Multi-point temperature measurements in packed beds using phosphor thermometry and ray tracing simulations

Abstract

Packed bed reactors are commonly found in the process industry, for example in flame-assisted calcination for cement production. Understanding the heat transfer inside the bed is essential for process control, product quality and energy efficiency. Here we propose a technique to determine the internal temperature distribution of packed beds based on a combination of lifetime-based phosphor thermometry, ray tracing simulations, and assimilation of temperature data using finite element heat transfer simulations. To establish and validate the technique, we considered a reproducible regular packing of 6 mm diameter aluminum spheres, with one of the spheres in the top layer being electrically heated. If a sphere inside the packing is coated with thermographic phosphors and excitation light is directed towards the packing, luminescence from the coated sphere exits the packed bed after multiple reflection and the sphere's temperature can be determined. Isothermal measurements showed that the temperature obtained by phosphor thermometry is independent of the luminescent sphere location. When imaging the luminescence on a camera, the luminescence distribution in recorded image depended, however, on the position of the sphere. Therefore, in setups with multiple phosphor-coated spheres, their signals can be separated using a least squares fit. We demonstrate the approach using a setup with three luminescent spheres and validated the temperature readings against thermocouple measurements. To obtain the spatial signatures for individual sphere positions required for the least squares fit, ray tracing simulations were used. These provide an efficient alternative to single sphere measurements that are only practical for regular spherical packed beds. Multi-point measurements were used as input to a finite element heat transfer simulations to determine parameters such as particle-to-particle air gap distance. With these, the full temperature distribution inside the bed could be assimilated from the measured values.