2D and quasi-2D DNS of turbulent convection in vertical layers

Abstract

Предложен новый итерационный метод решения контактной задачи, возникающей в классической модели многолистовой рессоры. Рессора представлена в виде пачки консольных балок (листов) постоянного поперечного сечения. Длины и толщины листов различны, ширина одинакова. В отсутствие нагрузки листы являются плоскими и плотно прилегают друг к другу; трение не учитывается. К свободному краю самого длинного листа приложена сосредоточенная сила, под действием которой листы испытывают слабый статический изгиб; контакт листов происходит с возможным отставанием. Задача состоит в отыскании сил взаимодействия листов. Новый метод основан на полученном авторами ранее аналитическом решении обобщения поставленной выше задачи (на листы действуют силы с произвольными заданными плотностями), но для двухлистовой рессоры. Для многолистовой рессоры это решение используется для каждой пары соседних листов при итерационном уточнении сил взаимодействия. Получен ряд ранее не известных картин контакта, которые не могут быть найдены традиционными методами.Ключевые слова: многолистовая рессора, контактная задача, итерационный метод, картины контакта листов A NEW NUMERICAL METHOD FOR THE CALCULATION OF THE MULTI-LEAF SPRING M.A. Osipenko and Yu.I. Nyashin Perm National Research Polytechnic University, Perm, RussiaA new iteration method for solving the contact problem of a multi-leaf spring encountered in the classical model is proposed. The spring represents the stack of cantilever beams (leaves) of constant cross-section. The leaves differ in length and thickness, but have the same width. In the absence of loading, the leaves fit each other closely. There is no friction between the leaves. The concentrated force is applied to the tip of the longest leaf. The leaves undergo weak static bending with unbonded contact. The problem consists in finding the forces of interaction between leaves. The proposed method is based on the analytical solution of the generalized contact problem (arbitrary loading) for the two-leaf spring obtained earlier by the authors. This analytical solution is used for adjacent leaves of the multi-leaf spring through iterative adjustment of interaction forces. This method gives a series of novel leaf contact patterns that cannot be obtained by the conventional methods.

High Rayleigh number convection in a cubic cell with adiabatic sidewalls

“…These deviations are not caused by measurement errors but as we will show below in Section 3.3 are results of reorientations of the large-scale circulation. A particular feature of turbulent convection in cubic cavities concerns the low-frequency oscillations of LSC [31,32]. This very specific phenomenon was observed for a limited range of governing parameters and can be useful for CFD codes validation.…”

“…Complex spatial structure and temporal behavior of large-scale circulation in cubic cavities [31,32] raise important question about the sensitivity of LSC characteristics to specific experimental realization. Therefore we deliberately constructed two setups without coordinating their technical details.…”

“…Regimes of LSC in rectangular tanks of different aspect ratios were studied experimentally in [31], where it was shown that the LSC strongly depends on the small variation of the cavity thickness. Threedimensional convective flows in a cubical cavity at Ra ¼ 4:4 Á 10 9 were experimentally and numerically studied in [32], where the variety of dynamical regimes was observed.…”