A new multiwavelength pyrometer: Design and feasibility study

A multiwavelength pyrometer is described in which the wavelength bands are selected with a direct vision prism and a diode array. The main optical and electronic parameters of the instrument are specified.Paper presented at the Second Workshop on Subsecond Thermophysics, September 20–21, 1990, Torino, Italy.     

Monte Carlo studies of multiwavelength pyrometry using linearized equations

Multiwavelength pyrometry has been advertised as giving significant improvement in precision by overdetermining the solution with extra wavelengths and using least squares methods. Hiernaut et al. [1] have described a six-wavelength pyrometer for measurements in the range 2000 to 5000 K. They use the Wien approximation and model the logarithm of the emissivity as a linear function of wavelength in order to produce linear equations. The present work examines the measurement errors associated with their technique.     

Error analysis by numerical simulation for a three-color pyrometer assuming a blackbody spectrum and a wavelength- and temperature-dependent emissivity

A numerical method devised to test ratio pyrometers has been used to explore the fitting of a blackbody spectrum and an emissivity model that assumes linear wavelength dependence and arbitrary temperature dependence. The slope and intercept coefficients for the emissivity and the temperature form three unknowns. The equations for the output of the three channels can be solved simultaneously for the emissivity coefficients and the temperature at any given time using the corresponding measured channel outputs. The stability of the solution is tested as a function of the temperature and equipment characteristics.Paper presented at the Second Workshop on Subsecond Thermophysics, September 20–21, 1990, Torino, Italy.     

Radiance temperatures (in the wavelength range 522–906 nm) of niobium at its melting point by a pulse-heating technique

Radiance temperatures (at six wavelengths in the range 522–906 nm) of niobium at its melting point were measured by a pulse-heating technique. The method is based on rapid resistive self-heating of the specimen from room temperature to its melting point in less than 1 s and on simultaneously measuring the specimen radiance temperatures every 0.5 ms with a high-speed multiwavelength pyrometer. Melting was manifested by a plateau in the radiance temperatureversus-time function for each wavelength. The melting-point radiance temperatures for a given specimen were determined by averaging the measured temperatures along the plateau at each wavelength (standard deviation of an individual temperature from the mean: 0.1–0.4 K). The melting-point radiance temperatures for niobium were determined, by averaging the results at each wavelength for 10 specimens (standard deviation: 0.3 K), as follows: 2497 K at 522 nm, 2445 K at 617 nm, 2422 K at 653 nm, 2393 K at 708 nm, 2337 K at 809 nm, and 2282 K at 906 nm. Based on estimates of the random and systematic errors arising from pyrometry and specimen conditions, the total error in the reported values is about 5 K at 653 nm and 6 K at the other wavelengths.Paper presented at the Second Workshop on Subsecond Thermophysics, September 20–21, 1990, Torino, Italy.     

Error analysis of a ratio pyrometer by numerical simulation

A numerical method has been devised to evaluate measurement errors for a three-channel ratio pyrometer as a function of temperature. The pyrometer is simulated by computer codes, which can be used to explore the behavior of various designs. The influence of the various components in the system can be evaluated. General conclusions can be drawn about what makes a good pyrometer, and an existing pyrometer was evaluated, to predict its behavior as a function of temperature. The results show which combination of two channels gives the best precision.Paper presented at the Second Workshop on Subsecond Thermophysics, September 20–21, 1990, Torino, Italy.     

