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

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:msub><a:mrow><a:mi>P</a:mi></a:mrow><a:mrow><a:mn>2</a:mn></a:mrow></a:msub><a:mo>−</a:mo><a:msub><a:mrow><a:mi>P</a:mi></a:mrow><a:mrow><a:mn>1</a:mn></a:mrow></a:msub></a:math> 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"><c:mfenced open="(" close=")"><c:mrow><c:mn>0.1</c:mn><c:mo>≤</c:mo><c:msub><c:mrow><c:mi>G</c:mi></c:mrow><c:mrow><c:mi>p</c:mi></c:mrow></c:msub><c:mo>≤</c:mo><c:mn>0.3</c:mn></c:mrow></c:mfenced></c:math> and for several values of the Bingham number <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" id="M3"><g:mfenced open="(" close=")"><g:mrow><g:mn>0</g:mn><g:mo>≤</g:mo><g:msub><g:mrow><g:mi>B</g:mi></g:mrow><g:mrow><g:mi>n</g:mi></g:mrow></g:msub><g:mo>≤</g:mo><g:mn>50</g:mn></g:mrow></g:mfenced></g:math> . 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.