Cylinder 1 - 北海道大学ring-me.eng.hokudai.ac.jp/takeda/FluidDynamics1/Cylinder...Cylinder 4...
Transcript of Cylinder 1 - 北海道大学ring-me.eng.hokudai.ac.jp/takeda/FluidDynamics1/Cylinder...Cylinder 4...
Cylinder 1
Flow past a circular cylinder
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Cylinder 2
Flow past a circular cylinder
Frame of reference
A
u1u0
u2
u0
A
u1
Cylinder 3
Flow past a circular cylinder
Reynolds number
A
u1
du0
ρ,µ
νµρ dudu 00Re ==
Cylinder 4
Flow past a circular cylinder
Reynolds number
Viscosity µ (15°C)Air : 1.78x10-5 kg/ms
Water : 1.14x10-3 kg/msdu0
νdu0Re = Kinematic Viscosity ν (15°C)
Air : 0.15 cm2/s Water : 0.01 cm2/s
Example
Air : d=1m, u0=1m/s → Re≈67KWater : d=1m, u0=1m/s → Re≈1M
Air : d=0.1mm, u0=1.5cm/s → Re≈0.1Water : d=1cm, u0=1.5cm/s → Re≈150
Cylinder 5
Flow past a circular cylinder
Flow patterns
Re<<1
Path of fluid elementsSymmetry for upstream and downstream
Effect of a cylinder is large and wide.
Cylinder 6
Flow past a circular cylinder
Flow patterns
Cylinder 7
Flow past a circular cylinder
Flow patterns
Re=10
Cylinder 8
Flow past a circular cylinder
Flow patterns
Re=41
Cylinder 9
Flow past a circular cylinder
Flow patternsIncreasing Re
Re≈30
Re≈40
Re=47
Cylinder 10
Flow past a circular cylinder
Flow patterns
Re=55
Re=67
Re=100
Cylinder 11
Flow past a circular cylinder
Flow patterns
von Karman vortex street
Cylinder 12
Flow past a circular cylinder
Flow patterns
Cylinder 13
Flow past a circular cylinder
Flow patterns
Wake : a flow behind a body
Cylinder 14
Free convection
Density at various temperature
0.997040.999100.99996Water
1.2151.2581.303Air (x10-3)780Torr
25°C15°C5°CDensity
g/cm3
Cylinder 15
Free convection
Internal and external flow
A
u1
Cylinder 16
Free convection external
g
Cylinder 17
Free convection internal
g
Cylinder 18
Free convection internal
g
Cylinder 19
Free convectionRayleigh Number
d
h
Properties of fluidsα : thermal expansion coefficientκ : thermal diffusivityν : kinematic viscosity
T2 T1Rayleigh Number
( )νκ
α 312 dTTgRa −
=g
Cylinder 20
Free convection
Prandtl Number
κν
=PrProperties of fluids
κ : thermal diffusivityν : kinematic viscosity
( ) Pr2
312
να dTTgRa −
=
Grashof Number
( )νκ
α 312 dTTgRa −
=
Cylinder 21
Free convectionConvection in a vertical slot
Control parameter : Ra
When T2>T1 & Ra is small
T2 T1
System parameter : Aspect ratio : h/d
Pr number : Prg
Cylinder 22
Free convectionConvection in a vertical slot
Ra=2.9x105
Ra=1.5x106Ra=1.3x105
h/d=15Pr=480
Cylinder 23
Free convectionConvection in a vertical slot
Distribution of vertical velocity3.1x104
2.95x105
6.6x105
3.6x106
Cylinder 24
Free convectionConvection in a horizontal layer
T1
If T1>T2 → equilibrium state
T2
If T2>T1
T1heaviercolder
hotter lighterT2
Equilibrium is unstable.
Cylinder 25
Free convectionConvection in a horizontal layer
T1
T2
Equilibrium is unstable.
Stabilizing effects :friction by viscosityheat conduction
At larger Ra number
Rayleigh-Benard convection
Critical Ra ≈ 1700
Cylinder 26
Free convectionConvection in a horizontal layer