Radiance temperatures (in the wavelength range 519–906 nm) of tungsten at its melting point by a pulse-heating technique

Radiance temperatures (at six wavelengths in the range 519–906 nm) of tungsten at its melting point were measured by a pulse-heating technique. The method is based on rapid resistive self-heating of the specimen from room temperature to its melting point in less than 1 s; and on simultaneously measuring the specimen radiance temperatures every 0.5 ms with a high-speed six-wavelength pyrometer. Melting was manifested by a plateau in the radiance temperature versus time function for each wavelength. The melting-point radiance temperatures for a given specimen were determined by averaging the measured temperatures along the plateau at each wavelength. The melting-point radiance temperatures for tungsten were determined by averaging the results at each wavelength for 10 specimens (standard deviation in the range 0.5–1.1 K, depending on the wavelength) as follows: 3319 K at 519 nm, 3236 K at 615 nm, 3207 K at 652 nm, 3157 K at 707 nm, 3078 K at 808 nm, and 2995 K at 906 nm. Based on estimates of the random and systematic errors arising from pyrometry and specimen conditions, the total uncertainty in the reported values is about ±7 K at 653 nm and ± 8 K at the other wavelengths.Paper presented at the Third Workshop on Subsecond Thermophysics, September 17–18, 1992, Graz, Austria.     

Measurements of thermophysical properties of nickel with a new highly sensitive pyrometer

A new, sensitive, and fast (response time, 100 ns) pyrometer used for the measurement of temperature in pulse heating experiments is described. The monochromatic instrument may use two detectors, namely, a Si diode and an InGaAs diode. Since monochromatic pyrometers usually are self-calibrated with the plateau of the melting transition of the investigated metal, a high sensitivity is desirable. The pyrometer is sensitive down to 1000 K and may be used at the melting plateau of copper, a reference point on the International Temperature Scale of 1990. A wide temperature range in a single measurement is possible with the use of a fast operational amplifier with linear and logarithmic outputs. Electrical resistivity, heat capacity, and enthalpy of nickel were measured in the temperature range 1500 to 2200 K using a fast pulse heating technique.Paper presented at the Third Workshop on Subsecond Thermophysics, September 17–18, 1992, Graz, Austria.     

Radiance temperatures (in the wavelength range 523–907 nm) of group IVB transition metals titanium,zirconium, and hafnium at their melting points by a pulse-heating technique

The melting-point radiance temperatures (at six wavelengths in the range 523–907 nm) of the Group IVB transition metals titanium, zirconium, and hafnium were measured by a pulse-heating technique. The method is based on rapid resistive self-heating of the specimen from room temperature to its melting point in less than 1 s and on simultaneously measuring the specimen radiance temperatures every 0.5 ms with a high-speed six-wavelength pyrometer. Melting was manifested by a plateau in the radiance temperature-versus-time function for each wavelength. The melting-point radiance temperatures for a given specimen were determined by averaging the measured temperatures along the plateau at each wavelength. The melting-point radiance temperatures for each metal were determined by averaging results for several specimens at each wavelength as follows: Based on estimates of the random and systematic errors arising from pyrometry and specimen conditions, the combined uncertainty (95% confidence level) in the reported values is about ±8K at each wavelength.     

Analysis of multiwavelength pyrometry using nonlinear chi-square fits and Monte Carlo methods

An analysis of multiwavelength pyrometry is made using Monte Carlo methods to evaluate the measurement error as a function of temperature for three, four, five, and six channels. Both a graybody and an emissivity with linear wavelength dependence are considered. ² is calculated using the observed intensity in each channel and is minimized with respect to the temperature and the emissivity coefficients, using the Levenberg-Marquardt method. The influence of spectral span of the channels and the weight function used in the ² fit are exmained. For the case of linear wavelength dependence, the solutions are found to be nonunique, even with six channels. The results show little improvement of precision with increasing number of channels beyond four channels when the nonlinear variable T is free. Both the spectral span and the weight function are shown to be important variables.     

Differential equations for a dynamic thermal conductivity experiment

The mathematical model that describes a dynamic thermal conductivity experiment is reconsidered by taking into account the role of thermal expansion. Two differential equations are presented that take into account the various physical phenomena occurring in a long thin rod directly heated by a current pulse. One of the two equations keeps variables space and time completely separate and is particularly useful for computer simulations.Paper presented at the Second Workshop on Subsecond Thermophysics, September 20–21, 1990, Torino, Italy.     

