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8/12/2019 Flow Patterns and Wind Forces
1/571
Flow Patterns andFlow Patterns and
Wind ForcesWind Forces
Tokyo Polytechnic UniversityTokyo Polytechnic University
The 21st Century Center of Excellence ProgramThe 21st Century Center of Excellence Program
Yukio TamuraYukio Tamura
Lecture 4Lecture 4
Flows Around Bluff BodiesFlows Around Bluff Bodies
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Flow Patterns AroundFlow Patterns AroundBluff BodiesBluff Bodies
Stream LinesStream Lines
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Flow pattern around a square prism (ParticleFlow pattern around a square prism (Particlepaths, 2D, Uniform flow, CFD)paths, 2D, Uniform flow, CFD)
Flow pattern around a square prism (StreakFlow pattern around a square prism (StreakLines, 2D, Uniform Flow, CFD)Lines, 2D, Uniform Flow, CFD)
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Flow pattern between building modelsFlow pattern between building models(Streak Lines)(Streak Lines)
Periodic vortices shed from a square prismPeriodic vortices shed from a square prism(Streak Lines, CFD)(Streak Lines, CFD)
K. Shimada
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Flow pattern around a square prismFlow pattern around a square prism(Stream lines, Wind tunnel, by T.(Stream lines, Wind tunnel, by T. MizotaMizota))
Temporal variation of flow pattern aroundTemporal variation of flow pattern arounda square prisma square prism (Stream lines, 2D, Uniform flow, CFD)(Stream lines, 2D, Uniform flow, CFD)
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Temporally averaged flow pattern aroundTemporally averaged flow pattern arounda square prisma square prism (Stream lines, 2D, Uniform flow, CFD)(Stream lines, 2D, Uniform flow, CFD)
Temporally averaged flow patternTemporally averaged flow patternaround a square prismaround a square prism
A: Front stagnationA: Front stagnationpointpoint
B: Rear stagnationB: Rear stagnationpointpoint
1, 2: Separation1, 2: Separationpointpoint
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Temporally averaged flow pattern around aTemporally averaged flow pattern around acircular cylindercircular cylinder
SPSP
SPSP
FPFP
RPRP
Temporally averaged flow pattern around aTemporally averaged flow pattern around arectangular cylinderrectangular cylinder
with a large side ratiowith a large side ratio
ReattachmentReattachment
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Inflow and outflow into an infinitesimalInflow and outflow into an infinitesimalhexahedronhexahedron
Inflow through the (Inflow through the (dydydzdz) plane:) plane:11 uu 11 uu((uu dxdx ))dydzdydz ((uu ++ dxdx ))dydzdydz22 xx 22 xx uu== dxdydzdxdydz (1)(1)xx
Inflow through the (Inflow through the (dzdzdxdx) plane:) plane: vv== dxdydzdxdydz (2)(2)yyInflow through the (Inflow through the (dxdxdydy) plane:) plane: ww== dxdydzdxdydz (3)(3)zz
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Law of Conservation of MassLaw of Conservation of Mass
((IncompressiveIncompressive Fluid) : Eq.(1)+Eq.(2)+Eq.(3)=0Fluid) : Eq.(1)+Eq.(2)+Eq.(3)=0 uu vv ww dxdydzdxdydz dxdydzdxdydz dxdydzdxdydz = 0= 0xx yy zzEquation of Continuity:Equation of Continuity:
uu vv ww ++ ++ = 0= 0xx yy zz(div vv == 0)
VorticityVorticity VectorVector :: = (= (,, ,, ) = rot) = rot vv ww vv == yy zz uu ww == zz xx vv uu == xx yy,, ,, = 2= 2xx, 2, 2yy,2,2zz :: VorticityVorticityxx,, yyzz : Rotational angular velocity: Rotational angular velocityaboutaboutxx andand axesaxes
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vv ttxx xx
yy
uu ttyy
Angular Velocity of RotationAngular Velocity of Rotation
11 vv uuzz == (( ))22 xx yy11
== 22
average
:: VorticityVorticity
NonNon--viscous andviscous and IrrotationalIrrotational FluidFluid
