Development of A Multi-Spectral Pyrometry Sensor for High-Speed Transient Surface-Temperature Measurements in Combustion-Relevant Harsh Environments
Abstract
:1. Introduction
2. Measurement Principle: Multi-Spectral Radiation Thermometry
- : Emitted radiation intensity (W/m2-μm) at wavelength λ (μm) and temperature T (K)
- : Emissivity at wavelength λ
- c1: 2π h co2 = 3.742 E8 W-μm4/m2
- c2: h co/kB = 14,388 μm-K,
2.1. LLS MRT: Linear Least-Squares Method
2.2. NLLS MRT: Constrained Non-Linear Least-Squares Optimization Method
3. Emissivity Model Selection
3.1. Linear vs. Non-Linear MRT
4. Wavelength Regions Selection
4.1. Wavelength Selection Rules of Thumb
4.2. Wavelength Selection to Avoid Measurement Interference from Combustion Gases
5. Multi-Start Method to Find Global Optimum
6. Instrument Setup and Calibration
6.1. Optical Probe and Instrument Hardware
6.2. Instrument Calibration
6.3. MRT Analysis
7. Bench Validation of the Instrument and the MRT Analysis
8. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Notice
References
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Average SNR | MRT Fitting Method | Average % Error In MRT-Calculated Temperature | |||||||
---|---|---|---|---|---|---|---|---|---|
600 °C | 650 °C | 700 °C | 750 °C | 800 °C | 850 °C | 900 °C | Average | ||
0–50 | LLS | 180 | 46.5 | 75.4 | 48.3 | - | - | - | 87.6 |
NLLS | 66.6 | 14.1 | 6.9 | 75.1 | - | - | - | 40.7 | |
50–150 | LLS | 15.0 | 258 | 24.0 | 14.4 | 9.7 | 34.5 | 1.9 | 51.1 |
NLLS | 0.56 | 11.8 | 25.0 | 10.6 | 2.6 | 5.7 | 4.7 | 8.7 | |
150–250 | LLS | - | - | 4.6 | 7.4 | 3.1 | - | 2.4 | 4.4 |
NLLS | - | - | 0.9 | 9.2 | 4.6 | - | 3.0 | 4.4 | |
250–500 | LLS | - | 6.0 | - | - | 0.1 | 6.4 | 5.4 | 4.5 |
NLLS | - | - | - | - | 4.9 | 5.4 | 5.1 | 5.1 | |
>500 | LLS | - | - | - | 7.5 | - | 3.7 | 3.9 | 5.0 |
NLLS | - | 1.2 | - | 5.8 | - | 5.7 | 5.0 | 4.4 |
Average SNR | n | Average % Error In MRT-Calculated Temperature | |||||||
---|---|---|---|---|---|---|---|---|---|
600 °C | 650 °C | 700 °C | 750 °C | 800 °C | 850 °C | 900 °C | Average | ||
0–50 | 4 | 66.6 | 14.1 | 6.9 | 75.1 | - | - | - | 40.7 |
7 | 10.6 | 14.5 | 21.9 | 72.5 | 31.3 | - | - | 30.2 | |
50–150 | 4 | 0.6 | 11.8 | 25.0 | 10.6 | 2.6 | 5.7 | 4.7 | 8.7 |
7 | 0.8 | 3.8 | 30.7 | 7.9 | 4.8 | 4.4 | 9.6 | 8.9 | |
150–250 | 4 | - | - | - | 9.2 | 4.6 | - | 3.0 | 5.6 |
7 | - | - | - | 4.3 | 4.6 | - | 4.8 | 4.6 | |
250–500 | 4 | - | - | 0.9 | - | 4.9 | 5.4 | 5.1 | 4.1 |
7 | - | 2.2 | 5.0 | 5.8 | 3.8 | 5.7 | 5.4 | 4.6 | |
>500 | 4 | - | 1.2 | - | 5.8 | - | 5.7 | 5.0 | 4.4 |
7 | - | - | - | - | - | 5.8 | 5.0 | 5.4 |
Analysis T (°C): | 610 | 714 | 819 | 911 | Avg. | |
---|---|---|---|---|---|---|
