Nonintrusive Temperature and Velocity Measurements in a Hypersonic Nozzle Flow

12 Pages·2002·0.39 MB·English

by  OByrne, S.

AIAA 2002-2917
Nonintrusive Temperature and
Velocity Measurements in a
Hypersonic Nozzle Flow
S. O’Byrne , P.M. Danehy
NASA Langley Research Center, Hampton, VA 23681
and A.F.P. Houwing
Australian National University, Canberra, Australia 0200
22nd AIAA Aerodynamic Measurement
Technology and Ground Testing Conference
June 24–26, 2002 / St Louis, MI
Forpermissiontocopyorrepublish,contacttheAmericanInstituteofAeronauticsandAstronautics
1801AlexanderBellDrive,Suite500,Reston,VA20191–4344
Nonintrusive Temperature and Velocity
Measurements in a Hypersonic Nozzle Flow
S. O’Byrne∗, P.M. Danehy†
NASA Langley Research Center, Hampton, VA 23681
and A.F.P. Houwing‡
Australian National University, Canberra, Australia 0200
Distributions of nitric oxide vibrational temperature, rotational temperature and
velocity have been measured in the hypersonic freestream at the exit of a conical noz-
zle, using planar laser-induced fluorescence. Particular attention has been devoted to
reducing the major sources of systematic error that can affect fluorescence tempera-
turemeasurements,includingbeamattenuation,transitionsaturationeffects,lasermode
fluctuations and transition choice. Visualization experiments have been performed to
improve the uniformity of the nozzle flow. Comparisons of measured quantities with a
simple one-dimensional computation are made, showing good agreement between mea-
surements and theory given the uncertainty of the nozzle reservoir conditions and the
vibrational relaxation rate.
Nomenclature shock tunnel differs fundamentally from the air flow
B Einstein B coefficient for stimulated encountered by a vehicle moving through air at hy-
absorption/emission, cm J−1 personic speed. The acceleration of the test gas in a
e Vibrational energy, J shock tunnel is generated by the expansion of shock-
vib
E Laser energy, J compressed gas which is in high-temperature thermal
F Transition rotational energy, cm−1 equilibrium in the nozzle reservoir. As the flow in the
G Transition vibrational energy, cm−1 nozzleexpands,therapiddecreaseinpressurecanlead
I Laser irradiance, W cm−2 to thermal and/or chemical freezing,1 where the colli-
J Rotational quantum number sion rate is insufficient for the chemical or vibrational
k Boltzmann constant, K−1 cm−1 energy to achieve equilibrium but sufficiently rapid to
l Flow length scale, m allow the rotational and translational energy compo-
flow
R Specific gas constant, J kg−1 K−1 nents to reach their equilibrium values.
Sig Fluorescence signal intensity, photons Sr−1 This vibrational or chemical nonequilibrium condi-
T Rotational temperature, K tion implies that the flow generated by these facilities
u Velocity x-component, m s−1 containsmorethermalenergythantheflowofequilib-
x Axial distance, m rium air with the same rotational temperature. The
Θ Characteristic temperature, K excess energy is liberated when the molecular colli-
vib
τ Characteristic V-T relaxation time, s sion rate becomes sufficiently high, for example down-
vib
stream of the bow-shock generated by a body. This
extraenergythengeneratesagreaterincreaseinrota-
Introduction tional temperature across the shock layer and more
surface heat-flux than expected from a comparable
FREE-PISTONshocktunnelshaveprovedtobeef-
equilibrium flow. Lack of quality measurements of
fective ground-test facilities for investigating the
this excess energy may cause its effects to be poorly
effectsofhigh-velocityflightonvehicles. Oneobstacle
estimated or ignored, sometimes leading to large dis-
to the use of these facilities for explaining the physics
crepancies between measurements and calculations.
of hypersonic flight is that the flow generated by a
It is especially difficult to completely model the vi-
∗NRCPostdoctoralFellow,HypersonicAirbreathingPropul- brational freezing of molecular species in nozzle flows.
sionBranch,MS168. AIAAmember. The vibration-translation (V-T) relaxation processes
†Research Scientist, Instrumentation Systems Development
are usually modeled using a simplified Landau-Teller
BranchMS236. AIAAmember.
‡Reader, Department of Physics and Theoretical Physics. mechanism.2,3 This model assumes the molecules be-
AIAAmember. have as harmonic oscillators, and this may not be the
Copyright(cid:176)c 2002bytheAmericanInstituteofAeronauticsand case for the sudden expansions in nozzle flows. The
Astronautics, Inc. No copyright is asserted in the United States
under Title 17, U.S. Code. The U.S. Government has a royalty- model also uses characteristic relaxation times deter-
freelicensetoexerciseallrightsunderthecopyrightclaimedherein mined empirically by measuring relaxation distances
for Governmental Purposes. All other rights are reserved by the
copyrightowner. behind shock waves,4,5 often at temperatures well
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American Institute of Aeronautics and Astronautics Paper 2002-2917
above those of expanding nozzle flows. The validity The T2 Facility
of these approximations has been a subject of intense The T2 free-piston shock tunnel facility has been
experimentalandtheoreticalscrutiny,astheprocesses in continual use since 1966, and can generate flows
ofexcitationbehindashockwaveandde-excitationin withstagnationenthalpiesbetween3and21MJkg−1.
