NASA Technical Reports Server (NTRS) 20120004219: Time-Average Molecular Rayleigh Scattering Technique for Measurement of Velocity, Denisty, Temperature, and Turbulence Intensity in High Speed Nozzle Flows

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by  NASA Technical Reports Server (NTRS)

AIAA 2004-706
42nd AIAA Aerospace Sciences Meeting and Exhibit
5 - 8 January 2004, Reno, Nevada
42nd AIAA Aerospace Sciences Meeting and Exhibit
5-8 January 2004 / Reno, NV
TIME-AVERAGE MOLECULAR RAYLEIGH SCATTERINGTECHNIQUE FOR
MEASUREMENT OF VELOCITY, DENSITY, TEMPERATURE, ANDTURBULENCE
INTENSITY IN HIGH SPEED NOZZLE FLOWS
Amy F. Mielke*
Richard G. Seasholtz†
NASA Glenn Research Center, Cleveland, OH 44135
Kristie A. Elam‡
Akima Corporation, Fairview Park, OH 44126
Jayanta Panda§
OAI, Brook Park, OH 44142
ABSTRACT particles is not an option, and where the environment is
too harsh for hot wire measurements. A similar
A molecular Rayleigh scattering based flow Rayleigh scattering technique has been used
diagnostic is developed to measure time average successfully in the past to make temperature and
velocity, density, temperature, and turbulence intensity velocity measurements in harsh environments1,2.The
in a 25.4-mm diameter nozzle free jet facility. The presented technique uses a slow scan, low noise CCD
spectrum of the Rayleigh scattered light is analyzed camera to record fringes formed by Rayleigh scattered
using a Fabry-Perot interferometer operated in the static light and reference laser light passing through a Fabry-
imaging mode. The resulting fringe pattern containing Perot interferometer. Nonlinear least squares analysis
spectral information of the scattered light isrecorded based on a kinetic theory model of Rayleigh scattering
using a low noise CCD camera. Nonlinear least squares is used to obtain density, velocity, and temperature
analysis of the fringe pattern using a kinetic theory information from the fringe images. A technique for
model of the Rayleigh scattered light providesestimates extracting turbulence intensity information from the
of density, velocity, temperature, and turbulence fringe image data is also investigated. Extracting
intensity of the gas flow.Resulting flow parameter turbulence intensity information from the fringe image
estimates are presented for an axial scan of subsonic data is a challenge since the fringe is broadened by not
flow at Mach 0.95 for comparison with previously only turbulence, but also by thermal fluctuations,
acquired pitot tube data, and axial scans of supersonic aperture effects from collecting light over a range of
flow in an underexpanded screeching jet. The issues scattering angles, and laser frequency drift over the
related to obtaining accurate turbulence intensity integration time of the measurement.The presented
measurements using this technique are discussed. technique is used to study subsonic and supersonic air
flows in a 25.4-mm diameter nozzle free jet facility.
INTRODUCTION
Point-wise measurements of turbulence
The objective of this work is to obtain high intensity aretraditionallyobtained using hot wire
accuracy measurements of time average velocity, anemometry or Laser-DopplerVelocimetry (LDV)3,4,5,6.
density, and temperature in unseeded flows using a However, these techniques have obvious disadvantages.
nonintrusive, point-wise measurement technique based Hot wire anemometry requires that a physical probe be
on molecular Rayleigh scattering. A measure of the placed in the flow field, hence disturbing the true flow
flow turbulence intensity is desired as well. The data characteristics. Although LDV is a nonintrusive
obtained from these measurements is useful for technique, it has the disadvantage of requiring seed
validation of computational fluid dynamics (CFD) particles in the flow, which always has difficulties
codes. This nonintrusive technique is particularly useful associated with it. Other optical based techniques for
in supersonic flows where seeding the flow with measuring turbulence intensity have been investigated.
Elliot and Boguszki7 investigated a filtered Rayleigh
scattering technique to make turbulence intensity
measurements using a pulsed laser to get instantaneous
quantities. Transient gradient spectroscopy (TGS)8, also
known as Laser-Induced Thermal Acoustics (LITA)9, is
a point-wise technique that measures instantaneous
temperature, velocity, and species concentrations, and
1
American Institute of Aeronautics and Astronautics
This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.
is capable of providing turbulence intensity
scattered light wave vectors, k and k , from light
information. Bridges et al10 used Particle Image 0 s
incident on a moving particle:
Velocimetry (PIV) to calculate turbulence in nozzle
flows from instantaneous 2-D velocity maps. Nakatani K=ks (cid:8)k0 (4)
et al11 developed a pulsed luminescence method in 4(cid:10)(cid:17) (cid:18) (cid:14)
K= K = sin s (5)
which the turbulence intensity is measured from the (cid:15) (cid:12)
(cid:19) (cid:16) 2 (cid:13)
diffusion width of the emission according to Taylor’s
diffusion theory. Garg and Settles12 developed a uk =K(cid:7)u/K (6)
technique based on focusing schlieren deflectometry to where (cid:19) is the wavelength of the incident light, and(cid:18)
s
make turbulence measurements in compressible flows. is the scattering angle between the incident and
The presented Rayleigh scattering technique is unique scattered light wave vectors. The geometry of the
in that it provides simultaneous time-average density, optical arrangement in an experiment can be designed
velocity, temperature, and turbulence intensity such that the desired velocity component is measured.
