多孔介质中非稳态Maxwell流体在振荡旋转圆盘上的斜驻点滑移流动研究

白羽; 向俊霖; 张艳; 刘春燕

doi:10.21656/1000-0887.450156

多孔介质中非稳态Maxwell流体在振荡旋转圆盘上的斜驻点滑移流动研究

doi: 10.21656/1000-0887.450156

白羽^{1, 2, ,},
向俊霖^{1, 2,},
张艳^{1, 2,},
刘春燕^{1, 2, ,}

1.
北京建筑大学理学院, 北京 100044
2.
建筑结构与环境修复功能材料北京市重点实验室, 北京 100044

基金项目:

国家自然科学基金 12102032

北京市教育委员会科技计划一般项目 KM202310016001

北京市教育委员会科技计划一般项目 KM202210016001

详细信息

作者简介:
向俊霖(2000—)，男，硕士生(E-mail: 1600408272@qq.com)

张艳(1972—)，女，教授，博士，博士生导师(E-mail: zhangyan1@bucea.edu.cn)

通讯作者:
白羽(1979—)，女，教授，博士，硕士生导师(通讯作者. E-mail: baiyu@bucea.edu.cn)

刘春燕(1992—)，女，博士，硕士生导师(通讯作者. E-mail: liuchunyan@bucea.edu.cn)

中图分类号: O357
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- 文章访问数: 30
- HTML全文浏览量: 10
- PDF下载量: 5
- 被引次数: 0
出版历程
- 收稿日期: 2024-05-27
- 修回日期: 2024-10-17
- 刊出日期: 2025-09-01

Oblique Stagnation Point Slip Flow of Unsteady Maxwell Fluid on an Oscillating-Rotating Disk in Porous Medium

BAI Yu^{1, 2
, ,},
XIANG Junlin^{1, 2
,},
ZHANG Yan^{1, 2
,},
LIU Chunyan^{1, 2
, ,}

1.
School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, P.R.China
2.
Beijing Key Laboratory of Functional Materials for Building Structure and Environmental Remediation, Beijing 100044, P.R.China

摘要

摘要:
研究了多孔介质中Maxwell流体在具有振荡速度的旋转圆盘上的非稳态斜驻点流动问题. 首先，考虑了流体的滑移效应，利用改进的Darcy-Maxwell本构关系和斜驻点流动特征建立了多孔介质中的非稳态流动模型，并通过求解常微分方程对压强项进行了修正. 接着，利用合理的相似变换将控制方程转化为耦合的无量纲偏微分方程组，用同伦分析方法首次得到了模型的近似解析解. 最后，绘制了随圆盘转速变化的二维流线图、在不同倾斜参数下的三维流线图、不同振幅下随时间变化的速度图，以及速度随其他参数变化的图形. 结果表明：Deborah数的增加使流体受离心力影响加大，流动加速；Darcy参数增大导致了多孔介质的孔隙增多，流速增加；增大滑移参数，一方面会减小圆盘附近流体受到的阻碍，促进流体流动，另一方面会减小离心力对远离圆盘的流体的影响，减缓流体流动. 这些结果为旋转涂层、薄膜制备等相关领域的进一步研究提供了理论指导.
- Maxwell流体 /
- 多孔介质 /
- 振荡旋转圆盘 /
- 斜驻点流动 /
- 同伦分析法
Abstract:
The unsteady oblique stagnation point flow of the Maxwell fluid over a rotating disk with an oscillatory velocity in porous medium, was investigated. To accurately model the unsteady flow in the porous medium, an advanced formulation of the Darcy-Maxwell constitutive relation was adopted, in view of the characteristics of the oblique stagnation flow. Furthermore, the slip effect of the fluid was considered, and the pressure term was modified through solution of related ordinary differential equations. Then, the similarity transformation was employed, to change the governing equations into a coupled set of dimensionless partial differential equations. With the homotopy analysis method, an approximate analytical solution to the problem was obtained for the first time. Finally, comprehensive visualizations of the flow dynamics were presented, including 2D streamlines varying with the disk rotational speed and 3D streamlines under varying inclination parameters. Additionally, velocity profiles over time for different amplitudes were plotted, and graphs illustrating the intricate dependence of the velocity on various parameters were provided. The results show that, the augmentation of the Deborah number magnifies the centrifugal force effect and accelerates the flow. The growth of the Darcy parameter causes a concomitant rise of porosity and a higher flow velocity. The increase of the slip parameter, on the one hand, leads to a reduction in the impedance exerted by the wall to the fluid in its vicinity, resulting in an acceleration of the flow, on the other hand, mitigates the impact of centrifugal force on the fluid farther away from the wall, consequently inducing a deceleration of the flow. The research enhances the understanding of the oblique stagnation flow phenomena and provides a foundation for further research in related fields such as spin coating and thin-film preparation.
- Maxwell fluid /
- porous media /
- oscillating-rotating disk /
- oblique stagnation flow /
- homotopy analysis method