an expanding nozzle flow may involve different phys- Although it has a shorter flow duration and smaller
ical processes. Recent experimental investigations in testsectionthansubsequentfree-pistonshocktunnels,
nitrogen and air flows6–9 tend to support the validity this facility is well suited to the development of new
of the Landau-Teller V-T mechanism for expanding diagnostic techniques, particularly those that require
nozzle flows, at least to a first approximation. Earlier a large number of tunnel runs for a good measure-
results indicating much faster relaxation rates10 have ment. The T2 facility has a much shorter turnaround
since been attributed to the presence of impurities in time and is much less expensive to run than larger
the flow. Calculations indicate that impurities such facilities. The small test section is particularly advan-
as water11 or metal contaminants12 from the tunnel tageous for laser-induced fluorescence measurements
walls significantly enhance the relaxation of molecular because it makes the facility less prone to systematic
species in nozzle flows. errors caused by attenuation of the laser sheet as it
Planar laser-induced fluorescence (PLIF) of nitric propagates through the flow.
oxide (NO) is used for the measurements presented Figure1showsthemaincomponentsoftheT2facil-
here. It is well established as a versatile diagnostic ity. Thefree-pistonshocktunnelisacombinationofa
technique and has been used to measure rotational shock tube and a hypersonic nozzle. This facility pro-
temperature,13–15 velocity,16 and pressure.17 Palmer duces high shock speeds by using a free-piston driver.
and Hanson18 measured rotational and vibrational The piston reservoir, shown at the left of Figure 1, is
temperature in a supersonic nozzle flow using NO filled with air to a predetermined pressure (4.3 MPa
PLIF. This measurement showed vibrational freezing in the case of the present experiments), at which time
of the NO molecules. the piston is released. The piston is then accelerated
Most relevant to this investigation is the work of bytheexpandinghigh-pressuregasand,inturn,adia-
Palma et al.,19 in which NO PLIF was used to mea- batically compresses the driver gas – typically helium
sure vibrational and rotational temperatures in the oramixtureofheliumandargon. Thesegasesarecho-
samefacilityasthesemeasurements,atadifferentfree- senbecausetheywillnotloseenergythroughchemical
stream condition. Palma et al. measured rotational reactions at the high temperatures in the test gas and
temperaturesingoodagreementwithcalculationsbut becausethelowmolecularweightofheliumallowsvery
themeasuredvibrationaltemperatures,althoughthey highshockspeedstobeattainedintheshocktube,due
showedfrozenvibrationalbehavior,didnotagreewith totheincreasedsoundspeedforagaswithlowmolec-
the calculation. This disagreement was attributed to ular weight.22 Filling pressures for the driver and test
nonlinearities in the imaging system and nonunifor- gases are included in Table 1.
mity in the flow assumed to be due to contamination Once the piston has compressed the driver gas suf-
bydrivergas. Inanefforttominimizetheseuncertain- ficiently, the mild steel diaphragm dividing the driver
ties in the freestream flow properties of this facility, gas in the compression tube from the test gas in the
the present paper describes experiments performed to shock tube bursts. The pressure of the driver gas is
accurately determine the velocity, rotational temper- initiallymuchhigherthanthepressureofthetestgas,
ature and NO vibrational temperature at the nozzle soashockwavepropagatesalongtheshocktube. The
exit of a free-piston shock tunnel using PLIF. shockwaveheatsandcompressesthetestgasandisre-
This paper begins with a discussion of the T2 free- flectedfromtheend-walloftheshocktube,onceagain
pistonshocktunnelfacility20 inwhichtheexperiments heating and compressing the test gas. Upon shock
wereperformed,themethodofcalculatingthenominal reflectionthehot,high-pressuretestgasburststhedi-
freestreamconditionsandthepitot-pressuremeasure- aphragm in the nozzle throat and expands through a
ments used to account for the nozzle boundary layer. conical converging-diverging nozzle. The nozzle has a
PLIF visualization experiments are used to determine 7.5◦ half-angle, a 7-mm throat diameter, is 259 mm
the cause and solution of nonuniformity in the nozzle long and has an exit-to-throat area ratio of 110.6.
flow. ThetheoryunderlyingNOPLIFthermometryis The nozzle design and the large initial pressure dif-
then summarized, emphasizing those aspects of PLIF ference between conditions in the nozzle reservoir and
measurements that have to be minimized to ensure at the nozzle exit – which is evacuated to approxi-
minimal systematic error. Finally, nozzle-exit rota- mately 20 Pa prior to the tunnel run – ensure that a
tional temperature, NO vibrational temperature and hypersonic flow is generated at the nozzle exit. After
velocity distributions are presented and compared to passing over the model, the test gas empties into the
thepredictionsofaone-dimensionalnozzlecalculation. dumptank. Attheseconditions,steadytestconditions
This investigation formed part of a more extensive in- last approximately 300 µs before driver gas contami-
vestigation of hypersonic viscous flows.21 nates the test flow.
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American Institute of Aeronautics and Astronautics Paper 2002-2917
dump(cid:13)
tank
test(cid:13)
piston (cid:13) compression(cid:13) nozzle (cid:13) section sting
launcher tube shock tube reservoir
sting holder
high pressure(cid:13) piston steel(cid:13) timing (cid:13)
reservoir diaphragm transducer conical(cid:13) windows
mylar(cid:13) instrumentation(cid:13)
nozzle
diaphragm port
Fig. 1 The T2 free-piston shock tunnel facility.
