Measurement of Gas Properties by Incoherent and Coherent Rayleigh Scattering Richard B. Miles...
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Transcript of Measurement of Gas Properties by Incoherent and Coherent Rayleigh Scattering Richard B. Miles...
Measurement of Gas Properties by
Incoherent and Coherent Rayleigh
Scattering
Richard B. MilesPrinceton University
Dept. of Mechanical & Aerospace Engineering
The Ohio State UniversityFrontiers in Spectroscopy
Feb 16-18, 2005
Two approaches to the measurement of local neutral gas temperature in a weakly ionized plasma
• Filtered Rayleigh Scattering (Joe Forkey, Walt Lempert, Pingfan Wu, Rene Tolboom)
– Uses an optically thick atomic cell for filtering the Rayleigh signal to reject background scattering
– Requires a tunable, narrow linewidth laser and an atomic or molecular vapor filter
– Yields a single point, line, or cross sectional plane measurement
– A single pulse (10 nsec) measurement possible if pressure is known
• Coherent Rayleigh Brillouin Scattering (Xinggau Pan, Mikhail Shneyder, Jay Grinstead, Peter Barker)
– Four wave nonlinear effect similar to CARS
– Gives very strong background rejection and high signal strength
– Requires one broad band laser and one narrow line tunable laser
– Yields a single point measurement, but a line measurement possible
Field Surrounding a Dipole
eR 2 cos
o
ik
r
1
r2
x ()e it ikr
4r
e sino
1
r2 ik
r k 2
x ( )e it ikr
4r
e k 2 sin x( )e it ikr
4ro
k=ω/c=2π/λ ~107 m-1. For r>> λ
0Re
x
y
z
r
a
ra
x��������������
The Dipole Field
2
sin,s
o
pE r
r
2
0 ,,
2s
s
c E rI r t
2 2 2
4 2
sin
2so
cpI
r
For Rayleigh scattering, the dipole is driven by an incident field that creates the polarization.
since
we have
p ����������������������������
The Induced Dipole
IEp
2 22
2 4 2sins I
o
I Ir
The induced polarization is proportional to the incident field. In the case of an atomic gas, the polarizability is a scalar.
and
IzzzIyzyz
IzyzIyyyy
IzxzIyxyx
EEp
EEp
EEp
For molecular gases, the polarizability is a tensor
Scattering Cross Section
Iss
s Ir
I2
1
2 22
2 4sinss
o
I
o
IP42
23
3
8
Iss I
P
42
23
3
8
o
ss
The differential scattering cross section is
Total Scattering Power integrate over a sphere surrounding the dipole
The total scattering cross section is
soss
ss d
Polarizability
2
132
2
n
n
No
2
2
2
24
3
2
124
n
n
Nss
2
4
3 1
3
32
N
nss
22
24
4 1sinss n
N
The polarizability can be written in terms of the index of refraction
Note that this comes from 20 0 0D E P E N E n E
with the 3/(n2+2) Lorentz-Lorenz factor added to account for the local field correction
This gives
If as in a gas 1n
and
(Air is ~1.00027)
Power Collectedfrom a single dipole
I
ss IP
ss
IIP
The optical system can only collect light from a small fraction of the sphere into which the light is scattered. The differential detected power per steradian is
The power collected from one dipole is that differential power integrated over the collector solid angle
Coherent vs Incoherent Scattering
•For coherent dipoles, the peak intensity is n2 times the single dipole intensity, but that only occurs where all the phases add. For many dipoles, this corresponds to a very small angle. At other angles, the intensity is low.
