Efficient inverse radiation analysis in a cylindrical geometry using a combined method of hybrid genetic algorithm and finite-difference Newton method

An inverse radiation problem was considered to estimate boundary conditions such as temperature distribution and emissivity in axisymmetric absorbing, emitting, and scattering medium, given the measured incident radiative heat fluxes. The finite-volume method was employed to solve a direct radiative transfer equation for a two-dimensional axisymmetric geometry. Various parameter estimators, such as conjugate-gradient method, hybrid genetic algorithm, and finite-difference Newton method, were employed to solve the inverse problems, while discussing their performances in terms of estimation accuracy and computational efficiency. Based on this, we proposed, as a best inverse analysis tool, a new combined method that adopted the hybrid genetic algorithm as an initial value selector and used the finite-difference Newton method as a parameter estimator.     

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.     

Apparent directional spectral emissivity determination of semitransparent materials

An inverse estimation method and corresponding measurement system are developed to measure the apparent spectral directional emissivities of semitransparent materials. The normal spectral emissivity and transmissivity serve as input for the inverse analysis. Consequently, the refractive index and absorption coefficient of the semitransparent material could be retrieved by using the pseudo source adding method as the forward method and the stochastic particle swarm optimization algorithm as the inverse method. Finally, the arbitrary apparent spectral directional emissivity of semitransparent material is estimated by using the pseudo source adding method given the retrieval refractive index and absorption coefficient. The present system has the advantage of a simple experimental structure, high accuracy, and excellent capability to measure the emissivity in an arbitrary direction. Furthermore, the apparent spectral directional emissivity of sapphire at 773 K is measured by using this system in a spectral range of 3 μm–12 μm and a viewing range of 0?–90?. The present method paves the way for a new directional spectral emissivity measurement strategy.     

Simulation on simultaneous estimation of non-uniform temperature and soot volume fraction distributions in axisymmetric sooting flames

For visualizing non-uniform absorbing, emitting, non-scattering, axisymmetric sooting flames, because conventional two-color emission methods are no longer suitable, a three-color emission method for the simultaneous estimation of temperature and soot volume fraction distributions in these flames is studied in this paper. The spectral radiation intensities at wavelengths of red, green, and blue, which may be derived from color flame images, are simulated for the inverse analysis. Then the simultaneous estimation is carried out from the spectral radiation intensities by using a Newton-type iteration algorithm and the least-squares method. In this method, a factor is used to balance the wide variation of spectral radiation intensities due to both the wide ranges of temperature and wavelength of the flame radiation. The results indicate that the three-color method is suited for the reconstruction of flame structures with single or double peaks with small difference between the peak and valley. For a double-peaked flame structure with larger peak and valley difference, reasonable result can be obtained just when the mean square deviations of measurement data are small, for example, not more than 0.01.     

吸收散射性三维矩形介质内辐射源项的反问题

提出了一种由边界出射辐射强度反演吸收散射性三维矩形介质内辐射源项分布的方法。该方法是在辐射传递方程离散坐标近似的基础上,用求目标函数极小值的共轭梯度法进行反演计算。通过对介质辐射特性、光学厚度等参数对反演精度影响的分析,结果表明,即使存在测量误差,本文所提出的方法可较精确地反演辐射源项。     

Multispectral infrared pyrometer for temperature measurement with automatic correction of the influence of emissivity

A new method for contactless temperature measurement has been developed.⁽¹⁾ It is applied advantageously to highly reflecting objects of moderate temperatures (emitting no visible radiation), where conventional methods fail. A set of data is collected by radiance measurement m a number of n narrow spectral bands. These data represent numerical values for a set of analytical equations of the radiation emerging from the object. Solving the set of equations leads to u ⩽ n unknowns, which are the temperature of the object, its emissivity and the temperature of its environment. Balancing calculation enhances the accuracy. Software simulations, including the balancing calculation, the radiation transfer and the hardware of the prospected multispectral radiometer optimized the whole system prior to hardware development. The finally assembled laboratory model, a ten channel filter spectrometer, proved to function as predicted. The temperature of objects about 500 K and an emissivity as low as 0.03 has been determined with less than 1% deviation from thermocouple measurement. Measurement at lower temperatures and/or higher emissivities or higher temperatures and/or lower emissivities is possible with comparable accuracy.     

Estimation of the optical properties of seawater from measurements of exit radiance

An inverse analysis for simultaneous estimation of the radiation phase function, single scattering albedo and optical thickness in natural waters, from the knowledge of the exit radiance measurements, is presented. A forward and an inverse model are utilized in our analysis. The forward model uses an analytical discrete-ordinates method for solving the radiative transfer equation and the inverse model contains an algorithm for least-squares estimation that is iteratively solved for retrieving the desired optical properties. The experimental data are simulated with synthetic data corrupted with noise. The results show that the optical properties, with the exception of the optical thickness, can be recovered with high accuracy, even for data with up to 10% noise.     

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.     