Thermal conductivity by a pulse-heating method: Theory and experimental apparatus

A new dynamic technique for the measurement of thermal conductivity at high temperatures has been developed at the IMGC. The specimen is brought to high temperatures with a current pulse; during cooling the heat content is dissipated by radiation and by conduction. The differential equation describing this process contains terms related to the heat capacity, the hemispherical total emittance, and the thermal conductivity of the material. If the first two properties are determined using the same specimen during subsecond pulse heating experiments, thermal conductivity may be evaluated by accurate measurements of the round-shaped temperature profiles established on the specimen during cooling. High-speed scanning pyrometry makes possible accurate measurements of temperatures and of temperature derivatives (with respect to space and time), which enables the differential equation describing the power balance at each point of the specimen to be transformed into a linear equation of the unknown thermal conductivity. A large overdetermined system of linear equations is solved by least-squares techniques to obtain thermal conductivity as a function of temperature. The theory underlying the technique is outlined, the experimental apparatus is described, and details of the measurement technique are given.Paper presented at the First Workshop on Subsecond Thermophysics, June 20–21, 1988, Gaithersburg, Maryland, U.S.A.     

A dynamic technique for measuring normal spectral emissivity of electrically conducting solids at high temperatures with a high-speed spatial scanning pyrometer

A dynamic (subsecond) technique is described for measuring normal spectral emissivity of electrically conducting solids at high temperatures, primarily in the range 1800 K up to near their melting point. The basic method involves resistively heating a tubular specimen from ambient temperature through the temperature range of interest in less than 1 s by passing an electrical current pulse through it, while using a high-speed spatial scanning pyrometer to measure spectral radiance temperatures along a 25-mm length on the specimen. This portion of the specimen includes a small rectangular hole that approximates a blackbody cavity. Measurements of spectral radiance temperature of the specimen surface as well as specimen true temperature enable the determination of the normal spectral emissivity of the surface via Planck's law. The applicability of the technique is demonstrated by measurements performed on molybdenum in the range 1900–2850 K.     

Radiance temperatures (in the wavelength range 525 to 906 nm) of vanadium at its melting point by a pulse-heating technique

The radiance temperatures (at six wavelengths in the range 525 to 906 nm) of vanadium at its melting point were measured by a pulse-heating technique. The method is based on rapid resistive self-heating of the specimen from room temperature to its melting point in less than 1 s and on simultaneously measuring the specimen radiance temperatures every 0.5 ms with a high-speed six-wavelength pyrometer. Melting was manifested by a plateau in the radiance temperature-vs-time function for each wavelength. The melting-point radiance temperatures for a given specimen were determined by averaging the measured temperatures along the plateau at each wavelength. The melting-point radiance temperatures for vanadium as determined by averaging the results at each wavelength for 16 specimens (standard deviation in the range 0.3 to 0.4 K. depending on the wavelength) are 2030 K at 525 nm, 1998 K at 622 nm, 1988 K at 652 nm, 1968 K at 714 nm, 1935 K at 809 nm, and 1900 K at 906 nm. Based on estimates of the random and systematic errors that arise from pyrometry and specimen conditions, the resultant uncertainty (2 SD level) in the reported values is about ±7 K at each wavelength.     

A new dynamic technique for the measurement of hemispherical total emittance

A new dynamic technique for the measurement of thermal conductivity under development at the IMGC requires accurate values of heat capacity and of hemispherical total emittance at high temperature. Until recently, these data were provided by subsecond pulse heating experiments performed on the same specimens in the same apparatus. The pulse heating technique is the most accurate method for the determination of heat capacity at high temperatures, but because of various experimental problems, the accuracy of hemispherical total emittance determinations is limited to 5%. A new method for a more accurate determination of hemispherical total emittance is proposed, which uses the same experimental data available from thermal conductivity experiments. An analysis of the temperature profiles measured during the free cooling indicates that regions with high-temperature gradients (toward the ends of the specimen) are the best regions for thermal conductivity measurements, while regions with low-temperature gradients (at the center of the specimen) are the best regions for hemispherical total emittance determinations. The new measurement method and some preliminary results are presented and discussed.Paper presented at the Second Workshop on Subsecond Thermophysics, September 20–21, 1990, Torino, Italy.     

