Effect of an upstream cylinder on the wake dynamics of two tandem cylinders with different diameters at low Reynolds numbers

Abstract

This paper presents a systematic numerical study on the fluid dynamics and flow structures around a cylinder with diameter D placed in the wake of another cylinder with a smaller diameter d. Reynolds numbers of Re = 100 and 150 (based on D) are considered so the flow is physically two-dimensional. The ratios d/D and L/D vary in the ranges of 0.4-1.0 and 1.0-8.0, respectively, where L is the distance from the center of the upstream cylinder to the forward stagnation point of the downstream cylinder. The analysis focuses on how d/D and L/D influence the Strouhal number St, wake topology, and fluid forces on the downstream cylinder and links them with the flow physics. The flow is classified into the reattachment and co-shedding flow regimes, with the latter being further subdivided into the prime vortex shedding, two-layer vortex shedding, and secondary vortex shedding (SVS) modes, and the detailed aspects of the three modes are discussed based on the time-averaged flow fields. The two vortex frequencies of the downstream cylinder can be detected only in the SVS mode, and in addition to the fundamental vortex frequency f 1, the shedding of the secondary vortex further results in the subharmonic frequency f 2. Only when the secondary shedding length L s∗ is < 10 does f 2 affect the downstream cylinder and lead to a pattern of alternating high- and low-amplitude peaks in the time history of the lift coefficient. A novel mechanism of secondary vortex formation is identified, and the critical spacing and the modulation of lift by f 2 are also discussed.