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Pyrometers Classification and Radiation Laws The simplest and oldest non-contact way ofestimating the temperature ofa radiating body is by observing its colour.. " Two-colourpyrometers o

Pyrometers Classification and

Radiation Laws

The simplest and oldest non-contact way ofestimating the temperature ofa radiating body

is by observing its colour Table 8 1 summarises the relationship between temperature and colour Using this method, experienced practitioners can estimate temperatures over about

700 °C, with a precision sufficient for simpler heat-treatment processes This is shown in a witty way in Figure 8.1, which is taken from Forsythe's paper (Forsythe, 1941) It was presented at the historical Symposium on Temperature in November 1939, a symposium that was a milestone in further development of thermometry.

Table 8.1 Temperature correlation with colours of radiating bodies

Temperature (°C) Colour Temperature (°C) Colour

s

i Figure 8.1 First pyrometric temperature measurement

Temperature Measurement Second Edition

L Michalski, K Eckersdorf, J Kucharski, J McGhee

Copyright © 2001 John Wiley & Sons Ltd ISBNs: 0-471-86779-9 (Hardback); 0-470-84613-5 (Electronic)

Pyrometers, also known as infrared thermometers, or radiation thermometers, are non-contact thermometers, which measure the temperature of a body based upon its emitted thermal radiation, thus extending the ability of the human eye to sense hotness No disturbance of the existing temperature field occurs in this non-contact method In pyrometry the most important radiation wavelengths which are situated between from 0.4 to

20 ltm belong to the visible and infrared (IR) radiation bands

In addition to the methods outlined in Chapter 1 it is also possible to classify pyrometers according to their spectral response and operating method, as shown in Figure 8.2 and described in more detail later

Manually operated, or hand operated, pyrometers : In manually operated pyrometers the human operator is an indispensable part of the measuring channel Figure 8 3 illustrates that the operator's eye acts as a comparator An eye comparison is made between the

one wavelength (0.65Eun) disappearingfilament M OA

U R

L T two wavelengths two-colour L E

pyrometers

0.65 ,um H

E

R

M

A _ _- -

total radiation

total pyrometers

A

I one wavelength

I wavelength band pyrometers + U

M A two wavelength bands two wavelength i T

c

:multi-wavelength

several wavelength bands pyrometers

Figure 8.2 Classification of pyrometers by wavelength and operating method

CLASSIFICATION OF PYROMETERS 153

OPTICAL OPERATOR'S

MEASURING OPERATOR INSTRUMENT v

REFERENCE UNIT

Figure 8.3 Structure of a manually operated pyrometer

radiation from the source with a signal from a reference unit whereupon the operator activates the read-out instrument

The following two types belong to the group ofmanually operatedpyrometers:

" Disappearing filament pyrometers based upon matching the luminance of the object and

of the filament, by adjusting the lamp current The observer's eye is the detector Their operating wavelength band is so narrow as to allow them to be regarded as monochromatic pyrometers ofAe = 0.65 Vim

" Two-colourpyrometers or ratio pyrometers deduce the temperature from the ratio of the radiation intensity emitted by the object in two different spectral wavebands, which are most commonly 0.55 and 0.65 pm

Automatic pyrometers : A simplified block diagram of an automatic pyrometer, which is shown in Figure 8.4, is composed of the following main parts:

" optical system concentrating the radiation on radiation detector,

" radiation detector which may be either a thermal or a photoelectric sensor,

" signal converter, conditioning the detector output signal before being displayed,

" measuring instrument, which may have an additional analogue or digital output

The following four types belong to the group of automatic pyrometers:

" Total radiation pyrometers using thermal radiation detectors, which are heated by the incident radiation In reality the wavelength band used is about 0.2 to 14 Pin resulting from transmissivity of the optical system

" Photoelectric pyrometers operate in chosen wavelength bands in which the signal is generated by photons bombarding a photoelectric detector

" Two-wavelength pyrometers, also called ratio pyrometers, in which the emitted radiation intensity in two wavelength bands is compared by photoelectric detectors

OPTICAL TARGET SYSTEM

DETECTOR

CONVERTER INSTRUMENT

Figure 8.4 Block diagram of an automatic pyrometer

" Multi-wavelength pyrometers, where the source radiation, which is concentrated in some wavelength bands, is incident upon photoelectric detectors They are used for measuring the temperature ofbodies with low emissivity

Automatic pyrometers are produced for use in stationary or portable applications However, the technical parameters of both types are nearly identical in practice Stationary pyrometers, which are usually more robust, can withstand higher ambient temperatures

8.2.1 Absorption, reflection and transmission of radiation

Thermal radiation is a part of electromagnetic radiation Let us assume that a radiant heat flux, (P, defined as a quantity of heat in a unit time, is incident on the surface of a solid Of this heat flux, the portion, (Da , is absorbed, whilst (DP is reflected and (D T is transmitted The following definitions are introduced:

" absorptivity, a = (Da /(D

" reflectivity, p =q) P/(D (8.l)

" transmissivity, r = (D, /(D

Applying the principle ofenergy conservation shows that for every solid:

In the case of transparent bodies, as represented in Figure 8.5, many internal reflections cause additional absorption For example, Harrison (1960) notes that the total reflected heat flux, (D P ,is composed ofthe primary heat flux (DpI , and a secondary one `fp

L _

REFLECTED

FLUX

OF~~Df1 P2 Owl ~T

u

Figure 8.5 Decomposition of the heat flux, (1), in a transparent body

RADIATION, DEFINITIONS AND LAWS 155 There are three specific cases :

I a =1, p = 0, ,r = 0 the body is a black body, which totally absorbs all incident radiation

2 a = 0, p =1, r = 0 the body is a white body, which totally reflects all incident radiation

3 a = 0, p = 0, z =1 the body is a transparent body as all of the incident radiation is completely transmitted

The concept of ablack bodyis very important in pyrometry Figure 8 6 presents some configuration properties approaching those of a black body Heinisch (1972) shows that in the cavities presented in Figure 8.6, total absorption of the incident radiation is reached by its multiple internal reflection

Similarly to the factors, a, p and z, which are valid for total radiation, the spectral properties, ax,pX and z?, at the wavelength A, may also be introduced:

as = (DA, /)

zX = (DXt /(D Equation (8.2) then becomes:

ak + pa + TX =1 (8.4) The values of a, p and z depend upon the material, its surface state and temperature while

ax, p) and z), additionally depend upon the wavelength, A

8.2.2 Radiation laws

Theradiant intensity W or the radiant exitanceis the heat flux per unit area expressed as the ratio of the heat flux dD, emitted from the infinitesimal element of the surface dA, to the surface area dA itself:

W = ~ W/m2

I

1 II, ~

d Figure 8.6 Models of a black body

In the same units as the radiant intensity, the heatflux density, q, of the incident radiation is given by:

This also takes account of the conduction and convection heat flux in addition to the radiation heat flux

The spectral radiant intensity, Wk, is defined as:

W~ = dW W/m2 pin (8.6) Planck's law gives the radiant flux distribution of a black body as a function of the wavelength and of the body's temperature by the relation :

WOA°~ -CC2IRT-1 (8.7)

where W°A is the spectral radiant intensity of a black body, W/m2pm (the suffix `o' will be used in future to indicate a black body), A is the wavelength, pin, T is the absolute temperature of the thermal radiator, K, c, is the first radiation constant whose value is

ci = 3.7415 x 10 -16 W m2 and c2 is the second radiation constant with a value of c2 = 14 388 pin K

For a given wavelength range, from Xi to )L2,equation (8.7) can be evaluated as:

Az elf-s

where W°,~_,~2 is the band radiant intensity of a black body

Hackforth (1960) has shown that if AT << c2, Planck's law of equation (8.7) can be replaced, using the same notation, by a simpler Wien's law:

elV eC2 11T

The spectral radiant intensity W°A of a black body as a function of wavelength A, at different temperatures, calculated from Planck's law, is shown in Figure 8.7 At all temperatures of importance in radiation pyrometry, the errors, which result from replacing Planck's law by Wien's law, are negligibly small The relative errors may be calculated from the relation :

RADIATION, DEFINITIONS AND LAWS 157

AWo; _ W.X,w - WWay W.,~,w.R,P1 =e /XT 8.10 where Wo3,W is the spectral radiant intensity calculated from Wien's law and WOX,pl is calculated as above from Planck's law

The relative errors calculated from equation (8.10) are presented in Table 8.2 as a function ofthe values ofthe product AT

Table 8.2 Relative errors resulting from replacing Planck's law in equation (8.7) by

Wien's law in equation (8.9) as a function of the value of the product AT

AT(m.K) 1 25x 10-3 1.5x10-3

W.),/W.?, (%) 0.001 0.007 0.08 0.8

Figure 8.7 shows that the maxima of the spectral radiant intensity are displaced towards the shorter wavelengths with increasing temperature At the given temperature, T, where the maximum is reached, the wavelength Amax , may be easily calculated from Wien's displacement law to obtain:

Amax T = 2 896 ltm K (8.11) For any given temperature, the area under the corresponding curve is a measure of the total power radiated at all wavelengths by a black body so that:

Wo = fWa,'-0 Ad1 (8.12) The ratio of the spectral radiant intensity, Wj, at the wavelength, A, of a non-black body to the spectral radiant intensity of a black body, Woj, at the same temperature is called the spectral emissivity cA

Wo;

If the spectral emissivity el of a given body is constant for each wavelength (i.e

al =constant) such a body is called a grey body Similarly to equation (8.13), if all wavelengths from 0 to oc, are taken into consideration, the term total emissivity, s, is used:

W

0

where Wis the radiant intensity of any given body and Wo is the radiant intensity of a black body at the same temperature

Following Kirchhoff's law, the spectral absorptivity, ak, of all opaque bodies equals their emissivity, cX, so that:

For a given wavelength band, from A, to ~2 ,Kirchhoff's law is expressed by:

V

' --_

1 '

11

-'

