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Transcript
Chapters 8
OPTICAL PYROMETRY
“ … try adding minus one to the denominator … ”
Max Planck (1900)
8.1 Historical Resume
Gustav Kirchoff, in 1860, defined a black body as a surface
that neither reflects nor passes radiation [1].
He suggested that such a surface could be realized by heating
a hollow enclosure and observing the radiation from a small
times access hole (e.g. a cylindrical hole of a depth from five
to eight times its diameter that radiates from one end closely
approximates black body).
Kirchoff defined the emissivity E of a non-black body as
the ratio of its radiant intensity to that of a similar black body
at the same.
Henri LeChatelier introduced, in 1892, the first practical
optical pyrometer.
It included an oil lamp as the reference light source, a red
glass filter to limit the wavelength interval, and an iris
diaphragm to achieve a brightness match between the light
source and the test body.
Wilhelm Wien, in 1896, derived his law for the distribution
of energy in the emission spectrum of a black body as
J b
c1 5

exp(c2 / T )
(8.1)
Where J represents intensity of radiation emitted by a black
body at temperature T, and wavelength λper unit wavelength
interval, per unit time, per unit solid angle, per unit area.
Max Planck, to remedy deviations that appeared between
(8.1) and the experimental facts at high values of λT
suggested, in 1900, the Mathematical expression
J b
c1 5

exp(c2 / T )  1
(8.2)
to describe the distribution of radiation among the various
wavelengths; that is, he simply added a -1 to the denominator
of Wien’s equation .
However , in attempting to explain the significance of -1 in
the denominator , Planck developed the quantum theory
( where in he postulated that electromagnetic waves can exist
only in the form of certain discrete packages or a quanta ).
Subsequently he received the Nobel Prize for his work.
The numerical values and the units, both in the International
System (SI) and in the U.S. Customary System, for all the
quantities involved in(8.2) are given in Table 8.1. An
example illustrates the use of (8.2).
Example 1. Find the intensity of radiation emitted by a
black body at 2200oR at a wavelength of 3μin both SI and U.S.
Customary units, and check. U. S. Customary
104 cm
  3  3[


1 ft
]  9.8425 106 ft
30.48cm
13.7411015 BTU . ft 2 / hr  (9.8425  106 ft )5
J b 
exp[0.08497 ft 0 R /(9.8425  106 ft  2200 0 R 0]  1
1.48762 1011
9 BTU
J b 
 2.99884 10
3.92408
e
1
hrft 3
T ( R) 2200
T (K ) 

 1222.22 K
1.8
1.8
3.7413 1012 J .cm2 / sec (3 ) 5
J b 
exp[1.43883cm.K /(3 1222.22 K )]  1
1.53963 106
J
4
J b  3.92408
 3.10369 10
e
1
sec cm3
That the SI answer checks the U. S. answer can readily be
seen by applying several conversion constants .That is
3
J
1
BTU
3600sec
(30.48
cm
)
J b  3.10369 104
[


]
3
3
3
sec cm 1.055056 10 J
hr
ft
9 BTU
 2.99882 10
hrft 3
In 1927 the International Temperature Scale (ITS) was
defined. Temperatures above the gold point (then 10630C)
were to be given by Wien’s equation (8.1) used in conjunction
with a disappearing filament optical pyrometer.
In 1948 the ITS was redefined so that temperatures above
the gold point were to be given by Planck’s equation (8.2) and
a disappearing filament optical pyrometer.
This definition of the higher temperatures continues to the
present (see Chapter 4).
Note that in practice it is the spectral radiance of the test
body (at its temperature) relative to that of a black body at the
gold point that defines its temperature on the IPTS according
to (4.4).
8.2 Principles of optical Pyrometry
An optical pyrometer [2], [3] consists basically of an optical
system and a power supply.
The optical system includes a microscope, a calibrated lamp
and a narrow band Wave filter, all arranged so that the test
body and the standard light source can be viewed
simultaneously.
The power supply provides an adjustable current to the lamp
filament (see Figures 8.1 and 8.2)
Optical pyrometry is based on the fact that the spectral
radiance from an incandescent body is a function of its
temperature [4],[5].
For black body radiation, the well-known curves of Plank’s
equation describe the energy distribution as a function of
temperature and wavelength (Figure 8.3).
If a non-black body is being viewed ,however, its
emissivity ,which is a function of wavelength and temperature,
must be taken into consideration ( Figure 8.4 ).
