Inverse radiation problem of temperature distribution in one-dimensional isotropically scattering participating slab with variable refractive index

In this paper, an inverse analysis is performed for estimation of source term distribution from the measured exit radiation intensities at the boundary surfaces in a one-dimensional absorbing, emitting and isotropically scattering medium between two parallel plates with variable refractive index. The variation of refractive index is assumed to be linear. The radiative transfer equation is solved by the constant quadrature discrete ordinate method. The inverse problem is formulated as an optimization problem for minimizing an objective function which is expressed as the sum of square deviations between measured and estimated exit radiation intensities at boundary surfaces. The conjugate gradient method is used to solve the inverse problem through an iterative procedure. The effects of various variables on source estimation are investigated such as type of source function, errors in the measured data and system parameters, gradient of refractive index across the medium, optical thickness, single scattering albedo and boundary emissivities. The results show that in the case of noisy input data, variation of system parameters may affect the inverse solution, especially at high error values in the measured data. The error in measured data plays more important role than the error in radiative system parameters except the refractive index distribution; however the accuracy of source estimation is very sensitive toward error in refractive index distribution. Therefore, refractive index distribution and measured exit intensities should be measured accurately with a limited error bound, in order to have an accurate estimation of source term in a graded index medium.     

Inverse problem of ship propeller cavitationnoise radiation

I.IntroductionInthecourseofnavigation,shipsinevitablyproducevariouskindsofnoiseradiation,whichbringusimportantinformation.Ononehand,manyresearchersdevotethemselvestothestudyofthetime-frequency-amplitudedomaincharacteristicsoftheshipnoiseradiationfield,whichistheregularmethodforstudyingthenoiseradiation,i.e.,thedirectproblem.ontheotherhand,theyareworkinghardatmakinguseofthelloiseradiationtoinferthestateofshipnavigationandtheconditionofthemainaPparatusonboard,etc.,andthisistheinverseproblemofthe…     

半透明平板边界入射辐射热流密度的反问题

对一维半透明平板内辐射、导热及边界对流耦合换热过程进行了研究。提出了一种由一侧边界出射辐射强度反演另一侧边界入射辐射热流密度的方法。通过对各向异性散射、吸收系数、散射系数、边界外侧来流温度、对流换热系数、半透明平板的导热系数和平板厚度等参数对反演精度影响的分析表明,方法是可行的。     

Analysis of the characteristics of time-resolved signals for transient radiative transfer in scattering participating media

Transient radiative transfer (TRT) in one-dimensional (1-D) homogeneous and inhomogeneous media with ultra-short pulse laser irradiated is investigated by means of the finite volume method (FVM) in the present research. Comparing with the steady radiative transfer (SRT), the extra time-resolved information can be obtained in TRT. Meanwhile, the propagation speed of short-pulse laser and the geometric thickness of the media should be considered in the simulation of TRT problem besides the optical thickness. A new nondimensional number ζ=ct_p/L is presented. For the homogeneous media, the temporal signals would overlap one another with different combinations of the pulse duration and the thickness of the media with the same ζ. Furthermore, in two-layer media, the influence of the scattering albedo, optical thickness and the geometric thickness of the participating media on ‘dual-peak’ are studied thoroughly. The improved expression of the ‘local minimum’ in the ‘dual-peak’ and the interface location of the multi-layer media are provided.     

Inverse radiation problem of axisymmetric turbulent sooting free flame

An iteration method is extended to reconstruct the time-averaged temperature distribution in turbulent axisymmetric sooting free flame by the multi-wavelength measured data of low time-resolution outgoing emission and transmission radiation intensities. A Gaussian probability density function is used to simulate the turbulent fluctuation of temperature. The reconstruction of time-averaged temperature profile consists of three steps. First, the time-averaged spectral absorption coefficient is retrieved from the time-averaged transmissivity data by iteration method. Then the time-averaged blackbody spectral radiation intensity is estimated from the low time-resolution outgoing spectral emission radiation intensities. Finally, the time-averaged temperature and its standard deviation are approximately reconstructed from the multi-wavelength time-averaged spectral emission radiation data by the least-square method. Both exact and noisy input data have been used to test the performance of the proposed inversion method. The results show that the time-averaged temperature profiles can be estimated with good accuracy by the presented inversion method, even with noisy input data, and the standard deviation of temperature is more sensitive to the measurement errors. In the case of large temperature fluctuation, the errors of estimation for time-averaged temperature profile are large if the turbulent fluctuation is not taken into account.     

