Unsteady turbulence structure in and downstream of a short elbow at post-critical Reynolds numbers

Abstract

Unsteady turbulence structures in and downstream of a short elbow (radius to pipe diameter ratio 1.0) were studied experimentally for sub-to-post-critical Reynolds numbers (Re = 1 × 105 to 3 × 105). Measurement of the velocity field was carried out using particle image velocimetry (PIV) combined with proper orthogonal decomposition (POD) analysis. The mean velocity, turbulence intensity, power spectrum, spatial variation of POD modes, and time variation of instantaneous velocity and vorticity fields were evaluated. The experimental results indicate that a separation region forms around the elbow exit, which is almost independent of the Reynolds number for the post-critical Reynolds numbers. The power spectrum analysis indicates that the periodic oscillation is observed at Strouhal number 0.5, and that it originates from interaction of the secondary flow in the elbow and the unsteady separating flow behavior near the exit of the inner elbow wall. Furthermore, POD analysis was conducted to clarify the variation of POD modes in the elbow flow. It was found that the periodic velocity fluctuation is generated by the oscillation of the flow in spanwise direction downstream of the elbow, which consists of a secondary flow structure directed to the inner elbow wall, and a streamwise longitudinal structure along the centerline of the elbow. The POD reconstructed velocity and vorticity fields indicate periodic oscillation of the entire secondary flow arising from unsteady oscillation of a pair of vortices in the cross section of the elbow; this condition prevails in and downstream of the elbow.