BARC/2011/E/008 BARC/2011/E/008
DEVELOPMENT OF RADIATION PYROMETER FOR TIME-RESOLVED MEASUREMENT OF TEMPERATURES IN SHOCK-WAVE COMPRESSION EXPERIMENTS by Amit S. Rav, K.D. Joshi and Satish C. Gupta Applied Physics Division
2011 BARC/2011/E/008
GOVERNMENT OF INDIA ATOMIC ENERGY COMMISSION BARC/2011/E/008
DEVELOPMENT OF RADIATION PYROMETER FOR TIME-RESOLVED MEASUREMENT OF TEMPERATURES IN SHOCK-WAVE COMPRESSION EXPERIMENTS by Amit S. Rav, K.D. Joshi and Satish C. Gupta Applied Physics Division
BHABHA ATOMIC RESEARCH CENTRE MUMBAI, INDIA 2011 BARC/2011/E/008
BIBLIOGRAPHIC DESCRIPTION SHEET FOR TECHNICAL REPORT (as per IS : 9400 - 1980)
01 Security classification : Unclassified
02 Distribution : External
03 Report status : New
04 Series : BARC External
05 Report type : Technical Report
06 Report No. : BARC/2011/E/008
07 Part No. or Volume No. :
08 Contract No. :
10 Title and subtitle : Development of radiation pyrometer for time-resolved measurement of temperatures in shock-wave compression experiments
11 Collation : 31 p., 11 figs., 1 tab.
13 Project No. :
20 Personal author(s) : Amit S. Rav; K.D. Joshi; Satish C. Gupta
21 Affiliation of author(s) : Applied Physics Division, Bhabha Atomic Research Centre, Mumbai
22 Corporate author(s) : Bhabha Atomic Research Centre, Mumbai - 400 085
23 Originating unit : Applied Physics Division, BARC, Mumbai
24 Sponsor(s) Name : Department of Atomic Energy
Type : Government
Contd... BARC/2011/E/008
30 Date of submission : March 2011
31 Publication/Issue date : April 2011
40 Publisher/Distributor : Head, Scientific Information Resource Division, Bhabha Atomic Research Centre, Mumbai
42 Form of distribution : Hard copy
50 Language of text : English, Hindi
51 Language of summary : English
52 No. of references : 14 refs.
53 Gives data on :
60 Abstract : We have developed a radiation pyrometer system for time resolved measurement of temperature in materials subjected to shock loading or to sudden deposition of energy by any other means. This instrument has four channels, with each channel equipped with interference filter and photo-receiver. The interference filter selects the desired wavelength in the visible to near infrared range and the photo-receiver converts the filtered radiation into an electrical signal. The FWHM bandwidth of the interference filter is ~10 nm around the selected central wavelength and the dynamic bandwidth of proto-receiver is ~125 MHz which corresponds to time resolution of ~3ns. The output of photo-receivers at each channel is recorded in fast Digital Storage Oscilloscope (DSO). The recorded intensities at a given instant of time for four wavelength are fitted to Plank's radiation law and the information about the temperature and emissivity of the object is obtained. A software code has been developed to analyze the experimental data for generating time resolved profile of temperature and emissivity. The instrument is demonstrated to make steady state temperature measurement of standard Tungsten Halogen Lamp Source (THLS) with an accuracy of ~5%. Also it has been used for the measurement of time resolved temperature profile of electrically exploded conducting wire (copper) having transient of the order of ~15 ns.
70 Keywords/Descriptors : PYROMETERS; TEMPERATURE MEASUREMENT; SHOCK WAVES; TIME RESOLUTION; PERFORMANCE TESTING; SPECIFICATIONS; THERMAL RADIATION
71 INIS Subject Category : S46
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Development of Radiation Pyrometer for Time-Resolved Measurement of Temperatures in Shock-Wave Compression Experiments
Amit S. Rav, K.D. Joshi and Satish C. Gupta
Applied Physics Division Bhabha Atomic Research Centre, Trombay, Mumbai, 400 085, India Email: [email protected] Abstract
We have developed a radiation pyrometer system for time resolved measurement of temperature in materials subjected to shock loading or to sudden deposition of energy by any other means. This instrument has four channels, with each channel equipped with interference filter and photo- receiver. The interference filter selects the desired wavelength in the visible to near infrared range and the photo-receiver converts the filtered radiation into an electrical signal. The FWHM bandwidth of the interference filter is ~10 nm around the selected central wavelength and the dynamic bandwidth of proto-receiver is ~125 MHz which corresponds to time resolution of ~3ns. The output of photo-receivers at each channel is recorded in fast Digital Storage Oscilloscope (DSO). The recorded intensities at a given instant of time for four wavelength are fitted to Plank’s radiation law and the information about the temperature and emissivity of the object is obtained. A software code has been developed to analyze the experimental data for generating time resolved profile of temperature and emissivity. The instrument is demonstrated to make steady state temperature measurement of standard Tungsten Halogen Lamp Source (THLS) with an accuracy of ~5%. Also it has been used for the measurement of time resolved temperature profile of electrically exploded conducting wire (copper) having transient of the order of ~15 ns.
