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On the origin of viscoelastic Taylor-Couette instability resulted from normal stress differences

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Abstract

In this paper, the effect of normal stress differences on the viscoelastic Taylor-Couette instability is studied numerically. The governing equations are discretized using FTCS finite difference method on a staggered mesh based on the artificial compressibility algorithm. Using the CEF model as the constitutive equation and the Carreau-Yasuda model as the viscometric functions, the flow between rotating cylinders has been studied for a range of radius ratios, Taylor numbers and rheological properties. It is shown that increasing the first normal stress difference destabilizes the flow field while increasing the negative second normal stress difference stabilizes the flow field. The main contribution of the current study is an answer to this question: How do the first and second normal stress differences affect the stability of viscoelastic flow between rotating cylinders? For this reason, we used the order of magnitude technique to obtain a force balance relation in the core region of flow. Based on this relation and numerical simulation, the origin of viscoelastic Taylor-Couette instability resulted from normal stress differences are studied in detail. Furthermore, a two dimensional analytical solution for the main flow velocity component between finite rotating cylinders is carried out considering the end effect of stationary walls.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran

    M. Norouzi, M. H. Sedaghat & M. M. Shahmardan

  2. Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran

    M. R. H. Nobari

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  1. M. Norouzi
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  2. M. H. Sedaghat
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  3. M. M. Shahmardan
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  4. M. R. H. Nobari
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Correspondence to M. Norouzi.

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Norouzi, M., Sedaghat, M.H., Shahmardan, M.M. et al. On the origin of viscoelastic Taylor-Couette instability resulted from normal stress differences. Korea-Aust. Rheol. J. 27, 41–53 (2015). https://doi.org/10.1007/s13367-015-0006-z

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  • DOI: https://doi.org/10.1007/s13367-015-0006-z

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