Computed Flow Conditions flow length scale, l , defined using
flow
The ESTC code23 is used to calculate the nozzle-
e
reservoir temperature (and hence the stagnation en- l = vib (2)
flow de /dx
thalpy),basedontheshockspeedandnozzle-reservoir vib
temperature measured by a pair of pressure trans-
This flow length scale is directly compared with
ducers in the shock tube. ESTC solves the one-
another length scale dictated by the vibrational re-
dimensional shock tube equation22 for a reflected
laxation rate at the local temperature and pressure
shock with initial speed given by the measured shock
conditions. This rate is calculated by STUBE using
speed. Thecalculatednozzle-reservoirpressureisthen
the Landau-Teller model for V-T relaxation time:
compared to the measured nozzle-reservoir pressure,
(cid:104) (cid:105)
and the flow conditions are isentropically expanded exp (K/T)13
or compressed until the computed reservoir pressure τ =C (3)
vib p
matches the measured pressure. In this way, the code
goes some way toward accounting for the losses in the
The constants C and K are taken from Ref. 3. The
facility. ESTCdoesnotaccountexplicitlyforphenom-
vibrational length scale l is given by the product
vib
ena such as shock-speed attenuation due to viscosity,
of the local flow velocity and τ . As the calculation
vib
energy loss by radiation and conduction to the shock
proceeds along the nozzle, the value of log(l /l )
flow vib
tube walls or cooling caused by the mixing of cooler
ismonitoredateachxposition. Themolecularspecies
driver gas with the test gas. The isentropic correction
is deemed to be frozen at the temperature for which
of the calculated pressure to the measured pressure
this ratio becomes negative. The code is then set to
partially compensates for these losses.
ensure freezing for this species and the calculation re-
The conditions at the nozzle exit are calculated us-
commenced until the freezing temperature of the next
ing the STUBE code.24 This nozzle code was specif-
species is reached. The sequence of steps is repeated
ically designed to determine free-piston shock tun-
for N , O and NO freezing temperatures.
2 2
nel freestream conditions. The code assumes one-
dimensional, inviscid nozzle flow, but accounts for Pitot Survey
chemical nonequilibrium using a 10-species reaction The boundary-layer displacement thickness in the
mechanism. It accepts as inputs the geometry of nozzle reduces the effective flow divergence angle, an
the flow, the chemical composition of the test gas, effect that is not accounted for in the inviscid STUBE
themeasurednozzle-reservoirpressureandthenozzle- calculation. Thedisplacementcausedbytheboundary
reservoir temperature as calculated by ESTC. These layerwasdeterminedusinganaxialpitot-pressuresur-
quantities are used to determine the chemical compo- vey at four locations, extending upstream and down-
sition and the state variables of the nozzle flow as a stream of the nozzle exit. The pitot pressure was
function of axial distance. measured using a PCB brand piezoelectric transducer
STUBEhasbeenmodifiedtoaccountforvibrational mounted in a cylindrical brass housing. The effec-
nonequilibriumusingasudden-freezingapproximation tive divergence angle of the nozzle was changed in
based upon that put forward in Ref. 1. Assuming the STUBE calculation until the measured and cal-
anequilibriumBoltzmanndistribution,thevibrational culatedpitotpressuremeasurementsagreed, asshown
energy of each species is given by3 in Fig. 2. Here the axial distance is plotted relative
to the nozzle exit. The best fit to the data for the
Θ
e = vib R (1) fluidinsidethenozzlewasachievedusingadivergence
vib exp(Θ /T)−1
vib half-angle of 6.8±0.3◦.
where Θ is a characteristic vibrational temperature Once the correct nozzle divergence angle was ascer-
vib
for the species and R is the specific gas constant. An tained, the freestream properties were calculated as a
initial calculation assuming vibrational equilibrium is function of axial distance. The nozzle-exit conditions
performed,andtherateofchangeofvibrationalenergy are summarized in Table 1. A 99% N , 1% O mix-
2 2
of each species is used to determine a characteristic ture was chosen for the shock tube fill condition. The
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American Institute of Aeronautics and Astronautics Paper 2002-2917
0.024 max = 18 000 max = 40 000
max
STUBE(cid:13) 6.5 (cid:176)(cid:13)
0.022 STUBE 6.8 (cid:176)(cid:13)
STUBE 7.0 (cid:176)(cid:13)
STUBE 7.5 (cid:176)(cid:13)
0.020 Experiment s)
nt
0 u
/ ppitot 0.018 50 mm al (co
p 0.016 gn
Si
0.014
(a)(cid:13) (b)(cid:13)
0.012 0
0.010 Fig. 3 PLIF images in the nozzle core flow ob-
-20 0 20 40 60 tained using the OP transition (a) prior to and
x (mm) 12
(b) after nozzle modifications. Maximum intensity
Fig. 2 Comparison of measured and calculated is measured in camera counts.
pitot pressures.
is shown in Fig. 3(a).
oxygen was added because the reactions in the reser- Upon inspection of the nozzle throat, some erosion
voir cause approximately 1% NO to be formed in the was noted 7 mm downstream of the secondary di-
reservoir and this chemical composition freezes in the aphragm. A very small forward-facing step, less than
nozzle, as shown in Table 1. The NO is sufficient to 0.2 mm high, was noted at the position of this mylar
provide a good fluorescence signal. Nitrogen was cho- diaphragm, where the nozzle begins to diverge. When
sen,ratherthanair,toprovideasimplerflowthatwas thethroatwasboredoutandcaretakentoensurethat
notasstronglyeffectedbythedissociationofO asan therewasnostepatthesecondarydiaphragmposition,
2
air flow at this stagnation enthalpy. the percentage of uniform images increased to 95%.
