Abstract. A mathematical model of the glaciation dynamics of the multilayer cylinder is suggested. The model reflects the specific feature of glaciation in salt water. The choice of effective model parameters and thermal characteristics of the increasing ice is considered. The calculations of problem using front-tracking finite difference method and using analytical solution found in quasi-stationary approximation are presented.
Different approaches to the modeling of thermodynamic processes in a gas flow at hyper-pressure are discussed and their equivalence is proved for any form of equation of state. The article presents arguments in favor of the approach in which temperature and density are chosen as independent thermodynamic variables and equation of sate is written in one of its analytical forms, for example, in the form of Redlich-Kwong equation of state. Explicit analytical expressions are obtained for the dependences of internal energy and specific heat at constant volume on gas temperature and density. It is proved that simplifications of the model of thermodynamic processes, which are based on the assumption of incompressibility of gas flow, are inadmissible, even in case of negligibly small inertial forces.
A mathematical model of the inflation of a spherical layer (shell) made of heat-conducting incompressible Newtonian liquid has been developed and examined. The model presents a set of differential equations, the analytical solution of which has been found in the form of the dependences of the velocity of liquid flow and the pressure in the liquid layer on the inner radius of the shell. Results of simulation of the shell inflation process under different conditions of gas pumping are presented and discussed.
Представлены модели оледенения и оттаивания внешней поверхности морского газопровода в северных морях. В модели оледенения предложена модификация условия Стефана, позволяющая учесть особенность нарастания льда в соленой воде. Приведены алгоритм численного решения нестационарной задачи оледенения (оттаивания) многослойной цилиндрической области методом явного выделения фронта и результаты расчета вариантов этих задач, представляющих практический интерес. Получены качественные оценки допустимости перехода к квазистационарному варианту модели оледенения (оттаивания) многослойных областей, приведено количественное условие допустимости квазистационарного приближения в расчетах оледенения (оттаивания) многослойной области. Эти оценки имеют большое значение при создании эффективных вычислительных алгоритмов расчета неустановившихся режимов транспортировки газа по морским газопроводам. Для задач оттаивания поверхности морского газопровода приведено уравнение, позволяющее найти минимальную толщину слоя льда в исследуемых условиях.
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