PARTICLE DYNAMICS SIMULATIONS OF THE NAVIER–STOKES FLOW WITH HARD DISKS

2004 ◽  
Vol 15 (10) ◽  
pp. 1413-1424 ◽  
Author(s):  
TATSUYA ISHIWATA ◽  
TERUYOSHI MURAKAMI ◽  
SATOSHI YUKAWA ◽  
NOBUYASU ITO
Keyword(s):  
Equations Of Motion ◽  
Local Equilibrium ◽  
Flow Simulation ◽  
Quantitative Agreement ◽  
Particle Dynamics ◽  
Navier Stokes ◽  
Hard Disks ◽  
Navier Stokes Equation ◽  
Dynamics Simulations ◽  
Energy And Momentum

Flow simulation with a particle dynamics method is studied. The fluid is made of hard particles which obey the Newtonian equations of motion and the collisions between particles are elastic, that is, energy and momentum are conserved. The viscosity appears autonomously together with the local equilibrium state. When a particle collides with a nonslip boundary, a new velocity is given randomly from the thermal distribution if the wall is isothermal, or a random reflection angle is selected if the wall is adiabatic. Shear viscosity is estimated from simulations of plane Poiseuille flow together with the confirmation that the system obeys the Navier–Stokes equation. Flows past a cylinder are also simulated. Depending on the Reynolds number up to 106, flow patterns are properly reproduced, and Kármán vortex shedding is observed. The estimated values of drag coefficient show quantitative agreement with experiments.

scholarly journals Direct Numerical Simulation of Gas–Particle Flows with Particle–Wall Collisions Using the Immersed Boundary Method

2018 ◽  
Vol 8 (12) ◽  
pp. 2387 ◽  
Author(s):  
Yusuke Mizuno ◽  
Shun Takahashi ◽  
Kota Fukuda ◽  
Shigeru Obayashi
Keyword(s):  
Immersed Boundary Method ◽  
Three Dimensional ◽  
Flow Simulation ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Navier Stokes Equation ◽  
Level Set Function ◽  
Boundary Method ◽  
The One ◽  
Energy And Momentum

We investigated particulate flows by coupling simulations of the three-dimensional incompressible Navier–Stokes equation with the immersed boundary method (IBM). The results obtained from the two-way coupled simulation were compared with those of the one-way simulation, which is generally applied for clarifying the particle kinematics in industry. In the present flow simulation, the IBM was solved using a ghost–cell approach and the particles and walls were defined by a level set function. Using proposed algorithms, particle–particle and particle–wall collisions were implemented simply; the subsequent coupling simulations were conducted stably. Additionally, the wake structures of the moving, colliding and rebounding particles were comprehensively compared with previous numerical and experimental results. In simulations of 50, 100, 200 and 500 particles, particle–wall collisions were more frequent in the one–way scheme than in the two-way scheme. This difference was linked to differences in losses in energy and momentum.

Learning the Dynamics of Objects by Optimal Functional Interpolation

2012 ◽  
Vol 24 (9) ◽  
pp. 2457-2472
Author(s):  
Jong-Hoon Ahn ◽  
In Young Kim
Keyword(s):  
Functional Data ◽  
Continuity Equation ◽  
Particle Concentration ◽  
Equations Of Motion ◽  
Navier Stokes ◽  
Conserved Quantities ◽  
Time Varying ◽  
Science And Engineering ◽  
Navier Stokes Equation ◽  
Over Time

Many areas of science and engineering rely on functional data and their numerical analysis. The need to analyze time-varying functional data raises the general problem of interpolation, that is, how to learn a smooth time evolution from a finite number of observations. Here, we introduce optimal functional interpolation (OFI), a numerical algorithm that interpolates functional data over time. Unlike the usual interpolation or learning algorithms, the OFI algorithm obeys the continuity equation, which describes the transport of some types of conserved quantities, and its implementation shows smooth, continuous flows of quantities. Without the need to take into account equations of motion such as the Navier-Stokes equation or the diffusion equation, OFI is capable of learning the dynamics of objects such as those represented by mass, image intensity, particle concentration, heat, spectral density, and probability density.