In general, to obtain the temperature of a test body, the
intensity of its radiation at a particular wavelength is
compared with that of a standard light source.
Red Filter
The very narrow band of wavelengths required for the
comparison just noted is established in part of the use of a red
filter in the optical system, and in part by the observer’s eye.
A red filter exhibits a sharp cutoff at λ=0.63μ(where
1μ=0.001mm)
This means that below about 1400℉, the intensity of
radiation transmitted by a red filter is too low to give adequate
visibility of the test body and the standard filament.
On the other hand, a red filter exhibits a high transmission
for λ>0.65μ (see Figure 8.5), so that it is the diminishing
sensitivity of the eye that provides the necessary cutoff at the
high end of the band.
The particular wavelength that is effective in optical
pyrometry is usually taken as 0.65μ
Brightness Temperature
Several steps are involved in determining temperature by an
optical pyrometer [6], [7]. First, the brightness of the test body
is matched against the brightness of the filament of a
calibrated lamp at the effective wavelength of 0.655μ.
Because the image is nearly monochromatic red, no color
difference is seen between the lamp filament and the test body,
and thus the filament seems to disappear against the
background of the target.
Of course, matching should be recognized as a null balance
procedure.
It is the optical equivalent of a Wheatstone bridge balance
to determine resistance measurements or a potentiometric
balance for voltage measurements.
Second, the filament current necessary for the brightness
match must be measured. For the highest accuracy , this is best
achieved by a potentiometric measurement across a fixed
resistor in series with the lamp filament .
Third , the filament current measurement , obtained at the
match condition , must be translated into brightness
temperature by means of a predetermined calibration
relationship ( see Sections 8.3 ) .
This calibration is predicated on the existence of a lamp
with a stable , reproducible characteristic with temperature and
time.
Finally , brightness temperature must be converted to actual
temperature through applying the emissivity of the test body
( see Tables 8.2, 8.3 , and 8.4 as well as the examples that
follow ) .
The brightness temperature is defined as that temperature at
which a blackbody would emit the same radiant flux as the test
body.
This is the temperature as observed with an optical
pyrometer. For non-black bodies the brightness temperature is
always less than the actual temperature. Thus according to
Table 8.2 a black body(ε= 1)
would appear 1 . 1 times as bright as carbon(ε=0.9) 2.3
times as bright as tungsten (ε=0.43) and 3.3 times as bright as
platinum(ε=0.3)
when all are at the same temperature . To say it another
way , the actual temperatures of these materials would be
2000oF for the black body , 2016℉ for the carbon , 2137℉ for
the tungsten , and 2198℉ for the platinum , when all indicate a
brightness temperature of 2000℉ ( according to Tables 8.2 ,
8.3 , and 8.4 ) .
From Wien’s law , (8.1) , the relationship between the actual
temperature (T) and the brightness temperature (TB) can be
approximated in terms of the pyrometer’s effective wavelength
of radiation(λ) the second radiation constant (c2) , and the
target emissivity(ε)
1 1 
  ln 
T TB c2
(8.3)
If the transmission (τ) of the viewing effective emissivity (ε)
should be used system in ( 8.3 ) is not unity , then the in place
of the source
Of course, if ε=l and τ=l the actual temperature will equal
the brightness temperature, since, according to (8.3), ln 1=0.
Equation 8.3, with (8.4) factored in, is solved graphically in
Figure 8.7, and tabularly in Tables 8.3 and 8.4.
Several examples will illustrate the use of these graphs and
tables.
Example 2
A target brightness temperature of 1600K is measured with
an optical pyrometer having an effective wavelength of 0.655
μ
At this wavelength the effective emittance of the target is
determined to be 0.6. Estimate and check the true target
temperature in degrees Celsius and in degrees Fahrenheit.
Graphical Solution
According to Figure 8.7a, at TB=1600K, and at ε=
0.6,ΔT=T-TB=62℃,
Thus T=TB+ΔT=1662K
Tabular Solution
According to Table 8.4 , at = 1327℃ ,
=
And at ε= 0.6,ΔT=62℃,
Graphical Solution According to Figure 8.7a, at TB=1600K,
and at ε= 0.6,which checks the graphical solution.
According to Tables 8.3 ,at TB=2421℉ and at ε=0.6
ΔT=112℉.