The uncertainties in Table 1 were estimated based Figure 3(b) is an example of the more uniform flow
upon the uncertainties in the nozzle expansion an- generatedafterredesignofthethroat. Theincreasein
gle,themeasuredshockspeedandthenozzle-reservoir signalwithdownstreamdistanceiscausedbythetem-
pressure. Calculationswereperformedat±1standard peraturedecreaseinthenozzleandthestreakinginthe
deviation of these properties, and the propagation of image is a result of normalizing the image to the spa-
the uncertainty through the calculation was used to tial laser intensity distribution. The improvement in
estimate the uncertainty in nozzle-exit properties. signaluniformityaftertheredesignofthethroatleads
to the conclusion that the nonuniformity was caused
Flowfield Uniformity
byboundary-layerseparationatthestepinthethroat.
The previous measurements of Palma et al.19 in
The separated boundary layer formed a re-circulating
this facility showed evidence of nonuniformity in one-
region that entrained cooler boundary-layer gas con-
third of PLIF images. This nonuniformity manifests
taining significantly less NO into the core flow. Over
as relatively large low-signal regions in the flow. That
several tunnel runs, the re-attachment of this bound-
studyconcludedthatthenonuniformitywascausedby
arylayercausedtheerosiondownstreamofthethroat.
driver gas contamination of the flowfield. This was a
cause for concern, as the measurements were obtained
PLIF Considerations
well before driver gas contamination was expected to
occur. The thermometry technique used in this study Thermometry
requires run-to-run flow repeatability and a uniform The theory of planar laser-induced fluorescence is
test gas flow, so it was important to make the flow as well known and has been considered elsewhere.25,26
reproducibleaspossible. AseriesofPLIFimagingex- Thetwo-linethermometrymethodusedinRef.27was
perimentswasperformedtoachievethis. Imagesofthe also used for these experiments. Two transitions are
freestream were obtained and parameters that might excited on succeeding tunnel runs using a thin sheet
affect the flowfield uniformity were varied in sequence of laser light. The technique can be performed during
toseeiftheyhadaneffectontheflowuniformity. The a single tunnel run to obtain instantaneous measure-
time after shock reflection at which images were ob- ments28 butthistechniquerequirestwolasersandtwo
tained, the composition of the compression tube gas, imaging systems, which were not available for these
the stagnation enthalpy of the flow and the test gas measurements. Run-to-run variations in the nozzle
compositionwerevaried,onefactoratatime,butnone reservoir pressure and shock speed varied by less than
ofthesehadasignificanteffectontheflowuniformity, 1%throughoutthemeasurements,andthenozzleflow
withsimilarnonuniformflowsoccurringtothosenoted waslaminarwithinthecoreflow,sotheassumptionof
inRef.19. Anexampleofthenonuniformflowimages run-to-run repeatability should be a good one.
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American Institute of Aeronautics and Astronautics Paper 2002-2917
Fill conditions Mixture p (kPa) T (K)
Test gas 1.1% O + 98.9% N 150 297
2 2
Driver gas 31.3% Ar + 68.7% He 118.6 297
Reservoir conditions p (MPa) T (K) H (MJ kg−1) u (ms−1)
0 0 0 s
Value 28.0 3831 4.75 2270
Uncertainty (%) 4.6 2.8 2.7 1.8
Freestream conditions p (kPa) T (K) u (m s−1) ρ (kg m−3) M Re (m−1)
∞ ∞ ∞ ∞ ∞ ∞
Nozzle exit (6.8◦) 8.1 425 2850 0.064 7.03 7.9 ×106
Uncertainty (%) 7.0 5.0 2.0 5.0 2.0 5.0 ×106
Freezing species N O NO
2 2
Freezing temperature (K) 2030 1277 606
Mole fractions N O N O NO Ar
2 2
Nozzle reservoir 0.9818 0.0019 0.0001 0.0034 0.0127 0.0001
Freestream 0.9835 0.0036 0.0000 0.0017 0.0111 0.0001
Table1 T2operatingconditionsfortheexperiment. Thefillconditions,shockspeedandnozzle-reservoir
pressure are measured. All other quantities are calculated.
If two transitions in the same vibrational level but eratestrongfluorescencesignals, theyhavebeenstud-
with differing rotational energies are excited by the ied extensively and they have been shown to not
laser, the rotational temperature can be determined have J(cid:48)(cid:48)-dependent quenching rates.29 Four transi-
using the relation tionswerechosenwithinthe(0,0)and(0,1)vibrational
(cid:161) (cid:162) bands. Their properties are summarized in Table 2.
F −F /k
J(cid:48)(cid:48) J(cid:48)(cid:48) These transitions were carefully chosen from the
T = (cid:181) 2 1 (cid:182) (4)
rot
ln E2B2(2J2(cid:48)(cid:48)+1)Sig1 large number of NO transitions available in the γ
E1B1(2J1(cid:48)(cid:48)+1)Sig2 bands. Non-overlapping transitions were chosen to
simplifycalculationsofthesystematicuncertaintydue
where Sig is the fluorescence signal intensity, E is the
tosaturationofthefluorescenceandabsorptionofthe
laserenergy,BistheEinsteincoefficientforstimulated
laser sheet. As shown in Table 2 the interference from
absorption for the transition, F is the rotational en-
surrounding transitions, ξ , is less than 0.15% for all
ergyofthetransition,kistheBoltzmannconstantand int
four transitions.