measurements at a point in a flow field. The ability to
make multiple property measurements simultaneously For higher density gases, the Gaussian model
is a valuable tool for jet flow research. is not accurate since the Rayleigh spectrum broadens
and eventually develops side-lobes as shown in figure
THEORY 3. A nondimensional parameter y is used to characterize
the density regime:
Molecular Rayleigh scattering is the result of p
y = (7)
elastic light scattering from gas molecules. The
(cid:20)Ka
frequency of the scattered light is equal to the
where p is the gas pressure and (cid:20) is the gas viscosity.
frequency of the incident laser light altered by the
Three density regimes are defined for typical 90o-
Doppler effect due to the motion of the molecules. The
scattering. A low density regime exists for y<<1 where
Rayleigh scattering spectrum contains information
the Gaussian model is valid. A high density regime
about the gas density, bulk velocity, and temperature.
exists for y>>1 where a Continuum model is valid. The
Figure 1 shows a Rayleigh scattering spectrum
regime for y ~ 1 requires the use of a kinetic theory
containing the narrow laser line and the broadened
model.13
Rayleigh spectral peak. The total intensity of the
Rayleigh spectrum is directly proportional to the gas
For our application y is approximately 1. A
density. The Doppler shift between the laser peak and
model developed by G. Tenti14,15 provides a kinetic
the Rayleigh peak is proportional to the bulk flow
model of Rayleigh-Brillouin scattering from molecular
velocity. The width of the Rayleigh spectrum is related
gases in all density regimes. The TENTI S6 model is
to the gas temperature.
the chosen spectrum model for least-squares fitting of
our data.
For low density gases, the Rayleigh spectrum
is accurately modeled by a Gaussian function:
The spectrum of the Rayleigh scattered light is
(cid:6) K(cid:7)u(cid:3)2
SR(xf )= 1 e(cid:8)(cid:4)(cid:5)xf(cid:8)Ka(cid:1)(cid:2) (1) ainntaelryfzeerodm uestienrg oap pelraanteadr mini trhroer s Ftaatbicr yi-mPaegroint g mode16.
(cid:10)
The fringes at the output of the interferometer are
where x is the dimensionless frequency defined as
f focused onto a CCD detector. The fringe intensity
2(cid:10)(f (cid:8) f )
xf = 0 , (2) pattern is a function of the Rayleigh spectrum, SR, and
Ka the Fabry-Perot instrument function, I . The Fabry-
FP
a is the most probable molecular speed defined as Perot instrument function is:
2(cid:11)T
a= , (3)
[ ]
m I (cid:23)(x ,r) = 1 (8)
where (cid:11) is the Boltzmann constant, T is the fluid FP f (cid:23)(x ,r)
1+F sin2 f
temperature, m is the molecular mass, f-f is the
0 2
frequency shift between the reference laser light and the
1
Rayleigh scattered light, and K is the interaction wave where F = , (9)
vector that defines the direction of the velocity sin2(cid:4)(cid:6) (cid:10) (cid:1)(cid:3)
(cid:4) (cid:1)
component, uk, being measured. As shown in figure 2, (cid:5)2Ne (cid:2)
the interaction wave vector, and hence the measured
(cid:23) is the phase change of the light between successive
velocity component, are defined by the incident and
reflections given by:
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4(cid:10)µd (cid:17)(cid:26)2 (cid:8)(cid:26)2 (cid:19)a (cid:14) (cid:30)p is the pixel width (square pixels are assumed),Af is
(cid:23)= (cid:15) R + x (cid:12), (10) the amount of light at the laser frequency, A is the
(cid:19) (cid:15)(cid:16) 2 c(cid:25) f (cid:12)(cid:13) amplitude of the light scattered from particleps, and B is
g
N is the effective finesse,(cid:1)µ is the refractive index of the amount of broadband light.If the flow is turbulent,
e
the medium in the Fabry-Perot cavity, d is the Fabry- the Rayleigh scattering spectrum S in equation (12) is
R
Perot mirror spacing,(cid:26)is the angle between the ray and replaced by the following spectrum:
optical axis ((cid:26) = r /f , (cid:26) = r/f ), r is the fringe radius "
R R L L R S (x ,u ,(cid:29) )= ! S (x ,u )p(u ,u ,(cid:29) )du
of the reference laser light, r is the radial position in the T f k uk R f k k k uk k
(cid:8)"
image plane, f is the fringe forming lens focal length,
L (13)
and (cid:25) = 2(cid:10)/K.
