The standard deviation of the same set of 344 images is shown in Fig. 6b, providing an indication of the location and magnitude of density fluctuations. The most significant fluctuations occur within the shear layer being shed at the top of the hemisphere with peak magnitudes of 12% occurring approximately 1 diameter downstream of the separation point. This should be contrasted with the peak density fluctuations on the order of 50% for the low-density vortex cores observed in the instantaneous images of Fig. 4. Thus, the statistical data mask the separate contributions of the large-scale wake motion and small vortices contained in the shear layer. In addition, the magnitude of fluctuations observed in the freestream is approximately 2–3% of the freestream value, which is in accordance with the estimated measurement uncertainty. The magnitude increases near the edges of the laser sheet, where the incident laser sheet intensity is relatively low-producing lower signal to noise ratios. In addition to data acquired along the centerline of the hemisphere a small number of additional images were acquired along planes offset from the centerline to assess the general three-dimensionality of the flowfield. In Fig. 7a an image is shown of a plane located onequarter of a diameter from the centerline plane. In this single image the wake structure appears to have a smaller overall scale than the centerline images; this is confirmed in average images, which show a reduction in the extent of the separated region but are not shown for sake of brevity. In general, the large-scale motion of the wake 8 AIAA Early Edition / REID, LYNCH, AND THUROW Downloaded by Brian Thurow on February 28, 2013 | http://arc.aiaa.org | DOI: 10.2514/1.J051678 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 the centerline 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 diameter from the centerline. is subdued, and the shear layer appears to contain a higher concentration of small vortex cores. Figure 7b shows a plane located one-half of a diameter from the centerline plane. The large-scale motion of the wake is again noticeably smaller than the centerline case, and freestream fluid appears to protrude down through the wake region. In this case the presence of distinct vortex cores is not observed as the laser sheet is no longer oriented perpendicular to the three-dimensional shear layer. Although not the focus of this investigation the level of detail provided in the images suggests their suitability for the application of established turbulence analysis tools, such as the spatial correlation, intermittency, and fractal analysis, to provide corroborating data that more fully elucidate the flowfield in concert with other nonintrusive measurement techniques, such as particle image velocimetry. a) Fig. 8 B. Separation Region Density Fields In addition to views at off-centerline planes a closer look was also taken at the apex of the hemisphere, where a shear layer develops after the boundary layer attached to the model separates. Figure 8 shows two representative images of this closeup region. Again, the freestream region is uniform with no discernable bias. Clear delineation can be seen between the freestream fluid and the growing shear layer. A prominent feature in both the images shown here, as well as a majority of the images acquired, is the presence of a strong lambda-type shock located at the same position as the shear-layer separation point. This same shock structure was observed in schlieren imaging acquired during tunnel qualification. In the data acquired for this study large differences were seen in the early development of the shear layer. Figure 8a is an example of early b) Pair of normalized density fields of a closeup region near the apex of the hemisphere. The color map for both images is equal and identical to Fig. 4. AIAA Early Edition / shear layer growth, which appears to only consist of a large-scale separated region, whereas Fig. 8b presents an alternate mode of formation, where structure also appears to exist within more coherent structures that contain stronger density drops indicative of vortical motion. 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 a straightforward manner. This permits the use of numerical integration to yield the OPL directly from the density data as shown in Eq. (1), where variations in OPL across the beam aperture represent distortion of the beam. Wave front distortion is typically represented by the optical path difference, (OPD): Downloaded by Brian Thurow on February 28, 2013 | http://arc.aiaa.org | DOI: 10.2514/1.J051678 OPD OPL − OPL (6) where OPL is the spatial average of the OPL across the aperture of the beam. In this section we present some representative wave front distortion calculations to illustrate the potential for density measurements to be used for aerooptic analysis. A more comprehensive analysis 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 field along a path originating at the center of the hemisphere. The wave front diameter was modeled as approximately one-third of the hemisphere diameter with the beam aperture discretized into 100 equally spaced light rays. Each of the rays was propagated from a distance at the center of the hemisphere into the freestream at an angle REID, LYNCH, AND THUROW 9 of 34 deg from the wall as illustrated in Fig. 9. Within the hemisphere the index-of-refraction value is set uniformly to unity. The OPL along each light ray was determined through numerical integration of the index of refraction along this path, where it is assumed that deflections of the ray are small in comparison to the index-ofrefraction gradients. The average OPL of all 100 rays is then used to determine OPL and OPD as given in Eq. (6). The uncertainty in OPL for each ray is estimated to be approximately 0.006 μm. This value was calculated using Eq. (1) to propagate the uncertainty in density to index of refraction and the central limit theorem to estimate the uncertainty in the OPL upon integration. This value is representative of the local, small-scale fluctuations observed in the calculated OPDs, whereas the large-scale fluctuations are observed to be on the order of 1.0 μm, indicating that the calculated wave fronts are high quality. Figure 9 presents two examples of this procedure. In Figs. 9a and 9c the integration region is identified, and a local coordinate system is defined with respect to the region. In Figs. 9b and 9d the respective values of the OPD for each wave front are given. These two examples have been chosen as being representative of the influences that both large- (on the order of the hemisphere diameter) and small-scale structures have on the resulting wave front. In Fig. 9a the shear layer grows with downstream