J(cid:48)(cid:48) is the rotational quantum number. The subscripts
TransitionswithsimilarEinsteinB coefficientswere
1 and 2 refer to the two laser-excited transitions.
chosen to ensure that the effect of saturation was the
Analogously, if two transitions with similar rota-
same for both transitions. This minimized the sys-
tional energies but in two different vibrational levels
tematic uncertainty due to saturation. As Table 2
are excited and their fluorescence detected, the vibra-
indicates, the values of I/I , the ratio of laser irra-
tional temperature can be determined from the laser sat
diance to the saturation irradiance, were made small
energies, relative signal strengths and spectroscopic
enough to ensure that the fluorescence signal was lin-
parameters using the relation
earwithlaserenergy. Strongtransitionssuchasthose
G −G in the Q-branch were avoided, to minimize the effect
v(cid:48)(cid:48) v(cid:48)(cid:48)
Tvib = (cid:104)2 1 (cid:105) (5) of absorption on the measurements.
kln E2B2Sig1
E1B1Sig2 The energy difference between the transitions was
made as large as possible for the rotational tem-
where G is the transition vibrational energy and the
perature measurements, while still providing ade-
other quantities are the same as those of Equation 4.
quate signal-to-noise at the high-J transitions. The
Transition Choice larger the energy separation, the smaller the effect
Rovibronic transitions within the A2Σ+ ←X2Π of signal uncertainty on measured temperature. A
bands (also known as the γ bands) of NO were used typical benchmark for desired energy separation is
for the PLIF thermometry and velocimetry experi- ∆F ≥kT.25 For the freestream conditions in this
ments. These bands were chosen because they gen- investigation,∆F =5.3kT, ensuring that fluctuations
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American Institute of Aeronautics and Astronautics Paper 2002-2917
Line v(cid:48)(cid:48) ν0 FJ Gv BJ(cid:48)J(cid:48)(cid:48) I/Isat ξint % absorption
(cm−1) (cm−1) (cm−1) (cm J−1) (%) (cm−1)
OP (2.5) 0 44 069.52 73.58 948.66 146.99 0.08 0.10 5.1
12
RR (28.5) 0 44 483.25 1498.97 948.66 152.75 0.08 0.00 0.31
22
OP (2.5) 1 42 193.59 73.41 2824.76 229.90 0.13 0.15 0.69
12
RR (28.5) 1 42 622.50 1483.11 2824.76 237.93 0.13 0.00 0.04
22
Table 2 Spectroscopic parameters for the four thermometry transitions.
in measured signal have only a small effect on mea- to a hydrogen/oxygen flame. The NO LIF generated
sured temperature. in this flame is captured by a photomultiplier tube
The transitions in Table 2 were chosen in two (Hamamatsu R446) at the exit of a spectrometer. An
pairs. Rotationaltemperaturewasmeasuredusingthe excitation scan is performed immediately before the
OP (2.5) and the RR (28.5) transition pairs in each tunnel run, to tune the laser to the center of the exci-
12 22
ofthev(cid:48)(cid:48) =0andv(cid:48)(cid:48) =1vibrationallevels. Twovibra- tation transition.
tionaltemperaturemeasurementsweremadeusingthe The narrowband excitation causes fluorescence to
pair of OP (2.5) transitions in the v(cid:48)(cid:48) = 0 and v(cid:48)(cid:48) = 1 the laser-excited band and higher vibrational bands,
12
vibrational levels and using the pair of RR (28.5) whichiscapturedusingacameraplacedperpendicular
22
transitions in the v(cid:48)(cid:48) = 0 and v(cid:48)(cid:48) = 1 vibrational lev- to the laser sheet. As much of this broadband fluores-
els. Thesymmetryofthischoiceoftransitionsenables cence is collected as possible, to maximize the signal.
foursetsoffluorescencemeasurementstoproducetwo This is particularly necessary when the v(cid:48)(cid:48) = 1 vibra-
rotationaltemperaturemapsandtwovibrationaltem- tional level is excited, where the population is small
perature maps that can be directly compared with compared to the ground vibrational state. A Schott
eachothertocheckforanysignificantsystematicerror UG5glassfilterisusedtoattenuatethesignalfromthe
duetothechoiceoftherotationalquantumnumberor laser-excitedvibrationalband,reducingthesystematic
vibrational level of the transitions. errorduetoradiativetrapping. Radiativetrappingoc-
Another experiment performed at these freestream curswhenthefluorescencegeneratedbythelasersheet
conditions,21 obtained PLIF rotational temperature excites further fluorescence in the fluid between the
measurementsusingsixdifferenttransitions. ABoltz- laser sheet and the camera. As this secondary fluores-
mannplotindicatedthatthev(cid:48)(cid:48)=0transitionsusedin cencedependsonthepopulationintheenergystateof
Table2 produced signals consistentwith a Boltzmann the excited transition, different proportions of the flu-
distribution for the NO population in that vibrational orescence signal are absorbed for different transitions,
band. leadingtosystematicerrorsinmeasuredtemperature.
