Comparison of interface models to account for surface tension in SPH method

The Smoothed Particle Hydrodynamics method (SPH) is a meshfree Lagrangian simulation methodwidely applied for fluid simulations due to the advantages presented by this method for solvingproblems with free and deformable surfaces. In many scientific and engineering applications, surface tension forces play an important or evendominating role in the dynamics of the system. For instance, the breakage (instability) of a liquid jetor film is strongly affected by the strength of the surface tension at the liquid-air interface.Simulating deforming phase interfaces with strong topological changes is still today a challengingtask. As a promising numerical method, here we use SPH to predict the interface instability at awater-air interface.With SPH, the main challenge in modelling surface tension at a free-surface is the accuratedescription of the interface (normal direction and curvature). When only the liquid phase is modelled(to decrease the computational cost), the standard SPH approximations to calculate the normaldirection and curvature of the interface suffer from a lacking “full support”, i.e. the omitted andtherefore missing gas particles. Various models for such free surface surface tension corrections werepresented, see e.g. among others Sirotkin et al., Ordoubadi et al. or Ehigiamusoe et al. Many of thesemodels follow the classical Continuum Surface Force (CSF) approach (Morris, Adami et al.) andincorporate different corrections/treatments at the surface. The objective of our ongoing study is to investigate the influence of different interface descriptions.We compare different free surface particle detection schemes, normal vector calculations andcurvature estimations for the quality of the resulting surface-tension effect. In this work, we focus ontwo-dimensional problems and consider a static drop and oscillating drops as test cases

Smoothed Particle Hydrodynamics for Navier-Stokes Fluid Flow Application

The aim of this publication is to introduce the particle based computational fluid dynamics (CFD) method smoothed particle hydrodynamics (SPH) and introduce an applicable and valid SPH implementation for practical cases. For this purpose, current research approaches are combined regarding performance and numerical stability.  The principles of the method, the mathematical basics and the discretization of the Navier-Stokes equations are clarified. Furthermore, the implementation of method-specific boundary conditions, wall, inlet and outlet, as well as several correction procedures and a surface tension setup into the present code framework are described. The advantages and validity of the method are shown based on different cases. The free surface fluid behavior of a dam break is compared to experimental data of the time dependent water level of selected positions. A Karman vortex street is validated by its Strouhal number for different Reynolds numbers. The frequency of an oscillating drop is analysed and compared to the analytical solution.  The SPH is utilized for pipe flows influenced by a backward facing step and shows an expected qualitative flow field

An SPH multi-fluid model based on quasi-buoyancy for interface stabilization up to high density ratios and realistic wave speed ratios

We introduce a Smoothed Particle Hydrodynamics (SPH) concept for the stabilization of the interface between two fluids. It is demonstrated that the change in the pressure gradient across the interface leads to a force imbalance. This force imbalance is attributed to the particle approximation implicit to SPH. To stabilize the interface a pressure gradient correction is proposed. In this approach the multi-fluid pressure gradients are related to the (gravitational and fluid) accelerations. This leads to a quasi-buoyancy correction for hydrostatic (stratified) flows, which is extended to non-hydrostatic flows. The result is a simple density correction which involves no parameters or coefficients. This correction is included as an extra term in the SPH momentum equation. The new concept for the stabilization of the interface is explored in five case studies and compared with other multi-fluid models. The first case is the stagnant flow in a tank: the interface remains stable up to density ratios of 1:1000 (typical for water and air) in combination with artificial wave speed ratios up to 1:4. The second and third cases are the Rayleigh-Taylor instability and the rising bubble, where a reasonable agreement between SPH and level-set models is achieved. The fourth case is an air flow across a water surface up to density ratios of 1:100, artificial wave speeds for water higher than that of air, and high air velocities. The fifth case is about the propagation of internal gravity waves up to density ratios of 1:100 and artificial wave speed ratios of 1:2. It is demonstrated that the quasi-buoyancy model may be used to stabilize the interface between two fluids up to high density ratios, with real (low) viscosities and more realistic wave speed ratios than achieved by other WCSPH multi-fluid models. Real wave speed ratios can be achieved, as long as the fluid velocities are not very high. Although the wave speeds may be artificial in many cases, correct and realistic wave speed ratios are essential in the modelling of heat transfer between two fluids (e.g. in engineering applications such as gas turbines)

Non-reflecting boundary conditions and tensile instability in smooth particle hydrodynamics

This thesis aimed at the understanding and further development of smoothed particle hydrodynamics (SPH). The first part described the implementations of non-reflecting boundary conditions for elastic- waves in SPH. The second part contains a stability analysis of the semi-discrete SPH equations and a new method for stabilising basic SPH in tension

Smoothed Particle Hydrodynamics Simulations for Dynamic Capillary Interactions

Complex interactions in porous media play an important role on many industrial and geotechnical applications, such as groundwater treatment, porous catalysts, carbon geosequestration, and oil recovery. Rate-dependent wetting effects are of great significance in understanding the multiphase behaviours of porous media thus further throw light on engineering solutions to the above problems. In this thesis, a modified smoothed particle hydrodynamics (SPH) model is applied to simulate (1) the contact angle dynamics and (2) stretching of liquid bridge at meso-scale. This SPH model adopted an inter-particle force formulation with short-range repulsive force and long-range attractive force to take into account single-phase and multiphase interactions. Particularly, a newly-introduced viscous force is imposed at the liquid-solid interface to capture the rate-dependent behaviours of contact angle without prescribing additional arbitrary condition or force. After identification of model parameters, the rate-dependent contact angle behaviours are studied for both wetting and dewetting phenomena. By analysing the contact angle results of fluid at triple-line region with different moving speeds, the dynamic contact angles and corresponding capillary numbers can be correlated by power law functions. The derived correlation and constants are compared with different forms of empirical power law functions and the results are satisfactory. Moreover, we investigated the properties of stretching liquid bridges, including shape evolution, liquid transfer ratio and flow condition under dynamic loading. Different stretching rates are applied, and the shapes of liquid bridge at same breakup distance is presented. By differentiating the wettability of top and bottom substrates, the liquid transfer ratio regarding wettability difference and substrate moving speed is studied