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

Abstract

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.

Numerical Computation for Modified Cross Model Fluid Flow Around the Circular Cylinder with Symmetric Trapezoidal Cavities

“…Due to the non-linearity of the governing equations as well as of viscosity model fitted through Modified Cross Model, the analytical solution is not possible, so we employed numerical arrangement Finite Element Method (FEM) to compute the approximate solutions [18][19][20][21][22][23][24]. The underlying discrete nonlinear equations have been solved by Newton method and the linearized inner system are solved with a direct solver PARDISO.…”

Effectiveness of splitter plate to control fluid forces on a circular obstacle in a transient flow: FEM computations

“…The stable finite element pair satisfying the inf–sup condition has been utilized. The Newton's iterative process is used to linearize the discrete non-linear systems 34 , 35 . For the solution of linearized system, PARDISO solver 36 is utilized which works for general system and is based on matrix factorization with special reordering of unknowns and reduce the number of iterations required to achieve the desired level of convergence.…”

“…Moreover, all results for the present work are attained by FEM-based simulations. Mahmood et al 34 , 35 have done FEM computation-based study for analysis of the viscous fluid flow characteristics inside a channel idriven-cavity. Also, described the effects of shape function for linear as well as quadratic profiles.…”

Numerical Computations of Entropy Generation and MHD Ferrofluid Filled in a Closed Wavy Configuration: Finite Element Based Study

“…The discrete systems of nonlinear algebraic equations are computed by utilizing the Newton method and the linearized inner system with a direct solver PARDISO. There are many benefits of using the PARDISO solver (see [27][28][29][30][31][32][33][34] for further information).…”