Equivalent slip length of flow around a super-hydrophobic cylinder
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arXiv
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| Format: | Preprint |
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2024
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| author | Li, Zhi-yong Xiao, Ya-kang Li, Yan-cheng Yu, Li Peng, Sai Xiong, Yong-liang |
| author_facet | Li, Zhi-yong Xiao, Ya-kang Li, Yan-cheng Yu, Li Peng, Sai Xiong, Yong-liang |
| contents | In this research, a two-dimensional numerical simulation is conducted to determine the equivalent wall slip length for flow around a circular cylinder featuring a super-hydrophobic surface. The super-hydrophobic surface is modeled as an alternating distribution of slip and no-slip conditions along the cylinder's surface. The smallest unit of this alternating pattern is referred to as a monomer. The study takes into account the Reynolds number and two critical dimensionless parameters: the gas fraction (GF) and the ratio l/a. GF indicates the proportion of the slip length relative to the total length of the monomer, while l/a denotes the ratio of the monomer length (l) to the cylinder's radius (a). The ranges considered for the Reynolds number, GF, and l/a are from 0.2 to 180, 0.1 to 0.99, and $π$/80 to $π$/5, respectively. A dimensionless number, the Knudsen number (Kn), is introduced to measure the ratio between the equivalent slip length ($λ$) and the cylinder's diameter (D). By equating the integral wall friction resistance on the cylinder surface, a quantitative relationship between the equivalent Kn and the parameters (Re, GF, l/a) is established. A meticulous comparison of flow parameters between the equivalent slip length model and the slip-no-slip scenario reveals that the slip length model is an effective approximation for the slip-no-slip alternating model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14116 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivalent slip length of flow around a super-hydrophobic cylinder Li, Zhi-yong Xiao, Ya-kang Li, Yan-cheng Yu, Li Peng, Sai Xiong, Yong-liang Fluid Dynamics In this research, a two-dimensional numerical simulation is conducted to determine the equivalent wall slip length for flow around a circular cylinder featuring a super-hydrophobic surface. The super-hydrophobic surface is modeled as an alternating distribution of slip and no-slip conditions along the cylinder's surface. The smallest unit of this alternating pattern is referred to as a monomer. The study takes into account the Reynolds number and two critical dimensionless parameters: the gas fraction (GF) and the ratio l/a. GF indicates the proportion of the slip length relative to the total length of the monomer, while l/a denotes the ratio of the monomer length (l) to the cylinder's radius (a). The ranges considered for the Reynolds number, GF, and l/a are from 0.2 to 180, 0.1 to 0.99, and $π$/80 to $π$/5, respectively. A dimensionless number, the Knudsen number (Kn), is introduced to measure the ratio between the equivalent slip length ($λ$) and the cylinder's diameter (D). By equating the integral wall friction resistance on the cylinder surface, a quantitative relationship between the equivalent Kn and the parameters (Re, GF, l/a) is established. A meticulous comparison of flow parameters between the equivalent slip length model and the slip-no-slip scenario reveals that the slip length model is an effective approximation for the slip-no-slip alternating model. |
| title | Equivalent slip length of flow around a super-hydrophobic cylinder |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2411.14116 |