Theoretical investigation on laminar-turbulent transition of flows through a rectangular duct

矩形管道流动层流-湍流转变的理论研究

基本信息

批准号：
15560052
负责人：
NAGATA Masato
金额：
$ 2.37万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2005
项目状态：
已结题

项目摘要

(1)Linear and nonlinear stability analyses on a convective flow in a channel produced by a homogeneously distributed heat source are carried out by imposing a periodic boundary condition on the side walls in the spanwise direction. We expect that the transition mechanism from laminar to turbulent flows in this system would not change much from the one in a rectangular duct case. From the linear analysis we find that there are two kinds of infinitesimal disturbances, transverse-roll type and longitudinal-roll type, which destabilise the flow in the case when the channel is placed almost vertically. Also we are able to obtain finite amplitude solutions resulting from the nonlinear interaction of these two kinds of disturbances.(2)A linear stability on the flow through a duct produced by a homogeneously distributed heat source is examined numerically. We obtain the following results. (i)There are, unexpectedly, several inflection points and reverse-flow points in the basic flow profile. They play important roles for the stability, of the flow. (ii)The flow through a duct at any aspect ratio can become unstable. (iii)The region in the parameter space where the flow becomes unstable coincides with the region where the basic flow profile is inflectional. (iv)The eigenfunction of the unstable mode propagates in the streamwise direction with the phase velocity equal to the average velocity of the basic flow.(3)As a nonlinear extension of the case (2)we derive higher order terms resulting from the nonlinear interaction of unstable eigenmodes, and the modification terms for the mean flow and the mean temperature. By taking into account the particular spatial symmetry in this system we identify the spatial structure of the finite amplitude solution that may bifurcate as a result of instability. The validity of the numerical code which incorporates the above has been checked partially.

(1)通过在翼展方向侧壁上施加周期性边界条件，对均匀分布热源产生的通道内对流流动进行线性和非线性稳定性分析。我们预计该系统中从层流到湍流的过渡机制与矩形管道情况下的过渡机制不会有太大变化。从线性分析中我们发现，在通道几乎垂直放置的情况下，存在两种无穷小的扰动，即横滚型和纵滚型，它们使流动不稳定。我们还能够得到这两种扰动的非线性相互作用所产生的有限幅解。(2)对均匀分布热源产生的流经管道的流动的线性稳定性进行了数值检验。我们得到以下结果。 (i)出乎意料的是，基本流动剖面中存在多个拐点和逆流点。它们对于流动的稳定性发挥着重要作用。 (ii)通过任何纵横比的管道的流动都可能变得不稳定。 (iii)参数空间中流动变得不稳定的区域与基本流动剖面拐点的区域一致。 (iv)不稳定模态的本征函数沿流向传播，相速度等于基本流的平均速度。(3)作为情况(2)的非线性扩展，我们推导出由非线性产生的高阶项不稳定本征模态的相互作用，以及平均流量和平均温度的修正项。通过考虑该系统中特定的空间对称性，我们确定了可能因不稳定而分叉的有限振幅解的空间结构。包含上述内容的数字代码的有效性已被部分检查。