= rot= rot vv == 00 Velocity potentialVelocity potential can becan be
assumed:assumed:
uu == ,, vv == ,, ww == xx yy zz
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Equation of Continuity:Equation of Continuity: uu vv ww ++ ++ = 0= 0xx yy zz uu == ,, vv == ,, ww == xx yy zz : Velocity potential: Velocity potential
LaplaceLaplace Equation:Equation:
22 22 22 ++ ++ = 0= 0xx 22 yy 22 zz 22
Flow PatternFlow Patternand Pressureand Pressure
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Stream line and flow velocityStream line and flow velocity
streamlin
ea
stream
lineb
Stream tube and flow velocityStream tube and flow velocity
Sectional Area:AA
Sectional Area:AB
Pressure:PA UUAA
UUBB
zzAA
zzBB
Pressure:PB
ClosedCurve:C
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IncompressiveIncompressive FlowFlow (Law of conservation of mass)(Law of conservation of mass)AAAAUUAA == AABBUUBB ==mmmm :: Air mass of inflow and outflow portionsAir mass of inflow and outflow portions
Increase of kinetic energy during unit timeIncrease of kinetic energy during unit timemm ((UUBB
22 UUAA22) (1)) (1)
22Increase of potential energy during unit timeIncrease of potential energy during unit time
mmgg ((zzBB zzAA) (2)) (2)Work done by pressure difference during unitWork done by pressure difference during unit
timetime ((PPAAAAAA))UUAA ((PPBBAABB))UUBB (3)(3) :: Air density,Air density, UUii :: Wind speed at pointWind speed at point iiPPii :: Pressure at pointPressure at point i,i,gg :: Gravity accelerationGravity accelerationzzii :: Altitude of pointAltitude of point ii
For the same stream tube:For the same stream tube:11
UUAA22 ++PPAA ++ gzgzAA22
11== UUBB22 ++PPBB ++ gzgzBB22 : Air density: Air densityUUii : Wind speed at point: Wind speed at point ii
PPii : Pressure at point: Pressure at point iigg : Gravity acceleration: Gravity accelerationzzii : Altitude of point: Altitude of point iiE .(1)+E .(2)= E .(3)Eq.(1)+Eq.(2)= Eq.(3)
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BernoulliBernoullis Equations Equation (Steady / Ideal flow)(Steady / Ideal flow)
11 UU 22 ++PP ++ g zg z ==HHTT (constant)(constant)22
: Air density: Air densityUU : Wind speed: Wind speedPP : Pressure: Pressure
gg : Gravity acceleration: Gravity accelerationzz : Altitude: AltitudeHHTT : Total pressure: Total pressure
(On Stream(On Stream
BernoulliBernoullis equation:s equation:11
UU 22 ++PPSS ==HHTT (constant)(constant)22 : Air density: Air densityUU : Wind speed: Wind speed
PPSS : Static pressure =: Static pressure =PP ++ gzgz11UU 22 : Dynamic pressure: Dynamic pressure22
HHTT : Total pressure: Total pressure
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BernoulliBernoullis equation:s equation:
11 UU 22 ++PPSS ==HHTT (constant)(constant)22
UU :: LargeLarge (Small)(Small)PPSS :: SmallSmall (Large)(Large)
Pressure distribution and resultant forcePressure distribution and resultant forceacting on a fluid cellacting on a fluid cell
High Pressure
Low Pressure
Resultant
Force
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Curved stream line andCurved stream line andpressure gradientpressure gradient
High Pressure
Low Pressure
Force
UU22 PP ++ = 0= 0rr nn
Wind Pressure at pointWind Pressure at point ii
ppii ==PPii PPRRPPii :: Pressure at pointPressure at point ii
PPRR :: Pressure at reference pointPressure at reference pointRR farfaraway from the body, where thereaway from the body, where thereis no effect of the body on the flowis no effect of the body on the flowfieldfield
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Stream lines around a square prism andStream lines around a square prism andspatial variation of pressurespatial variation of pressure
PPAA >>PPRR ((ppAA >0)>0)
