Basics of Lattice Boltzmann Method for Fluid Flows

Numerical Simulation of Turbulent Flow using Lattice Boltzmann Method

Supervised By: Ms. Romana Basit

Presented By: Sajjad Rasool Chaudhry

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

Outline

Introduction

• Project Objectives• Project Time-Line

Common Simulation Tools

Lattice Boltzmann Method•Introduction•Lattice Models•Lattice Boltzmann Equation•Boundary Conditions

Using LBM for Solving Turbulent Flow Problems

Questions & Answers



Project Objectives

Basic Understanding

Fluid Flows & Simulations

Techniques to Apply LBM

Project Specific Application of LBM

Coding in Fortran/C++

Generating Results

Comparison of Results

Thesis Writing

Introduction


Project Timeline


Computational Fluid Dynamics

Using numerical methods and algorithms to solve and analyze problems involving fluid flows



Computational Fluid Dynamics

Discretization

Multi-Scale Analysis




Discretization Multi-Scale Analysis

Top Down approach Bottom up approach

Difference Equations

(Conserved quantities)

Discrete Model(LGCA or LBM)

Partial Differential Equations

(NS)

Partial Differential Equations

(NS)


Lattice Boltzmann Method

Propagation •In lattice gases, particles live on the nodes of a discrete lattice. The particles jump from one lattice node to the next, according to their (discrete) velocity.

Collision•Then, the particles collide and get a new velocity. This is the collision phase. Hence the simulation proceeds in an alternation between particle propagations and collisions

LGCA


Lattice gases solve the N.S. equations of fluid flow. But;

The major disadvantage of lattice gases for common fluid

dynamics applications is the

occurrence of noise.

The lattice Boltzmann method solves this problem

by pre-averaging the lattice gas. It

considers particle distributions that live on the

lattice nodes, rather than the

individual particles.


From LGCA to LBM


A set of particles arranged in a pattern. And these particles

represents a certain number of molecules.

Particles are in motion just as molecules. And colliding with one

another. These collisions conserve mass and

momentum.


LATTICE



LATTICE

Arrangements of the lattice is represented by DnQm

Changes takes place in a lattice in 1 time step (∆t).



LATTICE

D1Q2D2Q7D2Q9D3Q15D3Q19


A Unique class of computational fluid dynamics (CFD) methods for fluid simulation.

Instead of solving the Navier–Stokes equations, the

Boltzmann equation is solved to simulate the flow of a Newtonian fluid.

The general form of the lattice Boltzmann equation is

where the is the concentration of particles that travels with velocity ci.

ωi is the deviation from the equilibrium state.




D2Q9 Lattice Model



),(),( tftf eq

ii xx

Lattice Boltzmann Equation



Lattice Boltzmann Equation



• τ(relaxation time) value is set by the user.

• ea is the velocity in a direction. “a” varies from (0-8)

•

wa=4/9 for a=0

wa= 1/9 for a=1,2,3,4

wa=1/36 for a=5,6,7,8



Periodic BCs

No-slip BCs

Slip BCs

Velocity and Pressure BCs

Boundary Conditions


UNSTEADY and highly IRREGULAR in space and time

3-DIMENSIONAL (even if the mean flow is only 2D)

Always ROTATIONAL and at HIGH REYNOLDS NUMBERS

DISSIPATIVE (energy is converted into heat due to viscous stresses)

strongly DIFFUSIVE (rapid mixing)

Turbulent Flows


Turbulent Flows

Additional transverse motion enhances the rate of energy and momentum exchange results an increase in the HEAT TRANSFER and the FRICTION coefficient.


Turbulent Flow Problems

• Initially laminar flows were the only interest for research and study through computational techniques.

• Only a small work has been done on turbulent flows in the past due to its complex and complicated nature.

• Complexities arise due to presence of large eddies and dissipating small structures.

• An extensive work has been done in this field of fluid flow during last two decades.



• Most widely used Technique is Large-Eddy Simulation (LES) using Multiple Relaxation Time (MRT) rather than Single Relaxation Time (SRT).

• Another Technique used for the same purpose is Direct Numerical Simulation (DNS).



Direct Numerical Simulation(DNS)

Although DNS is a well established and accurate technique but it is very expensive for available computer capability to simulate practical problems.

Can be used for low Re numbers but for higher Re numbers encountered in Industrial Applications, computational resources required by a DNS would exceed the capacity of the most powerful computers currently available.



Large-Eddy Simulation

(LES)

Efficiency and accuracy of LBE method have not been thoroughly investigated for large eddy simulations (LES) of turbulence.

Eliminates small scales of solution using low pass filtering and thus reduces the simulation cost.

Based on splitting fluid effective viscosity νe into molecular viscosity νt and eddy viscosity νo.


Turbulent Flows

Future Goals

As I am currently working on basic understanding of LBM and Turbulent flows, further and actual work of my project will be done in upcoming days. Its is just a beginning.

THANKS


Basics of Lattice Boltzmann Method for Fluid Flows

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