Variant slip effects, aspect ratios and steady-state criteria in unsteady cavities with direct PDE simulation of eddies

Numerical simulations of an unsteady laminar lid-driven cavity Newtonian flow are executed to demonstrate the formation of eddies under different aspect ratios and steady-state criteria. A couple of nonlinear unsteady partial differential equations (PDEs) of Navier Stokes satisfying a set of boundary conditions is examined with both inclusions of no-slip and free-slip effects. Finite difference method (FDM) is employed to solve the vorticity-stream function using a self-developed Matlab_® code embedded in a Graphical User Interface (GUI) to ease the cavity problem analysis by the end users. Four models are studied where Ansys Fluent_® employing the Finite Element Method (FEM) is used to verify the present FDM steady-state results produced for the first model. It is observed that the value of stream function begins to drop and streamline distribution changes shape when e ≤ 10⁻⁵. Refrainment of merging of secondary eddies also happens when the free-slip boundary condition effect passes the threshold value. The Stretching effect with free-slip BC in the fourth model regulates the fluid dynamics to reach the entire cavity sufficiently with no room for eddy formation by increasing the slip length to an intense value. Free-slip simulates free surface applications in geophysical occurrences (river and glacier), spilling dynamics, ship hull designs, technologies of coating and fuel spraying/injection.