PPBB >>PPRR ((ppBB >0)>0)
PPDD
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NavierNavier--Stokes EquationStokes Equation
Substantial DifferentiationSubstantial Differentiation
Velocity componentsVelocity components
uu = u= u((x,y,z,tx,y,z,t))
vv
= v= v
((x,y,z,tx,y,z,t
))
w = ww = w((x,y,z,tx,y,z,t))
Displacement of a small element of fluid atDisplacement of a small element of fluid at
point P during an infinitesimal intervalpoint P during an infinitesimal interval ttx = ux = u((x,y,z,tx,y,z,t))tty = vy = v((x,y,z,tx,y,z,t)) tt Eq.(aEq.(a))z = wz = w((x,y,z,tx,y,z,t))tt
P(P(x,y,z,tx,y,z,t))
Q(Q(x+x+xx,y+,y+yy,z+,z+zz,t+,t+tt))VVtt
}
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Changing rate (Changing rate (f /f /tt)) of a propertyof a propertyffff++ ff= f= f((x +x +x , y +x , y +y , z +y , z +zz,, t +t +tt ))ff ff ff ff==ff((x, y, z, tx, y, z, t)) ++x +x +y +y +z +z +ttxx yy zz tt
+ O(+ O(tt22))tt 0, substituting0, substituting Eq.(aEq.(a))DDff ff ff ff ff == ++ uu ++ vv ++ ww
DD
tt tt xx yy zzSubstantial AccelerationSubstantial Acceleration
DDuu uu uu uu uu == ++ uu ++ vv ++ ww DDtt tt xx yy zz
3535
Changing rate (Changing rate (f /f /tt)) of a propertyof a propertyffff++ ff= f= f((x +x +x , y +x , y +y , z +y , z +zz,, t +t +tt ))ff ff ff ff==ff((x, y, z, tx, y, z, t)) ++x +x +y +y +z +z +ttxx yy zz tt
+ O(+ O(tt22))tt 0, substituting0, substituting Eq.(aEq.(a))DDff ff ff ff ff == ++ uu ++ vv ++ ww DDtt tt xx yy zzSubstantial AccelerationSubstantial Acceleration
DDuu uu uu uu uu == ++ uu ++ vv ++ ww DDtt tt xx yy zz
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Velocity gradient and viscous stressVelocity gradient and viscous stress(Newtonian fluid)(Newtonian fluid)
ddUU == ddnn
NewtonNewtons Laws Lawof Viscosityof Viscosity
Coefficient of Viscosity 15Coefficient of Viscosity 15CC == 1.781.78101055 kg/m/s (Airkg/m/s (Air)) == 114114 101055 kg/m/s (Waterkg/m/s (Water))
Shear deformation velocityShear deformation velocityininxyxy -- planeplane
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Shear stresses acting onShear stresses acting onan infinitesimal hexahedron of fluidan infinitesimal hexahedron of fluid
vv uuxyxy== yxyx == (( ++ ))xx yyuuxxxx= 2= 2 xx
Total shear forces actingTotal shear forces actingxx--direction:direction:
xxxx yxyx zxzx(( ++ ++ )) ddxxddyyddzzxx yy zz
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NavierNavier Stokes Equations:Stokes Equations:
Inertial force per unit volumeInertial force per unit volume uu uu uu uu [[ ++ uu ++ vv ++ ww ]]tt xx yy zzSubstantial accelerationSubstantial acceleration
pp 22uu 22uu 22uu== ++ [[ ++ ++ ]]xx xx 22 yy 22 zz 22PressurePressure ViscousViscousgradientgradient stressstress
LocalLocal ((InstantaneousInstantaneous))accelerationacceleration
Convective accelerationConvective acceleration
NavierNavier Stokes Equations:Stokes Equations: uu uu uu uu [[ ++ uu ++ vv ++ ww ]]tt xx yy zzpp 22uu 22uu 22uu== ++ [[ ++ ++ ]]
xx xx 22 yy 22 zz 22 vv vv vv vv [[ ++ uu ++ vv ++ ww ]]tt xx yy zzpp 22vv 22vv 22vv== ++ [[ ++ ++ ]]yy xx 22 yy 22 zz 22 ww ww ww ww [[ ++ uu ++ vv ++ ww ]]tt xx yy zzpp 22ww 22ww 22ww== ++ [[ ++ ++ ]]zz xx 22 yy 22 zz 22
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NonNon--dimensional expression ofdimensional expression of NavierNavier StokesStokesEquations:Equations:
uu** uu** uu** uu** ++ uu** ++ vv** ++ ww** tt ** xx** yy** zz**pp** 11 22uu** 22uu** 22uu**== ++ [[ ++ ++ ]]xx** ReRexx** 22 yy** 22 zz** 22
x y zx y z t U pt U p
xx**
== ,, yy** == ,, zz** == ,, tt** == ,, pp** == L L L LL L L L UU22u v wu v w ULUL
uu**== ,, vv** == ,, ww** == ,, ReRe == UU U UU U
Reynolds NumberReynolds NumberULUL ULULReRe == == LL 33 UU22/ L/ L
== LL 22 U / LU / LInertial ForceInertial Force
