Experimentalandnumericalstudiesofflowsthroughandwithinhigh-rise

Experimental and numerical studies offlows through and within high-rise building arrays and their link to ventilation strategy
Jian Hang a,b,Yuguo Li a,n,Mats Sandberg c
a Department of Mechanical Engineering,The University of Hong Kong,Haking Wong Building,Pokfulam Road,Hong Kong SAR,China
b Guangdong Provincial Key Laboratory of Building Energy Efficiency and Application Technologies,Guangzhou University,Guangzhou,China
c KTH Research School,Laboratory of Ventilation an
d Air Quality,University of G¨a vle,80176G¨a vle,Sweden
a r t i c l e i n f o
Article history:
Received15October2010
Received in revised form
30June2011
Accepted1July2011
Available online20July2011
Keywords:
Wind tunnel
Numerical simulation
High-rise building array
Turbulence
Velocity
Urban canopy
a b s t r a c t
Urban ventilation implies that wind from rural areas may supply relatively clean air into urban
canopies and distribute rural air within them to help air exchange and pollutant dilution.This paper
experimentally and numerically studied suchflows through high-rise square building arrays as the
approaching rural wind is parallel to the main streets.The street aspect ratio(building height/street
width,H/W)is from2to5.3and the building area(or packing)density(l p)is0.25or0.4.Wind speed is
found to decrease quickly through high-rise building arrays.For neighbourhood-scale building arrays
(1–2km at full scale),the velocity may stop decreasing near leeward street entries due to vertical
downward mixing induced by the wake.Strong shear layer exists near canopy roof levels producing
three-dimensional(3D)vortexes in the secondary streets and considerable air exchanges across the
boundaries with their surroundings.Building height variations may destroy or deviate3D canyon
vortexes and induced downward meanflow in front of taller buildings and upwardflow behind taller
buildings.With a power-law approaching wind profile,taller building arrays capture more rural air and
experience a stronger wind within the urban canopy if the total street length is effectively limited.
Wider streets(or smaller l p),and suitable arrangements of building height variations may be good
choices to improve the ventilation in high-rise urban areas.
Crown Copyright&2011Published by Elsevier Ltd.All rights reserved.
1.Introduction
In high-rise compact urban areas like Hong Kong and Manhattan
in New York,urban airflow is generally weak because high-rise
building arrays produce strong resistances to the approaching wind,
as a result,gaseous pollutants released by vehicle emissions(Fenger,
1999)may stay for a long time within street networks producing
traffic air pollution and associated health effects in urban air
environments.Wind from the surrounding rural areas may supply
relatively clean air into urban canopies and remove airborne
pollutants out,so it is important to study how to enhance the
capacity of rural windflowing through high-rise urban areas and
how to distribute rural air within such urban canopies more
effectively,i.e.improving air exchanges between urban areas and
their surrounding rural areas.
Numerical simulations using large-eddy simulation(LES)or RANS
(Reynolds-averaged Navier–Stokes equation)turbulence models,
wind tunnel andfield measurements are important methods to
study theflow and dispersion in urban areas.In two-dimensional
(2D)street canyon models,street aspect ratios(street height/street
width,H/W),roof shapes,etc.are important parameters for pollutant
removal and air exchange through the canyon roofs.Oke(1988)and
Sini et al.(1996)reported threeflow regimes depending on different
aspect ratios(street height/street width,H/W),i.e.the isolated
roughnessflow regime(IRF,in which the aspect ratio is less than
0.1–0.125),the wake interferenceflow regime(WIF,with an aspect
ratio of0.1–0.67),and the skimmingflow regime(SF,with an aspect
ratio of0.67–1.67).Meroney et al.(1996)performed experimental
studies of pollutant dispersion in2D street canyons with these three
flow regimes.Xie et al.(2006)and Li et al.(2009)found the fourth
flow regime of the multi-vortex regime,i.e.there are two or more
vortexes in2D deep street canyons with aspect ratios of more than
1.67.For such2D deep canyons,wind near the street ground is weak,
and airborne pollutants produced by vehicle emissions are difficult to
be removed out through canyon roofs.General urban canopies are
three-dimensional(3D)structures.Street aspect ratios,building
arrangements,total street length,building area densities(l p,i.e.
the ratio between the plan area of buildings viewed from above(A p)
and the total underlying surface area(A d)),frontal area densities(l f,
i.e.the ratio between the frontal area of buildings facing the wind(A f)
and the total underlying surface area(A d))and street orientations(or
ambient wind directions),etc.are important urban parameters.