Radiance Temperatures (in the Wavelength Range 527 to 1500 nm) of Palladium and Platinum at Their Melting Points by a Pulse-Heating Technique

The radiance temperatures (at seven wavelengths in the range 527 to 1500 nm) of palladium and platinum at their respective melting points were measured by a pulse-heating technique. The method, based on rapid resistive self-heating of a specimen from room temperature to its melting point in less than 1 s, used two high-speed pyrometers to measure specimen radiance temperatures every 0.5 ms during the heating and melting period. Melting was manifested by a plateau in the radiance temperature-versus-time function for each wavelength. The melting-point radiance temperatures for a given specimen were determined by averaging the measured temperatures along the plateau at each wavelength. The melting-point radiance temperatures for each metal as determined by averaging the results for several specimens at each wavelength are as follows. Based on uncertainties arising from pyrometry and specimen conditions, the expanded uncertainty (two-standard deviation level) is about ±7 K for the reported values in the range 527 to 900 nm and about ±8 K for the reported values at 1500 nm.     

Measurement of Melting Point and Radiance Temperature (at Melting Point and at 653 nm) of Hafnium-3 (wt. %) Zirconium by a Pulse Heating Method

A subsecond duration pulse heating method is used to measure the melting point and radiance temperature (at 653 nm) at the melting point of hafnium containing 3.12 weight percent zirconium. The results yield a value of 2471 K for the melting point on the International Practical Temperature Scale of 1968. The radiance temperature (at 653 nm) of this material at its melting point is 2236 K, and the corresponding normal spectral emittance is 0.39. Estimated inaccuracies are: 10 K in the melting point and in the radiance temperature, and 5 percent in the normal spectral emittance.     

Evaluation of thermal conductivity from temperature profiles

A new dynamic technique for the measurement of thermal conductivity is being developed at IMGC. The experiment consists in bringing the specimen to high temperatures with a current pulse and in measuring the temperature profiles during the free cooling period. Different techniques can be used to extract the information on thermal conductivity from the profiles. The numerical computation of thermal conductivity from the experimental temperature profiles in absolute space is possible, but it is difficult and cumbersome because one must know and take into the account the exact position of the infinitesimal elements of the specimen in different profiles. Computations in tube-space (a fictitious space where no thermal expansion occurs) are simpler and lead to less complex numerical computations. Complementary techniques to evaluate thermal conductivity as a function of temperature or at constant temperature are presented with a discussion of advantages and disadvantages of each method. Computer simulations have tested the precision of the complex software. Numerically generated temperature profiles from known thermophysical properties have been obtained and thermal conductivity has been recomputed from the profiles. The relative difference using different computational approaches and different fitting functions is always less than 0.1%.Paper presented at the Third Workshop on Subsecond Thermophysics, September 17–18, 1992, Graz, Austria.     

Radiance Temperatures (in the Wavelength Range 521 to 1500 nm) of Rhenium and Iridium at Their Melting Points by a Pulse-Heating Technique

The melting-point radiance temperatures (at seven wavelengths in the range 521 to 1500 nm) of rhenium and iridium were measured by a pulse-heating technique. The method is based on rapid resistive self-heating of the specimen from room temperature to its melting point in less than 1 s and on simultaneously measuring the specimen radiance temperature every 0.5 ms with two high-speed pyrometers. Melting was manifested by a plateau in the radiance temperature-versus-time function for each wavelength. The melting-point radiance temperatures for a given specimen were determined by averaging the measured temperatures along the plateau at each wavelength. The melting-point radiance temperatures for each metal were determined by averaging results for several specimens at each wavelength. The results are as follows. Based on estimates of the random and systematic errors arising from pyrometry and specimen conditions, the expanded uncertainty (two standard-deviation level) in the reported values is ±8K.