An improved direct-forcing immersed boundary method with inward retraction of Lagrangian points for simulation of particle-laden flows

Abstract The direct-forcing immersed boundary is widely adopted to study particle-laden flows. The effective hydrodynamic diameter of the particle is much or less overestimated by the original immersed boundary method, depending on the particle Reynolds number and grid resolution. In this paper, we propose an improved method to dynamically correct the effective hydrodynamic diameter by retracting inward the Lagrangian points to varying distances. The retraction distance is determined by querying a function fitted in this paper. The improved method is tested and validated by several cases, including falling of a spherical particle under gravity, the uniform flow past two stationary particles and the drafting-kissing-tumbling phenomenon of two settling particles. It turns out the improved method not only provides better results for the drag force but also predicts the flow field more accurately. What's more, due to the insensitivity to grid resolution, the improved method is suitable for simulating large-scale fluid–particle systems such as fluidized bed, which are computationally expensive.

[1]  J. Westerweel,et al.  Collision model for fully resolved simulations of flows laden with finite-size particles. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  M. Lai,et al.  An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity , 2000 .

[3]  Arthur T. Andrews,et al.  Multiscale modeling of gas-fluidized beds , 2006 .

[4]  Gianluca Iaccarino,et al.  IMMERSED BOUNDARY METHODS , 2005 .

[5]  Jungwoo Kim,et al.  An immersed-boundary finite-volume method for simulations of flow in complex geometries , 2001 .

[6]  J. Pinton,et al.  Velocity measurement of a settling sphere , 2000 .

[7]  Liang-Shih Fan,et al.  Particle wake effects on the drag force of an interactive particle , 1994 .

[8]  Zhaosheng Yu,et al.  A direct-forcing fictitious domain method for particulate flows , 2007, J. Comput. Phys..

[9]  Markus Uhlmann,et al.  Direct numerical simulation of horizontal open channel flow with finite-size, heavy particles at low solid volume fraction , 2013, 1301.5771.

[10]  J. Bec,et al.  Slipping motion of large neutrally buoyant particles in turbulence , 2013, Journal of Fluid Mechanics.

[11]  S. Biringen,et al.  Numerical Simulation of a Cylinder in Uniform Flow , 1996 .

[12]  C. Peskin.  The immersed boundary method , 2002, Acta Numerica.

[13]  Shl Sebastian Kriebitzsch,et al.  A methodology for highly accurate results of direct numerical simulations : drag force in dense gas–solid flows at intermediate Reynolds number , 2014 .

[14]  Wim-Paul Breugem,et al.  A second-order accurate immersed boundary method for fully resolved simulations of particle-laden flows , 2012, J. Comput. Phys..

[15]  Three-dimensional particle-resolved direct numerical simulation study of behaviors of a particle settling near a vertical wall , 2015 .

[16]  S. Tenneti,et al.  Particle-Resolved Direct Numerical Simulation for Gas-Solid Flow Model Development , 2014 .

[17]  P. P. Brown,et al.  Sphere Drag and Settling Velocity Revisited , 2003 .

[18]  Jan Dušek,et al.  Breaking of axisymmetry and onset of unsteadiness in the wake of a sphere , 2000, Journal of Fluid Mechanics.

[19]  Chao-An Lin,et al.  Simulations of two sedimenting-interacting spheres with different sizes and initial configurations using immersed boundary method , 2015 .

[20]  Andrea Prosperetti,et al.  A second-order method for three-dimensional particle simulation , 2005 .

[21]  Kun Luo,et al.  An improved moving-least-squares reconstruction for immersed boundary method , 2015 .

[22]  J. Dusek,et al.  Hydrodynamic forces acting on a rigid fixed sphere in early transitional regimes , 2006 .

[23]  S. Lele.  Compact finite difference schemes with spectral-like resolution , 1992 .

[24]  A. Jameson,et al.  Some recent developments in numerical methods for transonic flows , 1985 .

[25]  V. C. Patel,et al.  Flow past a sphere up to a Reynolds number of 300 , 1999, Journal of Fluid Mechanics.

[26]  C. Peskin.  Flow patterns around heart valves: A numerical method , 1972 .

[27]  R. Clift,et al.  Bubbles, Drops, and Particles , 1978 .

[28]  M. Uhlmann.  An immersed boundary method with direct forcing for the simulation of particulate flows , 2005, 1809.08170.

[29]  L. Sirovich,et al.  Modeling a no-slip flow boundary with an external force field , 1993 .

[30]  Boyce E. Griffith,et al.  On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems , 2005 .

[31]  Abdullah Abbas Kendoush.  Calculation of flow resistance from a spherical particle , 2000 .

[32]  Yoshinobu Morikawa,et al.  Fluid-dynamic interaction between two spheres , 1982 .

[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.  3D Simulation of fluid-particle interactions with the number of particles reaching 100 , 1997 .

[35]  Yanwen Ma,et al.  A High Order Accurate Difference Scheme for Complex Flow Fields , 1997 .

[36]  R. Verzicco,et al.  Combined Immersed-Boundary Finite-Difference Methods for Three-Dimensional Complex Flow Simulations , 2000 .

[37]  Xu Xuchang,et al.  Drag force in dense gas-particle two-phase flow , 2003 .

[38]  Jianren Fan,et al.  Response of force behaviors of a spherical particle to an oscillating flow , 2010 .

[39]  J. Kuipers,et al.  Drag force in discrete particle models : continuum scale or single particle scale? , 2013 .

[40]  Laszlo Fuchs,et al.  On the interaction between two fixed spherical particles , 2007 .

[41]  Chunning Ji,et al.  A novel iterative direct-forcing immersed boundary method and its finite volume applications , 2012, J. Comput. Phys..

[42]  Kun Luo,et al.  Full-scale solutions to particle-laden flows: Multidirect forcing and immersed boundary method. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  Jianren Fan,et al.  Combined multi-direct forcing and immersed boundary method for simulating flows with moving particles , 2008 .

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

[45]  J. Kuipers,et al.  Drag force of intermediate Reynolds number flow past mono- and bidisperse arrays of spheres , 2007 .

[46]  I. Orlanski.  A Simple Boundary Condition for Unbounded Hyperbolic Flows , 1976 .

[47]  Inchul Kim,et al.  Three-dimensional flow over two spheres placed side by side , 1993, Journal of Fluid Mechanics.

[48]  S. Elghobashi.  Particle-laden turbulent flows: direct simulation and closure models , 1991 .