Analytical Investigation of Viscoelastic Stagnation-Point Flows with Regard to Their Singularity
Singularities in the stress field of the stagnation-point flow of a viscoelastic fluid have been studied for various viscoelastic constitutive models. Analyzing the analytical solutions of these models is the most effective way to study this problem. In this paper, exact analytical solutions of two-...
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MDPI AG
2021-07-01
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| author | Jie Liu Martin Oberlack Yongqi Wang |
| author_facet | Jie Liu Martin Oberlack Yongqi Wang |
| author_sort | Jie Liu |
| collection | DOAJ |
| description | Singularities in the stress field of the stagnation-point flow of a viscoelastic fluid have been studied for various viscoelastic constitutive models. Analyzing the analytical solutions of these models is the most effective way to study this problem. In this paper, exact analytical solutions of two-dimensional steady wall-free stagnation-point flows for the generic Oldroyd 8-constant model are obtained for the stress field using different material parameter relations. For all solutions, compatibility with the conservation of momentum is considered in our analysis. The resulting solutions usually contain arbitrary functions, whose choice has a crucial effect on the stress distribution. The corresponding singularities are discussed in detail according to the choices of the arbitrary functions. The results can be used to analyze the stress distribution and singularity behavior of a wide spectrum of viscoelastic models derived from the Oldroyd 8-constant model. Many previous results obtained for simple viscoelastic models are reproduced as special cases. Some previous conclusions are amended and new conclusions are drawn. In particular, we find that all models have singularities near the stagnation point and most of them can be avoided by appropriately choosing the model parameters and free functions. In addition, the analytical solution for the stress tensor of a near-wall stagnation-point flow for the Oldroyd-B model is also obtained. Its compatibility with the momentum conservation is discussed and the parameters are identified, which allow for a non-singular solution. |
| first_indexed | 2024-03-10T09:19:18Z |
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| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T09:19:18Z |
| publishDate | 2021-07-01 |
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| spelling | doaj.art-e4df65a09ab84dcca6f3732db714089e2023-11-22T05:21:48ZengMDPI AGApplied Sciences2076-34172021-07-011115693110.3390/app11156931Analytical Investigation of Viscoelastic Stagnation-Point Flows with Regard to Their SingularityJie Liu0Martin Oberlack1Yongqi Wang2Chair of Fluid Dynamics, Department of Mechanical Engineering, Technical University of Darmstadt, Otto-Berndt-Str. 2, 64287 Darmstadt, GermanyChair of Fluid Dynamics, Department of Mechanical Engineering, Technical University of Darmstadt, Otto-Berndt-Str. 2, 64287 Darmstadt, GermanyChair of Fluid Dynamics, Department of Mechanical Engineering, Technical University of Darmstadt, Otto-Berndt-Str. 2, 64287 Darmstadt, GermanySingularities in the stress field of the stagnation-point flow of a viscoelastic fluid have been studied for various viscoelastic constitutive models. Analyzing the analytical solutions of these models is the most effective way to study this problem. In this paper, exact analytical solutions of two-dimensional steady wall-free stagnation-point flows for the generic Oldroyd 8-constant model are obtained for the stress field using different material parameter relations. For all solutions, compatibility with the conservation of momentum is considered in our analysis. The resulting solutions usually contain arbitrary functions, whose choice has a crucial effect on the stress distribution. The corresponding singularities are discussed in detail according to the choices of the arbitrary functions. The results can be used to analyze the stress distribution and singularity behavior of a wide spectrum of viscoelastic models derived from the Oldroyd 8-constant model. Many previous results obtained for simple viscoelastic models are reproduced as special cases. Some previous conclusions are amended and new conclusions are drawn. In particular, we find that all models have singularities near the stagnation point and most of them can be avoided by appropriately choosing the model parameters and free functions. In addition, the analytical solution for the stress tensor of a near-wall stagnation-point flow for the Oldroyd-B model is also obtained. Its compatibility with the momentum conservation is discussed and the parameters are identified, which allow for a non-singular solution.https://www.mdpi.com/2076-3417/11/15/6931viscoelastic modelsstagnation-point flowstress singularitiesWeissenberg numbers |
| spellingShingle | Jie Liu Martin Oberlack Yongqi Wang Analytical Investigation of Viscoelastic Stagnation-Point Flows with Regard to Their Singularity Applied Sciences viscoelastic models stagnation-point flow stress singularities Weissenberg numbers |
| title | Analytical Investigation of Viscoelastic Stagnation-Point Flows with Regard to Their Singularity |
| title_full | Analytical Investigation of Viscoelastic Stagnation-Point Flows with Regard to Their Singularity |
| title_fullStr | Analytical Investigation of Viscoelastic Stagnation-Point Flows with Regard to Their Singularity |
| title_full_unstemmed | Analytical Investigation of Viscoelastic Stagnation-Point Flows with Regard to Their Singularity |
| title_short | Analytical Investigation of Viscoelastic Stagnation-Point Flows with Regard to Their Singularity |
| title_sort | analytical investigation of viscoelastic stagnation point flows with regard to their singularity |
| topic | viscoelastic models stagnation-point flow stress singularities Weissenberg numbers |
| url | https://www.mdpi.com/2076-3417/11/15/6931 |
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