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REMOTE DETECTION OF HYDROGEN LEAKS USING LASER INDUCED
A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
UNIVERSITY OF FLORIDA
Sameer Subhash Paranjpe
The author would like to thank Dr. Jill Peterson for her guidance and support. I
would also like to thank my fellow students Raghuram Vempati, Philip Jackson, Murray
Fisher, Matthew Gabriel and Ryan Ferguson for their assistance in various portions of the
TABLE OF CONTENTS
A C K N O W L E D G M E N T S ......... .................................................................................... iii
LIST OF TABLES ............. ............................... .......... .......... .. vi
LIST OF FIGURE S ......... ..................................... ........... vii
ABSTRACT .............. .................. .......... .............. xi
1 INTRODUCTION ............... ................. ........... ................. ... .... 1
2 LITER A TU R E REV IEW ............................................................. ....................... 6
M ie Scattering .................................................................................................... ...... 6
R ayleigh Scattering ........... ..................................................................... ....... .. .
Buoyant Jet Theory ............... ................ ......... ......................... .9
3 THEORETICAL FRAM EW ORK .................................... ......................... .. ......... 10
Elastic and Inelastic Light Scattering .................................. .................................... 10
Elastic Scattering M echanism .......................................................... ............... 10
M ie T theory ................................... ............................11
Calculation of intensity distribution functions I1 and I2 ...................................14
R ayleigh Theory .................................................. ..... .................... .. ... 15
Photon arrival rate calculations for Rayleigh and Mie theory.............................17
Scattering Cross Section Considerations.........................................................18
Buoyant Jet Theory ................. ............................ ..... ...... 18
Froude N um ber C alculation .............. ................................. ............... ... 19
Buoyant Jet Profiles and Concentration Variation ...........................................20
4 EXPERIM ENTAL SCHEM E .............................................................................23
Collection at 900 and B ackscatter......................................... .......................... 23
B ack Scatter C onsiderations..................................................... ................... .30
D ata R recording Procedure.............................. ........................... ... .............30
5 RESULTS AND DISCU SSION ........................................... .......................... 32
Comparison of Theoretical and Experimental Photon Arrival Rate...........................32
Calculation of Theoretical Rayleigh Photon Arrival Rate. ................................32
Calculation of Theoretical Mie Photon Arrival Rate .......................................33
Calculation of Total Theoretical Photon Arrival Rate. .....................................38
Calculation of Experimental Photon Arrival Rate................... ..... ............38
D ata A analysis Techniques ................................................ .............................. 41
Integrated area m ethod. .............................................. ............................. 42
Peak V oltage M ethod. ............................................... .............................. 43
Analysis of Recorded Data .......... ........ ...................................... 46
C ase I: A rgon-ion laser............ .................................................... ........ 46
P eak voltage variation ............................................ ........... ............... 46
N orm alized peak voltage variation ................................... .................48
Standard deviation profiles...................................... ......................... 48
Case II: Pulsed Nd:YAG laser; pure helium ............................................... 50
P eak voltage variation .............................................. ......... ............... 50
N orm alized Peak Voltage Variation .................................... ............... 51
Standard deviation profiles...................... ........................... 51
Case III: Pulsed Nd:YAG laser; 20%helium ,80% nitrogen.............................52
P eak voltage variation ............................................ ........... ............... 52
Norm alized peak voltage variation. .................................. .................53
Standard D aviation Profiles. ............................................. ............... 54
M easurements in Backscatter ................................. ................................... 55
6 CON CLU SION S .................................... ... ........... .......... ........... 58
LIST OF REFEREN CES ................................................................... ............... 60
B IO G R A PH IC A L SK E TCH ..................................................................... ..................62
LIST OF TABLES
3-1 Scattering cross section at a wavelength of 532 nm............................................18
3-2 Froude number calculations show that the criteria for buoyant jet is met for all
combinations of flow fluids, nozzle diameters and downstream distances.............20
5-1 Particle counter data show the particle distribution in the lab ..............................34
5-2 Shows that average peak voltage recorded after 300 pulses in shear layer is a
conv erg ed m ean .................................................. ................. 4 5
5-3 Control volume to leak diameter ratio for all three cases shows that the ratio is
far less for backscatter than 900 scattering .................................... ............... 57
LIST OF FIGURES
3-1 M ie scattering geom etry ......... ......... ................ ........................ ............... 11
3-2 Ii (perpendicular) and I2 (parallel) intensity distribution functions from the
interactive w ebpage .................. ................................. ..... .. ........ .... 15
3-3 Ii (perpendicular) and I2 (parallel) intensity distribution functions from McCartney. 15
3-4 Instantaneous and time averaged profiles of a typical buoyant jet...........................21
3-5 Concentration variation with r for z = 2 ....................................... ............... 22
4-1 Experimental scheme for collection of scattered light at 90.............. ................24
4-2 Experimental scheme for collection of scattered light at a 1800 (back scatter) .......25
4-3 Nozzle mounting showing three dimensional motion capability...........................27
4-3 Photomultiplier tube linearity tested as a function of flash lamp voltage ..............29
4-4 Calculation of nozzle traverse distances ....................................... ..................... 31
5-1 Theoretical photon arrival rate calculations. ...................................................33
5-2 Model M shows maritime distribution of aerosols (McCartney 1979, page 139) ...35
5-3 M odel M duplicated on a log-normal scale................................... ............... 36
5-4 Comparison of number density of maritime and lab aerosols..............................37
5-5 Effect of maritime and lab aerosol distribution on Mie scattered intensity ............37
5-6 Typical waveform of a burst seen on the oscilloscope....................................39
5-7 Points in shear layer where measurements are made ............................................40
5-8 Comparison of experimental and theoretical photon arrival rates .........................41
5-9 Convergence studies of normalized area and averaged area...............................42
5-10 Waveform with varying glare at four downstream locations ...............................43
5-11 All four waveforms normalized with their individual peaks.................................44
5-12 Voltage variation for Argon-Ion laser. ............................... ............................... 47
5-13 Normalized peak voltage variation for argon-ion laser.........................................48
5-14 Percent standard deviation variation for near field case. .......................................49
5-15 Percent standard deviation for far field case .................................... .................49
5-16 Voltage variation for pulsed Nd:YAG laser.................................. ............... 50
5-17 Normalized peak voltage variation for Nd:YAG laser.................. ... ............ 51
5-18 Standard deviation variation for Nd:YAG laser for pure helium...........................52
5-19 Relative size of beam and leak diameter ........................................ .............52
5-20 Voltage variation for the pulsed Nd:YAG laser for the mixture.............................53
5-21 Normalized peak voltage variation for Nd:YAG laser for the mixture .................54
5-22 Percent standard deviation variation for Nd:YAG laser for the mixture of helium
and nitrogen to simulate the optical properties of nitrogen................. ......... 54
5-23 Schematic ofbackscatter on a time basis shows separation between beam dump
glare and scattered signal from the nozzle. ................................... ............... 55
5-24 Normalized area variation shows a reduction in scattered intensity in presence of
helium (backscatter); Nozzle diameter = 1/4" ; Re =500; Fr = 290 .........................56
a = particle radius (m)
C = concentration of the flow fluid (kg/m3)
C* = dimensionless density
CPMT = photomultiplier tube calibration constant
D = diameter of the nozzle (m ; ")
E' = Electric vector of the incident wave (V/m)
Fr = Froude number =Re/Gr2
G= gravitational acceleration (m/s2)
Gr = Grashof number = g(pa-po)D3/po"
H' = Magnetic vector of the incident wave (N/Ampere-m)
o = Incident laser power (W; photons/pulse)
1 = length of control volume (m)
m = mass flow rate (kg/s)
n = gas index of refraction at known reference conditions
n(r) = number density per radius interval (molecules/m3/micron)
N= molecular number density (molecules/m3)
Nd = number of data points.
r = radial distance from jet centerline (m)
rx-y= cross co-relation coefficient
Re = Reynolds number = pvD/ u = 4m/ 7tDg
v = velocity of buoyant jet (m/s)
V= photomultiplier tube voltage (V)
x = percent helium
y = distance from jet centerline normal to beam
z = downstream distance (mm)
a = size parameter = 27na/X
P = spread angle
0 = angle of observation measured from the forward to scattering directions.
p = scattering angle
y = wave function
rI = optical efficiency of transmitting and collecting lenses
Q = solid angle of the collection optics
X = wavelength of laser light (nm)
c = differential scattering cross section (m2/sr)
p = density of gas (kg/m3)
[ = dynamic viscosity of gas (Pa-s)
u = dynamic viscosity of gas
a = ambient
cl = centerline
i = species
m = mixture
o =jet exit condition
Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science
REMOTE DETECTION OF HYDROGEN LEAKS USING LASER INDUCED
Chair: Jill Peterson
Major Department: Mechanical and Aerospace Engineering
The current study examines the use of laser induced Rayleigh/Mie scattering as a
means of remotely detecting hydrogen leaks. An axisymmetric vertical buoyant jet at a
Reynolds number of 500 was used to simulate the hydrogen leak and the scattered signal
indicating hydrogen concentration was examined at different downstream locations.
