The aim of this study is to develop a two-dimensional pressure-based Navier-Stokes solver for incompressible/compressible flows. Main variables are Cartesian velocity components, pressure and temperature while density is linked to pressure via equation of state. Modified SIMPLE algorithm is used to achieve pressure-velocity coupling. Finite Volume discretisation is performed on non-orthogonal and boundary-fitted grids. Collocated variable arrangement is preferred because of its advantage on staggered arrangement in non-orthogonal meshes. Face velocities are calculated using Rhie-Chow momentum interpolation scheme to avoid pressure checkerboarding effect. The solver is validated by solving a number of benchmark problems.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2016-08-10T13:09:08Z No. of bitstreams: 2 Dissertação - Adriana Batista da Silva - 2016.pdf: 3286914 bytes, checksum: 7be43fd6757af8224a3358e36202f297 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-08-10T13:12:09Z (GMT) No. of bitstreams: 2 Dissertação - Adriana Batista da Silva - 2016.pdf: 3286914 bytes, checksum: 7be43fd6757af8224a3358e36202f297 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-08-10T13:12:09Z (GMT). No. of bitstreams: 2 Dissertação - Adriana Batista da Silva - 2016.pdf: 3286914 bytes, checksum: 7be43fd6757af8224a3358e36202f297 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-04-29 / Financiadora de Estudos e Projetos- Finep / Linear Programming is an operational search tool applied to problem solving aimed at the optimization of a study system. This study aims to show some applications of linear programming and how it can be used as a motivating teaching skills of Mathematics in High school. We will cover two methods of linear programming problems resolution, Graphics resolution method and the algebraic solution way, which is the Simple Method. We so decided to solve under the assistance of these two methods quoted, optimization problems with two or three variables, since the problems with multiple variables do not match the curriculum of mathematics for high school. We suggest the use of two free applications for mobile phones, to solve optimization problems with several variables, in order to contribute in a di erent approach, seeking to boost in students, interest in the study of mathematics. / A Programação Linear é uma ferramenta da Pesquisa Operacional aplicada à solução de problemas que objetivam a otimização de um sistema de estudo. O presente trabalho busca mostrar algumas aplicações da Programação Linear e como ela pode ser utilizada como elemento motivador no ensino da Matemática no Ensino Médio. Abordaremos dois métodos de resolução de problemas de Programação Linear, o método de Resolução Grá ca e a forma algébrica de solução que é o Método Simplex. Vamos solucionar com auxílio desses dois métodos citados, problemas de otimização com duas e três variáveis, já que problemas com várias variáveis não se adequam a matriz curricular de Matemática para o Ensino Médio. Sugerimos a utilização de dois aplicativos gratuitos para celulares, que solucionam problemas de otimização com várias variáveis como forma de contribuir com uma abordagem diferente, visando despertar no aluno, o interesse pelo estudo da Matemática.

A method to solve the Navier-Stokes equations for incompressible viscous flows is proposed. This method is SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm to iteratively solve the two-dimensional laminar steady momentum equations and based upon finite volume method on staggered grids. Numerical tests are performed on several cases of the flow in the lid-driven cavity, as well as of the flow after a backward-facing step with SIMPLE and SIMPLER (SIMPLE Revised) methods. Finally, results are compared qualitatively and quantitatively with numerical and experimental results available in the literature for different Reynolds numbers to validate the methods.

The modern gas turbine engine industry needs a simpler and faster method to facilitate the design of gas turbine combustors due to the enormous costs of experimental test rigging and detailed computational fluid dynamics (CFD) simulations. Therefore, in the initial design phase, a couple of preliminary designs are conducted to establish initial values for combustor performance and geometric characteristics. In these preliminary designs, various one-dimensional models using analytical and empirical formulations may be used. One of the disadvantages of existing models is that they are typically geometric dependant, i.e. they apply only to the geometry they are derived for. Therefore the need for a more versatile design tool exists. In this work, which constitutes the first step in the development of such a versatile design tool, a single equation-set network simulation model to describe both steady state compressible and incompressible isothermal flow is developed. The continuity and momentum equations are solved through a hybrid type network model analogy which makes use of the SIMPLE pressure correction methodology. The code has the capability to efficiently compute flow through elements where the loss factor K is highly flow dependant and accurately describes variable area duct flow in the case of incompressible flow. The latter includes ducts with discontinuously varying flow sectional areas. Proper treatment of flow related non-linearities, such as flow friction, is facilitated in a natural manner in the proposed methodology. The proposed network method is implemented into a Windows based simulation package with a user interface. The ability of the proposed method to accurately model both compressible and incompressible flow is demonstrated through the analyses of a number of benchmark problems. It will be shown that the proposed methodology yields similar or improved results as compared to other’s work. The proposed method is applied to a research combustor to solve for isothermal flows and flow splits. The predicted flows were in relatively close agreement with measured data as well as detailed CFD analysis. / Dissertation (MEng (Mechanical Engineering))--University of Pretoria, 2005. / Mechanical and Aeronautical Engineering / unrestricted