Three-dimensional extensions to Jeffery–Hamel flow
Three-dimensional extensions to Jeffery–Hamel flow
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DOI：
10.1016/s0169-5983(01)00017-x
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发表时间：
2001-07
影响因子：
1.5
通讯作者：
S. Stow;P. Duck;R. Hewitt
中科院分区：
文献类型：
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作者：
S. Stow;P. Duck;R. Hewitt
我们考虑了两种粘性流动，它们都处于一类与经典的Jeffery-Hamel解密切相关的三维流动状态。在第一种构型中，我们考虑两个平面之间的流，以α角相交，并由交点附近的线源类解驱动(就像在经典的二维Jeffery-Hamel流中一样)。然而，此外，我们还允许沿平面相交线的方向流动(以便捕捉更广泛的三维解决方案)。在这种流动中，有两种可能的解决方案；第一种方案源于Jeffery-Hamel流的分叉，而第二种方案描述了经典的Jeffery-Hamel形式的径向速度(也具有零方位速度分量)，但轴向速度由径向流动确定。这两种解决方案都完全在纳维斯托克斯框架内。在第二种构型中，我们考虑了高雷诺数的三维扩张通道内的流动，通常情况下，非直壁接近对称平面，并受到压力梯度的驱动。找到了相似解，并与Jeffery-Hamel流建立了联系，对于流经直(但非平行)通道壁的特殊情况，又找到了附加的三维解。这一类中的一个成员(对应于流经直壁通道的流动，在轴向和跨通道方向上都是由线性增加的压力驱动的)，导致了另一族精确的Navier-Stokes解。
We consider two viscous flows, both of which are in a class of three-dimensional flow states that are closely related to the classical Jeffery–Hamel solutions. In the first configuration, we consider a flow between two planes, intersecting at an angle α, and driven by a line-source-like solution in the neighbourhood of the apex of intersection (just as in classical, two-dimensional, Jeffery–Hamel flow). However, in addition we allow for a flow in the direction of the line of intersection of the planes (in order to capture the broader class of three-dimensional solutions). In this flow, two solution scenarios are possible; the first of these originates as a bifurcation from Jeffery–Hamel flow, whilst the second scenario describes a radial velocity of the classical Jeffery–Hamel form (also with a zero azimuthal velocity component), but with an axial velocity determined from the radial flow. Both of these solutions are exact within the Navier–Stokes framework. In the second configuration, we consider the high Reynolds number, three-dimensional flow in a diverging channel, with (generally) non-straight walls close to a plane of symmetry, and driven by a pressure gradient. Similarity solutions are found, and a connection with Jeffery–Hamel flows is established for the particular case of a flow through straight (but non-parallel) channel walls, and again, additional three-dimensional solutions are found. One member of this general class (corresponding to the flow through a straight-walled channel, driven by linearly increasing pressure in both the axial and cross-channel directions), leads to a further family of exact Navier–Stokes solutions.