Modeling free surface flows in presence of an arbitrary moving object

Abstract In this study, a numerical algorithm is developed for simulating the interactions between a liquid and a solid object in presence of a free-surface. The presented model is the fast-fictitious-domain method integrated into the volume-of-fluid (VOF) technique used for tracking the free surface motion. First, the governing equations are solved everywhere in the computational domain including the solid object. Next, a rigid body motion is projected onto the region occupied by the solid. The evaluation of the acting forces on the solid object and the application of the no-slip boundary condition on the solid–liquid interface are performed implicitly. In the model developed in this study, the no-slip condition is imposed by attributing a high viscosity to the solid region. The model is validated by a comparison of the simulation results with those of the available experiments in the literature for a sphere during its entry into a liquid free surface and for the free fall of one and two circular particles inside a liquid. For all cases considered, the results are in good agreement with those of the experiments and other numerical studies.

[1]  C. Clanet,et al.  Making a splash with water repellency , 2007, cond-mat/0701093.

[2]  N. Patankar.  A formulation for fast computations of rigid particulate flows , 2001 .

[3]  Roger H. Rangel,et al.  Collision of multi-particle and general shape objects in a viscous fluid , 2008, J. Comput. Phys..

[4]  Elias Balaras,et al.  An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting with moving boundaries , 2006, J. Comput. Phys..

[5]  Xinying Zhu,et al.  Application of the CIP Method to Strongly Nonlinear Wave-Body Interaction Problems , 2006 .

[6]  S. Chandra,et al.  On a three-dimensional volume tracking model of droplet impact , 1999 .

[7]  D. Gilbarg,et al.  Influence of Atmospheric Pressure on the Phenomena Accompanying the Entry of Spheres into Water , 1948 .

[8]  Torben P. Grumstrup,et al.  Cavity ripples observed during the impact of solid objects into liquids. , 2007, Physical review letters.

[9]  Duck-Gyu Lee,et al.  Impact of a superhydrophobic sphere onto water. , 2008, Langmuir : the ACS journal of surfaces and colloids.

[10]  Gretar Tryggvason,et al.  Direct numerical simulations of bubbly flows. Part 1. Low Reynolds number arrays , 1998, Journal of Fluid Mechanics.

[11]  Feng Xiao,et al.  Regular Article: A Computational Model for Suspended Large Rigid Bodies in 3D Unsteady Viscous Flows , 1999 .

[12]  P. G. Ciarlet,et al.  Numerical Methods for Fluids, Part 3 , 2003 .

[13]  Howard H. Hu.  Direct simulation of flows of solid-liquid mixtures , 1996 .

[14]  J. M. Bush,et al.  Water entry of small hydrophobic spheres , 2009, Journal of Fluid Mechanics.

[15]  P. G. Ciarlet,et al.  Numerical methods for fluids , 2003 .

[17]  Neelesh A. Patankar,et al.  A new mathematical formulation and fast algorithm for fully resolved simulation of self-propulsion , 2009, J. Comput. Phys..

[18]  M. Moghisi,et al.  An experimental investigation of the initial force of impact on a sphere striking a liquid surface , 1981, Journal of Fluid Mechanics.

[19]  Masashi Kashiwagi,et al.  A CIP-based method for numerical simulations of violent free-surface flows , 2004 .

[20]  Dimos Poulikakos,et al.  Wetting effects on the spreading of a liquid droplet colliding with a flat surface: Experiment and modeling , 1995 .

[21]  Minh Do-Quang,et al.  Numerical simulation of the coupling problems of a solid sphere impacting on a liquid free surface , 2010, Math. Comput. Simul..

[22]  C. Clanet,et al.  Dynamics of transient cavities , 2007, Journal of Fluid Mechanics.

[23]  N. Patankar,et al.  A formulation for fully resolved simulation (FRS) of particle-turbulence interactions in two-phase flows , 2008 .

[24]  R. W. Wood.  A Study of Splashes , 1909 .

[25]  D. Joseph,et al.  Nonlinear mechanics of fluidization of beds of spherical particles , 1987, Journal of Fluid Mechanics.

[26]  Neelesh A. Patankar,et al.  A fast projection scheme for the direct numerical simulation of rigid particulate flows , 2005 .

[27]  Pengzhi Lin,et al.  A fixed-grid model for simulation of a moving body in free surface flows , 2007 .

[28]  M. Pasandideh-Fard,et al.  SIMULATING DROPLET IMPACT ON A SUBSTRATE OF ARBITRARY SHAPE , 2001 .

