Linear stability of flow in an internally heated rectangular duct
Linear stability of flow in an internally heated rectangular duct
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DOI：
10.1017/s0022112005008487
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发表时间：
2006-03-25
影响因子：
3.7
通讯作者：
Nagata, M
中科院分区：
文献类型：
--
作者：
Uhlmann, M;Nagata, M
在Boussinesq假设的框架下，数值研究了均匀内加热、恒温无滑壁和驱动压力梯度作用下垂直矩形管道内流动的线性稳定性。基于修正的Chebyshev多项式的Galerkin方法被用来离散线性化的Navier-Stokes方程在其最紧凑的形式，即消除压力和流向速度，并利用固有的对称性。本文提出了在Grashof空间和Reynolds空间中基本流动的一种根据弯曲性质的分类。结果发现，流动失去稳定性在所有的纵横比为有限的热浮力和压力的组合与相反的迹象。在方形管道中，不稳定区域位于基本速度分布呈现附加拐点的范围内。不稳定的本征函数得到的所有基本对称模式，包括快速传播的大型结构位于附近的拐点附近的管道中心。
The linear stability of flow in a vertical rectangular duct subject to homogeneous internal heating, constant-temperature no-slip walls and a driving pressure gradient is investigated numerically in the framework of the Boussinesq hypothesis. A Galerkin method based upon modified Chebyshev polynomials is used to discretize the linearized Navier-Stokes equations in their most compact form, i.e. eliminating the pressure and the streamwise velocity and making use of the intrinsic symmetry properties. A classification of the basic flow in Grashof and Reynolds space in terms of inflectional properties is proposed. It is found that the flow loses stability at all aspect ratios for a combination of finite thermal buoyancy and pressure forces with opposed signs. In the square duct, the unstable region lies inside the range where the basic velocity profile exhibits additional inflection lines. Unstable eigenfunctions are obtained for all basic symmetry modes, consisting of rapidly propagating large-scale structures located in the vicinity of the inflection lines near the centre of the duct.