Finite-Volume and Finite-Difference Analysis Using Non-Uniform Grids of the Thermal and Hydrodynamic Entrance in a Parallel-Plate Channel

• Main Author: 范彭閔
• Other Authors: H.Y. Lei
• Format: Others
• Language: zh-TW
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/48149424299363373577

碩士 === 國立臺灣海洋大學 === 機械與機電工程學系 === 99 === The Finite-Volume, Finite-Difference, and Finite-Element Methods are three most widely used numerical simulations in engineering applications. The Finite-Volume Method (FVM) is more commonly used in the field of fluid flow and heat transfer analysis. Each Node of solution is surrounded by a non-overlapping control volume, and integration is performed over the control volume so that conservation (such as: mass, momentum and energy) is achieved in each control volume. The Finite-Difference Method (FDM) uses Taylor series to represent its derivatives in a differential equation, the accuracy is determined from the truncation error of its series expansion. FDM is easy to be understood with less physical meaning. The Patankar's SIMPLER Algorithm for both the FVM and FDM were applied in the solution scheme in order to effectively and quickly calculate the pressure, velocity, and temperature field. Programs written in FORTRAN using uniform and non-uniform grids were run to analyze the fluid flow and heat transfer in a parallel plate channel. Comparisons were made with those of analytical solutions for fully developed flow and thermal entry length problem to verify the advantages of the use of non-uniform grids over those of uniform grids. It was found both the FVM and FDM could lead to correct solutions for fully developed flow and uniform flow inlet problems by comparing results of those analytical solution or empirical formula. Energy equation was also solved numerically for the thermal entry length problem and results were compared with analytical solutions at different Reynolds (Re) and Prandtl (Pr) numbers. The arrangement of non-uniform grids is determined at lower Re by comparison with the results of those uniform grids for the case of combined hydrodynamic and thermal entry length. FVM and FDM programs with non-uniform grids were also run at higher Re up to 2000 in an effort to study the efficiency in computation time and grids. It is found that a saving in grids and computation time up to 95% is possible using non-uniform grids set up. Other non-uniform grids methods (such as Hoffmann) or fluid flow and heat transfer with obstacles in a parallel plate could be explored for the future study. Keywords: Reynolds number, Nusselts Number, Finite-Volume, Finite-Difference, Uniform grids, Non-uniform grids