Flow of the Bingham-Papanastasiou Regularized Material in a Channel in the Presence of Obstacles: Correlation between Hydrodynamic Forces and Spacing of Obstacles

Abstract

The numerical modeling and simulation for the stationary Bingham fluid flow around two confined circular cylinders with various gap ratios are studied. The singularity in the model’s apparent viscosity is dealt by Papanastasiou’s regularization. The model equations are discretized by adopting the methodology based on finite element method (FEM) by choosing a mixed higher order LBB-stable P 2 − P 1 finite element pair. The direct solver PARADISO has been utilized to solve the linearized system of equations. Hydrodynamic forces represented by drag and lift coefficients are computed, and a correlation coefficient is calculated for the gap ratios 0.1 ≤ G p ≤ 0.3 and for several values of the Bingham number 0 ≤ B n ≤ 50 . Line graphs for horizontal and vertical velocities are drawn. Moreover, velocity and pressure profiles are plotted for pertinent values of the parameters. Plug and shear zones are revealed via velocity snapshots in the domain. Pressure is nonlinear in the vicinity of the obstacles and becomes linear downstream in the cylinders as expected in channel flows.

Features of the power-law fluid over cylinders in a channel via gap aspects: Galerkin finite element method (GFEM)-based study

“…According to Table 2, when the gap spacing is exceeded, not only does the number of domain elements but also the number of boundary elements grow from G p 0.1 to G p 0.3, which is a computed conclusion. The numerical scheme (FEM) for the numerous approximations of the Navier stokes equation with the hybrid grid was generated on a very high refinement level and also criteria of convergence for non-linear iteration, which is already described in [29][30][31][32][33][34][35][36]. Table 3 provides specifics on a number of different meshing levels that can occur in a flow pattern that includes a circular cylinder.…”

Computational Analysis of Fluid Forces on an Obstacle in a Channel Driven Cavity: Viscoplastic Material Based Characteristics

“…In this direction, the conforming element pair P 2 − P 1 is selected for the velocity and pressure approximations. This element is a stable pair satisfying the inf-sup condition [40][41][42][43]. Newton's method is applied to solve discrete nonlinear algebraic systems, and the inner linear subproblems are solved using a direct solver.…”

“…Due to the high nonlinearity of the model, exact solutions to such problems are rare; therefore, we apply FEM computation for the numerical approximation of the governing equations. In this direction, the conforming element pair ℙ 2 − ℙ 1 is selected for the velocity and pressure approximations This element is a stable pair satisfying the inf-sup condition [40][41][42][43]. Newton's method is applied to solve discrete nonlinear algebraic systems, and the inner linear subproblems are solved using a direct solver.…”

Statistical Analysis of Hydrodynamic Forces in Power-Law Fluid Flow in a Channel: Circular Versus Semi-Circular Cylinder

“…Among many numerical tools reported in the literature to deal with the mechanics of fluid flow, the finite element method (FEM) is the prominent one. The functionality of the finite element method and the mathematical modeling for our problem is described in references [36][37][38][39][40][41][42].…”