Table of Contents
Page No.
1. Introduction 1
2. Theory of Radiation Temperature Measurement (Pyrometry) 2
3. Instrument Design for Pyrometer 4
3.1. Radiation Collection from the Target 5 3.2. Distribution of Light in different Channels 6 3.3. Wavelength Selection 7 3.4. Detection of Radiation Intensity 7 3.5. Recording of Data 8
4. Calibration of System 8
5. Development of Code for Estimation of Temperature and Emissivity 10
5.1. Theory of Least Square Method for Parameter Estimation 10 5.2. Code Development 13 5.3. Uncertainty Calculation 15
6. Experiments 17
6.1. Validation of Pyrometer by Measuring Temperature of Standard 17 Radiation Source 6.2. Time Resolved Temperature Measurement of Electrically Exploding 19 Wire
7. Conclusion & Future Development 23
8. Acknowledgement 23
9. References 24 1. Introduction
Shock compression of materials generates not only very high pressures but also high temperatures in the materials. The Hugoniot equation of state (the relation between shock pressure P and density ) of the material can be determined by planer steady shock wave loading experiments by measuring quantities like shock velocity, pressure profile and particle velocity history and using these quantities along with three conservation laws of mass, momentum and energy. However for determination of complete thermodynamic behavior of the compressed state, measurement of temperature is required. The measurement of temperature gives insight into the partition of the total energy in the shocked system [1-3] and provides additional information on the complete equation of state, solid-solid phase transition and melting of shock compressed materials [4-9].
Temperature is generally measured by observing some physical phenomena that is dependent on temperature, such as change in resistance, volumetric expansion, development of vapour pressure and spectral characteristic etc. Depending on the nature of contact between the medium of interest and the device, the temperature measurement techniques are classified as invasive, semi-invasive and non-invasive. Invasive techniques use the transducer in direct contact with the medium of interest, for example a liquid in glass thermocouple immersed in a liquid. In semi-invasive techniques, the surface of interest is treated in some way to enable remote observation, for instance the use of thermochromic liquid crystals, which change colour with temperature. Non-invasive techniques on the other hand, like Radiation pyrometry, are non contact where medium of interest is observed remotely.
A typical dynamic compression experiments lasts for about few micro-seconds and changes in pressure and temperature occurs on time scale of the order of few tens of nano-seconds or smaller. The conventional invasive methods of temperature measurement (thermocouples, resistance temperature detector or RTD etc) require the sensor to thermally equilibrate with the medium of interest through conduction of 1
heat. The process of attaining thermal equilibrium between sensor and the medium is much slower than the rate at which the temperature increases in the shocked medium, so such invasive methods cannot be used for measurement of temperature in shocked medium. On the other hand, a radiation pyrometer, measures the intensities of electromagnetic radiation emitted by the object using photo-detectors with response time of about a few nanoseconds. Since the radiation pyrometry is a non contact technique, it is specifically useful for measurement of temperature in the processes where contamination/intrusion has to be avoided.
This report describes the development of a radiation pyrometer at our laboratory at BARC. In section 2 we introduce the basic concepts in the theory of radiation pyrometer. Section 3 presents the details of the instruments for recording the radiation intensities at various wavelengths. In section 4, we present the procedure for calibration of pyrometer. Section 5 details the development of computer code for retrieving temperature and emissivity from the radiation intensity data. Section 6 provides the experimental method for validation of the pyrometer. Finally in section 7, we present conclusion and discussion for future developments.
2. Theory of Radiation Temperature Measurement (Pyrometry)
Pyrometers use the fact that all objects above absolute zero Kelvin radiate and absorb thermal energy. This thermal energy, which is the measure of the average atomic kinetic energy, is radiated in the form of electromagnetic radiation.
The thermal radiation consists of electromagnetic radiation of wavelength band between 0.1 µm and 100 µm in electromagnetic spectrum (Figure 1). The band of wavelength emitted will depends on the temperature. As the temperature rises, the intensities of thermal radiation increases and the band of emitted spectrum shifts to smaller wavelength. This is manifested as a common experience that higher the temperature the brighter the object appears.
