○H. NAKAYAMA

T. TAMURA (Tokyo Institute of Technology, JAPAN)

LES ANALYSIS ON FLUCTUATING DISPERSION

IN ACTUAL URBAN CANOPY

Robins et al., 1977a,bOgawa et al., 1983Li et al., 1983Oikawa et al., 1998

In the case of accidental release of toxic and flammable gas from industrial facilities, it is necessary to estimate not only mean but also fluctuating concentrations around buildings.

The characteristics of fluctuating concentrations around a building model have been investigated by wind tunnel experiments.

BACKGROUND and MOTIVATIONS

Plume dispersion in the wake of a building model

･ The structure of concentration 　　　　 fluctuation field in the wake of a 　　　　 building model･ The relationship between peak and 　　 　 mean concentrations･ Prediction of peak concentration based 　 on probability density functions

On the other hand, as a potential problem, it can be assumed that the accidental spillage for the transportation and storage of hazard materials or poison gas dispersion by terrorist occur even in urban area. Therefore, flow and plume dispersion in regular arrays of cubes as urban model have been studied by wind tunnel and field experiments.

Plume dispersion in the typical urban model

･ The lateral concentrations profiles of a plume emitted from the point source located at the half height of building model are Gaussian.･ In a gap between two cubes instantaneous high concentrations frequently occur and downwind of a cube fluctuations of concentration become continuous and smooth.

Macdonald,1997Mavroidis,2001

However, taking into consideration aspects of actual urban canopy, the height and width of buildings, their arrangement, the spacings between them and the width of the streets change variously.

Therefore, aspects of actual urban roughness are so complicated that characteristics of plume dispersion in surface layer are very different from those of plume dispersion in typical urban model arrayed regularly.

OBJECTIVES

･ Investigate the characteristics of flow and plume dispersion in actual urban canopy ･ Estimate peak concentrations based on various kinds of roughness elements for safety analysis

We carry out Large-Eddy Simulation for plume dispersion in Actual Urban Area.

We have focused on …

A normal plate ： height,H side length,2HPoint source ： height,H 2H upstream of a plate

Model of dispersion field around a normal plate in turbulent boundary layer

z

y

x

turbulent boundary l ayer

point source

Ue

H2H

o2H

H

Numerical 　 validation

･ Compare LES results with　 experimental data

A free-stream velocity

tracer gas

C2H4

turbulence grid

roughness elementswith L-shaped cross sections

fast-response flame ionization detector

plume

turbulent boundary layer

point source

Ue (=2m/s)

Air

normal plate

Experimental model for plume dispersion around a normal plate

Schematic of wind tunnel experimental arrangement

(at Central Research Institute of Electric Power Industry)

(a)Generation of inflow turbulence (b)Normal plate in turbulent boundary layer (a)DRIVER UNIT for Spatially-Developing Boundary Layer (Size: 26.7H×20H×6.7H Grid points:200×240×100)

3 bars of type A (0.4H×20H×0.5H)1 bar of type B (0.4H×20H×0.7H)40 cubes of type C (0.4H×0.4H×0.4H)

(b)MAIN COMPUTATIONAL UNIT for Plume Dispersion over A Normal Plate (Size: 30H×20H×6.7H Grid points:360×240×100)

A normal plate: height: H, side length: 2H Blockage: less than 5%

Numerical model for plume dispersion around a normal plate

To develop a thick boundary layer

To induce sufficient velocity fluctuation

At the entrance; uniform inflow is imposed

At the entrance; inflow turbulence obtained at the exit in driver unit is imposed

6.7H

20H 26.7H14.7H

H2H

6.7H

20H10H

20H

inflow turbulenceuniform inflow

Coupling algorithm: MAC method Time integration: Adams-Bashforth scheme Time step: Δ ｔ =0.001 The Re number: 5000 (=UeH/ν)　　　　　　 Flow field: 　　 Spatial discretization: a fourth-order accurate central difference

Concentration field: Spatial discretization: Convection term; CIP scheme Diffusion term; A fourth-order accurate central difference

Numerical discretization and algorithm

Governing equations and LES model

0

i

i

x

u

ijijjij

jii Sxx

p

x

uu

t

u

21

jjj

j hxx

uc

t

c

continuity equation ：

Navier-Stokes ：

scalar conservation ：

The incompressible Navier-Stokes, scalar conservation and continuity equations are presented by the following grid-filtered form:

