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

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

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

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

Project Timeline

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

Computational Fluid Dynamics

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

Common Simulation Tools

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

Computational Fluid Dynamics

Discretization

Multi-Scale Analysis

Common Simulation Tools

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

Common Simulation Tools

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)

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

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

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

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.

Lattice Boltzmann Method

From LGCA to LBM

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

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 Boltzmann Method

LATTICE

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

Lattice Boltzmann Method

LATTICE

Arrangements of the lattice is represented by DnQm

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

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

Lattice Boltzmann Method

LATTICE

D1Q2D2Q7D2Q9D3Q15D3Q19

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

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.

Lattice Boltzmann Method

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

Lattice Boltzmann Method

D2Q9 Lattice Model

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

Lattice Boltzmann Method

D2Q9 Lattice Model

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

Lattice Boltzmann Method

),(),( tftf eq

ii xx

Lattice Boltzmann Equation

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

Lattice Boltzmann Method

Lattice Boltzmann Equation

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

Lattice Boltzmann Method

• 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

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

Lattice Boltzmann Method

Periodic BCs

No-slip BCs

Slip BCs

Velocity and Pressure BCs

Boundary Conditions

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

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

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

Turbulent Flows

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

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

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.

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

Turbulent Flow Problems

• 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).

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

Turbulent Flow Problems

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.

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

Turbulent Flow Problems

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.

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad

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

Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad