Numerical simulation of flows past flat plates using volume penalization
- PDF / 732,843 Bytes
- 15 Pages / 439.37 x 666.142 pts Page_size
- 9 Downloads / 217 Views
Numerical simulation of flows past flat plates using volume penalization Kai Schneider · Mickaël Paget-Goy · Alberto Verga · Marie Farge
Received: 22 December 2012 / Revised: 29 April 2013 / Accepted: 12 September 2013 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2014
Abstract We present numerical simulations of two-dimensional viscous incompressible flows past flat plates having different kind of wedges: one tip of the plate is rectangular, while the other tip is either a wedge with an angle of 30◦ or a round shape. We study the shear layer instability of the flow considering different scenarios, either an impulsively started plate or an uniformly accelerated plate, for Reynolds number Re = 9500. The volume penalization method, with either a Fourier spectral or a wavelet discretization, is used to model the plate geometry with no-slip boundary conditions, where the geometry of the plate is simply described by a mask function. On both tips, we observe the formation of thin shear layers which are rolling up into spirals and form two primary vortices. The self-similar scaling of the spirals corresponds to the theoretical predictions of Saffman for the inviscid case. At later times, these vortices are advected downstream and the free shear layers undergo a secondary instability. We show that their formation and subsequent dynamics is highly sensitive to the shape of the tips. Finally, we also check the influence of a small riblet, added on the back of the plate on the flow evolution.
Communicated by Eduardo Souza de Cursi. K. Schneider (B) M2P2-CNRS, Aix-Marseille Université, 38 rue F. Joliot-Curie, 13541 Marseille Cedex 20, France e-mail: [email protected] M. Paget-Goy M2P2-CNRS, Aix-Marseille Université, 38 rue F. Joliot-Curie, 13451 Marseille Cedex 20, France A. Verga IM2NP-CNRS, Aix-Marseille Université, Avenue Escadrille Normandie Niemen, Case 142, 13397 Marseille Cedex 20, France M. Farge LMD-CNRS, Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France
123
K. Schneider et al.
Keywords Instability of shear layers · Vortex dynamics · Computational methods in fluid dynamics · Free shear layers · Wavelets · Spectral methods Mathematics Subject Classification (2000) 65M70
Primary 65M85; Secondary 76D17 · 65T60 ·
1 Introduction Flow past a thin flat plate moving normal to the free stream has been subject to many experimental, theoretical and numerical investigations (Pierce 1961; Saffman 1995; Koumoutsakos and Shiels 1996). When the plate is impulsively started from rest (relatively to the flow), a primary spiral vortex forms and develops at the edges of the plate. At later times, when these start-up vortices are advected downstream, the formation of secondary vortices along the primary vortex sheet are observed, for sufficiently large Reynolds numbers. The study of the start-up vortex can be traced back to the work on ‘Fluid motion at very small viscosity’ of Prandtl (1905) who analyzed its initial evolution and showed that it can be described by a class of sel
Data Loading...