The UG5 filter also attenuates the influence of broad-
PLIF System band flow luminosity caused by impurities in the flow
ThePLIFsystemusedintheseexperimentsconsists and the elastic Mie and Rayleigh scattering from the
of an excimer-pumped dye laser, frequency-doubled laser.
using a BBO I crystal to provide 3–5 mJ of tunable The timing of the PLIF measurement was auto-
radiation between 225 and 240 nm with a spectral mated by a computer-controlled timing board, set to
linewidth of 0.18 cm−1. This system is very similar a delay of 350 µs after shock reflection in the noz-
tothatusedinRef.19,butthePrincetonInstruments zle reservoir. The camera intensifier was gated for
ICCD camera used to capture the fluorescence signal 330 ns immediately after the laser pulse, to maximize
has significantly better dynamic range and linearity the signal-to-noise ratio.
properties than the system used in that investigation. Nine images were obtained at each transition. The
All the optics in the system are UV-grade fused sil- camera background image and the scatter image in
ica. Thelasersheetisformedusingacombinationofa Fig. 5 were subtracted from each image, and the av-
cylindrical and spherical lens. In the test section, the erage of the images and laser energies was calculated.
sheet is 40-mm wide and 0.7±0.1-mm thick. Pulse-to- Equation 4 was used, with the data for rotational en-
pulse variations in relative laser energy are measured ergyandEinsteinBcoefficientinTable2,todetermine
by diverting a small portion of the beam onto a pair the rotational temperature distributions. Vibrational
of quartz diffusers and then to a photodiode. A beam temperature distributions were calculated in the same
splitter is used to divert 8% of the sheet onto a dye way,butusingEquation5andthevibrationalenergies
cell. A CCD camera images the dye fluorescence sig- and B coefficients from Table 2. The camera gain was
nal, which is used to normalize the PLIF signal for setatthesamevalueforalloftheimages,sonocorrec-
spatial intensity variations across the laser sheet. An- tion for changes in camera gain was required. Spatial
other beam splitter diverts some of the laser output variations in laser irradiance were monitored using a
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American Institute of Aeronautics and Astronautics Paper 2002-2917
the gas is excited the tagged molecules advect down-
0.5 m (cid:13)
spectrometer stream, fluorescing as they move. After the 500-ns
Photomultiplier(cid:13) delay, the camera is gated for 10 ns and captures the
tube
Dump tank
PLAN VIEW fluorescence from the excited gas. The displacement
Beam dump oftheadvectedgascanbemeasuredbyfittingaGaus-
Cylindrical lens(cid:13)Spherical lens H2/O2 flame(cid:13) sian to the laser line image and calculating the center
Prism periscope f = 0.03 m of that curve. Knowing the delay between the laser
f = 1.0 m Beamsplitter firingandthegatingoftheintensifierallowstheveloc-
Photodiode
ity to be calculated from the measured displacement.
Diffusers
Nozzle The imaged region extends from 8 to 24 mm below
Beamsplitter Prism SIDE VIEW Beamsplitter the axis of symmetry of the flow. The imaging system
225-245 nm was limited to this length to ensure that the displace-
Frequency doubler Spherical lens(cid:13)
450-490 nm f = 1.0 m ment of the tagged gas was measurable on the CCD.
Dye laser Schott UG5(cid:13) For a 2700 ms−1 velocity and a magnification of 23
(Lambda Physik (cid:13) Filter
308 nm ScanMate II) CCD camera(cid:13) Dye cell pixels mm−1, the tagged particles would be displaced
(ELxacmimbedra l aPsheyrsik (cid:13) (EEV Photon) Intensified CCD camera(cid:13) by 31 pixels.
EMG 150ETS) I(CPCrinDc)eton Instruments (cid:13) Two measurements of velocity were made for this
experiment, using the overlapping QQ (19.5) and
22
Fig. 4 Apparatus for PLIF temperature measure-
QQ (2.5) transitions at 44 227.7 cm−1. These transi-
ments. 11
tions were chosen because they exhibit strong fluores-
cence at the freestream conditions. This is important
as the fluorescence lifetime at these conditions is ap-
(cid:13)expansion wave proximately 100 ns, and after a delay of 500 ns the
signalintensityhasdecayedtolevelsthatarenearthe
resolving limit of the camera system.
Immediatelybeforethetunnelrunthetestsectionof
xit thetunnelwasfilledwithalow-pressurestaticmixture
e
zzle core flow of 1% NO in N2 and the fluorescence in the mixture
no was imaged. Thus, the initial location of the laser
line could be measured, providing a reference posi-
tion for the displacement during the tunnel run. This
boundary layer wasimportantbecausethesemeasurements,unlikethe
flat-plate boundary- layer velocity measurements in
Ref. 30, did not have a surface with a no-slip bound-
ary condition that could act as a zero-displacement
0 20 40 60 reference. Those previous measurements showed an
x (mm)
average systematic error of 0.43 pixels displacement
between the dump tank images and the images in the
0 100 200
signal (counts) shock tunnel, caused by movement of the model and
imagingsystemduringthemexperiment. Thisimplies
Fig.5 Imageoflaserscatter, showingtheposition
an average systematic error of -50 ms−1 in the mea-
of the imaged region relative to the nozzle exit for
sured velocity.
the temperature measurements.
Results
dyecellandtheimageswereindividuallycorrectedfor
Temperature
these variations before averaging.