Axial Leakage Flow-Induced Vibration of Thin Cylindrical Shell With Respect to Circumferential Vibration

2002 ◽  
Author(s):  
Katsuhisa Fujita ◽  
Atsuhiko Shintani ◽  
Masakazu Ono
Keyword(s):  
Cylindrical Shell ◽  
Equations Of Motion ◽  
Fluid Pressure ◽  
Navier Stokes ◽  
Leakage Flow ◽  
Thin Cylindrical Shell ◽  
Flow Induced Vibration ◽  
Navier Stokes Equation ◽  
Coupled Equations ◽  
Unstable Vibration

In this paper, the dynamic stability of a thin cylindrical shell subjected to axial leakage flow is discussed. In this paper, the third part of a study of the axial leakage flow-induced vibration of a thin cylindrical shell, we focus on circumferential vibration, that is, the ovaling vibration of a shell. The coupled equations of motion between shell and liquid are obtained by using Donnell’s shell theory and the Navier-Stokes equation. The added mass, added damping and added stiffness in the coupled equations of motion are described by utilizing the unsteady fluid pressure acting on the shell. The relations between axial velocity and the unstable vibration phenomena are clarified concerning the circumferential vibration of a shell. Numerical parametric studies are done for various dimensions of a shell and an axial leakage flow.

scholarly journals A non-conventional discontinuous Lagrangian for viscous flow

2017 ◽  
Vol 4 (2) ◽  
pp. 160447 ◽  
Author(s):  
M. Scholle ◽  
F. Marner
Keyword(s):  
Variational Formulation ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Local Equilibrium ◽  
Navier Stokes ◽  
Mathematical Treatment ◽  
Navier Stokes Equations ◽  
New Formalism ◽  
Limiting Case ◽  
Physical Phenomena

Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier–Stokes equations which to-date has remained elusive. A key feature is that the resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier–Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided.

Simulation of Magneto-Rheological Fluids Using Lattice Boltzmann Method

2004 ◽  
Author(s):  
A. Yadav ◽  
R. Calhoun ◽  
P. E. Phelan ◽  
A. K. Vuppu ◽  
A. A. Garcia ◽  
...  
Keyword(s):  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Complete Solution ◽  
Particle Dynamics ◽  
Rotating Magnetic Field ◽  
Navier Stokes ◽  
Complete Analysis ◽  
Boltzmann Transport ◽  
Navier Stokes Equation ◽  
Magneto Rheological

Lattice Boltzmann (LB) simulations of Magneto-rheological fluids under a rotating magnetic field are presented in this paper. The LB method gives a complete solution of Navier-Stokes equation based on the Boltzmann transport equation. A relatively good agreement of normalized number of aggregated particles in experiments and simulations is found. Results pertaining to variation of chain length vs. Mason number are also shown. A complete analysis and comparison of forces on the particles found from LB simulations and from simple Particle dynamics (PD) type approach is also shown. Another aim of this study was to determine under what conditions do we need to solve the complete Navier-Stokes equations and under what conditions a simplistic but very fast simulation method like particle dynamics will work for Magneto-rheological fluids.

scholarly journals Shape control and compartmentalization in active colloidal cells

2015 ◽  
Vol 112 (34) ◽  
pp. E4642-E4650 ◽  
Author(s):  
Matthew Spellings ◽  
Michael Engel ◽  
Daphne Klotsa ◽  
Syeda Sabrina ◽  
Aaron M. Drews ◽  
...  
Keyword(s):  
Mirror Symmetry ◽  
Shape Control ◽  
Navier Stokes ◽  
Distributed Energy ◽  
Navier Stokes Equation ◽  
Entire Volume ◽  
Autonomous Machines ◽  
Matter System ◽  
Dynamics Simulations ◽  
Over Time

Small autonomous machines like biological cells or soft robots can convert energy input into control of function and form. It is desired that this behavior emerges spontaneously and can be easily switched over time. For this purpose we introduce an active matter system that is loosely inspired by biology and which we term an active colloidal cell. The active colloidal cell consists of a boundary and a fluid interior, both of which are built from identical rotating spinners whose activity creates convective flows. Similarly to biological cell motility, which is driven by cytoskeletal components spread throughout the entire volume of the cell, active colloidal cells are characterized by highly distributed energy conversion. We demonstrate that we can control the shape of the active colloidal cell and drive compartmentalization by varying the details of the boundary (hard vs. flexible) and the character of the spinners (passive vs. active). We report buckling of the boundary controlled by the pattern of boundary activity, as well as formation of core–shell and inverted Janus phase-separated configurations within the active cell interior. As the cell size is increased, the inverted Janus configuration spontaneously breaks its mirror symmetry. The result is a bubble–crescent configuration, which alternates between two degenerate states over time and exhibits collective migration of the fluid along the boundary. Our results are obtained using microscopic, non–momentum-conserving Langevin dynamics simulations and verified via a phase-field continuum model coupled to a Navier–Stokes equation.

