Numerical simulation of Bingham fluid flows in a lid-driven skewed cavity

Abstract

The laminar flow of viscoplastic fluids inside a lid-driven skewed cavity has been investigated using a numerical scheme based on finite volume method considering Bingham model. Viscoplasticity is characterized by a yield stress, below which the materials behave as solids, and above which they deform and flow according to different constitutive relations. The governing two dimensional unsteady incompressible Navier-Stokes equations were initially non-dimensionalized using appropriate transformation. Then the dimensionless form of these equations is transformed to curvilinear coordinates to simulate complex geometry. The transformed equations are then discretized with appropriate boundary conditions to deal with the non-orthogonal grids. The code is first validated against the existing benchmark results for two-dimensional lid driven square cavity problem considering both Newtonian and non-Newtonian fluids. Then the code is applied to the skewed cavity problem involving non-Newtonian fluid which can be described by the Bingham model. The constitutive equation is regularized as proposed by Papanastasiou [1]. Moreover, grid independence test has been performed for a skewed cavity for different values of Bingham numbers. Reynolds number and Bingham number are two important parameters which can describe the flow behavior of Bingham fluid in the skewed cavity. In this research, the skewness of the geometry has been changed by changing the skew angle. The consequent numerical results are presented in terms of the velocity and streamlines for the different values of Bingham numbers having a different angle of a skewed cavity.