标题： 微重力下圆柱液层自由热对流振动的分岔：数值与解析研究 显示英文标题

标题： Bifurcations of Free Thermal Vibrational Convection in Cylindrical Fluid Layer in Micro-Gravity: Numerical and Analytical Research

摘要： 封闭腔体内非等温流体受振动影响的分析对于规划空间技术实验至关重要。 这些过程的控制和优化严重依赖于对液体对振动响应的理解。 为此，进行了无限平面和圆柱形流体层的理论研究。 我们研究了流体响应的简单情况——圆柱形流体层中的热振动对流，其边界为刚性导电边界。 结果发现，热振动对流的稳定模式会经历各种分岔。 分岔会导致传热发生剧烈变化。 广义Lorenz模型（GLM）被推广并用于分析由腔体形状和振动Rayleigh数变化引起的分岔。 发现了平均流动流函数、振动Rayleigh数和腔体曲率三维空间中稳态表面的形状。 针对平面和圆柱形流体层进行了数值二维解。 基于GLM模型的分析结果与直接数值模拟获得的数据进行了比较。 发现了具有极值的分岔曲线。 因此，可以观察到复杂形状的分岔。 还展示了与空间实验的对比及其讨论。 显示英文摘要

摘要： The analysis of vibration effect on non-isothermal fluid in closed cavity is important for planning technological experiments in space. Control and optimization of these processes critically depend on the understanding of liquid response to the vibrations. With this aim the theoretical investigation for infinite plane and cylindrical fluid layers are performed. We investigated simple case of the fluid response-thermal vibrational convection in a cylindrical fluid layer with rigid conducting boundaries. It is found that steady modes of thermal vibrational convection are subjected to various bifurcations. Bifurcations cause sharp changes in heat transfer. The Lorenz model is generalized (GLM) and used to conduct the analysis of bifurcations caused by the changing of the cavity shape and vibrational Rayleigh number. The shape of steady-state surface in 3D space of the streamfunction of mean flow, vibrational Rayleigh number and the cavity curvature is found. The numerical 2D solution is performed for plane and cylindrical fluid layers. The results of the analysis based on the GLM model are compared with the data obtained by direct numerical simulation. The bifurcation curve with extremum is found. Thus, bifurcations of complex shape could be observed. Comparisons with space experiments and its discussions are presented.