dynamic similarity
DESCRIPTION
Dynamic Similarity. http://www.typefreediabetes.com/Articles.asp?ID=150. http://www.eosnap.com/?tag=strait-of-gibraltar. inertial vs viscous. Reynolds Number. Flow is laminar when Re < 1000. Flow is in transition to turbulence when 100 < Re < 10 5 to 10 6. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Dynamic Similarity](https://reader036.vdocuments.mx/reader036/viewer/2022062315/5681649a550346895dd674e6/html5/thumbnails/1.jpg)
Dynamic Similarity
http://www.typefreediabetes.com/Articles.asp?ID=150
upgDtuD
2
http://www.eosnap.com/?tag=strait-of-gibraltar
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upgDtuD
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21)zu
yu
xu
xp
zuw
yuv
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21)zu
yu
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xp
zuw
yuv
xuu
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Re2
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ULLU
LUxu
xuuinertial vs viscous
TtHgpHzLxUu
Reynolds Number
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Low Re
High Re
Flow is laminar when Re < 1000
Flow is in transition to turbulence when 100 < Re < 105 to 106
Flow is turbulent when Re > 106, unless the fluid is stratified
UL
Re
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Consider an oceanic flow where U = 0.1 m/s; L = 10 km; kinematic viscosity = 10-6 m2/s
610
100001.0Re 910
Is friction negligible in the ocean?
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21)zu
yu
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zuw
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FrgHULgHLU
xp
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21inertial vs pressure
TtHgpHzLxUu
Froude Number
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1 gHUFr
1 gHUFr
http://www.yourlocalweb.co.uk/greater-manchester/city-of-manchester/higher-blackley/pictures/
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21)zu
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EuUpLULp
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21 pressure vs inertial
TtHgpHzLxUu
Euler Number
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http://www.freefoto.com/browse/1222-02-0?ffid=1222-02-0
Great Fountain Geyser, Yellowstone National Park, USA
2UpEu
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http://ya.astroleague.org/?p=1445
2UpEu
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StTULLUTU
xuu
tu
2local vs inertial
TtHgpHzLxUu
Strouhal Number
UAfSt
f = frequency of motion; A = amplitude of motion – for flying or swimming organisms (fin or wing)
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Taylor at al. (2003, Nature 425, 707-711(16 )doi:10.1038/nature02000)
http://www.nature.com/nature/journal/v425/n6959/fig_tab/nature02000_F1.html#figure-title
“Left panels, root-flapping motion; right panels, heaving motion. Amplitude, twice wing chord; static angle of attack, 15°; flow speed, 1.5 ms-1; smoke wire visualizations made at end of downstroke.
a, For St < 0.10, flow separates at the sharp leading-edge, but no discrete vortex forms.
b, For 0.10 < St < 0.25, a leading-edge vortex forms but is shed before the downstroke ends.
c, For 0.25 < St < 0.45, the leading-edge vortex is shed as the downstroke ends.
d, For St > 0.45, trailing edge separation produces a characteristic mushroom-shaped wake.
At higher St, the wing collides with shed vorticity on the upstroke, giving an energetically inefficient mode.”
UAfSt
AfAfU 3.33.0
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Dynamic Similarity
http://www.typefreediabetes.com/Articles.asp?ID=150
upgDtuD
2
http://www.eosnap.com/?tag=strait-of-gibraltar
UTLStUpEugHUFr
UL
2
Re