Research on Temperature Field Reconstruction Based on RBF Approximation with Polynomial Reproduction Considering the Refraction Effect of Sound Wave Paths

The temperature field distribution directly reflects the combustion condition in a furnace. In this paper, acoustic thermometry to reconstruct temperature distribution is investigated. A method based on radial basis function approximation with polynomial reproduction (RBF-PR) is proposed in order to improve the accuracy and stability of the method based on RBF approximation. In addition, the refraction effect of sound wave paths is considered in the process of reconstruction. The curved lines with refraction effect are numerically calculated by solving differential equations, which show that sonic waves curve towards the zones of higher temperature. The reconstructed performance is validated via numerical simulation using four temperature distribution models. Results and analysis show that the proposed method has much greater accuracy than the method based on RBF approximation, and when considering the effect of refraction, our method can reconstruct more excellent reconstruction performance than others, which do not take into account the refraction effect of sound wave paths.