Numerical study of hydrodynamic forces of nonlinear fluid flow in a channel-driven cavity: Finite element-based simulation

This communication is aimed at presenting the flow behavior of viscoplastic materials in a channel driven-cavity by utilizing the Bingham constitutive equation in conjunction with the modification proposed by Papanastasiou. The whole system has been represented by a model consisting of coupled nonlinear partial differential equations. In addition, the governing equations were nondimensionalized by making use of the appropriate set of variables and the computations were carried out using the finite element method. A finite element space including quadratic polynomial DOUBLE-STRUCK CAPITAL P-2 is chosen for the approximation of velocity profiles whilst a space containing linear polynomials is used for the estimation of pressure DOUBLE-STRUCK CAPITAL P-1. The hydrodynamics forces like drag and lift values on cylindrical obstacle whose center is located at (1.5, 1.5) are computed against various values of Bingham number. Moreover, pressure drop values between the back and front of the square obstacle have also been tabulated.

Automated summary

This study presents the flow behavior of viscoplastic materials in a channel driven-cavity using the Bingham constitutive equation with the modification proposed by Papanastasiou. A model consisting of coupled nonlinear partial differential equations is used to represent the system. The governing equations are nondimensionalized and the computations are carried out using the finite element method. The drag and lift values on a cylindrical obstacle and the pressure drop values across a square obstacle are computed and tabulated for different Bingham numbers.