Studies so far on3D urban canopies mainly focused on the
flow and pollutant dispersion around an isolated building(Li and
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journal homepage:/locate/jweia
Journal of Wind Engineering
and Industrial Aerodynamics
0167-6105/$-see front matter Crown Copyright&2011Published by Elsevier Ltd.All rights reserved.
doi:10.1016/j.jweia.2011.07.004
n Corresponding author.Tel.:þ852********;fax:þ852********.
E-mail address:liyg@hku.hk(Y.Li).
J.Wind Eng.Ind.Aerodyn.99(2011)1036–1055
Stathopoulos,1997),in rectangular building arrays(Chang and Meroney,2001;Chang and Meroney,2003)and cube or square building arrays with different building area densities(Hanna et al.,2002;Cheng et al.,2003;Lien and Yee,2004;Di Sabatino et al.,2007;Boppana et al.,2010),in random urban-like obstacles (Xie et al.,2008)and in idealised city models with different overall city forms(Hang et al.,2009).Britter and Hanna(2003), Belcher(2005),Ahmad et al.(2005)and Kanda(2006a)provided some reviews of such studies.As described by Roth(2000)and Belcher(2005),for3D urban canopies,wind speed decreases due to the drag force by buildings.Wind interacts with buildings and produces strong shear layer at canopy tops,inducing3D turbulent mixing and converting some fraction of mean kinetic energy into turbulent kinetic energy.Moreover,previous studies mainly emphasised on3D building arrays with aspect ratios(H/W)of less than2and focused on local airflows inside the streets in contrast to those above roof tops.This paper was more interested in3D high-rise building arrays with aspect ratios of not less than 2,and aimed to investigate how to improve the capacity of the upstream rural windflowing through such urban canopies in contrast to the upstream rural wind.
Hanna et al.(2002)numerically studied wind conditions in some sparse cube arrays(street aspect ratio H/W¼2/3,building area density l p¼0.16)finding that allflow characteristics approach stream-wise equilibrium state after typically three rows of obstacles.Lien and Yee(2004)investigated airflows in a seven-row cube array(l p¼0.25,H/W¼1),and reported that the meanflow and the turbulence stop decreasing and reach an approximate stream-wise equilibrium since the fourth row.However Lien and Yee(2005)analysed the drag force produced by seven buildings and the results displayed that the drag coefficients for the fourth,fifth and sixth rows differ from each other.Hang and Li(2010)pointed out that stream-wise equilibrium reported in Lien and Yee(2004)is false and wind speed stops decreasing after the fourth row only because the wake behind the cube array may induce downward flows across street roofs and bring some air into the cube array.A real stream-wise equilibrium in building arrays implies that not only the velocity and turbulence stop decreasing,but also the drag forces produced by buildings stop varying.To verify it,Hang and Li(2010) studied seven-row,fourteen-row and twenty-one-row cube arrays (l p¼0.25,H/W¼1),finding that stream-wise equilibrium does not exist in the seven-row array but does appear in the fourteen-row and twenty-one-row arrays.Such process(i.e.stream-wise equilibrium)for high-rise compact building arrays with aspect ratios (H/W)of not less than2and building area densities(l p)of not less than0.25was rarely studied.
In addition,most previous studies concentrated on turbulent flows and pollutant dispersion in urban-type building arrays with parallel approaching winds.Kim and Baik(2004)performed numer-ical simulations of cube arrays with ambient wind directions of01, 151and451.They reported that the capacity of pollutant removal decreases when the incident wind angle increases.Hang et al. (2009)studied pollutant dispersion in idealised round city models with ambient wind directions of01,151,301and451.They found that small incident wind angles of01and151are better for the pollutant removal and air exchange than large incident angles of301
x
z
y
Fig.1.Model descriptions in wind tunnel tests:(a)Medium arrays with uniform heights in Case[2-2,1-1,6,0.25]or Case[2.67-2.67,1-1,6,0.25],(b)a medium array with a building height variation in Case[2-2.67,1-1,9,0.25],(c)a packed array in Case[2.67-2.67,0.5-0.67,9,0.4].(d)A hotwire in wind tunnel measurements.
(e)Vertical profile of the velocity and turbulence at Point S5and S5A in Case[2.67-2.67,0.5-0.67,9,0.4]in wind tunnel data.Each case name denotes an aligned square array[H1/B-H2/B,W1/B-W2/B,row number,the building area density].
J.Hang et al./J.Wind Eng.Ind.Aerodyn.99(2011)1036–10551037
and 451.Wind tunnel experiments performed by Hagishima et al.(2009)confirmed that rotating the aligned cube array by 451may increase the drag coefficient of buildings by an approximate average of 46%.It seems that,with large incident wind angle,buildings may produce stronger drag force and generate more recirculation regions within the building array,i.e.enhance turbulent mixing and reduce the flow capacity of pollutant dilution by mean flows.So it is better to design the main streets parallel to the local prevailing wind direction.Kanda (2006b)carried out a series of large eddy simulations (LES)and found that staggered arrays tend to produce stronger drag force to the approaching wind than the aligned arrays.Here this paper mainly considered the best situation,i.e.to study the flow character-istics through and within 3D high-rise aligned building arrays with an ambient wind direction of 01.
Chang and Meroney (2003)and Cheng et al.(2003)utilised LES turbulence models and the RANS (Reynolds-averaged Navier–Stokes)k –e models to investigate urban airflows in rectangular building arrays or cube arrays.The LES models are known to simulate turbulence structure more precisely,but require much longer computational time in contrast to the RANS turbulence models.As an elementary study,this paper first used the RANS k Àe turbulence models to simulate urban airflows within high-rise building arrays considering the constraints of the computa-tion power.When the approaching wind is weak or there is no
wind,not only turbulence induced by vehicle motion (Baker and Hargreaves,2001;Solazzo et al.,2008)but also the thermal buoyancy force due to shading and radiation trapping effects by buildings (Smith et al.,2001;Xie et al.,2005;Yang and Li,2009)may significantly affect or dominate urban airflows.This study assumed there is a considerable approaching wind and disre-garded the effects of thermal buoyancy force and vehicle motion.
2.Model Descriptions 2.1.Wind tunnel measurements
This paper experimentally studied wind conditions in some aligned building arrays (see Fig.1)in a closed-circuit boundary layer wind tunnel at Laboratory of Ventilation and Air Quality,the University of G¨avle,Sweden.The working section of this wind tunnel is 11m long,3m wide and 1.5m tall.Square building models (the building width B ¼30mm,the building height H ¼60mm ¼2B or H ¼80mm ¼2.67B )were used,corresponding to square buildings of 30m wide and 60or 80m tall at full scale (i.e.the scale ratio is 1:1000).The main streets were parallel to the approaching wind and the secondary streets were perpendi-cular to it.The rows of buildings from upstream regions to
x y
z
V1
30mm
H =60mm
H =80mm
W 2=30mm W 1=30mm
V2V3V4V5V6V7V8V9
y
B = 0mm
x
Street width W =building width B Building area density is 0.25
O
Point O is (0,0)
Case [2-2.67, 1-1, 9, 0.25] (H =2B or 2.67B )
Fig.1.(continued )
J.Hang et al./J.Wind Eng.Ind.Aerodyn.99(2011)1036–1055
1038
downstream regions are defined as rows no.1,2,3,4,5y N (N is
the final row number);then the secondary streets (canyons)behind building no.i were named as canyon no.i.x ,y ,z are the stream-wise,lateral and vertical directions,respectively.To explain these tests more easily,x /B ¼0is defined as the location of the windward entry.The plane of y /B ¼0is the vertical symmetric plane of the middle main street.Three kinds of square building arrays were studied in wind tunnel experiments:two six-row medium arrays with uniform building heights (11col-umns,6rows,see Fig.1a;the building area density l p ¼(B ÂB/(B þW 1)(B þW 2))¼0.25as street widths W 1/B ¼W 2/B ¼1,the frontal area densities l f ¼(H ÂB/(B þW 1)(B þW 2))¼0.5or 0.67as H ¼2B or H ¼2.67B ),a nine-row medium array with various building heights (12columns,9rows,see Fig.1b;H is 2B for rows no.1,3,5,7and 9,and H is 2.67B for rows no.2,4,6and 8;W ¼B ,l p ¼0.25and l f ¼0.58assuming the average building height is 2.33B ),a nine-row packed array with a uniform height (10columns,9rows,see Fig.1c;l p ¼(B ÂB/(B þW 1)(B þW 2))¼0.4as the main streets W 1/B ¼0.5and the secondary streets W 2/B ¼0.67,l f ¼(H ÂB/(B þW 1)(B þW 2))¼1.07as H ¼2.67B ).All these four building arrays were named as Case [building heights H 1/B -H 2/B ,street widths W 1/B -W 2/B ,the total row number,the building area density l p ].So four test cases are studied using wind tunnel experiments as summarised in Table 1,i.e.Case [2-2,1-1,6,0.25]and Case [2.67-2.67,1-1,6,0.25]for two medium arrays with uniform heights (see Fig.1a),Case [2-2.67,1-1,9,0.25]for a medium array with building height variations (see Fig.1b),and Case [2.67-2.67,0.5-0.67,9,0.4]for a packed array with a uniform height (see Fig.1c).As shown in Table 1,the building area density is 0.25or 0.4and the frontal area density is from 0.5to 1.07.The reference Reynolds number is from 13,760to 19,082.
