Abstract
The recirculation which is developed during the flows inside pipes present a high interest in many industrial applications. In the present paper, a Cartesian grid method is presented which can be applied in pipes geometry approximation, even if the solid bounds are not lying on grid lines. A refinement technique using rectangular nested sub-girds is applied in order to avoid the unnecessary grid cells in the areas with no particular flow interest and cluster the grid when is needed. Important and useful for the industries results are extracted by these numerical simulations and estimations regarding the exact position and extend of the recirculation zones and the relating points. The estimation is taking placefor incompressible laminar, viscous flows inside inclined step channelsfor a range of inclination angles and Reynolds numbers values. The Navier – Stokes equations are solved using the artificial compressibility method according to the necessary boundary conditions arrangement. Flow results are presented for several grid sizes and Reynolds numbers focused on the recirculationzones length, in upper and lower channel’ walls. Accepted accuracy of the flow results is produced using the aforementioned refinement algorithm, while the flow zones can be located according to the inlet flow rate, in order to avoid possible problems in the industries as corrosion or energy losses.
Highlights
The computational models are flexible tools for the industrial flow applications as useful results can be extracted for the optimization of the production line
The flow characteristics, variables distribution, certain data information and points of upper and lower bound separation zones have been analytically presented for various values of Re
For the physical domain discretization, we use Cartesian grids, despite of the non-Cartesian bounds existence and in order to overcome the high computational memory which is needed due to the grid cells number and reduce the computational time without decreasing the accuracy of the solution, we develop a block-nested refinement algorithm, which can be applied to the channel flow domain
Summary
The computational models are flexible tools for the industrial flow applications as useful results can be extracted for the optimization of the production line. In many channels’ flow simulation and estimation cases, the uniform Cartesian grid requires high computational memory without any benefit to the accuracy of the results. The main results are not limited only to velocity or pressure distribution, and to locate the exact position of the recirculation zone extend at the upper and lower wall of the channels It is expected such a flow pattern due to the sudden step inside the channels. The grid methodology is developed using only Cartesiangrid lines, which is quite acceptable for such geometries providing robust results [10] This method is based on Tseng approach[11], while it has been already applied successfully for pipe flows prediction in our recent research work [12]. The final results provide acceptable accuracy and have been validated with other computational techniques and literature corresponded ones
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