computational fluid mechanics intro

8/12/2019 computational fluid mechanics intro

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FUNDAMENTS OF CFD1.

33:45 PM

Introduction

2.3:45 AM 5 PM

ComputationalHeat TransferDevelopment

Series of Invited Lecture onCFD:

Developments, Appl ications & Analysis

NIT Hamirpur

To pic I : In tr o d uc tio n1.

CFD:What is it?

3.

CFD:Why?

2.

CFD:How it is ?

Series of Invited Lecture onCFD:

Developments, Appl ications & Analysis

NIT Hamirpur

Contents

01.

CFD: What is it?

Definition

Role

Major Aspects

03.

CFD: Why

02.

CFD: How is it?

Grid Generation

Finite Volume Method

Solution Methodology


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01. CFD: What is it

?

Definition

Role

Major Aspects

1

CFD: Defination

Computational Fluid Dynamics (CFD) is a theoretical

method of scientific and engineering investigation,concerned with the development and

application of avideo-camera like tool - a software - which is used toanalyze a fluid dynamics as well as heat and masstransfer problem in a unified

way.

Here, the software is like a virtual video-camera andresults in a movie where each picture gives a fluid-dynamics information, i.e., flow-properties.

Vortex Shedding Fluid Flow

across a Circular Cylinder at Re=100

Vortex Shedding Fluid Flow

across a Circular Cylinder at Re=100


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Vorticity Contours at Re=100 Group of Fish Like Locomotion

Dam Break Simulation 2D Film-Boiling Over a Superheated Plate


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Granular Flow CFD: Role

Analogy between a video-camera and a CFD

software.Analytical (CFD) solution are like a virtual video

camera of infinite (finite) spatial as well as temporalresolution.

The role of CFD software is not limited to creatingscientifically excitin

g fluid dynamic movie of flowproperties but also to create engineering relevantmovie of engineering parameters, for a unifiedcause-and-effect study of various heat and fluidflow situations.

CFD: Major Aspects

There are three major aspects of CFD

Development

Application Analysis

With a continuous development and a wider

application of CFD, the definition of Navier-

Stokes equations and CFD has broaden.

02. CFD: How is it?

Grid Generation


Solution Methodology

2


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CFD: How is it?

SolutionMethodology

It consists of

1. Solution Method: Amethod to solve theset of algebraicequations

Explicit and Implicit Methodfor unsteady state formulation

Iterative method for steadystate formulation.

2. Implementation Details

3. Solution Algorithm

Grid-Generation

A method to convert the completedomaininto certain fixed numbero f Control Vo lumes (CVs). Thepoints located at the centroid ofthe CVsare calledas grid points.They areof twotypes:

Cartesian, Cylindrical and SphericalGrid: used for simple geometry.

Curvilinear-Structured andUnstructured Grid: used for complexgeometry.


A method to obtain a systemof algebraic equations, withunknowns as flow propertiesat thegridpoints,obtainedby

Physics based Approach:Applying conservation laws to the CVsand using certain approximations.

Mathematics based Approach:Applying volume integral to thegoverning partial differential equations,using gauss divergence theorem forcertain terms and using certainapproximations.

L 2

L 1

i

j

1 imax1

jmax

Boundary CVs:

i=1 & imax;

j=2 to jmax-1

j=1 & jmax;

i=2 to imax-1

P

N

S

EW

InteriorCVs:

i=2 & imax-1;

j=2 to jmax-1

j=2 & jmax-1;

i=2 to imax-1

Outer Square Boundary

Plate

Inner Square Boundary

Square Hole

Both the Boundaries are

aligned along direction of

Cartesian Coordinates

Heat Transfer in a Square

Plate with a Square Hole


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Heat Transfer in a Squareplate with a Circular Hole

The Outer SquareDomain Boundary is

aligned along the

direction of Cartesian

Coordinates

Inner Circular Domain

Boundary is aligned

along the direction of

cylindrical coordinates

Complex Domain & Unstructured Grids

x

y

PressureForce

Pressure

Force inX-direction

PressureForce in

Y-direction

ZERO

Body Forceor Heat

Generation

Body Force

inX-direction

Body Forcein

Y-direction

HeatGained by

HeatGeneration

ViscousForce or

HeatConduction

Viscous

Force inX-direction

ViscousForce in

Y-direction

HeatGained by

Conduction

ACROSSthe CV

X-Momentum

Y-Momentum

Energy

Conservation Laws: Mass, Momentum & Energy

INSIDE theCV

Mass

X-Momentum

Y-Momentum

Energy

Rate of Change

Unsteady Advection Diffusion S o u r c e

Mass Zero

X-Mom.

Energy

Y-Mom.