Helium was used as a substitute for hydrogen for safety reasons. The scattering cross
section of hydrogen is 0.23 times the scattering cross section of air and the scattering
cross section of helium is 0.015 times the scattering cross section of air. A mixture of
20% helium and 80% nitrogen was also used at the same Reynolds number of 500, since
the scattering cross section of this mixture equals the scattering cross section of
hydrogen. The principal challenges in RLS detection were electronic shot noise and Mie
scattering. The electronic shot noise was found to induce less than 0.1% uncertainty for
an averaging time of 1 second. A Nd:YAG pulse laser operating at a wavelength of
532 nm was used and the scattered signal from the helium leak was collected at 90 to the
incident beam and focused onto a photomultiplier tube. The signal from the
photomultiplier tube was read through a high speed digital oscilloscope. The repeatability
and reproducible of the data was established using a set of convergence studies. It was
found that the amplitude of the Rayleigh/Mie signal decreased by 25% and the standard
deviation increased by 45% in the presence of helium. This increase in standard deviation
is more than the established values of 305. Non dimensionalized profiles collapsed to a
classic similar shape, further documenting experimental results.
Hydrogen is an attractive fuel source. However, leak detection is essential if it is to
become a widespread, easily used and safe source of energy. It is relatively simple to
determine whether a system is leaking hydrogen by identifying pressure drops. Finding
the source of the leak however can be time consuming, costly and dangerous. The
conventional method of leak detection involves the use of contact sensors. The following
are the typical varieties of contact sensors commonly used for leak detection.
Catalytic bead sensors. These sensors consist of two beads surrounding a wire
operating at a temperature of around 4500C. One of the beads is passivated. This ensures
that it does not react with gas molecules. The other bead is coated with a catalyst to
promote a reaction with the gas. The beads are generally placed on separate legs of a
Wheatstone bridge circuit. When hydrogen is present, there is no measurable effect on
the passivated bead, but there is a significant effect on the catalyzed bead. The increase in
heat increases the resistance in that leg of the Wheatstone bridge circuit, which in turn
changes the bridge balance signal, and this serves as the sensor signal. These sensors are
usually used in the 1 to 5 % hydrogen range. The response time of the sensor varies,
ranging from 10 to 30 seconds for full-scale response.
Semiconductor sensors. These sensors use semiconducting oxides whose
electrical resistance changes in the presence of hydrogen due to a reduction reaction.
These sensors generally operate at temperatures above ambient. The disadvantage of
these sensors is that the oxides change their resistance as the oxygen concentration in the
environment changes, making these sensors unsuitable for such environments. They have
a fast response time and detection limits of 0-1000 ppm hydrogen.
Electrochemical sensors. Electrochemical sensors are composed of an anode and
cathode sandwiching a chemically sensitive electrolyte. When hydrogen passes over the
electrolyte, a reversible chemical reaction occurs. This generates a current proportional to
the gas concentration. However, oxygen is required to ensure chemical reversibility. This
implies that the sensor is not environmentally independent. Electrochemical sensors are
typically used to detect hydrogen in the range of 100 to 1000 ppm. Response times can be
as low as several seconds, although typically these sensors are specified at 30 to 50
seconds for full-scale response.
Resistive palladium alloy sensors. The surface of palladium acts catalytically to
break the H-H bond in diatomic hydrogen and allows the monatomic hydrogen to diffuse
into the material. Palladium can dissolve more than 600 times its volume in hydrogen.
The level of dissolved hydrogen proportionally changes the electrical resistivity of the
metal. No other gases or environmental controls are necessary for these measurements.
Hydrogen field effect transistor. By using palladium as the gate material for a
standard field effect transistor, small changes in the resistivity of the palladium produce
large changes in the current-voltage characteristics of the FET. This sensor technology
works well in the range of 50 to 1000 ppm range of hydrogen.
Although all these systems can effectively detect hydrogen leaks, the sensors are
intrusive and have to be physically inserted into the suspect area. However due to the low
combustion limits (4%) of hydrogen, for safety issues in most applications, it would be
advantageous if the leak could be detected without actually inserting a probe in the
suspected area. The current study explores a novel remote detection technique.
Laser Induced Rayleigh/Mie Scattering
This method uses a laser directed at a suspected leak source. As the laser pulse
moves through air, the electromagnetic wave interacts with aerosols in the atmosphere
and the molecules of the component gases. This causes some of the incident laser light to
scatter in all directions, with varying intensities depending on the particle type and size.
Substantial information can then be obtained by looking at the intensity of scattered light.
The principal advantages of this technique are that it is non intrusive, it does not alter the
flow pattern, and it has high spatial and temporal resolution.
Almost 99% of the light scattered by atmospheric particles is elastically scattered.
Rayleigh and Mie scattering are the two types of elastic light scattering theories. The
mechanism of elastic light scattering and the quantification of the scattering cross section
and scattered intensity terms are dealt in Chapter 3. Mie theory was developed by the
German physicist G. Mie (1908). It is in terms of complex series solutions and is valid for
particles of all sizes. If the particle size becomes very large, then Mie theory can be
simplified using geometric optics. However, for particles with a diameter much less
(approximately 0.06 times or less) than the wavelength of incident light, the Mie theory
reduces to a single term simplification called the Rayleigh theory. The amount of light a
particular particle can scatter can be defined in terms of its scattering cross section. Thus
a particle with a higher scattering cross section would scatter more light than a particle
with a lower scattering cross section. For Rayleigh/Mie scattering, the scattering cross
section is a dominant function of the particle size, wavelength of incident light and
refractive index of the particle. The scattering cross section of hydrogen is about 1/5th that
of the surrounding air molecules. Hence the intensity of light scattered by hydrogen is
expected to be less than the intensity of light scattered by the surrounding air molecules.
In the absence of hydrogen, there would be a steady signal from the atmosphere that
would consist of the Mie signal from the aerosols and Rayleigh signal from the air
molecules. In the presence of hydrogen, we should expect this signal to fall.
The primary objective of this study is to detect the fall in scattered intensity in the
presence of hydrogen. Because of safety issues, helium, which has a scattering cross-
section 0.015 times that of air is used for the experimentation. In order to match the
scattering cross section of hydrogen, a mixture of 20% helium and 80% nitrogen is also
used. The scattered intensity is directly proportional to the scattering cross section. The
proportionality constant depends on the experimental conditions. For a fixed
experimental set up, the scattered signal from a given control volume would be the same
if the product of scattering cross section and number density of species in that control
volume is identical. Hence, as seen in Chapter 3, the scattered signal from a mixture of
20% helium and 80% nitrogen and from pure hydrogen are the same.
A second objective is to test the limits of detection. The measurements are taken at
four different downstream locations for this purpose. Also measurements are taken in
back scatter to test the feasibility of the technique for field measurements.
Two nozzles with diameters of 14" (6.3mm) and /2" (12.6mm) are used for
simulating the leak. A continuous wave low power argon ion laser is used with the 4"
nozzle and a high power pulsed Nd:YAG laser was used with the 12" nozzle. For each
nozzle diameter the data is recorded for the two cases of pure helium and the mixture of
20% helium and 80% nitrogen. The Reynolds number is fixed at 500 for each case and
Froude numbers are calculated as discussed in Chapter 3. For all combinations of
Reynolds and Froude numbers the leak is an axisymmetric vertical buoyant jet. The mean
and fluctuating temperature and concentration profiles of a buoyant jet are well
established. Since the leak is a buoyant jet it is expected that the variation of recorded
scattered voltage would follow these profiles.
Mie theory is the general solution for scattering of a plane electromagnetic wave by
a particle of arbitrary size. In 1908 Mie first derived the relations for calculating various
scattering characteristics of electromagnetic radiation, by homogenous, absorbing spheres
of any diameter. The Mie solution was obtained via the solution of the wave equation
which originates from the more fundamental Maxwell relations. The details of the Mie
solution from these basic equations have been dealt with in references such as Kerker
(1969), and Bohren and Huffman (1983).
The solution involves series expansions called the angular intensity distribution
functions. These distribution functions are complex and involve the calculation of
Legendre polynomials and Riccati-Bessel functions. Over the past 30 years numerous
algorithms and subroutines have been developed mostly in FORTRAN and C to calculate
these functions. The first subroutine for calculating the scattering functions was
developed by Dave (1970) and incorporates the first 10 terms of the series expansion.
Wiscombe (1980) developed algorithms for calculating the intensity distribution
functions. These functions were plotted as a function of scattering angle and were robust
for any given combination of particle size, incident wavelength and refractive index. An
interactive webpage was developed by Prahl (2000) which allows the computation of the
intensity distribution functions at any value of scattering angle for input values of
incident wavelength, particle size and refractive index. This subroutine is used for the
theoretical calculations of Mie scattered intensity in this study. The results of the
subroutine are verified against published values of the angular intensity distribution
functions in Kerker (1969) .The comparison is discussed in Chapter 3. McCartney (1976)
lists standard aerosol distribution for continental and maritime distributions. Using these
particle distributions, the number of particles of a particular size can be calculated as
discussed in Chapter 5. Knowing the particle size distribution, the intensity distribution
functions can be calculated using the subroutine by Prahl (2000). The details of these
calculation are shown in Chapter 5.
Mie scattering from particles has been used as a probe for monitoring concentration
fluctuations. This technique called Marker nephelometry uses light scattered from seeded
particles in a flow (Mie scatters) as a concentration probe. Since its introduction in 1961
by Rosenweig et al. (1961), this technique has proven to be a very useful probe for
monitoring real time fluctuations manifested by seeded particles in the flow. Becker et
al.(1967) and Shaughnessy and Morton (1977) have described the application of this
technique. The same technique has been used for 2-D measurements by Long et
al.(1981). These workers used a plane of light to illuminate particles in a flow field and
used a television camera to get a digitized 2-D image of turbulent mixing.
For particles smaller than the incident wavelength (diameter < 0.06 wavelength)
only the first term of the Mie solution is needed to predict the intensity of scattered light.