2
Figure 1: The Electromagnetic Spectrum
Figure 2: The Spectral densities at different temperatures
3
A relationship between the intensity of radiation at a particular wavelength λ and absolute temperature T is governed by Planck’s law [10]. The radiant flux density I(λ) as power of electromagnetic radiation per unit of wavelength is expressed as:
C2 5 T 1 I() C1 (e 1) (1)
-16 2 Where, C1 and C2 are constants which equals 1.191 × 10 W.m /sr and 0.01439 m.K respectively; is wavelength; T is the temperature of radiating source; and is the emissivity of the source. Emissivity is measured on a scale from 0 to 1 is the ratio of electromagnetic flux that is emanated from the source to the flux emanated from the black body source at the same temperature.
Once we have measured the radiation intensities I() at different wavelengths, the temperature T and emissivity are estimated from the measured intensities data at different wavelengths by fitting to the Plancks’s law (Equation 1). Spectral densities for different temperatures are shown in Figure 2.
3. Instrument Design for Pyrometer
The schematic and actual photograph of the instrument developed in our laboratory is displayed in figure 3 and 4. The functions of various parts of the pyrometer instrument are the following.
3.1 Radiation collection form the target
3.2 Distribution of light in different channels
3.3 Wavelength Selection
3.4 Detection of Radiation Intensity
3.5 Recording of Data
4
Fast Digital Storage Oscilloscope Electrical O/p PD F
L (600
F (532 nm) nm) L FC L PD Electrical BS O/p Fast Digital Storage Oscilloscope Optical Input BS L From Target Electrical Radiation Source O/p Fast Digital BS Storage Oscilloscope
F L PD
F (750 nm) (700
nm) BS = Beam Splitter L PD = Photo‐detector with Amplifier L = Lens PD F = Interference Filter Electrical FC = Fiber Connector O/p
Fast Digital Storage Oscilloscope
Figure 3: Schematic diagram of the Radiation Pyrometer
3.1. Radiation Collection form the Target
The radiation collection system (Figure 5) is the part of instrument, which collects radiation from the target object, couples it into the fiber, and transport the collected radiation to the instrument where it gets detected. The fiber used in the pyrometer for radiation collection from the target is all silica glass fiber (both core and clad of the fiber are made up of silica glass) having 600 m diameter and 0.22 numerical aperture (NA). For effective coupling of the radiation from the target to the fiber, a collimating lens of 15mm focal length and 12.5 mm diameter is used. The effective NA of the radiation collection system (fiber along with the collimating lens) is about 0.01. The area of the target covered by the radiation collection system at distance
5
about 10 cm from the target is about 165 mm2 ( 14.5 mm) which could be without radiation collection system is about 1,662 mm2 ( 46 mm).
3.2. Distribution of Light in different Channels
The distribution of collected radiation in various channels in the instrument is carried out by using beam splitters. The radiation collected from the target is received at the other end of the fiber and is collimated using a lens ( 12.5 mm & FL 15 mm) inside the pyrometer instrument. This collimated beam of radiation is divided in two parts using first beam splitter ( 25mm) having 50/50 transmission and reflection ratio. The transmitted and reflected radiation is further divided by passing each of
Photo Receiver
With Amplifier Focusing Filter
Lens
Beam 1 Splitter Silica Fiber Beam Photo Receiver Splitter With Amplifier Beam Splitter Photo Receiver With Amplifier
Photo Receiver With Amplifier
Figure 4: Photograph of Radiation Pyrometer Instrument at our laboratory
6
Silica Fiber
SMA Fiber Collimating Lens Connector
Lens and Fiber holding arrangement
Figure 5: Light collection system of Pyrometer
these through similar kind of beam splitters. This way the input radiation is divided into four almost equal parts. The angle of all three beam splitters are so adjusted that the reflected and transmitted light falls on the respective wavelength selection system.
3.3. Wavelength Selection
As shown in the figure 3, the selection of the four wavelengths for measurements is carried out by passing the each part of the collected radiation through the narrow band interference filter of different central wavelengths. Each interference filter consists of multiple layer of evaporated coatings on the substrate such that the optical property of the filter results from wavelength interference rather than absorption. The bandwidth of the filter depends on the number of cavities and the coating thickness. The interference filters used for the wavelength selection have full width half maximum (FWHM) bandwidth of 10 nm with about ~50% transmission at the central wavelength.
3.4. Detection of Radiation Intensity
The detection system converts the radiation falling on it in to an equivalent electrical signal, and this system mainly determines the transient time response of the instrument. The detection system consists of focusing lens and the photo-receiver. The focusing lens (plano-convex lens having effective focal length of 15 mm and 7
diameter of about 12.5 mm), focus the filtered radiation on to the active area of the photo-receiver. The photo receiver has a silicon PIN photo-diode and an amplifier. The photo diode has detector area of 0.5 mm2 and spectral range of 300 nm – 1050 nm, for converting filtered radiation into an electrical signal. The amplifier has a bandwidth of 125 MHz and trans-impedance gain of 40 V/mA, for increasing the signal level of the photo-diode output. This detection system is capable of measuring transient change in radiation intensity of the order of ~3 ns.