and the model of the particle scattering is modified as:
In our experiment, Rayleigh scattered light
from a defined probe volume is collected into a Ap yq+!(cid:30)p xq+!(cid:30)p "! p(u ,u ,(cid:29) )I (x ,r)du dxdy
multimode optical fiber. The fiber carries the light to (cid:30)2p yq xq (cid:8)" k k uk FP f k
another area where a Fabry-Perot interferometer is used
(14)
to spectrally resolve the light. A low-noise CCD camera
where a Gaussian probability distribution is assumed
is placed at the output of the Fabry-Perot interferometer
for the velocity component, u ,
k
and a fringe forming lens focuses the interference fringe
pattern onto the CCD detector. The total expected (cid:8)1(cid:4)(cid:6)uk(cid:8)uk(cid:1)(cid:3)2
number of photoelectron counts incident on the detector p(u ,u ,(cid:29) )= 1 e 2(cid:4)(cid:5) (cid:29)uk (cid:1)(cid:2) , (15)
plane without the Fabry-Perot interferometer in the k k uk (2(cid:10))1/2(cid:29)u
k
optical path is expressed as: and the turbulent fluctuations are assumed to be
(cid:30)P nL (cid:19)(cid:31) t(cid:6)d(cid:29)(cid:3) isotropic with standard deviation:
N = 0 x (cid:4) (cid:1)sin2(cid:18) (11)
R hc (cid:5)d(cid:31)(cid:2) s (cid:29) = (u(cid:8) u )2 1/2 =(cid:17)(u (cid:8)u )2(cid:14)1/2 (16)
where (cid:30) is the overall system efficiency including uk (cid:15)(cid:16) k k (cid:12)(cid:13)
detector quantum efficiency and other losses, P is the The turbulence intensity is generally defined as:
0
power of the incident laser beam, n is the molecular (cid:29)
number density, L is the probe volume length, (cid:31) is the TI = uk (17)
x U
solid light collection angle, t is the data acquisition j
where the turbulent fluctuations are normalized by the
(cid:6)d(cid:29)(cid:3)
time, (cid:4) (cid:1)is the differential scattering cross-section jet centerline velocity at the nozzle exit, U. This model
(cid:5)d(cid:31)(cid:2) function is used to estimate the unknown pjarameters
of the gas molecules, h is Planck’s constant, and c is the from the experimental data.
speed of light. If we assume that illumination is uniform
over the entire fiber face, then the model function for
Measurement uncertainty
theamount of energy collected on the qth pixel of the
detector, expressed as photoelectron counts including
The lower bound on the uncertainty indensity,
light at the laser frequency, light scattered from
velocity,temperature, and turbulence intensity
particles (Mie scattering) and background light,as
measurements using Rayleigh scattering is set by the
imaged through the Fabry-Perot, is:
photon statistical noise. Estimates of the measurement
uncertainty in the unknown parameters for this
Nq =(cid:10)Nrm2Rax yqy+!q(cid:30)p xqx+!q(cid:30)p(cid:8)+!""SR(xf )IFP(xf ,r)dxfdxdy ftReuacnohc ntlioioqwnu eeor f cb aaon su ebnted o 1o7fb. utFanoiknrn eaod wm bney a csaulrceumlaetnint gth tahte i sC ara mer-
+ Af yq+!(cid:30)p xq+!(cid:30)Ip (x ,r)dxdy parameters,(cid:1)=[%1,%2,%3,...], the variance of the
(cid:30)2p yq xq FP f0 estimates of the parameters %i is:
A y +(cid:30) x +(cid:30) [ ]
+ p q! p q!Ip (x ,r)dxdy+B (12) V(%ˆ )= &(cid:8)1 (18)
(cid:30)2p yq xq FP f g i
wherermax is the radius of the image of the fiber face, where (cid:2)is the Fisher information matrix given (for
(x,y) are the position coordinates in the image plane, Poisson statistics) by:
r = (x(cid:8)x )2+(y(cid:8)y )2 where (x ,y ) are the
0 0 0 0
coordinates of the center of the fringe pattern, (xq,yq) are & =( 1 ’ Nq ’ Nq (19)
the coordinates of the lower left corner of the qth pixel, i,j q Nq ’%i ’%j
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A process governed by Poisson statistics is one in than 40%. At higher Mach numbers, the error in
which the mean is equal to the variance. In this case, temperature will be larger for the same turbulence
the mean of the photon counts is theoretically equal to intensity.
the variance of the counts.