This single term simplification called the Rayleigh theory has been extensively discussed
in literature notably by McCartney (1976) and Kerker (1969). Van de Hulst (1981)
addressed the issue of assuming Rayleigh scattering to be single and independent of
surrounding scatters. At 1 atm pressure and at a temperature of 300 K, air molecules are
separated by distances over 600 radii. He estimated that 3 radii distance between
surrounding scatters is sufficient separation to ensure independent scattering. This means
that the assumption of no multiple scattering is valid for air molecules for pressures much
higher than atmospheric pressures.
Rayleigh light scattering is an ideal probe for gas temperature and concentration
measurements since it is non-obtrusive, direct and has high spatial and temporal
resolution. Using the Rayleigh scattered signal the number density of species under
consideration can be calculated and since for an ideal gas at constant pressure, the
number density is inversely proportional to temperature, the temperature can be known.
Using this relation Muller-Dethelfs and Weinberg (1979) first used Rayleigh light
scattering for temperature measurements in flame speed experiments. Dibble et al. (1980)
used this technique to measure temperature fluctuations in premixed flames and also
demonstrated that this technique could be extended to turbulent diffusion flames where
the fuel and air have been carefully chosen to have identical Rayleigh scattering cross
sections. Pitz et al. (1976) use RLS to measure temperature in a hydrogen-air flame.
Horton and Peterson (1999) carried out transient temperature measurements in an ideal
gas using laser induced RLS. Flow visualizations and transient temperature
measurements were done in an axisymmetric impinging jet in a rapid thermal chemical
vapor deposition reactor using RLS by Matthew and Peterson (2002). Robben (1975)
evaluated the spectral broadening of Rayleigh scattered light to derive a temperature in
turbulent flow measurements. Rayleigh light scattering has also been used for monitoring
the concentration fluctuations which occur in isothermal turbulent flows by Graham et al.
(1974) and Dyer (1979). Pitts and Kashiwagi (1983) used RLS for the study of turbulent
mixing. Bryner and Pitts (1992) used RLS for combustion studies.
One of the major disadvantages of RLS is background glare, which is at the same
wavelength as that of the scattered beam and is impossible to filter from the signal. Glare
minimization is possible by blackening the surfaces. Otugen (1993) used a dual line
detection RLS technique for gas temperature measurements in which they eliminated
surface scattered laser light from the Rayleigh signal by using two wavelengths. A
primary assumption in this study was that the ratio of the surface reflection at two
wavelengths is constant. The results indicated that accurate temperature measurements
were possible even when the laser light background intensity was twice the Rayleigh
Buoyant Jet Theory
As previously stated, in this study the leak is created using pure helium and a
mixture of 20% helium and 80% nitrogen. The density of both pure helium and the
mixture of helium and nitrogen is different from the surrounding fluid (air). The
Reynolds number is set at 500. As discussed in Chapter 3 the leak for both cases could be
assumed to be an axisymmetric vertical buoyant jet. The mean and fluctuating
temperature and concentration profiles of a buoyant jet are well established in numerous
references notably Rodi (1982), Chen and Rodi (1980) and Schlichting (1979). In this
study, the recorded scattered voltage and standard deviation profiles were compared with
these well established concentration profiles.
Elastic and Inelastic Light Scattering
There are two types of light scattering mechanisms: elastic scattering and inelastic
scattering. In inelastic scattering there is a loss in energy of the incident wave and the
scattered wave is emitted at a frequency different from the incident wave i.e hVincident
hvscattered. One of the types of inelastic light scattering is termed as Raman scattering and
it involves a change in either the vibrational or rotational quantum number of the
In elastic scattering of light, there is no loss of energy between the incident and the
scattered wave. i.e hVincident= hVscattered. Elastic scattering is 2 to3 orders of magnitude
greater than inelastic scattering. This is the primary reason for choosing elastic scattering
as a measurement technique since the signal strength is expected to be 2 to 3 orders of
magnitude higher than the inelastic signal making it more easily discernible. The
mechanism of elastic scattering is discussed in detail in below.
Elastic Scattering Mechanism
Consider an electromagnetic wave traveling through atmosphere. Scattering occurs
whenever it encounters an obstacle in its path. This obstacle could be a gas molecule,
dust particle or aerosols. For simplification, the term molecule is used in this description
of the mechanism of elastic scattering. A molecule can be considered a mechanical
oscillator carrying unequal masses and opposite charges at the center and periphery. The
elastic scattering theory assumes that the molecules are non polar. This means that the
negative charge is uniformly distributed over the periphery and can be assumed to be at
the center. Hence the electric dipole moment, which is the product of the charge and the
separation distance, is zero in its stable state. In the presence of an electromagnetic wave
the charges are forced apart due to the external electric field of the wave and an induced
dipole moment is created. Since the field strength of the external electric field varies
periodically, the induced dipole oscillates synchronously with the field. This oscillating
dipole then emits a secondary wave at the same frequency as that of the primary wave.
This secondary wave is the scattered wave.
Figure 3-1 shows the scattering geometry for Mie scattering.
Figure 3-1. Mie scattering geometry.
The Mie theory describes the scattering of a plane electromagnetic wave by a
particle of arbitrary size. The Mie theory originates from the exact solution of scattering
of an electromagnetic wave equation (derived from the Maxwell relations) by a particle
and has been discussed in detail by Kerker (1969). A scattered wave is generated
whenever a plane wave is incident upon a particle possessing a discrete boundary and a
refractive index different from the surrounding medium.
In spherical co-ordinates the wave equation can be described as
[1 Or2 8 + 1 8 sinO 8 + 1 2 + k = 0 (3.1)
rr2r r r2 siniO 0 0 r2 sin2 O(p2
The solutions to this equation are the Hertz- Debye potentials which can be
obtained by the method of separation of variables as follows:
V = R(r)O(9)D((p) (3.2)
Each of these functions satisfies the following ordinary differential equations:
d2rR(r) + [k2 n(n+)] rR(r) =0 (3.3)
1 d (sinO d0(_)) + [n(n+l) m2 ] 0(0) = 0 (3.4)
sinO dO dO sin20
d2Dj() + m2((P) = 0 (3.5)
where n and m are integers.
The solutions of equation 3.3 are the Riccati Bessel functions defined as
n(kr) = (tkr/2) 2 Jn +12 (kr) (3.6)
(kr) = -(tkr/2) / Nn + 1 (kr)
where Jn + 12 (kr) and Nn + 12 (kr) are the half integer order Bessel and Neumann functions.
The solutions of equation 3.4 are the associated Legendre polynomials given by
0 = Pn(m)(cos) (3.7)
The solutions to 3.5 are the sin(myp) and cos(mp).
The general solution of the scalar wave equation (3.1) (the Hertz -Debye
potentials) can be obtained from a linear superposition of all of the particular solutions.
The Hertz Debye potentials represent the solution for the incident wave, the scattered
wave and the wave inside the particle. Only the Hertz Debye potentials for the scattered
wave are discussed here. The Hertz Debye potentials for the scattered wave can be
expressed in terms of an infinite series and are called the angular intensity distribution
functions Ii and 12. I1 and 12 are proportional to the perpendicular polarized and parallel
polarized components of the light scattered at an angle 0 respectively.
11 = I Z 2n+l (anrnC(cos0)+ bnTn(cos0))|2 (3.8)
12 = I Z 2n+l (anTn(cos0) + bn7n(cos0))|2 (3.9)
where 7,(cos0) = PnlcosO) (3.10)
and n((cos0) = d P(l)(cos0)
The constants an and bn are obtained from the boundary conditions that the tangential
components of the electric and magnetic field of the incident wave are continuous over
the entire surface of the sphere. If the number density (N) of the particle is known then
the Mie scattering cross section for a single particle size can be defined as
oMie = )2 N(11+I2) (3.11)
The Mie scattering cross section is an indication of the intensity of light that would be
scattered from a particle of arbitrary size.
Calculation of intensity distribution functions Ii and 12
From equations (3.8) and (3.9) it can be seen that the intensity distribution
functions Ii and I2 are in terms of complex infinite series and involve the calculation of
the Legendre polynomials for every value of n. Also the constants an and bn involve the
calculation ofRiccati Bessel functions for every value ofn. As stated in Chapter 2,
subroutines for the calculation of Iand 12 are available. In this study one such program
developed by the Oregon Medical Laser Center is used. The input parameters are the
incident wavelength, particle size and refractive index. McCartney (1979) states that the
refractive index of crystalline haze aerosols can be assumed to have a value of 1.33. The
aerosols are assumed to be dielectric. This value is used throughout this study. It is to be
noted that the angular intensity distribution functions depend on the refractive index and
the value of 1.33 imposes a limiting condition since it does not take into account dry
particles like soot. The values of I1 and I2 obtained from this subroutine are compared
with published values of I and I2 in McCartney (1979). The comparison is done for five
combinations of incident wavelength, refractive index and particle size. A typical
comparison is shown in figures 3-2 and 3-3. Size parameter gives the relation between
the size of the particle and the wavelength of incident light and is defined as
a = 27a (3.12)
Figure 3-1 shows the values of I and I2 obtained as a function of scattering angle
for a size parameter (a) of 0.5 (particle radius of 0.044 microns) and refractive index of
sphere of 1.33. Using the program and figure 3-2 is obtained from McCartney for the
same input parameters. The two figures are identical, establishing the accuracy of the
\\ / -- perpendicular
Nl C CO C N T COO
Observation angle (deg)
Figure 3-2. Ii (perpendicular) and I2 (parallel) intensity distribution functions for size
parameter =5, and refractive index =1.33 obtained from the interactive
S a 0.5
2 r = 0.044 nm
10-4 I l Il
0 20 40 60 80 100 120 140 160 180
Observation angle, 0 (deg)
Figure 3-3. Ii (perpendicular) and I2 (parallel) intensity distribution functions for size
parameter =5, and refractive index =1.33 from McCartney.