== Viscous ForceViscous Force 77 101044LL UU (Air)(Air)
(m/s)(m/s) Reference SpeedReference Speed
(m)(m) Reference LengthReference Length 99 101055LL UU (Water)(Water)
T =T = 1515C,C,PP = 1013hPa= 1013hPa == 1.22 kg/m1.22 kg/m33 == 1.781.78101055 kg/m/s (Air)kg/m/s (Air) == 114114 101055 kg/m/s (Water)kg/m/s (Water)Dynamic ViscosityDynamic Viscosity == // == 1.451.45101055 mm22/s (A)/s (A) == // == 1.141.14101066 mm22/s (W)/s (W)
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HagenHagen--Poiseuille flow in a straight circularPoiseuille flow in a straight circulartubetube
-- Laminar flowLaminar flow-- A parabola profileA parabola profile-- Quantity of flowingQuantity of flowing
r 4pQ
--r :r : Radius of tubeRadius of tube
-- Viscosity meterViscosity meter
Flow around a circular cylinderFlow around a circular cylinderin an ideal flow (Nonin an ideal flow (Non--viscous)viscous)
H.P.H.P. H.P.H.P.
L.P.L.P.
(FP)
(RP)
AccelerateAccelerate DecelerateDecelerate
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Surface Boundary LayerSurface Boundary Layer
Flow near surface of bodyFlow near surface of body
WallSurf
ace
Flowv
elocity
Boun
darylayer
Flow around a circular cylinderFlow around a circular cylinderin an ideal flow (Nonin an ideal flow (Non--viscous)viscous)
H.P.H.P. H.P.H.P.
L.P.L.P.
(FP)
(RP)
AccelerateAccelerate DecelerateDecelerate
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-- Separated shear layerSeparated shear layer
-- Vortex sheetVortex sheet
-- Shear layer instabilityShear layer instability
Flow near the separation pointlow near the separation pointSeparation
Point
-- Separated shear layerSeparated shear layer
-- Vortex sheetVortex sheet
-- Shear layer instabilityShear layer instability
Flow near the separation pointFlow near the separation point
SeparationPoint
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Flow separation from body surfaceFlow separation from body surface(Viscous Flow)(Viscous Flow)
SP
FP
(a) Definition of circulation (b) Rigid vortex and Circulation
Circulation and vorticity
CirculationCirculationCC == CC UUcoscosdsds
ClosedCurve:C
ClosedCurve: C
Area:AAngularVelocity
--CC = 2= 200AA-- VorticityVorticity = 2= 200
CC ==rr00 22rr== 2200 rr22 == 2200AArr
rr00
==CC/A/A
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- CirculationC = (UA UB )
Circulation along a line ofCirculation along a line ofvelocit discontinuitvelocit discontinuit
Unit Length : 1
Closed Curve:C
Line of VelocityDiscontinuity
Causes of Wind ForcesCauses of Wind Forces
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Flow around a circular cylinderFlow around a circular cylinderin an ideal flow (Nonin an ideal flow (Non--viscous)viscous)
H.P.H.P. H.P.H.P.
L.P.L.P.
(FP)(RP)
AccelerateAccelerate DecelerateDecelerate
-- DDAlambertAlambertss ParadoxParadox
Pressure distribution on a circular cylinder inPressure distribution on a circular cylinder inthe ideal nonthe ideal non--viscous flowviscous flow
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Flow separation from body surfaceFlow separation from body surface(Viscous Flow)(Viscous Flow)
SP
FP
Pressure distribution on a circular cylinder inPressure distribution on a circular cylinder inactual viscous flowactual viscous flow
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Superimposition of a rotational flow around aSuperimposition of a rotational flow around acircular cylinder with a uniform flowcircular cylinder with a uniform flow
UniformUniformFlowFlow
CirculationCirculation
Stream lines around a circular cylinderStream lines around a circular cylinderin a uniform ideal flow superimposed onin a uniform ideal flow superimposed on
a clockwise circulationa clockwise circulation
FlowFlowVelocityVelocity Lift Force:Lift Force:UU
L.P.L.P.