3.5. Recording of Data
The equivalent electrical signal generated by the photo receiver is recorded on the fast digital storage oscilloscope having analog bandwidth of 1 GHz and sampling rate of 5 GS/s with a total recording time of 2 ms at highest resolution. To avoid the loss of information, the recording speed of the oscilloscope was chosen to be faster than the response time of the photo-receiver. The oscilloscope used has the facility of recording the data in ASCII text format or Microsoft Excel format apart from its standard format of recording in “.isf” format.
4. Calibration of System
Calibration of the pyrometer instrument provides the information about the response of each optical channel corresponding to the radiance of calibrating source including losses in optical path due to reflection and transmission in different optical components such as, collimating lens, beam splitters, interference filters and response of photo detectors. For the radiation pyrometer, the calibration determines the factor which indicates the amount of radiance at the input of the system required to generate unit output voltage. Unit of calibration factor for the system is given as radiance per unit volts, i.e., watt per square meter per unit wavelength per unit solid angel per unit volts (Wm-2nm-1sr-1V-1). For the calibration of the radiation pyrometer, standard radiation sources whose output radiance is well characterized is used.
8
Channel 1 2 3 4
Wavelength 532±5 600±5 700±6 750±6.5 (nm)
Light Intensity 1.309 x 1012 1.717 x 1012 2.107 x 1012 2.205 x 1012 (W/sr/m2)
Output Signal 0.0424 0.0248 0.103 0.0472 (V)
Calibration Value 3.087 x 1013 6.923 x 1013 2.045 x 1013 4.671 x 1013 (W/sr/m2/V)
Table 1: Calibration Values for Four Channels using Calibrated QTH lamp
In present study the standard source used is 250W/24V Quartz Tungsten Halogen (QTH) lamp from M/s. Sciencetech. The QTH lamp along with its housing and power supply, is calibrated by M/s. Optikon Corporation using standards traceable to the National Institute of Standards and Technology (NIST). The lamp is supplied with the measured radiance data from 380 nm to 1068 nm in the interval of 4 nm with a colour temperature of 3528 K.
During calibration process, the image of entire QTH lamp filament was made to fall completely within the active area of the photodiodes in each channel. The continuous radiation of the lamp is chopped and the voltage values have been obtained from the oscilloscope record. Calibration is carried out with the same components as in the experiments. The calibration factor of each channel has been calculated by dividing the spectral radiant intensity of the calibrated QTH lamp by the recorded voltage signal of each channel. Table 1 shows the calculated calibration factors for the aligned pyrometer.
9
5. Development of Code for Estimation of Temperature and Emissivity
The measured I() at various wavelengths along with the knowledge of the value
of C1 and C2, can be used to estimate the best fit values of the unknown parameters temperature and emissivity for Planck’s law. The present instrument is developed for the measurements of the radiance at four different wavelength. These measurements generate four pair of measured intensity, wavelength data. The non linear least square fit of these data is used to estimate the value of the unknown temperature and emissivity. In the next section a general purpose least square method for parameter optimization for a non linear function is developed, and this method is applied to estimate temperature and emissivity by performing least square fit to the radiation intensities to the Planck’s function.
5.1. Theory of Least Square Method for Parameter Estimation
The fundamental concept of parameter estimation involves the determination of optimal values of parameters (temperature and emissivity in our case) for a numerical model (Planck’s radiation law in our case) that predicts dependent variable outputs
(I(i)) of a function, based on observations of independent variable (i) inputs. The least squares criterion [11] (Gauss-Newton method) minimizes the sum of squares of
residuals between measured outputs (I(1) to I(4)) and output values of the numerical 0 0 model (I (1) to I (4)) that are predicted from the values of independent variables and estimated parameters. One of the important part of the technique is that the original non linear function is converted to approximate linear function using Taylor series expansion. Least-square theory is then, used to obtain new estimate of the parameters that move in the direction of minimizing squares of residual.
10
The nonlinear function can be presented as:
yi f xi ;a0 , a1, a2... ei yi f xi ei (2)
Where yi is the measured value of dependent variable; f(xi; a0, a1, a2…) is the function of the independent variable xi and nonlinear function of parameter a0, a1, a2 and ei is the random error.