The Mie solution is a complex mathematical solution. For particles of size much
less than the wavelength of incident light, the Mie series solution converges in one term
and is called the Rayleigh theory. The Rayleigh theory was originally put forth by Lord
Rayleigh (J.W. Strutt, third Baron of Rayleigh) in 1871, long before the Mie solution was
developed (1908). Later on it was proved that the Rayleigh theory is actually a single
term simplification of the Mie theory. Lord Rayleigh put forth the Rayleigh theory
principally to explain the blue color of the sky. He assumed that the particles were
spherical, isotropic, much smaller than the wavelength of incident light and denser than
the surrounding medium. Through straightforward dimensional reasoning he arrived at
the conclusion that scattering varies directly with the square of the particle volume and
inversely as the fourth power of the wavelength of incident light.
The scattering by gas molecules is in the Rayleigh regime because of the small size of
the molecules. McCartney (1976) gives a good physical description of Rayleigh
scattering. He states that for the Rayleigh theory to be applicable, a 1 or the particle
radius should be at least 0.03 times less than the wavelength of incident light. The
following are the assumptions about the molecules for Rayleigh scattering.
1. The molecules are non ionized implying that there is no overall charge over the
entire molecule. This means that the molecule does not experience a net force in
an electric field.
2. The molecules are non polar meaning that the electronic charge is uniformly
distributed over the shell and could be treated to be at the center. Even though the
polar assumption is made in the original theory, the Rayleigh theory is valid for
non-polar particles as well.
3. The molecule is isotropic implying that the forces experienced within the
molecule are balanced.
4. The molecule is linear which means that the binding forces within the molecule
obey Hooke's law.
5. The molecules are lightly damped meaning that the amplitude of oscillation does
not become too large at frequencies near resonance.
These assumptions are applicable to ordinary gas molecules like nitrogen and helium.
Based on these assumptions McCartney (1976) derives the differential Rayleigh
scattering cross section for perpendicular polarized scattered light as
oRayleigh = 1285 a6 n2 1 (3.13)
34 n2 + 2
As seen from equation (3.13) the Rayleigh scattering cross section is independent of the
scattering angle and has an inverse fourth power dependence on the wavelength of
incident light. It also depends on the refractive index (n) of the particle.
Photon arrival rate calculations for Rayleigh and Mie theory
Knowing the Rayleigh and Mie scattering cross sections the intensity of scattered
light can be calculated for a given set of experimental constants. Both the Rayleigh and
Mie scattering cross sections are applicable for an individual molecule and are not
functions of the gas number density N assuming independent scattering. For a given
volume of a gas the intensity of scattered light is linearly proportional to the gas number
density. The scattering from multiple molecules in a given volume can be considered to
be additive, independent and incoherent because of the random spacing and thermal
motion of the gas molecules.
Thus for an incident beam of energy Io ,scattered from a control volume with
molecular number density N, the intensity of the scattered beam is proportional to the
scattering cross section of the molecule, the number density and the energy of incident
Iscat = C(IooN) (3.14)
The proportionality constant is defined by the scattering geometry, namely the
solid angle of the collection optics (Q), control volume (dV) and optical efficiency of the
collection optics (r). In this study, the scattered beam was collected using a 60 mm
diameter lens at a distance of 250 mm from the scattering volume which define the solid
angle. The control volume depends on the angle at which the scattered beam is collected
and is discussed in chapter 4. The optical efficiency was assumed to be 90% for each
optical surface the scattered beam is passed through. Thus for Rayleigh scattering the
intensity of scattered light from a control volume containing a mixture of gases is given
And scattered intensity for Mie scattering is given by
Imie = (Io)(rl)(dV)(Q)X(NGMie)i (3.16)
Knowing the Rayleigh and Mie scattered intensities, the total scattered intensity received
at the collection lens can be calculated as
Itotal = IRayleigh + IMie (3.17)
Scattering Cross Section Considerations
In this study, pure helium and a mixture of 20% helium and 80% nitrogen are
used. The scattering cross section of helium is 0.015 times the scattering cross section of
air and the scattering cross section of pure hydrogen is 0.23 times the scattering cross
section of air. In order to match the scattering cross section of hydrogen, a mixture of
20% helium and 80% nitrogen is used. The differential scattering cross sections of
hydrogen, helium and nitrogen are listed at a wavelength of 532 nm in table 3-1.
Table 3-1. Scattering cross section at a wavelength of 532 nm.
Gas Scattering Cross Section (a) (m2/sr)
Air (Nitrogen) 8.16E-32
Knowing these values, the mixture concentration of 20% helium and 80% nitrogen are
obtained using the following relation (x = % helium)
Hydrogen = X Ghelium + (1-X) Gnitrogen. (3.18)
Buoyant Jet Theory
Buoyancy forces arise in a jet if the density of the flow fluid is different from the
density of the surrounding fluid. In the absence of buoyancy forces the jet is called a non
buoyant jet. In the other limiting case when the buoyancy force dominates the flow, the
jet is called a plume. Thus the non buoyant jet has about the same density as the
surrounding environment so that the buoyancy forces are absent, whereas a pure plume
has no initial momentum. The densities of both flow fluids used for the experiments- pure
helium and the mixture of helium and nitrogen are different from the density of the
surrounding fluid (ambient air). The Froude number is used to characterize whether a jet
is a non buoyant jet, a buoyant jet or a plume-Chen and Rodi (1980). The Froude number
is the ratio of inertial forces to buoyancy forces and is defined as
Fr = Re/Gr2 (3.19)
Reynolds number is the ratio of the inertial forces to the viscous forces and can be written
Re = vd (3.20)
The Grashof number (G) is defined as
And it is the ratio of buoyant to viscous forces.
In a non buoyant jet, only the Reynolds number is of influence (Fr=oo) whereas in
pure plumes only the Grashof number is dominant (Fr=0). For an axisymmetric vertical
jet, the limiting condition for a buoyant jet is defined in Chen and Rodi as follows
0.5 < Fr-1/2 (po/pa-1/4 (z/D) < 5 (3.22)
Froude Number Calculation
Two different nozzle diameters of 1/4" and 1/2" are used. Also two flow fluids (pure
helium and mixture of 20% helium and 80% nitrogen) are used. Four different cases are
considered: 12" diameter nozzle with pure helium, 12" diameter nozzle with a mixture of
20% helium and 80% nitrogen, 14" diameter nozzle with pure helium and 14" diameter
nozzle for a mixture of 20% helium and 80% nitrogen. The measurements are taken for
four downstream distances of 2, 4, 6, and 8 nozzle diameters. The Reynolds number is
chosen as 500 for each case.
The criterion for buoyant jet (equation 3.21) is tested for all four combinations of
nozzle diameters and flow fluid and at all four downstream distances. Table 3-2 lists the
values of Froude numbers for all four combinations of nozzle diameters and flow fluid
and for the two limiting cases of 2 and 8 nozzle diameters downstream.
Table 3-2. Froude number calculations show that the criteria for buoyant jet is met for all
combinations of flow fluids, nozzle diameters and downstream distances
Cases Reynolds Froude 0.5 < Fr-1/2(o/a)-1/4z/D <5
Number(Re) Number(Fr) 2 nozzle 8 nozzle
2 nozzle 8 nozzle
1. 1/2 "; He 500 36.5 0.521 2.08
2. 1/2"; 20%He, 500 64.5 0.54 2.16
3. /4"; He 500 292.5 0.88 3.52
4. /4 "; 20%He, 500 516.5 0.94 3.76
Buoyant Jet Profiles and Concentration Variation
Figure 3-4 shows the instantaneous and time averaged profiles of a buoyant jet.
The jet centerline is characterized by a potential core near the nozzle exit. Inside the
potential core, the concentration of the flow fluid is 100%. The shear layers define the jet
spread angle (P).The edge of the shear layers mark the boundary of the time averaged
profile. The concentration of the flow fluid varies from a 100% at the jet centerline to 0
% at the edge of the shear layers. Chen and Rodi (1980) have listed the spread angles of
non- isothermal jets. In this study a spread angle of 130 is found for a vertical round
Chen and Rodi (1980) summarize empirical data predicting the axial spread of an
axisymmetric vertical buoyant jet. The concentration at any point in the shear layer of a
buoyant jet can be calculated using the following relation.
C- Ca = exp [-Ko(r/z)2 ] (3.23)
tme Averaged Profile
Figure 3-4. Instantaneous and time averaged profiles of a typical buoyant jet.
The constant Kc is related to the jet spread angle 0 as
Kc = In 2/(tanp/2)2
So, for ajet spread angle of 130 Kc = 53.4
For a vertical buoyant jet, the centerline concentration (Cc ) is found from the
dimensionless density (C ) using the following equation
Co- Ca= C* = 4.4Fr l/(po/pa) -7/16 (z/D)-5/4
Using this value of Kc the concentration of the flow fluid at any point in the flow
can be calculated using equation 3.22.
For both the 1/2" diameter nozzle and the /4" diameter nozzle, C- Ca/Ccl- Ca is
plotted as a function of radial distance (r) for a downstream distance (z) of 2 nozzle
diameters for each case as seen in figure 3-5.
Figure 3-5. Concentration variation with r for z = 2 is Gaussian in nature for both nozzle
diameters of 14 and /2".
