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.     

Influence of turbulent fluctuation on reconstruction of temperature profile in axisymmetric free flames

An iteration method is extended to analyze the influences of the turbulent fluctuation on the reconstruction of Reynolds time-averaged temperature in turbulent axisymmetric free flames when the temperature profiles are retrieved by the low time-resolution data of outgoing emission and transmission radiation intensities. A simplified probability density function is used to simulate the turbulent fluctuation of temperature and absorption coefficient. The effects of turbulent fluctuating intensities on the estimation of the Reynolds time-averaged temperature and absorption coefficient are examined. The results show that the effects of turbulent fluctuation on the reconstruction of time-averaged absorption coefficient are not significant. In the case of weak turbulent fluctuation, the influences of turbulent fluctuation on the estimation of time-averaged temperature profiles are small. But in the case of strong turbulent fluctuation, the influences of turbulent fluctuation on the estimation of time-averaged temperature profiles are significant.     

Temperature measurements of high-temperature semi-transparent infrared material using multi-wavelength pyrometry

Temperature measurements inside semi-transparent materials are important in many fields. This study investigates the measurements of interior temperature distributions in a one-dimensional semi-transparent material using multi-wavelength pyrometry based on the Levenberg–Marquardt method (LMM). The investigated material is semi-transparent Zinc Sulfide (ZnS), an infrared-transmitting optical material operating at long wavelengths. The radiation properties of the one-dimensional semi-transparent ZnS plate, including the effective spectral–directional radiation intensity and the proportion of emitted radiation, are numerically discussed at different wavelengths (8.0–14.0 μm) and temperature distributions (400–800 K) to provide the basic data for the temperature inversion problem. Multi-wavelength pyrometry was combined with the Levenberg–Marquardt method to resolve the temperature distribution along the radiative transfer direction based on the line-of-sight spectral radiation intensities at multiple wavelengths in the optimized spectral range of (11.0–14.0 μm) for the semi-transparent ZnS plate. The analyses of the non-linear inverse problem show that with less than 5.0% noise, the inversion temperature results using the Levenberg–Marquardt method are satisfactory for linear or Gaussian temperature distributions in actual applications. The analysis provides valuable guidelines for applications using multi-wavelength pyrometry for temperature measurements of semi-transparent materials.     

Determination of soot temperature, volume fraction and refractive index from flame emission spectrometry

An inversion scheme based on tomographic reconstruction of flame emission spectra has been developed for nonintrusive characterization of soot temperature and volume fraction fields within an optically thin axisymmetric flame by extracting characteristic information on soot refractive index from spectral gradients of emission spectra. Its performance is assessed by providing input data obtained from intensities simulated by a direct code based on experimental data for a flame available in the literature. Proposed method was found to be especially powerful in the near-infrared range for accurate prediction of flame properties where spectral variation of optical constants is significant.     

Monte Carlo ray-tracing simulation for radiative heat transfer in turbulent fluctuating media under the optically thin fluctuation approximation

The Monte Carlo ray-tracing method (MCRT) based on the concept of radiation distribution factor is extended to solve radiative heat transfer problem in turbulent fluctuating media under the optically thin fluctuation approximation. A one-dimensional non-scattering turbulent fluctuating media is considered, in which the mean temperature and absorption coefficient distribution are assumed and the shape of probability density function is given. The distribution of the time-averaged volume radiation heat source is solved by MCRT and direct integration method. It is shown that the results of MCRT based on the concept of radiation distribution factor agree with these of integration solution very well, but results of MCRT based on the concept of radiative transfer coefficient do not agree with these of integration solution. The solution of time-averaged radiative transfer equation by the concept of radiative transfer coefficient should be treated with caution.     

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.     