location and is host to a number of smallscale eddies that also develop in extent. However, the density fluctuations within the eddies are relatively small as compared to observations in other images. The main density fluctuations within the image are associated with the interface between the wake region and the freestream. In this case the wake is growing in the downstream direction, and the interface is inclined relative to the freestream direction such that there is a relatively steep gradient in a) b) c) d) Fig. 9 Two examples of wavefront calculations. a) and c) show the density field and region of integration; b) and d) show, respectively, the associated values of the OPD. Downloaded by Brian Thurow on February 28, 2013 | http://arc.aiaa.org | DOI: 10.2514/1.J051678 10 AIAA Early Edition / density across the beam aperture. Because of this, we consider this image to be dominated by the large-scale motion of the wake as opposed to the steep density drops associated with vortex cores. The effect of this flow pattern on the wave front in shown in Fig. 9b. The general trend of the wave front is a tilted wave front where OPD decreases with increasing x 0 . This behavior is due to the increasing length of low-density (i.e., low index of refraction and shorter OPL) fluid through which the beam must pass to get to the freestream. As such, the distortion of the wave front is seen to be dominated by the large-scale wake motion. We point out that a real beam passing through this flow would be deflected in the −x 0 ’ direction due to the tilt 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 lowdensity wake is oriented roughly horizontal relative to the freestream, producing a milder density gradient associate with the wake across the beam aperture. Thus, the effect of the intense eddy in the shear layer should have a more pronounced effect on the wave front distortion than the wake. The resulting wave front shown in Fig. 9d, however, does not exhibit a strong feature that can clearly be associated with the intense eddy contained in the shear layer. Rather, the distorted wave front is relatively flat in comparison to Fig. 9b due to the horizontal inclination of the large wake region. In addition, the effect of the eddy is somewhat counteracted by a high-density region of fluid positioned slightly upstream. By examining the full set of images acquired along the centerline similar trends were observed. The dominant source of fluctuations in OPD can be associated with the large-scale motions of the wake region with the contributions of individual eddies contained in the shear layer, even intense ones, having a lesser effect on the wave front distortion. This follows from intuition, and because the calculation of the OPL is an integration the magnitude of fluctuations in density can at 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 for this 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 of the density. The results found here were for a particular beam size pointed in a particular direction. Using the same set of data similar analysis could be performed for beams with different characteristics. We also note that this technique can also be extended to perform a statistical analysis of the wave front distortions, enabling parameters, such as the OPD ensemble average and standard deviation, to be determined. Because the wave front is calculated after the run is complete it is also possible to develop optimization routines to modify the beam aperture and angle in concert with the integration approach to reduce the effects of aerooptical distortion in a way that would be difficult with direct optical measurements. VI. Conclusions A technique has been demonstrated for measuring density in a high-speed, compressible flowfield through the use of acetone planar laser-induced fluorescence (PLIF). Key aspects of the present implementation of the technique include uniform seeding of acetone vapor throughout the flow, an in situ calibration procedure based on the uniform properties of the freestream, and the modeling of uncertainty in the fluorescence signal due to uncertainty in the local pressure. The uncertainty due to pressure is estimated to be 2.5% with the overall uncertainty estimated to be approximately 8% without low-pass filtering and 3.5% with low-pass filtering. Thus, the most significant improvements are expected to come through increased signal-tonoise ratio (SNR) of the images. This can be realized through the use of higher energy laser pulses, spatial beam shaping to more uniformly distribute the energy contained in the incident pulse, and the use of more sensitive cameras with high-dynamic range. The utility of the technique was demonstrated through the visualization of the density field in the wake region and separated shear layer generated by a wall-mounted hemisphere. The resulting density fields revealed highly complex, intermittent, and three-dimensional REID, LYNCH, AND THUROW structures in the wake. Prominent features included a sharp interface between the low-density wake and the higher density freestream, the position of which exhibited a large-scale flapping type of motion. This interface was also populated by a number of small diameter, lowdensity structures that provide for a smoother transition between the freestream and wake region. These smaller structures are believed to be associated with pressure wells at the core of strong vortical motions. The drop in density at the core of these vortices can be quite significant, dropping to 50% of the freestream value in some cases. Finally, near the separation point, distinct lambda-type shock structures appeared to be a dominant feature throughout the testing. Overall, this technique was very effective at visualizing the density field 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 indexof-refraction field. The main weakness to this method is that it has not been 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 for the estimation and analysis of aerooptic effects. A significant advantage for the use of planar density data is the ability to simulate varying beam parameters, such as aperture and size using a single image. Acknowledgments An Air Force Office of Scientific Research (AFOSR) Young Investigator Program Grant (FA9550-08-1-0150) funded this work. The authors would like to thank Abhishek Bichal and Tim Fahringer for assistance with experiments, Andy Weldon for continued assistance with machining work, and David Wall for designing the transonic facility and assisting with its construction. The authors would also like to thank Anwar Ahmed from Auburn University for the use of a new wave Solo 200XT Particle Image Velocimetry (PIV) laser. 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