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<p>The work investigates numerically the influence of elastic force and polymer concentration on the behavior of two-dimensional viscoelastic flow past a square cylinder. The Oldroyd-B constitutive model is implemented for the characterization of the viscoelastic flow behavior. The coupled conservation and the constitutive equations are solved using a finite volume method in a non-uniform structured collocated grid system. The roles of the Weissenberg number (<i>Wi</i>) and the polymer viscosity ratio (1-<i>β</i>) are studied for the range <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(0 \le Wi \le 5\)</EquationSource> </InlineEquation>, 1-<i>β</i> = 0.01, 0.04, and 0.1 and Reynolds number <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(10 \le {\text{Re}} \le 4\)</EquationSource> </InlineEquation> 0. The elastic force causes suppression of the wake behind the object while the polymer concentration leads to an increase in the stretching strength of the wake. A fully developed flow in a confined domain of blockage ratio 0.1 is considered for the study. It is observed that higher the value of <i>Re</i> and the polymer viscosity (1-<i>β</i>), a lower <i>Wi</i> is required for the wake suppression. The wake behind the square cylinder increases in both lateral and longitudinal directions with an increase of <i>Wi</i> and polymer viscosity ratio (1-<i>β</i>). It is further observed that the influence of polymer viscosity ratio on the flow structure around the cylinder has a significant impact in increasing the wake size and drag force at low <i>Wi</i> and <i>Re</i>.</p> Graphical abstract <p></p>

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Effect of polymer concentration on the wake structure for the viscoelastic flow behind a square cylinder

  • 期刊论文

  • 发表日期：

    2025年12月14日

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  • Om Prakash Pandit,
  • Dipankar Chatterjee,
  • Sourabh Khambra

摘要

The work investigates numerically the influence of elastic force and polymer concentration on the behavior of two-dimensional viscoelastic flow past a square cylinder. The Oldroyd-B constitutive model is implemented for the characterization of the viscoelastic flow behavior. The coupled conservation and the constitutive equations are solved using a finite volume method in a non-uniform structured collocated grid system. The roles of the Weissenberg number (Wi) and the polymer viscosity ratio (1-β) are studied for the range \(0 \le Wi \le 5\) , 1-β = 0.01, 0.04, and 0.1 and Reynolds number \(10 \le {\text{Re}} \le 4\) 0. The elastic force causes suppression of the wake behind the object while the polymer concentration leads to an increase in the stretching strength of the wake. A fully developed flow in a confined domain of blockage ratio 0.1 is considered for the study. It is observed that higher the value of Re and the polymer viscosity (1-β), a lower Wi is required for the wake suppression. The wake behind the square cylinder increases in both lateral and longitudinal directions with an increase of Wi and polymer viscosity ratio (1-β). It is further observed that the influence of polymer viscosity ratio on the flow structure around the cylinder has a significant impact in increasing the wake size and drag force at low Wi and Re.

Graphical abstract