João Marcelo Vedovoto

Mathematical and Numerical Modeling of Turbulent Flows

The present work is devoted to the development and implementation of a computational framework to perform numerical simulations of low Mach number turbulent flows over complex geometries. The algorithm under consideration is based on a classical predictor-corrector time integration scheme that employs a projection method for the momentum equations. The domain decomposition strategy is adopted for distributed computing, displaying very satisfactory levels of speed-up and efficiency. The Immersed Boundary Methodology is used to characterize the presence of a complex geometry. Such method demands two separate grids: An Eulerian, where the transport equations are solved with a Finite Volume, second order discretization and a Lagrangian domain, represented by a non-structured shell grid representing the immersed geometry. The in-house code developed was fully verified by the Method of Manufactured Solutions, in both Eulerian and Lagrangian domains. The capabilities of the resulting computational framework are illustrated on four distinct cases: a turbulent jet, the Poiseuille flow, as a matter of validation of the implemented Immersed Boundary methodology, the flow over a sphere covering a wide range of Reynolds numbers, and finally, with the intention of demonstrating the applicability of Large Eddy Simulations - LES - in an industrial problem, the turbulent flow inside an industrial fan.

Modelling and simulation of a compression cylinder-piston system with combustion reaction

In flammable gases, due to the energy stored in its molecular bonds, the construction of systems to transform the chemical energy into mechanical energy was possible. These systems were named motor. With the combustion reaction, a high rate of energy is supplied to the system in the form of heat. Expanding it suddenly and due to the action of an external force against this expansion, the movement becomes oscillatory. Within this context, the present paper contributes to the computational simulation and study of sensitivity of the velocity of the piston, the temperature and the density of the gas in the combustion process, in an integral formulation, given equations for mass, energy, momentum and molar concentration balance. The Arrhenius’ equation, numerical methods for solving differentials equations system and integral formulation using Reynolds Transport Theorem (RTT) are also used. The study is done gradually in order to understand in detail all the variables from ideal conditions. The gas is assumed to be ideal, the cylinder is perfectly sealed and the flow is assumed to be instantaneously homogeneous. The system works as a set containing gas, which is compressed by an external force. Initially, there is no friction and the system is considered adiabatic. So it was possible to understand the variation of the parameters in a model that does not lose energy. Conversely, it is conservative. The final system has friction between the piston and the cylinder wall, change of heat through the wall of the system and combustion reaction, then comparison and analysis were done. The first model response is an oscillatory system with perpetual motion, because there is no dissipation and energy is always constant. The last model response is also oscillatory, but the system tends to be static, due to the non conservation of energy. Heat transfer through the cylinder walls was observed and the temperature oscillates, tending to the prescribed temperature. As a response the density decreases, showing that the volume of the system increases, characterizing the behavior of the pressure and temperature of an ideal gas. When the chemical reaction of combustion is added, there is a very sudden increase of the temperature and volume of the system, because the rate of energy was very high.