EXPERIMENT
The Cramer-Rao lower bound estimates for
our actual Fabry-Perot interferometer and CCD system, Image data were acquired in a free jet and
assuming the TENTI S6 spectrum model for the analyzed using the described nonlinear least-squares
Rayleigh scattered light and including read noise, method to obtain time-average density, velocity, and
overall efficiency of the system, and other significant temperature measurements.In some cases,we
factors, have been calculated for various flow cases attempted to obtain turbulence intensity measurements.
representing a range of y-parameter values.The lower Figure 6 shows a schematic of the experiment setup.
bound measurement uncertainty in density, velocity, The top section of the figure shows the setup around the
and temperature when fitting for ), u, T, (cid:29) ,x , and y jet facility including the laser, collection optics, and
k uk 0 0
were about 0.1%, 0.3 m/s, and 0.3%, respectively. optical fiber. The lower section of the figure shows the
Figure 4 shows the lower bound measurement optical processing system, which was located in a
uncertainty in (cid:3) for y-parameters ranging from 0.75 separate, quiet area away from the noisy jet since the
u
k processing equipment is extremely sensitive to
to 1.9 for (cid:3) =5, 10, and 20 m/s. As y increases, the
u vibration and temperature fluctuations.
k
uncertainty level decreases. Also, as (cid:3) decreases, the
u
k A convergent nozzle was operated over a
uncertainty becomes even greater to the point where the
Mach number range of 0.15-0.95 in the subsonic flow
uncertainty in (cid:3) exceeds the actual value of(cid:3) .
u u regime,and at Mach 1.19 and 1.4 in the underexpanded
k k
flow regime. Since the measurement technique relies on
The ability to extract turbulence information having a clean gas flow, the unheated compressed air
from the spectrum improves as the Rayleigh spectrum supplied to the primary jet was passed through micron
deviates from a Gaussian. This occurs only for y greater filters to reduce the amount of dust, oil and water in the
than about 0.8. For y less than this value, the Rayleigh air. Additionally, an air blower and filter system
spectrum is close to Gaussian and the effect of provided a 200-mm diameter filtered, low speed (~20
turbulence broadening, which is assumed to be m/s) coflow around the primary jet to clean the
Gaussian, cannot be separated from the Rayleigh entrained ambient air. The coflow allowed particle-free
spectrum. The dependence of turbulence measurement measurements to be made well outside the shear layer
on spectral shape indicates that having the right model and further downstream than would be possible
of the spectrum is extremely important. From the lower otherwise. The total pressure of the air flow was
bound analysis, we conclude that the ability to obtain measured by a pressure transducer located in the
meaningful turbulence information is restricted to flows plenum of the jet.
where (cid:3) is greater than 10 m/s and y is greater than
u
k A 5W, 532 nm, single-frequency,
0.8.
Nd:Vanadate CW laserwith 2.25-mm output beam
The model of the imaged fringe pattern
diameter provided the incident light for the system. The
described above was used to generate simulated images
laser light was focused by a 350-mm focal length lens
with conditions similar to those expected in our
to a 200µm diameter beam at the probe volume
experiment. Simulated images were generated with a
location.Rayleigh scattered light is polarization
known amount of turbulence intensity over a range
dependent, so a half-wave plate was used to align the
TI=0 to 100% assuming isentropic flow conditions for
peak scattering plane with the collection optics. The
Mach 0.6. Poisson noise was added to the images.
beam was oriented in the horizontal direction, 45o to the
These images were analyzed fitting for ), u,T, x , and
k 0 flow axis. The collection optics were arranged such that
y , while TI was assumed to be 0%. The purpose of this
0 light was collected at a nominal scattering angle of 90o,
exercise was to determine how the estimated ), u, and
k and was first collimated by a f/3.67 300-mm focal
Tvalues vary from the true values if turbulence is
length achromat, and then focused by a 160-mm focal
ignored. Figure 5 is a plot of the error in temperature as
length achromat on the face of a 0.55-mm diameter
a function of turbulence intensity.This gives an
multimode optical fiber. The combination of fiber
indication of the expected error in the temperature
diameter, laser beam diameter, and magnification ratio
measurement if turbulence is ignored. If the turbulence
provided a probe volume with a length of 1.03-mm and
intensity is less than 40% in this case, the error in the
cross-sectional area of 0.155-mm2.
temperature measurement is negligible (less than 2%).
The velocity varied by less than 1 m/s and the density
varied by less than 2% for turbulence intensities less
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The laser, transmitting optics, and receiving parallel during the times when spectral data was not
optics were all mounted on a x-y traversing system so being acquired. When the data acquisition cycle was
that the probe volume could be moved to any location started, the prisms that direct the fringes towards the
in the jet plume. The incident and scattering wave stabilization camera were removed from the optical
vectors were arranged such that the axial component of path and a reference fringe image was acquired using
the velocity was measured. When necessary, a mirror the low noise CCD camera and 10 ms exposure time.
and diffuser were placed in the beam path to direct Figure7a shows a typical fringe image formed by
unscattered laser light into the fiber for stabilization of reference laser light obtained in this experiment. The
the Fabry-Perot interferometer, and also to obtain mirror and diffuser, which allow reference laser light to
reference laser fringe data. be directed into the fiber in the test cell,were removed
from the optical path so that the laser beam was
The 20-m length optical fiber was routed to a directed through the probe volume in the flow field.
