Investigation of cavitation noise using Eulerian-Lagrangian multiscale modeling

We have employed the large eddy simulation (LES) approach to investigate the cavitation noise characteristics of an unsteady cavitating flow around a NACA66 (National Advisory Committee for Aeronautics) hydrofoil by employing an Eulerian-Lagrangian based multiscale cavitation model. A volume of fluid (VOF) method simulates the large cavity, whereas a Lagrangian discrete bubble model (DBM) tracks the small bubbles. Meanwhile, noise is determined using the Ffowcs Williams-Hawkings equation (FW-H). Eulerian-Lagrangian analysis has shown that, in comparison to VOF, it is more effective in revealing microscopic characteristics of unsteady cavitating flows, including microscale bubbles, that are unresolvable around the cloud cavity, and their impact on the flow field. It is also evident that its evolution of cavitation features on the hydrofoil is more consistent with the experimental observations. The frequency of the maximum sound pressure level corresponds to the frequency of the main cavity shedding for the noise characteristics. Using the Eulerian-Lagrangian method to predict the noise signal, results show that the cavitation noise, generated by discrete bubbles due to their collapse, is mainly composed of high-frequency signals. In addition, the frequency of cavitation noise induced by discrete microbubbles is around 10 kHz. A typical characteristic of cavitation noise, including two intense pulses during the collapsing of the cloud cavity, is described, as well as the mechanisms that underlie these phenomena. The findings of this work provide for a fundamental understanding of cavitation and serve as a valuable reference for the design and intensification of hydrodynamic cavitation reactors.     

A theory of composites perspective on matrix valued Stieltjes functions

A series of physically motivated operations appearing in the study of composite materials are interpreted in terms of elementary continued fraction transforms of matrix valued, rational Stieltjes functions.