Numerical simulation of single and multiphase flows using incompressible smoothed particle hydrodynamics

In this work, we have presented a multiphase Incompressible Smoot hod Particle Hydrodynamics (ISPII) method with an improved interface treatment procedure. To be able to demonstrate the effectiveness of the proposed interlace' treatment which can handle complex multiphase how problems with high density and viscosity ratios, we have' modeled several challenging two and three' phase flow problems: namely, single vortex flow, square bubble ({('formation under the effect of surface tension force, bubble deformation in shear flow. Newtonian bubble rising in viscous and viscoelastic liquids subjected to the combined ('fleets of surface tension and buoyancy force's, and finally the deformation of a droplet located at the interface' of two immiscible fluids. The proposed interface treatment include's the usage of (i) cubic spline ke'rnel function for discretizing expiations associated with the calculation of the surface tension force' while the quintic spline for the' discretization of governing equations anel the relevant boundary conditions, (ii) smoothing of transport parameters through weighted arithmetic and harmonic interpolations, and (iii) finally, a new discretization scheme for calculating the pressure gradient. The surface tension force is calculated using the1 so-called Continuum Surface Force (C’SF) model. It is shown that with the application of the improved interface' treatment, it becomes possible to modi'] multiphase flow problems with the density and viscosity ratios up to 1000 and 100. respectively, and the usage of cubic spline for the C’SF model significantly improves the quality of the calculated interface, thereby eliminating the interphase particle penetrations and in turn leading to the calculation of more accurate velocity and pressure fields. The new interface treatment method is extensively tested on the above given benchmark problems and the results of these simulations are validated against available numerical and experimental data in literature, and excellent agreement is observed between ISPH and literature results. Furthermore, within the scope of this thesis study, we have also presented numerical solutions for flow over an airfoil and a square obstacle' using the ISF’H method with an improved solid boundary treatment approach, referred to as the Multiple Boundary Tangents (MBT) method. It was shown that the MBT boundary treatment technique is very effective for tackling boundaries of complex shape's. Also, we' have' purposed the usage of the repulsive component of the' Lennard-.Jones Potential (UP) in the advection equation to repair particle fracture's occurring in me SPII inethe)d elue to the tendency of SPII particles to follow the stream line trajectory. This approach is named as the artificial particle displacement method. Numerie-al results suggest that the improved ISPH method which is consisting of the MBT method, artificial particle displacement and the corrective SPH discretization scheme enables one to obtain very stable and robust SPH simulations. Flow over a backward facing step, the square obstacle and NACA airfoil geometry with the angle of attacks between 0° and 15c in a laminar flow held with relatively high Reynolds numbers have' been simulated. We illustrated that the improved ISPH method is able to capture the complex physics of bluff-hotly Hows naturally such as the flow separation, wake formation at the trailing edge, and tlx- vortex shedding. The single phase ISPH results art' validated with a mesh-dependent Finite' Element Method (F'EM) and excellent agreements among the results were observed. Finally, preliminary introduction to phase specific surface tension formulation for numerical simulation of three-phase flows is presented. The proposed method is investigated through tin' simulation of a droplet located at the interface of two immiscible fluids as well as diamond droplet deformation. The extendibility of the proposed surface tension formulations for three-phase flows to two-phase flows is also investigated. It is observed that till' results obtained from the numerical simulations are in very good agreement with the analytical ones