Inversion of combustion gas temperature/concentration profile with radiation/turbulence interaction using SRS

The spectral remote sensing (SRS) method is applied to the combustion gas with radiation/turbulence interaction to invert the temperature and concentration profiles. The flame is made and controlled to be optically thin per each fluctuation length so that spatially fluctuating gas layer can be treated equivalently as timewisely fluctuating one sharing identical expression in the radiative transfer equation. Then, the spectral intensity, temperature and concentration distributions are measured for the inversion and as the reference solutions. From the inversion results, we find that SRS can successfully invert the coupled temperature/concentration fluctuation amplitudes and mean values. For the two cases of experiment, inverted values are in good agreement with measured ones. However, SRS cannot find the detailed local fluctuation parameter such as pattern or phase, etc. as far as they do not affect the resulting radiative intensity. So, it is deduced that the pattern or phase is not so influential, whereas the mean value and the fluctuation amplitude of temperature/concentration profile are important parameters for the radiative intensity in the case of the optically thin condition. Further, the radiation/turbulence interaction is verified to play an important role in the radiation.     

Anisotropic emission characteristics of semitransparent spherical particle with spherically asymmetric temperature distribution

The Monte Carlo ray-tracing method (MCRT) based on the concept of radiation distribution factor is extended to study the anisotropic emission characteristics of semitransparent spherical particle with spherically asymmetric temperature distribution. The dimensionless apparent spectral radiative intensity of particle emission is calculated by the radiation distribution factor. The effects of the related parameters on the dimensionless apparent spectral radiative intensity are analyzed and discussed. The results show that the anisotropy of particle emission increases with the spherically asymmetry of particle temperature, and the refractive index and the particle optical thickness strongly affect the anisotropic emission characteristics of semitransparent spherical particle with spherically asymmetric temperature distribution.     

Efficient inverse radiation analysis of temperature distribution in participating medium based on backward Monte Carlo method

An efficient numerical inverse radiation analysis based on the backward Monte Carlo (BMC) method is presented to determine the three-dimensional (3-D) temperature distribution in a large rectangular enclosure containing the participating medium, using radiative intensities in the visible range received by charge-coupled device (CCD) cameras. For large radiative sources and small detectors, when the radiation onto a small spot and onto a small direction cone is desired, the BMC method is more efficient than the forward Monte Carlo (FMC) method. Because the temperature reconstruction from the measured radiative intensities is an ill-posed inverse problem, least-square QR decomposition (LSQR) method is introduced to determine the meaningful temperature distribution. In order to gain insight into the effects on the accuracy of temperature distribution reconstruction, the detailed analyses are made using numerical simulations. The results show that the temperature distribution can be reconstructed accurately for the exact and noisy data.     

基于光谱线性拟合的宽波段光源波动补偿方法

宽波段光源在工作过程中,光强通常会随供电电源输出功率的变化而波动。宽波段光源波段内各个波长的光谱强度将会发生不同程度的波动。为解决光源光强波动时其波段内各个波长光谱强度的补偿问题,提出了一种基于光谱线性拟合的补偿方法。使用这种方法,只需测量光源波段光强的变化,就可以补偿各个波长光谱强度的波动。通过分析理想黑体全波段辐射出射度与光谱辐射出射度的近似线性关系。建立了宽波段光源波段光强与光谱强度的线性模型。实验装置主要由卤素灯珠、光源电源、光阑、光谱仪及计算机构成。调节电源的输出功率,得到一组卤素灯珠在不同输入功率下的相对光谱强度。测量不同功率下卤素灯珠光谱强度来验证该方法补偿效果。按线性关系拟合了卤素灯珠光谱强度与其波段光强关系式,并分析了拟合误差。实验表明：卤素灯珠的光谱强度与其波段光强具有很好的线性关系,可以用波段光强按线性关系来补偿其光谱强度的波动。随着卤素灯珠输入功率的增大,补偿后的光谱强度的相对误差绝对值下降。在卤素灯珠输入功率范围内,使用该方法补偿的光谱强度在绝大部分(92%)波长下相对误差绝对值可在5%以内。     