The Modeling and Flow Simulation of 40BZ6-15 Centrifugal Pump

2011 ◽  
Vol 317-319 ◽  
pp. 789-793
Author(s):  
Xiao Feng Shang ◽  
Liang Tong ◽  
Zhi Jian Wang
Keyword(s):  
Velocity Field ◽  
Centrifugal Pump ◽  
Pressure Field ◽  
Three Dimensional ◽  
Flow Simulation ◽  
Internal Flow ◽  
Navier Stokes ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Navier Stokes Equation

The three-Dimensional model of 40BZ6-15 centrifugal pump is built by the Solidworks software. This paper employs three-D Navier-Stokes equation and standard equation, and uses MRF and STMPLE algorithm to simulate the internal flowing of the 40BZ6 centrifugal pump. The velocity field and pressure field are gained. Through a further analysis, the rule of the internal flow of the centrifugal pump is unveiled, and then the simulative results are compared with the experimental ones, which can provide the base for the further improvement of the centrifugal pump.

History forces and the unsteady wake of a cylinder

1999 ◽  
Vol 393 ◽  
pp. 99-121 ◽  
Author(s):  
J. R. CHAPLIN
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Stokes Equation ◽  
Oscillatory Flow ◽  
Numerical Solutions ◽  
Asymptotic Properties ◽  
Quantitative Agreement ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Unsteady Wake

History forces on a stationary cylinder in arbitrary unsteady rectilinear flow are calculated by means of a model based on the asymptotic properties of the steady-state wake. The results capture many features found in numerical solutions of the Navier–Stokes equation for the same flows, though quantitative agreement deteriorates as the Reynolds number increases over the range 2 to 40. The cases studied are the impulsive start, stop, and reverse, and oscillatory flow.

A Continuum - Molecular Dynamics Hybrid Method for Micro- and Nano-Fluid Flow

2010 ◽  
Author(s):  
Ali Kharazmi ◽  
Reza Kamali
Keyword(s):  
Molecular Dynamics ◽  
Stokes Equations ◽  
Computer Code ◽  
Quantitative Agreement ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Nano Fluid ◽  
Dynamics Simulations ◽  
The Continuum ◽  
Overlap Region

A computer program based on a Molecular Dynamics-Continuum hybrid numerical method has been developed in which the Navier-Stokes equations are solved in the continuum region and the atomistic molecular dynamics in molecular region. The prepared algorithm and the computer code are capable of computing flows in micro and nano-scale geometries. The coupling between the continuum equations and the molecular dynamics is constructed through constrained dynamics within an overlap region where both molecular and continuum equations are solved simultaneously. An Overlap region is introduced in two directions to improve the choice of using molecular region in smaller areas. The proposed method is used to simulate steady and start-up Couette flow showing quantitative agreement with results from analytical solutions and full molecular dynamics simulations.

scholarly journals Stochastic Approaches to Deterministic Fluid Dynamics: A Selective Review

Water ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 864 ◽  
Author(s):  
Ana Bela Cruzeiro
Keyword(s):  
Fluid Dynamics ◽  
Variational Principle ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Time Derivative ◽  
Probabilistic Methods ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

We present a stochastic Lagrangian view of fluid dynamics. The velocity solving the deterministic Navier–Stokes equation is regarded as a mean time derivative taken over stochastic Lagrangian paths and the equations of motion are critical points of an associated stochastic action functional involving the kinetic energy computed over random paths. Thus the deterministic Navier–Stokes equation is obtained via a variational principle. The pressure can be regarded as a Lagrange multiplier. The approach is based on Itô’s stochastic calculus. Different related probabilistic methods to study the Navier–Stokes equation are discussed. We also consider Navier–Stokes equations perturbed by random terms, which we derive by means of a variational principle.

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