The pressure–velocity correlation in oscillatory turbulent flow between a pair of bluff bodies Shinnosuke Obi * , Norihiko Tokai Department of Mechanical Engineering, Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama 223-8522, Japan Received 29 October 2005; received in revised form 23 January 2006; accepted 4 March 2006 Available online 15 June 2006 Abstract Turbulent flow measurements were conducted between two bluff bodies set in uniform flow in tandem arrangement. The velocity field obtained with PIV was averaged with respect to either time or phase of periodic pressure oscillation induced by vortex shedding from the bluff body, i.e., Reynolds decomposition or three-level decomposition. The Reynolds stresses caused by periodic fluid motion was found excessively large compared with those related to turbulent fluctuations in the entire flow field in observation. The PIV data were used to solve the discrete Poisson equation of instantaneous pressure. The effect of organized vortex motion caused strong correlations between velocity and pressure gradient when observed from the framework of the Reynolds averaging. Ó 2006 Elsevier Inc. All rights reserved. Keywords: Turbulent wake; PIV; Reynolds stress; Pressure–velocity correlation; URANS; Three-level decomposition 1. Introduction Turbulence models based on the Reynolds-averaged Navier–Stokes (RANS) approach often fail to predict flows associated with massive separation, in contrast to LES which can correctly capture large-scale turbulent fluid motion typically found in such flows. It is generally recog- nized that the poor performance of the RANS models is due to the shortcomings of the statistical approach itself in representing the coherent structure in turbulence. On the other hand, the development of conventional RANS models have relied upon the knowledge of simple shear flows in nearly equilibrium state; hence it is likely that the turbulent transport process, which is relatively impor- tant in non-equilibrium flows, is not correctly incorporated into the existing models. In particular, the treatment of pressure diffusion transport, which is strong in free shear flows, is still far below a satisfactory level, partly because of the relatively few experimental information on the pres- sure–velocity correlation. The knowledge about such pro- cesses in flows in an out-of-equilibrium state is desired for the development of RANS-based turbulence models. The turbulent wake of a bluff body put in a uniform flow is a typical example of a problem where RANS-based mod- els exhibit their disadvantage. The length of the wake cal- culated by RANS models is usually too long compared to experiment and/or LES (e.g., Bosch and Rodi, 1998). This is usually attributed to the vortices shed from the body; hence the application of unsteady RANS (URANS) has become attractive as an alternative to LES (Iaccarino et al., 2003). The theoretical basis for URANS is, however, not firm enough to make this approach a standard tool for engineering design. Detailed discussions based on experi- mental data are desired. Turbulent flows associated with periodic motion have often served as attractive topics for experiments in the past. The three-level decomposition technique (Hussain and Reynolds, 1970) has been used as a standard tool to 0142-727X/$ - see front matter Ó 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.ijheatfluidflow.2006.03.021 * Corresponding author. Tel.: +81 45 566 1499; fax: +81 45 566 1495. E-mail address: obsn@mech.keio.ac.jp (S. Obi). www.elsevier.com/locate/ijhff International Journal of Heat and Fluid Flow 27 (2006) 768–776