Mass


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CFD: How is it?Fi ni te Vol um e M et ho d for Computational Fluid Dynamics

A Novel

Physics

based

Control

Volume

The

Traditional

Mathematics

based

Two Levels ofApproximations

Governing

PDEs

Gauss Div. Theorem

Approximations

V

Discretized LAEs

(Linear Algebraic Equations)

FluidMechanics

& Heat

TransferCourse

limV 0

Navier-Stokes

Equations

Mass

Momentum

Energy

Conservation

Laws Continuity

Momentum

Energy

Tnb=4000C Ti,jmax=400

0C Grid Points

Internal:

at 2500C

Boundary:

at 100/200/

300/4000C

Twb=1000C

T1,j=1000C

jmax=7

6

5

4

3

2

j=1 xy

Teb=3000C

Timax,j=3000C

Tsb=2000C Ti,1=200

0C

i=1 2 3 4 5 6 imax=7

n+1

n

E x p l i c i t M e t h o d

Unsteady State Heat Conduction: Computational Stencil

1

, , ,

n nP P nb nb

n b E W N S

a T a T b

CFD: How is it?


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S o l u t i o n M e t h o d o l o g y f o r

U n s t e a d y C o m p u t a t i o n a l h e a t C o n d u c t i o n

A Novel Physics basedThe Traditional

Mathematics

basedS i n g l e S t e p

( )

( ) ( )

( ) ( )

P P

E E W W

N N S S

a T t t

a T t a T t

a T t a T t

b

( )P

T t t

x xq y

y yq x

xi r s t S t e p :( ) ( ) ( ); ( ) ( ) ( )

( ) ( ) ( ); ( ) ( ) ( )

x x E E P P x P P W W

y y N N P P y P P S W

q t c T t c T t q t d T t d T t

q t e T t e T t q t f T t f T t

S e c o n d S t e p :

( ) ( ) ( ) ( )

( ) ( )

conducti on x x x y y y

P P P conducti on

Q t q t q t y q t q t x

T t t T t g Q t

xq y

yq x

N

P EW

S

y

03. CFD: Why 3

CFD: Why?

Now a days, a computer simulation and analysis have

become an integral part of a design and optimization study.

CFD is more commonly used as a powerful analysis, than adesign and optimization, tool by scientists as well as

engineers - dealing with fluid dynamics and heat-transfer

problems; in various industry such as aerospace,

automobile, turbo-machinery, chemical, electronics

cooling, biomedical, etc.

CFD: Why?

In academics, CFD is taught as an under-graduate

elective and post-graduate course, in different

branches of engineering. The increasing importance of CFD development,

application and analysis, in the industry as well as

research organizations, along with the lack of trained

manpower in this area has greatly increased the

importance of this course.


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Brief History Modern Trends2

Brief History of Developments of CFD Difficulties in Solving for Pressure

Discretization Method, Geometry and Grid

Modern Trends in CFD Cartesian Grid Method

Multilevel Cartesian Grid Method

Parallel Computing

Industrial Applications

Difficulties in Solving for Pressure

Three conservation laws based equations (mass,

momentum and energy) and three dependent variables

(pressure, velocity and temperature).

Law of conservation of momentum and energy have a

term as rate of change of momentum and energy

No rate of change of pressure term in the massconservation law

No explicit equation for pressure and continuity equation

needs to be converted into an equation for pressure.

Difficulties in Solving for Pressure

This resulted in a stream-function vorticity method and was one

of the first popular method in CFD - limited to 2D and steady-

state problems.

To circumvent these limitations, a pressure-velocity formulationcalled as pressure correction approach was proposed where thecontinuity equation was employed as a constraint to derivecorrect pressure field - through a detailed iterative solutionprocedure.

However, there was an issue of pressure velocity decouplingand the first remedy suggested was solution on a staggeredgrid.


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Discretization Method, Geometry & Grid

Early development of CFD started with FDM for problems - called as

simple geometry problem. The Cartesian/Cylindrical/Spherical geometry problems were solved in

a uniform or nonuniformgrid, where one of the grid line fits to the

boundary of the computational domain -called as body fitted grid.

With advances in CFD and more application to industrial problems,

there was a need to develop method for computing flows in complex

geometry.

Initially, this was attempted with FDM on a body-fitted (a) Cartesian

and (b) curvilinear grid

Discretization Method, Geometry & Grid

This led to development of FVM where the governing PDEs

are solved directly in the physical complex/curved domain, onbody-fitted curvilinear structured grid.

However, implementation of staggered grid was found almost

impossible for complex geometry and another remedy to

obtain physical solution in co-located grid was proposed as

usage of momentum interpolation.

This continued for quite some time with further development

from the FVM based solution in structured to multi-block

structured to unstructured body-fitted grid system.

Thank You for Your attention

Welcome for any Questions,

Comments, and Suggestions

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