Numerical study of low Reynolds hybrid discretized convergent-divergent (CD) channel rooted with obstructions in left/right vicinity of CD throat

Abstract

Installing obstructions in the path of the flowing stream in a Convergent-Divergent channel results in complex Reynolds Navier-Stokes (NS)-equations and an exact solution in this direction is not feasible. The current work is a notable attempt in this direction, reporting the evaluation of hydrodynamic forces faced by case-wise installation of infinite cylinders as obstacles to a continuous fluid stream. To be more specific, Newtonian fluid is initiated from inlet with bound of parabolic profile. The outlet of CD channel is carried with Neumann condition. The optimized path of installation of obstacle includes: (i) Two circular shaped cylinders are installed in left and right vicinity of CD throat (ii) Circular cylinder in right vicinity of CD throat is optimized with square cylinder (iii) Circular cylinder in left vicinity of CD throat is optimized with square cylinder. The flow field is mathematically modelled in terms of steady Reynolds NS-equations. The comparative solution is reported by using finite element method along rectangular and triangular elements as a hybrid meshing scheme. The obtained outcomes are shared by means of contour and line graphs. Optimized values of hydrodynamic forces subject to installed obstacles in convergent-divergent channel are reported by doing line integration around the outer surfaces of obstructions. It is observed that in each case, the obstructions in left vicinity of CD throat admits inciting values of drag coefficient as compared to obstruction rooted in right vicinity of CD throat.

Keywords

• Convergent-divergent
• Channel
• Circular/square obstructions
• Newtonian stream
• Drag and lift forces
• Hybrid meshing