KuttaKutta--JoukowskiJoukowskiss TheoremTheorem
H.P.H.P.
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-- Starting vortexStarting vortex
A vortex generated when an airfoil starts toA vortex generated when an airfoil starts tomove in a stationar flowmove in a stationary flow
Just after startingJust after starting
LiftLift
= 0
= 0
= 0 = = +
+
Starting vortexStarting vortex
((KuttaKuttass Condition,Condition,JoukowskiJoukowskissHypothesisHypothesis ))
A starting vortex and a remainingA starting vortex and a remainingcirculation around an airfoilcirculation around an airfoil
((KelvinKelvins Times Time--Invariant CirculationInvariant CirculationTheoremTheorem ))
Release of a vortex stuck to an airfoilRelease of a vortex stuck to an airfoilby sudden stop of motionby sudden stop of motion
Sudden stop of motionSudden stop of motion
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Turbulence after airplaneTurbulence after airplane
2 5m/sec 2 5m/sec
Reynolds NumberReynolds Numberandand
Flow PatternsFlow Patterns
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Variation of flow pattern around a circularVariation of flow pattern around a circularcylinder due to Reynolds numbercylinder due to Reynolds number
ReRe < 5< 555101033
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--dd : Diameter of particles: Diameter of particles
attached to the surfaceattached to the surface--DD : Diameter of a circular: Diameter of a circular
cylindercylinder
Variation of drag coefficient of a circularVariation of drag coefficient of a circularcylinder due to Reynolds numbercylinder due to Reynolds number
OkajimaOkajima
D
ragCoefficient
D
ragCoefficientCCDD
Reynolds Number :Reynolds Number :ReRe members buildingsmembers buildings
RRcrcr : Critical Reynolds: Critical ReynoldsNumberNumber
RRcrcr1010 101022 101033 101044 101055 101066 101077
Variation of mean drag coefficient of aVariation of mean drag coefficient of acircular cylinder with turbulencecircular cylinder with turbulence
intensity and Reynolds number (2D)intensity and Reynolds number (2D)
Reynolds NumberReynolds NumberReRe
DragCoe
fficient
DragCoe
fficientCCDD
TurbulenceTurbulenceIntensityIntensity
SmoothSmoothFlowFlow
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3.2.153.2.15
Variation of the critical ReynoldsVariation of the critical Reynoldsnumbers of a sphere and a circularnumbers of a sphere and a circular
cylinder with turbulence indexcylinder with turbulence indexIIuu((D/LD/L ))
1/51/5(Bearman, 1968)(Bearman, 1968)
Critical Reynolds NumberCritical Reynolds Number
RR
crcr
CircularCircularCylinderCylinder
Sphere (Dryden etSphere (Dryden etal.)al.)
TurbulenceIndex
TurbulenceIndexIIu
u((D/LD/L
yy))1/51/5
Field data of mean drag coefficients ofField data of mean drag coefficients ofactual circular structures (chimneys etc.)actual circular structures (chimneys etc.)