In the above equation the measured dependent variable is the intensity, independent variable is wavelength, and function is having a form of Planck’s law with two parameters (temperature and emissivity) with nonlinear dependence as shown in equation 1. The Taylor series expansion of Planck’s radiation law (a non linear function) curtailed after first derivative can be written as: I 0 ( ) I 0 ( ) I 0 ( ) I 0 ( ) i j i j T (3) i j 1 i j T
Where j is present intensity, j+1 is next prediction, is (j+1 - j) and T is (Tj+1 - Tj )
Equation 3 is the linearised model of the Planck’s radiation law with respect to two parameter i.e. temperature and emissivity. The equation 3 can be combined with equation 2 to give functional form where least square method can be applied as given as follows: I( ) I( ) I( ) I 0 ( ) i j i j T (4) i i j T 0 Where I(i) is the measured value of the radiance for different wavelength and I (i) is the calculated output values using Plancks’s radiation law at different wavelength;
The above equation in matrix form can be written as:
D Z j A (5) Where:
11
I( ) I( ) 1 1 I( ) I 0 ( ) T 1 1 I( ) I( ) 0 2 2 I(2 ) I (2 ) T . . . Z j D and A . T . . . . . I( ) I( ) 0 i i I(i ) I (i ) T
Applying least square theory to the equation 5 gives the solution as:
T T Z j Z j A Z j D (6)
The above equation can be solved for the {A}, which can be employed to compute the refined estimate for the parameter as:
Tj+1 = Tj + T and j+1 = j + (7)
The above procedure is repeated until convergence is achieved. The criteria for convergence chosen for the parameter estimation is minimization of sum of square of residuals between measured outputs (I(1) to I(4)) and output values of the numerical 0 0 model (I (1) to I (4)) that are predicted from input observations, i.e. the minimization of {D2}. This convergence criteria is also called minimization of chi- square (2). The value of 2 is given as:
2 2 0 2 0 2 0 2 D I(1 ) I (1 ) I(2 ) I (2 ) . . . I(i ) I (i ) (8)
The process of parameter estimation is an iterative process. During the process, the parameter to be estimated (temperature and emissivity) are adjusted such that the 2 2 2 value of j+1, is less than the value of j. When the value of is less than the tolerance criteria value, the process of iteration completes and the parameter values corresponding to the iteration is the final result of the least square process.
12
5.2. Code Development
For estimation of the fitted parameters using the general least square method described above, we have developed a computer code in ‘C’ language. The input screen of the code is shown in the figure 6.
As shown in figure 6, the code accepts various inputs for forming matrices [Zj],
{Dj}and {A}. These inputs are number of measurement points, there values and number of parameters to be estimated. The order of [Zj] matrix in mn, where m is the number of channel in the system while, n is the number of parameters to be estimated. For our present case the order of [Zj] matrix is 42. Similarly the order of
{Dj} is m1, where m indicates the same value as in case of [Zj] and the order of {A} is 21 for two parameter estimation.
One of the input to the code is the initial estimates for the two parameters i.e. temperature and emissivity. These inputs are used to calculate first iteration and from there on the program itself find out the next iteration value. To find out the next iteration value equation 6 need to be solved for {A} using initial estimation of parameters. The newly computed values of {A} are combined with the initial estimate of the parameters using equation 7 to find out the estimate for the next 2 iteration. To validate the new estimate values, the j+1 value using new estimate is 2 2 compared with the j values using initial estimate. If the j+1 value is less than the 2 j , the newly computed parameter estimate is accepted as the initial estimate for the next iteration cycle other wise the initial estimate of the parameters are modified in 2 2 such a way the value of j+1 become less than the j value. This iteration process is 2 2 repeated until the values of j+1 and j become close to each other within the acceptable limit. The logical flow chart of the process of iteration is shown in figure 7.
Another input to the program indicates that the mode of data input could be either from the ASCII file or from the keyboard. Generally for the single point data the 13
measured radiances are entered through keyboard and output is recorded in the output file. While in case of calculation of the temperature profile the data is formatted in the input file and is provided as the input to the code.
The formatted input file is the one which contains the stored data from oscilloscope after preprocessing if required. The preprocessing of data may include filtering of high frequency (>signal frequency) noise components and averaging for data reduction. The data for the input file is obtained from the oscilloscope where they are recoded as the equivalent electrical output of the radiance (I(i)) values for each channel.
Figure 6: Input Screen Capture of the developed code
14
Start B
Read Input A Calculate Dj+1 Matrix Apply Calibration Calculate 2 j+1 Calculate Zj Matrix
No Calculate Provide Modify estimate If 2 2 Dj Matrix Estimation for j & for j & Tj j+1 < j
Calculate 2 Yes j
Accept & T No If Solve Equation 6 Start new iteration 2 2 j+1 ‐ j == Determine and with j+1 & Tj+1 0
Calculate new value Yes of j+1 & Tj+1
Convergence B A Achieved. Read new input
Figure 7: Logical Flow chart of the developed code.