基于氧气A波段发射谱线临近空间大气温度的反演及分析

基于氧气A波段的临边辐射强度模拟数据对临近空间高度（60～110 km）的大气温度反演进行了研究及结果分析。首先, 基于正演模型分别模拟了无噪声和加入噪声情况下的临边辐射强度模拟值,基于这两种模拟数据分别进行了临近空间大气温度反演,并对氧气A波段中的所有谱线的反演结果进行了分析,确定了氧气A波段各谱线权函数变化规律可作为温度观测的判断依据。温度通过影响线强和自吸收两部分来影响辐射强度,且温度对它们的影响正好相反,权函数就是用来表示温度对辐射强度影响大小的函数,而反演结果的差距可从其权函数中得到规律。在无噪声情况下,当温度对自吸收的影响小于对线强的影响时,权函数未发生正负翻转,温度反演精度较高,平均反演偏差为4.1 K;当温度对自吸收的影响大于对线强的影响时（主要位于60～80 km高度）,权函数发生正负翻转,原因是自吸收降低了辐射强度对温度的灵敏度,此时温度的反演精度较差,平均反演偏差达到34.9 K。此外,在有噪声的情况下,强线比弱线的抗干扰能力更强,反演精度更高,在实际观测中也更适合用于温度的反演,所以线强的强弱也是谱线选择的另一个重要的依据。基于辐射弱线, 进一步通过人为提高信噪比来分析辐射强度对反演精度的影响,结果表明：辐射越强,信噪比越大,温度的反演精度越高,反之则越低。当气辉谱线线强达到10-26时, 也可以用于80 km以上的温度反演并获得较好的反演结果, 反演精度<5 K。     

湍流脉动对发动机尾喷焰红外信号的影响

本文用简化的概率密度函数模拟温度的脉动,分析了轴对称火箭发动机尾喷焰湍流脉动对时均辐射信号的影响。分析结果表明,在不同的探测波长上,湍流脉动引起的时均辐射信号变化不同;由于光谱吸收系数总体上随温度的升高而降低,且降低的速率比Planck函数随温度的升高的速率大,从而导致随湍流温度脉动强度的升高尾喷焰时均辐射信号在不同波长处有不同程度的降低。     

Abel inversion using Legendre polynomials approximations

An improved Abel inversion method based on Legendre polynomials approximations is presented for reconstructing the original radial distribution of plasma emission coefficients from projected intensities. The method uses the technique of overlapping two near segments for obtaining an excellent approximation of the intensity distribution. The approximated function of the intensity profile is a combination of various shifted Legendre polynomials which in the Abel inverse equation can be integrated exactly to deduce the emission coefficient. It is shown, using simulated intensity data with and without noise inverted for a comparison with those obtained by other methods, that the method is more accurate and has a better property of noise resistance. It is well suited for applying to experimental intensities distorted by noise.     

Simulations of sooting turbulent jet flames using a hybrid flamelet/stochastic Eulerian field method

The stochastic Eulerian field method is applied to simulate 12 turbulent C₁?C₃ hydrocarbon jet diffusion flames covering a wide range of Reynolds numbers and fuel sooting propensities. The joint scalar probability density function (PDF) is a function of the mixture fraction, enthalpy defect, scalar dissipation rate and representative soot properties. Soot production is modelled by a semi-empirical acetylene/benzene-based soot model. Spectral gas and soot radiation is modelled using a wide-band correlated-k model. Emission turbulent radiation interactions (TRIs) are taken into account by means of the PDF method, whereas absorption TRIs are modelled using the optically thin fluctuation approximation. Model predictions are found to be in reasonable agreement with experimental data in terms of flame structure, soot quantities and radiative loss. Mean soot volume fractions are predicted within a factor of two of the experiments whereas radiant fractions and peaks of wall radiative fluxes are within 20%. The study also aims to assess approximate radiative models, namely the optically thin approximation (OTA) and grey medium approximation. These approximations affect significantly the radiative loss and should be avoided if accurate predictions of the radiative flux are desired. At atmospheric pressure, the relative errors that they produced on the peaks of temperature and soot volume fraction are within both experimental and model uncertainties. However, these discrepancies are found to increase with pressure, suggesting that spectral models describing properly the self-absorption should be considered at over-atmospheric pressure.     

