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Méthodes particulaires pour la simulation des sillages tridimensionnels

Abstract : This work is devoted to the development of a particle method in order to solve the three-dimensional Navier-Stokes equations. Since the Biot-Savart law is by far too expensive in three dimensions, an hybrid grid-particle method is chosen. This method is then applied to simulations and control of three-dimensional cylinder wakes.The first part deals with the numerical method itself. We begin with a presentation of the lagrangian model and the methodology used to compute the velocity field, which is essential in the scheme. The chapter 2 describes how boundary layers are computed. The whole fractional step algorithm is eventually presented in chapter 3, which also presents remesh and grid-particle interpolation techniques and diffusion computation. The code is then validated on a vortex ring simulation, this ring colliding with a cylindrical solid at moderate Reynolds numbers (between 400 and 2000). The second part applies this numerical method to the computation of turbulent wakes developed behind a three-dimensional circular cylinder (chapter 4), and then to their control in chapter 5.It is now well-known that bidimensional solutions are unstable for high enough Reynolds numbers. The three-dimensional instabilities are identified through their spectrum. They have a dramatic effect on wake forces and self-frequency. Chapter 5, related to control, intends to demonstrate several aspects. An open-loop control is performed by means of a rotary oscillation of the cylinder with constant frequency and amplitude. Low frequency and high frequency are considered. We show that the the high frequency control makes the drag coefficient decrease by 43%, with a Reynolds number of 550. Moreover, we show that the turbulent wake goes back to a bidimensional state when the amplitude is high enough.
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Submitted on : Monday, February 16, 2004 - 6:12:26 PM
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Philippe Poncet. Méthodes particulaires pour la simulation des sillages tridimensionnels. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2001. Français. ⟨tel-00004699⟩

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