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To deal with the staircase approximation problem in the standard finite-difference time-domain (FDTD) simulation, the two-dimensional boundary condition equations (BCE) method is proposed in this paper. In the BCE method, the standard FDTD algorithm can be used as usual, and the curved surface is treated by adding the boundary condition equations. Thus, while maintaining the simplicity and computational efficiency of the standard FDTD algorithm, the BCE method can solve the staircase approximation problem. The BCE method is validated by analyzing near field and far field scattering properties of the PEC and dielectric cylinders. The results show that the BCE method can maintain a second-order accuracy by eliminating the staircase approximation errors. Moreover, the results of the BCE method show good accuracy for cylinder scattering cases with different permittivities.

A generalized method to estimate a two-dimensional (2D) distribution of temperature and wavelength-dependent emissivity in a sooty flame with spectroscopic radiation intensities is proposed in this paper. The method adopts a Newton-type iterative method to solve the unknown coefficients in the polynomial relationship between the emissivity and the wavelength, as well as the unknown temperature. Polynomial functions with increasing order are examined, and final results are determined as the result converges. Numerical simulation on a fictitious flame with wavelength-dependent absorption coefficients shows a good performance with relative errors less than 0.5% in the average temperature. What's more, a hyper-spectral imaging device is introduced to measure an ethylene/air laminar diffusion flame with the proposed method. The proper order for the polynomial function is selected to be 2, because every one order increase in the polynomial function will only bring in a temperature variation smaller than 20 K. For the ethylene laminar diffusion flame with 194 ml min−1 C2H4 and 284 L min−1 air studied in this paper, the 2D distribution of average temperature estimated along the line of sight is similar to, but smoother than that of the local temperature given in references, and the 2D distribution of emissivity shows a cumulative effect of the absorption coefficient along the line of sight. It also shows that emissivity of the flame decreases as the wavelength increases. The emissivity under wavelength 400 nm is about 2.5 times as much as that under wavelength 1000 nm for a typical line-of-sight in the flame, with the same trend for the absorption coefficient of soot varied with the wavelength.

In order to improve the reconstruction performance for ill-posed emission tomographic problems with limited projections, a generalized interpolation method is proposed in this paper, in which the virtual lines of projection are fabricated from, but not linearly dependent on, the measured projections. The method is called the virtual projection (VP) method. Also, an iterative correction method for the integral lengths is proposed to reduce the error brought about by the virtual lines of projection. The combination of the two methods is called the iterative virtual projection (IVP) method. Based on a scheme of equilateral triangle plane meshes and a six asymmetrically arranged detection system, numerical simulations and experimental verification are conducted. Simulation results obtained by using a non-negative linear least squares method, without any other constraints or regularization, demonstrate that the VP method can gradually reduce the reconstruction error and converges to the desired one by fabricating additional effective projections. When the mean square deviation of normal error superimposed on the simulated measured projections is smaller than 0.03, i.e., the signal-to-noise ratio (SNR) for the measured projections is higher than 30.4, the IVP method can further reduce the reconstruction error reached by the VP method apparently. In addition, as the regularization matrix in the Tikhonov regularization method is updated by an iterative correction process similar to the IVP method presented in this paper, or the Tikhonov regularization method is used in the IVP method, good improvement is achieved.

The DRESOR (Distribution of Ratios of Energy Scattered by the medium Or Reflected by the boundary surface) method is applied for radiative heat transfer in a one-dimensional medium with a nonlinear gradient index and gray boundary surfaces. In this proposed method, the DRESOR values calculated by the Monte Carlo method express quantitatively the impact of scattering on radiative transfer and the radiative intensity with high directional resolution of high precision can be easily obtained. With given media characteristics and boundary conditions, the temperature and radiative flux distributions inside the medium are calculated under the condition of radiative equilibrium. It is shown, in the cases studied, that the DRESOR method has a good accuracy. The temperature distributions have a node with different kinds of sine changed gradient index distributions under the same boundary emissivity. The impact of the gradient index on the radiative heat transfer is considerable, and the same as that of the ratios of its amplitude and average index. Besides, the effects of optical thickness, boundary emissivity and scattering phase function on radiative transfer also should be paid adequate attention.

In this review paper, the recent achievements in measurements of soot volume fraction and temperatures in a coflow, diffuse Ethylene-air flame by visible image processing are briefly outlined. For the inverse analysis of the radiative properties and temperatures, different methods show different features. The least-squares method, a regularization method and a linear programming method are all suitable for this problem, and a linear programming method can give more reasonable results. The red, green and blue flame images, which can be captured by some colour CCD camera, can be taken approximately as monochromatic images, and can be used to reconstruct temperature and soot volume fraction. But more ideal is the true monochromatic images filtered by filters at certain wavelengths. Finally, the optically-thin assumption, which is adopted widely, will cause large errors, about 100 K for temperature and 50% for soot volume fraction, as the absorption of the flame medium is neglected.

An improved soot diagnostics technique based on tomographic reconstruction of flame emission spectra has been developed for an axisymmetric laminar diffusion flame without optically-thin assumption. Emission from the flame is scanned along the horizontal lateral axis of flame at several altitudes above the burner. At each measurement position, the local line-of-sight flame emission spectra is collected by a spectrometry over a spectral range of 700-1100 nm. Inversion of these data through one-dimensional tomography using a three-point Abel inversion yields radial distributions of the soot radiation from which soot volume fraction profiles are extracted. Traditionally, this procedure was applied only in the optically-thin flames for which the self-attenuation term of emitted radiation is ignored. However, this self-attenuation term is considered by iterative calculations in the paper. The configuration of the investigation flame is similar to the flames reported in the literatures. The results by the conventional method is found to be almost twice to the results by the improved method. This discrepancy revealed that the optically-thin assumption for the flames will cause serious errors in the conventional method, and the improved method could overcome this deficiency effectively.