Signal intensities in the raw images varied from
Velocimetry approximately 500 counts above background for the
Thefreestreamvelocitywasmeasured29.0±0.5mm RR (28.5) v(cid:48)(cid:48) = 1 transition to 30 000 counts for
22
downstream of the nozzle exit, using the tagging ve- the OP (2.5) v(cid:48)(cid:48) = 0 transition, for a camera with
12
locimetry technique outlined in Ref. 30. This tech- a dynamic range of 65 535 counts. The maximum sig-
nique was chosen because it is simple, accurate and nal level was well below the measured linear dynamic
requires only a minor modification of the thermom- range of the camera. The standard deviations in the
etry arrangement in Fig. 4. The 30-mm focal length signalsateachofthefourtransitionswere13%forthe
cylindricallensisreplacedwitha100-mmlensrotated OP (2.5)v(cid:48)(cid:48) =0,20%fortheRR (28.5)v(cid:48)(cid:48) =0tran-
12 22
by 90◦. This rotation allows the laser to excite a nar- sition and 25% for the two v(cid:48)(cid:48) = 1 transitions. Similar
row line of NO molecules in the flow. The camera measurements before the nozzle modifications men-
is delayed by 500 ns with respect to the laser. After tioned previously had standard deviations of 23% for
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American Institute of Aeronautics and Astronautics Paper 2002-2917
the OP12(2.5) transition, showing a considerable de- Trot v’’ = 0 Trot v’’ = 1
creaseintheuncertaintyafterthenozzlemodification. 30 30
The standard deviation for the OP (2.5) transition
12 20 20
was the same as that observed in PLIF temperature
measurements in a static test cell.21 This indicates 10 10
thatthemeasurementuncertaintyisdominatedbythe mm) CL mm) CL
r ( r (
laser and imaging systems, particularly the effect of 10 10
mode competition in the laser on the spectral overlap
20 20
between the laser and the transition.
30 30
Thecalculateduncertaintyintherotationaltemper-
40 40
ature for a single pixel measurement was ±8 K (2%)
usingthev(cid:48)(cid:48) =0transitionsand±17K(4%)usingthe 50 50
v(cid:48)(cid:48) = 1 transition pair. Comparison with the 4% un- 20 30 40 50 60 20 30 40 50 60
x (mm) x (mm)
certaintiesquotedintheexperimentsofPalmaetal.19
showsthattheimprovedcamerasystemandmoreuni- 200 250 300 350 400 450 500 200 250 300 350 400 450 500
form nozzle flow have halved the uncertainty. T (K) T (K)
Temperature maps obtained using the four transi-
tion pairs are presented in Fig. 6. The upper two Tvib OP12 (2.5) Tvib RR22 (28.5)
images show the rotational temperature distributions 30 30
while the lower two images show the measured vibra- 20 20
tional temperature. As expected, the best signal-to-
10 10
noiseratiointherotationaltemperaturewasobtained mm) CL mm) CL
using the two (0,0) band transitions; for the vibra- r ( r (
tional temperature, the two OP (2.5) transitions had 10 10
12
theleastuncertaintybecausethesignallevelsforthese 20 20
transitions were higher than for the RR (28.5) tran-
22 30 30
sitions.
40 40
As the flow features are clearest in the top left im-
50 50
ageforrotationaltemperatureusingtheOP (2.5)and
12 20 30 40 50 60 20 30 40 50 60
RR (28.5) v(cid:48)(cid:48) = 0 transitions, we will discuss them x (mm) x (mm)
22
first. The dark region at the bottom of the image in-
dicates the area of the test section outside the nozzle 500 750 1000 1250 1500 500 750 1000 1250 1500
T (K) T (K)
flow. In this region, the signal intensity was not suffi-
cient to make reliable temperature measurements. At Fig. 6 Rotational and vibrational temperature
the left of the image, near r = 30 mm on either side mapsobtainedusingthefourtransitionsinTable2.
of the center line, there is a region of elevated tem-
perature, caused by the nozzle boundary layer. This
temperature increase decays with axial distance from 20-mm region in the center of the temperature map.
the nozzle exit as the expansion from the nozzle exit This allows a direct comparison of the two measure-
cools the flow that was in the nozzle boundary layer. ments made by exciting transitions in different vibra-
There also seems to be a slight decrease in rotational tional levels.
temperature toward the symmetry axis of the nozzle. Thetworadialprofilescoincidebetweenr =30mm,
This is most likely caused by a reflected pattern of where the laser enters the flow, and r = 0 mm.
weakshocksandexpansionwavesthatcanformwithin Thereafter, the v(cid:48)(cid:48) = 0 rotational temperature shows
a conical nozzle. The rotational temperature clearly a systematic increase while the temperature distribu-
decreases with axial distance from the nozzle exit, as tionforthev(cid:48)(cid:48) =1measurementismoresymmetrical.
