Аннотации:
Представлены результаты численного моделирования стационарных
конвективных течений в ячейке Хеле–Шоу при подогреве снизу. Выполнен
линейный анализ устойчивости механического равновесия и проанализирован переход от одновихревого течения к двухвихревому при учете в математической модели зависимости вязкости жидкости от температуры. Для
различных вариантов тепловых граничных условий получены поля функции тока при разных числах Рэлея, по которым определены сценарии интенсификации конвекции с ростом надкритичности. The results of direct numerical simulation of stationary convective flows in a vertical Hele–Shaw
cell under the uniform heating from below are presented in this paper. The calculations have been
fulfilled for realistic values of the heat-transfer coefficient on vertical wide boundaries and model
thermal conditions on narrow vertical walls. The approximation of plane trajectories has been applied to
calculate the flows in the Hele–Shaw cell. The linear stability analysis is executed for the situation when
the viscosity depends on the temperature. An analytical formula for critical values of Rayleigh number
has been deduced which determine the threshold of convection in dependence on parameters of the
problem. It has been shown that the numerical simulation imitating the full-scale experiment gives
adequate description of the transition from one-vortex stationary flow to the two-vortex steady regime
when the dependence of viscosity on the temperature is taken into account in mathematical model. The
equations system of thermal convection in Boussinesq approximation was solved by the method of finite
differences at the “PGU-Tesla” supercomputer of the Research Academic Center “Parallel and
Distributed Calculations” in Perm State University. The fields of stream function in vertical section have
been calculated which confirm the effect of the vortices centers displacement to the bottom of the cavity.
Описание:
В.А. Демин, М.И. Петухов,
Пермский государственный национальный исследовательский университет, г. Пермь,
Российская Федерация
E-mail: demin@psu.ru. V.A. Demin, M.I. Petukhov
Perm State National Research University, Perm, Russian Federation
E-mail: demin@psu.ru