An inverse analysis of a transient 2-D conduction-radiation problem using the lattice Boltzmann method and the finite volume method coupled with the genetic algorithm

This article deals with the simultaneous estimation of parameters in a 2-D transient conduction-radiation heat transfer problem. The homogeneous medium is assumed to be absorbing, emitting and scattering. The boundaries of the enclosure are diffuse gray. Three parameters, viz. the scattering albedo, the conduction-radiation parameter and the boundary emissivity, are simultaneously estimated by the inverse method involving the lattice Boltzmann method (LBM) and the finite volume method (FVM) in conjunction with the genetic algorithm (GA). In the direct method, the FVM is used for computing the radiative information while the LBM is used to solve the energy equation. The temperature field obtained in the direct method is used in the inverse method for simultaneous estimation of unknown parameters using the LBM-FVM and the GA. The LBM-FVM-GA combination has been found to accurately predict the unknown parameters.     

Circular radiation heat shields with temperature dependent emissivities: transient and steady-state analyses

Radiation heat loss is an important type of heat loss in thermal systems. In this work, a numerical study of the transient response of two circular radiation heat shields inserted between two parallel and circular surfaces of emissivities ε₁ and ε₂ is presented. The same dimensions have been assumed for the two main radiating surfaces and the two radiation shields. The radiation shields are assumed to have different emissivities on their top (ε₃ and ε₅) and bottom ( ε₄ and ε₆) surfaces, and both are assumed to be different but linear functions of temperature. A specific configuration is investigated in detail to highlight the transient temperature and heat transfer characteristics of the system. Some new results for the transient temperature and heat transfer characteristics of the system such as the effect of shield location, shield emissivities, the temperature dependence of shield emissivities, system dimensions, temperatures of the hot and cold surfaces and emissivities of the hot and cold surfaces are presented for future references. It has been observed that increasing the temperature of the first radiation shield by changing a parameter such as surface emissivity or distance between the radiation shield or the temperature of the hot surface, will not necessarily decrease the temperature of the second radiation shield.     

Radiation transport for MHD pollution control

A method for calculation of radiation cooling of MHD exhaust gases in a steam generator is given. A two-group radiation transport equation is derived which takes account of both an optically-thick diffusing component with an effective mean-free-path and an optically-thin component. The diffusing components cools the region near the wall making a radiation boundary layer. Real gas emissivities are used, based on known band profiles and strengths for the expected gas composition. Gas-dynamic effects are included and compressible and incompressible flows treated. Comparison is made with a simple, optically-thin calculation using radiation data of Hottel which gives results consistent with the average determined by the diffusion model. The radiation emission determines the gas cooling rate in the steam generator and, hence, the nitric oxide emission rate with stack gases. Results of a detailed gas-kinetic calculation based on two stage combustion show that for reasonable furnace size the NO emission rate is reduced below the corresponding EPA standard for coal combustion.     

Increase in radiation intensity in a quasi-spherical “double liner”/“dynamic hohlraum” system

A concept of the magnetic implosion of quasi-spherical liners, concentration of their kinetic energies, conversion of energy into thermal radiation, confinement of its energy in the cavity of an emitting plasma shell in the “double liner”/“dynamic hohlraum” system, and the irradiation of a spherical target is proposed for the physics of high energy densities and inertial confinement fusion. The radiation intensity on the target was shown to increase considerably due to capture of radiation in the process of converting the kinetic energy of the liner into radiation. The dynamics of the liners and the generation of radiation are simulated by the ZETA code using a physical model developed for a nonequilibrium plasma in a cylindrical geometry. The effect of the instability and inhomogeneity of the liners on confinement of radiation energy is estimated.     

Application of hemisphere radiation shields with temperature-dependent emissivity for reducing heat transfer between two concentric hemispheres

The radiation network method has been applied to calculate the net radiation heat transfer between two concentric hemispheres separated by two hemispherical radiation shields with temperature-dependent surface emissivities. Three different materials are chosen for radiation shields: aluminum oxide, silicon carbide, and tungsten. The reduction in heat transfer with shields depends not only on the surface characteristics of the two shields, but also on the locations of the shields. Three illustrative examples are presented to illustrate the effects of temperature dependent emissivities and shield locations on the percentage heat transfer reduction. The analysis can be used to study other cases as warranted.     

The influence of furnace wall emissivity on steel charge heating

Radiation heat transfer is one of the most important heat transfer modes in high-temperature applications. It is a strongly non-linear process, which depends on the temperature and emissivity of heat exchange surfaces, their geometrical configuration and properties of the surrounding atmosphere. Heat exchange intensity between the surfaces depends mainly on their temperature differences. However, their emissivities influence significantly the radiation heat transfer process as well. Emissivity is a function of surface state or atmospheric chemical reactions, temperature and wavelengths. Because of these non-linearities, it is very complicated to evaluate such a real problem by numerical simulation, and experimental work seems to be the most reliable evaluation procedure. We applied special high-temperature coatings of different emissivities on furnace walls to evaluate the dependence between the furnace wall emissivity and steel charge heating. The emissivity analyses of the coatings used and emissivity measurement results in dependence on wavelength are presented in this paper. The dependence of the charge heating on the furnace wall emissivity, the importance of emissivity wavelength dependence and significant differences of the emissivity effect in electrical and gas heated furnaces are shown. The possible consequences and practical benefits are also discussed in this paper.     