[29]  Jordi Blasco,et al.  A Fictitious Domain, parallel numerical method for rigid particulate flows , 2009, J. Comput. Phys..

[30]  T. E. TezduyarAerospace,et al.  3d Simulation of Fluid-particle Interactions with the Number of Particles Reaching 100 , 1996 .

[31]  A. May.  Vertical Entry of Missiles into Water , 1952 .

[32]  Tayfun E. Tezduyar,et al.  Simulation of multiple spheres falling in a liquid-filled tube , 1996 .

[33]  N. Patankar,et al.  A fast computation technique for the direct numerical simulation of rigid particulate flows , 2005 .

[34]  Tayfun E. Tezduyar,et al.  Advanced mesh generation and update methods for 3D flow simulations , 1999 .

[35]  A. May.  Effect of Surface Condition of a Sphere on Its Water‐Entry Cavity , 1951 .

[36]  J. Brackbill,et al.  A continuum method for modeling surface tension , 1992 .

[37]  R. Rangel,et al.  Numerical investigation of particle–particle and particle–wall collisions in a viscous fluid , 2008, Journal of Fluid Mechanics.

[38]  Daniel D. Joseph,et al.  Distributed Lagrange multiplier method for particulate flows with collisions , 2003 .

[39]  Howard H. Hu,et al.  Direct simulation of fluid particle motions , 1992 .

[40]  R. Glowinski,et al.  A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow , 2001 .

[41]  Mathieu Martin,et al.  A numerical method for fully resolved simulation (FRS) of rigid particle-flow interactions in complex flows , 2009, J. Comput. Phys..

[42]  Tayfun E. Tezduyar,et al.  Finite element methods for flow problems with moving boundaries and interfaces , 2001 .

[43]  S. H. Davis,et al.  On the motion of a fluid-fluid interface along a solid surface , 1974, Journal of Fluid Mechanics.

[44]  Mathieu Coquerelle,et al.  ARTICLE IN PRESS Available online at www.sciencedirect.com Journal of Computational Physics xxx (2008) xxx–xxx , 2022 .

[45]  Tayfun E. Tezduyar,et al.  A Numerical model based on the mixed interface‐tracking/interface‐capturing technique (MITICT) for flows with fluid–solid and fluid–fluid interfaces , 2007 .

[46]  Myoungkyu Lee,et al.  Cavity dynamics in high-speed water entry , 1997 .

[47]  D. Wan,et al.  Direct numerical simulation of particulate flow via multigrid FEM techniques and the fictitious boundary method , 2006 .

[48]  D. Kershaw.  The incomplete Cholesky—conjugate gradient method for the iterative solution of systems of linear equations , 1978 .

[49]  J. M. Bush,et al.  The water entry of decelerating spheres , 2009 .

[50]  G. Kuwabara,et al.  Splash Produced by a Smooth Sphere or Circular Cylinder Striking a Liquid Surface , 1987 .

[51]  Neelesh A. Patankar,et al.  A distributed lagrange multiplier based computational method for the simulation of particulate-Stokes flow , 2005 .

[52]  Tayfun E. Tezduyar,et al.  Computation of flow problems with the Mixed Interface-Tracking/Interface-Capturing Technique (MITICT) , 2007 .

[53]  Frederick Stern,et al.  Sharp interface immersed-boundary/level-set method for wave-body interactions , 2009, J. Comput. Phys..

[54]  R. Glowinski,et al.  A distributed Lagrange multiplier/fictitious domain method for particulate flows , 1999 .

[55]  Greg Turk,et al.  Rigid fluid: animating the interplay between rigid bodies and fluid , 2004, ACM Trans. Graph..

[56]  G. Amberg,et al.  The splash of a solid sphere impacting on a liquid surface: Numerical simulation of the influence of wetting , 2009 .

[57]  H. Abelson.  Pressure measurements in the water-entry cavity , 1970, Journal of Fluid Mechanics.

[58]  E. Roohi,et al.  Transient simulations of cavitating flows using a modified volume-of-fluid (VOF) technique , 2008 .

[59]  Tayfun E. Tezduyar,et al.  Methods for 3D computation of fluid-object interactions in spatially periodic flows , 2001 .

[60]  R. Glowinski,et al.  A new formulation of the distributed Lagrange multiplier/fictitious domain method for particulate flows , 2000 .

[61]  T. Etoh,et al.  Impact jetting by a solid sphere , 2004, Journal of Fluid Mechanics.