5.3. Uncertainty Calculation
The uncertainty in the estimation of temperature and emissivity due to system parameters such as error in voltage measurement, bandwidth of filters, variation in temperature of the calibration source etc., have been estimated using procedure given below. 15
I(i ) I(i ) I Tm and I m (9) Tm m
Rearranging above equations we get:
1 1 I( ) I( ) i i Tm I and m I (10) Tm m
Where Tm is the uncertainty in the temperature estimation; m is the uncertainty in the emissivity estimation; Tm and m is the estimated temperature and emissivity; I is the uncertainty in the measured intensity; I(i)/Tm is the derivative of radiation law at estimated temperature; and I(i)/m is the derivative of radiation law at estimated emissivity;
Analytically the measured intensity is given as:
V 1 (11) m 5 C2 / iTcs I *C 1 i e 1 Vcal
Where Vm is the measured voltage during actual temperature measurement; Vcal is the voltage measured at the time of calibration; and Tcs is the temperature of the calibration source;
Using the relation given in equation 10 the uncertainty in the measured intensity at each channel due to system parameters such as error in voltage measurement, bandwidth of filters, variation in calibration source temperature etc. can be estimated as follows:
I(i ) I(i ) I(i ) I(i ) I Tcs Vcal Vm i (12) Tcs Vcal Vm i
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The value of I is calculated for each channel at the calibration source temperature using the measured voltage Vm at the respective channel in the actual experiment. The final uncertainty in the estimated temperature and emissivity is calculated using equation 10, where the partial derivative of Planck’s law is computed at the estimated temperature and emissivity.
6. Experiments
The performance of the radiation pyrometer has been validated by measuring the temperature of the standard radiation source, Tungsten Halogen Light Source (THLS). The measurement of steady state temperature using THLS is important for verifying the measurement procedure and the estimation of the possible uncertainties in the measurement. After validation of the instrument, it has been used by us to carry out time resolved temperature measurement of the electrically exploding wires.
6.1. Validation of Pyrometer by Measuring Temperature of Standard Radiation Source
The pyrometer and computer code developed by us is tested by measuring the temperature of the standard radiation source, Tungsten Halogen Light Source (THLS) whose temperature is well characterized independently. The radiation from the source is collected by the light collection system of the pyrometer and divided into four channel using beam splitters inside the pyrometer. Each channel corresponds to single wavelength (532, 600, 700 and 750 nm), converts the radiation intensity into the equivalent electrical signal using photo-receiver. Output of these receivers is recorded on the digital storage oscilloscope. The recorded data is analyzed using the computer code developed in the present study.
The temperature of THLS estimated from measured radiation using developed code turns out to be 3009 K as compared to the specified value of 2850 K i.e. the agreement between the temperatures measured using our pyrometer system and that 17
specified by the manufacturer is within ~ 5.5%. Table 2 shows the uncertainty in the measurement using equation 10 for each channel. As shown in the Table 2 that the calculated uncertainty in the measured temperature of the light source is ~ 3.1% while that of emissivity is ~ 24%. Due to the week dependence of spectral radiance on emissivity in Planck’s law, the emissivity is poorly constrained by spectral radiance data. However strong dependence of spectral radiance on temperature leads to relatively small uncertainties in temperature measurement [2]. The quality of the least square fit is shown in the Figure 8. The plot shows four measured spectral radiance form the THLS. It represents the best fitting grey body function with T = 3009 K.
Parameter 532 nm 600 nm 700 nm 750 nm Remark
Average 3.1 % of the Tm (K) 93.39 102.58 94.98 88.98 Tm is 94.98 measured value
Average 23.8% of the m 0.278 0.271 0.2156 0.189 m is 0.238 measured value
Table 2: Calculated Error or uncertainty in the measurement
12
/sr) 2 10
W/m 8 11
6
4 Measured Data Points Planck's Curve @ T = 3009 K 2
0 Spectral Radiance (10 500 550 600 650 700 750 800 850 Wavelength (nm) Figure 8: Plot of spectral radiance measured with the best fitting grey body cure corresponding to T=3009K 18
6.2. Time Resolved Temperature Measurement of Electrically Exploding Wire
Figure 9 displays the experimental layout of capacitor bank used for exploding conductors [12]. The capacitor bank used for the experiments for determining temperature profile of the exploding wire has a capacitance of 8F and having a capacity of delivering peak current of ~ 70 kA within 750 ns to the load. In this experiment large current (4.6 kA) generated by this capacitor bank (8 µF capacitor charged up-to 3.8 kV) is fed in to a thin metallic conductor (copper/aluminum wire) through transmission line. The total circuit inductance, which involves the inductance of capacitor bank, triggered spark gap switch, and transmission line is maintained as low as possible. A pick-up loop is also used for the measurement of the current (I) and its time derivative (dI/dt).
