An Analytical Model for the Time Constants of Optical Fiber Temperature Sensing

An optical fiber temperature sensor can be a useful in-pile temperature sensor for TREAT (Transient REAtor Test facility) due to its simplicity, size, and ability to measure temperatures along its length. However, the optical fiber would need to be encased in a protected capillary tube to survive the reactor environment for an extended period of time and to install the fiber in the reactor. Surrounding the fiber with a capillary tube reduces the heat transfer rate and, therefore, the temperature response of the fiber. The goal of this paper is to determine the time constants, and therefore to predict the response time, of the fiber for a fiber and capillary tube system of known dimensions and properties as well as to determine methods to improve the response of the sensors. For our analysis, a stainless steel capillary tube was chosen, and argon was selected to fill the gap between the capillary tube and the fiber. A mathematical model in the radial dimension was created using an electrical-thermal analogy with known thermal resistances and capacitances of the system. This model was used to analyze the temperature response of the fiber when: a step change in temperature was applied to the outer surface of the fiber; a step change in temperature was applied to the outer surface of the capillary tube in a capillary tube-gap-fiber system; and the capillary tube-gap-fiber system is instantaneously plunged into a conducting medium. At each stage, the analytical results were compared with the predictions of an ANSYS finite-element model under the same conditions.