building aerodynamics€¦ · Öcondensation Örelase of latent heat Öfurther heating further...
TRANSCRIPT
Dr. Goricsán István, 2008Balczó Márton, Balogh Miklós, 2009
Budapesti Műszaki és Gazdaságtudományi Egyetem, Áramlástan Tanszék1
Wind in the atmosphere
The atmospheric boundary layer
BUILDING AERODYNAMICSBME GEÁT MW08
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TROPICAL CYCLONES
The tropical cyclone Catarina near the shore of Brazil, photographerd from the International Space Station, March 26, 2004
Eye of hurricane ‘Katrina’ Aug 28, 2005photographed from an airplane.
Hurricane (Atlantic Ocean), typhoon (Indian Ocean), Cyclone (PacificOcean)
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TROPICAL CYCLONES
• From 26°C ocean temperature > very high evaporation
• Warm air transported by convection up to the tropopusecondensation relase of latent heat further heating further uprise low pressure
at the sea surface inducing strong horizontal flows to the eye (positive feedback)
• Warm dry air is entering the centre from above the hurricane’s eye
• Pressure difference 50 - 100mbar compared to the environment
• A hurrican is a thermodynamic machine cooling the ocean and transporting heat andmoisture into the higher levels of the atmosphere
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TROPICAL CYCLONES
• Eye 15-40 km diamater• Eyewalls: max. speed 200-300 km/h. Moving velocity: 20-30km/h• High level outflow is counter-rotating• if reaching solid terrain, the driving force, latent heat transport is prohibited• If heading north, gets weakes and turns into an extratropical storm.
30
TROPICAL CYCLONES
Luis hurrikán1995 aug. 27-szept. 11.
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TROPICAL CYCLONES
1 sec = 10 min90km
Hurrrivane Luis, Sept 1995
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TROPICAL CYCLONES
The effects
• Wind damage (Épület, autók stb.)
• 15-20m waves on the shore
• Low pressure elevates water level
• High participation (300 mm/24h , Texas, 1921: 750mm!! – difficult to measure)
floodings (+ 5m)
Hurricane watch:
• Meteorological radar (from the 1950’s), satellites (from the 1970’s),
• Fly-in with manned or unmanned airplanes, to measure wind speed and pressures(dropsondes)
• Hurricane season: July - September
• 100 tropical lows annaually, from which 6-7 develop to hurricanes (wind higher thanBeaufort 12)
• Global climate change: oceans getting hotter (T< 26 C) higher probability!
National Hurricane Center (USA) szimulációja
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Span Systems Inc.
Open ait theatre with tensile fabric roof(St Augustine, Florida, USA)
34
Open air theatre destroyed by a hurricane(Porthsmouth, Virginia, USA)
35
HURRICANE OBSERVATIONS
Unmanned Aerial vehicle
Dropsonde (verticalprofiling)
36
HURRICANE OBSERVATIONS
Unmanned Aerial vehicle
Dropsonde (verticalprofiling)
37
HURRICANE OBSERVATIONS
Unmanned Aerial vehicle
Dropsonde (verticalprofiling)
38
TROPICAL CYCLONES
Hurricane paths 1985-2005
• sea winds
• Urban winds
• orographic winds
• Can be strengthened by other effects : e.g: bora
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LOCAL WINDS
different albedo, heat capacity of surfaces andconsequently varying temperature of air
daily periodocity
morning evening
Orographic wind
• In the morning: southern slopes warm updraft : wind from the valley
Anabatic wind
• In the late afternon: faster cooldown of slopes due to radiation (effect strongerwithout forest coverage) cold downdrafts
Catabatic wind
Thin layer of wind (some meters – some 10 meters), 2-4 m/s max. speed(can be blocked by buildings)
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LOCAL WINDS
http://www.tpub.com/weather2/3-23.htm
Desert winds:
Cyclones generated above desert areas (high T)
and modified by local effects
Scirocco: Mediterranean sea
Samum: Palestine
Khamsin,
haboob: Egypt (causing transport of sand to the Alps - blood rain)
Brickfielder: Australia (very dry hot wind)
Pampero: Argentina
Mistral: catabatic wind strengthened by orographic effects in the valley of the Rhone river. (Bay of Biscaya, Western Franc: anticyclonic = high pressure, Gulf of Genova: low pressure)
Buran: eastern Asian cyclone, snow storm
Bora: High speed wind at the NE shore of Adriatic Sea coming from the mountains (up to 200km/h wind speed, and 14 days of endurance)
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REGIONAL WINDS
Monsoon (- circulation)
• Seasonal reversing wind with annual changes of wind direction 2x a year (min. 120°)
• cause: ITCZ and asymmetric heating of land and sea
• Low pressure areas above desert areas in summer (Indus-plain, Tibetianhighlands, Siberia) ITCZ is moved towards the north
• Southeast trade winds turn to southwest (Coriolis force!) and transport moist air tothe land.