Error % in Calculated T | (Narrow λ region) Selected λ: 1.5, 1.6, 1.7, 1.8 um | 1.37 | 1.29 | 1.19 | 1.12 | 1.24 |
(Broader λ region) Selected λ: 1.0, 1.4, 1.8, 2.0 um | 0.34 | 0.21 | 0.14 | 0.09 | 0.20 |
Guess # | Initial Guess T (C) | Initial Guess T (K) | MRT Calculated T (C) | SSE | Error in MRT Calculated T (%) |
---|---|---|---|---|---|
1 | 500 | 773.2 | 910.5 | 0.039 | −0.09 |
2 | 550 | 823.2 | 910.5 | 0.040 | −0.09 |
3 | 600 | 873.2 | 910.5 | 0.031 | −0.09 |
4 | 650 | 923.2 | 910.5 | 0.036 | −0.09 |
5 | 700 | 973.2 | 910.5 | 0.036 | −0.09 |
6 | 750 | 1023.2 | 979.1 | 1.803 | 7.44 |
7 | 800 | 1073.2 | 979.3 | 1.779 | 7.46 |
8 | 850 | 1123.2 | 979.3 | 1.781 | 7.46 |
9 | 900 | 1173.2 | 979.3 | 1.781 | 7.46 |
10 | 950 | 1223.2 | 979.2 | 1.783 | 7.46 |
11 | 1000 | 1273.2 | 979.4 | 1.776 | 7.47 |
12 | 1050 | 1323.2 | 979.1 | 1.799 | 7.44 |
13 | 1100 | 1373.2 | 979.3 | 1.776 | 7.47 |
14 | 1150 | 1423.2 | 910.8 | 0.001 | −0.06 |
15 | 1200 | 1473.2 | 979.4 | 1.776 | 7.47 |
16 | 1250 | 1523.2 | 910.5 | 0.036 | −0.09 |
17 | 1300 | 1573.2 | 979.4 | 1.776 | 7.47 |
18 | 1350 | 1623.2 | 979.2 | 1.786 | 7.45 |
19 | 1400 | 1673.2 | 979.4 | 1.776 | 7.47 |
True-T (°C) | 400 | 448 | 501 | 553 | 601 | 698 | 802 |
MRT-T (°C) | 394 | 449 | 506 | 565 | 616 | 715 | 819 |
% Error | 1.5 | 0.2 | 1.1 | 2.2 | 1.6 | 2.4 | 2.3 |
Accuracy (%) | 98.5 | 99.8 | 98.9 | 97.8 | 98.4 | 97.6 | 97.7 |
2-Sigma Precision (%) | 99.72 | 99.84 | 99.92 | 99.96 | 99.97 | 99.99 | 99.96 |
SNR(Average) | 63 | 137 | 265 | 488 | 815 | 1858 | 2492 |
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Neupane, S.; Jatana, G.S.; Lutz, T.P.; Partridge, W.P. Development of A Multi-Spectral Pyrometry Sensor for High-Speed Transient Surface-Temperature Measurements in Combustion-Relevant Harsh Environments. Sensors 2023, 23, 105. https://doi.org/10.3390/s23010105
Neupane S, Jatana GS, Lutz TP, Partridge WP. Development of A Multi-Spectral Pyrometry Sensor for High-Speed Transient Surface-Temperature Measurements in Combustion-Relevant Harsh Environments. Sensors. 2023; 23(1):105. https://doi.org/10.3390/s23010105
Chicago/Turabian StyleNeupane, Sneha, Gurneesh Singh Jatana, Timothy P. Lutz, and William P. Partridge. 2023. "Development of A Multi-Spectral Pyrometry Sensor for High-Speed Transient Surface-Temperature Measurements in Combustion-Relevant Harsh Environments" Sensors 23, no. 1: 105. https://doi.org/10.3390/s23010105
APA StyleNeupane, S., Jatana, G. S., Lutz, T. P., & Partridge, W. P. (2023). Development of A Multi-Spectral Pyrometry Sensor for High-Speed Transient Surface-Temperature Measurements in Combustion-Relevant Harsh Environments. Sensors, 23(1), 105. https://doi.org/10.3390/s23010105