Simulating open-channel flows and advective diffusion phenomena through SPH model

Abstract

The present thesis treats Computational Fluid Dynamics based on particle\nmethods. The fully Lagrangian approach Smoothed Particle Hydrodynamics\n(SPH) is developed for two-phase flows. The model is extended to\nresearch fields of environmental hydraulic and open-channel flows. SPH is\na Lagrangian, meshless and particle model. It was born about 30 years ago\nto solve gas-dynamics problems in open space (Lucy, 1977 [1]; Gingold and\nMonaghan, 1977 [2]). For many years, the SPH method has been applied\nto problems in the astrophysical field, as documented in the review paper\nby Benz (1990) [3]. During the last decades, the SPH method has been increasingly\nmodified and extended to provide approximations to the partial\ndifference equations (PDEs) in a wide range of scientific and engineering\napplications particularly in the hydrodynamic field. Monaghan (1994) [4]\nwas the first to apply the SPH scheme to fluid-dynamics problems. After\nthat, the SPH approach has been successfully extended to multiphase flows\n(see e.g. Grenier et al., 2009 [5]) and fluid-structure interaction problems\n(see e.g. Colagrossi and Landrini, 2003 [6]). Following the SPH method,\nthe motion of a continuum medium is described using an interpolation\ntechnique which allows to approximate functions and differential operators\non an irregular distribution of points. In the standard SPH, where\na weakly compressible fluid is considered, the discretized continuity and\nmomentum equations are linked via a state equation.\nFirstly, an algorithm is developed to treat upstream/downstream boundary\nconditions for 2D open-channel flows in SPH context. For this purpose\ntwo suitable sets of particles (in/out-flow particles) are defined allowing\nthe enforcement of different upstream and downstream flow conditions.\nIn particular this permits to avoid generation of unphysical pressure\nshock waves due to a direct creation/deletion of fluid particles. As first\ntest case, the proposed algorithm is validated for a viscous laminar flow\nin open channel considering Reynolds numbers of order O(102). The obtained\nresults are compared with analytical ones in order to heuristically\ncheck the convergence of the numerical scheme. The simulations are performed\nfor a time interval long enough to reach steady state conditions.\nThe suitability of the in/out-flow algorithm has been highlighted comparing\nthe velocity field with the analytical Poiseuille solution. The second\ntest case deals with a hydraulic jump for which different upstream and\ndownstream conditions are needed. Several types of jumps, obtained varying\nthe flow Froude number, are investigated with particular reference\nto the location of the jump and the velocity field. Comparisons between\nthe numerical results and the classical theory of the hydraulic jump are\nprovided, showing good agreements.\nIn the second part of the thesis, the SPH model is applied to evaluate\nthe concentration field of pollutants in water. A Lagrangian formalism is\nformulated to solve the fickian diffusion equation considering pollutants\nwith the same density as the water. Furthermore, a SPH form of the advective\ndiffusion equation is also developed for pollutant-water, taking into\naccount the effects of molecular diffusion and natural advection induced\nvii\nby differences between the fluid densities. These equations are coupled\nwith the fluid mechanics equations. Attention is paid to the numerical\naspects involved in the solution procedure and to the optimization of the\nmodel parameters. Environmental engineering problems concerning diffusion\nand natural advection phenomena occur in the presence of a pollutant\nin still water. Numerical tests referring to a strip and a bubble of contaminant\nin a water tank with different initial concentration laws have been\ncarried out. The results obtained by the proposed SPH models are compared\nwith other available SPH formulations, showing an overall better\nagreement with standard analytical solutions in terms of spatial evolution\nof the concentration values. Capabilities and limits of the proposed SPH\nmodels to simulate advective diffusion phenomena for a wide range of\ndensity ratios are discussed.\nAs future perspectives, coupling the two aspects considered in this thesis,\nit will be developed a numerical code for the simulation of the concentration\nfield along a water stream by an intake of pollutants.\nviii