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Can a classical system as walking oil droplets on a vibrating surface simulate the single and double slit Quantum Mechanics experiment? A systematic investigation reveals that the answer is no, but that the classical system exhibits rich and fascinating structures.
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Hard particle erosion and cavitation damage are two main wear problems that can affect the internal components of hydraulic machinery such as hydraulic turbines or pumps. If both problems synergistically act together, the damage can be more severe and result in high maintenance costs. In this work, a study of the interaction of hard particles and cavitation bubbles is developed to understand their interactive behavior. Experimental tests and numerical simulations using computational fluid dynamics (CFD) were performed. Experimentally, a cavitation bubble was generated with an electric spark near a solid surface, and its interaction with hard particles of different sizes and materials was observed using a high-speed camera. A simplified analytical approach was developed to model the behavior of the particles near the bubble interface during its collapse. Computationally, we simulated an air bubble that grew and collapsed near a solid wall while interacting with one particle near the bubble interface. Several simulations with different conditions were made and validated with the experimental data. The experimental data obtained from particles above the bubble were consistent with the numerical results and analytical study. The particle size, density and position of the particle with respect to the bubble interface strongly affected the maximum velocity of the particles.
In this paper, we present an efficient, accurate and fully Lagrangian numerical solver for modeling wave interaction with oscillating wave energy converter (OWSC). The key idea is to couple SPHinXsys, an open-source multi-physics library in unified smoothed particle hydrodynamic (SPH) framework, with Simbody which presents an object-oriented Application Programming Interface (API) for multi-body dynamics. More precisely, the wave dynamics and its interaction with OWSC is resolved by Riemann-based weakly-compressible SPH method using SPHinXsys, and the solid-body kinematics is computed by Simbody library. Numerical experiments demonstrate that the proposed solver can accurately predict the wave elevations, flap rotation and wave loading on the flap in comparison with laboratory experiment. In particularly, the new solver shows optimized computational performance through CPU cost analysis and comparison with commercial software package ANSYS FLUENT and other SPH-based solvers in literature. Furthermore, a linear damper is applied for imitating the power take-off (PTO) system to study its effects on the hydrodynamics properties of OWSC and efficiency of energy harvesting. In addition, the present solver is used to model extreme wave condition using the focused wave approach to investigate the extreme loads and motions of OWSC under such extreme wave conditions. It worth noting that though the model validation used herein is a bottom hinged oscillating Wave Energy Converter (WEC), the obtained numerical results show promising potential of the proposed solver to future applications in the design of high-performance WECs.
We are modelling multi-scale, multi-physics uncertainty in wave-current interaction (WCI). To model uncertainty in WCI, we introduce stochasticity into the wave dynamics of two classic models of WCI; namely, the Generalised Lagrangian Mean (GLM) model and the Craik--Leibovich (CL) model. The key idea for the GLM approach is the separation of the Lagrangian (fluid) and Eulerian (wave) degrees of freedom in Hamiltons principle. This is done by coupling an Euler--Poincare {it reduced Lagrangian} for the current flow and a {it phase-space Lagrangian} for the wave field. WCI in the GLM model involves the nonlinear Doppler shift in frequency of the Hamiltonian wave subsystem, which arises because the waves propagate in the frame of motion of the Lagrangian-mean velocity of the current. In contrast, WCI in the CL model arises because the fluid velocity is defined relative to the frame of motion of the Stokes mean drift velocity, which is usually taken to be prescribed, time independent and driven externally. We compare the GLM and CL theories by placing them both into the general framework of a stochastic Hamiltons principle for a 3D Euler--Boussinesq (EB) fluid in a rotating frame. In other examples, we also apply the GLM and CL methods to add wave physics and stochasticity to the familiar 1D and 2D shallow water flow models. The differences in the types of stochasticity which arise for GLM and CL models can be seen by comparing the Kelvin circulation theorems for the two models. The GLM model acquires stochasticity in its Lagrangian transport velocity for the currents and also in its group velocity for the waves. The Kelvin circulation theorem stochastic CL model can accept stochasticity in its both its integrand and in the Lagrangian transport velocity of its circulation loop.
We present a theoretical expression for the acoustic interaction force between small spherical particles suspended in an ideal fluid exposed to an external acoustic wave. The acoustic interaction force is the part of the acoustic radiation force on one given particle involving the scattered waves from the other particles. The particles, either compressible liquid droplets or elastic microspheres, are considered to be much smaller than the acoustic wavelength. In this so-called Rayleigh limit, the acoustic interaction forces between the particles are well approximated by gradients of pair-interaction potentials with no restriction on the inter-particle distance. The theory is applied to studies of the acoustic interaction force on a particle suspension in either standing or traveling plane waves. The results show aggregation regions along the wave propagation direction, while particles may attract or repel each other in the transverse direction. In addition, a mean-field approximation is developed to describe the acoustic interaction force in an emulsion of oil droplets in water.
Wave--current interaction (WCI) dynamics energizes and mixes the ocean thermocline by producing a combination of Langmuir circulation, internal waves and turbulent shear flows, which interact over a wide range of time scales. Two complementary approaches exist for approximating different aspects of WCI dynamics. These are the Generalized Lagrangian Mean (GLM) approach and the Gent--McWilliams (GM) approach. Their complementarity is evident in their Kelvin circulation theorems. GLM introduces a wave pseudomomentum per unit mass into its Kelvin circulation integrand, while GM introduces a an additional `bolus velocity to transport its Kelvin circulation loop. The GLM approach models Eulerian momentum, while the GM approach models Lagrangian transport. In principle, both GLM and GM are based on the Euler--Boussinesq (EB) equations for an incompressible, stratified, rotating flow. The differences in their Kelvin theorems arise from differences in how they model the flow map in the Lagrangian for the Hamilton variational principle underlying the EB equations. A recently developed approach for uncertainty quantification in fluid dynamics constrains fluid variational principles to require that Lagrangian trajectories undergo Stochastic Advection by Lie Transport (SALT). Here we introduce stochastic closure strategies for quantifying uncertainty in WCI by adapting the SALT approach to both the GLM and GM approximations of the EB variational principle. In the GLM framework, we introduce a stochastic group velocity for transport of wave properties, relative to the frame of motion of the Lagrangian mean flow velocity and a stochastic pressure contribution from the fluctuating kinetic energy. In the GM framework we introduce a stochastic bolus velocity in addition to the mean drift velocity by imposing the SALT constraint in the GM variational principle.
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