•For incoherent scattering, the interference washes out, so the intensity increases as n, i.e. linearly with the number of dipoles and the scattering is not well collimated
Incoherent Scattering
I 1
2En
n 2
I nI1
For Rayleigh scattering, the density fluctuations in the air cause the interference to be washed out in all but the forward direction, where all the path lengths are the same because there is no scattering delay, so the phase of the scattered light matches the phase of the propagating light. In this direction Rayleigh scattering is suppressed and the effect reduces to the index of refraction
n= # of molecules in the observed volume
Rayleigh Signal
dNVIP ssIDET
detector
Laser
•N = the number of dipoles per unit volume•V=the illuminated volume of the sample•ΔΩ=the collection solid angle•η=the detector and optical system efficiency•II=the incident laser intensity
Narrow linewidth laser
Test Section
Camera
Molecularor atomic vapor
Cell
Filtered Rayleigh Scattering
Rayleigh scattering is very weak•High power laser is needed•Exclusion of background scattering
Iodine
• Simple to build - cell is close to room temperature
• Overlaps both doubled YAG and argon ion lasers– Note that with injection locking, both Ar++ and
Nd:YAG are tunable over many iodine lines
• Maximum attenuation is 105 because of weak continuum absorption
Absorption Spectrum of Iodinein Doubled YAG region
Optically Thick Iodine Absorption Spectrum(measured and modeled: 3 Torr) Forkey
500,000 Frame per Second Imaging of Supersonic Air withCO2 Nanoparticles and an Iodine Filter
3 22 6
2 4
8
3ss
o
V r
3particles V r
Particles in the Rayleigh range (2πr<<λ) have a large cross section so they can be used for flow visualization
Shock-Wave/Boundary-Layer Interaction in Mach 3 Wind Tunnel
Pulse-Burst Laser
Box Car
Flow
MHz Camera
I2 Cell
I2 CellLensPD1
PD2 Optics=0.532m
PC
x
y
z
Laser Sheet Orientation:x-y:streamwisex-z:planform
CO2 as a Seed Material• ~1% CO2 is added to the air upstream of the
supersonic wind tunnel plenum chamber
• As the flow expands through the nozzle, CO2 condenses into clusters as temperature drops
• In the thermal boundary layer, the temperature recovers to close to the plenum temperature and CO2 clusters sublime
Upper limit of the average CO2 cluster size is estimated around 10 nm.
Models predicted that the CO2 clusters rapidly condense or sublime so they accurately mark the temperature discontinuity in the boundary layer
Mach 2.5 FLOW
240 ANGLE RAMP
Mach 3 core flowFlow velocity ~600 m/s0.053 cm-1 shift
Laser tuned tohighlighthigh velocity
Laser tuned toobservelower velocity
Visualization of Mach 8 Flow over Three Dimensional Body
X-33 Space Vehicle Model 4:1 Elliptic Cone
Mach 8 Flow Over 4:1 Elliptic Cone
Three Dimensional Unsteady Boundary Layer:• Pressure gradient between major and minor axis generates crossflow along circumferential direction• Crossflow vortices are predicted to cause early boundary layer transition
Y-Z
X-Z
FLOW
X-Y
Laser Sheet Orientations• Streamwise (X-Y)• Planform (X-Z)• Spanwise (Y-Z)
Simultaneous Imaging of Two Planes 500 kHz, Rex=1.6×106
Spanwise View
Planform ViewFlow
Flow
Volumetric Imaging of Boundary Layer at Mach 8 Using Sequential Spanwise Images
•Pulse-burst imaging of centerline boundary layer in planform orientation revealed slowly-evolving structures• 3-dimensional image of transitional boundary layer is reconstructed under “frozen flow” assumption
Planform Single-shottaken at 16 µs
Flow
16 s
12 s
8 s
4 s
0 s
37.7 mm
8.8 mm20 s
Flow moving out of plane
Spanwise sequential slicestaken by pulse-burst laser
3-D Reconstruction of 4:1 Centerline Region(Rex=1.57 million)FLOW
Boundary Layer Structure over 2:1 Elliptic Cone (Rex=1.3 million)
Pressure, Temperature and Velocity Images in Air by Filtered Molecular
Scattering
• Mach 2 vertical supersonic jet is observed
• The laser is expanded to a sheet and frequency tuned
• Multiple images give the local, frequency shifted Cabannes line convolved with the iodine filter line at each pixel
• Deconvolution knowing the iodine filter shape gives the Cabannes line shape at each pixel
• Pixel by pixel curve fitting to theory gives T, v, P
Rayleigh Scattering Spectrum(of Nitrogen)
Rotational Raman 12 cm-1
Vibrational Raman
2331 cm-1
Cabannes 0.03 cm-1
Y = scattering length / mean free path
Cabannes Line Broadening
Scattering length, Λ
k1 k2
1 2
2k k K
max / 2laser
observerLasersource
Kinetic Regime
• If Y < 1, then in the Knudsen Regime – no collective effects. The Cabannes line is Gaussian in this regime
• If Y > 1, then in the hydrodynamic regime – collective effects dominate – Acoustic waves are important– In this regime there are three peaks, a central peak
associated with non propagating entropy fluctuations and two side Brillouin peaks associated with propagating sound waves
Cabannes (central Rayleigh) Line in AirShowing the Y parameter effect
-6 -4 -2 0 2 4 6
0.0
0.1
0.2
0.3
0.4
0.5
Re
lati
ve
In
ten
sity
(A
.U.)
