Simulating Soft Coral Vibrations with a Wake Oscillator Model and 3D-Printed Flexible Branching Structures

Soft corals sway with the low-frequency swell of surface waves, and vibrate at a high frequency due to vortex-induced vibrations. It is hypothesized that these high-frequency vibrations allow the soft-coral colony to intercept more food particles and thus improve its feeding. In this conference talk, we present a simulation workflow to couple a co-rotational beam finite element formulation with a wake-oscillator model and an empirical drag formulation. This workflow allows simulating the low frequency, large amplitude sway of the branched structure and its high frequency response to vortex-induced vibrations. To validate these simulations, we perform water tunnel experiments on 3D-printed idealized coral colony structures. Simulations and experiments are performed for ramified structures with different numbers of branches, and for incrementing reduced velocity. Whereas a cantilevered beam exhibits well-defined and spaced-out lock-in ranges where the frequencies of vibration and of vortex shedding coalesce, a ramified structure with more and more branches exhibits a more and more continuous lock-in over increasing reduced velocity. A ramified structure with many branches possesses natural frequencies close to one another. There is thus always a natural frequency close to the frequency of vortex shedding. Moreover, the natural frequencies of branched structures are unenvenly spaced. Single frequency, high amplitude response is observed when vortex shedding occurs in a region of low frequency density, and multimodal, low amplitude response is observed when it occurs in a dense frequency region. Flexibility allows the coral colony to lower the drag it faces under fluid flow. The vibrationnal response of the colony allows it to "sweep more water" and encounter more particles. Whereas a beam without branches can maximize this gain in the lock-in region of the second mode, a branched structure smooths out the capture gain over a larger reduced velocity range. The code developed in this work is integrated in the open source co-rotational finite element software ONSAS.