--1/4 inch nozzle
--1/2 inch nozzle
So r- q-t .- Wo LON C 0 o O I%- I- W- o
S.- ri Ci i 4 4 ..6 i 6 r
Collection at 90 and Backscatter
The goal of the project is to detect the change in intensity of scattered light in the
presence of hydrogen. Rayleigh scattering is independent of the angle at which the
scattered light is collected but the Mie signal depends on the scattering angle. Initially,
the collection optics were set at 900 to the incident beam and the measurements were
focused on a single point of the beam as seen in figure 4-1. An advantage of this optical
configuration is that the glare from the incident beam on the scattered signal is minimum
at this angle since the minimum incident beam area is visible to the photomultiplier tube.
For field measurements since the exact position of the leak could be at any distance
from the laser, the drawback with a 900 scattering scheme would be that the collection
optics consisting of the collecting, focusing lenses, filter, photomultiplier tube and the
digital oscilloscope would have to be moved depending on the position of the suspected
leak. It would be ideal to use a scheme in which the collection optics could be kept
stationary. This can be done by using a backscatter scheme in which the incident light is
passed between two 4" (101.6mm) square mirrors and the scattered light is collected at a
1800 using the two mirrors. The mirrors are 90% reflective at a wavelength of 532 nm.
The backscatter scheme is shown in figure 4-2. For the backscatter scheme, since the
angle of observation is a 1800, the control volume is defined by the beam area and the
pulse width of 5 ns (1.5m). This leads to a fall in the signal to noise ratio as the leak
occupies only 0.6% of the control volume as discussed in Chapter 5.
40 4- Collecting lens
4- Focusing lens
I -Band pass filter
4- Photomultiplier tube
Figure 4-1. Experimental scheme for collection of scattered light at 900
The back scattering scheme uses the same set of collection optics as that for the 900
scattering scheme except that the 900 scheme uses a 60 mm collecting lens. From ray
tracing it is found that the beam divergence angle of the scattered beam arriving at the
mirrors was 0.40 and so the scattered rays reflected from the mirrors are effectively
collimated and could be focused on the photomultiplier tube.
Band pass filter
4- Photomultiplier tube
Figure 4-2. Experimental scheme for collection of scattered light at a 1800 (back scatter)
The following components constitute the optical set up shown in figures 4.1 and
Laser. Initially the experimentation was done using an argon ion laser operated
on the 488 nm wavelength. The laser power was set at 3 W and the beam diameter was
1mm with a beam divergence angle of 0.060. The argon ion laser is a continuous beam
low power laser. In order to amplify the scattered signal and for higher temporal
resolution a pulsed Nd:YAG laser was also used. The laser power is 200 mJ/pulse at a
wavelength of 532 nm. The pulse width was 5 nanoseconds and the frequency is 10 Hz.
The beam diameter is 6 mm with a beam divergence angle of 1.1. Since the beam
diameter was larger than the Argon-Ion laser, the Nd:YAG laser defined a larger control
volume than the Argon-Ion laser. Thus two different power lasers at two wavelengths are
used for the experiments.
Nozzle. The leak was simulated using a nozzle. The laser beam was passed
directly over the nozzle. The nozzle is placed at a distance of 8 feet (20.32 cm) from the
laser for the 900 scattering scheme. Using the beam divergence angle, the beam diameter
over the nozzle was calculated to be 1.1 mm for the Argon ion laser and 8 mm for the
pulsed Nd:YAG laser. In order to analyze the effect of the relative size of the beam and
leak, two different nozzle diameters are used. For initial measurements using the argon
ion laser a 1/2" (12.6mm) nozzle was used. For the pulsed laser a /4 (6.3mm) diameter
nozzle was used. Thus for the argon ion laser, the beam diameter is 11.5 times less than
the leak diameter whereas for the Nd:YAG laser the beam diameter is 1.25 times more
than the leak diameter. The back scattering scheme uses the pulsed Nd:YAG laser with
the 14 diameter nozzle. The nozzle is placed at a distance of 20 feet (50.8 cm) from the
laser and the beam diameter is 10 mm over the nozzle. The Reynolds number of the leak
is set at 500 for both nozzle diameters and the Froude number was calculated as
discussed in chapter 3 and presented in table 3.1. This combination of Reynolds and
Froude number ensured that the leak is a buoyant jet. The nozzle is covered with a black
felt drape to minimize glare. The mass flow rate of pure helium and the mixture of
helium and nitrogen is monitored using mass flow controllers.
Nozzle mounting. Three micrometer traverses are used for mounting the nozzle
for three dimensional motion. Each traverse has a least count of 0.05 mm. Figure 4-3
shows the schematic of the mounting used. This allowed the measurements to be taken at
different downstream locations.
Traverse 3 Y
Figure 4-3. Nozzle mounting showing three dimensional motion capability.
Beam dump. The incident laser beam was trapped using a beam dump. The beam dump
was placed at a distance of 20 feet from the nozzle to minimize glare.
Collection optics. The scattered beam was collected using a set of collection
optics which consisted of a collecting lens, focusing lens, band pass filter and a
photomultiplier tube. The collection optics were covered with a black felt drape in order
to eliminate additional glare.
Collecting lens. The collecting lens is a 60 mm diameter lens and has a focal
length of 250 mm. As seen from figure 4-1 the focal point of the lens coincides with the
nozzle position so that scattered light collected by the lens is collimated. As seen from
figure 4-2 the collection lens was not used for the backscattering geometry because the
scattered beam reflected from the two mirrors was collimated.
Focusing lens. The focusing lens is a 60 mm diameter lens and had a focal length
of 124 mm. The collimated beam from the collecting lens is focused on the
Photomultiplier tube using the focusing lens.
Band pass filter. For the Nd:YAG laser, the band pass filter is a 532 nm line
filter that blocks background light at other wavelengths from reaching the photomultiplier
tube. The band pass filter was kept at a distance of 3 mm from the Photomultiplier tube.
Photomultiplier tube. The scattered beam is focused on the Photomultiplier tube.
The Photomultiplier tube is a Hamammatsu model number HC 120-01 tube and has a
built in amplifier with adjustable gain. It has a rise time of 2 ns and a bandwidth of 23
Khz. This means that the photomultiplier tube can distinguish between two signals that
are 44 microseconds apart. Since the frequency of the pulse laser is 10 Hz the interval
between two consecutive pulses is almost Ims. Hence for a 900 scattering geometry, the
photomultiplier tube can distinguish between two consecutive pulses. From the
manufacturer's specifications the calibration constant of the photomultiplier is found to
be 121 V/nW which allows the conversion of the voltage recorded on the photomultiplier
tube into power. The Photomultiplier tube has a 0.015 mm optical slit mounted on it to
minimize the intensity of scattered light. The Photomultiplier tube converts the photonic
signal to electrical voltage which is then sent to a high speed digital oscilloscope. It is
important to note that even though the photomultipliers are considered to be highly linear
devices, the linearity generally occurs over a lesser range for the pulsed Nd:YAG laser. (X
= 532 nm) at varying flash lamp discharge voltage. Figure 4-4 displays the
photomultiplier tube voltage as a function of varying flash lamp discharge voltage.
660 R2 =0.9931
600 -* Series1
580- Linear (Series1)
0.9 1 1.1 1.2 1.3 1.4
Figure 4-3. Photomultiplier tube linearity tested as a function of flash lamp voltage
High Speed Digital Oscilloscope. The photomultiplier tube signal is recorded on a
high speed digital oscilloscope (LeCroy). It has two channel simultaneous data
acquisition capabilities. It is triggered externally using the pulsed laser. The trigger time
is 180 ns which means that the laser sends an electric signal to the oscilloscope exactly
180 ns before it fires the pulse so that the oscilloscope can be set to capture the scattered
signal. The oscilloscope acquires data over a time period of 50 microseconds. The
measurements are recorded and readout on a spreadsheet.
Control Volume. For the 900 scheme, the control volume is defined by the beam
diameter and the length of the control volume is defined by the width of the optical slit
Back Scatter Considerations
As previously stated the back scattering scheme is used to test the feasibility of the
technique for field measurements. An important consideration for field measurements is
the ability to detect the leak over longer distances. Hence the leak is created by placing
the nozzle at a distance of 20 feet (50.8 cm) the laser beam. The beam dump is placed at a
distance of 10 feet (25.4 cm) from the nozzle. The control volume is defined by the beam
diameter and the length of the control volume for this case is defined by the pulse width
Data Recording Procedure
The measurements were done at four different downstream locations of 2, 4, 6 and
8 nozzle diameters for the pulsed Nd:YAG laser and two downstream locations of 2 and
6 nozzle diameters for the argon ion laser. For each downstream distance the nozzle was
traversed along the direction of the beam using the micrometer traverse as shown in
figure 4-3. The steps in which the nozzle was traversed was calculated from the spread
angle of the jet as seen in figure 4-4. The distances la, 2b, 3c and 4d varied depending on
the nozzle diameters (1/4" or 1/2"). This was done so that the measurements done at all four
downstream distances could be graphed on the same scale of r/z.
b 2 8d r
1 6d y
Figure 4-4. Calculation of nozzle traverse distances for downstream distances of 2,
4, 6 and 8 nozzle diameters using jet spread angle of 130.
RESULTS AND DISCUSSION
Comparison of Theoretical and Experimental Photon Arrival Rate
This section discusses how the theoretical and experimental photon arrival rates
compare. In chapter 3 the equations for calculating the Rayleigh photon arrival rate
(equation 3.15) and Mie photon arrival rate (equation 3.16) are presented. The total
theoretical photon arrival rate is calculated as a sum of the Rayleigh and Mie photon
arrival rates (equation 3.17).
Calculation of Theoretical Rayleigh Photon Arrival Rate.
In the presence of helium, the Rayleigh photon arrival rate can be calculated by
modifying equation 3.15 as follows. The percent helium (x) was varied from 0 to 100 and
the resulting photon arrival rate is shown in figure 5.1.