The velocity and turbulence intensity were measured using hotwire anemometers,including horizontal profiles along the street centreline of the middle main street at the height of z ¼B ,and vertical profiles at many points.As shown in Fig.1a–c,Point V0and S0are points with a distance of 30mm (B )in front of the first building no.1.Point V6in Fig.1a and Point V9in Fig.1b and c are points with a distance of 30mm (B )behind the final building no.N (N ¼6in Fig.1a and N ¼9in Fig.1b and c).For all other points,Point V i represents the centre point inside the secondary streets (canyons)of no.i and point S i denotes the centre point of the crossing or intersection no.i .
For the measurement of velocity and turbulence intensity using hotwire anemometers,the sampling frequency was 100Hz.
W 1=15mm B =30mm
W 2=20mm
V1V2V3V0V5S11234
567
89x y
S0
S2S3S5
S7S8S9V7V8V9
30mm
O Point O is (0,0)
Building area density is 0.4
30mm
S5A
Case [2.67-2.67, 0.5-0.67, 9, 0.4] (H =2.67B , W 1=0.5B , W 2=0.67B )
x y
z
Fig.1.(continued )
J.Hang et al./J.Wind Eng.Ind.Aerodyn.99(2011)1036–10551039
Since this study used the measurement time of 20,40s and 60s at the start finding that the measured data changed little (i.e.the variation is less than the measured error),so the measurement time was selected as 20s (i.e.number of samples is 2000)to shorten the time and fees running wind tunnel.During wind tunnel measure-ments,corrections due to variations in air temperature were accomplished automatically.Calibrations of hotwire anemometers were made using the same cables and measurement equipments,and data were fit to a fourth order polynomial.During wind tunnel experiments hotwires were located above the wind tunnel floor as shown in Fig.1d and during the calibrations hotwires were placed over a small hole outside of the wind tunnel where exactly controlled calibration airflows may blow out upwardly.A test was done to investigate the measurement repetitiveness,i.e.measuring the velocity at the same points twice using the same measurement parameters above,finding that the maximum data variation was less than 70.025m/s,so for points with small velocity (for example less than 0.2m/s),the exactness of wind tunnel data was limited.It should be noted that,the hotwire is only sensitive to velocity components,which are perpendicular to it (i.e.the vertical (z )velocity w and the stream-wise (x )velocity u ,see Fig.1d).So the velocity measured by the hotwire was actually the value of ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u 2þw 2p .In this paper,the hotwires only located where the span-wise (y )velocity v is zero,including at points in the upstream free flow,at the centre points of the secondary streets and along the main street centerlines.Therefore,the measured values of ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu 2þw 2p were equal to the velocity magnitude (U ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu 2þv 2þw 2p ).Similarly for fluctuating velocity components,if the span-wise
fluctuating velocity ffiffiffiffiffiffiffiffi
v 0v 0p is large (for example for points in the
y
(Stream-wise)0
12345678
z / B
0.0
012345678Velocity (m s -1
)
1
2
34
Turbulent kinetic energy (m 2s -2)
0.10.20.30.40.50.6Fig.1.(continued )
Table 1
Summary of high-rise aligned square building arrays (building width B ¼30mm)studied in wind tunnel experiments or CFD simulations.
Street-scale arrays studied by both wind tunnel tests and CFD
H 1/B-H 2/B
W 1/B -W 2/B
Rows
L/B
l p l f
Reference Reynolds number (Re H )[2.67-2.67,1-1,6,0.25]a 2.67-2.671-16110.250.6719082[2-2,1-1,6,0.25]2-21-16110.250.513760[2-2.67,1-1,9,0.25]
2-2.671-1
9170.250.5816317[2.67-2.67,0.5-0.67,9,0.4]
2.67-2.670.5-0.67914.30.4 1.07
19082Neighbourhood-scale arrays studied by CFD simulations only H 1/B-H 2/B W 1/B -W 2/B Rows L/B l p
l f
Re H ¼r U ref H/m [2-2,1-1,18,0.25]
2-2
1-118350.250.513760[2.67-2.67,1-1,18,0.25] 2.67-2.671-118350.250.6719082[2.67-2.67,1-1,28,0.25] 2.67-2.671-128550.250.6719082[2-2.67,1-1,18,0.25]
2-2.671-1
18350.250.5816317[2.67-2.67,0.5-0.67,21,0.4]
2.67-2.67
0.5-0.67
21
34.3
0.4
1.07
19082
a
Each test case is named as Case [H 1/B -H 2/B ,W 1/B -W 2/B ,the total row number,l p ].H 1and H 2represent building heights for rows of an odd and even number respectively.W 1is the street width of the main streets,which are parallel to the approaching wind and W 2is that of the secondary streets.l p and l f are the building area density and frontal area density,respectively.L is the total street length.For reference Reynolds number (Re H ),U ref is the reference velocity at the average building height in far upstream free flow (or at domain inlet).