separate room where the Fabry-Perot interferometer and Rayleigh scattered light from the probe volume was
detection optics were located. The lower section of collected and sent through the optical fiber to the
figure 6 shows the layout of the detection system. The optical processing system. Two consecutive Rayleigh
light exiting the fiber was collimated by an 80-mm images were acquired using the CCD camera and 1 s
focal length lens. A portion (~10%) of this light was exposure time.Figure 7b shows a typical fringe image
split off and sent toward a set of photomultiplier tubes formed by Rayleigh scattered light. The region of the
(PMT’s) operated in the photon counting mode for the detector where the measurements were taken happened
density measurement. The light that was split off was to have some bad pixels. These pixels were not used in
split again by a 50/50 beamsplitter before reaching the the image processing. The Rayleigh fringe shown
PMT’s. Half of the light was sent to one PMT and half corresponds to a velocity of 240 m/s. The peak of the
was sent to the other. Each PMT made an independent Rayleigh fringe is shifted from the reference fringe
measurement of the density at the same point in the peak by the Doppler shift associated with this velocity.
flow, and the average of the two PMT signals provided For our experimental arrangement, the fringe diameter
the mean density measurement.The rest of the light that decreased as velocity increased. Also the Rayleigh
was not sent to the PMT’s was directed through the fringe is more diffuse than the reference fringe due to
planar mirror Fabry-Perot interferometer. The thermal broadening.
interferometer had 70-mm diameter mirrors with 85%
reflectivity, 9.6 GHz free spectral range (FSR), and Immediately following the capture of two
reflective finesse of approximately 19. Rayleigh fringe images, the PMT’s were triggered to
collect density data for 10 seconds at 10 kHz sampling
When not acquiring flow data, a stabilization rate. The mirror and diffuser were then replaced in the
routine was performed to maintain parallelism between optical path to direct reference laser light to the optical
the Fabry-Perot mirrors and also to maintain a constant processing location and obtain a second reference
reference fringe radius. This procedure requires laser fringe image at 10 ms exposure time. The second
light to be directed into the optical fiber and through the reference fringe was used to check for drift in the laser
Fabry-Perot interferometer, and a prism assembly to be frequency. If the fringe radius drifted by more than 3-
placed at the output of the interferometer. The feedback µm between the first and second reference fringe
data is collected by the video camera shown in the images, then the Rayleigh data for that acquisition cycle
lower section of figure 6. Seasholtz et al18 gives a was rejected. The prisms were moved back into the
detailed description of the stabilization procedure. optical path and control was restored to the stabilization
routine to reestablish the desired fringe radius, in case
When obtaining flow data, the prisms were the system had drifted during data acquisition due to a
removed from the optical path and the light exiting the change in laser frequency or temperature fluctuations
interferometer was focused by a 200-mm focal length inside the Fabry-Perot interferometer.The time needed
fringe forming lens onto the detector of a slow scan, to completethe acquisition process for a single data
low noise CCD camera with 27-µm square pixels. This point was approximately 1 minute. This procedure was
formed a 1.38 mm (50 pixel) diameter image of the repeated for each data point.
fiber face at the detector plane. The diameter of the
optical fiber limited us to imaging only the central RESULTS
fringe of the concentric fringe interference pattern.
Calibration
A standardized procedure was used for
collecting data at a single point in the flow field. The Reference fringe images were acquired over a
stabilization routine was used to maintain the reference range of fringe radii from 50 to 500 µm to determine an
fringe radius at the desired target value and the mirrors effective finesse relationship and incident intensity
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American Institute of Aeronautics and Astronautics
pattern to use for the Rayleigh image processing. The temperature were partially correlated using the chosen
reference images were fit for amplitude, A, effective model function.
f
finesse, N, fringe radius, r , and center position, (x ,
e R 0
y ). The baseline noise level was accounted for by The finesse and intensity profile relations were
0
subtracting a mean value at each pixel obtained from a determined from data taken on one particular day and
series of images taken with the laser light off and the were applied to data taken on other days. Different
camera shutter closed. The finesse and intensity effective efficiency factors were determined from the
amplitude were functions of radius in the image plane calibration data taken on each particular day and
as shown in figures 8 and 9. The reason that these applied to data taken only on that day. For each day the
parameters are not uniform across the image plane may efficiency factors were fairly repeatable with values
be a result of defocusing as we move away from the being about 0.9%. The image files were fit for u,T, x ,
k 0
lens centerline or imperfections in the Fabry-Perot and y , with ) determined from the PMT data. Figures
0
mirrors.The finesse and intensity pattern relationships 11, 12, and 13 show the differences between the
were incorporated into the model for the Rayleigh measured density, velocity, and temperature and the
fringe analysis. isentropic values for four different run days with the
calibrated finesse and intensity profile relations and
Calibration data for the Rayleigh scattered efficiency factors applied. The reference fringe radius
light was acquired over a range of velocities from 50 to was obtained from the reference fringe image.