IRayleigh = (Io)(rl)(dV)(Q)N(xHe + (1-x) Gair) (5.1)
Io = 7.07E+6mj/m2-pulse = 1.88E22 photons/ m2-pulse(Nd:YAG laser);
3.8E+6 W/ m2 (Argon-Ion laser)
f = (0.9)5
dV = 1.2 E-8m3 (900 scatter); 1.2E-4m3 (backscatter)
Q = t(60)2/(250)2 sr (900 scatter); (2)(101.6)2/(12100)2 sr (backscatter)
N = 2.2E25 molecules/m3
OHe= 1.22E-33 m2/sr
Gair = 8.16E -32 m2/sr
S6.20E+09 Rayleigh photon
0 5.20E+09- arrival rate
S9 Mie photon arrival
S3.20E+09 total photon arrival
'I 2.20E+09 rate
0 10 20 30 40 50 60 70 80 90 100
Figure 5-1. Theoretical photon arrival rate calculations show that Rayleigh signal is
higher than Mie signal.
Calculation of Theoretical Mie Photon Arrival Rate
Equation 3.16 is used for the calculation of the Mie photon arrival rate.
IMie = Io)(l)(dV)(Q)1(N, Mie)i (3.16)
The two unknowns in this equation are Ni and (oMie)i
The calculation of (oMie)i involves the use of the intensity distribution functions II
and 12 If the particle size is known, these functions can be calculated for a give
wavelength of incident light using the subroutine as discussed in Chapter 3. Two size
distributions were used to determine the size of particles in the ambient air and also the
number density of particles of a particular size.
Distribution 1 uses the data from a LASAIR II particle counter. Table 5-1 shows a
typical output of the particle counter data.
The sampling is done in the laboratory for a sampling time of 1 minute and the
volume of particles sampled over this period is 1 cubic feet. The particle size is given in
column 1. Columns 2 and 3 give the lower and upper limits of the number of particles of
the corresponding size. An average of columns 2 and 3 is taken. Thus using the LASAIR
II data, the number density-particles per m3 (N i) of a particular size are known. For each
particle of size of 0.3, 0.5, 1, 5, 10, 25 microns the Mie scattering subroutines are used to
calculate II and 12 at a wavelength of 532 nm for the pulsed Nd:YAG laser. Knowing II
and 12 ,oMie is calculated using equation 3.11 and the Mie scattered intensity using
equation 3.16. To account for the presence of helium equation 3.16 was modified as
lMie= IoTllQNGMie(1-xHe) (5.2)
Table 5-1. Particle counter data show the particle distribution in the lab.
Number of particles/ft3 Number of particles/ft3
Particle size (microns) (lower limit) (upper limit)
(lower limit) (upper limit)
0.3 25268 27272
0.5 7864 9222
1 1164 1298
5 100 104
10 12 12
25 1 1
For distribution 2 the typical maritime aerosol distribution in McCartney (1969) is
used. Figure 5-2 shows particle distribution for stratospheric dust particles or hailstones
(model H), continental aerosols (model L) and maritime aerosols (model M). The
maritime aerosol distribution (model M) is chosen since it is appropriate for Cape
The number density per radius interval n(r) for this distribution is calculated using
the following fit (McCartney)
n(r) = ar" exp(-br7) (5.3)
Where the constants a, b ,a, y have the following empirically determined values
a = 5333
b = 8.9443
io3 ----------- --
H L M -
0.01 0.1 1.0
Particle radius (pm)
Figure 5-2. Model M shows maritime distribution of aerosols which is used to calculate
the particle size distribution.(McCartney 1979, page 139)
Using the values of particle size (r) ranging from 0 to 25 microns, and the above
values of the constants, the model M (log-log scale) was duplicated on a regular scale as
shown in figure 5-3.
S200 Model M
M 50 -
0.1 1 10 100
Figure 5-3. Model M duplicated for calculating the number density using radius interval
on a log-normal scale.
The number density is calculated for the same particle radii as the LASAIR II data.
(i = 0.3, 0.5, 1, 5, 10 and 25 microns) by integrating the area under the curve shown in
figure 5-2 using following equation. The interval (i) to (i+1) represents the difference
between the two consecutive particle radii
Ni = 0.5(n(r)i + n(r)i+1)I (5.4)
The values of number density -Ni (particles/m3) obtained from equation are
compared with the values of Ni from the particle counter (Table 5.1). Figure 5-4 shows
this comparison. As seen from the figure the particle distribution for maritime and lab
aerosols is similar.
For distribution 2 since the number density and the particle radius are known
(equation 5.4) the Mie scattering cross section and the intensity of Mie scattered signal is
calculated using the same approach as in distribution 1.
Figure. 5-4. Comparison of number density of maritime and lab aerosols shows similarity
Figure 5-5 shows the comparison between the Mie photon arrival rates for the two
distributions. The value of IO used is that for the pulsed Nd:YAG laser.
- Maritime distribution
- lab data
20 40 60
Figure 5-5. Effect of maritime and lab aerosol distribution on Mie scattered intensity
shows that both signals are of the same order of magnitude.
As seen from the graph, both signals are of the same order of magnitude. The
maximum difference between the two signals (55%) is for the case of 0% helium since all
Mie scattering particles have been displaced, and no ambient air is in the control volume.
Both signals tend to zero as the helium concentration approaches 100%. This figure
shows that the Mie signal would be of the same order and smaller for maritime field
measurements as that for laboratory measurements.
Calculation of Total Theoretical Photon Arrival Rate
For the calculation of IMie the data from the particle counter is used since it
represents aerosol distribution for the experimental conditions. Knowing IRayleigh and
IMie, the total theoretical photon arrival rate is calculated using equation 3.17. Figure 5-1
shows the variation of Rayleigh, Mie and total photon arrival rate with percent helium.
The value of IO used here is for the pulsed Nd:YAG laser.
An important result of the theoretical study is that the Mie scattered signal is lesser
than the Rayleigh scattered signal. Initially it was reasoned that the Mie scatters would
augment the scattered signal since in the presence of helium the total signal would fall
due to reduction in Mie signal. This study shows that although this factor is present it
influences the total scattered signal to a lesser degree.
Calculation of Experimental Photon Arrival Rate
The voltage as a function of time waveform obtained on the oscilloscope represents
the total scattered intensity recorded at the photomultiplier tube per pulse.
Figure 5-6 shows a typical waveform of a burst seen on the oscilloscope. The
waveform is recorded at a downstream distance of 4 nozzle diameters with no flow fluid.
Integrating this waveform using equation 5.5 gives the total scattered intensity per
VPMT = 0.5(Vi +Vi+l)(0.1) (5.5)
where (i) represents the time scale from 0 to 100 microseconds varied in steps of 0.1
0.3 -- waveform
0 10 20 30 40 50 60 70 80 90
Figure 5-6. Typical waveform of a burst seen on the oscilloscope (Downstream distance
of 4 nozzle diameters, no flow fluid)
The Photomultiplier tube calibration constant (CPMT) at the wavelength of 532
nm is found to be 121 V/nW from the manufacturers specifications. The measurements
are done using the pulsed ND:YAG laser at 6 different helium concentrations of 0, 20,
40, 60 80 and 100% using the /4" diameter nozzle. As discussed in buoyant jet theory
(Figure 3-5) the flow fluid (helium) concentration can be predicted in the shear layer for a
combination of downstream distances and radial distance (r/z). The downstream distance
(z) is fixed at 2 nozzle diameters. From equation 3.23 it is seen that for a fixed value of z,
the radial distance (r) can be calculated if the concentration C is known since the
centerline concentration of the flow fluid (Ccl) is known using equation 3.25 and the
concentration of flow fluid (Ca) in the ambient is 0%.
C- Ca = exp [-Ko(r/z)2 ] (3.23)
Thus for 6 different values of C (0, 20, 40, 60, 80 and 100), the measurements are
made for the corresponding values of radial distance(r) obtained from equation 3.23.
Figure 5-7 shows the values of radial distance r where the measurements are made for
each value of C.
Figure 5-7. Figure shows points in shear layer where measurements are made
corresponding to each value of C using pulsed Nd:YAG laser and /4" nozzle at a
downstream distance of 2 nozzle diameters. Re = 500; Fr = 290.
For each measurement the integrated area under the voltage- time curve on the
oscilloscope represents the total scattered signal per burst. Equation 5.6 is used to convert
the voltage recorded for each measurement into scattered signal in photons per pulse.
experimental= VtPMTX/CPMThc (5.6)
Figure 5-8 shows the comparison of the experimental and theoretical photon arrival
rates for varying percentages of helium.
S8.E+09 R2 = 0.9978
a 7.00E+09 -
0 0 theoretical photon
6.00E+09 arrival rate
S5E9 experimental photon
5 Arrival rate
F 4.00E+09 Linear (experimental
'E 3.E+09 photon arrival rate)
1 .0 0 E + 0 9 . . ..----
0 10 20 30 40 50 60 70 80 90100
Figure 5-8. Comparison of experimental and theoretical photon arrival rates.
The experimental and theoretical photon arrival rates are of the same order of
magnitude with a maximum error of 57.3% for the case of 100% helium and a minimum
error of 11.3% for the case of 0% helium. A linear regression of the experimental photon
arrival rate gives a coefficient of 0.99 indicating a constant additional factors)
contributing to the error independent of percent helium. This constant error can be
attributed to 1.Background glare, which is at the same wavelength as that of scattered
signal. 2. Deviation of optical efficiency of each collection surface from the assumed
value of 90%. 3. Ambient air in control volume at jet edges.