• In winter: cold dry winds from northeast (intensified trade wind)
• Orographic effects: pld. Himalaya
• Monsoon:
• North-Australia
• West Africa
• India
• East-Asia
• Gulf of Mexico (weak)
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WINDS MODIFYING THE PLANETARY CIRCULATION
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GLOBAL ATMOSPHERIC CIRCULATION - SUMMARY
Surface wind directions ans pressure in January (Weischet, 1977)T: low pressure; H: high pressure
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GLOBAL ATMOSPHERIC CIRCULATION - SUMMARY
Surface wind directions ans pressure in July (Weischet, 1977)T: low pressure; H: high pressure
High temporal variability of wind speed and direction
• Wind observations in a fixed observation point:
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WIND SPEED FLUCTUATIONS
( ) ( )trwvu
trV ,,⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
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EXAMPLE OF STRUCTURES CAUSING WIND FLUCTUATIONS
Forrá
s: D
r. K
ristó
f Ger
gely
• Von Kármán vortex street– one specific frequency of vortex separation
• Mixture of frequencies
• Signalling the pass of vortices ofdifferent size
• Max. freq: some Hz (T = 0.1s)
► spectral analysis useful
47
ATMOSPHERIC TURBULENCE
Transformation from time domainto frequency domain:
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FREQUENCY ANALYSIS OF SIGNALS
( ) ( )ωFtf ⇒
Euler formula:
Fourier-transformation: Conversion to time domain:( ) ( )πθπθθπ 2sin2cos2 ⋅+= ie i
( ) ( )∫+∞
∞−
−⋅= dtetfF tiωπω 2 ( ) ( )∫+∞
∞−
⋅= ωω ωπ deFtf ti2
F(ω) complex function: amplitude and phase
Az ampl. squared: powers spectrum
day/night
weathercyclonesfronts
seasons
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WIND POWER SPECTRUM
• shows the contribution of met. Scales to the wind genesis
• right section of the plotis important when addressing building aerodynamics
turbulenceMean wind
( ) ( ) ( ) ( ) kt,rwjt,rvit,rut,rV ⋅+⋅+⋅=
( ) ( ) ( )∫==T
dttruT
rutru0
,1,
Mean wind:
Similarly :( )rv ( )rw
( ) ( ) ( )rut,rut,ru, −=Velocity fluctuation:
( )t,rv, ( )t,rw,
Similarly:
u(r,t)
w(r,t)
v(r,t)
V(r,t)
( )rv
( )rw
( )ru
( )t,rw,
( )t,ru,
( )t,rv,
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DESCRIPTION OF TURBULENT FLOWS
( ) ( ) 0,10
,, == ∫T
dttruT
ru ( ) 0, =rv ( ) 0, =rw
Temporal average of fluctuations:
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DESCRIPTION OF TURBULENT FLOWS
( ) ( ) ( ) ( )( ) ( )rdtrut,ruT1dtt,r'u
T1t,r'u 2
u
T
0
2T
0
22 σ=−== ∫∫Root mean square of fluctuations = squared deviation of velocity
Root mean square of fluctuations:
[ ]s/m,, wvu σσσ
uT u
uσ
=
uT v
vσ
=
uT w
wσ
=
Quotient of stnadard deviation and mean windvelocity [-]
• Laminar flows: verylow turbulenceintensity
• Growing flowvelocity: highturbulence (shownby stronger mixing)
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DEFINITION OF TURBULENCE INTENSITY
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TURBULENT KINETIC ENERGY
Kinetic energy of an elementar mass:2)t(V
21
m)t(E
=
2)t(V21
m)t(E =Average kinetic energy:
( )
( )2w
22v
22u
2
222
wvu21
wvu21
m)t(E
σ++σ++σ+
=++= ( ) ( ) ( )rurru 22u
2 =σ+
The total kinetic energy of the turbulent flow is larger than that of a laminarflow with the same mean wind velocity!