Thus T=2421+112=2533℉ Or T=1662K
.
which checks the graphical solution.
Numerical Solution For small temperature differences, by
Wien’s law (8.1)
T ~
TB 2
c
2
1
ln
'
(8.5)
0.655 106 m 1600  K 2  1 
T `~
ln 
  60C
0.014388mK
 0.6 
2
which once more provides a close check to the graphical and
tabular solutions.
Example 2.
The clean surface of liquid nickel, when viewed through an
optical pyrometer having the conventional effective
Wavelength 0.655μ yields a brightness temperature of 2600℉.
Estimate and check the true nickel temperature.
.
Tabular Solution According to Table 8.3, at TB =2600℉,
and with an effective emissivilty estimated to be 0.37,
according to Table 8.1,
T = 257℉. Thus T= T = 2857℉. According to Table 8.4 , at
TB = 1427℃, and ε=0.37
by double interpolation
T
= 143℃
Thus T=1427+143=1570℃= 2858℉
which is consistent with the Fahrenheit solution.
Graphical Solution According to Figures 8.7b , at
TB= 1700K, and atΔT = 142℃ ε=0.37
Thus T=1427+142=1569℃=2856℉
which check the tabular solutions.
Numerical Solution According to (8.5),
0.655 106 17002
1
T ~
ln
 131C
0.014388
0.37
which provides a fair check to the graphical and tubular
solutions. Since Δt is large in this of example, the
approximation (8.3) is not as reliable as for smaller Δt.
Brightness temperature thus depends on the sensitivity of
the eye to differences in brightness, and on a knowledge of the
mean effective wavelength of the radiation being viewed.
It does not depend on the distance between the test body
and the optical pyrometer, however.
We must be sure that the radiation observed is that being
emitted by the test body rather than reflected radiation, since
there is no relationship between the temperature of a surface
and the radiation it reflects.
Also, smoke or fumes between the optical pyrometer and
the target must be avoided as must dust or other deposits on
the lenses, screens , and lamp windows .
Pyrometer Lamp
Of all the elements in the optical pyrometer, the pyrometer
lamp is the most important, since it provides the reference
standard for all radiance measurements.
The most stable lamps consist of a pure tungsten filament
enclosed in an evacuated glass tube.
The vacuum is necessary to minimize convection and
conduction heat transfer effects.
The tungsten is always annealed before calibration and, once
calibrated, can be used typically for 200 hours before
recalibration is required .
Although theoretically the optical pyrometer has no upper
temperature limit, practically, for long term stability, the lamp
filament cannot be operated above a certain current or
brightness. This limit corresponds approximately to 1350℃.
Absorbing Glass Filter
Glass filters , which absorb some of the radiation being
viewed , are used when temperatures higher than 1350℃ are
being measured in order to reduce the apparent brightness of
the test body to values that the filament can be made to match .
Thus it is not necessary to operate the standard lamp
filament at as high a temperature as would normally be called
for by the brightness of the test body.
Such practice adds to the stability and life of the filament.
The absorbing glass filters are inserted between the objective
lens and the pyrometer lamp as shown in Figures 8.1 and 8.2.
Thus a black body at a temperature above 1350℃ appears
the same through the absorbing glass as another black body
would appear in the same pyrometer without a screen at a
temperature below 1350℃.
In addition, use of the proper glass screen allows closer
color matching between the pyrometer lamp and the attenuated
source, and this leads to more precise brightness matching.
Black Body
The emissivity of most materials is such a variable quantity
and so strongly dependent on surface conditions [10] that it
becomes almost mandatory to sight on the test body in a black
body furnace.
In lieu of laboratory-type testing in the highly favorable
conditions of a black body furnace, one can often approximate
a black body in field-type applications;
For example, if the surface temperature of an incandescent
material in a test rig is required, a small hole can be drilled
directly into the surface for sighting purposes.
The hole depth should be about five times its diameter, as
previously mentioned.
Regardless of the emissivity of the hole walls, the multiple
reflections inside the cavity makes the hole radiate
approximately as a black body.
Temperatures based on such techniques are almost certain to
be more valid than temperatures based on flat surface
sightings, as corrected by estimated surface emissivities.
In any case, whenever black body conditions prevail, if the
brightness match is achieved, and if the pyrometer is properly
calibrated, then
Tobserved  Tbrightness  TIPTS
Hot Gas Measurements
The radiation characteristics of hot gases are not like those
of hot solids in that gases do not emit a continuous spectrum
of radiation.
