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24 Οκτ 2013 (πριν από 5 χρόνια και 5 μήνες)

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Introduction of

Computational Fluid Dynamics

by

Wangda Zuo

M.Sc.

Student of Computational Engineering

Lehrstuhl
für Strömungsmechanik

FAU Erlangen
-
Nürnberg

Cauerstr. 4, D
-
91058 Erlangen

JASS 2005, St. Petersburg

Title of Presentation

2

What is Computational Fluid Dynamics(CFD)?

Why and where use CFD?

Physics of Fluid

Navier
-
Stokes Equation

Numerical Discretization

Grids

Boundary Conditions

Numerical Staff

Case Study: Backward
-
Facing Step

Contents

3

What is CFD?

Mathematics

Navier
-
Stokes Equations

Fluid Mechanics

Physics of Fluid

Fluid

Problem

Computer Program

Programming

Language

Simulation Results

Computer

Grids

Geometry

Numerical

Methods

Discretized Form

Comparison&
Analysis

C

F

D

4

What is Computational Fluid Dynamics(CFD)?

Why and where use CFD?

Physics of Fluid

Navier
-
Stokes Equation

Numerical Discretization

Grids

Boundary Conditions

Numerical Staff

Case Study: Backward
-
Facing Step

Contents

5

Why use CFD?

Simulation(CFD)

Experiment

Cost

Cheap

Expensive

Time

Short

Long

Scale

Any

Small/Middle

Information

All

Measured Points

Repeatable

All

Some

Security

Safe

Some Dangerous

6

Where use CFD?

Aerospace

Automotive

Biomedical

Chemical
Processing

HVAC

Hydraulics

Power Generation

Sports

Marine

Temperature and natural
convection currents in the eye
following laser heating.

Aerospace

Automotive

Biomedicine

7

Where use CFD?

reactor vessel
-

prediction of flow
separation and residence time effects.

Streamlines for workstation
ventilation

HVAC

Chemical Processing

Hydraulics

Aerospacee

Automotive

Biomedical

Chemical Processing

HVAC(Heat Ventilation
Air Condition)

Hydraulics

Power Generation

Sports

Marine

8

Where use CFD?

Flow around cooling towers

Marine

Sports

Power Generation

Aerospace

Automotive

Biomedical

Chemical Processing

HVAC

Hydraulics

Power Generation

Sports

Marine

9

What is Computational Fluid Dynamics(CFD)?

Why and where use CFD?

Physics of Fluid

Navier
-
Stokes Equation

Numerical Discretization

Grids

Boundary Conditions

Numerical Staff

Case Study: Backward
-
Facing Step

Contents

10

Density
ρ

Physics of Fluid

Fluid = Liquid + Gas

Substance

Air(18ºC)

Water(20ºC)

Honey(20ºC)

Density(kg/m
3
)

1.275

1000

1446

Viscosity(P)

1.82e
-
4

1.002
e
-
2

190

Viscosity
μ:

resistance

to flow of a fluid

11

What is Computational Fluid Dynamics(CFD)?

Why and where use CFD?

Physics of Fluid

Navier
-
Stokes Equation

Numerical Discretization

Grids

Boundary Conditions

Numerical Staff

Case Study: Backward
-
Facing Step

Contents

12

Conservation Law

in

out

M

Mass

Momentum

Energy

13

Navier
-
Stokes Equation I

Mass Conservation

Continuity Equation

Compressible

Incompressible

14

Navier
-
Stokes Equation II

Momentum Conservation

Momentum Equation

I : Local change with time

II : Momentum
convection

III: Surface force

IV: Molecular
-
dependent momentum exchange(
diffusion
)

V: Mass force

15

Navier
-
Stokes Equation III

Momentum Equation for Incompressible Fluid

16

Navier
-
Stokes Equation IV

Energy Conservation

Energy Equation

I : Local energy change with time

II:
Convective

term

III: Pressure work

IV: Heat flux(
diffusion
)

V: Irreversible transfer of mechanical energy into heat

17

What is Computational Fluid Dynamics(CFD)?

Why and where use CFD?

Physics of Fluid

Navier
-
Stokes Equation

Numerical Discretization

Grids

Boundary Conditions

Numerical Staff

Case Study: Backward
-
Facing Step

Contents

18

Discretization

Discretization Methods

Finite Difference

Straightforward to apply, simple, sturctured grids

Finite Element

Any geometries

Finite Volume

Conservation, any geometries

Analytical Equations

Discretized Equations

Discretization

19

Finite Volume I

General Form of Navier
-
Stokes Equation

Integrate over the

Control Volume(CV)

Local change with time

Flux

Source

Integral Form of Navier
-
Stokes Equation

Local change

with time in CV

Flux Over

the CV Surface

Source in CV

20

Finite Volume II

Conservation of Finite Volume Method

A

B

A

B

21

Finite Volume III

Approximation of Volume Integrals

Interpolation

Upwind

Central

Approximation of Surface Integrals ( Midpoint Rule)

22

Discretization of

Continuity Equation

One Control Volume

Whole Domain

23

Discretization of

Navier
-
Stokes Equation

FV Discretization of Incompressible N
-
S Equation

Convection

Diffusion

Time Discretization

Explicit

Implicit

Source

24

What is Computational Fluid Dynamics(CFD)?

Why and where use CFD?

Physics of Fluid

Navier
-
Stokes Equation

Numerical Discretization

Grids

Boundary Conditions

Numerical Staff

Case Study: Backward
-
Facing Step

Contents

25

Grids

Structured Grid

+ all nodes have the same number of
elements around it

only for simple domains

Un
structured Grid

+ for all geometries

irregular data structure

Block Structured Grid

26

What is Computational Fluid Dynamics(CFD)?

Why and where use CFD?

Physics of Fluid

Navier
-
Stokes Equation

Numerical Discretization

Grids

Boundary Conditions

Numerical Staff

Case Study: Backward
-
Facing Step

Contents

27

Boundary Conditions

Typical Boundary Conditions

No
-
slip(Wall), Axisymmetric, Inlet, Outlet, Periodic

Inlet ,u=c,v=0

o

No
-
slip walls: u=0,v=0

v=0, dp/dr=0,du/dr=0

Outlet, du/dx=0

dv/dy=0,dp/dx=0

r

x

Axisymmetric

Periodic boundary condition in
spanwise direction of an airfoil

28

What is Computational Fluid Dynamics(CFD)?

Why and where use CFD?

Physics of Fluid

Navier
-
Stokes Equation

Numerical Discretization

Grids

Boundary Conditions

Numerical Staff

Case Study: Backward
-
Facing Step

Contents

29

Solver and Numerical
Parameters

Solvers

Direct:
Cramer’s rule, Gauss elimination, LU decomposition

Iterative:
Jacobi method, Gauss
-
Seidel method, SOR method

Numerical Parameters

Under relaxation factor, convergence limit, etc.

Multigrid, Parallelization

Monitor residuals (change of results between iterations)

Number of iterations for steady flow or number of time steps for

Single/double precisions

30

What is Computational Fluid Dynamics(CFD)?

Why and where use CFD?

Physics of Fluid

Navier
-
Stokes Equation

Numerical Discretization

Grids

Boundary Conditions

Numerical Staff

Case Study: Backward
-
Facing Step

Contents

31

Case Study

Backward
-
Facing Step

u

Wall

Wall

32