=m
Eössz
Kinetic energy of the mean flow:
( )222átlag wvu21
mE
++= +
Kinetic energy of fluctutations(turbulent kinetic energy, TKE):
( )2w
2v
2u2
1m
TKEσ+σ+σ=
day/night
weathercyclonesfronts
seasons
turbulenceMean wind
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TURBULENT KINETIC ENERGY
• Area below the curve ~ TKE
• Distribution of TKE by frequency / vortex size
Large vortices in the atmospherefall a part to smaller ones.At the end, smallest vorticesdissipate their kinetic energy toheat. (because real flows areviscous)The spectrum of winf is formed bythis mechanism to a typical shape.
Turbulent energy cascade
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TURBULENT KINETIC ENERGY SPECTRUM
Big whorls have little whorls That feed on their velocity,
And little whorls have lesser whorls And so on to viscosity.
(Lewis F. Richardson*, 1922)
*English mathematician, physicist, meteorologist (1881-1953), who created the concept of numerical weather prediction
Momentum transportfrom the mean flow: vortices aredeveloped on theedges of flowobstacles
Inertial domain: a energy of largestructures passedto smaller flowstructures
Molecular dissipation: kinetic energy turns intoheat
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TURBULENS KINETIKUS ENERGIA SPEKTRÁLIS MEGOSZLÁSA
The planetary boundary layer (PBL), also known as the atmospheric boundary layer (ABL), is the lowest part of the atmosphere and its behavior is directly influenced by its contact with a planetary surface. Heat, momentum and moisture transportbetween earth and atosphere occurs in the ABL. Flow in the ABL is mostly turbulent, transport isdone by turbulent vortices (turbulent diffusion).
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THE ATMOSPHERIC BOUNDARY LAYER
• Driving force: free atmosphere, gestrophic or cyclonic winds• On the surface : velocity = 0• Thermal convection• Surface roughness and elevation has major influence on its shape and
thickness• Thickness can vary in time ( – time scale ≤ 1day)• 3D flow – w cannot be neglected
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THE ATMOSPHERIC BOUNDARY LAYER
Momentum equations:
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EKMAN LAYERGeostrophic wind,
acting forces: Coriolis and pressure gradient force, flow || isobars
• Friction on the surface V < Vg
• Coriolis-force smaller wind directiondeflected towards the pressuregradient.
• Max.deflection : 45°
0np1fVg =
∂∂
ρ−
( )z
'w'vfUnp1
∂∂
+=∂∂
ρ
( )z
'w'ufV0∂
∂+=
X :
Y :
The ‘Fram’ in the ice
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FRIDTJOF NANSEN’S EXPEDITION WITH FRAM (1893-1896)
• Journey of the FRAM (continuous)• Nansen and Johansen by cayak and hound
sledge (dashed) ‘Fram’s cross-sectionNansen (1861-1930)
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EKMAN-SPIRAL, SUBLAYERS
Surface layer (Prandtl layer)
boundary layer thickness ~ 10% of tropospherewidth, ~ 1 km, but can vary between 200 m - 5 km
Surface layer: wind speed, temperature change with height.
Turbulence induced by surfaceroughness / obstacles and thermalconvection
constant flux of mass heat etc.
Wind direction approximatelyconstant
Typical height: 50 m, can varybetween 5-200 m
roughness or canopy layer: windspeed influenced strongly bybuildings, groves trees: chaotic (3D) dominance of turbulent movement.
