Effect of an upstream cylinder on the wake dynamics of two tandem cylinders with different diameters at low Reynolds numbers
Xiangjun Shan
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 f1, the shedding of the secondary vortex further results in the subharmonic frequency f2. Only when the secondary shedding length Ls* is <10 does f2 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 f2 are also discussed.