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Analytical Investigation of Viscoelastic Stagnation-Point Flows with Regard to Their Singularity

Liu, Jie ; Oberlack, Martin ; Wang, Yongqi (2022):
Analytical Investigation of Viscoelastic Stagnation-Point Flows with Regard to Their Singularity. (Publisher's Version)
In: Applied Sciences, 11 (15), MDPI, e-ISSN 2076-3417,
DOI: 10.26083/tuprints-00021231,
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Item Type: Article
Origin: Secondary publication via sponsored Golden Open Access
Status: Publisher's Version
Title: Analytical Investigation of Viscoelastic Stagnation-Point Flows with Regard to Their Singularity
Language: English
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.

Journal or Publication Title: Applied Sciences
Volume of the journal: 11
Issue Number: 15
Publisher: MDPI
Collation: 17 Seiten
Classification DDC: 600 Technik, Medizin, angewandte Wissenschaften > 600 Technik
Divisions: 16 Department of Mechanical Engineering > Fluid Dynamics (fdy)
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 1194: Interaction between Transport and Wetting Processes
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 1194: Interaction between Transport and Wetting Processes > Research Area B: Modeling and Simulation > B06: Higher Order Schemes for Direct Numerical Simulation for Wetting and De-Wetting Problems based on Discontinuous Galerkin Methods
Profile Areas > Thermo-Fluids & Interfaces
Date Deposited: 09 May 2022 12:07
Last Modified: 09 May 2022 12:07
DOI: 10.26083/tuprints-00021231
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-212315
Additional Information:

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

URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/21231
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