Maximum time-resolved hemispherical reflectance of absorbing and isotropically scattering media

This paper presents a parametric study of the time-resolved hemispherical reflectance of a plane-parallel slab of homogeneous, cold, absorbing, and isotropically scattering medium exposed to a collimated Gaussian pulse. The front surface of the slab is transparent while the back surface is assumed to be cold and black. The 1-D time-dependent radiation transfer equation is solved using the modified method of characteristics. The parameters explored include (1) the optical thickness, (2) the single scattering albedo of the medium, and (3) the incident pulse width. The study pays particular attention to the maximum transient hemispherical reflectance and identifies optically thin and thick regimes. It shows that the maximum reflectance is independent of the optical thickness in the optically thick regime. In the optically thin regime, however, the maximum hemispherical reflectance depends on all three parameters explored. The transition between the optically thick and thin regimes occurs when the optical thickness is approximately equal to the dimensionless pulse width. Finally, correlations relating the maximum of the hemispherical reflectance as a function of the optical thickness, the single scattering albedo of the materials, and the incident pulse width have been developed. These correlations could be used to retrieve radiation characteristics or serve as initial guesses for more complex inversion schemes accounting for anisotropic scattering.     

Inverse transient radiation analysis in one-dimensional non-homogeneous participating slabs using particle swarm optimization algorithms

Particle Swarm Optimization (PSO) algorithms, including standard PSO, Stochastic PSO, and Multi-Phase PSO, are applied to solve the time-domain inverse transient radiation problems in the present research. Time-resolved transmittance and reflectance signals of four different measuring models serve as the measurement data, which estimate absorption, scattering coefficients, and geometric position within one-dimensional non-homogeneous media by inverse simulation. To check retrieval performances and accuracies of PSO-based approaches, four different inverse transient radiation cases are investigated to deal with one homogeneous layer, two-layer, three-layer, and continuous non-homogenous media. The influences of different searching ranges, swarm sizes, and maximum fly velocities on the fitness function of PSO are discussed. Meanwhile, the effects of measurement errors on the reconstruction accuracy are also investigated. All the results confirm that radiative parameters could be estimated accurately with measurement noise using PSO-based approaches.     

反传热问题及其在深冷处理传热分析中的应用

深冷处理作为一种新的材料处理工艺,越来越受到人们的关注,目前深冷处理使材料性能提高的机理尤其是与升降温过程的耦合关系等还尚未完全清楚,需开展更深入的研究,而传热分析是此方面研究的基础。反传热分析方法是研究深冷处理传热问题的一种可行方法。较为详细地叙述了反传热问题的定义及其求解方法,介绍了反传热在深冷处理传热分析中的初步应用,并对深冷处理中应用反传热方法存在的问题进行了探讨。     

An Inverse Problem of Determining Coefficients in a One-Dimensional Radiative Transport Equation

We consider an inverse problem of determining unknown coefficients for a one-dimensional analogue of radiative transport equation. We show that some combination of the unknown coefficients can be uniquely determined by giving pulse-like inputs at the boundary and observing the corresponding outputs. Our result can be applied for determination of absorption and scattering properties of an optically turbid medium if the radiative transport equation is appropriate for describing the propagation of light in the medium.     

