Effect of fluid elasticity on the numerical stability of high-resolution schemes for high shearing contraction flows using OpenFOAM

Abstract

Viscoelastic fluids due to their non-linear nature play an important role in process and polymer industries. These non-linear characteristics of fluid, influence final outcome of the product. Such processes though look simple are numerically challenging to study, due to the loss of numerical stability. Over the years, various methodologies have been developed to overcome this numerical limitation. In spite of this, numerical solutions are considered distant from accuracy, as first-order upwind-differencing scheme (UDS) is often employed for improving the stability of algorithm. To elude this effect, some works been reported in the past, where high-resolution-schemes (HRS) were employed and Deborah number was varied. However, these works are limited to creeping flows and do not detail any information on the numerical stability of HRS. Hence, this article presents the numerical study of high shearing contraction flows, where stability of HRS are addressed in reference to fluid elasticity. Results suggest that all HRS show some order of undue oscillations in flow variable profiles, measured along vertical lines placed near contraction region in the upstream section of domain, at varied elasticity number $E\approx 5$. Furthermore, by $E$, a clear relationship between numerical stability of HRS and $E$ was obtained, which states that the order of undue oscillations in flow variable profiles is directly proportional to $E$.