2. navier-stoke equation 3. classification ... - riam …the riam-compact is based on large-eddy...

Takanori UCHIDA

Research Institute for Applied Mechanics (RIAM),Kyushu University,

6-1 Kasuga-koen, Kasuga-city, Fukuoka 816-8580, JAPAN

CONTENTCONTENT1. Supplementary: Incompressible, Viscosity, Karman Vortex street,Bluff body flow

2. Navier-Stoke equation

3. CLASSIFICATION of Fluid Dynamics: CFD, EFD, TFD, FDM, LES

CONTENT

1. Supplementary: Incompressible, Viscosity, Karman Vortex street,Bluff body flow

2. Navier-Stoke equation

3. CLASSIFICATION of Fluid Dynamics: CFD, EFD, TFD, FDM, LES

Key words : Incompressible, Viscosity, Bluff bodyKey words : Incompressible, Viscosity, Bluff body◆Incompressible :

NO contraction and expansionNO density (mass) change

◆Viscosity : All the existing fluids

◆Bluff Body : Most of the existing obstacles

SOME SUPPLEMENTARYSOME SUPPLEMENTARY

In the room In the AtmosphereFlow

Flow

SCALE

Order : cm

Order : km

Theodore von Theodore von KKáármrmáánn(May 11, 1881 – May 7, 1963 : Aged 81 )

He contributed to the advancement of AERODYNAMICS !He discovered the Kármán vortex street at 30 years old in 1911 !

Origin of Origin of KKáármrmáánn Vortex StreetVortex Street

Taketo Mizota (Fukkuoka Institute of Technology) St Christopher and the vortexA Kármán vortex in the wake of St Christopher's heels.Nature 404, 226 (16 March 2000)

Bologna in Italy

Streamline Body, Bluff bodyStreamline Body, Bluff body

Incompressible Viscous Flow Passing a Foil (Streamline Shape)

(Angle of attack=0 degrees)

(Angle of attack=22 degrees)

(Angle of attack

=45 degrees)

Flow

When the angle of attack grows When the angle of attack grows even a little, separation always occurs. even a little, separation always occurs.

Stall state

IN LANDING

STALL STATE

IN FLYING

CONTENT

1. Supplementary: Incompressible, Viscosity, Karman Vortex street,Bluff body flow

2. Navier-Stoke equation

3. CLASSIFICATION of Fluid Dynamics: CFD, EFD, TFD, FDM, LES

Claude Louis Marie HenriNavier10 Feb 1785 – 21 Aug 1836France

Sir George Gabriel Stokes13 Aug 1819 – 1 Feb 1903Ireland

2i i i

jj i j j

u u up 1ut x x Re x x

Navier-Stokes equation

Temporalterm

Convectiveterm

PressureGradient

term

Viscousterm

Re : Reynolds number

Osborne Reynolds23 Aug 1842-21 Feb 1912England

CONTENT

1. Supplementary: Incompressible, Viscosity, Karman Vortex street,Bluff body flow

2. Navier-Stoke equation

3. CLASSIFICATION of Fluid Dynamics: CFD, EFD, TFD, FDM, LES

Classification of FLUID DYNAMICSClassification of FLUID DYNAMICS★ Computational Fluid Dynamics : (CFD)We try to clarify flow by using Computer.

★ Experimental Fluid Dynamics : (EFD)We try to clarify flow by using Wind tunnel or Towing tank.

★ Theoretical Fluid Dynamics : (TFD)We try to clarify flow Analytically.

CFD EFD TFD

CFDCFDComputational Fluid Dynamics

Choice of the NUMERICAL METHOD AND TURBULENCE MODELChoice of the NUMERICAL METHOD AND TURBULENCE MODEL

Phase1

Phase2

Which numerical methodis chosen ?

Which turbulence modelis chosen ?

◆ FDM (Finite Difference Method)

◆ FVM (Finite Volume Method)

◆ FEM (Finite Eelement Method)

◆DNS (Direct Numerical Simulation)

◆LES (Large Eddy Simulation)

◆RANS (Reynolds Averaged Navier-Stokes eq.)

Idea of FDMIdea of FDM

2

2 0d Tdx

1 12

1 1

2 0

2 0

i i i

i i i

T T Tx

T T T

1

2

3

4

5

6

1 0 0 0 0 0 1001 2 1 0 0 0 00 1 2 1 0 0 00 0 1 2 1 0 00 0 0 1 2 1 00 0 0 0 0 1 0

TTTTTT

①Governing equation

②Difference equation

③Simultaneous algebraic equations

④Solving matrix

◆Direct method :Gauss elimination method

◆Iteration method : Jacobi method, Gauss-Seidel method,SOR method etc

⑤Obtaining solution

Discretization

100℃(B.C.)

0℃(B.C.)

Continuum

100℃ 0℃Unknown number

T1

x

T2 T3 T4 T5 T6

T2=80℃，T3=60℃，T4=40℃，T5=20℃

Example : One dimensional heat conduction

Application of FDM to CFDApplication of FDM to CFD

Filtering operation

The RIAMThe RIAM--COMPACT is based onCOMPACT is based on

LLargearge--EEddyddy SSimulation (imulation (LESLES)) Technique.Technique.

+

Grid Scale (GS) part Subgrid Scale (SGS) part

In LES, Large-scale turbulent motion is computed explicitly, and only the effect of the small-scale motion has to bemodeled.

Thank you for your attention !