Determining directional emissivity: Numerical estimation and experimental validation by using infrared thermography

Little research has examined that inaccurate estimations of directional emissivity form a major challenge during both passive and active thermographic measurements. Especially with the increasing use of complex curved shapes and the growing precision of thermal cameras, these errors limit the accuracy of the thermal measurements. In this work we developed a technique to estimate the directional emissivity using updated numerical simulations. The reradiation on concave surfaces is examined by thermal imaging of a homogeneous heated curved metal and nylon test sample. We used finite element modelling to predict the reradiation of concave structures in order to calculate the parameters of an approximating formula for the emissivity dependent on the angle to the normal vector on each element. The differences between experimental and numerical results of the steel test sample are explained using electron microscopy imaging and the validation on different materials. The results suggest that it is possible to determine the errors of thermal imaging testing of complex shapes using a numerical model.     

Finite element analysis of concurrent radiation and conduction in participating media

A method is proposed to calculate temperature, conductive and radiative heat flux distributions in a participating medium. The method is based on the simultaneous solution of two non-linear and mutually conjugated equations describing distribution of both temperature and the so-called radiation function in the medium. In the case of isotropic scattering, the latter quantity, is proportional to the local energy density of radiation. The solution of the coupled non-linear equations is based on the finite element spatial discretization combined with the iterative technique.     

Reconstruction of time-averaged temperature of non-axisymmetric turbulent unconfined sooting flame by inverse radiation analysis

A multi-wavelength inversion method is extended to reconstruct the time-averaged temperature distribution in non-axisymmetric turbulent unconfined sooting flame by the multi-wavelength measured data of low time-resolution outgoing emission and transmission radiation intensities. Gaussian, β and uniform distribution probability density functions (PDF) are used to simulate the turbulent fluctuation of temperature, respectively. The reconstruction of time-averaged temperature consists of three steps. First, the time-averaged spectral absorption coefficient is retrieved from the time-averaged transmissivity data by an algebraic reconstruction technique. Then, the time-averaged blackbody spectral radiation intensity is estimated from the outgoing spectral emission radiation intensities. Finally, the time-averaged temperature is approximately reconstructed from the multi-wavelength time-averaged spectral emission radiation data by the least-squares method. Noisy input data have been used to test the performance of the proposed inversion method. The results show that the time-averaged temperature distribution can be estimated with good accuracy, even with noisy input data. The accuracy of the estimation decreases with the increase of turbulent fluctuation intensity of temperature and the effects of assumed PDF on the reconstruction of temperature are small.     

Modified method of characteristics in transient radiation transfer

This paper presents the modified method of characteristics for simulating multidimensional transient radiative transfer in emitting, absorbing and scattering media. The method is based on the method of characteristics that follows photons along their pathlines. It makes use of a fixed set of points, and unlike the conventional method of characteristics, it follows the photons backward in space. Test problems involving diffuse irradiation in 1-D and 3-D participating media and collimated irradiation in 1-D participating media were considered. The results show good agreement with analytical and numerical solutions reported in literature. The scheme is fast and was able to capture the sharp discontinuities associated with the propagation of a radiation front in transient radiation transport.     

轴对称介质内辐射源项反演算法

结合Abel变换和离散坐标法,提出了一种基于CCD相机采集的单幅辐射图像重建轴对称发射-吸收介质内辐射源项分布的反演算法。通过在求解辐射正问题得到的准确值的基础上,添加随机噪声模拟试验测量数据,分析了网格数目、辐射源项分布形式、吸收系数和测量误差对算法反演精度的影响。测试结果表明:该算法对测量误差不敏感,在有测量误差的情况下也能够准确的重建介质内的辐射源项分布。     

Noninvasive detection of inhomogeneities in turbid media with time-resolved log-slope analysis

Detecting foreign objects embedded in turbid media using noninvasive optical tomography techniques is of great importance in many practical applications, such as in biomedical imaging and diagnosis, safety inspection on aircrafts and submarines, and LIDAR techniques. In this paper we develop a novel optical tomography approach based on slope analysis of time-resolved back-scattered signals collected at the medium boundaries where the light source is an ultrafast, short-pulse laser. As the optical field induced by the laser-pulse propagates, the detected temporal signals are influenced by the optical properties of the medium traversed. The detected temporal signatures therefore contain information that can indicate the presence of an inhomogeneity as well as its size and location relative to the laser source and detection systems. The log-slope analysis of the time-resolved back-scattered intensity is shown to be an effective method for extracting the information contained in the signal. The technique is validated by experimental results and by Monte Carlo simulations.     

