Mecánica de Fluidos

1. Optimization of the surface shape of hydro/aerodynamic bodies

Surface rugosity and shapes at micro scale level have a direct influence on aero/hydrodymamic performance. An example of this is shown in nature: shark skin presents small denticles which allows to reduce drag and hence improve performance of sharks inside water [1,2].

Different studies have been conducted in order to reproduce this surface geometry in different applications such as swimming suits, aircraft coatings, and others. However, these studies try to mimic the microstructre of the shape in order to improve the performance. There has not been studies that involve the search for optimal shape that mixes easiness of manufacture and optimum performance. Current swimming suits (from Speedo) presents a 9.5 % increase of performance, meanwhile shark skin improves up to 20 % performance compared with flat surfaces [3].

Another application seen in aerodynamics is called vortex generator (VG), and consist of a small vane attached to the surface. VG creates a vortex and reduces size of the boundary layer thus delays flow separation and aerodynamic stalling. They are widely used in racing cars and aircrafts because improve overall performance [4,5]. However, optimum shapes, distribution, and interaction with different types of fluids have not been found, and therefore conclusive sizes and shapes for optimum performance into fluids have not been achieved.

The optimization is the procedure by which a selected group of design variables are appropriately chosen to provide the best design performance.  Performance is defined according to the specific needs as for example minimum drag, maximum lift, minimum weight. In other words, is the selection of the best solution from all the feasible ones to perform a task. Optimization using CFD has been studied from different points of view and multiple approaches have been developed.

The first applications to minimize the drag on wing profiles can be found in [6]. More recently, general optimization procedures are created and a variety of optimisation techniques are used to achieve optimum designs. Mohammadi and Pironneau [7] show developments on shape optimization for aeronautical applications based on the adjoint method. A gathering of different methods and specific applications is presented on [8] with an engineering emphasis. The shape optimization using a derivative of the objective function with respect to the domain is a widely used method on solid mechanics. Applications of shape derivatives to fluids mechanics can be found in Mohammadi and Pironneau [7].

The aim of the project is to optimise the surface shape (at micro scale level) of hydro/aerodynamic bodies in order to improve its performance. Given the nature of the problem, a multiscale approach must be considered to model the fluid interacting with the structure. Therefore variational multiscales seems like a good choice to model the fluid [9]. Also, Variational multiscale is capable of dealing with the turbulence.

The ultimate goal, and great challenge, is to apply shape optimization techniques to microscale level in order to find best performance of fluid structure interaction problems at macroscale level. Applications of this study are important to automotive, aerospace and rapid transport industries to reduce fuel consumption and improve operation conditions.

References

[1] AW Lang, P Motta, P Hidalgo, and M Westcott. Bristled shark skin: a microgeometry for boundary layer control? Bioinspiration & biomimetics, 3(4):046005, 2008.
[2] Brian Dean and Bharat Bhushan. Shark-skin surfaces for fluid-drag reduction in turbulent flow: a review. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences,368(1929):4775–4806, 2010.
[3] Johannes Oeffner and George V Lauder. The hydrodynamic function of shark skin and two biomimetic applications. The Journal of experimental biology, 215(5):785–795, 2012.
[4] Tomas Melin, Simone Crippa, Martin Holl, and Miroslav Smid. Investigating active vortex generators as a novel high lift device. In 25th International Congress of the Aeronautical Sciences, ICAS, 2006.
[5] RV Chima. Computational modeling of vortex generators for turbomachinery. In ASME Turbo Expo 2002: Power for Land, Sea, and Air, pages 1229–1238. American Society of Mechanical Engineers, 2002.
[6] O. Pironneau. On optimum design in fluid mechanics. Journal of Fluid Mechanics, 64:97–110, 6 1974.
[7] B. Mohammadi and O. Pironneau. Applied optimal shape design. Journal of Computational and Applied Mathematics, 149(1):193 – 205, 2002. Scientific and Engineering Computations for the 21st Century - Methodologies and Applications Proceedings of the 15th Toyota Conference.
[8] Dominique Thvenin and Gbor Janiga. Optimization and Computational Fluid Dynamics. Springer Publishing Company, Incorporated, 1st edition, 2008.
[9] Thomas JR Hughes, Gonzalo R Feijoo, Luca Mazzei, and Jean-Baptiste Quincy. The variational multiscale method—a paradigm for computational mechanics. Computer methods in applied mechanics and engineering, 166(1):3–24, 1998.

Contact

Manuel Julio Garcia Ruiz
mgarcia@eafit.edu.co
http://mecanica.eafit.edu.co