Numerical study of two-dimensional steady incompressible laminar flow over a backward-facing step at moderate reynolds number

This thesis describes the application of computational techniques to numerically investigate the 2D steady incompressible laminar flow over a backward-facing step moderate range of Reynolds number. This study comprisestwo parts; the influence of under relaxation factors (URFs) on convergence characteristics of solution for the transport equation and velocities (x- and z- directions) for the URFs values between 0.05 and 1.0 was examined. In the first part of study, a model of sudden expansionhannel was constructed and simulations were performed by using PHOENICS;a Computational Fluid Dynamics (CFD) software. The values of error percentage of pressure and velocities variables of 430 simulations have been tabulated. Based on these values, graphical technique was applied to determine the best combinations of URFs for momentum and pressure correction equations have been conducted by concentrating on convergence criteria less than 1 x 10-6 and the assessment of interpolation solution for convective and diffusive terms in the transport equation. We found that for upbetween 0.1 and 1.0, the best combined URFs for velocities is between 0.1 to 0.5 to achieve lower err (p) within shorter time period. Meanwhile, to achieve lower err (w) during the computation, the URFs are between 0.6 and 0.8.We also found that the recommended values of u p to achieve lower err (u) during the computation are between 0.6 and 1.0.In this second part of study, a model of sudden expansion channel based on Erturk (2008) has been constructed. The stream linescontours of each simulation have been plotted and main recirculation complex have been identified. The locations of the separation and reattachment points in the main reattachment zone and other recirculation zones on the bottom and upper surfaces of the sudden expansion channel were quantitatively determined. For range of Reynolds numbers between 100 and 3000, HYBRID and UPWIND schemes have been used and 60 simulations were performed. At lower range of Reynolds number between 100 and 500, 12nonlinear schemes based on QUICK, FROMM and CUS scheme used to perform simulation and the streamlines of each simulation have been plotted and their main reattachment zone and other separation and reattachment zones were compared. The schemes used in this second part of study are SMART, HQUICK,UMIST, CHARM, VAN1, VAN2, OSPRE, VANALB, SUPBEE, MINMOD,KOREN and HCUS. It was found that the length of main reattachment zone is increasing when the Reynolds number is increased gradually from 100 to 1200. For beyond of Re = 1200, the flow exhibits more complex flow structure.

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