A Hybrid-Inverse Method for Predicting the Temperature Profile Along a Blackbody Optical Fiber Thermometer
Heat Transfer, Volume 7
This thesis has been read by each member of the following graduate committee and by majority vote has been found to be satisfactory ________________________________ ____________________________________ Date Matthew R. Jones, Chair ________________________________ ____________________________________ Date Alan R. Parkinson ________________________________ ____________________________________ Date Dale R. Tree BRIGHAM YOUNG UNIVERSITY As chair of the candidate's graduate committee, I have read
... thesis of David G. Barker in its final form and have found that (1) its format, citation, and bibliographical style are consistent and acceptable and fulfill university and department style requirements; (2) its illustrative materials including figures, tables, and charts are in place; and (3) the final manuscript is satisfactory to the graduate committee and is ready for submission to the university library. A blackbody optical fiber thermometer consists of an optical fiber whose sensing tip is given a metallic coating. The sensing tip of the fiber forms an isothermal cavity, and the emission from this cavity is approximately equal to the emission from a blackbody. Standard two-color optical fiber thermometry involves measuring the spectral intensity at the end of the fiber at two wavelengths. The temperature at the sensing tip of the fiber can then be inferred using Planck's law and the ratio of the spectral intensities. If, however, the length of the optical fiber is exposed to elevated temperatures, erroneous temperature measurements will occur due to emission by the fiber. This thesis presents a method to account for emission by the fiber and accurately infer the temperature at the tip of the optical fiber. Additionally, an estimate of the temperature profile along the fiber may be obtained. A mathematical relation for radiation transfer down the optical fiber is developed. The radiation exiting the fiber and the temperature profile along the fiber are related to the detector signal by a signal measurement equation. Since the temperature profile cannot be solved for directly using the signal measurement equation, two inverse minimization techniques are developed to find the temperature profile. Simulated temperature profile reconstructions show the techniques produce valid and unique results. Tip temperatures are reconstructed to within 1.0%. Experimental results are also presented. Due to the limitations of the detection system and the optical fiber probe, the uncertainty in the signal measurement equation is high. Also, due to the limitations of the laboratory furnace and the optical detector, the measurement uncertainty is also high. This leads to reconstructions that are not always accurate. Even though the temperature profiles are not completely accurate, the tiptemperatures are reconstructed to within 1%-a significant improvement over the standard two-color technique under the same conditions. Improvements are recommended that will lead to decreased measurement and signal measurement equation uncertainty. This decreased uncertainty will lead to the development of a reliable and accurate temperature measurement device. on the task of solving this problem. Had he not, I would not be graduating for another year, and I would have missed the many opportunities I have had because of this research. I wish to thank him for his guidance through the theory, the math, the writing and the editing. I appreciate his patience while working with a not-so-humble graduate student, and will be always grateful for the many professional lessons he has taught me. I especially appreciate his insights into learning that have forever affected my opinion of education and its purpose. I wish to acknowledge funding for this research from the College of Engineering and Technology at Brigham Young University, and from an undergraduate research grant from the Office of Research and Creative Activities at Brigham Young University. My desire for learning how things work is undoubtedly a product of my heritage. My grandfather, Dee H. Barker, is a chemical engineer. My father, Gary T. Barker, is mechanical engineer. I thank both of them for their example of successful engineering and of hard work. I wish to also thank my mother, Susan E. Barker, for teaching me faith and patience. My wife, Robyn, is my motivation. Her love for me and our interdependence on each other have propelled me through the sometimes rough waters of this research. I wish to thank her for her willingness to listen to my complaints and problems and for trying to understand. Most importantly, I would like to thank her for being so excited for my accomplishments throughout the research-that excitement continually pushed me forward.