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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
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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
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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
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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
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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.
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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
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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.
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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.
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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
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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
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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
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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.
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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):
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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.
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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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G. Elliott
Associate Editor