In the current work, an investigation has been carried out for the Bingham fluid flow in a channel-driven cavity with a square obstacle installed near the inlet. A square cavity is placed in a channel to accomplish the desired results. The flow has been induced using a fully developed parabolic velocity at the inlet and Neumann condition at the outlet, with zero no-slip conditions given to the other boundaries. Three computational grids, C1, C2, and C3, are created by altering the position of an obstacle of square shape in the channel. Fundamental conservation and rheological law for viscoplastic Bingham fluids are enforced in mathematical modeling. Due to the complexity of the representative equations, an effective computing strategy based on the finite element approach is used. At an extra-fine level, a hybrid computational grid is created; a very refined level is used to obtain results with higher accuracy. The solution has been approximated using P2 − P1 elements based on the shape functions of the second and first-order polynomial polynomials. The parametric variables are ornamented against graphical trends. In addition, velocity, pressure plots, and line graphs have been provided for a better physical understanding of the situation Furthermore, the hydrodynamic benchmark quantities such as pressure drop, drag, and lift coefficients are assessed in a tabular manner around the external surface of the obstacle. The research predicts the effects of Bingham number (Bn) on the drag and lift coefficients on all three grids C1, C2, and C3, showing that the drag has lower values on the obstacle in the C2 grid compared with C1 and C3 for all values of Bn. Plug zone dominates in the channel downstream of the obstacle with augmentation in Bn, limiting the shear zone in the vicinity of the obstacle.

The reliability of the usage of a splitter plate (passive control device) downstream of the obstacle, in suppressing the fluid forces on a circular obstacle of diameter $$D = 0.1\;\;{\text{m}}$$ D = 0.1 m is studied in this paper. The first parameter of the current study is the attachment of a splitter plate of various lengths $$(L_{i} )$$ ( L i ) with the obstacle, whereas the gap separation $$(G_{i} )$$ ( G i ) between the splitter plate and the obstacle, is used as a second parameter. The control elements of the first and second parameters are varied from $$0.1$$ 0.1 to $$0.3$$ 0.3 . For the attached splitter plates of lengths $$0.2$$ 0.2 and $$0.3$$ 0.3 , the oscillatory behavior of transient flow at $$Re = 100$$ R e = 100 is successfully controlled. For the gap separation, $$0.1$$ 0.1 and $$0.2$$ 0.2 similar results are obtained. However, it is observed that a splitter plate of too short length and a plate located at the inappropriate gap from the obstacle, are worthless. A computational strategy based on the finite element method is utilized due to the complicated representative equations. For a clear physical depiction of the problem, velocity and pressure plots have been provided. Drag and lift coefficients the hydrodynamic benchmark values are also evaluated in a graphical representation surrounding the obstacle’s peripheral surface as well as the splitter plate. In a conclusion, a splitter plate can function to control fluid forces whether it is attached or detached, based on plate length and gap separation between obstacle and plate, respectively.

Hydrodynamic forces are crucial in engineering applications; therefore, various research initiatives have been conducted to limit them. In this research, a passive control technique to investigate the fluid forces acting on a circular cylinder in a laminar flow regime is studied. The reliability of the usage of a splitter plate (passive control device) downstream of the obstacle in suppressing the fluid forces on a circular obstacle of diameter D=0.1 is presented. The first parameter of the current study is the attachment of splitter plates of various lengths (Li)with the obstacle, whereas the gap separation (Gi) between the splitter plate and the obstacle is used as a second parameter. The control element of the first and second parameters are varied from 0.1 to 0.3. For the attached splitter plates of lengths 0.2 and 0.3, the oscillatory behavior of transient flow at Re=100 is successfully controlled. For the gap separations 0.1 and 0.2, the suppression of vortex shedding is also observed. However, it is observed that a splitter plate of too short length and a plate located at an inappropriate gap from an obstacle are worthless. Moreover, the present study is extended for power-law fluid in the same domain, and maximum drag reduction is achieved using the same strategy as for Newtonian fluid. The finite element method is utilized as a computational strategy for complicated nonlinear governing equations. For a clear physical depiction of the problem, velocity and pressure plots have been provided. It is concluded that the presence of a splitter plate has suppressed the vortex shedding and the flow regime turns out to be steady, as is evident from the nonoscillatory drag and lift coefficients.

The current work is an analysis of the laminar, two-dimensional, and transient flow over a circular cylinder with a two-branched splitter plate. For complex nonlinear governing equations, the finite element method is used as a computational approach. The objective of the current study is to determine the best conditions using geometrical characteristics along with the impact of Reynolds number R e .The geometric parameters, α which is the angle of separation between the pair of splitter plates of length L and G / D which is the gap from diameter ratio of the splitter plate to cylinder diameter, are the controlling tools for the present study. Due to its little impact on flow characteristics, it was discovered that using a two-branched splitter plate in Reynolds numbers under 100 is not desirable. A complete vortex shedding has been achieved with α = 0 ° and G / D = 2 at R e = 100 and also the periodic behavior of velocity has been controlled. The least drag force is observed at an angle of 30 ° between the two plates compared to another angle of 0 ° . It is not advised to use two splitter plates at angles more than 30 ° because this will not further contribute in the drag reduction. Since the gap to diameter ratio between the splitter plates and the cylinder increased up to a significant value, the overall control on hydrodynamic effects is achieved. It is concluded that the maximum drag reduction of 48% over the cylinder has taken place when the R e   i s   200 , α   i s   30 ° , a n d   G / D   i s   2 .