A Fast Tomographic Reconstruction Method for Flame Temperature Distribution Measurement Based on Direct Solution Algorithm

Biao Zhang,Jian Li,Wei-Jian Peng,Chuan-Long Xu,Zhi-Hao Li

doi:10.3389/fenrg.2021.790581

Abstract

The rapid and accurate measurement of the flame temperature distribution is of great significance to the structural design and health diagnosis of the engine. Aiming at the low reconstruction efficiency of traditional flame temperature distribution reconstruction algorithms, a Direct Solution algorithm for flame temperature distribution reconstruction is proposed in this paper based on the structural characteristics of the reconstruction equations. By setting several numerical cases, the performance of the Direct Solution algorithm and some commonly used traditional algorithms, such as Simultaneous Algebraic Reconstruction Technique (SART), Least Squares QR-factorization (LSQR) algorithm, Non-Negative Least Squares QR-factorization (NNLS) algorithm, is compared in the reconstruction of the flame temperature distribution. The results show that the efficiency of the Direct Solution method is 169.4, 7.4, and 3483.3 times higher than that of the SART, LSQR, and NNLS algorithms under the condition of 40 × 40 grids. In addition, with the increase of the number of grids, the growth rate of the reconstruction time of the Direct Solution algorithm is much lower than that of other algorithms. The overall reconstruction accuracy of the Direct Solution algorithm is better than that of SART and LSQR algorithms. This shows that it has an excellent comprehensive performance and has a great application prospect in the rapid reconstruction of the temperature distribution.

Highlights

Thrust-to-weight ratio is a comprehensive index to measure the performance level and working ability of aero engines
Two numerical cases of flame temperature distribution reconstruction are designed to illustrate the performance of the proposed direct solution algorithm compared with the current main tomographic algorithms, such as Simultaneous Algebraic Reconstruction Technique (SART), LSQR, and Non-Negative Least Squares QR-factorization (NNLS) algorithm
In order to evaluate the performance of the Direct Solution algorithm proposed in this paper, several common traditional reconstruction algorithms of flame temperature distribution are selected for comparison, such as SART (Liu et al, 2017), LSQR (Liu et al, 2010), NNLS (Li et al, 2019) algorithms

Summary

Introduction

Thrust-to-weight ratio is a comprehensive index to measure the performance level and working ability of aero engines. It is necessary to develop a flame temperature distribution reconstruction algorithm that greatly improves the reconstruction efficiency under the premise of ensuring accuracy and is less affected by the increase in the number of grids. It takes the generalized source term finite volume method as the model of the forward problem and the proposed direct solution algorithm as the inverse method for reconstructing the temperature distribution.

Results

Conclusion