Reynolds NumberReynolds NumberReRe
DragCoe
fficient
DragCoe
fficientCCDD
101066 101077 101088
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Vortices Shed From BluffVortices Shed From BluffBodiesBodies
Karman vortices shed fromKarman vortices shed froma square prisma square prism
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Karman vortex streetsKarman vortex streets
wwvv//ppvv = 0.281= 0.281
Periodic lateral force due to alternatePeriodic lateral force due to alternatevortex sheddingvortex shedding
FFLL
FFLL
KuttaKutta--JoukowskiJoukowskiss TheoremTheorem
FFLL == UU
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Vortex shedding and Strouhal NumberVortex shedding and Strouhal Number
UU ffvvBBffvv == SS ,, SS == BB UU
--ffvv : Shedding frequency of Karman vortices: Shedding frequency of Karman vortices-- SS : Strouhal number: Strouhal number-- UU : Wind Speed: Wind Speed--BB : Reference Length: Reference Length
UU BB
CFD by K. Shimada
Variation of Strouhal numberVariation of Strouhal numberwith Reynolds numberwith Reynolds number
(Circular cylinder, 2D, Uniform flow,(Circular cylinder, 2D, Uniform flow, SheweShewe 19831983))
Reynolds NumberReynolds NumberReRe
Strouha
lNumber
Strouha
lNumberSS
101055 101066 101077
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(a) front side (b) rear side(a) front side (b) rear sideFlow around a buildingFlow around a building
(a) Small(a) SmallH/BH/B (Aspect Ratio)(Aspect Ratio) (b) Large(b) LargeH/BH/BVortex formation behind building modelsVortex formation behind building models
(T.Tamura)
BBBB
HHHH
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Static Wind ForcesStatic Wind Forces
Velocity PressureVelocity Pressureandand
Wind Pressure CoefficientWind Pressure Coefficient
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Wind speed at reference pointind speed at reference pointfar away form body and stagnation pointar away form body and stagnation point
SPSPUU00 = 0,= 0,PP00
UURRPPRR
Wind Pressure at Stagnation PointWind Pressure at Stagnation Point
pp00 ==PP00PPRR = (1/2)= (1/2) UURR22Velocit Pressure (D namicVelocity Pressure (Dynamic
Wind Pressure CoefficientWind Pressure Coefficient
ppkkCCpkpk == 11UURR2222ppkk ==PPkk PPRR
ppkk :: Wind pressure at pointWind pressure at pointkkPPkk :: Static pressure at pointStatic pressure at pointkkPPRR :: Reference static pressureReference static pressure :: Air densityAir densityUURR :: Reference wind speedReference wind speed
Velocity Pressure :Velocity Pressure : qqRR
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Stagnation point of a 3D buildingStagnation point of a 3D building
Internal Pressure CoefficientInternal Pressure Coefficient
andand
External Pressure CoefficientExternal Pressure Coefficient
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0.50.5
CCpepe = + 0.8= + 0.8 CCpipi == 0.340.34 0.40.4Internal SpaceInternal Space
0.50.5External pressure coefficientExternal pressure coefficient CCpepe and internaland internal
pressure coefficientpressure coefficient CC ii
Equilibrium Equation of FlowsEquilibrium Equation of FlowsThrough Gaps:Through Gaps:-- The flow is proportional to the velocityThe flow is proportional to the velocity
at each gap.at each gap.
-- The velocity is assumed to beThe velocity is assumed to beproportional to the square root of theproportional to the square root of thepressure difference between the gap.pressure difference between the gap.0.80.8 CCpipi
= 2= 2CCpipi + 0.5+ 0.5 ++ CCpipi + 0.4+ 0.4CCpipi == 0.340.34
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Temporal variations of mean internal pressuresTemporal variations of mean internal pressuresFull(Full--scale Kato et al. 1996scale, Kato et al., 1996)
GroundGround7th story7th story
13th13th18th18th24th24th
M
eanInternalPressure(
M
eanInternalPressure(hPahPa))
GroundGround7th7th
13th13th
18th18th
24th24th
Variation of mean internal pressures with referenceVariation of mean internal pressures with referencevelocity pressure (Fullvelocity pressure (Full--scale, Kato et al., 1996)scale, Kato et al., 1996)
24th story24th story
18th18th
1313thth
(Office)(Office)
13th13th
7th7th
DifferenceFromReferencePressure(
