This paper presents results of three-dimensional direct numerical simulations (DNS) and global linear stability analyses of a viscous incompressible flow past a finite-length cylinder with two free flat ends. The cylindrical axis is normal to the streamwise direction. The work focuses on the effects of aspect ratios (in the range of $0.5\leq {\small \text{AR}} \leq 2$ , cylinder length over diameter) and Reynolds numbers ( $Re\leq 1000$ based on cylinder diameter and uniform incoming velocity) on the onset of vortex shedding in this flow. All important flow patterns have been identified and studied, especially as ${\small \text{AR}}$ changes. The appearance of a steady wake pattern when ${\small \text{AR}} \leq 1.75$ has not been discussed earlier in the literature for this flow. Linear stability analyses based on the time-mean flow has been applied to understand the Hopf bifurcation past which vortex shedding happens. The nonlinear DNS results indicate that there are two vortex shedding patterns at different $Re$ , one is transient and the other is nonlinearly saturated. The vortex-shedding frequencies of these two flow patterns correspond to the eigenfrequencies of the two global modes in the stability analysis of the time-mean flow. Wherever possible, we compare the results of our analyses to those of the flows past other short- ${\small \text{AR}}$ bluff bodies in order that our discussions bear more general meanings.

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Abstract. The flow-induced lateral vibration phenomenon of the terminal sensitive bullets (TSB) when it is dispersed by the airborne distributor is taken as the research background. Based on the Fluent, the flow around a rotating short cylindrical TSB ( ⁄ < 1) is simulated and analyzed varying with relative rotation velocity at high Re number (1×10 5 ≤ ≤ 3×10 6 ). The simulation results show that the flow field structure of the short cylinder with two free ends is different from the symmetry of the short cylindrical flow field with one free end, and there is no horseshoe vortex. Compared to the long cylinder with double free ends, the of the short cylinder is more sensitive to the change of Re. With the increase of , the of the short cylinder decreases, and the value is between the infinite cylinder and the sphere in the non-critical region. When the short cylinder rotates at the angular velocity , the top vortex bends and deforms to a 'C' shape on the leeward side where the fluid is accelerated. Due to the periodic disturbance of the detector, the aerodynamic coefficient of the rotating TSB is periodically vibrated. In a single cycle, the waveform of the shows a 'W' shape, and the waveform of the is 'M'.