Transcript Evolution of Black Hole Masses from Quasar Gas Dynamics

"Development of a sonar for
finding gas compositions"
J. C. Vyas,
Crystal Technology Section, Technical Physics Division,
BARC
Out line
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Introduction
Gas sensors
Energy transfer in gases
Our system
Some results
Conclusion
Introduction
• Usually, gases are identified by more elaborate physicochemical methods, such Chromatography, or by Mass spectrometers, or by IR absorption line intensities etc.
• Most of these techniques need elaborated procedures and time to
find or identify the composition of gas mixtures.
• Gas handling and utility applications need quick and rugged
methods to find gas composition.
A gas sensor
• An ideal gas sensor is that which can find (identify) a
specific gas quantitatively, in a mixture of two or more
gases, in shortest possible time, and without damaging the
composition of the gases. The system should be
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Rugged
Able to detect any gas in a given gas mixture
Possibly non-invasive
Smallest response and dead time (if any)
With best possible resolution
Stable (with respect to time and constituent components)
Without (or minimum of) the wear and tear or aging problems, and
Easy to handle, etc
Types of gas sensors
• No ideal gas sensor system exists at present commercially,
but with compromises on some of the requirements,
solutions can be found. There are several types of gas
sensors available, such as
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Infrared absorption based
Chromatography based
Thin film (redox-conductivity) based solid state
Fibre-optic based solid state
Mass spectroscopy based, etc
• We searched in the ultrasonic field and fabricated an
Ultrasonic Gas Detection System (a kind of gas SONAR).
The Sonar
• A sonar is acronym for (a device that uses) sound energy pulses
for navigation and ranging.
• The device is used in several non-destructive methods, such as
depth finding in deep waters (sea / river beds), or mechanical
strength of structure. A modified version is used for imaging
(medical use) of human organs (such as in sonography), etc.
• Can such technique be used for measuring gas composition ?
Energy transfer
• In materials, mechanical energy transfer takes place via
physical collisions. For elastic collisions both energy and
momentum need to be conserved.
m1u1 + m2u2 = m1v1 + m2v2
• And
(1/2){m1u12+ m2u22 = m1v12 + m2v22}
• If the body is rigid, the mechanical energy transfer within
the body material is via conduction mode, but in fluids an
additional convective mode also come into play in some
proportion.
• We neglect direct radiation part (in the low energy per
particle regime).
Speed of energy transfer
• The speed of mechanical energy transfer within specific
material is the speed by which the energy travels in a
material from one site to another, and known as speed of
sound in common terminology.
• This speed depends upon the response time of nearest
neighbour, which in turn related with the rigidity or the
strength of bonding within the structure. So in solids the
speed is relatively larger, and largest for the strongest
(bond) material. In diamond it’s value is 17500 m/s and
reflects further in large thermal conductivity (at R.T. it is
20-25W/cmK, exceeds that of copper by a factor of five).
Energy transfer In fluids
• Fluids differ from solids. In case of liquids we have a fixed
volume during mechanical energy transfer, but flexible
movement of constituent molecules.
• Gases are a part of fluids, but volume has a strong relation
with the pressure term. The volume and the shape depend
upon the container vessel.
• In gases the physical parameters of basic concern are the
gas pressure, and the temperature of the gas medium.
Sound speed in Gas media
• Gases are special fluids, in which
sound / ultrasound velocity
depends upon externally
controllable physical parameters,
the pressure, the specific heat ratio,
and the average molecular weight
(density) of the medium.
• If the physical parameters of the
gas medium can be controlled by
external means properly (to remain
confined around certain fixed
value), the sound / ultrasound
velocity becomes a direct function
of gas density.
Some formulation
• In gaseous medium for a reasonably constant temperature
conditions, the sound (or ultrasound frequencies  10 MHz)
speed is given by
v = ( P / )0.5
Here,
v = Speed of sound / ultrasound (m.s-1)
 = Ratio of molar heat capacity of the gas (Cp/Cv)
P = Pressure of the gas medium (in Pa)
 = Density of the gas (kg.m-3)
What happens in gas mixtures
• For a gas mixture this relation becomes (for constant
temperature conditions)
vmix = (mixP / mix )0.5
vmix = Speed of sound / ultrasound for gas mixture (m.s-1)
mix = Ratio of molar heat capacity of the gas (Cp/Cv)mix
P
= Pressure of the gas medium (in Pa) for mixture
mix = Density of the gas mixture (kg.m-3)
• The sound speed changes with the density of gas mixture, and
may be used to provide the composition of unknown gas in the
mixture, provided the mix is also known for the gas mixture.
