On the viscous core boundary layer of the injection and suction driven channel flows with expanding or contracting walls
On the viscous core boundary layer of the injection and suction driven channel flows with expanding or contracting walls
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DOI：
10.1002/zamm.201700003
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发表时间：
2018-06
期刊：
影响因子：
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通讯作者：
J. Majdalani;Li-Jun Xuan
中科院分区：
文献类型：
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作者：
J. Majdalani;Li-Jun Xuan
这项工作扩展了一系列的研究，致力于分析的层流在多孔通道收缩壁。这个问题最初是用来模拟平板推进剂药柱回归。在确定了一个微妙的端点奇异性，影响前一个解决方案在其三阶导数，拉伸变量被引入到捕捉快速变化的通道的核心。核心是指中间截面平面，在那里剪切层由于壁处的硬吹而发生位移。然后使用带有对数校正的匹配渐近展开式，在从四阶导数开始的连续积分之后，得到一个复合解。在此过程中，内部校正是从控制堆芯附近对称注入驱动流的四阶方程中检索的。由此产生的近似表示在广义超几何函数，并确认使用数值和限制过程验证。复合解决方案被证明优于前者，外解决方案，作为核心接近或作为注射雷诺数增加。在不破坏前一种解在薄核区域外的实用性的情况下，匹配渐近近似的发展使我们能够抑制经常被忽视的奇异项，从而确保在影响压力分布及其法向梯度的三阶和四阶导数下一致有效的结果。
This work extends a sequence of studies devoted to the analysis of the laminar flow in porous channels with retracting walls. This problem was originally used to model slab propellant grain regression. After identifying a subtle endpoint singularity that affects the former solution in its third derivative, a stretched variable is introduced to capture the rapid variations in the channel's core. The core refers to the midsection plane where the shear layer is displaced due to hard blowing at the walls. Then using matched‐asymptotic expansions with logarithmic corrections, a composite solution is developed following successive integrations that start with the fourth derivative. In the process, the inner correction is retrieved from the fourth‐order equation governing the symmetric injection‐driven flow near the core. The resulting approximation is expressed in terms of generalized hypergeometric functions and is confirmed using numerics and limiting process verifications. The composite solution is shown to outperform the former, outer solution, as the core is approached or as the injection Reynolds number is increased. Without undermining the practicality of the former solution outside the thin core region, the development of a matched‐asymptotic approximation enables us to suppress the often overlooked singular terms, thus ensuring a uniformly valid outcome down to the third and fourth derivatives, which affect the pressure distribution and its normal gradients.