Study for the computational resolution of the conservation equations of mass, momentum and energy. Application to different aeronautical and industrial engineering problems

The following final degree dissertation composes a study of the computational resolution of the Navier-Stokes equations. The objective of the work is to introduce the student to the field of Computational Fluid Dynamic (CFD) simulations. This is done by creating self-made codes able to solve problems proposed by the Heat and Mass Transfer Technological Center (CTTC) of the Polytechnic University of Catalonia (UPC). The equations of mass, momentum and energy are solved by means of the Finite Volume Method (FVM) with an algorithm based on the Fractional Step Method (FSM) for incompressible fluids. All the codes are self-programmed and verified by the student in C++ language. Emphasis is made in understanding the different theoretical and computational implications of the Navier-Stokes equations. The different problems are chosen specifically to treat as many aspects of the incompressible NavierStokes equations as possible. Their difficulty increases progressively, starting from a simple conduction heat transfer problem and ending in the study of turbulence. The contribution of the convective and diffusive terms is deeply analyzed, firstly by solving a pure diffusion case and then by finding the numerical solution of a general convection-diffusion equation. The Fractional Step Method is employed to solve both internal flow (with forced and natural convection) and external flow (around a square cylinder). Different aspects about turbulence are studied and implemented to the resolution of the Burgers equation and a three-dimensional channel flow. To finalize the work, a proposal for future steps is given in relation to a more advanced research project, based on a deeper study of turbulence models and High Performance Computing (HPC).