The next job: find relations
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The density of a gas mixture for densities of individual
gases ρi and gas concentration xi for the ith species (with
normalization  xi = 1), may be given by
ρm =  xi ρi
This relation for only two gases with x = x1 and so x2 = (1-x) becomes
ρm = xρ1 + (1-x)ρ2
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Similarly, the relation for molar specific heat ratio of a gas
mixture be written. For the case of two gases only can be
expressed in terms of individual molar specific heat
capacities in first approximation, with as above notations
m = { xi Cpi /  xi Cvi }={xCp1 + (1-x)Cp2}/{xCv1 + (1-x)Cv2}
Strategy
• Fabricate a system, which can measure the speed of sound
for any gas / gas mixture. The system should be handy, and
must have capacity to provide data as fast as possible
(almost on line), and look at the results.
Practical problems
• Sound speed in gas media is independent of frequency from ultra
low to few MHz (for constant P and T conditions).
• Sound from the mechanical sources in the lab or industry, may
complicate measurements (up to about ~ 40kHz, and so go to
higher frequencies).
• Higher frequency (a better precision, an advantage!), in the
measurement of sound speed, and this also reduces the size of the
measurement cell.
• However, higher frequencies also have some basic problems
– Attenuation (increases with increasing frequency in exponential way)
– Fabrication of suitable transducers becomes more difficult
The scheme
• Armed with the functional relations of the density, and the
specific heat ratio of the gas mixture with corresponding
individual gas parameters, measurement of sound speed in
the gas mixture, and in one of the individual gas (the
background gas), should provide the unknown concentration
of specific gas in the gas mixture
• The information on the gas density, and the molar specific
heat capacity ratio, can be obtained from the literature or
elsewhere or by direct measurements.
• For measuring the sound speed, a small pulse be sent
through the gas media over a fixed distance and it’s eco be
registered in time (known as time of flight (TOF)).
Control of other parameters
• Gas pressure and its temperature are main
parameters, to be controlled properly.
• In normal ambient air, the pressure is nearly one
atm., (= 105 Pa), and relatively easier to control.
• For flowing gas conditions (at normal flow), the
pressure difference may be controlled. Further, in
the speed expression we have (P / ), which is
almost a constant quantity, at normal pressures
• The temperature of the gas media is certainly a
more difficult parameter to control with an
arbitrary accuracy. However, it can be controlled to
some extent by use of thermal baths etc., but still
with certain level of inherent fluctuations.
Process of Measurement
• In practice, for all the signals traveling to a fixed distance, one can use the
TOF values directly, to find out gas concentration in the sample.
• In pulse catch mode one needs two transducers operating at same frequency.
However, one can use a single transducer and register the reflected (echo)
signal in time.
• An ultrasound signal (~500 kHz) of short duration (signal width about 5 to 10
) is created and passed through the gas medium
• The reflected pulse after traveling a path-length of about 500 , is detected
and the TOF is recorded
Process of … …
• The Time of Flight (TOF), is measured for the gas mixture tm, and for
the pure background gas t1 and t2 , and the gas concentration x is
calculated (for low concentrations of the unknown gas) by
x =  (tm - t2)
With  = (tm+t2)/(t12-t22), and t1 is the TOF for pure unknown gas.
It is possible to measure  graphically also for low concentrations and
so measurement of parameter t1 is not always needed.
• For small concentrations of unknown gas, parameter , may be
considered as an approximate constant for the cases tm  t2.
The electronics and measurement cell
• We have used a commercial pulser-receiver model 4400
MX, which can measure TOF with resolution of about 20 ns
in the 0 to 2 ms range.
• The transducer generates ultrasound at central frequency 500
kHz in pulse mode, and also detects the echo of the reflected
signal.
• The transducer is fixed in a closed test chamber (vol. ~60
cm3) filled with normal air at 1 atm., pressure and it has
provision for insertion of sample gas, into it.
Experiments
• Temperature of the test chamber was maintained at 25 or 260C, using a water
jacket.
• The pulser sends a short signal (pulse) of about 20 s for every 20 to 50 ms
time interval, and the same transducer detects the reflected eco. In present cell
design TOF of about 700 - 850 s (for the background gas) measured.
• TOF values were recorded for samples of clean air with time, and average
value was taken out (the value of t2), it was 793 s. It was seen that within lab
the variation in t2 was less than 0.1 s for a time period of about 30 min.