Reflection error correction of gas turbine blade temperature

Accurate measurement of gas turbine blades’ temperature is one of the greatest challenges encountered in gas turbine temperature measurements. Within an enclosed gas turbine environment with surfaces of varying temperature and low emissivities, a new challenge is introduced into the use of radiation thermometers due to the problem of reflection error. A method for correcting this error has been proposed and demonstrated in this work through computer simulation and experiment. The method assumed that emissivities of all surfaces exchanging thermal radiation are known. Simulations were carried out considering targets with low and high emissivities of 0.3 and 0.8 respectively while experimental measurements were carried out on blades with emissivity of 0.76. Simulated results showed possibility of achieving error less than 1% while experimental result corrected the error to 1.1%. It was thus concluded that the method is appropriate for correcting reflection error commonly encountered in temperature measurement of gas turbine blades.     

An inverse radiative transfer problem of simultaneously estimating profiles of temperature and radiative parameters from boundary intensity and temperature measurements

A parallel-plane space filled with absorbing, emitting, isotropically scattering, gray medium is studied in this paper. The boundary intensity and boundary temperature profiles are calculated for the inverse analysis. For the simultaneous estimation of temperature, absorption and scattering coefficient profiles in the medium, the sum of residuals of boundary intensity and temperature after being weighted by a balance factor is minimized through using a Newton-type iteration algorithm and the least-squares method. To avoid over-updating for the parameters, the relative updating magnitude during the iteration process is constrained not to be >0.5. It is shown that the boundary intensity measurement alone is not enough to estimate simultaneously the temperature (source) and the radiative properties (both absorption and scattering coefficients) when the measurement data contain sensitive random errors. The boundary temperature measurement can serve as a necessary supplementation to the boundary intensity to make this kind of inverse radiative transfer problem resolvable. It was shown that a compensation relationship between absorption and scattering coefficients makes it difficult to fix them accurately. Parabolic profiles for the three parameters are used to validate the estimation method. When the optical thickness approaches 4.0, the results for the radiative properties are not acceptable, although the result for temperature profile is reasonable. This means the method needs further improvements.     

Étude tridimensionnelle du transfert radiatif dans un milieu semi-transparent diffusant anisotrope par la méthode des transferts discrets modifiée

The development of the modified discrete transfer method (MDT) in a three-dimensional rectangular configuration allowed us to simulate the thermal behaviour of a semi-transparent, grey, absorbing emitting and anisotropically scattering medium at the radiative equilibrium. An internal source distributes heat uniformly in the medium while the walls of the enclosure that surround it, opaque, grey, diffuse for emission and reflection, are submitted to prescribed temperatures. A linear variation law of the temperature, as well as the scattered radiation intensity, within a grid cell associated with the direction set of the discrete ordinates method has been adopted. A grid close enough to each inner wall was necessary for a better estimation of the incident flux near the singularities of the considered system. These global improvements led to a new version of the stable MDT method, as accurate as the zonal method and as flexible as the discrete ordinates one.     

Emissivity estimates

A variational expression is developed to estimate the overall and angular emissivities for a halfspace geometry described by the equation of transfer. In contrast to the usual variational procedure of postulating a functional and then proving correctness, the appropriate functional is derived using a Lagrange multiplier technique. With asymptotic trial functions, simple expressions for the emissivities result. This variational estimate of the overall emissivity is exceeding accurate when compared to exact results for an isotropic phase function. The angular emissivity, a more detailed quantity, is estimated with less accuracy. The formalism is not restricted to an isotropic phase function, but is valid for general anisotropic scattering. As an example of an anisotropic phase function, the case of Thomson scattering is considered. The emissivity for this phase function is found to be slightly larger than that for isotropic scattering.     

Radiative heat transfer in a plane-layer mixture of non-gray particulates and molecular gases

The interaction between particulate clouds and molecular gases with respect to radiative heat transfer in a one-dimensional, plane-parallel geometry is investigated. The particulates are assumed to have a non-gray absorption coefficient with a power-law dependence on wavenumber. The absorption coefficient of the molecular gases is described by the popular exponential wide-band model. Heat transfer rates are determined through the evaluation of internal and external slab emissivities of the particulate cloud and through evaluation of slab band absorptances for the molecular gases, modified to account for the interaction with the particles. Simple, closed-form expressions for the slab emissivities and slab absorptances are also introduced, resulting in good accuracy.     

Error Estimation at the Information Reconciliation Stage of Quantum Key Distribution

Quantum key distribution (QKD) offers a practical solution for secure communication between two distinct parties via a quantum channel and an authentic public channel. In this work, we consider different approaches to the quantum bit error rate (QBER) estimation at the information reconciliation stage of the post-processing procedure. For reconciliation schemes employing low-density parity-check (LDPC) codes, we develop a novel syndrome-based QBER estimation algorithm. The algorithm suggested is suitable for irregular LDPC codes and takes into account punctured and shortened bits. Testing our approach in a real QKD setup, we show that an approach combining the proposed algorithm with conventional QBER estimation techniques allows one to improve the accuracy of the QBER estimation.