300 m/s (y = 0.7 to 0.9) to obtain an overall efficiency Turbulence intensity was assumed to be 0% since
factor for the detection system. The calibration data previous analysis showed that measurements are not
were taken at a location in the flow that was 3 significantly affected by assuming zero turbulence for
diameters downstream of the nozzle exit on the flow low turbulence cases. The standard deviation of the
centerline where the true flow parameters are known error is shown on each figure. The densities are within
relatively accurately from the isentropic flow equations. 1% of their true (isentropic) values, velocities fall
There was some question about the exact scattering within 2-3 m/s of their true values, and temperatures are
angle of the optical system. Therefore, the Rayleigh within 2% of their true values. Although the finesse
image data were fit for scattering angle (cid:18), effective and intensity profile calibrations were not performed
s
efficiency (cid:30), reference fringe radius r , and center for each day of data collection, the accuracy of the
R
position (x , y ), while the density, ), velocity, u, and recovered values on the other days was not sacrificed.
0 0 k
temperature,T, values were held fixed at the known
isentropic values. Light at the laser frequency and light The calibration data was acquired at a location
scattered from particles was negligible and was ignored where turbulence levels were on the order of 1% or less
in the model for analysis of all Rayleigh fringe data. ((cid:3) (cid:4) 3 m/s). The images were analyzed again, this
u
The resulting scattering angle was approximately 92.3o. k
time also fitting for the turbulentvelocity fluctuations
Using this scattering angle in the model, the Rayleigh
rather than assuming them to be zero. The results
image data were fit for (cid:30), r , x , andy , while the
R 0 0 indicate that the error in turbulence intensity was very
density,),velocity, uk, and temperature,T, values were high for these flows, and there is greater error as
held fixed to obtain a mean effective efficiency factor velocity decreases since the y-parameter decreases with
for each day that data was acquired. Turbulent velocity decreasing velocity. Also, velocity fluctuations are very
fluctuations(cid:3) were assumed to be zero since the small at this location in the core of the jet, so we expect
u
k
probe volume was well within the potential core. The the turbulence estimates to have a high level of
broadband light and read noise were accounted for in uncertainty.The temperature measurements also had
the same manner as in the reference fringe image higher errors than expected because the broadening of
processing described above. the spectrum was mistaken as broadening from
turbulence. The high estimates of (cid:3) indicate that we
u
k
The same calibration points that were used to cannot measure turbulence in these flows.
determine the efficiency factor of the detection system
were also used to calibrate the density data from the Converging nozzle, Mach 0.95 flow
PMT’s. A calibration was performed on each day that
data was taken. The relationship between density and An axial scan of Mach 0.95 flow issuing from
photon counts is linear, as shown in figure10 where a 25.4-mm diameter converging nozzle was performed
density is plotted as a function of mean photon counts along the jet axis. Pitot tube velocity data is available
for a typical calibration data set. The PMT data is used for similar flow conditions to use for comparison
as a measure of the density rather than fitting for it in purposes. Figure 14demonstrates good agreement
the least squares analysissince the density and between the velocities obtained using both
measurement methods. This gives confidence that the
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American Institute of Aeronautics and Astronautics
velocity results obtained from the Rayleigh scattering In the potential core of the jet flow, (cid:29) is low
uk
measurement method are reliable. and we cannot fit for turbulence. In regions outside of
the mixing layer where temperatures are high, they
Underexpanded flows value is too low to extract turbulence. For our
measurements, the only regions where we can expect to
Centerline axial scans were performed in extract turbulence is in the mixing regions of high
Mach 1.19 and Mach 1.4 underexpanded flows using a Mach number flows where temperature is low and the
converging nozzle. The Rayleigh image data were expected (cid:29) is high. In general, we should be able to
uk
processed with the assumption that TI is zero, which is measure turbulence in cases where y is greater than or
not exactly accurate, so the temperature calculations equal to 1. This is the case for high density flows at any
may be shifted from their true values since the scattering angle, and lower density flows using forward
additional broadening from turbulence may be scattering. Although turbulence cannot be extracted in
construed as thermal broadening. Figures 15, 16, and 17 all cases, it has been shown that low levels of
show density, velocity, and temperature as a function of turbulence do not affect the ability to measure
axial position for Mach 1.19 and Mach 1.4 temperature, if we assume zero turbulence.
underexpanded flows. The isentropic flow conditions
for fully expanded flow corresponding to the measured Based on the findings from this work there are
total and static pressures are shown on each plot as a several things we would like to look at in the future. We
reference, although the isentropic flow relations are no would like to make measurements in higher density
longer valid in these underexpanded flows.The shock flows and in low density flows using forward scattering
structure can be seen in these plots as characterized by to show that we can measure turbulence in these cases.