DifferenceFromReferencePressure(mmAq
mmAq))
Mean Velocity Pressure at TopMean Velocity Pressure at Top
(after altitude compensation)(after altitude compensation)
InternalInternalPressure CoefficientPressure Coefficient
CCpipi = p= pii // qqRRpp
ii
:: qqRR
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Wind Force CoefficientWind Force Coefficient
3.2.3
Wind pressure and wind forcesWind pressure and wind forcesdefined for axes fixed to bodydefined for axes fixed to body
Projected
Width:B
(Body Length:
h)
pp
FFXX
FFYY
UU
xx
yy
MMZZ
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Wind ForcesWind Forces
FFXX == SSpp coscoshhdsdsFFYY == SSpp sinsinhhdsdshh : Body length: Body length
Wind Force CoefficientsWind Force Coefficients
FFXX FFYYCCFXFX == ,, CCFYFY == 11 11 UURR22AA UURR22AA22 22
AA : Projected area =: Projected area =BhBh
Aerodynamic Moment CoefficientsAerodynamic Moment Coefficients
MMZZCCMZMZ == 11 UURR22ALAL22MMZZ : Aerodynamic Moment: Aerodynamic MomentAA : Projected area: Projected areaLL : Reference Length: Reference Length
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AlongAlong--wind force and acrosswind force and across--wind forcewind forcedefined for the axes fixed to winddefined for the axes fixed to wind
AlongAlong--wind Force:wind Force:FFDD
AcrossAcross--wind Force:wind Force:FFLL
(Drag)(Drag)
(Lift)(Lift)
Wind pressure coefficient and wind forceWind pressure coefficient and wind forcecoefficient for a buildingcoefficient for a building
with an internal spacewith an internal space
AlongAlong--wind Force Coefficientwind Force Coefficient
CCFF == CCpe,Wpe,W CCpe,Lpe,LCCpe,Wpe,WCCpe,Lpe,L
CCpe,Spe,S
CCpe,Spe,S
CCpipi
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Static Wind ForcesStatic Wind Forces
Acting On Bluff BodiesActing On Bluff Bodies
Variations of mean drag and lift coefficientsVariations of mean drag and lift coefficientswith attacking anglewith attacking angle (2D)(2D)
Turbulent FlowTurbulent Flow
TurbulentTurbulentFlowFlow SmoothSmooth
FlowFlow
SmoothSmoothFlowFlow
DragCoefficient
DragCoefficientCCDD
LiftCoefficient
LiftCoefficientCCLL
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Effects of turbulence on mean dragEffects of turbulence on mean dragcoefficients of 2D prismscoefficients of 2D prisms
Turbulence IntensityTurbulence IntensityIIuu(%)(%)
DragCoefficient
DragCoefficientCCDD
Entrainment effects of turbulenceEntrainment effects of turbulence
(a)(a)Flat plate (Flat plate (D/BD/B = 0.1) (b) Prism (= 0.1) (b) Prism (D/BD/B = 0.5)= 0.5)
Effects of turbulence on separated shearEffects of turbulence on separated shearlayerslayers (Laneville et al., 1975)(Laneville et al., 1975)
Large DragLarge Drag
Small DragSmall Drag
Large DragLarge Drag
SmallSmall
DragDrag
Smooth FlowSmooth FlowTurbulent FlowTurbulent Flow
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Variation of mean drag coefficient, backVariation of mean drag coefficient, back--pressure coefficient, and wake stagnationpressure coefficient, and wake stagnationpoint with side ratio (2D, Uniform flow)point with side ratio (2D, Uniform flow)
D/BD/B
DragCoefficient
DragCoefficient
CCDD
Back
Back--pressurecoefficient
pressurecoefficientCC
pbpb
Wakestagnationpoint
Wakestagnationpoint
XXwsws
0.620.62
Back pressureBack pressureCCpbpb
Variation of mean drag coefficients of 3DVariation of mean drag coefficients of 3Drectangular prisms with aspect ratiorectangular prisms with aspect ratio
H/BH/B
D/BD/B : Side Ratio: Side RatioH/BH/B : Aspect Ratio: Aspect RatioTurbulentTurbulent
UniformUniform
Dr
ag
C oef
ficie
nt
Dra
gC
oef
fic
ien
tCC
DD
HH
BB
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Mean pressure distributionMean pressure distributionon a lowon a low--rise building modelrise building model
Shimizu Corp.
Instantaneous pressure distributionInstantaneous pressure distributionon a lowon a low--rise building model (45rise building model (45 Wind)Wind)
Shimizu Corp.
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Instantaneous pressure distributionInstantaneous pressure distributionon a lowon a low--rise building model (45rise building model (45 Wind)Wind)
Shimizu Corp.
