Study for the computational resolution of conservation equations of mass, momentum and energy using finite volume techniques

Abstract

The following bachelor’s thesis focuses on the numerical resolution of the conservation equations of mass, momentum, and energy. The main objective of the study is to introduce the student to the field of Computational Fluid Dynamics (CFD) by solving several problems proposed by the Heat Transfer Technology Center (CTTC). Each case is simulated through a self-developed code programmed in the C++ language and the corresponding results are verified based on reference data provided by scientific articles. First, both the mathematical formulation and the numerical methods used throughout the work are introduced. In these chapters, the conservation equations are developed and the finite volume method (FVM) is described. Next, the four proposed cases are solved, presented in an orderly manner and following a consistent methodology. Each case includes the theory of the governing equations, the discretization and description of the problem, the algorithm implemented in the programmed code and, finally, the analysis and verification of the results. To conclude, a summary of the budget is included, the environmental implications of the project are described and the final conclusions of the work are presented. The complexity of the problems studied increases progressively, incorporating new concepts as each of them is explored in greater depth. It begins with a simple heat transfer case by conduction, with pure diffusion, and continues with a problem in which the convection term is analyzed by solving the general transport equation. Finally, the numerical resolution of the incompressible Navier-Stokes equations is addressed. This last part is based on the Fractional Step Method (FSM) and includes both a forced convection case, where the fluid motion is induced by boundary conditions, and a natural convection case in which the buoyancy generated by temperature gradients is responsible for the motion.