Bingham fluid flow simulation in a lid-driven skewed cavity using the finite-volume method

ABSTRACT

In this paper, laminar flow of non-Newtonian (Bingham) fluid is studied numerically in a two-dimensional lid-driven skewed cavity that incorporates Papanastasiou exponential regularization approach of Bingham constitutive model [Papanastasiou, Flows of materials with yield, J. Rheol. 31 (1987), pp. 385–404]. Numerical simulation has been done using the finite-volume method with collocated grid arrangement. The governing equations including continuity and momentum are initially non-dimensionalized using appropriate transformation. To simulate irregular shape cavity flow problem, body-fitted non-orthogonal grids are used, and governing equations have been transformed to generalized curvilinear co-ordinates. In this study, two dimensionless parameters namely, Reynolds number and Bingham number are considered. A wide range of skew angles are considered which comprises both acute and obtuse angles. The obtained results are presented in terms of velocity and streamlines with yielded/unyielded region for different values of Bingham number and Reynolds number having different angles of the skewed cavity. The present results may be serve as benchmark results for comparison purpose in the case of non-Newtonian (Bingham) fluid flow.

KEYWORDS:

• Non-Newtonian fluid
• skewed cavity
• Bingham fluid model
• finite-volume method
• curvilinear co-ordinates
• non-orthogonal mesh

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 76Axx
• 76Dxx

Acknowledgments

The first author gratefully acknowledges the Government of the People's Republic of Bangladesh for providing the financial support for completing her PhD during 2017–2019. She also thanks to the ‘Center for Scientific Computing’ of the North South University (NSU) for using the computational facility. The second author would like to thank the PGI group for providing the University developer licence of ‘PGI Accelerator Fortran/C/C++ compiler for a Workstation in Linux’. We wish to thank the anonymous reviewer for helping us to plot the correct shapes of yielded and unyielded zones in Figures 9–12.

Disclosure statement

No potential conflict of interest was reported by the authors.