Study and turbulence control of the laminar-turbulent transition in the spherical Couette flow

球形库埃特流层流-湍流转变的研究与湍流控制

基本信息

批准号：
08650198
负责人：
NAKABAYASHI Koichi
金额：
$ 1.41万
依托单位：
Nagoya Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至 1997
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08650198/
关键词：
Spherical Couette flow Chaos Laminar-Turbulent Transition Poincare section First Return Map Correlation Dimension Trasition Scenario Numerical Simulation スパイラルTG渦

项目摘要

The laminar-turbulent transition of spherical Couette flow was investigated by laboratory experiment, theoretical analysis and numerical simulations. Calculating the correlation dimension and drawing the Poincare section, it is revealed for case of clearance ratio beta=0.14 that the flow field traces a scenario as follows ; steady state--> periodic state --> quasi-periodic state --> chaos --> periodic state --> steady state --> periodic state --> chaos. It is also shown that in the quasi-periodic state the first return map becomes irreversible as the Reynolds number increases. For other cases of clearance ratio, it is found that fluctuation disappearance phenomenon occurs in a range of beta=0.13-0.17. A finite-difference method for solving three-dimensional, time-dependent incompressible Navier-Stokes equations in spherical polar coordinates is presented. A new algorithm, which is second-order accurate in time and space, is considered, and decoupling between the velocity and the pressure is achieved by this algorithm. It is demonstrated that the numerical code is valid for solving three-dimensional, unsteady incompressible Navier-Stokes equations spherical polar coordinates. The numerical code was then used to compute the spherical Couette flow between two spheres with the inner sphere rotating for case of clearance ratio beta=0.14, and we successfully simulated the subcritical and supercritical flows. In particular, careful direct numerical simulations on the spiral TG vortex flow has been performed, and systematical analysis has been carried out to explore the detailed structure, evolution process and generation mechanism of the spiral TG vortex flow.

通过实验室实验，理论分析和数值模拟研究了球形cOUTETE流动的层流扰动过渡。计算相关维度并绘制PoinCare部分，对于清除比beta = 0.14的情况显示，流场的范围如下。稳态 - >周期状态 - >准周期状态 - >混乱 - >周期状态 - >稳态 - >周期状态 - >混乱。还表明，在准周期状态下，随着雷诺数的增加，第一个返回图变得不可逆。对于其他清除比的情况，发现波动消失现象发生在beta = 0.13-0.17的范围内。提出了一种用于求解三维，时间依赖性不可压缩的Navier-Stokes方程的有限差分方法。考虑了一种新的算法，该算法在时间和空间上是二阶精确的，并且该算法实现了速度和压力之间的脱钩。已经证明，数值代码对于求解三维，不稳定的不可压缩的Navier-Stokes方程有效。然后，使用数值代码来计算两个球之间的球形轴向流，内部球旋转以旋转，以确保清除比beta = 0.14，我们成功地模拟了亚临界和超临界流。特别是，已经对螺旋TG涡流流进行了仔细的直接数值模拟，并进行了系统分析以探索螺旋TG涡流流的详细结构，演化过程和生成机制。