2. navier-stoke equation 3. classification ... - riam …the riam-compact is based on large-eddy...
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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
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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
![Page 3: 2. Navier-Stoke equation 3. CLASSIFICATION ... - RIAM …The RIAM-COMPACT is based on Large-Eddy Simulation (LES) Technique. + Grid Scale (GS) part Subgrid Scale (SGS) part In LES,](https://reader033.vdocuments.mx/reader033/viewer/2022041906/5e635de5d401866bdc71f4dd/html5/thumbnails/3.jpg)
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
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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 !
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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
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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
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IN LANDING
STALL STATE
IN FLYING
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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
![Page 9: 2. Navier-Stoke equation 3. CLASSIFICATION ... - RIAM …The RIAM-COMPACT is based on Large-Eddy Simulation (LES) Technique. + Grid Scale (GS) part Subgrid Scale (SGS) part In LES,](https://reader033.vdocuments.mx/reader033/viewer/2022041906/5e635de5d401866bdc71f4dd/html5/thumbnails/9.jpg)
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
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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
![Page 11: 2. Navier-Stoke equation 3. CLASSIFICATION ... - RIAM …The RIAM-COMPACT is based on Large-Eddy Simulation (LES) Technique. + Grid Scale (GS) part Subgrid Scale (SGS) part In LES,](https://reader033.vdocuments.mx/reader033/viewer/2022041906/5e635de5d401866bdc71f4dd/html5/thumbnails/11.jpg)
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
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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.)
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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
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Application of FDM to CFDApplication of FDM to CFD
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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.
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Thank you for your attention !