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We present a spatially varying Robin interface condition for solving fluid‐structure interaction problems involving incompressible fluid flows and nonuniform flexible structures. Recent studies have shown that for uniform structures with constant material and geometric properties, a constant one‐parameter Robin interface condition can improve the stability and accuracy of partitioned numerical solution procedures. In this work, we generalize the parameter to a spatially varying function that depends on the structure's local material and geometric properties, without varying the exact solution of the coupled fluid‐structure system. We present an algorithm to implement the Robin interface condition in an embedded boundary method for coupling a projection‐based incompressible viscous flow solver with a nonlinear finite element structural solver. We demonstrate the numerical effects of the spatially varying Robin interface condition using two example problems: a simplified model problem featuring a nonuniform Euler‐Bernoulli beam interacting with an inviscid flow and a generalized Turek‐Hron problem featuring a nonuniform, highly flexible beam interacting with a viscous laminar flow. Both cases show that a spatially varying Robin interface condition can clearly improve numerical accuracy (by up to two orders of magnitude in one instance) for the same computational cost. Using the second example problem, we also demonstrate and compare two models for determining the local value of the combination function in the Robin interface condition.

 

The fluid dynamics of a bubble collapsing near an elastic or viscoelastic material is coupled with the mechanical response of the material. We apply a multiphase fluid–solid coupled computational model to simulate the collapse of an air bubble in water induced by an ultrasound shock wave, near different types of materials including metals (e.g. aluminium), polymers (e.g. polyurea), minerals (e.g. gypsum), glass and foams. We characterize the two-way fluid–material interaction by examining the fluid pressure and velocity fields, the time history of bubble shape and volume and the maximum tensile and shear stresses produced in the material. We show that the ratio of the longitudinal acoustic impedance of the material compared to that of the ambient fluid, $Z/Z_0$ , plays a significant role. When $Z/Z_0<1$ , the material reflects the compressive front of the incident shock into a tensile wave. The reflected tensile wave impinges on the bubble and decelerates its collapse. As a result, the collapse produces a liquid jet, but not necessarily a shock wave. When $Z/Z_0>1$ , the reflected wave is compressive and accelerates the bubble's collapse, leading to the emission of a shock wave whose amplitude increases linearly with $\log (Z/Z_0)$ , and can be much higher than the amplitude of the incident shock. The reflection of this emitted shock wave impinges on the bubble during its rebound. It reduces the speed of the bubble's rebound and the velocity of the liquid jet. Furthermore, we show that, for a set of materials with $Z/Z_0\in [0.04, 10.8]$ , the effect of acoustic impedance on the bubble's collapse time and minimum volume can be captured using phenomenological models constructed based on the solution of Rayleigh–Plesset equation. 

Erosion of solid surfaces due to cavitation has been studied for decades. However, it has been a long debate that which mechanism, namely shockwaves, microjets towards the surface, or both, during the cavitation bubble collapse is the primary factor responsible for that erosion. In this project we investigate the small-scale mechanisms of material erosion induced by the collapse of a single cavitation bubble close to a wall. More specifically, our experimental setup includes modification of the initial nucleus size, the maximum bubble radius, the stand-off distance to the wall, the material softness, and the initial flow temperature. We record the evolution of the bubble using high speed cameras as well as the local impacts on the materials. With the help of specifically designed cold-wires, we also measure the temperature in the liquid and in the bubble. Two different methods are used to generate the bubble: (i) an acoustic shockwave of variable intensity, (ii) a YAG laser, which may introduce a high temperature at the start. We also combine the two methods in which the laser initially creates a nucleus, then the shockwave triggers the expansion of the bubble. The objectives of the project are included in this paper, while some first results will be presented at the CAV2018 conference.