Eulerian-Lagrangian method for simulation of cloud cavitation

We present a coupled Eulerian-Lagrangian method to simulate cloud cavitation in a compressible liquid. The method is designed to capture the strong, volumetric oscillations of each bubble and the bubble-scattered acoustics. The dynamics of the bubbly mixture is formulated using volume-averaged equations of motion. The continuous phase is discretized on an Eulerian grid and integrated using a high-order, finite-volume weighted essentially non-oscillatory (WENO) scheme, while the gas phase is modeled as spherical, Lagrangian point-bubbles at the sub-grid scale, each of whose radial evolution is tracked by solving the Keller-Miksis equation. The volume of bubbles is mapped onto the Eulerian grid as the void fraction by using a regularization (smearing) kernel. In the most general case, where the bubble distribution is arbitrary, three-dimensional Cartesian grids are used for spatial discretization. In order to reduce the computational cost for problems possessing translational or rotational homogeneities, we spatially average the governing equations along the direction of symmetry and discretize the continuous phase on two-dimensional or axi-symmetric grids, respectively. We specify a regularization kernel that maps the three-dimensional distribution of bubbles onto the field of an averaged two-dimensional or axi-symmetric void fraction. A closure is developed to model the pressure fluctuations at the sub-grid scale as synthetic noise. For the examples considered here, modeling the sub-grid pressure fluctuations as white noise agrees a priori with computed distributions from three-dimensional simulations, and suffices, a posteriori, to accurately reproduce the statistics of the bubble dynamics. The numerical method and its verification are described by considering test cases of the dynamics of a single bubble and cloud cavitaiton induced by ultrasound fields.Comment: 28 pages, 16 figure

Numerische Modellierung und Simulation von Kavitationsblasenwolken mit einer Lagrange-Euler-Methode

In this thesis, the Lagrangian-Eulerian coupling model is proposed to investigate dynamically the cavitation bubble cloud. Based on the Lagrangian-Eulerian one-way coupling model, the homogeneous cavitation nucleation inside microchannel is studied. Furthermore, we develop the Lagrangian-Eulerian two-way coupling for the numerical simulation of the bubble cluster with pressure wave interaction and the bubble cloud Rayleigh collapse.In dieser Doktorarbeit wird das Lagrange-Euler-Kopplungsmodell vorgeschlagen, um die Kavitationsblasenwolke dynamisch zu untersuchen. Basierend auf dem Lagrange-Euler-Einweg-Kopplungsmodell wird die homogene Kavitationskeimbildung im Mikrokanal untersucht. Darüber hinaus entwickeln wir die Lagrange-Euler-Zweiwege-Kopplung zur numerischen Simulation des Blasenclusters mit Druckwellenwechselwirkung und dem Rayleigh-Kollaps der Bubble Cloud

Numerical simulation and analysis of multi-scale cavitating flows using a hybrid mixture-bubble model

The aim of this research is to model and analyse multi-scale cavitating flows with a certain emphasis on small sub-grid vapour structures. Cavitating flows include vapour structures with different length scales, from micro-bubbles to large cavities. The correct estimation of small-scale cavities can be as important as that of large-scale structures, since cavitation inception as well as the resulting noise, erosion, pressure shocks and strong vibrations occur at small time and length scales. For numerical analysis, while popular homogeneous mixture models are practical options for simulation of large-scale flows, they are normally limited in representation of the small-scale cavities due to high computational expenses and inherent simplifications. In this study, a hybrid cavitation model is developed by coupling a homogeneous mixture model with a Lagrangian bubble model. In this model, large cavity structures are modelled using a mixture model, while small sub-grid structures are tracked as Lagrangian bubbles.The coupling of the mixture and the bubble models is based on an improved algorithm which is compatible with the flow physics and the governing equations are revised to take into account the bubble effect on the continuum flow.The Lagrangian bubble model is based on a four-way coupling approach in which various effective forces on bubble transport are taken into account and a new algorithm is introduced to model bubble-bubble collisions. Besides, the bubble dynamics is calculated based on the local pressure effect by introducing an improved form of the Rayleigh-Plesset equation. The other contributions include implementing a new submodel for prediction of bubble break-up as well as correcting the bubble wall boundary condition and revising the void handling scheme.Apart from the model development, for validation of the solver, a set of experimental tests on cavitating flow around a surface-mounted bluff body are performed in this study. Then, a multi-scale test case is simulated using both the new hybrid model and the traditional mixture model. The comparison of the results with the experimental data shows considerable improvements in both predicting the large cavities as well as capturing the small-scale structures using the hybrid model. More accurate results (as compared to the traditional mixture model) can be achieved even with considerably lower mesh resolution. The results, among others, show that small-scale cavities not only are important at the inception and collapse steps, but also influence the development of large-scale structures