; ,

140 K

WAVELENGTH 1 jim lack body, W~, versus wavelength at different temperatures

equation

inaccordance with Planck's lawin

RADIATION, DEFINITIONS AND LAWS 159

When all wavelengths from 11 > 0 to '12 > oo are taken into consideration, the corresponding form for equation (8 15a), which is also valid, then becomes:

(8.15b) where a is the total absorptivity, and s is the total emissivity

The Stefan-Boltzmann law, which represents the dependence of the total radiant intensity, W., ofa black body upon the temperature, T, is expressed as:

W,, = JAo Wo,d;, = aO Ta

where W,,; is the spectral radiant intensity of a black body as given by Forsythe (1941), The radiation constant ofa black body, a,, has a value a, = 5.6697x10_8 W/m2 K4 Equation (8.16) can be expressed in a more readily usable form as:

4

where Co is the technical radiation constant ofa black body, with the value:

Co = 6o x 108 = 5.6697 W/m2 K4 For grey bodies equation (8.16a) becomes:

4

W = C°£

100

( T

where Co is as before, and8is the total emissivity

In technical practice the majority of real bodies may be regarded as grey ones

8.2.3 Total emissivity and spectral emissivity

Spectral emissivity eA and total emissivity, ewere defined by equations (8 13) and (8.14) Knowledge of the values of c and e,, , especially at A = 0.65 Vm, for different materials, is necessary, to be able to calculate the corrections to be introduced when making pyrometric temperature measurements The emissivity of different materials, which depends heavily upon the surface state, its homogeneity and temperature, may only be determined approximately Worthing (1941) describes methods for the measurement of emissivity Comparison of the properties of different materials, independent of their surface state may be made using the specific total emissivity, e', and the specific spectral emissivity,

E'.. The values of e' and e;L are determined for the direction normal to surface for flat

samples, which should be polished and sufficiently thick This last condition allows semi-transparent bodies to be regarded as totally opaque The values of E and E,~ are also determined for the direction normal to the surface Approximate values for the emissivity of different materials are given in Tables XIX and XX.

It must be stressed that uneven, rough and grooved surfaces may have much higher values of emissivity than are their specific emissivities.

Using the Maxwell theory of electromagnetism, Considine (1957), following Drude, have proposed an approximate formula to calculate thespecific spectral emissivity, E;1, of

metalsas:

where K = 0.365 S2-'"z, p is the resistivity in S2cm, andAis the wavelength in cm.

Equation (8.18) which is valid forA >2 pm, uses the original units of Drude The emissivity

of non-conductors,which is a function of the material refractive index, n,l, is given in

BS 1041, p 5 by the formula:

4nj

(nX +1)2 where nAwhich is the refractive index of the material, has a value in the range of 1 5 to4

for most inorganic compounds and in the range 2.0 to 3.0 for metallic oxides For most clean metals the emissivity is low, with a value of about 0.3 to 0.4, falling sometimes to 0.1 for aluminium Spectral emissivities of metals become lower at lower temperatures where the wavelengths are longer Non-metallic substances have emissivities of about 0 6 to 0.96, which do not vary greatly with temperature It should be borne in mind, that the appearance

of metals in visible light cannot be a basis for predicting their emissivities Most non-metals, such as wood, brick, plastic and textiles at 20 °C have a value of total emissivity nearly equal to unity.

8.2.4 Radiant heat exchange

Consider two parallel surfaces, having identical areas A and the respective temperatures and emissivities TI , T2, El , 02, emitting thermal radiation towards each other with the intensities given by the Stefan-Boltzmann law in equation (8.16a) The heat flux (power) (D12 exchanged between these surfaces, for T1 > T2, is given by:

where Co is the technical radiation constant, and A is the radiating area.

RADIATION, DEFINITIONS AND LAWS 161

If one of the bodies of area A I is placed inside another one of area A2 and with A1 < A2, then equation (8.20) becomes:

biz (1/s,)+(A~~A2,

)[(1/EZ)-1] [( 100

)4-(100)4

(8.20a)

In the very important practical case whenA2 > 3A1, equation (8.20a) becomes:

X12 = A1E1Co

[

(101)4

-~00\4

(8.20b)

Lambert's directional law which describes the radiant intensity of a black body as a function of the radiation direction, is given by:

Woe = Way_ cos(p (8.21) where Wo,, is the radiant intensity of an element of area under the angle rP between the radiation direction and the direction normal to the surface, and Woe is the radiant intensity

as before but in the direction normal to the surface

Radiant intensity, W,1, in the direction normal to the surface is 7T times smaller than the total radiant intensity

Equation (8 21) is only partially valid for non-black bodies Large deviations from Lambert's law, which can be observed especially for polished metals when rp > R/4, are caused by the dependence of the emissivity upon the observation angle Some definitions, taken from illumination technique, are also used in optical pyrometry, in the case when the thermal radiation takes place in the visible wavelength range Luminosity, I,,, is the radiant flux propagated in an element of solid angle Radiance, L, also called luminance, which is a density of luminosity of a surface in a given direction, is expressed as:

cos (P dA where dA is the area of an element of the radiating surface and T is the angle between the radiant flux direction and the direction normal to the surface

Radiance is a deciding factor in the subjective impression ofthe body's brightness