Instead, the emissivity of a gas exhibits a rapid variation
with wavelength . That is gases which radiate or emit strongly
only at certain characteristic wavelengths, correspond to
absorption principles of radiation pyrometry lines (see entirely
Figure 8.8).
It is clear that different from those just de- scribed are called
for in the temperature measurement of gases , and the
appropriate literature should be consulted for further
information [11] .
At least three types of calibration are to be distinguished in
optical pyrometry.
Primary
This type of calibration is done only at the National Bureau
of Standards [2], [12]. The filament current required to
balance the standard lamp brightness against pure gold held at
the gold point temperature in a black body furnace constitutes
the basic point in the calibration.
Higher temperature points are determined by a complex
method that is detailed in NBS Monograph 41, and is based on
the use of tungsten strip lamps and sectored disks.
Representative uncertainties in achieving the IPTS by optical
pyrometry are:±4℃ at the gold point,± 60℃ at 2000℃ ;
and 40℃ at ±4000℃.
In this type of calibration [3], [4] the output of a primary
pyrometer(i.e., one calibrated at the NBS) is compared with
that of a secondary pyrometer (i.e., one to be calibrated) when
the pyrometers are sighted alternately on a tungsten strip lamp
operated at different brightnesses.
Such lamps are highly reproducible sources of radiant
energy and can be calibrated with respect to brightness
temperatures from 800 to 2300℃, with accuracies only
slightly less than would be obtained according to the IPTS .
Note that in this method the source need not be a black body
so long as the pyrometers are optically similar.
Industrial
Two secondary optical pyrometers can be intercompared
periodically by sighting them alternately on the same source.
Note that here the source need not be a black body and the
comparison pyrometers need not have primary calibrations.
The method is most useful for indicating the stability of the
pyrometers, and thus can indicate the need for a more basic
calibration.
8.4 The Two-Color Pyrometer
The accuracy of a temperature determination by the singlecolor optical pyrometer just discussed is based on black body
furnace sightings or on known emissivities.
A two-color pyrometer, on the other band, is used in an
attempt to avoid the need for emissivity corrections.
The principle of operation is that energy radiated at one
color increases with temperature at a different rate from that at
another color [13], [14].
The ratio of radiances at two different effective wavelengths
is used to deduce the temperature.
The two-color temperature will equal the actual temperature
whenever the emissivity at the two wavelengths is the same.
Unfortunately this is seldom true.
All that can be said is that when the emissivity does not
change rapidly with wavelength, the two-color temperature
may be closer to the actual temperature than the single-color
brightness temperature.
If the emissivity change with wavelength is large, however,
the converse is true. Kostkowski [13] of the NBS indicates
that, in any case, the two-color pyrometer is less precise than
the single-color optical pyrometer,
Typically, when both were sighted on a black body, the
optical came within 2℃ of the known temperature, whereas
the two-color pyrometer was on by 30℃.
8.5 Automatic optical Pyrometer
Since 1956 the automatic optical pyrometer has dominated
the field of accurate high-temperature measurement.
In such an instrument, the pyrometer lamp current is
adjusted automatically and continuously by detector that views
alternately the target and the pyrometer lamp.
Thus a brightness-temperature balance is achieved by the
automatic optical pyrometer which, in principle, has
considerably greater sensitivity and precision than a manually
adjusted pyrometer that depends on the subjective judgment of
the human eye (see Figure 8.9) [3], [9], [15].
Figures 8.9 Operational diagrams of
(a) manually-adjusted optical pyrometer, and
(b) automatic optical pyrometer (after Leeds and Northrup).
Accuracies obtainable with commercial automatic optical
pyrometers are on the order of ±7℉ for 1500-2250℉, and of
±12℉ from 2250-3200℉.
The operation of an automatic optical pyrometer can best be
understood by referring to Figure 8.10. A revolving mirror
alternately scans the target and the standard lamp filament at
high speed.
The optical system thus projects alternately an image of the
target and of the lamp filament onto the photo multiplier tube.
One technique for determining brightness temperature is to
adjust the reference lamp current until a null intensity is
sensed in the photo multiplier output current.
Another is to maintain the constant lamp current and
determine brightness temperature by sensing an off-balance
meter reading.
In either case, a direct reading of brightness temperature is
forthcoming, and hence the designation automatic optical
pyrometer [8].