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BOUNDARY LAYER STRUCTURE ABOVE ROUGH TERRAIN
K)zln(u)z(u*
+⋅κ
=
• Turbulent momentum exchange betweenlayers:
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LOGARITHMIC BOUNDARY LAYER PROFILE
zuK'w'u M ∂
∂==
ρτ
• K-theory: shear stsess proportianal to thegradient of the mean wind profile
• Turbulent vortices cause an additionalviscosity (turbulent viscosity)
• KM not constant, and can be determined usingturbulence models
ν>>MK
τ constant in the surface layer
( ) .állu'w'u 2* ===ρτ
u* - friction velocity(fictitious quantity with
velocity dimension)
zuK *M ⋅⋅κ=
Simple assumption: Km 0 at the surfaceκ – Kármán-constant = 0.41
zu
zu *
∂∂
=κ
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅
κ=
0zzlnu)z(u
*
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LOGARITHMIC BOUNDARY LAYER PROFILE
d0 – displacement height(if the whole boundary layer is shifted upwards)
z0 – roughness length
)z
dzln(1u
)z(u0
0*
−⋅
κ=
• d0+ ln z0 at U/Uref = 0
z0=0.1, α=0.185
)z
dzln(
1u
)z(u
0
0
*
−⋅
κ=
α
⎟⎟⎠
⎞⎜⎜⎝
⎛−
−=
0ref
0
ref dzdz
u)z(u
empirical power function
65
LOG-LAW AND POWER LAW WIND PROFILES
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LOG-LAW AND POWER LAW WIND PROFILES
• Power law wind profiles measured in wind tunnel
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WIND PROFILES FROM ON-SITE MEASUREMENTS
≈0.75⋅h≈0.75⋅h≈0≈0d0 [m]0.24 – 0.40.18 – 0.240.12 – 0.180.08 – 0.12a [-]
0.5 - 20.1 – 0.55⋅10-3 – 10-110-5 – 5⋅10-3z0 [m]
Forests, urban area
Suburban area, groves
Farmland, grass Ice, snow, calm water
description
very roughroughmediumsmoothSurface category
Forrás: http://www.gi.alaska.edu/~heike/Barrow2005/h_chargingADV.jpg
Forrás: http://earthobservatory.nasa.gov/Laboratory/Biome/Images/picgrassland.jpg
Forrás: http://www.aerometrex.com.au/AdelaideMetro/Suburban_Adelaide.jpg
Forrás: http://www.usatravel.hu/fckep/Image/Missouri/.thumb_Kansas_City.jpg
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PROFILE PARAMETERS
*u u5,245,2 ⋅÷=σ
*v u2,2 ⋅=σ
*w u25,1 ⋅=σ5.0:8.0:1T:T:T wvu =
ATMOSPHERIC TURBULENCE IS ANISOTROPIC!69
TURBULENCE INTENSITY IN THE ATMOSPHERIC BOUNDARY LAYER
α
⎟⎟⎠
⎞⎜⎜⎝
⎛−
−=
0ref
0
ref dzdz
u)z(u
uT u
uσ
=
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PROFILE PARAMETERS
( )( ) ( )DC
red
red2u
uu
fBE
fAz
z,fSf
⋅+
⋅=
σ⋅
71
WIND SPECTRA
Forrás: Yu et al (2008): HurricaneWind Power Spectra, Cospectra, and Integral Length Scales72
WIND SPECTRA
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BOUNDARY LAYER GENERATION IN WIND TUNNELS
ábra: E. J. Plate. Engineering Meteorology (1982)
1. Confuser2. Turbulence generators3. Roughness elements4. Adjustable roof5. Flow preparation section6. Measurement section - model on turntable7. Fan8. Diffuser
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BOUNDARY LAYER GENERATION IN WIND TUNNELS
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BOUNDARY LAYER GENERATION IN WIND TUNNELS
closedtest section
5 or 7preparation section length [m]
0.5inlet turbulece intensity [%]
22max. wind speed [m/s]
1.4measurement section height [m]
2.2measurement section width [m]
2measurement section length [m]