Light Collection for Pyrometer
Exploding Transmission Conductor Line
LR
Triggered 8 F Capacitor Rail Gap Switch
Figure 9: Scematic of experimental setup
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On discharge of capacitor through the wire, due to ohmic heating the wire heats up, its resistance goes up, on further heating the wire turns to molten state and then to vaporization state. Throughout this heating process the resistance of the wire keeps on increasing. The process occurs so fast that inertia prevents it from expanding. Finally the large current through the dense vaporized material further heats it and this material expands explosively at time called the ‘burst time’. At this time the current derivative profile shows a sharp dip and the wire material is expected to reach its maximum temperature at this time. Once the vaporized material starts expanding, its temperature is expected to fall. As an electrical arc is established through the metallic vapor, the resistance drops and the current increases further heating the material. This phenomenon is called ‘Re-striking’. The temperature profile after the burst time will depend on the competition between the resistive heating of the wire material and it’s cooling due to expansion.
This experimental setup has been used to study the temperature profile of the electrically exploding wire. Two experiments were performed using copper wire of length 10 mm and diameter 77m. The intensity record using pyrometer setup at four wavelengths (532, 600, 700 and 750 nm) during exploding wire experiment were recorded on oscilloscope. These records were analyzed offline using developed code. The findings of the experiment were described in next section.
The measurement of transient temperature is important to verify the dynamic range and time response of the pyrometer. Dynamic range is important to quantify the peak temperature that can be measured in the particular configuration while time response is important for identifying how much fast varying temperatures can be measured using the developed pyrometer.
The transient temperature generated in the copper wire of length 10 mm and diameter 77m, due to rapid ohmic heating, achieved by a electric discharge from a capacitor bank of 8 µF charged up-to 3.8 kV is measured using developed radiation
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2 10
8 1.5 6 Current (kA) Current 1 4 Temperature 2 0.5 Temperature (eV) 0
0 -2 0 100 200 300 400 500 Time (ns) Figure 10: The estimated temperature profile of the exploding copper wire along with the measured current.
2 10
8
1.5
Current Current (kA) Temperature 6
1 4
2
Temperatrue (eV) 0.5 0
0 -2 0 100 200 300 400 500 Time (ns) Figure 11: The estimated temperature profile of the exploding copper wire along with the measured current.
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pyrometer. The transient temperature profile of the copper wire is calculated using the measured radiation data at four different wavelengths corresponding to each channel, is shown in the figure 10. Along with the temperature profile, the current signal measured using single turn pick-up loop is also presented in figure 10 [13]. The current waveform reaches to the burst current of ~ 4.5 kA for the wire around 100 ns after start and the time is called burst time. Around burst time the temperature starts increasing and reaches to the peak value of ~1.5 eV in a time interval of 70 ns after burst. The measured temperature profile reaches a stable value of 0.3 eV as current approaches to zero value at about ~150 ns after the burst. This value of peak temperature is comparable with the measured value available from other sources [14].
Another experiment was performed to repeat the measurement of the transient temperature of the same copper wire of length 10 mm and diameter 77m, using electric discharge from a capacitor bank of 8 µF charged up-to 3.6 kV. The obtained result (Figure 11) shows an interesting feature of a very short (50 ns) re-striking of current after the initial burst of the copper wire at ~ 135ns from start of current. As expected temperature start increasing from the time of first burst (~100ns) and reaches a high value of about 1.35 eV at ~ 135 ns. Interestingly the current waveform shows that the current once again start rising at ~135 ns and start depositing more energy to the wire. The temperature profile also shows similar trend as it starts decreasing after the reaching high value of 1.35 eV, once the current starts decreasing after burst of wire, but again temperature starts rising once the current starts rising (after ~ 160 ns), depositing more energy to the wire resulting in the increase in the wire temperature to the peak value of ~1.96 eV.
The reason for this behavior of the wire could be the instability of the vapour phase of the wire. After the first burst the wire may not have been converted fully to the vapour phase and the energy present in the capacitor bank supplied to the combined mixture of vapour and molten metal forces to starts conducting the current again. The interesting pattern of the current and temperature profile is further being
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investigated and more experiments are planned to verify the above postulate and supporting analysis is being carried out.
7. Conclusions & Future Development
Radiation pyrometer has been developed for the measurement of transient temperatures having very fast rise time, which are generated during dynamic compression, or during sudden deposition of thermal or electrical energy into an object. The radiation pyrometer is equipped with photo-receiver having dynamic bandwidth of 125 MHz and it is capable of measuring transient temperature with time resolution of about 3 ns. The instrument is demonstrated to make steady state temperature measurement with an accuracy of ~ 5%. The pyrometer has been used for time resolved measurement of temperature having rise time or the fall time of the order of ~15 ns.