Numerical simulation and analysis of multi-scale cavitating flows

Cavitating flows include vapour structures with a wide range of different length scales, from micro-bubbles to large cavities. The correct estimation of small-scale cavities can be as important as that of large-scale structures, because cavitation inception as well as the resulting noise, erosion and strong vibrations occur at small time and length scales. In this study, a multi-scale cavitating flow around a sharp-edged bluff body is investigated. For numerical analysis, while popular homogeneous mixture models are practical options for large-scale applications, they are normally limited in the representation of small-scale cavities. Therefore, a hybrid cavitation model is developed by coupling a mixture model with a Lagrangian bubble model. The Lagrangian model is based on a four-way coupling approach, which includes new submodels, to consider various small-scale phenomena in cavitation dynamics. Additionally, the coupling of the mixture and the Lagrangian models is based on an improved algorithm that is compatible with the flow physics. The numerical analysis provides a detailed description of the multi-scale dynamics of cavities as well as the interactions between vapour structures of various scales and the continuous flow. The results, among others, show that small-scale cavities not only are important at the inception and collapse steps, but also influence the development of large-scale structures. Furthermore, a comparison of the results with those from experiment shows considerable improvements in both predicting the large cavities and capturing the small-scale structures using the hybrid model. More accurate results (compared with the traditional mixture model) can be achieved even with a lower mesh resolution

Simulations of cavitation - from the large vapour structures to the small bubble dynamics

Very few people around us know the meaning of the word cavitation, except from those who saw the movie "The Hunt for Red October" and can relate cavitation to Sean Connery in a submarine. Some of them know that it corresponds to the formation of bubbles, due to a pressure drop, and causes erosion and noise. However, cavitation is much more complex. A large amount of research work has been done over the last thirty years in order to improve the understanding of the interactions between the various physical processes involved. The present work aims at gaining more knowledge about cavitation in water turbines. Some of the properties of cavitation at a water turbine runner blade are similar to those at a hydrofoil in a water test tunnel. Therefore, the overall purpose of this work is to improve the numerical models for cavitation inception and development on a hydrofoil. The focus of this thesis lies on numerical methodologies that include the broad range of cavity sizes, using appropriate models for each specific phenomenon. The smallest bubbles, called nuclei, are tracked in the flow with the Discrete Bubble Model, and their dynamics is resolved with the Rayleigh-Plesset equation. This approach can predict how the nuclei are transported over a hydrofoil to regions of low static pressure, where they grow and either collapse or contribute to the formation of large-scale vapour cavities. The large non-spherical structures are commonly modelled using the Volume-Of-Fluid method together with a mass transfer model for vaporisation and condensation. This approach predicts the development of the vapour cavity, such as its breakup and the shedding process observed experimentally in the context of cavitating hydrofoils. The present work implements the above-mentioned models in the OpenFOAM C++ library, and performs simulations to assess the performance of the models. A new multiscale model is developed, implemented and used on a cavitating hydrofoil. The multi-scale model includes both the small spherical bubbles, the large non-spherical vapour structures, and the transition between those regimes

Numerical investigation of high-speed droplet impact using a multiscale two-fluid approach

A single droplet impact onto solid surfaces remains a fundamental and challenging topic in both experimental and numerical studies with significant importance in a plethora of industrial applications, ranging from printing technologies to fuel injection in internal combustion engines. Under high-speed impact conditions, additional complexities arise as a result of the prompt droplet splashing and the subsequent violent fragmentation; thus, different flow regimes and a vast spectrum of sizes for the produced secondary flow structures coexist in the flow field. The present work introduces a numerical methodology to capture the multiscale processes involved with respect to local topological characteristics. The proposed methodology concerns a compressible Σ-Υ two-fluid model with dynamic interface sharpening based on an advanced flow topology detection algorithm. The model has been developed in OpenFOAM® and provides the flexibility of dealing with the multiscale character of droplet splashing, by switching between a sharp and a diffuse interface within the Eulerian-Eulerian framework in segregated and dispersed flow regions, respectively. An additional transport equation for the interface surface area density (Σ) introduces important information for the sub-grid scale phenomena, which is exploited in the dispersed flow regions to provide an insight into the extended cloud of secondary droplets after impact on the target. A high-speed water droplet impact case has been examined and evaluated against new experimental data; these refer to a millimetre size droplet impacting a solid dry smooth surface at velocity as high as 150m/s, which corresponds to a Weber number of ~7.6×10^5. At the investigated impact conditions compressibility effects dominate the early stages of droplet splashing. A strong shock wave forms and propagates inside the droplet, where transonic Mach numbers occur; local Mach numbers up to 2.5 are observed for the expelled surrounding gas outside the droplet. The proposed numerical approach is found to capture relatively accurately the phenomena and provide significant information regarding the produced flow structure dimensions, which is not available from the experiment

Numerical prediction of small scale cavities using a coupled mixture-bubble model

In this study a hybrid Eulerian mixture - Lagrangian bubble model is developed for numerical simulation of cavitating flows.\ua0In this model, the large scale cavities are represented in the Eulerian framework using the homogeneous mixture model, while\ua0the small sub-grid structures are tracked as Lagrangian bubbles. Also, at each time step small cavity structures in the Eulerian\ua0framework are transformed to the Lagrangian framework to be treated as sub-grid bubbles and vice versa. Using this model, it\ua0is possible to represent various cavity structures of different length scales with reasonable computational cost