Generalized eikonal of partially coherent beams and its use in quantitative imaging

The generalized eikonal of a partially coherent paraxial wave is introduced via a differential equation describing the evolution of the time-averaged intensity. The theoretical formalism provides an analytical tool for the study of partially coherent imaging systems. It also makes possible quantitative phase retrieval and compositional mapping of weakly absorbing samples using phase-contrast imaging with broadband polychromatic radiation of known spectral distribution. An experimental demonstration is presented of the quantitative reconstruction of the projected thickness of a sample, given a phase-contrast image obtained using a polychromatic microfocus x-ray source.     

Measurement of multi-wavelength optical amplifier by using the I/O power-curve fitting technique

A low-cost and accurate measurement scheme for characterizing multi-wavelength optical amplifiers is experimentally demonstrated by using an amplified spontaneous emission source and a DWDM multiplexer. By linearly fitting the input and output optical spectral densities, the gain and noise figure of the optical amplifier are determined. The measured results agree well with the data obtained by time-domain-extinction method.     

Three-dimensional non-grey gas radiative transfer analyses using the statistical narrow-band model

Three-dimensional non-grey gas radiation analyses were conducted using the statistical narrow-band model with updated band parameters and three implementation methods: the exact or the correlated formulation, the non-correlated expression, and the grey-band approximation with the absorption coefficient estimated using the local properties. The accuracy of the two approximate narrow-band implementation methods was evaluated for both low-resolution spectral intensity and spectrally integrated radiative source term and wall heat flux in a rectangular enclosure containing (1) isothermal pure water and (2) a CO₂/H₂O/N₂ mixture with a furnace type gas temperature distribution. For spectrally integrated quantities, results of the grey-band approximation are very close to those of the non-correlated formulation and are in qualitative agreement with the results of the correlated formulation. The two approximate methods are capable of predicting qualitatively correct and fairly accurate distributions of low-resolution spectral radiation intensities for the isothermal case. However, they predict less accurate low-resolution spectral intensities for the non-isothermal case.     

Entanglement of two-qubit photon beam by magnetic field

We show how the photon input parton distribution function (PDF) may be calculated with good accuracy and used in an extended DGLAP global parton analysis in which the photon is treated as an additional point-like parton. The uncertainty of the input photon PDF is relatively small, since the major part of the distribution (which is produced by the coherent emission of the photon from a proton that remains intact) is well known. We present the expected photon PDFs and compare the predictions with ZEUS data for isolated photon electroproduction at negative rapidities.     

