Inverse estimation of sectional gas temperature in a duct having multiple temperature peaks

Abstract

In monitoring the status within a combustor duct, the sectional temperature information on the gas medium is essential. The sectional temperature distribution in a ducted combustor can be inversely estimated by the acoustic pyrometry using the measured time delay between a system of sensor-actuator pairs. The acoustic inverse problem involved in such measurement can be formulated by employing the inverse Radon transform. The radial basis function with finite number of interpolation points can approximate the sound speed variation during traveling between two points in the duct wall. The entire temperature field distribution can be obtained by using the spatial interpolation. As a test example, a gas temperature field with two peak temperatures or hot spots is adopted for the reconstruction target. The interpolation points are chosen by using the genetic algorithm to minimize the singularity of transfer function. Once the temperature field is initially calculated, the obtained retarded time data is used to increase the number of retarded time vectors. The divergence of inverse solution due to the measurement noise is prevented by adopting the Tikhonov regularization in a modified form. The results show the successful detection of position and magnitude of peak temperatures with reasonable accuracy.