SPH modeling of plane jets into water bodies through an inflow/outflow algorithm

This paper deals with the development and application of a two-dimensional weakly compressible Smoothed Particle Hydrodynamics (SPH) model to study plane jets propagating into still fluid tanks and current flows. These flow processes occurring in different water bodies are here treated through an appropriate algorithm to model inlet/outlet boundary conditions which are defined by different sets of particles. SPH equations of fluid mechanics including viscous and interface stabilization terms are adopted to determine the flow field induced by the fluid interaction. Flow phenomena induced by jet injection in a water body occur in natural and anthropic environments such as pollutant discharge into reservoirs, rivers and coasts, or in several engineering applications such as marine outfalls. Three test cases with different initial configurations are simulated: injection of a jet at the top and at the bottom of a water tank, and upstream of a channel flow (coflow jet). The proposed SPH model is validated both near the jet nozzle and far from it, comparing the obtained jet trajectories, widths and velocities with other numerical approaches, laboratory experiments and analytical solutions.

[1]  Salvatore Marrone,et al.  An accurate SPH modeling of viscous flows around bodies at low and moderate Reynolds numbers , 2013, J. Comput. Phys..

[2]  J. Monaghan.  SPH without a Tensile Instability , 2000 .

[3]  Kamil Szewc,et al.  Simulations of single bubbles rising through viscous liquids using Smoothed Particle Hydrodynamics , 2013 .

[4]  J. H. Sun,et al.  Flapping Instability of Vertically Impinging Turbulent Plane Jets in Shallow Water , 2001 .

[5]  J. Monaghan.  Simulating Free Surface Flows with SPH , 1994 .

[6]  F. Aristodemo,et al.  SPH numerical modeling of wave–perforated breakwater interaction , 2015 .

[7]  Salvatore Marrone,et al.  Simulating free-surface channel flows through SPH , 2010 .

[8]  J. Monaghan.  Smoothed particle hydrodynamics , 2005 .

[9]  David Le Touzé,et al.  An Hamiltonian interface SPH formulation for multi-fluid and free surface flows , 2009, J. Comput. Phys..

[10]  Pawel Bujnowski,et al.  Aspiration and Cooperation in Multiperson Prisoner's Dilemma , 2009 .

[11]  Guirong Liu,et al.  Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments , 2010 .

[12]  F. Aristodemo,et al.  Assessment of Dynamic Pressures at Vertical and Perforated Breakwaters through Diffusive SPH Schemes , 2015 .

[13]  D. F. Fletcher,et al.  Numerical simulation of a laminar jet flow: a comparison of three CFD models , 1993 .

[14]  R. E. Baddour,et al.  Comparison of Far-Field Turbulent Structure of a Rectangular Surface Jet to Three-Dimensional Free and Wall Jets , 2008 .

[15]  Robert G. Bell,et al.  Ocean Disposal Of Wastewater , 1993 .

[16]  A. Colagrossi,et al.  δ-SPH model for simulating violent impact flows , 2011 .

[17]  P. Koumoutsakos.  MULTISCALE FLOW SIMULATIONS USING PARTICLES , 2005 .

[18]  Gerhard H. Jirka,et al.  Integral Model for Turbulent Buoyant Jets in Unbounded Stratified Flows. Part I: Single Round Jet , 2004 .

[19]  Marshall P. Tulin,et al.  Gridless simulations of splashing processes and near-shore bore propagation , 2007, Journal of Fluid Mechanics.

[20]  H. Matthies,et al.  Classification and Overview of Meshfree Methods , 2004 .

[21]  Clemens Herschel,et al.  Discussion of Precise Weir Measurements by Ernest W. Schoder and Kenneth B. Turner , 1929 .

[22]  Ben Hunt,et al.  Effect of lobe pumping on human albumin: development of a lobe pump simulator using smoothed particle hydrodynamics 1 , 2006, Biotechnology and applied biochemistry.

[23]  J. Riley,et al.  The spread of a turbulent plane jet issuing into a parallel moving airstream , 1967, Journal of Fluid Mechanics.

[24]  W. Rodi,et al.  Experiments on vertical plane buoyant jets in shallow water , 1986, Journal of Fluid Mechanics.

[25]  Salvatore Marrone,et al.  Numerical diffusive terms in weakly-compressible SPH schemes , 2012, Comput. Phys. Commun..

[26]  Salvatore Marrone,et al.  Propagation of gravity waves through an SPH scheme with numerical diffusive terms , 2011, Comput. Phys. Commun..

[27]  L. J. S. Bradbury,et al.  The structure of a self-preserving turbulent plane jet , 1965, Journal of Fluid Mechanics.

[28]  Andrea Colagrossi,et al.  A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH , 2009, Comput. Phys. Commun..

[29]  J. Monaghan,et al.  Smoothed particle hydrodynamics: Theory and application to non-spherical stars , 1977 .

[30]  Paul W. Cleary,et al.  Application of Smoothed Particle Hydrodynamics for modelling gated spillway flows , 2014 .

[31]  J. Middleton.  The asymptotic behaviour of a starting plume , 1975, Journal of Fluid Mechanics.

[32]  A. Colagrossi,et al.  Viscous bubbly flows simulation with an interface SPH model , 2013 .

[33]  W. Quinn,et al.  Streamwise Evolution of a Square Jet Cross Section , 1992 .

[34]  M. Davidson,et al.  Strongly Advected Jet in a Coflow , 2002 .

[35]  As Arris Tijsseling,et al.  Smoothed particle hydrodynamics simulations of flow separation at bends , 2014 .

[36]  Chin Tsau Hsu,et al.  EXPERIMENTS ON VERTICAL TURBULENT PLANE JETS IN WATER OF FINITE DEPTH , 2001 .

[37]  A. Colagrossi,et al.  Numerical simulation of interfacial flows by smoothed particle hydrodynamics , 2003 .

[38]  A. Colagrossi,et al.  Theoretical considerations on the free-surface role in the smoothed-particle-hydrodynamics model. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  Ashkan Rafiee,et al.  A simple SPH algorithm for multi‐fluid flow with high density ratios , 2013 .

[40]  Salvatore Marrone,et al.  Simulating 2D open-channel flows through an SPH model , 2012 .

[41]  R. Antonia,et al.  The interaction region of a turbulent plane jet , 1984, Journal of Fluid Mechanics.

[42]  Turbulence Structure of Plane Surface-Jets in a Weak Coflowing Stream for Different Initial Wake Conditions , 1998 .

[43]  Stefano Sibilla,et al.  SPH simulations of a vertical 2-D liquid jet introduced from the bottom of a free surface rectangular tank , 2008 .

[44]  F. Aristodemo,et al.  Two-phase SPH modelling of advective diffusion processes , 2010 .

[45]  Wolfgang Rauch,et al.  On the Reynolds number sensitivity of smoothed particle hydrodynamics , 2014 .

[46]  Mihai Basa,et al.  Permeable and non‐reflecting boundary conditions in SPH , 2009 .

[47]  Andrea Colagrossi,et al.  A set of canonical problems in sloshing, Part I: Pressure field in forced roll-comparison between experimental results and SPH , 2009 .