Abstract
In this paper we will give an overview of our studies on turbulent flow over rough surfaces such as shark skin, which have a drag reducing effect known as shark-skin effect. Our mathematical model is restricted to the flow in the viscous sublayer. Here, the turbulences which occur in the flow above this layer enter through a boundary condition. The flow equations are the steady state Navier-Stokes equations with a Couette flow profile given through two boundary conditions: a diagonal flow on the top and the no-slip condition on the rough surface. Direct simulations are performed via stabilized finite elements. For a better approximation of the boundary isoparametric finite elements are used. Our first calculations give a drag reduction of rough surfaces up to 8% whereas 15% is obtained with an improved model. We will discuss this amount of drag reduction and how it can be compared with experimental results. For gaining insight in the details of the flow, how it is influenced by the different shapes of microstructures, and how their drag reducing mechanism can be explained, we used scientific flow visualization. We will present a short overview of the methods employed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D.W. Bechert, M. Bruse, and W. Hage, Experiments with three-dimensional riblets as an idealized model of shark skin, Experiments in Fluids 28, 403–412 (2000)
R. Becker, and R. Rannacher, A feed-back approach to error control in finite element methods: Basic analysis and examples, East-West J. Numer. Math 4(4),237–264 (1996)
R. Becker, and M. Braack, A finite element pressure gradient stabilization for the Stokes equation based on Local Projections, Calcolo 38(4), 173–199 (2001)
R. Becker, and R. Rannacher, An optimal control approach to a posteriori error estimation in finite element methods, Acta Numerica 2001 (2001)
K.G. Blüchel, and F. Malik, Faszination Bionik. Die Intelligenz der Schöpfung, Mcb Verlag (2006)
E. Friedmann, Riblets in the viscous sublayer. Optimal Shape Design of Microstructures, PhD thesis, Ruprecht - Karls - University Heidelberg (2005)
E. Friedmann, The optimal shape of riblets in the viscous sublayer, J. Math. Fluid Mech., Birkhäuser Basel, 2008. DOI 10.1007/s00021-008-0284-Z
E. Friedmann, and Th. Richter, Optimal microstructures. Drag reducing mechanism of riblets, J. Math. Fluid Mech., submitted (2007)
E. Friedmann, and Th. Richter, The effect of different in- and outflow conditions modeled on a microscopic flow problem on the macroscopic drag force, Nonlinear Anal.: Real World Applications, Multiscale Problems in Science and Technology: Challenges to Mathematical Analysis and Perspectives, submitted (2008)
W. Hage, Zur Widerstandsverminderung von dreidimensionalen Riblet-Strukturen und anderen Oberflächen, Mensch & Buch, Verlag (2005)
W. Jäger, and A. Mikelić, Couette flows over a rough boundary and drag reduction, Comm. Math. Phys. 232, 429–455 (2003)
F.H. Post, T. van Walsum, W.C. de Leeuw, A.J.S. Hin, Visualization Techniques for Vector Fields with Applications to Flow Data, CWI Quarterly 7(2), 131–146 (1994)
A. Mojetta, Haie - Biografie eines Räubers, Jahr Verlag GmbH & Co (1997)
F.H. Post, B. Vrolijk, H. Hauser, R.S. Laramee and H. Doleisch, Feature Extraction and Visualization of Flow Fields, Eurographics 2002 State-of-the-Art Reports (2002)
H. Schlichting, and K. Gersten, Boundary-Layer Theory, 8th revised and enlarged edition, Springer-Verlag, Berlin (2000)
K. Sch. Steuben and G. Krefft, Die Haie der Sieben Meere, Verlag Paul Parey (1995)
P. Thiede, Aerodynamic Drag Reduction Technologies Proceedings of the CEAS/DragNet European Drag Reduction Conference, 19–21 June 2000, Potsdam, Germany
M. Van Dyke, An Album of Fluid Motion, Parabolic Pr. (1988)
A. Wierse, R. Lang, U. Lang, H. Nebel, D. Rantzau, The Performance of a Distributed Visualization System, Visualization Methods in High Performance Computing and flow Visualization (1996)
http://www.HLRS.de Cited 29th April 2008
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Friedmann, E., Portl, J., Richter, T. (2009). A Study of Shark Skin and Its Drag Reducing Mechanism. In: Rannacher, R., Sequeira, A. (eds) Advances in Mathematical Fluid Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04068-9_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-04068-9_16
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04067-2
Online ISBN: 978-3-642-04068-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)