Numerical solutions to laminar flow tranfer in a rectangular duct using non-uniform grids

• Main Authors: You-Wei Lin, 林佑威
• Other Authors: 雷顯宇
• Format: Others
• Language: zh-TW
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/30399959799777754765

碩士 === 國立臺灣海洋大學 === 機械與機電工程學系 === 95 === As technology advances unceasingly, the applications in computational fluid dynamics(CFD) and the capabilities of hardwares such as computers have expanded as well. All these have made reliable analysis of numerical simulation an important tool besides the analytic and experimental method in scientific researches and application of engineering. The number of grids is one of the key factor in numerical method. non-uniformed grids only use denser grids in areas with greater variations in physical properties. This would decrease the computation time and the expenditure of computer resources. Researches in the flow field of rectangular duct started as early as the '70s, however, because of the limitation of computer resources at the time, experiment was the primary method comparing to the analytic method and numerical simulations. Such as Hossian & Raupp[16] & Quadir & Zamir[15] verify the analytical solution of the fully developed flow of rectangular duct mentioned in Berker[9]. This thesis mainly uses the FORTRAN system written by the SIMPLER Algorithm of Patankar. More specifically, it uses the staggered grid in SIMPLER algorithm to simulate the correct 3-D, steady laminar flow with constant wall temperature in a rectangular duct and compares the non-uniform grids and the uniform grids by Fletcher[2] to verify that the non-uniform grids will reach the same solution with less number of grid. The effect of variations in non-uniform grid in flow and temperature field are also studied. The thesis first simulates the cross section of the entrances as a set of 2-D parallel plates, and then tests it with 2 different inlet velocity- fully developed flow and uniform flow. Next, the entrance length and local Nu number are calculated and then compared with related studies and experimental correlation to verify the capability of the specific FORTRAN used. After that, a set of numerical solutions that's accurate enough from the more densely distributed uniform grids is found and set as the standard. Then, it is verified that an equally accurate solution can be attained with a less densely distributed non-uniform grid. Using the advantage of non-uniform grid, do several tests with different Reynold's number in the laminar flow and find the best parameter of α and β (α= 0.1, β= 3.5). Then, plug these values (α and β) into the solution of the temperature field and slightly increasing and decreasing the valued of the parameter. It is found after the above tests that under the same parameter of the non-uniform grid, a large amount of grid can be saved in the flow and temperature field and save computation time while retaining a satisfactory solution. (This thesis supports that saving 80% is the most appropriate in a 3-D steady laminar flow.) The specific program constructed in this thesis provides a basic structure for the flow and temperature field of the non-uniform grid system in a 3-D rectangular duct. It can be expanded to study the effects of obstruction, new thermal boundary condition, and further applied to turbulent flow.