Frequency (GHz)
Cabannes Line of Air at standard conditions with doubled YAG laser with detection at 90o
Y = 0.7
Mach 2 Underexpanded Supersonic Air Jet
Average image Single shot image
Temperature, pressure and velocity of a Mach 2 free jetwith weak crossing shocks
Coherent Rayleigh Brillouin Scattering (CRBS)
• Two pump beams create moving gratings• Ponderomotive forces drive moving, grating like density
fluctuations in the synchronized velocity groups• Coupling is to the polarizability of the molecule – force
occurs for monatomic as well as polyatomic molecules• The density of gratings created reflects the thermal
velocity distribution• Probe laser Bragg scatters off the density gratings• Temperature is found from the spectral profile of the
coherent signal beam observed ~10 meters from the sample volume
Coherent Rayleigh-Brillouin Scattering
Physical process
z
The optical dipole force produces the density fluctuations. Polarizable molecules feel a force toward the region of high field
Coherent Rayleigh Scattering in Weakly Ionized Gases
How is the intensity spectrum related to temperature?
• The molecules with velocity close to the wave phase velocity will be reorganized by the ponderomotive force leading to a moving density grating
• I() is then related to f(v=/k).
• Conclusion is: The width of the intensity spectrum depends on (T/m)1/2. The spectrum is closely Gaussian, about 10% wider than the spontaneous Rayleigh spectrum.
v = /k
f(v)
v
• Theory based on the Wang-Chang-Uhlenbeck Equation
• Internal energy modes considered• Perturbative method, linearized equation, model
collision term• Gas density perturbation waves: generation by the
optical dipole force and relaxation through particle collisions
Coherent Rayleigh-Brillouin Scattering in molecular gases
Theory
Coherent Rayleigh-Brillouin Scattering in molecular gases
Theory: Wang-Chang-Uhlenbeck equation
i ii v i
coll
f fv f a f
t t
( . ) ( , , )i in r t f v r t dv
1 2 sin( )z
k E EFa a kz t
m m
The forcing term is from the laser interaction and accelerates along the z axis:
At equilibrium, fi has a Gaussian distribution of velocities
and a Boltzmann distribution of states.
fi is the space –velocity-time distribution function for
molecules in state i.
Perturbation Approach
0( , , ) ( )i if v r t n x v3/ 2 2
2 20 0
1( ) exp( )
vv
v v
i
b
j
b
E
k Ti
i E
k Tj
j
g ex
g e
At equilibrium, the distribution function is
0( , , ) ( ) 1 ( , , )i i if v r t n x v h v r t
where and
The distribution function is assumed to be perturbed and the equations are solved for the dimensionless parameter, ih
1ih
, , 0 2 /bv k T M
Gas parameters needed
• Mass
• Shear viscosity
• Bulk viscosity
• Thermal conductivity
• Dimensionless internal specific heat capacity (1 for O2 and N2, 2 for CO2)
Yip & Nelkin (1964) theory for monatomic gases Pan, Shneider & Miles, PRL, 2002
The Experiment• Argon plasma at 50mb
• Pump laser is Frequency doubled Nd:YAG– 24.8 GHz (FWHM) with 250 MHz longitudinal mode structure
– Split and intersected in the gas at 1780 crossing angle
– Focal diameter is 200 μm diameter
– 6 mJ per pulse
– Polarized out of plane
• Probe laser is injection locked and tunable frequency doubled Nd:YAG– 150 MHz linewidth
– ~1 mJ per pulse
– Polarized in plane
• Fabry Perot Etalon– 99.6% mirror reflectivity at 532 nm
– Finesse of 215
– Free Spectral Range of 11.85 GHz
• Wavelength Monitoring Etalon FSR = 900 +/- 0.2 MHz
Experimental Details
• The pump beams produce a spectrum of interference patterns
– The patterns only couple to the gas over the region of kinetic motion
– The pump line width is broad compared to the kinetic spectrum, so it is considered constant
– The 250 MHz beat frequency is removed by Fourier transforming, filtering, and then back transforming the data
• The probe laser is scanned and the intensity of the scattering is monitored by a fixed etalon
– The intensity of the shifted scattering is a measure of the number of molecules in the kinetic (velocity) state that produces that shift.