high to low velocity fluctuations. Figure 18 is a In the current work, temperature fluctuations and
schlieren photograph of the Mach 1.19 underexpanded aperture broadening were not taken into account in the
flow showing the shock structure. The temperature and model. A quick check indicated that aperture
density plots show fluctuations in accordance with the broadening would not significantly affect results of this
shock locations indicated by sharp velocity fluctuations study. Since extracting turbulence information is highly
in figure16. The shocks in the Mach 1.19 flow are dependent on the shape of the spectrum, having the
closer together than in the Mach 1.4 flow. Far correct model for the spectrum is important. Both
downstream of the nozzle exit, theshock structure aperture broadening and temperature fluctuations will
dissipates and the density approaches ambient. It is have an effect on the spectral shape and it is important
difficult to make a statement of accuracy for the to include theireffects in the model.
velocity and temperature measurements since we do not
have data to compare them with. There are several other approaches to
measuring turbulence based on Rayleigh scattering.
Discussionand Future Work One approach is to record a number of instantaneous
spectra using a pulsed laser and use the velocities
The density, velocity, and temperature obtained from these spectra to calculate the turbulence
measurements using the Rayleigh scattering technique intensity. Another approach is to use the dynamic
described showed good agreement with expected technique using a CW laser and high sampling rate data
values, even when turbulence is ignored. Extracting acquisition which we have developed independently of
turbulence intensity proved to be a difficult task in the this work18. This technique works well for measuring
flows studied here. The ability to extract turbulence velocity and density fluctuations, but currently is not
information is dependent on the shape of the Rayleigh capable of dynamic temperature measurement. A third
spectrum. For y less than 0.8 the Rayleigh spectrum is approach is to add particlesto the flow and use the
close to Gaussian and the turbulence broadening, which spectral broadening of the peak resulting from particle
is assumed to be Gaussian, cannot be separated from scattering to measure turbulence. The width of the Mie
the Rayleigh spectrum. When y is greater than 0.8 the scattering spectral peak is only the instrumental
Rayleigh spectrum deviates from a Gaussian and allows bandwidth of the Fabry-Perot when no turbulence is
the turbulence to be decoupled from the thermal present. For turbulent flows, the broadening of the peak
broadening of the Rayleigh spectrum. Also, the should give a sensitive measure of the turbulence.
uncertainty in turbulence is much greater for small
values of (cid:29) . From a lower bound uncertainty analysis CONCLUDING REMARKS
uk
we determined that the ability to obtain turbulence is
restricted to flows were y is greater than 0.8 and (cid:29) is A Rayleigh scattering techniqueto measure
uk
greater than 10 m/s. time average velocity, density, temperature, and
turbulence intensity was developed. The technique
allowed measurement of density, velocity, and
7
American Institute of Aeronautics and Astronautics
temperature with accuracies of 1%, 2-3m/s, and 2%,
respectively. Simulations showed that for low 9 Hart, R.C., Balla, R.J., and Herring, G.C.,
turbulence flows the estimates of density, velocity, and “Nonresonant referenced laser-induced acoustics
temperature are not significantly affected if turbulence thermometry in air,” Applied Optics, vol. 38, pp.
intensity is assumed to be 0%. Comparison of pitot tube 577-584, 1999.
velocity data with velocity results from the Rayleigh
scattering technique for Mach 0.95 flow showed very 10 Bridges, J., Wernet, M., and Brown, C., “Control of
good agreement. Axial scans of two underexpanded Jet Noise Through Mixing Enhancement,”
flows revealed shock locations. NASA/TM-2003-212335, 2003.
Turbulence intensity could not be recovered in 11 Nakatani, N., Matsumoto, M., Ohmi, Y, and Yamada,
any flow cases studied here due to either low turbulence T., “Turbulence measurement by the pulsed
or low y-parameter. Future work is planned to study luminescence method using a nitrogen pulse laser,”
higher y-parameter cases where it is expected that J Phys E: Sci Instrum, vol. 10, pp. 172-176, 1976.
turbulence estimates can be made with some degree of
accuracy. 12 Garg, S., and Settles, G.S., “Measurements of a
supersonic turbulent boundary layer by focusing
REFERENCES schlieren deflectometry,” Exp Fluids, vol. 25, pp.
254-264, 1998.
1Seasholtz, R.G., and Greer, L.C., “Rayleigh Scattering
Diagnostic for Measurement ofTemperature and 13 Greytak, T.J., and Benedek, G.B., “Spectrum of Light
Velocity in Harsh Environments,” AIAA98-0206, Scattered from Thermal Fluctuations in Gases,”
1998. Phys Rev Letters, vol. 17, pp. 179-182, 1966.
2Panda, J., and Seasholtz, R.G., “Velocity and 14Boley, C.D., Desai, R.C., and Tenti, G., “Kinetic
temperature measurement in supersonic free jets Models and Brillouin Scattering in a Molecular
using spectrally resolved Rayleigh scattering,” Gas,” Canadian Journal of Physics, vol. 50, pp.