As the present pyrometer records the radiation intensities at four wavelength and the analysis process procedure assumes that the emissivity is constant. However, when the temperature variation in the shocked (or exploding) sample is very large it is important to include in the analysis the variation of emissivity with temperature. This necessitates recording the radiation intensity data at large number of wavelengths. We are upgrading the instrument to record the radiation intensities at six wavelengths. Also, the optical arrangement of the instrument is being miniaturized, so that the pyrometer becomes portable.
8. Acknowledgement
We are highly thankful to Dr. T. C. Kaushik and Shri Alok Saxena for providing support for conducting exploding wire experiment to test the instrument. We are also thankful to Mrs. Archana Kushwaha and Shri A.B. Kalsarpe for assisting in experimental work.
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9. References
[1] G.A. Lyzenga & Thomas J. Ahrens, “Multiwavelength optical pyrometer for shock compression experiments”, Rev. Sci. Instrum. 50(11) Nov. 1979, pp 1421. [2] Mark B. Boslough & Thomas J. Ahrens, “A sensitive time-resolved radiation pyrometer for shock-temperature measurements above 1500K”, Rev. Sci. Instrum. 60(12) Dec. 1989, pp 3711. [3] H.B. Radousky & A.C. Mitchell, “A fast UV/visible pyrometer for shock temperature measurements to 20,000K”, Rev. Sci. Instrum. 60(12) Dec. 1989, pp 3707. [4] Oleg V. Fat’yanov, Toshiyuki Ogura Malcom F. Nicol, Kazutaka G. Nakamura & Ken-ichi Kondo, “Time-resolved two-band infrared radiometry of carbon tetrachloride under shock compression up to 10 GPa”, Applied Physics Letters, 77(7) August 2000, pp 960. [5] David Portouche-Sebban, David B. Holtkamp. R. Richard Bartsch, Huan Lee & Gerald G Schmitt, “Application of high speed, low temperature infrared pyrometer in pulsed power experiments”, Rev. Sci. Instrum. 72(7) July 2001, pp 3008. [6] Satish C. Gupta, Stanley G. Love and Thomas J. Ahrens, “ Shock Tempertarue in
Calcite (CaCO3) at 95 to 160 GPa”, Eart Planet. Sci. Lett. 201 (2002), pp 1-12. [7] D. Partouche-Sebban, D.B. Hotlkamp, J.L. Pelissier, J. Taboury, A. Rouyer, “An investigation of shock induced temperature rise and melting of bismuth using high speed optical pyrometry”, Shock Waves (2002) 11, pp 385-392. [8] D. Partouche-Sebban & J.L. Pelissier, “Emissivity and temperature measurements under shock loading, along the melting curve of bismuth”, Shock Waves (2003) 13, pp 69-81. [9] A. Seifter, M.R. Furlanetto, M. Grover, D.B. Holtkamp, G.S. Macrum, A.W. Obst, J.R. Payton, J.B. Stone, G.D. Stevens, D.C. Swift, L.J. Tabaka, W.D. Turley & L.R. Veeser, “Use of IR pyrometry to measure free-surface temperatures of partially melted tin as a function of shock pressure”, Journal of Applied Physics, 105, 2009, pp 123526.
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[10] Jacob Fraden, Infrared Thermometers; Measurements, Instruments and Sensors Handbook, edited by John G. Webster, CRCnetBase 1999. [11] S.C. Chapra & R.P. Canale “Numerical Methods for Engineers”, Fouth Edition, Tata McGraw-Hill Edition. [12] Amit S. Rav, A. K. Saxena, K. D. Joshi, T. C. Kaushik and Satish C. Gupta, “Radiation Pyrometer for Time Resolved Temperature Measurement in Ultra Fast Phenomenon”, National Symposium & Exhibition on Trends in Explosive Technology (TEXT-2008), Chandigarh, (Nov 2008) [13] Amit S. Rav, A. K. Saxena, K. D. Joshi, T. C. Kaushik and Satish C. Gupta, “Time Resolved Radiation Pyrometer for Transient Temperature Measurement”, DAE Solid State Physics symposium (DAE-SSPS-2010), Manipal University, 26th – 30th Dec. 2010. [14] A. Grinenko, Ya. E. Krasik, S. Eflmov, A. Fedotov, V.Tz. Gurovich and V.I. Oreshkin, “Nanosecond time scale, high power electrical wire explosion in water” Physics of Plasmas, 13, 042701-14, (2006)
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