flow patterns and wind forces

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


2/572

Flow Patterns AroundFlow Patterns AroundBluff BodiesBluff Bodies

Stream LinesStream Lines


3/573

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)


4/574

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


5/575

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)


6/576

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


7/577

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


8/578

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


9/579

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


10/5710

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


11/5711

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


12/5712

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


13/5713

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)


14/5714

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


15/5715

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


16/5716

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


17/5717

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


18/5718

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

}


19/5719

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


20/5720

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


21/5721

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


22/5722

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


23/5723

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)


24/5724

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


25/5725

Surface Boundary LayerSurface Boundary Layer

Flow near surface of bodyFlow near surface of body

WallSurf

ace

Flowv

elocity

Boun

darylayer


H.P.H.P. H.P.H.P.

L.P.L.P.

(FP)

(RP)



26/5726

-- 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


27/5727

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


28/5728

- 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


29/5729


H.P.H.P. H.P.H.P.

L.P.L.P.

(FP)(RP)


-- DDAlambertAlambertss ParadoxParadox

Pressure distribution on a circular cylinder inPressure distribution on a circular cylinder inthe ideal nonthe ideal non--viscous flowviscous flow


30/5730

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


31/5731

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.


32/5732

-- 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


33/5733

Turbulence after airplaneTurbulence after airplane

2 5m/sec 2 5m/sec

Reynolds NumberReynolds Numberandand

Flow PatternsFlow Patterns


34/5734

Variation of flow pattern around a circularVariation of flow pattern around a circularcylinder due to Reynolds numbercylinder due to Reynolds number

ReRe < 5< 555101033


35/5735

--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


36/5736

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.)


DragCoe

fficient

DragCoe

fficientCCDD

101066 101077 101088


37/5737

Vortices Shed From BluffVortices Shed From BluffBodiesBodies

Karman vortices shed fromKarman vortices shed froma square prisma square prism


38/5738

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


39/5739

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))


Strouha

lNumber

Strouha

lNumberSS

101055 101066 101077


40/5740

(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


41/5741

Static Wind ForcesStatic Wind Forces

Velocity PressureVelocity Pressureandand

Wind Pressure CoefficientWind Pressure Coefficient


42/5742

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


43/5743

Stagnation point of a 3D buildingStagnation point of a 3D building

Internal Pressure CoefficientInternal Pressure Coefficient

andand

External Pressure CoefficientExternal Pressure Coefficient


44/5744

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


45/5745

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


46/5746

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


47/5747

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


48/5748

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


49/5749

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


50/5750

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


51/5751

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


52/5752

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.


53/5753

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


54/5754

(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


55/5755

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


56/5756

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


57/57

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

flow patterns and wind forces

Documents