Three-dimensional vortex dynamics and transitional flow induced by a circular cylinder placed near a plane wall with small gap ratios

Abstract

The flow past a cylinder in proximity to a plane wall is investigated numerically for small gap ratios. Three vortex dynamic processes associated with different hairpin vortex generation mechanisms are identified for the first time, and the wake-induced turbulent transition is analysed. The vortex shedding is suppressed at $G/D = 0.1$ , while the spanwise vortex is generated via a Kelvin–Helmholtz instability and evolves into hairpin vortices. For $G/D= 0.3$ , the upper and lower rollers alternatively shedding from the cylinder, interact with the secondary vortex. The split secondary vortex merges with the upper roller and results in a new vortex downstream, which develops into hairpin vortices. When $G/D = 0.9$ , the secondary vortex interacts with the lower roller and then evolves into hairpin vortices. A tertiary vortex induced by the secondary vortex is observed, rotating in the opposite direction to the secondary vortex the wake-induced transitions share the same route. The velocity fluctuations deviate from the optimal growth theory in the pre-transitional region. In the transitional region low-frequency disturbances penetrate the sheltering edge to generate streaks where the disturbance energy declines. In the turbulent region the logarithmic layer is formed, indicating that the turbulent equilibrium is established.

Vortex dynamics and boundary layer transition in flow around a rectangular cylinder with different aspect ratios at medium Reynolds number

“…Additionally, the u rms profiles obtained from the wall boundary layer transition induced by a wake of a circular cylinder with large gap ratios are consistent with the theory (Ovchinnikov, Piomelli & Choudhari 2006;Mandal & Dey 2011;He et al 2013). However, for small gap ratios, these profiles deviate from the optimal disturbance theory due to the strong direct interaction between the boundary layer and the wake, as reported by Li et al (2022a). In present flows, the u rms profiles also deviate from the optimal disturbance theory, indicating that the boundary layer transitional mechanism here differs from the bypass transition induced by FST.…”

“…The three-dimensional destabilization of the KH vortices leads to the development of hairpin vortices (LE vortices), which is the primary cause of the second growth in this regime. This mechanism is similar to the transition flow induced by a wake of a circular cylinder with gap ratios less than or equal to 1.8 (He et al 2013;Li et al 2022a). Moreover, the three-dimensional instabilities cause a redistribution of disturbance energy during the second exponential growth, as also observed in the transition induced by a circular cylinder wake (Li et al 2022b).…”

“…The intense shear effects cause regions of high momentum to form the head of the hairpin vortices, while regions of low momentum develop into their legs. This generation process of hairpin vortices is akin to that observed in the interaction between the wake of a circular cylinder and a wall boundary at a very small gap ratio (Li et al 2022a). Although these two flow configurations are different, the hairpin vortices in both flows are evolved from KH vortices.…”

“…In the present study, the polynomial order and the number of Fourier planes are set to and for all three cases, following the simulations at the same in the studies of Li et al. (2022 a , b ), in which the flow past a circular cylinder in proximity to a plane wall was investigated.

Figure 2.The partial domain with a macromesh for in the – plane.

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“…Dynamic mode decomposition (DMD) (Schmid 2010) and Fourier mode decomposition (FMD) (Basley et al 2011;Ma et al 2015;Zhang & Zhou 2024) are significant mode analysis tools, and were widely used in the previous studies (He, Wang & Pan 2013;Wang et al 2018;Wang & Wang 2021a,b;Li et al 2022a).…”