expectedofanexpandingnozzleflow. Thev(cid:48)(cid:48)=1tem- This difference is caused by beam absorption in the
perature map is similar, except that the temperature OP (2.5) v(cid:48)(cid:48) = 0 PLIF image. The population in this
12
increase at the nozzle boundary layer is not apparent state is much larger than for any of the other transi-
and the signal-to-noise ratio is generally worse. The tions and causes a measurable systematic error in the
two vibrational temperature maps in the lower half of temperature for r < 0 mm, as a much greater pro-
Fig.6showaconstantvibrationaltemperatureconsis- portion of the laser-sheet energy is absorbed by this
tent with vibrationally frozen flow. transition than for the other three transitions. As
Aclearerunderstandingoftheradialrotationaltem- Table 2 shows, the fluorescence from the RR (2.5)
22
perature distributions can be seen in the line plot of v(cid:48)(cid:48) = 0 transition absorbs 5% of the laser energy per
Fig. 7. This plot is of the signal in the top two rota- centimeter, while the absorption of the energy for the
tional temperature images of Fig. 6, averaged over a other transitions is negligible. Further support to the
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American Institute of Aeronautics and Astronautics Paper 2002-2917
440 v(cid:146)(cid:146) = 0 440 v(cid:146)(cid:146) = 0
v(cid:146)(cid:146) = 1 v(cid:146)(cid:146) = 1
LINUS v(cid:146)(cid:146) = 0 STUBE
LINUS v(cid:146)(cid:146) = 1
420 420
400 400
K) 380 K) 380
T ( T (
360 360
340 340
320 320
300 300
-30 -20 -10 0 10 20 30 20 25 30 35 40 45 50 55 60
r (mm) x (mm)
Fig. 7 Line plot of rotational temperature radial Fig. 8 Axial rotational temperature distribution
distributions for the v(cid:48)(cid:48) = 0 and v(cid:48)(cid:48) = 1 mea- for the v(cid:48)(cid:48) = 0 and v(cid:48)(cid:48) = 1 transition pairs, with the
surements, 40-mm downstream of the nozzle exit. STUBE predicted distribution.
Dashed lines indicate calculations of systematic er-
ror calculated by the LINUS program.
by adding a third pressure transducer to the shock
tube. Using this attenuated speed would reduce the
reasoningthatthetemperaturedifferenceisduetoab- calculated freestream temperature by 35 K, so the
sorption can be seen from the dashed lines in Fig. 7. agreement in that case would not be as good as that
Theselinesrepresentcalculationsofthesystematicer- shown in Fig. 8. An unsteady simulation of the shock
rorduetoabsorptionbasedupontheassumptionthat tunnel operation, accounting for the changing shock
the temperature is a uniform 390 K across the nozzle. speed, would be required to more accurately simulate
These calculations were performed using the LINUS the effect of shock speed attenuation on the reservoir
NO laser-induced fluorescence modeling code of Dr. conditions.
P.C. Palma.31 Temperature distributions were calcu- The vibrational temperature images in Fig. 6 show
lated using the two transition pairs used to measure constant temperatures in both the radial and axial
the two experimental distributions. The calculated directions. The axial vibrational temperature distri-
temperature distributions show very similar trends to butions are presented in Fig. 9. As for the rotational
the experimental distributions, with an obvious sys- temperature plots, the vibrational temperature is av-
tematic error in the v(cid:48)(cid:48) = 0 temperature distribution. eragedovera5-mmregioncenteredatthenozzleaxis.
Figure 8 shows a comparison between the axial dis- Thethickersolidlineindicatestemperaturecalculated
tributionofrotationaltemperatureobtainedusingthe using the OP (2.5) v(cid:48)(cid:48) = 0 and OP (2.5) v(cid:48)(cid:48) = 1
12 12
v(cid:48)(cid:48) = 0 and the v(cid:48)(cid:48) = 1 transition pairs. The measure- transitionpairandthethinnerlinecorrespondstothe
ments were averaged over a 5-mm region centered at temperature calculated using the RR (28.5) v(cid:48)(cid:48) = 0
22
theaxis. Therotationaltemperaturedistributioncom- and RR (28.5) v(cid:48)(cid:48) = 1 line pair. The average mea-
22
putedusingtheSTUBEnozzlecodefortheconditions sured NO vibrational temperature is 1162±40 K for
in Table 1 is included as the dashed line. The two the v(cid:48)(cid:48) = 0 line pair and 1145±60 K for the v(cid:48)(cid:48) = 1
measured temperature distributions agree to within pair. Asfortherotationaltemperaturemeasurements,
thequoteduncertainty,bothintermsofthemeasured the two vibrational temperature measurements agree
temperature and the variation with axial distance. with each other to within the measurement uncer-
The rotational temperature decreases from 405 K at tainty. Unliketherotationaltemperaturedistribution,
20mmfromthenozzleexitto360Kat60mmfromthe the vibrational temperature is constant in the direc-
nozzle exit. The fact that the two temperature mea- tion of flow. This indicates vibrationally frozen flow.
surements are in agreement is an indirect indication TheresultsofRef.19showsimilarvibrationallyfrozen
that the rotational energy states obey a Boltzmann behavior at slightly different freestream conditions in
distribution. The agreement with the rotational tem- the same facility.
perature calculated using STUBE is also good. The The STUBE NO vibrational temperature calcula-
STUBE result agrees both in the absolute tempera- tion disagrees with both experimental temperature
ture and the temperature gradient when the average measurements by a factor of two. The most likely
shock speed is used to calculate the freestream condi- cause of this disagreement, also found in the vibra-
tions. tional temperature measurements of Ref. 19, is the
Despitethisgoodagreement,itshouldbenotedthat modeling of the V-T interactions, as described pre-
Ref. 31 measured attenuation in shock speed of 6% viously. Apart from the fact that STUBE does not
9 of 11
American Institute of Aeronautics and Astronautics Paper 2002-2917