Liu, Jie ; Oberlack, Martin ; Wang, Yongqi (2022)
Analytical Investigation of Viscoelastic Stagnation-Point Flows with Regard to Their Singularity.
In: Applied Sciences, 2022, 11 (15)
doi: 10.26083/tuprints-00021231
Artikel, Zweitveröffentlichung, Verlagsversion
 | Es ist eine neuere Version dieses Eintrags verfügbar. |
Kurzbeschreibung (Abstract)
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.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2022 |
| Autor(en): | Liu, Jie ; Oberlack, Martin ; Wang, Yongqi |
| Art des Eintrags: | Zweitveröffentlichung |
| Titel: | Analytical Investigation of Viscoelastic Stagnation-Point Flows with Regard to Their Singularity |
| Sprache: | Englisch |
| Publikationsjahr: | 2022 |
| Publikationsdatum der Erstveröffentlichung: | 2022 |
| Verlag: | MDPI |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Applied Sciences |
| Jahrgang/Volume einer Zeitschrift: | 11 |
| (Heft-)Nummer: | 15 |
| Kollation: | 17 Seiten |
| DOI: | 10.26083/tuprints-00021231 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/21231 |
| Zugehörige Links: | |
| Herkunft: | Zweitveröffentlichung aus gefördertem Golden Open Access |
| Kurzbeschreibung (Abstract): | 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. |
| Status: | Verlagsversion |
| URN: | urn:nbn:de:tuda-tuprints-212315 |
| Zusätzliche Informationen: | This article belongs to the Special Issue Viscoelasticity: Mathematical Modeling, Numerical Simulations, and Experimental Work Keywords: viscoelastic models; stagnation-point flow; stress singularities; Weissenberg numbers |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 600 Technik, Medizin, angewandte Wissenschaften > 600 Technik |
| Fachbereich(e)/-gebiet(e): | 16 Fachbereich Maschinenbau 16 Fachbereich Maschinenbau > Fachgebiet für Strömungsdynamik (fdy) DFG-Sonderforschungsbereiche (inkl. Transregio) DFG-Sonderforschungsbereiche (inkl. Transregio) > Sonderforschungsbereiche DFG-Sonderforschungsbereiche (inkl. Transregio) > Sonderforschungsbereiche > SFB 1194: Wechselseitige Beeinflussung von Transport- und Benetzungsvorgängen DFG-Sonderforschungsbereiche (inkl. Transregio) > Sonderforschungsbereiche > SFB 1194: Wechselseitige Beeinflussung von Transport- und Benetzungsvorgängen > Projektbereich B: Modellierung und Simulation DFG-Sonderforschungsbereiche (inkl. Transregio) > Sonderforschungsbereiche > SFB 1194: Wechselseitige Beeinflussung von Transport- und Benetzungsvorgängen > Projektbereich B: Modellierung und Simulation > B06: Verfahren höherer Ordnung für die direkte numerische Simulation von Be- und Entnetzungsproblemen auf Basis der Discontinuous Galerkin Methode Profilbereiche Profilbereiche > Thermo-Fluids & Interfaces |
| Hinterlegungsdatum: | 09 Mai 2022 12:07 |
| Letzte Änderung: | 10 Mai 2022 05:18 |
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- Analytical Investigation of Viscoelastic Stagnation-Point Flows with Regard to Their Singularity. (deposited 09 Mai 2022 12:07) [Gegenwärtig angezeigt]
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