Global instability and mode selection in flow fields around rectangular prisms

Abstract

Large-eddy simulations of the unsteady flows around rectangular prisms with chord-to-depth ratios (B/D) ranging from 3 to 12 are carried out at a Reynolds number of 1000. A particular focus of the study is the physical mechanisms governing the global instability of the flow. The coherent structures and velocity spectra reveal that large-scale leading-edge vortices (L vortices) are formed by the coalescence of Kelvin–Helmholtz rollers. Based on dynamic mode decomposition, the interactions between the L vortex and the trailing-edge vortex (T vortex) at different B/D values are revealed. It is found that the phase difference between the L and T vortices is the critical factor promoting a stepwise increase in the Strouhal number with increasing B/D. According to the phase analysis, there are two types of pressure feedback-loop mechanisms maintaining the self-sustained oscillations. When B/D = 4–5, the feedback loop covers the separation region, and the global instability is controlled by the impinging shear-layer instability. When B/D = 3 and 6–12, the feedback loop covers the entire chord, and the global instability is controlled by the impinging leading-edge vortex shedding instability. Self-sustained oscillations of the shear layer still exist after a splitter plate is placed in the near wake, indicating that the T vortex shedding is not essential in triggering the global instability. Nevertheless, with the participation of the T vortex, the primary instability mode may be reselected due to the upper and lower limits of the shedding frequency imposed by the T vortex.

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

“…It can be found that the current St(L) is in great agreement with the experimental results. The present results also match the LES results from Zhang et al (2023), although there is a very small deviation, which may be due to the difference in numerical methods.…”

“…The subsequent secondary instability of the KH vortex indicates its limited persistence over a short range. This secondary destabilized KH vortex then transforms into the LE vortices, as also noted in the study by Zhang et al (2023). However, the present DNS results provide clearer identification of hairpin vortices compared with previous studies.…”

“…The Strouhal number St(L) based on the streamwise dimension of the rectangular cylinder is used to validate the present numerical model. The present results are shown in figure 3, compared with available experimental and numerical results carried out by Nakamura et al (1991) and Zhang et al (2023), respectively. It can be found that the current St(L) is in great agreement with the experimental results.…”

“…Accurate classification of flow regimes based on aspect ratio also depends on the Reynolds number (Re), which is defined using the inflow velocity U 0 and D. When Re exceeds 300, shedding of vortices from both the LE and TE occurs at the same frequency f , leading to an increase in the Strouhal number, given by St(L) = f L/U 0 , in the two regimes. One regime is dominated by the LE vortex shedding, and St(L) changes in a stepwise manner with increasing aspect ratio for Re up to 2000 (Okajima 1982;Nakamura, Ohya & Tsuruta 1991;Ozono et al 1992;Mills et al 1995;Tan, Thompson & Hourigan 1998;Chiarini, Quadrio & Auteri 2022c;Zhang et al 2023). The second regime, instead, is dominated by the TE vortex shedding, and St(L) increases almost linearly with L/D (Chiarini et al 2022c).…”

“…As a result, the shedding frequency is locked to the passing frequency of the LE vortices over the TE. In another study by Zhang et al (2023), three-dimensional unsteady flows around rectangular cylinders were investigated using large-eddy simulation (LES) at Re = 1000. The aspect ratio of the cylinders ranged from 3 to 12.…”