Turbulência em Fluidos

Objectives

Introduce the theory and engineering applications of turbulent flows, and to provide knowledge that allows i) the identification of the main consequences of turbulent motion in industrial and engineering systems, ii) the estimation and computation of quantities of interest arising from the turbulence dynamics and, iii) to choose the best modelling and simulation approaches for particular engineering applications.

Syllabus

Navier-Stokes equations, Boussinesq approximation, dissipation rate, theorems of Helmholtz and Kelvin; Kelvin-Helmholtz and Tollmien-Schlichting instabilities, dynamic systems and chaos, Lorenz equations; The energy cascade of Richardson-Kolmogorov, the scales of turbulence, the dissipation law; Reynolds equations and Reynolds stresses, closure problem, turbulent viscosity; Direct and large-eddy simulations, one point closures, measurement of turbulent flows; Wall flows, kinetic energy budget, convective boundary layer, classical solutions for free shear flows; k-ε model, second order models, limitations of one point closures; Filtered Navier-Stokes equations, Smagorinsky model; Kármán-Howarth equation, the classical theory of turbulence, Obukhov’s law; Richardson’s law, inertial transport, Diffusion equation, turbulent diffusivity.

Prerequisites

Approval in Fluid Mechanics I and II or equivalent course.

Cross Competence Component

The work to be carried includes the following soft skills: critical and innovative thinking, decision making, teamwork, leadership and oral communication, use of computer and multimedia tools and presentation.

Laboratorial Component

Aquisition of a velocity signal in a turbulent flow using a hot-wire and post- processing of this data to retrieve several important turbulence quantities.

Programming And Computing Component

Execution of numerical simulations of unsteady flows using a non-comercial code (in house), and extension of the code to solve and analyse specific problems proposed by the teaching staff.With respect to the skills defined in the Computer and Programming Skills report, this work comprises the skills of Abstraction; Automation; Decomposition; Debug; Generalization and Algorithmic Reasoning.

Ethical Principles

All members of a group are responsible for the group’s work In any assessment, every student shall honestly disclose any help received and sources used. In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.