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24 Οκτ 2013 (πριν από 3 χρόνια και 9 μήνες)

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1

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

Unsteady

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
unsteady flow



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

Thank you for your attention!