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

A NUMERICAL STUDY OF A NEW SPRAY APPLICATOR

This study focuses on the design and development of a new spray applicator design utilizing effects of imposed pressure oscillations in conjunction with cavitation collapse energy to create distribution of fine droplets. An oscillating horn placed inside the nozzle performing high frequency oscillations is envisioned to provide the necessary pressure perturbations on the exiting liquid jet, while the nozzle geometry design in configured to amplify cavitation process. Initially, a two-zone approach modeling the nozzle interior and exterior in a separate fashion and later, a coupled strategy is proposed. Parametric studies describing the effect of horn stroke length, frequency, its position inside the nozzle in combination with different nozzle designs and liquid flow rates are explored to identify their contribution in obtaining desired cavitation characteristics. In this regard, incorporation of a backward facing step profile within the nozzle shows strong capability of generating the required cavitation and flow field distribution at the nozzle exit. The velocity modulations occuring at the nozzle exit due to oscillating horn structure result in a wide gamut of liquid structures specific to the imposed oscillation frequency and modulation amplitude. The disintegration characteristics of these modulated liquid jets are studied using a Volume-of-Fluid (VOF) interface capturing approach based on finite volume methodology employing an interface compression scheme. VOF methods are validated against experimental results and then subsequently used to study scaling parameters governing the modulated liquid jets. To perform coupled interior-exterior nozzle computations with cavitation, two new cavitation models are presented: First, a model based on Homogeneous Equilibrium assumptions for tracking cavitation events in a compressible framework is presented. Owing to its inability to simulate incompressible cavitating flows, a new cavitation event tracking model based on a Cavitation-Induced-Momentum-Defect (CIMD) correction approach is formulated utilizing a scalar transport model for vapor volume fraction with relevant transport, diffusion and source terms. Validations of both the models against experimental observations are detailed. Coupled internal-external liquid flow computations from the proposed atomizer design using a VOF-CIMD strategy shows strong potential for rapid drop formation in the presence of cavitation effects. A prototype model of a new spray applicator design is presented

Numerical Modeling of Deformation, Oscillation, Spreading and Collision Characteristics of Droplets in an Electric Field

Electric field induced flows, or electrohydrodynamics (EHD), have been promising in many fast-growing technologies, where droplet movement and deformation can be controlled to enhance heat transfer and mass transport. Several complex EHD problems existing in many applications were investigated in this thesis. Firstly, this thesis presents the results of numerical simulations of the deformation, oscillation and breakup of a weakly conducting droplet suspended in an ambient medium with higher conductivity. It is the first time that the deformation of such a droplet was investigated numerically in a 3D configuration. We have determined three types of behavior for the droplets, which are less conducting than ambient fluid: 1) oblate deformation (which can be predicted from the small perturbation theory), 2) oscillatory oblate-prolate deformation and 3) breakup of the droplet. Secondly, a numerical study of droplet oscillation placed on different hydrophobic surfaces under the effect of applied AC voltage including the effect of ambient gas was investigated. The presented algorithm could reproduce droplet oscillations on a surface considering different contact angles. It has been found that the resonance frequency of the water droplet depends on the surface property of the hydrophobic materials and the electrostatic force. Thirdly, a new design of an electrowetting mixer using the rotating electric field was proposed which offers a new method to effectively mix two droplets over a different range of AC frequencies. Two regimes were observed for droplet coalescence: 1) coalescence due to the high droplet deformation, 2) coalescence due to the interaction of electrically induced dipoles. Fourthly, the spreading and retraction control of millimetric water droplets impacting on dry surfaces have been investigated to examine the effect of the surface charge density and electric field intensity. The effect of the surface charge on the spreading of droplets placed gently on surfaces was investigated in the first part. It was found that the maximum spreading diameter increases with an increasing charge. In the second part, the impact of a droplet on a ground electrode was considered. It was also found that in order to keep the maximum diameter after the impact, less charge is needed for surfaces with lower contact angle. Finally, the interaction between two identical charged droplets was investigated numerically. The effects of the impact velocity, drop size ratio and electric charge on the behavior of the combined droplet were investigated. It was shown that two conducting droplets carrying charges of the same polarity under some conditions may be electrically attracted. The formation of charged daughter droplets has been investigated and it was found that the number of the satellite droplets after collision appears to increase with an increase in the droplet charge

Effects of Internal Gas Explosion on an Underwater Tunnel Roof

An underwater reinforced concrete tunnel roof is subjected to an internal gas explosion. Dynamic analyses are performed for three cases, namely, (1) an uncoupled solution, (2) class II coupling analysis and (3) full model with class I and II couplings. Three load cases are considered, dead (gravity) load, uniformly distributed vertical loads from sand and water and finally an internal pressure gas explosion. Linear and non-linear constitutive relationships are considered for the materials constituting the gas explosion problem. Results include time deflection of tunnel roof, time histories of stresses in vertical reinforcing bars and contours of concrete stresses for tunnel roof. By conducting analyses from various models, the question whether the tunnel would be damaged to such an extent that its serviceability would be impaired is investigated

Direct numerical simulation of bubble-bubble and droplet-droplet interaction using a Surface Thin Film model

This dissertation deals with the simulation of dispersed multiphase flow. The particle-particle and particle-fluid interactions in this class of flows play an important role on the hydrodynamics and fluid transport phenomena that govern the overall flow behaviour. Accurate computational modelling of the particle-particle and particle- fluid interactions is thus required to correctly model the flow. The aim of this study is to use a Direct Numerical Simulation approach based on a smoothed Volume Of Fluid method to model particle-particle interactions in a dispersed multiphase flow at a fundamental level, and employing a surface thin film model, to drastically reduce the computational effort required. A multiscale modelling approach is followed with the smoothed Volume Of Fluid simulation on the particle scale and the surface thin film model simulation on the thin- film scale. The resulting governing equations are the Navier-Stokes equations for an incompressible viscous multiphase Newtonian fluid undergoing laminar and isothermal three-dimensional flow, the interface advection equation and the reduced order surface thin film equation. The model equations are discretized using the Finite Volume Method and implemented into the open source software OpenFOAM®. The numerical solution is obtained by solving the resulting non-linear system of equations implicitly on a structured computational grid on parallel processors using a pressure correction algorithm to converge the pressure at each time step. The study is restricted to gas-liquid systems where particles could either be bubbles or droplets; rigid particles are not considered. The model is tested against experimental results from binary collision of hydrocarbon droplets. Good qualitative numerical results are obtained at a practical computational cost

Destruction of preferential accumulation using Lorentz force interactions.

The effect of electric charge, residing on particles, upon the phenomenon of preferential accumulation is investigated using direct numerical simulations of forced isotropic turbulence. It is well known that particles with a certain range of Stokes numbers preferentially accumulate, or de-mix, due to action of turbulent motion. Here it is shown that charged particles interact with each other through an electric field generated by non-uniformity of particle distribution. This interaction mitigates preferential accumulation at a bulk charge density level that is practically relevant and commensurate with the first few centimetres of a spray plume, the region where non-homogeneous particle concentration typically forms. It is suggested that use of electric charge could be useful in improving mixture preparation for spray combustion applications