基于Abel逆变换的激光诱导等离子体辐射特性研究

激光诱导击穿光谱(LIBS)作为一种新型的物质成分测量方法已经在越来越多的领域得到广泛应用，但是与传统的分析方法相比，LIBS技术的分析性能还需进一步提高。LIBS技术的理论基础是激光诱导等离子体，从物理机理上研究等离子体特性，对LIBS系统实验参数的优化具有指导作用，也为提高LIBS技术的检测能力奠定理论基础。激光诱导等离子体是一个与空间相关的非稳态辐射源，空间分辨光谱测量是探究等离子体物理特性的重要手段之一。为研究激光诱导等离子体的辐射特性，采用1 064 nm的Nd∶YAG调Q固体激光器烧蚀合金钢样品产生等离子体，利用空间分辨装置测量二维空间的等离子体辐射光谱信号，通过分析可知实验采集的光谱信号是信号探测器测量路径上的积分光谱强度，由此计算得到的等离子体参数也是观测路径上的平均值。为了深入研究等离子体由内层到外层的辐射规律，首先测量得到等离子体路径积分光谱强度的横向空间分布，然后以等离子体为光学薄和圆柱对称的前提条件，采用三次样条函数算法对路径积分光谱强度进行Abel逆变换，反演得到等离子体由内层到外层谱线辐射率的径向空间分布。选取等离子体辐射光谱中的原子谱线Fe Ⅰ: 374.55 nm和Mn Ⅰ: 403.08 nm为研究对象，分析等离子体辐射光谱的空间分布特征，研究结果表明，等离子体辐射路径积分光谱强度的横向分布呈现出中心位置强度大边缘位置强度小的特征，这是由于等离子体膨胀扩张的结果引起的；通过Abel逆变换得到等离子体光谱辐射率的径向分布，结果表明等离子体从内层到外层谱线的辐射率经过了先增加后减小的变化规律，等离子体中心处出现辐射率的极小值，造成这种现象的主要原因是由于等离子体辐射源中心区域具有较低的电子密度；选取等离子体辐射光谱中Fe元素的11条原子谱线，采用Boltzman法分别由谱线相应的积分光谱强度和辐射率计算等离子体温度，得到等离子体温度的横向空间和径向空间的二维分布，两者具有类似的变化规律；由等离子体温度的横向空间分布可以看出，随着离样品表面距离的增加，等离子体温度呈现单调减小的趋势，等离子体中心到边缘区域等离子体温度逐渐降低，这是由等离子体膨胀扩张以及与环境气体相互作用共同的结果；由等离子体温度的径向空间分布可以看出等离子体由内层到外层等离子体温度逐渐降低，这是由于等离子体膨胀扩张冷却引起的。由此可见，采用Abel逆变换能够实现等离子体由内层到外层的辐射特性分析，为深入理解等离子体产生和演变的物理机理提供实验依据，从而为提高激光诱导击穿光谱技术的分析性能奠定理论基础。     

Präzisionsmessungen am Spektrum des Wasserstoffplasmas

Detailed and precise investigations on the Balmer spectrum of a hydrogen arc have been made in order to compare the measured absolute values of the spectral emission coefficients with the existing theories, the results being of special interest with respect to line broadening calculations and to the lowering of the ionization energy. The plasma is generated in a stationary high power cascade arc at atmospheric pressure. The experiment covers the temperature range between 12000 and 20000 K, where all emission coefficients show maxima in their temperature dependence. To keep self-absorption within the plasma as low as possible, the investigations have been carried out in side-on observation. The extended gas layer of almost constant intensity surrounding the maxima ensures very accurate results of the side-on measurements. For the necessary precise calibration of the optical system both a standard carbon arc and tungsten strip lamps have been used. As the intensity of these different radiation standards only shows a few percent deviation, a very high accuracy can also be established for the measured hydrogen emission coefficients. After evaluating an average radial temperature distribution at first the absolute emission coefficients of five selected wavelengths are plotted vs. temperature and compared with theory, whereby a very good agreement is found. The emission coefficients of the continuous radiation thus confirm the lowering of the ionisation energy according to Griem used in the calculations. In the following the spectral intensities for 16250 K, i.e. the temperature in the neighbourhood of which all the maxima occur, are represented vs. wavelength to investigate the spectral dependence of the emission coefficients. Again an excellent agreement with theories of continuous radiation and line profiles is found. The experimental line shape ofH _α, however, is described much better by Vidal's ‘Unified Theory” than by Griem's standard profile. When the maxima of the emission coefficients appear appr. at half the tube radius, the side-on distributions of the intensity show a flat top in the center and their value is almost independent of the arc current. Because of these qualities and of the reliability of the theoretical calculations of the spectrum finally the hydrogen arc is recommended for a radiation standard both for the visible and the UV region.