Finite element simulations for stationary Bingham fluid flow past a circular cylinder

Abstract

This paper presents the stationary Bingham fluid flow simulations past a circular cylinder placed in a channel. The governing equations of motion are discretized using the mixed finite element method. The biquadratic element Q 2 is used to approximate the velocity space and P 1 disc for the pressure space. This LBB-stable finite element pair Q 2 =P disc 1 leads to an accuracy of third and second order in L 2-norm for velocity and pressure approximations, respectively. The discrete version of the nonlinear system is linearized by the Newton's method, and the linear subproblems as an inner loop are coped with UMFPACK solver. Code validation and grid independence study is also presented to confirm the reliability of the results. Simulations are carried out for various values of dimensionless Bingham number Bn, and its impact is investigated with great detail by demonstrating the velocity, viscosity and pressure contours. The benchmark quantities like drag coefficient (C D) and lift coefficient (C L) are also discussed graphically and quantitatively. Moreover, two different locations of the circular cylinder are considered for the analysis of hydrodynamic forces.

Finite Element Analysis on Bingham–Papanastasiou Viscoplastic Flow in a Channel with Circular/Square Obstacles: A Comparative Benchmarking

“…After having done the code validation, further parametric study for Bingham number is performed for the case of square cylindrical obstacle and quantities of interest are computed and a quantitative comparison is tabulated against circular obstacle case given in [33].…”

Numerical Computation of MHD Thermal Flow of Cross Model over an Elliptic Cylinder: Reduction of Forces via Thickness Ratio

“…e code has also been validated for steady flow in order to strengthen the reliability of the results to be achieved for the proposed study. Finally, the current code has also been validated against the study by Mahmood et al [31] in Table 4.…”

“…In recent decades, three-dimensional numerical simulation of a variety of physical issues seems to have become widespread with the invention of fast, multiprocessor personal computers, including simple computer cluster management. It was noted that information still scarce is available in the literature in non-Newtonian fluid flows, especially polymer melts in molding process are evaluated in [26][27][28][29][30][31][32].…”

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

“…The materials like toothpaste and tomato ketchup are yield stress oriented. The rheology of such is investigated by many researchers [18][19][20][21][22][23][24]. There are some recent discussion and hypothesis about the existence of yield stress.…”