Regularization methods were combined with line-of-sight tunable diode laser absorption spectroscopy(TDLAS)to measure nonuniform temperature distribution.Relying on measurements of 12 absorption transitions of water vapor from 1300 nm to 1350 nm,the temperature probability distribution of nonuniform temperature distribution,for which a parabolic temperature profile is selected as an example in this paper,was retrieved by making the use of regularization methods.To examine the effectiveness of regularization methods,truncated singular value decomposition(TSVD),Tikhonov regularization and a revised Tikhonov regularization method were implemented to retrieve the temperature probability distribution.The results derived by using the three regularization methods were compared with that by using constrained linear least-square fitting.The results show that regularization methods not only generate closer temperature probability distributions to the original,but also are less sensitive to measurement noise.Particularly,the revised Tikhonov regularization method generate solutions in better agreement with the original ones than those obtained by using TSVD and Tikhonov regularization methods.The results obtained in this work can enrich the temperature distribution information,which is expected to play a more important role in combustion diagnosis.
The influence of particle size on the effective permittivity of a particle-gas mixture in the presence of particle clusters was studied using numerical analysis involving the three-dimensional finite element method.The effective permittivity of the mixture was obtained by calculating the electrostatic energy generated in the computation domain.Numerical results show that for fixed volume fraction of particles in the mixture,the effective permittivity of the mixture increases with decreasing particle size.Static experiments were carried out by using a differential capacitance sensor with parallel plates.The variation of the effective permittivity with particle size is shown by experimental data to agree with the numerical results.The methodology described and the results obtained in this paper may be used to help modify the measurement of particles volume fraction in the presence of particle clusters when a capacitance sensor is used.
