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

SPH with the multiple boundary tangent method

In this article, we present an improved solid boundary treatment formulation for the smoothed particle hydrodynamics (SPH) method. Benchmark simulations using previously reported boundary treatments can suffer from particle penetration and may produce results that numerically blow up near solid boundaries. As well, current SPH boundary approaches do not properly treat curved boundaries in complicated flow domains. These drawbacks have been remedied in a new boundary treatment method presented in this article, called the multiple boundary tangent (MBT) approach. In this article we present two important benchmark problems to validate the developed algorithm and show that the multiple boundary tangent treatment produces results that agree with known numerical and experimental solutions. The two benchmark problems chosen are the lid-driven cavity problem, and flow over a cylinder. The SPH solutions using the MBT approach and the results from literature are in very good agreement. These solutions involved solid boundaries, but the approach presented herein should be extendable to time-evolving, free-surface boundaries

ISPH modeling of Rayleigh–Taylor instability

This paper presents a Smoothed Particle Hydrodynamics (SPH) solution to a Rayleigh-Taylor Instability (RTI) problem in an incompressible viscous two-phase immiscible fluid with an interfacial tension. The evolution of the fluid-fluid interface is numerically investigated for four different density ratios. The simulation outcomes are compared with existing results in literature. Three stages of instability, namely the exponential growth rate, the formation of circular form at the crest of spike and the appearance of the final shape of instability, are discussed for different density ratios. It is shown that the numerical algorithm used in this work is capable of capturing the complete physics behind the RTI, such as interface evolution, growth rate and secondary instability accurately, and successfully

Brownian dynamics of rigid particles in an incompressible fluctuating fluid by a meshfree method

A meshfree Lagrangian method for the fluctuating hydrodynamic equations (FHEs) with fluid-structure interactions is presented. Brownian motion of the particle is investigated by direct numerical simulation of the fluctuating hydrodynamic equations. In this framework a bidirectional coupling has been introduced between the fluctuating fluid and the solid object. The force governing the motion of the solid object is solely due to the surrounding fluid particles. Since a meshfree formulation is used, the method can be extended to many real applications involving complex fluid flows. A three-dimensional implementation is presented. In particular, we observe the short and long-time behaviour of the velocity autocorrelation function (VACF) of Brownian particles and compare it with the analytical expression. Moreover, the Stokes-Einstein relation is reproduced to ensure the correct long-time behaviour of Brownian dynamics.Comment: 24 pages, 2 figure

Study on SPH Viscosity Term Formulations

For viscosity-dominated flows, the viscous effect plays a much more important role. Since the viscosity term in SPH-governing (Smoothed Particle Hydrodynamics) equations involves the discretization of a second-order derivative, its treatment could be much more challenging than that of a first-order derivative, such as the pressure gradient. The present paper summarizes a series of improved methods for modeling the second-order viscosity force term. By using a benchmark patch test, the numerical accuracy and efficiency of different approaches are evaluated under both uniform and non-uniform particle configurations. Then these viscosity force models are used to compute a documented lid-driven cavity flow and its interaction with a cylinder, from which the most recommended viscosity term formulation has been identified

APPLICATION OF SMOOTHED PARTICLE HYDRODYNAMICS METHOD FOR SIMULATING INCOMPRESSIBLE LAMINAR FLOW

The paper presents the smoothed particle hydrodynamics (SPH) method, a numerical method for simulating fluid dynamics phenomena, based on particle systems. The SPH method approximates continuum with a finite number of particles which carry physical properties and serve as approximation points for spatial functions. Integral approximations of field functions and their derivatives are described using smoothing kernel functions which have to satisfy a number of conditions to ensure consistency with a given order. Particle approximations are also shown. This method can be used for simulating either compressible or incompressible flows if the special equation of state, proposed by Morris et al., is applied. A computer algorithm is developed for two standard benchmarking cases, the Poiseuille and the Couette flow. It is shown that the simulation results agree fairly well with the analytical series solution. Nevertheless, some combinations of time step for numerical integration and sound speed can lead to non-physical phenomena. Like any other numerical method, SPH has its advantages and disadvantages noted through practical use and theoretical considerations, which are briefly described in this paper