Temporal stability of multiple similarity solutions for porous channel flows with expanding or contracting walls
Temporal stability of multiple similarity solutions for porous channel flows with expanding or contracting walls
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DOI：
10.1063/5.0051846
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Yanxiao Sun;P. Lin;Zhenlin Guo
中科院分区：
文献类型：
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作者：
Yanxiao Sun;P. Lin;Zhenlin Guo
本文分析了不可压缩层流沿均匀多孔扩张或收缩孔道流动的多个相似解(流型)的时间稳定性。本文通过考察一般形式(包括相似形式和非相似形式)扰动下的时间稳定性，推广了文献[1]中关于相似扰动的最新结果。基于线性稳定性理论，建立了与流动方程相关的二维特征值问题，并在交错网格上用有限差分方法进行了数值求解。线性稳定性分析表明，在墙膨胀比α(−5≤α≤3的范围内，解的稳定性与在[1]中相似形式摄动下的稳定性相同。进一步发现，膨胀比α对I型流动的稳定性有很大的影响：在壁面收缩(α<；0)的情况下，横流雷诺数(R)的稳定区域随着收缩比(|α|)的增加而增加，在壁面扩张和0<；α≤1的情况下，稳定区域随着扩张比(α)的增加而增加；在1≤α≤3的情况下，键入相应的作者电子邮件地址：p.lin@dundee.ac.uk(平林)提交给流体物理2021年7月24日的预印本。S是The au th or‘S p ee reew ed，a cc ep ted m an us cr IP t.h ow Ev er，在所有存在的R中，S都是稳定的。P L E A S E C IT E T H是一个R T IC L E A S D O I：1 0.1 0 63/5.0 5 1 1 8 4 6 I流对所有存在的R是稳定的。其他类型的流动(类型II和类型III，−5，≤α≤3，以及类型IV，α=3)总是不稳定。作为一种非线性稳定性分析或线性稳定性分析的验证，直接求解了原始的具有一般形式的初始摄动的二维非线性时变问题。结果表明，非线性稳定性分析与线性稳定性分析是一致的。
In this paper, the temporal stability of multiple similarity solutions (flow patterns) for the incompressible laminar fluid flow along a uniformly porous channel with expanding or contracting walls is analyzed. This work extends the recent results of similarity perturbations of [1] by examining the temporal stability with perturbations of general form (including similarity and non-similarity forms). Based on the linear stability theory, two-dimensional eigenvalue problems associated with the flow equations are formulated and numerically solved by a finite difference method on staggered grids. The linear stability analysis reveals that the stability of the solutions is same with that under perturbations of a similarity form within the range of wall expansion ratio α (−5 ≤ α ≤ 3 as in [1]). Further, it is found that the expansion ratio α has a great influence on the stability of type I flows: in the case of wall contraction (α < 0), the stability region of the cross-flow Reynolds number (R) increases as the contraction ratio (|α|) increases; in the case of wall expansion and 0 < α ≤ 1, the stability region increases as the expansion ratio (α) increases; in the case of 1 ≤ α ≤ 3, type Corresponding author Email address: p.lin@dundee.ac.uk (Ping Lin ) Preprint submitted to PHYSICS OF FLUIDS July 24, 2021 T hi s is th e au th or ’s p ee r re vi ew ed , a cc ep te d m an us cr ip t. H ow ev er , t he o nl in e ve rs io n of r ec or d w ill b e di ffe re nt fr om th is v er si on o nc e it ha s be en c op ye di te d an d ty pe se t. P L E A S E C IT E T H IS A R T IC L E A S D O I: 1 0 .1 0 6 3 /5 .0 0 5 1 8 4 6 I flows are stable for all R where they exist. The flows of other types (types II and III with −5 ≤ α ≤ 3 and type IV with α = 3) are always unstable. As a nonlinear stability analysis or a validation of the linear stability analysis, the original nonlinear two-dimensional time dependent problem with an initial perturbation of general form over those flow patterns is solved directly. It is found that the stability with the non-linear analysis is consistent to the linear stability analysis.