V. V. Cherepanov

Mathematical simulation of high-porosity fibrous materials and determination of their physical properties

A statistical mathematical model of fibrous high-porosity composite material is described. This model is used for studying the basic radiative and thermophysical properties of material. It is demonstrated how the use of the model helps significantly extend the capabilities of experimental methods and enables one to compare the calculation and experimental results and obtain parameters of material which were previously hardly accessible for determination.

Numerical and experimental determination of the temperature dependence of the spectral and integral emissivities of quartz ceramics of various porosity

The optical parameters of quartz ceramics (absorption and scattering indices) are determined by solving the inverse problem of radiation transfer based on the total-reflection spectra of two layers with different thicknesses measured in the wavelength range of 0.5–18 μm. The spectra of hemispherical emissivities and integral thermal emissivities are calculated in the temperature range of 20–1400°C. The influence of porosity on the optical parameters and emissivities is analyzed in the range of 7–11%.

Determining the Size of Pores in a Partially Transparent Ceramics from Total-Reflection Spectra

A technique is proposed for determining the pore-size distribution based on measuring the dependence of total reflectance in the domain of partial transparency of a material. An assumption about equality of scattering-coefficient spectra determined by solving the inverse radiation transfer problem and by theoretical calculation with the Mie theory is used. The technique is applied to studying a quartz ceramics. The poresize distribution is also determined using mercury and gas porosimetry. All three methods are shown to produce close results for pores with diameters of <180 nm, which occupy ~90% of the void volume. In the domain of pore dimensions of >180 nm, the methods show differences that might be related to both specific procedural features and the structural properties of ceramics. The spectral-scattering method has a number of advantages over traditional porosimetry, and it can be viewed as a routine industrial technique.

Calculation of the Optical Properties of Quartz Ceramics Based on Data on Its Structure

The optical parameters of quartz ceramics from a previously proposed identification method and simulation using different optical models of the material are compared. The identification method is based on deliberately measuring hemispherical spectral reflectances for layers of different thicknesses and solving the inverse problem using asymptotic formulas. Mathematical models are constructed based on the Mie theory on the assumption of independent scattering of electromagnetic radiation by fragments of the material. The material is considered as a polydisperse packing of spheres, the sizes of which are determined by data on the material structure. Both a grain surrounded by gas and a pore in monolithic material are considered as a scatterer. Data on the material structure were gathered using optical microscopy, static laser scattering, and mercury porosimetry. The best agreement with the results of the identification method is demonstrated by the model of ceramics in the form of a glass monolith with spherical voids. Comparative analysis eliminates uncertainty in the form of the scattering phase function and shows that the scattering is close to isotropic.

Determination of optical parameters of partially transparent materials by the invariant embedding method

A method of invariant immersion to solve the inverse problem of identification of the indicators of the absorption and scattering of heat-resistant quartz ceramics by the spectra of the total reflection coefficients from a layer consisting of two different materials has been applied. An original numerical implementation of the method for the calculation of the functions of the reflection and transmission by the layer of the scattering and absorbing materials with reflective boundaries has been introduced. Its distinctive feature is the use of the equation matrix form in quadratures, which accelerates greatly the calculations in the MATLAB software. The results of the invariant immersion method are compared to asymptotic formulas and the Monte Carlo simulation results.

The modeling of radiation transfer in highly-porous composite materials with strong scattering

In this report the problems, which arise during the radiative transfer of highly-porous thermal protective material with high spectral albedo of scattering, were studied. A three-step iterative numerical method based on splitting the problem operator by physical processes was developed. The method is useful and does not need any restrictions in initial approach and optical thickness of a layer. Results of computational modeling are given below.

Functional optimization technique for numerical solution of the radiative transfer equation

A numerical method for solving the time-independent radiative transfer problem in a flat layer with given properties and temperature distribution is proposed. This method avoids the numerical diffusion; rather, it is based on a gradient procedure for the functional minimization of the residual of the radiative transfer integral equation. Means for suppressing computational instabilities are proposed that reduce requirements for the approximation of the operators in the optimization problem but do not change the problem objective functional.

Mathematical Model of Heat Transfer in High-Porous Materials

The main purpose of this study was to confirm operability and effectiveness of the complex methods developed for theoretical prediction and experimental-computational determining some properties of modern highly porous materials, used as thermal protection shields in objects of space engineering, power engineering, etc. Them concern Fibrous Materials (FM), Open-Cell Reticulated Foams (OCRF) etc. The basis for the method proposed is in the combination of Direct Mathematical Simulation (DMS) for global structure of the complex irregular systems, which have the property of local regularity and Inverse Heat Transfer Problem (IHTP) methods. This approach makes possible to obtain and to predict such properties as radiation and molecular thermal conductivities, energy accommodation coefficient, complex refractive index, scattering indicatrix, scattering and absorption factors, etc. Such problems are of great practical importance in the study of material properties.Copyright