Data-Driven Model of the Response of Flexible Hydrofoils in Cloud Cavitation

The objective of this work is to discover the equations that govern the response of stiff and flexible hydrofoils in cloud cavitation via the usage of Sparse Identification of Nonlinear Dynamics (SINDy). Cavitation is a special form of separated multiphase flow relevant for a diverse range of hydrodynamic lifting bodies such as propellers, flow control surfaces, energy harvesting and energy saving devices that operate at high speeds and/or near the free surface. Since many lifting devices are effectively thin plates or beams subject to high loading, flow-induced deformations and vibrations may occur. The deformations modify the surrounding flow, changing the cavity dynamics and resulting response. In this work, we employ SINDy to discover the coefficients of the nonlinear dynamical system based on experimental data for a stiff stainless steel (SS) and a flexible composite (CF) hydrofoil in cloud cavitation collected at the Australian Maritime College in the Cavitation Research Laboratory water tunnel. We aim to determine the variation of fluid added mass and damping coefficients with the effective cavitation parameter, as well as the resulting fluctuating lift coefficients due to fluid-structure interaction using SINDy, and compare the coefficients with the physics-based reduced-order model (ROM) of the cloud cavitation response of flexible hydrofoils presented in Young et al. (2022).

The results show that in general, while the linear fluid added mass and damping coefficients are approximately the same between the data-driven and physics-based ROM, there were noticeable differences in the trend and magnitude for the nonlinear fluid added mass and damping terms, as well as the rigid hydrofoil cavity forcing terms. Despite these differences, the governing equations with nonlinear damping predicted by SINDy can capture the dominant frequencies of the SS and CF hydrofoils in unsteady cavitating flow. However, the usage of SINDy is limited to the cavitation number range where the intensity of load fluctuations caused by unsteady cloud cavitation is higher than the ambient noise. For this experimental setup, this range is 0:3 <= s <= 0:8. Additional data or more accurate numerical modeling would be needed for proper model development and validation.