Numerical modeling of the formation of D-T mixture spherical layer in micro-targets of LTS

The article presents a two-dimensional economical computational model of the formation of D-T mixture cryogenic layer in a spherical shell. The model is based on the description of the motion of the gas phase in the Boussinesq approximation. The thermal problem is a Stefan problem with a gas-solid phase transition. The technique is based on the finite volume method, the use of a structured mobile grid, whose movement is associated with the separation of the phase front, implicit approximations and the method of splitting two-dimensional equations in directions into one-dimensional equations. It is numerically shown that, due to natural radioactivity, the target is symmetrized. A calculated estimation of the symmetrization time for one geometry of the target with different filling coefficients is carried out.

HEAT EXCHANGE OF ELECTRIC CONDUCTIVE LIQUID IN THE SUPPLY OF HEAT TO THE INNER SURFACE OF THE SPHERICAL LAYER AT SMALL VALUES OF THE REYNOLD'S MAGNETIC NUMBER

Представлены результаты численного моделирования нестационарного теплообмена и магнитной гидродинамики электропроводной жидкости в сферическом слое. Исследовано влияние малых значений магнитного числа Рейнольдса и теплоты джоулевой диссипации на эволюцию структуры течения жидкости, поле температуры, магнитной индукции и распределение чисел Нуссельта. The results of numerical simulation of unsteady heat transfer and magneto hydrodynamics of an electrically conductive fluid in a spherical layer are presented. The influence of small values of the magnetic Reynolds number and the heat of Joule dissipation on the evolution of the structure of the fluid flow, the field of temperature, magnetic induction and the distribution of Nusselt numbers is investigated.

HEAT EXCHANGE OF ELECTRIC CONDUCTIVE LIQUID WHEN DEPLOYING THE HEAT FROM THE INNER SURFACE OF THE SPHERICAL LAYER AT SMALL VALUES OF THE REYNOLD'S MAGNETIC NUMBER

Представлены результаты численного моделирования нестационарного теплообмена и магнитной гидродинамики электропроводной жидкости в сферическом слое. Исследовано влияние малых значений магнитного числа Рейнольдса и диссипации джоулевой теплоты на эволюцию структуры течения жидкости, поле температуры, магнитной индукции и распределение чисел Нуссельта. The results of numerical simulation of unsteady heat transfer and magneto hydrodynamics of an electrically conductive fluid in a spherical layer are presented. The influence of small values ​​of the magnetic Reynolds number and dissipation of Joule heat on the evolution of the structure of the fluid flow, the field of temperature, magnetic induction and the distribution of Nusselt numbers is investigated.

Energy Method for the Elliptic Boundary Value Problems with Asymmetric Operators in a Spherical Layer

Three-dimensional elliptic boundary value problems arising in the mathematical modeling of quasi-stationary electric fields and currents in conductors with gyrotropic conductivity tensor in domains homeomorphic to the spherical layer are considered. The same problems are mathematical models of thermal conductivity or diffusion in moving or gyrotropic media. The operators of the problems in the traditional formulation are non-symmetric. New statements of the problems with symmetric positive definite operators are proposed. For the four boundary value problems the quadratic energy functionals, to the minimization of which the solutions of these problems are reduced, are constructed. Estimates of the obtained quadratic forms are made in comparison with the form appearing in the Dirichlet principle for the Poisson equation

HEAT EXCHANGE OF ELECTRIC CONDUCTIVE LIQUID AT LARGE VALUES OF THE REYNOLD'S MAGNETIC NUMBER

Представлены результаты численного моделирования нестационарного конвективного теплообмена и магнитной гидродинамики электропроводной жидкости в сферическом слое при граничных условиях для температуры первого рода. Исследовано влияние величины магнитного числа Рейнольдса на эволюцию структуры течения жидкости, поле температуры, магнитной индукции и распределение чисел Нуссельта. The results of numerical simulation of unsteady convective heat transfer and magneto hydrodynamics of an electrically conductive fluid in a spherical layer under boundary conditions for a temperature of the first kind are presented. The influence of the value of the magnetic Reynolds number on the evolution of the structure of the fluid flow, the field of temperature, magnetic induction and the distribution of Nusselt numbers is investigated.

About Limit Transitions in Spatial Homogenization Problems for Two-Component Dielectric Composites with Extremal Moduli for One of Phases

The spatial problem of calculating the effective permittivity of two-component composite, consisting of a base material filling a spherical layer and one spherical inclusion, is considered. The homogenization problem is solved by effective moduli method with calculation of the energy characteristics in the composite medium and in its individual phases. In the obtained solution, the limit transitions are made for two extreme cases: pores or inclusions with zero dielectric constant and conductive inclusions with infinitely high dielectric constant. The solutions of these problems are compared with the solutions of homogenization problems for a medium with void and for a medium with conductive inclusion boundary. In problems with one basic material, the properties of inclusions were taken into account only by the corresponding boundary conditions on the interface. It is shown that calculations of the effective permittivity by energy criterion give correct results in all the cases considered, while the calculations by the average permittivity for a composite with a conductive inclusion boundary may be erroneous.

Генерация второй гармоники-суммарной частоты в тонком сферическом слое. IV. Оптимизационный анализ

A numerical maximization of the intensity of the generated radiation of second harmonic–sum frequency from a thin spherical layer is carried out. It is found that, for all the considered anisotropy types and any size of the spherical layer, the maximum of the intensity is observed at the same parameters of the problem, and an increase in the particle size leads to an increase in generated spatial power density. It is shown that, for large particle sizes, the intensity of the generated radiation is proportional to the fourth power of the particle radius. The distribution law of the generated power density is found analytically for one of the anisotropy types in the case of codirectional incidence of waves on a spherical particle of small radius.

Генерация второй гармоники-суммарной частоты в тонком сферическом слое. I. Аналитическое решение

The problem of the simultaneous second–harmonic and sum–frequency generation by two coherent plane electromagnetic waves with elliptical polarizations and equal frequencies in a thin spherical layer is solved in the Rayleigh–Gans–Debye model. The second–order dielectric susceptibility tensor is chosen in a form containing four independent components (including one chiral component). Fundamental differences are shown between the problem statements as well as between solutions to the problem of second–order nonlinear generation by several coherent electromagnetic waves and the problem of sum–frequency generation in the limiting case of equality of the frequencies of the incident waves. Combinations of parameters are determined at which the spatial distribution of the radiation generated as a result of incidence of two plane waves coincides with the distribution of second–harmonic radiation generated by one plane wave. The limiting cases of the obtained solution are considered: small and large radii of the spherical particle. In these cases the contributions of the chiral and non-chiral anisotropy coefficients to the generated radiation are determined.