On the solution of a vectorial radiative transfer equation in an arbitrary three-dimensional turbid medium with anisotropic scattering

The authors developed a numerical method of the boundary-value problem solution in the vectorial radiative transfer theory applicable to the turbid media with an arbitrary three-dimensional geometry. The method is based on the solution representation as the sum of an anisotropic part that contains all the singularities of the exact solution and a smooth regular part. The regular part of the solution could be found numerically by the finite element method that enables to extend the approach to the arbitrary medium geometry. The anisotropic part of the solution is determined analytically by the special form of the small-angle approximation. The method development is performed by the examples of the boundary-value problems for the plane unidirectional and point isotropic sources in a turbid medium slab.     

Heat transfer by radiation and conduction in fibrous media without axial symmetry

Coupled radiative and conductive heat transfer in a fibrous medium formed by silica fibres is investigated in this paper by not taking account of the axial symmetry for the distribution of fibres or the boundary conditions. Radiative properties of the medium are calculated by using the Mie theory. The model obtained depends only on optical parameters (indices of silica) and on morphological parameters (diameter and orientation of the fibres, density of the medium). Simulations make it possible to study the strongly anisotropic behaviour of the scattering of the radiation by a fibre and to study the influence of various parameters on the radiative properties of the medium. The results of the Mie theory make possible the simulation of the heat transfer coupled by radiation and conduction. To do this, we introduce a new numerical scheme able to simulate heat transfer in the lack of axial symmetry. With this model, we can show the effects of distribution of fibres and temperature on the thermal behaviour of the medium as well as showing the importance of the phenomenon of scattering in fibrous media.     

轻介质传输中辐射热传导近似成立的判别因子

从辐射输运方程出发,通过递推的方法,推导并得到了包含高级修正的辐射能流表达式。利用这个表达式,分析了辐射在轻介质中传输时,辐射热传导近似的成立条件。热传导近似的成立条件总是要求温度空间变化尺度与自由程之比远大于某个值,该值即判别因子,它表征热传导近似条件满足的苛刻程度,其值越大,热传导近似就越难满足。讨论得出：当同时考虑轫致和散射过程时,这一判别因子的值在3~60之间。并进一步分析了密度的空间变化以及1维球坐标下的半径对判别因子的影响。     

Estimation of emissivities in a two-dimensional irregular geometry by inverse radiation analysis using hybrid genetic algorithm

An inverse radiation analysis is presented for estimating the wall emissivities for an absorbing, emitting, scattering media in a two-dimensional irregular geometry with diffusely emitting and reflecting opaque boundaries from the measured temperatures. The finite-volume method was employed to solve the radiative transfer equation for 2D irregular geometry. The hybrid genetic algorithm which contains local optimization algorithm was adopted to estimate wall emissivities by minimizing an objective function, while reducing computation time. It was found that an increase in the standard deviation in measurements significantly deteriorated the estimation of wall emissivities. Thus, a very accurate measurement was required in inverse radiation for better estimation of wall emissivities, especially, in a high temperature environment.     

Simultaneous estimation of the temperature and heat rate distributions within the combustion region by a new inverse radiation analysis

A new inverse radiation analysis is presented for estimating the heat rate and temperature distributions in the combustion region from the information of the temperature and heat flux profiles of wall elements in the system. The Monte Carlo method is employed to solve the radiative heat transfer equation. The inverse radiation problem is posed as a minimization problem of the least squares criterion, which is solved by the conjugate gradient method. The performance of the present technique of inverse analysis is evaluated and the effects of the errors of the absorption coefficient, emissivity and convective heat transfer coefficient on the inverse analysis are investigated. The results show that the present technique is robust and yields accurate estimation even with noisy measurement.