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图 1 模型图

Figure 1. The model diagram

下载: 全尺寸图片幻灯片

图 2 非零辅助参数

Figure 2. Nonzero auxiliary parameters

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图 3 二维流线图(τ=1，S_p=0.2，β₂=0.2，A₀=1，Da=0.6，De=0.6，γ=1)

Figure 3. The 2D streamlines(τ=1, S_p=0.2, β₂=0.2, A₀=1, Da=0.6, De=0.6, γ=1)

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图 4 三维流线图(τ=1，S_p=0.2，β₁=0.2，β₂=0.2，A₀=1，Da=0.6，De=0.6)

Figure 4. The 3D streamlines(τ=1, S_p=0.2, β₁=0.2, β₂=0.2, A₀=1, Da=0.6, De=0.6)

下载: 全尺寸图片幻灯片

图 5 不同A₀对应的速度u的三维非稳态分布

Figure 5. The 3D unsteady distributions of u for different A₀ values

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图 6 不同De对应的速度v

Figure 6. Curves v for different De values

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图 7 不同S_p对应的速度v

Figure 7. Curves v for different S_p values

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图 8 不同Da对应的速度v

Figure 8. Curves v for different Da values

下载: 全尺寸图片幻灯片

表 1 f″(0)对比结果

Table 1. Comparison results of f″(0)

γ	S_p=0，De₁ =0，A=0，Da=0，m=12
γ	ref. [32]	ref. [30]	present
0	1.311 94	1.311 937 694	1.311 9
1	1.575 39	1.573 920 484	1.573 5
2	2.295 1	2.295 642 287	2.295 6
3	3.365 7	3.365 654 471	3.365 7
5	6.260 2	6.259 875 006	6.259 9
10	16.522 9	16.522 814 801	16.523 3

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表 2 g′(0)对比结果

Table 2. Comparison results of g′(0)

γ	S_p=0，De₁ =0，A=0，Da=0，m=12
γ	ref. [32]	ref. [30]	present
0	-1.074 67	-1.074 669 925	-1.074 6
1	-1.110 0	-1.109 999 72	-1.110 0
2	-1.196 8	-1.196 830 974	-1.196 7
3	-1.305 5	-1.305 521 615	-1.305 4
5	-1.532 0	-1.531 982 498	-1.531 9
10	-2.033 0	-2.033 027 951	-2.032 9

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多孔介质中非稳态Maxwell流体在振荡旋转圆盘上的斜驻点滑移流动研究

doi: 10.21656/1000-0887.450156

作者简介:
向俊霖(2000—)，男，硕士生(E-mail: 1600408272@qq.com)

张艳(1972—)，女，教授，博士，博士生导师(E-mail: zhangyan1@bucea.edu.cn)

通讯作者:
白羽(1979—)，女，教授，博士，硕士生导师(通讯作者. E-mail: baiyu@bucea.edu.cn)

刘春燕(1992—)，女，博士，硕士生导师(通讯作者. E-mail: liuchunyan@bucea.edu.cn)

计量

Oblique Stagnation Point Slip Flow of Unsteady Maxwell Fluid on an Oscillating-Rotating Disk in Porous Medium

计量

目录

留言板

多孔介质中非稳态Maxwell流体在振荡旋转圆盘上的斜驻点滑移流动研究

doi: 10.21656/1000-0887.450156

作者简介: 向俊霖(2000—)，男，硕士生(E-mail: 1600408272@qq.com) 张艳(1972—)，女，教授，博士，博士生导师(E-mail: zhangyan1@bucea.edu.cn)

通讯作者: 白羽(1979—)，女，教授，博士，硕士生导师(通讯作者. E-mail: baiyu@bucea.edu.cn) 刘春燕(1992—)，女，博士，硕士生导师(通讯作者. E-mail: liuchunyan@bucea.edu.cn)

计量

出版历程

Oblique Stagnation Point Slip Flow of Unsteady Maxwell Fluid on an Oscillating-Rotating Disk in Porous Medium

计量

出版历程

目录

作者简介:
向俊霖(2000—)，男，硕士生(E-mail: 1600408272@qq.com)

张艳(1972—)，女，教授，博士，博士生导师(E-mail: zhangyan1@bucea.edu.cn)

通讯作者:
白羽(1979—)，女，教授，博士，硕士生导师(通讯作者. E-mail: baiyu@bucea.edu.cn)

刘春燕(1992—)，女，博士，硕士生导师(通讯作者. E-mail: liuchunyan@bucea.edu.cn)