In this study, we employ model constants in flow and scalar fields, Cd, Cc, respectively, by Dynamic procedure. The incompressible Navier-Stokes and scalar conservation equations are presented by the following test-filtered form:

model constant in flow field, Cd ：

model constant in scalar field, Cc ：

)~~~

(2 22ijijdij SSSSCL

～

)~~~

( 22

jjcj x

cS

x

cSCP

～

ijijjij

jii STxx

p

x

uu

t

u ~2

~1

~~~

jjj

j Hxx

uc

t

c

~~~

Navier-Stokes ：

scalar conservation ：

ijij

ijijd MM

MLC

jj

jjc QQ

QPC

)~~~

(2 22ijijij SSSSM

jjj x

cS

x

cSQ

22~~~

Vertical profiles of mean velocity and turbulence intensity at the position of point source

Point source(z/δ=0.27)

Characteristics of inflow turbulence and dispersion plume(Results obtained by wind tunnel experiment and LES)

Turbulence intensity obtained by LES is smaller in the upper part than that obtained by wind tunnel experiment

δ: thick of turbulent boundary layer

Power spectrum of velocity fluctuation at the position of point source

Vertical spreading rates of a plume(Pasquill-Gifford chart)

Characteristics of inflow turbulence and dispersion plume(Results obtained by wind tunnel experiment and LES)

Both of vertical spreading rates obtained by LES and wind tunnel experiment correspond to values between stability conditions C and D.

Power spectra obtained by LES are a little smaller than the Karman type in lower and higher frequency sides

The case without a normal plate

The case with a normal plateConcentration field

Vorticity

Point source

Point source

The animation of plume dispersion in the case with and without a normal plate

Mean concentration

Numerical validation for concentration fields in the case without a normal plate

R.m.s concentration

Mean concentration

R.m.s concentration

Numerical validation for concentration fields in the case with a normal plate

In the case without a normal plate In the case with a normal plate

Numerical validation for time series of concentration fluctuation at the position, x/H=6

Wind tunnel experiment

Wind tunnel experiment

LES LES

Numerical validation for concentration fields around a normal plate

Application to plume dispersion in actual urban area

Numerical model for plume dispersion in actual urban areas

Kasumigaseki area(Government office quarter)

Kanda area(Commercial area)

In this study, we carry out LES for Kasumigaseki and Kanda areas of Tokyo as actual urban areas.

Aspect of surface roughness・ Large groups of massive buildings ･ Green area with few trees

　 Aspect of surface roughness･ Large groups of high-rise buildings･ Street canyon embedded into a dense built-up area ･ Green area with few trees

1 km1 km

Profiles of roughness height and density

Kasumigaseki KandaRoughness density,λ: 0.2794 0.4490

p:probability density function of roughness heightδ:thickness of turbulence boundary layer(=500m)λ:roughness density defined as the ratio of the total frontal area of the obstacles to the lot area of the obstacles

Kasumigaseki area

Kanda area

Profile of p.d.f of roughness height

Profile of roughness density

d

f

A

A Af: the total frontal area of the obstacles

Af: the total area covered by the obstacles

Two sites in Tokyo

Kasumigaseki KandaRoughness density,λ : 0.2794 0.4490Normalized roughness length,Zo/h : 0.060 0.026 　　　　

Zo:Roughness length h:Roughness height

Profiles of roughness density and length

Kasumigaseki area

Kanda area

(obtained by using Raupach’s curve)

Kasumigaseki area

Kanda area

NNW wind

0

10N

NNENE

ENE

E

ESE

SESSE

SSSW

SW

WSW

W

WNW

NWNNW

above 0.3m/sabove 0.5m/s

In central area of Tokyo, the frequency of the NNW wind is dominant.Therefore, we report the results for NNW wind direction.

The profiles of wind direction in Tokyo

NNW wind

Kanda areaKasumigaseki area

(a)Generation of inflow turbulence

(a)DRIVER UNIT for Spatially-Developing Boundary LayerSize: 5H×1.25H×H Grid points:250×250×100

3 bars of type A (0.075H×1.25H×H)1 bar of type B (0.1H×1.25H×H)

15 cubes of type C (0.06H×0.06H×0.06H)

30 cubes of type D (0.05H×0.05H×0.05H)

(b) MAIN COMPUTATIONAL UNIT for Urban Dispersion(Size: 1.25H×1.25H×H Grid points:250×250×100)

