Two-degree-of-freedom flow-induced vibrations of a D-section prism

Abstract

This paper presents a comprehensive study of flow-induced vibrations of a D-section prism with various angles of attack $\alpha$ ( $= 0^{\circ }\unicode{x2013}180^{\circ }$ ) and reduced velocity $U^*$ (= 2–20) via direct numerical simulations at a Reynolds number ${Re} = 100$ . The prism is allowed to vibrate in both streamwise and transverse directions. Based on the characteristics of vibration amplitudes and frequencies, the responses are classified into nine different regimes: typical VIV regime ( $\alpha = 0^{\circ }\unicode{x2013}30^{\circ }$ ), hysteretic VIV regime ( $\alpha = 35^{\circ }\unicode{x2013}45^{\circ }$ ), extended VIV regime ( $\alpha = 50^{\circ }\unicode{x2013}55^{\circ }$ ), first transition response regime ( $\alpha = 60^{\circ }\unicode{x2013}65^{\circ }$ ), dual galloping regime ( $\alpha = 70^{\circ }$ ), combined VIV and galloping regime ( $\alpha = 75^{\circ }\unicode{x2013}80^{\circ }$ ), narrowed VIV regime ( $\alpha = 85^{\circ }\unicode{x2013}145^{\circ }$ ), second transition response regime ( $\alpha = 150^{\circ }\unicode{x2013}160^{\circ }$ ) and transverse-only galloping regime ( ${\alpha = 165^{\circ }\unicode{x2013}180^{\circ }}$ ). In the typical and narrowed VIV regimes, the vibration frequencies linearly increase with increasing $U^*$ . In the hysteretic and extended VIV regimes, the vibration amplitudes are large in a wider range of $U^*$ as a result of the closeness of the vortex shedding frequency to the natural frequency of the prism because of the shear layer reattachment and separation point movement. In the two galloping regimes, the transverse amplitude keeps increasing with $U^*$ while the streamwise amplitude stays small or monotonically increases with increasing $U^*$ . In the combined VIV and galloping regime, the vibration amplitude is relatively small in the VIV region while drastically increasing with increasing $U^*$ in the galloping region. In the transition response regimes, the vibration frequencies are galloping-like but the divergent amplitude cannot persist at high $U^*$ . Furthermore, a wake mode map in the examined parametric space is offered. Particular attention is paid to physical mechanisms for hysteresis, dual galloping and flow intermittency. Finally, we probe the dependence of the responses on Reynolds numbers, mass ratios and degrees of freedom, and analyse the roles of the shear layer reattachment and separation point movement in the appearance of multiple responses.