Data Analysis Techniques
As previously stated for each burst the scattered signal from the photomultiplier
tube is recorded as a voltage-time curve on the oscilloscope. Two techniques of analyzing
the recorded voltage are considered. The Nd:YAG pulse laser with the 14" nozzle is used
for both techniques and the flow fluid is pure helium for both cases.
Integrated area method
Initially a set of 1000 data points per burst are captured from the oscilloscope and
the integrated area under the voltage as a function of time curve is computed. For the
measurements, the downstream distance is 2 nozzle diameters, Reynolds number is 500
and Froude number is 290. The measurements are done in the shear layer of the leak at a
radial position corresponding to 60% helium concentration as shown in figure 5-7. This is
because the maximum variation of recorded voltage is expected to be in the shear layer
edge since the intermittency of the turbulence is maximum.
This procedure was repeated for a set of pulses at the same nozzle position shown
in figure 5-7 until the areas converged. Figure 5-9 shows the convergence studies for the
> normalizd running
S0 average of area
S-1 6 7 8 normalized inidvidual
Figure 5-9. Convergence studies of normalized area and averaged area shows that the
area converged in 10 pulses.
Series 1 represents the running average of the integrated area normalized with
respect to the mean of 10 pulses. As seen from the graph, for a measurement in the shear
layer a set of 10 pulses are enough for convergence. The maximum percent variation of
any individual area from the mean is 3% and the maximum percent variation of the
running average of area from the mean is 2.6%.
Peak Voltage Method
Two studies are undertaken to validate the use of peak voltage rather than
integrated area as a repeatable and reproducible data measurement technique. A
convergence study is also done to determine the number of peaks required for data
measurement. These studies are carried out using the pulsed Nd:YAG laser with the /4"
Study 1. For four downstream positions (z) of 2, 4, 6, and 8 nozzle diameters the
waveform is recorded along the jet centerline (r=0) as seen in Figure 5-10.
: 0.5 __ z/d=2
> 0.4 i z/d=4
| 0.3 i \ z/d=6
> 0.2 z/d=8
-0.1 10 20 30 40 50 60 70 80 90
Figure 5-10. Waveform with varying glare at four downstream locations.
All four measurements are done in room air with no helium flowing through the
nozzle. In this case we expect that the Rayleigh and Mie scattering signals are constant
and the only variable in each case was the glare from the nozzle.
All four waveforms were normalized with the corresponding peak as shown in
figure 5.11. It is seen that all four waveforms fall on top of each other and it is impossible
to distinguish between them. A four way cross correlation analysis of the waveforms was
done using the following relation
rx-y= Xi- x)(yi-y) (5.7)
4 ((x- x)Nd)2) y-Y)Nd)2)
The cross correlation coefficient was 99.7%. The high cross correlation coefficient
supports the hypothesis that the peak voltage contains sufficient information of each
m 0.6 z/d=4
> 0.4 z/d=6
0 -........ ........ .. ..... .... ..
-0.2 10 20 30 40 50 60 70 80 90 100
Figure 5-11. All four waveforms normalized with their individual peaks to
remove glare, the waveforms are indistinguishable.
Study 2. In this study, a correlation analysis of the peak voltage and the
corresponding integrated area is done for 10 pulses at the same nozzle position in the
shear layer as that used with the integrated area studies above (Figure 5.7). The flow fluid
is 100% helium and the Reynolds and Froude numbers are 500 and 290 respectively and
radial position corresponding to 60% helium concentration. The downstream distance is 2
nozzle diameters. The correlation coefficient is 99.3% which again supports the relation
between peak and area for a given pulse.
Peak Convergence Study. From the previous two studies it is established that
the peak contains all necessary information about the waveform and the peak and area are
related. The convergence study is undertaken to establish the number of pulses required
for convergence. The downstream distance is 2 nozzle diameters and the Reynolds and
Froude numbers are 500 and 290 respectively for 100% helium. The measurements are
done in the same position in the shear layer of the leak as for the previous two cases of
integrated area and comparison of integrated area and peak (Figure 5.7) (radial position
corresponding to 60% helium concentration. The average peak voltage is recorded after
the 1st, 100th, 200th, 300th, 400th and 500th pulse. Table 5.2 lists the voltage recorded
after each measurement. Column 3 of the table gives percent variation between two
consecutive values of recorded voltage.
Table 5-2. Shows that average peak voltage recorded after 300 pulses in shear layer is a
Pulse Number Average peak voltage (Vi) (Vi Vi-)/V
Pulse Number (Vi- -1)
100 576 4.7%
200 564 2.1%
300 559 0.88%
400 563 0.76%
500 558 0.89%
As seen from table 5.1 the variation between average peak voltage is less than 1%
if the peak voltage was recorded after 300 pulses. Also these measurements are carried
out in the edge of the shear layer of the jet where the fluctuations in the flow are
maximum. Hence it is concluded that for any nozzle position, recording the average peak
voltage after 300 pulses is a reliable data measurement technique.
Analysis of Recorded Data
Figure 5-6 shows the comparison between the predicted (theoretical) and the
measured (experimental) photon arrival rates. As stated earlier these studies are carried
out using the pulsed Nd:YAG laser with a /4" diameter nozzle at a downstream distance
of 2 nozzle diameters. This section discusses the variation of peak voltage and standard
deviation of the recorded voltage for the following four cases:
* Argon-ion laser with a 1/2" diameter nozzle at downstream distances of 2 and 4
nozzle diameters for pure helium for 900 scattering scheme.
* Pulsed Nd:YAG laser with a /4" diameter nozzle at downstream distances of 2, 4, 6
and 8 nozzle diameters for pure helium for 900 scattering scheme.
* Pulsed Nd:YAG laser with a /4" diameter nozzle at downstream distances of 2and 4
nozzle diameters for a mixture of 20% helium and 80% nitrogen for 900 scattering
* Pulsed Nd:YAG laser with a /4" diameter nozzle at downstream distances of 2, 6,
10 and 16 nozzle diameters for pure helium in back scatter.
The nozzle was traversed in the radial (r) direction as discussed in chapter 4 for the
900 scattering scheme and in the (y) direction for the back scatter scheme.
Case I: Argon-ion laser
Peak voltage variation
Initially the measurements were carried out using the argon-ion laser (X =488 nm)
at two downstream distances of 2 and 6 nozzle diameters. The nozzle diameter of 12" is
used with the argon-ion laser and the flow fluid is pure helium. The Reynolds number of
the leak is 500 and the Froude number is 35. the nozzle traverse distance for each
measurement at each downstream position were calculated as discussed in Chapter 3.
Three sets of measurements were done at each downstream position. Figure 5-11 shows
the average of the normalized peak for all 3 measurements. Also shown are the error bars
at both downstream locations corresponding to the standard deviation of each
measurement point. The x- axis is the nozzle traverse distance (r) in mm. As seen from
the figure, the scattered voltage reaches a minimum value of zero at the jet centerline for
both downstream distances. Also the voltage variation inside the shear layer is visible.
Hence due to the presence of helium in the shear layer, there is a fall in voltage inside the
shear layer. As the downstream distance increases, the jet spreads out and the fall occurs
over a wider radius.
*"$ 1 11E K
-15 -10 -5 0 5 10 15
Figure 5-12. Voltage variation for Argon-Ion laser shows that there is a fall in voltage in
presence of helium; 1/2" nozzle at two downstream distances; Re =500; Fr
As seen from figure 5-12, the fall in peak voltage at the jet centerline which
corresponds to 100% helium. Also, the fall in voltage occurs only in the presence of
helium. At the ambient where there is no effect of flow fluid on the recorded voltage, the
voltage remains constant. The fall in voltage in presence of helium occurs because 1.
Helium molecules have a scattering cross section which is 0.015 times the cross section
of the surrounding air molecules. 2. Molecules of the flow fluid displace some aerosols in
their path which are Mie scatters. Hence there is a fall in the intensity of scattered light
Normalized peak voltage variation.
The raw peak voltage was normalized with the centerline voltage (Vi- Va)/(Vcl -
Va) as shown in figure 5-13. The normalized concentration profile plotted in chapter 3 is
also shown as a function of r/z From figure 5-13 it is seen that the voltage variation
follows a similar Gaussian distribution as that of well established normalized
concentration profile of a axisymmetric vertical buoyant jet.
S / concentration
-2.0 -1.0 0.0 1.0 2.0
Figure 5-13. Normalized peak voltage variation for argon-ion laser for pure helium; Re=
500; Fr=3.5; nozzle diameter = 1/2
Standard deviation profiles
Figure 5-14 shows the variation of the normalized standard deviation ratioed to the
centerline voltage o/(Vmax Vcl) for the downstream distance of 2 nozzle diameters The
downstream distance of 2 nozzle diameter represents the near field regime of the buoyant
jet. It is seen that inside the potential core, the standard deviation falls as expected.
S 10 -
-1.40 -1.12 -0.84 -0.56 -0.28 0.00 0.28 0.56 0.84
Figure 5-14. Percent standard deviation variation for near field case showing the reduced
fluctuation in the potential core.
Figure 5-15 shows the variation of the normalized standard deviation of the data
radioed to the centerline standard deviation for the far field case after the shear layers
-1.40 -1.12 -0.84 -0.56 -0.28 0.00 0.28 0.56 0.84
Figure 5-15. Percent standard deviation for far field case after shear layers have
The percent standard deviation is above the typical maximum variation of 30%. A
possible reason for this is there is an additional factor of Mie scattering contributing to
the increased standard deviation of the recorded voltage.
Case II: Pulsed Nd:YAG laser; pure helium
Peak voltage variation.
