MATHEMATICAL MODELLING OF NEWTONIAN FLUIDS FLOW PHENOMENA THROUGH DIFFERENT RATIOS OF BACKWARD STEP DUCT

Abstract

The COMSOL Multi Physics CFD package is chosen here to develop the numerical 
model called as Galerkin least square finite element method and compute the steady state 
solution of the governing equations such as continuity and momentum equations in 
Cartesian coordinates form. The Newtonian fluid transported into the backward step duct 
with different aspect ratios (1: 6 and 1: 12) and change in characteristics length to 
observe the streamline patterns of the velocity, vortex enhancement on the basis of fluid 
inertia and vortex intensity. The research problem has vast application in the field of 
industries particularly to design the shapes of the rectangular tanks and observe the flow 
phenomena either compressible (gases) or incompressible (liquids). The streamline 
patterns are observed on different Reynolds number (01 to 600) and various ratios (1:6 
and 1:12) of the backward step duct. Two vortices primary (lower left corner) and 
secondary (upper right corner) are visualized at various Reynolds numbers. At low 
Reynolds number (01), only primary vortex observed at the left lower corner of the 
backward step duct in both ratios. But due to growing Reynolds number, the primary 
vortex is increased largely in size but the secondary vortex increased also but very slowly 
in size. The primary vortex size is highly observed in the left lower silent corner of the 
backward step duct in the ratio 1:12 other than the ratio 1:6. Also, vortex intensity and 
vortex lengths plots justified the same enhancement due to growing the Reynolds 
number. Further, computed the empirical equations on the vortex intensity with various 
Reynolds numbers. The numerical results are compared with the available mathematical 
solutions by the use of CFD packages such as Flow 3D, ANSYS and others.