To develop a thick boundary layer

To induce sufficient velocity fluctuation 5H

H

1.25HTo simulate urban boundary layer

Computational model for urban dispersion

1.25H

1.25H

H

Kasumigaseki area Kanda area

0.01 0.1 1

U/U∞

0.001

0.01

0.1

1

z/δ

1/4 power lawLES

∞

z/δ

0.01 0.1 1

U/U∞

0.001

0.01

0.1

1

z/δ

1/4 power lawLES

∞

z/δ

∞

ｚ/δ

0 0.1 0.2

uirms/U∞

0

1

2z/δ

urms(LES)vrmswrms

∞

ｚ/δ

0 0.1 0.2

uirms/U∞

0

1

2z/δ

urms(LES)vrmswrms

0.001 0.01 0.1 1 100.001

0.01

0.1

1

Karman typez/δ=0.20z/δ=0.50z/δ=0.90z/δ =0.9z/δ =0.5z/δ =0.2

fLux/UfE

(f)/

u’2

0.001 0.01 0.1 1 100.001

0.01

0.1

1

Karman typez/δ=0.20z/δ=0.50z/δ=0.90z/δ =0.9z/δ =0.5z/δ =0.2

fLux/UfE

(f)/

u’2

Vertical profile of mean velocity

Power spectrum of velocity fluctuation

Vertical profile of turbulence intensity

Characteristics of inflow turbulence in driver unit

Uniform inflow Inflow turbulence

Kasumigaseki area Kanda areaAverage building height : 10.46m 14.69mRoughness height,h : 10.46m 14.69mThe zero-place displacement,d : 9.92m 11.75mRoughness length,Zo : 1.255m 0.76m(obtained by Raupach’s curve)The exponent in the power law,α : 0.22 0.20 　　　　

Log-log profiles of mean velocity in urban areas

A B C D E A B C D E

21010 )(log016.0)(log096.024.0 oo zz (obtained by using Counihan’s equation)

Kasumigaseki Kanda

Flow field near the ground surface in Kasumigaseki

UU 6.01.0 ～The range of velocity

Red: strong windYellow:weak windBlue:revised flow

Air flow

UU 6.01.0 ～The range of velocity

Red: strong windYellow:weak windBlue:revised flow

Flow field near the ground surface in Kanda

Air flow

Dispersion field near the ground surface in Kasumigaseki

Point source

The range of concentration

initialinitial CeCe 25 0.10.1 ～

Air flow The position of point source: above the main street

Point source

The range of concentration

initialinitial CeCe 25 0.10.1 ～

Dispersion field near the ground surface in Kanda

Air flow

Flow and Dispersion fields near the ground surface in Kasumigaseki area

Flow and Dispersion fields near the ground surface in Kanda area

Mean concentration field R.m.s. concentration field

Dispersion fields near the ground surface in Kasumigaseki area

Maximum concentration field

Point source Point source Point source

The range of concentrationinitialinitial CeCe 25 0.10.1 ～

Large groups of massive buildings

Green area with few trees

Dispersion fields near the ground surface in Kanda area

Mean concentration field R.m.s. concentration field Maximum concentration field

Point source Point source Point source

The range of concentrationinitialinitial CeCe 25 0.10.1 ～

Large groups of high-rise buildings

Dense built-up area

Point source

②

Time series of concentration fluctuation in Kasumigaseki area

Kasumigaseki area

① ②

①

inside the wake outside the wake

①

Kanda area

Point source

①

②

in street canyon

inside the wake

②

Time series of concentration fluctuation in Kanda area

Conclusions

1. The value of roughness height is set to be same as that of average building height and the value of the zero-place displacement is set to be 80% of roughness height, we estimate roughness length obtained by Raupach’s curve. As the results, profiles of the computed mean velocity are almost corresponding to those of the power law obtained by Counihan’s equation except near the ground surface.

2. In sparse array of massive buildings, the effect of plume entrainment by each buildings wake is so large that the spatial distributions of mean and r.m.s fields are distorted and a core with large values of mean and r.m.s concentrations is located also in the buildings wake.

We show numerical validation for the results of dispersion field around a normal plate compared with the results obtained by wind tunnel experiment and carry out LES for flow and plume dispersion in actual urban areas.

2. On the other hand, in dense built-up area, the effect of plume entrainment by each buildings wake is small but the effect of the existence of street canyon is so large that plume is transported easily downstream above main street. Therefore, a core with large values of mean and r.m.s concentrations is located in street canyon.

3. The concentration fluctuates smoothly and continuously inside the buildings wake by active turbulence mixing between air flow and a plume. However, instantaneous high concentrations frequently occur in street canyon.

(a)a shot for upward extension 　　 of the separated shear layer

(b)a shot for a roll-up 　　 of the separated shear layer

Instantaneous contours for vorticity and concentration

a plume core moves up due to upward extension of the separated shear layer

a plume core is entrained into wake region due to a roll-up of the separated shear layer

(c)Vertical concentration flux

Strong negative concentration flux due to a roll-up of the separated shear layer

Kasumigaseki area Kanda area

Dispersion fields at the height of urban canopy