• A known amount of gas say SF6 was injected into the chamber (cell) using
calibrated syringe and corresponding TOF data was recorded. This step was
repeated for several different concentrations of the test gas. A typical set of
data based on observed TOF v/s SF6 gas concentration is shown in next frame.
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TOF values (microsec.)
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799
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797
796
795
794
793
792
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60
SF6 Gas Conc. (mol %) in Air
Resolution
• Electronically we resolve down to 20 ns. The slope of line in graph,
indicates that 0.0559 vol % (~560 ppm) of SF6 gas in air, corresponds to 1
s change in TOF, and so, ideally (in present set up), we can resolve 10
ppm of SF6 gas in air!
• According to our own study the temperature fluctuations T cause variation
in TOF values, say t, and the correspondence is given by (T/T) = 2(t/t)
• For a typical case, assuming T  (± 0.5K), at T = 300K, corresponding t
value is (t/1200). Let a typical value of TOF, is t ~ 800 s, for this case the
spread t comes out to be 0.67 s, which corresponds to the SF6 gas
resolution of about 400 ppm in air.
• Notice, that if we can maintain T  ± 0.1K, the corresponding resolution
for SF6 gas becomes around 100 ppm. But to get best resolution by this set
up, that is 10 ppm, the temp. fluctuations must be limited to T  ± 0.01 K.
Response time
• The system does not have a measurable dead time. However, the
pulse repeating period may be considered as the time in which next
set of data on TOF will be available, this time is about 20 to 50 ms.
• The time in which the injected gas molecules diffuse in the
measurement cell is of few millisecond (ms) order, and can be
considered negligible.
• Since, in 1 sec we have about 20 to 50 data points, the system is
capable to work as almost online for detecting sample gases.
• It may be noted that gases do take a finite time to reach from the
leakage site to the sensor location. This part varies with respect to
different site locations, the relative position of the sensor w.r.t.
source position, and therefore can not be taken into account.
Limitations of the system (important !)
• This system measures a change in the average density. So if
one is looking for possible leakage of a specific gas, he is
not always sure in case if it comes from some other gases
present in the lab.
• However, such limitation is in fact, a blessing in disguise for
the safety of equipments and personals, as one gets
information on change in gas ambient immediately, and may
provide an early alert to control system (if needed) about
such an event of other gas leak.
• The gas composition resolution depends upon the nature of
sample gas as well as the background gas parting in the
relative density of gas mixture, and so it’s value will be
different for different combinations.
Conclusions
• Ultrasonic pulse sensor can be used to detect gas compositions or
gas leakage almost on line (more than 20 data points per second
can be obtained in present set up).
• In present set up although ultimate resolution (electronically
possible) one can get is about 10 ppm, for SF6 gas, but actual gas
resolution is limited by the temperature fluctuations of the gas
media in the cell.
References
•
A. B. Bhatiya,“Ultrasonic Absorption, An introduction to the theory of sound absorption and dispersion in
gases liquids and solids”, Oxford, Clarendon press, 1967
•
G. Hallewell, et al, Nucl. Instr. Meth. in Phys. Res., A264 (1988) 219
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Vyas J.C. et al, “A non-invasive Quantitative Method for H2 Gas Detection in Air,” DAE Solid State Physics
Symp. 2004, p-342
•
J.C. Vyas et al, “A non-invasive ultrasonic gas sensor for binary gas mixtures,” Sensors and Actuators B 115
(2006) 28
•
J.C. Vyas and V.R. Katti, “Effect of temperature fluctuations on resolution of ultrasonic non-invasive gas
sensor for gas/air binary systems,” Proc. of 12 th Natl, seminar on phys and Techl., of sensors (NSPTS-12,
march 7-9, 2007) ed: A.K. Debnath and S.K. Gupta, p-158
•
J.C. Vyas at el, “Sensing of SF6 gas in air using non-invasive ultrasonic gas sensor,” International Conf., on
sensors and related networks (SENNET –07) Dec 12-14, 2007, VIT Univ, Vellore (Tamilnadu) India, p-82
•
J.C. Vyas, and V. R. Katti, “Ultrasonic gas sensor as secondary standard for composition measurement of
binary gas mixtures, DAE solid state physics Symp. Myssore Univ., Myssore,” Ed: Amitabh Das et al, 52
(2007), p-413
•
J.C. Vyas at el, “Sensing of SO2 gas in binary mixture with N2 gas using ultrasonic gas sensor and its
comparison with other standard methods. Exploration and Research for Atomic Minerals,” Vol. 19 (2009)
233-237.