Numerical simulation of natural convection secondary
regimes
arising after losses of base flow stability
I.A. Ermolaev, A.I. Zhbanov, V.S. Koshelev
Department of Physics, Saratov State University, Saratov, Russia
Convective flows are very sensitive to the influence of any sort of external and internal factors and display the significant diversity of instability mechanisms. The characteristic features of secondary convective regimes, arising as a result of stability loss crisis of base flow, are unsingularity, symmetry infringement and etc. There are reseach papers (e.g., [1]) on movement and heat transfer at a small excess of critical level, executed on the basis of approach equations. However, research of flow structure and field of temperatures at a moderate and strong excess of critical level is possible, as appears, only on the basis of complete nonlinear equations of convection.
At present, many calculations of finite-amplitude secondary convective flows for regimes exceeding the critical level (e.g., [2], [3], [4]) are carried out. As a rule, these calculations are related to comparatively simple-form dimensional areas with model conditions on borders. The finite difference method is usually chosen as the numerical method.
The present work offers the numerical simulation of natural convection secondary stationary regime, arising as a result of the loss of base flow stability compararing to the entry disturbances. As the initial model of the fluid mechanics equations in Boussinesq's approach, recorded in variables of "vorticity vector - stream function - temperatur " in two- dimensional cartesian coordinates system were used. To find the limit regimes the task with entry data was solved. Some initial disturbance was set in the integration area. The development of disturbances in time, field structure of flow and temperatures for branches of stationary solutions beyond the stability threshold was considered.
Galerkin's finite elements method enabling to take into consideration additional factors, influencing on disturbances development, such as boundaries curvature and their thermal properties, was used as the numerical method. Boundary conditions could be given in the form of Dirichlet's, Neuman's or Newton's conditions (the impedance).
The results of the direct numerical simulation of natural convection secondary finite-amplitude regimes in limited areas with heat-conductive borders were obtained.