AIAA99-0296, 1999. 2158-73, 1972.
3 Lau, J.C., Morris, P.J., and Fisher, M.J., 15 Tenti, G., Boley, C.D., and Desai, R.C., “On the
“Measurements in subsonic and supersonic free jets Kinetic Model Description of Rayleigh-Brillouin
using a laser velocimeter,” J Fluid Mech, vol. 93, Scattering from Molecular Gases,” Canadian
pp. 1-27, 1979. Journal of Physics, vol. 52, pp 285-290, 1974.
4 Lau, J.C., Whiffen, M.C., Fisher, M.J., and Smith, 16 Vaughan, J.M., The Fabry Perot Interferometer,
D.M., “A note on turbulence measurements with a History, Theory, Practice, and Applications, Adam
laser velocimeter,” J Fluid Mech, vol. 102, pp. 353- Hilger, Bristol, pp. 89-134,1989.
366, 1981.
17 Whalen, A.D., Detection of Signals in Noise,
5 Flack, R.D., “Influence of turbulence scale and Academic Press, New York, pp. 327-332, 1971.
structure on individual realization laser velocimeter
biases,” J Phys E: Sci Instrum, vol. 15, pp. 1038- 18Seasholtz, R.G., Panda, J., and Elam, K.A.,
1044, 1982. “Rayleigh scattering diagnostic for measurement of
velocity and density fluctuation spectra,”
6 Heist, D.K., and Castro, I.P., “Point measurement of AIAA2002-0827, 2002.
turbulence quantities in separated flows-a
comparison of techniques,” Meas Sci Technol, vol.
7, pp. 1444-1450, 1996.
7 Elliott, G.S., and Boguszki, M., “Filtered Rayleigh
Scattering: Toward Multiple Property
Measurements,” AIAA2001-0301, 2001.
8 Li, Y., Roberts, W.L., and Brown, M.S.,
“Investigation of Gaseous Acoustic Damping Rates
by Transient Grating Spectroscopy,” AIAA Journal,
vol. 40, pp. 1071-1077, 2002.
8
American Institute of Aeronautics and Astronautics
V
K=k- k
s o detector
RAYLEIGH
LASER
)
T ks
(cid:18)
k s
source o
Figure 1. Rayleigh scattering spectrum. Figure 2. Light scattering from a moving particle.
1.6 40
1.4
y=0.08 s
y units 11..02 yy==03..8216 , m/(cid:29)uk 30
bitrar 0.8 y=8.15 y in 20
ar nt
ude, 0.6 ertai (cid:29)uk= 5 m/s
mplit 0.4 Unc 10 10 m/s
A
0.2 20 m/s
0.0
0
-2 -1 0 1 2
0.8 1.0 1.2 1.4 1.6 1.8 2.0
Dimensionless Frequency, x
f y-parameter
Figure 3. Rayleigh spectrum as a function of Figure 4. Lower bound for uncertainty in estimate of
dimensionless frequency for various y-parameter values. (cid:29) as a function of y-parameter. Parameters fit are:),
uk
u, T, (cid:29) ,x , y .
k uk 0 0
50
40
30
K
,n
e
Tis20
-
T
10
0
0 20 40 60 80 100
TI (in simulted image),%
Figure 5. Error in estimate of temperature for Mach
0.6 flow. Turbulence is added to simulated image,
but the fitting procedure assumes zero turbulence.
9
American Institute of Aeronautics and Astronautics
TEST CELL
M1, P, L1, M2
M1,M2,M3=Turning Mirrors
M3 P=Polarizer
Filtered coflow D=Diffuser
BD=Beam Dump
PV=Probe Volume
BS1=90/10 beamsplitter
PV BS2=50/50 beamsplitter
Jet
L1, f=350mm
L2, f=300mm
L3, f=160mm
L4, f=80mm
Nd:Vanadate L2 L5, f=160mm
5W Laser L6, f=40mm
D L3 BD L7, f=225mm
L8, f=200mm
0.55mm dia.
Optical fiber
LOFT PMT1
Video camera
BS2 PMT2
L7
L6
L5
CCD camera 0.55mm dia.
Optical fiber
Prisms BS1
L8 L4
Fabry-Perot Interferometer
Figure 6. Schematic of experiment arrangement.
30000 2000
25000 1800
20000 11460000
15000 1200
10000 1800000
5000 2 4 6 8 10 50001000015000200002500030000 600 2 4 6 8 10 600800100012001400160018002000
2 2 2 2
4 4 4 4
6 6 6 6
8 8 8 8
10 10 10 10
Figure 7a. Fabry-Perot fringepattern image for the Figure 7b. Fabry-Perot fringe pattern image for
reference laser light. Rayleigh light corresponding to a velocity of 240m/s.
10
American Institute of Aeronautics and Astronautics