Figure 5-16 shows the variation of raw peak voltage with respect to the nozzle
position for pure helium for the downstream distances of 2, 4, 6 and 8 nozzle diameters
for the pulsed Nd:YAG laser (X=532 nm) using the 14 nozzle. The Reynolds number is
500 and Froude number is 290. As seen from the graph, for each individual downstream
distance the voltage tends to remain constant outside the shear layer (ambient) due to
absence of helium. As observed with the argon-ion laser, the fall in voltage occurs over a
wider radius as the jet spreads out. Also the minimum voltage is recorded at the jet
-30 -20 -10 0 10 20 30 40
Figure 5-16. Voltage variation for pulsed Nd:YAG laser shows a similar profile of fall in
voltage in presence of helium; Re= 500; Fr=290; nozzle diameter = 14 "
Normalized Peak Voltage Variation
Figure 5-17 shows the variation of the normalized peak voltage for all four
downstream distances for the pulsed Nd:YAG laser for the case of pure helium. Also
shown is the theoretical normalized concentration profile plotted in chapter 3 as a
function of r/z.
-2 -1 0 1 2
Figure 5-17. Normalized peak voltage variation for Nd:YAG laser for pure helium; Re=
500; Fr=290; nozzle diameter = /4 "
Standard deviation profiles
Figure 5-18 shows the standard deviation profiles for all four downstream distances
of 2, 4, 6 and 8 nozzle diameters. Comparing figure 5-18 with the standard deviation
profiles for the Argon-ion laser (figures 5-14 and 5-15), it is seen that the standard
deviation variation is less distinct for the Nd:YAG laser. A possible reason for this could
be the effect of the relative size of beam and nozzle (leak) diameters. The beam diameter
for the argon ion laser is 1/10th the diameter of the nozzle whereas for the pulsed laser it
was 1.2 times the nozzle diameter (Figure 5-19). This factor was an additional variance
for the pulsed laser.
18 -x XXx
16 X X
14 XX x *z/d=2
12 *zld=4X g L M
S 6- X z/d=8
-1.47 -1.10 -0.74 -0.37 0.00 0.37 0.74 1.10 1.47
Figure 5-18. Standard deviation variation for Nd:YAG laser for pure helium; Re= 500;
Fr=290; nozzle diameter = 1/4 "
Figure 5-19. Relative size of beam and leak diameter for the Argon-ion and pulsed
Case III: Pulsed Nd:YAG laser; 20%helium ,80% nitrogen
Peak Voltage Variation
Figure 5-20 shows the variation of peak voltage for a mixture of 20% helium and
80% nitrogen for a downstream distance of 2 and 4 nozzle diameters for the pulsed
Nd:YAG laser. This mixture of helium and nitrogen matches the scattering cross section
of hydrogen as discussed in Chapter 3 and hence the amount of light scattered by the
mixture is expected to be identical to that of Hydrogen. The Reynolds and Froude
number were 500 and 515 respectively.
-15 -10 -5 0 5 10 15 20
Figure 5-20. Voltage variation for the pulsed Nd:YAG laser for the mixture of helium
and nitrogen shows that there is a fall in voltage; nozzle diameter 1" ;Re=500,
Fr = 515.
The fall in voltage from figure 5-20 is 30 mV (6%) for the downstream distance of
2 nozzle diameters. The fall in voltage for z/d=2 for the case of 100% helium is 155 mV
(30 %) as seen in figure 5-16.
Normalized peak voltage variation.
Figure 5-21 shows the normalized peak variation for the mixture at the downstream
distances of 2 and 4 nozzle diameters.
A comparison with the normalized concentration shows that the two profiles are
Figure 5-21. Normalized peak voltage variation for Nd:YAG laser; Re= 500; Fr=515;
nozzle diameter = 1/ for a mixture of helium and nitrogen to simulate the
optical properties of nitrogen.
Standard Deviation Profiles.
-1.47 -1.10 -0.74 -0.37 0.00 0.37 0.74 1.10 1.47
Figure 5-22. Percent standard deviation variation for Nd:YAG laser; Re= 500; Fr=515;
nozzle diameter = 1/ for a mixture of helium and nitrogen to simulate the
optical properties of nitrogen
The standard deviation profiles of the mixture for both downstream distances of 2
and 4 nozzle diameters are shown in figure 5-22. The standard deviation for the mixture
0 4 normalized
> / concentration
-2 -1 0 1 2 3
is more than the standard deviation of pure helium for the two distances. The presence of
two flow fluids (helium and nitrogen) shows in the increased standard deviation.
Measurements in Backscatter
The principal issue in backscatter is distinguishing between the scattered signal and
beam dump glare. Figure 5-23 is a schematic of the backscatter geometry represented on
a time scale. The time difference between the scattered beam from the nozzle and
reflected beam from the beam dump is approximately 20ns. Thus the photomultiplier
tube should be able to distinguish between the two signals 20 ns apart. The minimum
bandwidth of the photomultiplier tube required is 5 VMHz. It was impossible to
distinguish between the two signals using the Hammamatsu tube. (Bandwidth 23 KHz).
Nd:YAG laser nozzle Beam dump
Figure 5-23. Schematic of backscatter on a time basis shows separation between beam
dump glare and scattered signal from the nozzle.
The waveform seen on the oscilloscope contained both the beam dump glare and
the scattered signal. In order to distinguish between the signal and glare the
measurements with helium for a typical nozzle position was normalized with a
measurement without helium for the same nozzle position. Since the measurements were
done in backscatter, the nozzle was traversed in a direction perpendicular to that of the
beam(y-direction). Figure 5-24 shows the data in backscatter.
c 1u 1 z/d=2
S0.95 E a z/d=6
E 0.9 z/d=10
-15 -10 -5 0 5 10 5 10 15
Figure 5-24. Normalized area variation shows a reduction in scattered intensity in
presence of helium (backscatter); Nozzle diameter = 4"; Re =500; Fr = 290
There is a fall in the normalized area in the presence of helium near the jet
centerline for all downstream distances. For the case of downstream distance of 2 nozzle
diameters, the fall in normalized area is about 0.15 V (15%). For the 900 scattering
scheme for the pulsed Nd:YAG laser, the fall in voltage is approximately 30% (Figure 5-
16) and 50% for the Argon-Ion laser for the downstream case of 2 nozzle diameters for
pure helium (Figure 5-12). The control volume for the backscatter geometry is defend by
the 6mm diameter beam and the pulse width of 5 ns (1.5m) (4.29E-5m3). For the 900
scattering scheme, the control volume is defined by the 6mm diameter beam and the
0.015mm optical slit (4.29E-m3) for the Nd:YAG laser, and 1mm diameter beam and the
0.15mm optical slit for the Argon-Ion laser. (7.05E-12m3). The leak diameter for the
pulse laser is /4"whereas for the Argon-Ion laser its /2" Thus for the 900 scattering
geometry for both Argon-Ion and Nd:YAG cases, the leak occupies 100% of the control
volume whereas for the backscatter geometry the leak occupies only 0.6% of the control
volume as seen from table 5-3.
Table 5-3. Control volume to leak diameter ratio for all three cases shows that the ratio is
far less for backscatter than 900 scattering.
Geometry Nozzle Diameter (D) Control Volume(CV) CV/D (percent)
Backscatter,Nd:YAG 6.35E-3 m 4.29E-5m3 0.6
90 Nd:YAG 6.35E-3 m 4.29E-5m3 100
90 Argon-Ion 12.7E-3 m 4.29E-5m3 100
This might have lead to the lesser fall in intensity of scattered light in the presence
of helium for backscatter geometry.
The primary objective of this study is to establish the feasibility of laser induced
light scattering as a leak detection technique for hydrogen. There are two primary reasons
that support this objective.
1. The fall in voltage at the centerline of the leak indicating reduced scattered
intensity both in the presence of pure helium (oHelium = 0.015 GAir) and a mixture of 20%
helium and 80% nitrogen (GMixture = GHydrogen= 0.23 GAir) 2. Standard deviation in excess
of 30% for pure helium (argon ion laser). Both of these were due to the reduced intensity
of Rayleigh scattering by helium molecules.
The theoretical studies of Mie scattered intensity show that the Mie signal is the
same order of magnitude for the laboratory and maritime particle distributions. This
result is important for field measurements as the effect of Mie scattering on the total
signal would be approximately the same. Initially it was thought that the fall in voltage
would be amplified due to the Mie scatters. However, from the theoretical study it was
seen that Mie signal is less than the Rayleigh signal. Hence the lack of Mie scatters in the
control volume reduces the fall in voltage in the presence of Rayleigh scattering due to
helium and nitrogen molecules.
Concentration measurements in the presence of Mie scattering have been
successfully done in the lab environment.The backscattering scheme is used principally
to test the feasibility of this technique for field measurements. Since for laboratory
measurements the scattered signal from the photomultiplier tube and the reflection from
the beam dump are only 40 ns apart, it was impossible to distinguish between the two
signals for the photomultiplier tube used for the experiments. This lack of temporal
discrimination severely limits the overall signal to noise ratio for this configuration. The
signal to noise ratio can be improved with better overall temporal response devices.
A fall in voltage at the centerline of the flow is observed for both pure helium and
the mixture of 20% helium and 80% nitrogen for all four downstream distances. This
indicates that a leak could be detected at downstream distances as low as 8 nozzle
diameters. Also leak detection is feasible when taken in context of the overall full field
* In order to determine the effect of background light, a dual line detection system
should be used.
* A study to determine the polarization effect of the incident beam on the scattered
signal should be done.
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Sameer Paranjpe finished his undergraduate degree in mechanical engineering from
the University of Bombay in 2002. He is pursuing his master's degree in mechanical
engineering at the University of Florida. He has been a research assistant under Dr. Jill
Peterson since August 2002.