Mean pressure distributionsMean pressure distributionson a lowon a low--rise building model (45rise building model (45 Wind)Wind)
Conical VorticesConical Vortices
Shimizu Cor
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(a) 0(a) 0 WindWind (b) 45(b) 45 WindWindMean pressure distributionsMean pressure distributionson a lowon a low--rise building modelrise building model
--0.50.5
-- 0.50.5
-- 0.50.5
-- 0.50.5
--0.60.6
--0.60.6
-- 0.60.6
-- 0.60.6-- 0.60.6
-- 0.60.6
-- 0.40.4
-- 0.40.4 -- 0.40.4
-- 0.70.7
-- 0.70.7-- 0.80.8
-- 0.80.8
-- 0.30.3
-- 0.10.1
-- 0.10.1
-- 0.90.9
-- 0.90.9
-- 1.01.0
-- 1.01.0
-- 1.41.4
-- 1.41.4
0.10.1
0.10.1 0.20.2
0.20.2
0.40.4
0.40.4
-- 0.40.4
-- 0.30.3
-- 0.30.3
-- 0.30.3
-- 0.40.4-- 0.40.4
-- 0.40.4-- 0.50.5
-- 0.50.5-- 0.50.5-- 0.80.8
-- 0.80.8 -- 0.80.8-- 1.11.1-- 1.31.3 -- 1.21.2
0.40.40.30.3 0.30.30.20.2
-- 0.30.3
Conical vortices generatedConical vortices generatedfrom corner eavesfrom corner eaves
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Instantaneous pressure distributionInstantaneous pressure distributionon a highon a high--rise building modelrise building model
Shimizu Corp.
(a) 0(a) 0 WindWind (b) Glancing(b) Glancing WindWindMean pressure distributionsMean pressure distributionson a highon a high--rise building modelrise building model
0.80.8
0.70.7
0.60.6
0.50.5
0.40.4 0.40.4
-- 0.70.7
-- 0.60.6
-- 0.60.6 -- 0.60.6
-- 0.50.5
-- 0.80.8
-- 0.80.8
-- 0.60.6
-- 0.80.8
-- 0.80.8-- 0.60.6
-- 0.50.5
-- 1.21.2-- 0.30.3
-- 0.70.7
-- 1.01.0
-- 0.90.9
-- 0.40.4
-- 0.50.5
-- 0.80.8-- 0.90.9
-- 0.70.7-- 0.80.8
0.80.8
0.70.7
0.60.6
0.50.5
0.30.30.40.4
-- 0.70.7
-- 0.60.6
-- 0.60.6
-- 0.50.5
-- 0.70.7-- 0.90.9-- 0.80.8 -- 0.80.8
-- 0.50.5
-- 0.50.5
1515
1515
00
00
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Surface flow pattern near the tip ofSurface flow pattern near the tip of3D circular cylinder3D circular cylinder (Oil film technique, view(Oil film technique, view
obli uel from behind,obliquely from behind, Lawson, 1980Lawson, 1980))
SP 180SP 180
(a) Post(a) Post--supercritical Regime (b) Subsupercritical Regime (b) Sub--critical Regimecritical Regime
ReRe = 2.7= 2.75.45.4101066 ReRe =1.33=1.33101044Vertical distributions of local mean dragVertical distributions of local mean drag
coefficients of 3D circular cylinderscoefficients of 3D circular cylinders
Drag CoefficientDrag Coefficient CCDDDrag CoefficientDrag Coefficient CCDD
DD
HH
zz
Distance
fromtip
Distance
fromtipz/Dz/D
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3 2 182 18
Mean pressure distributionMean pressure distributionon a circular cylinderon a circular cylinder ((SachSach, 1972), 1972)
Potential FlowPotential Flow
SubSub--criticalcritical
SupercriticalSupercritical
MeanPressureCoefficient
MeanPressureCoefficientCC
pp
Mean press re distrib tions on a f llMean pressure distributions on a full
PressurePressuretaptap
PressurePressuretaptap
1mm1mm barbar
2mm2mm barbar
SurfaceSurfaceRoughnessRoughness
WindWindSpeedSpeed
FullFull--scalescale 121240 m/s40 m/s
MeanPressureCoefficient
MeanPressureCoefficientCC
pp
SmoothSmooth 10 m/s10 m/s
1mm1mm 5 m/s5 m/s1mm1mm 10 m/s10 m/s2mm2mm 10 m/s10 m/s