www.elsevier.nl/locate/jnlabr/yjfls Journal of Fluids and Structures 19 (2004) 49–62 A flow study around a time-dependent 3-D asymmetric constriction J. Anagnostopoulos, D.S. Mathioulakis* School of Mechanical Engineering/Fluids Section, National Technical University of Athens, 9 Heroon Polytechniou Ave., Zografos Athens 15710, Greece Received 30 September 2002; accepted 13 October 2003 Abstract The flow field around a time-dependent 3-D asymmetric tube constriction was studied and comparisons were made with the corresponding 2-D case. Both experimental (LDV-PIV) and numerical (finite volume) tools were employed for Reo1000, Sto0.3 and 50% maximum passage reduction. The basic features of the flow were 3-D separation and reattachment, vortex generation especially after the middle of the cycle (max. constriction), and vortex destruction before the end of the cycle. The snake-type shape of the streamlines, known from the 2-D case, was not observed on the symmetry plane of the examined flow due to the secondary flow action. r 2003 Elsevier Ltd. All rights reserved. 1. Introduction Flows in tubes of time-dependent cross-sectional area are met in many bioengineering applications. Blood flow in arteries is a characteristic example due to their moving walls and particularly in coronary arteries being squeezed during heart systole (Liu and Yamaguchi, 1999). The phenomenon of a self oscillating collapsible tube under small transmural pressure (Conrad, 1969; Kamm and Shapiro, 1979; Bertram et al., 1994; Kounanis and Mathioulakis, 1999), the operation of the so called ‘‘intra-aortic balloon pump’’ employed as a means for temporary heart assistance (Papaioannou et al., 2002) and the valveless pump (Manopoulos et al., 2001), are other physiological examples in which the flow is through tubes of time varying area either locally or along a certain length. The flow field in a two dimensional (2-D) channel with a moving constriction has been studied in the past both numerically and experimentally by Pedley and Stephanoff (1985) and Ralph and Pedley (1988). The basic parameters involved in this problem are, the Reynolds number Re ¼ U b D=n; where U b is the mean bulk velocity, D the tube diameter and n the kinematic viscosity, the Strouhal number St ¼ fD=U b , where f is the frequency of the moving constriction, and finally the nondimensional amplitude of the constriction e ¼ h=D; where h is the amplitude of the constriction. The basic element of the flow structure in a 2-D moving constriction for Reo1000; Sto0:1 and eo0:5 is the generation and propagation of a vortex train of alternate sign, close to the channel walls (Pedley and Stephanoff, 1985; Ralph and Pedley, 1988). The propagation speed of each vortex is inversely proportional to St, while its strength increases with Re. In the numerical study of Ralph and Pedley (1989) the flow field was examined using both viscous and inviscid momentum equations keeping the flow rate fixed either upstream or downstream of the constriction. Through this study it was found that even in case of zero viscosity, the flow field downstream of the constriction looked similar with the viscous one. However, there was a difference concerning vorticity, which did not decay in time for the ARTICLE IN PRESS *Corresponding author. Tel.: +30-210-77-21-028; fax: +30-210-77-21-057. E-mail address: mathew@fluid.mech.ntua.gr (D.S. Mathioulakis). 0889-9746/$-see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfluidstructs.2003.10.002