Finite element simulations of Herschel–Bulkley visco-plastic materials over a cylinder: Drag and lift correlation analysis

Abstract

This study employs a two-dimensional and incompressible flow of Herschel–Bulkley visco-plastic materials in order to investigate the hydrodynamic forces that are acting on a barrier that is located close to the inlet of a channel. As the benchmark configuration, the flow domain that has been selected is a channel that still contains the impediment. The two important parameters of the Herschel–Bulkley Model (HBM) are the yield stress [Formula: see text] and power law index n. Obtaining special situations within the HBM, such as Newtonian, power-law, and Bingham fluids, can be accomplished by assigning certain values to these parameters at the appropriate times. Utilizing a numerical strategy grounded in the Finite Element Method (FEM), we tackle the nonlinearity of the governing equations as well as the viscosity models. As a result of this nonlinearity, FEM becomes an essential tool. The generation of a refined hybrid mesh is done in order to guarantee accuracy in the computations. The stable finite element pair ([Formula: see text]) has been selected for discretization purposes. The discretized nonlinear system is linearized with Newton’s method and subsequently, a direct linear solver PARDISO has been employed in the inner iterations. The pressure, velocity, and viscosity profiles are plotted for various values of n and Bingham number (Bn). In addition, the velocity behavior is observed along the y-direction in a channel through line graphs. Code validation is done as a special case [Formula: see text] and a good agreement is found with the results available in the literature. Finally, a correlation analysis has been performed for the drag coefficient [Formula: see text] and lift coefficient [Formula: see text].