Lattice Boltzmann Method and Its Applications in Multiphase Flows - PowerPoint PPT Presentation

1 / 35
About This Presentation
Title:

Lattice Boltzmann Method and Its Applications in Multiphase Flows

Description:

LBM Multiphase Model Based on Kinetic Theory. Temperature variations in lattice Boltzmann models; ... Lattice Boltzmann model can be derived form kinetic theory; ... – PowerPoint PPT presentation

Number of Views:979
Avg rating:3.0/5.0
Slides: 36
Provided by: xiao8
Category:

less

Transcript and Presenter's Notes

Title: Lattice Boltzmann Method and Its Applications in Multiphase Flows


1
Lattice Boltzmann Method and Its Applications in
Multiphase Flows
  • Xiaoyi He
  • Air Products and Chemicals, Inc.
  • April 21, 2004

2
Outline
  • Lattice Boltzmann method
  • Kinetic theory for multiphase flow
  • Lattice Boltzmann multiphase models
  • Applications
  • Conclusions

3
A Brief History of Lattice Boltzmann Method
  • Lattice Gas Automaton (Frisch, Hasslacher,
    Pomeau,, 1987)
  • Lattice Boltzmann model (McNamara and Zanetti
    (1988)
  • Lattice Boltzmann BGK model (Chen et al 1992 and
    Qian et al 1992)
  • Relation to kinetic theory (He and Luo, 1997)

4
Lattice Boltzmann BGK Model
  • fa density distribution function
  • t relaxation parameter
  • f eq equilibrium distribution

5
Kinetic Theory of Multiphase Flow
  • BBGKY hierarchy

6
Intermolecular Interaction
  • Lennard-Jones potential

Interaction models
7
Model for Intermolecular Repulsion
For D1 (repulsion core)
8
Model for Intermolecular Attraction
For D2 (attraction tail), by assuming
We have
9
Model for Intermolecular Attraction
Vm is the mean-field potential of intermolecular
attraction
For small density variation
where
Control phase transition
Control surface tension
10
Kinetic Model for Multiphase Flow
Boltzmann equation for non-ideal gas / dense fluid
11
Kinetic Model for Multiphase Flow
Chapman-Enskog expansion leads to the following
macroscopic transport equations
Mass transport equation
Momentum transport equation
12
Kinetic Model for Multiphase Flow
Comments on momentum transport equation 1.
Correct equation of state 2. Thermodynamically
consistent surface tension
3. Thermodynamically consistent free energy
(Cahn and Hillary, 1958)
13
Kinetic Model for Multiphase Flow
Energy transport equation
14
Kinetic Model for Multiphase Flow
Comments on energy transport equation 1.Total
energy needs include both kinetic and potential
energies, otherwise the pressure work becomes
2. Last term is due to surface tension and it is
consistent with existing literature (Irving and
Kirkwood, 1950)
15
LBM Multiphase Model Based on Kinetic Theory
  • Temperature variations in lattice Boltzmann
    models
  • Discretization of velocity space
  • Discretization of physical space
  • Discretization of temporal space.

16
Temperature in Lattice Boltzmann Method
  • Non-isothermal model model is still a challenge
  • Small temperature variations can be modeled
  • Need for high-order velocity discretization
  • Isothermal model is well developed

17
Isothermal Boltzmann Equation for Multiphase Flow
18
Discretization in Velocity Space
  • Constraint for velocity stencil
  • Further expansion of f eq

19
Discretization in Velocity Space
wa weight coefficients
9-speed model
7-speed model
20
Discretization in Physical and Temporal Spaces
  • Integrate Boltzmann equation
  • Discretizations in velocity, physical and
    temporal spaces are
  • independent in principle
  • Synchronization simplifies computation but
    requires
  • Regular lattice
  • Time-step constraint

21
Further Simplification for Nearly Incompressible
Flow
  • Introduce an index function f

22
Applications
  • Phase Separation
  • Rayleigh-Taylor instability
  • Kelvin-Helmholtz instability

23
Phase Separation
Van der Waals fluid T/Tc 0.9
24
Rayleigh-Taylor Instability (2D)
Re 1024 single mode
25
RT instability (2D) Single mode Density ratio
31 Re 2048
26
RT instability (2D) Multiple mode Density ratio
31
hB /Agt2 0.04
27
RT instability (3D) single mode Density ratio
31 Re 1024
28
RT instability (3D) single mode Density ratio
31 Re 1024 Cuts through spike
29
RT instability (3D) single mode Density ratio
31 Re 1024 Cuts through bubble
30
KH instability Effect of surface tension Re
250 d1/d2 1
Ca 0.29
Ca 2.9
31
Other Applications
  • Multiphase flow in porous media (Rothman 1990,
    Gunstensen and Rothman 1993)
  • Amphiphilic fluids (Chen et al, 2000)
  • Bubbly flows (Sankaranarayanan et al, 2001)
  • Hele-Shaw flow (Langaas and Yeomans, 2000).
  • Boiling flows (Kato et al, 1997)
  • Drop break-up (Halliday et al 1996)

32
Challenges in Lattice Boltzmann Method
  • Need for better thermal models
  • Need for better model for multiphase flow with
    high density ratio
  • Need for better mode for highly compressible
    flows
  • Engineering applications

33
Conclusions
  • Lattice Boltzmann method is a useful tool for
    studying multiphase flows
  • Lattice Boltzmann model can be derived form
    kinetic theory
  • It is easy to incorporate microscopic physics in
    lattice Boltzmann models
  • Lattice Boltzmann method is easy to program for
    parallel computing.

34
Thank You!
35
Acknowledgement
  • Raoyang Zhang, ShiyiChen, Gary Doolen
  • Xiaowen Shan
Write a Comment
User Comments (0)
About PowerShow.com