– The probe is polarized orthogonal to the pump to eliminate background noise
Coherent Rayleigh-Brillouin Scattering
Experiment setup
Experiment setup photo in Weakly Ionized Gases
Coherent Rayleigh Scattering in Weakly Ionized Gases
Data shows the mode structure of the pump laser
Coherent Rayleigh Scattering in Weakly Ionized Gases
A sample result in argon gas (Tthermocouple = 293 K +/- 1 K)
Coherent Rayleigh Scattering in Weakly Ionized Gases
A sample result in argon glow discharge
Coherent Rayleigh-Brillouin Scattering in atomic gases
b=0
Data and model for nitrogen
N2 b=0.73 , agrees with previous measurements
Data and model for oxygen at 292 K
b=1.0 , differs from previous measurements (0.4 )
Data and model for oxygen
O2 Sensitivity of the measurement
CO2 Bulk Viscosity Sensitivity
CO2 Measurement and fitη=0.25 (frozen: γ=1.4)
Summary
Developed an alternative optical method to measure bulk viscosity.
New frequency regime, ~GHz. High frequency wave phenomena: ~1.
Convenient for measuring gas mixtures (Martian and other planetary atmospheres)
Convenient for measurements over a wide range of temperatures
Acknowledgments
This work was supported by the Air Force Office of Scientific Research under the Plasma Rampart Program.
Raman Excitation (RE)Tagging step
Interrogation step
Oxygen X (ground) State
Oxygen B State
Laser Induced Electronic Fluorescence (LIEF)
RELIEF ENERGY LEVEL DIAGRAM
Thermal Diffusion RELIEF Lines in Static Dry Air at 362 K
1 s
100 s
200 s
300 s
400 s
Thermal Diffusion of RELIEF Lines in Static Air1 pixel = 20.33 m
Linear Fit to Thermal Diffusion of RELIEF LineD = 0.26 cm2/sec
Maximum Time Between Tagging and Interrogation for Moist Air
RELIEF Line at the Tagging Position and After 7 sec Delayin Turbulent Subsonic Free Air Jet
A. Noullez, G. Wallace, W. Lempert, R.B. Miles, and U. Frisch, "Transverse Velocity Increments in Turbulent Flow Using the RELIEF Technique," J. Fluid Mechanics 339, 1997, pp. 287-307.
RELIEF Velocity measurement in the 1 meter diameter R1D Test Facility at AEDCAn X was written into the air and the displacement measured and compared with a
pitot probe measurement
flow direction
RELIEF(displaced)
Rayleigh(initial)
Region averaged in vertical dimension
3.6 mm
Simultaneous Tagging (Rayleigh Scattering) and Interrogation (RELIEF)Image in the R1D Facility at AEDC
Horizontal Displacement for AEDC Velocity MeasurementVelocity is 202.4 +/- 0.25 m/sec
Comparison of Pitot and RELIEF Velocity Measurements at AEDC
RELIEF for Supersonic Mixing (Glenn Diskin, NASA)The core helium jet is seeded with 1% oxygen
Helium core jet is seeded with ~1% O2 so it can be tracked
18 mm
28 mm
43 mm