J.Hang et al./J.Wind Eng.Ind.Aerodyn.99(2011)1036–1055
1040
wake of buildings),it may introduce significant inaccuracy in the measurement of turbulence intensity using a single hotwire.
2.2.Numerical models
The Reynolds-averaged Navier–Stokes(RANS)equations with standard kÀe turbulence model are widely used to model urban turbulentflows.The continuity equation,the momentum conservation equations and two transport equations for the turbulent kinetic energy(k or TKE)and its dissipation rate(e) are solved to get time-averagedflow variables,including density r,static pressure p,the stream-wise,span-wise and vertical velocity components(u,v,w)and turbulent quantities(k,e).The time-averaged governing equations are as follows:
@ðr u iÞ
@x i
¼0ð1Þ
@ðr u i u jÞ
@x j
¼
@
@x j
mþ
m
t
s k
@u
i
@x j
À
@p
@x i
þ
2
3
r@k
@x i
ð2Þ
@ðr u j kÞ
@x j
¼
@
@x j
mþ
m
t
s k
@k
@x j
þG kÀreð3Þ
@ðr u j eÞ
@x j
¼
@
@x j
mþ
m
t
s e
@e
@x j
þc e1
e
k
G kÀr c e2
e2
k
ð4
Þ
25.0B
121.3B
33.3B
z
x
Domain top
Domain inlet
Domain outlet
Urban canopy
N
o
r
m
l
i
z
e
d
v
e
r
t
i
c
a
l
l
o
c
a
t
i
o
n
z
/
B
Velocity (m s-1)
5
10
15
20
25
N
o
r
m
l
i
z
e
d
v
e
r
t
i
c
a
l
l
o
c
a
t
i
o
n
z
/
B
Turbulence intensity
Fig.2.(a)Computational domain in the plane of x–z.(b)Vertical profiles of the velocity(left)and turbulence intensity(right)measured in the upstream freeflow.(c)Gird generation in the planes of x–z and x–y in Case[2.67-2.67,1-1,6,0.25].
J.Hang et al./J.Wind Eng.Ind.Aerodyn.99(2011)1036–10551041
f C e1,C e2,C m,s k,s e g¼f1:44,1:92,0:09,1,1:3gð5Þ
In Eqs.(1)–(4),m t¼r C m k2/e is the turbulent viscosity,m is the viscosity of air,and G k is the turbulent kinetic energy production (¼m tð@u i@x jÞð@u i=@x jþ@u j=@x iÞ),the density r is a constant in iso-thermal urban airflows.
For computationalfluid dynamics(CFD)simulations,a code ‘Ventair’using Fortran language was developed,in which3D urban airflowfield was modelled by the RANS standard k–e turbulence model described above.The transport equations for the momentum and turbulence properties were discretized by finite volume techniques.The hybrid upwind/central differencing scheme was used to discretize the advection terms,with an option of the second-order upwind scheme and the QUICK scheme.The discretized differential equations were solved by the SIMPLE algo-rithm.An under-relaxation factor of0.5for the mean velocities and pressure,and values of less than0.5for the turbulent properties were used to avoid divergence problems.
In CFD simulations,the same model scale as that in wind tunnel measurements was used(i.e.in order of cm).The building arrays in wind tunnel experiments are sufficiently wide in the span-wise(or lateral)direction(y).Fig.1e shows the measured vertical profile of the velocity and turbulence at point S5and S5A in Case[2.67-2.67,0.5-0.67,9,0.4](see Fig.1c).The velocity profile in the middle main street(Point S5)and its neighbouring main streets(Point S5A)may be confirmed approximately the same considering the measurement errors due to hotwires and building geometries.This indicates that wind in the middle main street was mainly affected by the externalflow above these building arrays,and was scarcely affected by the externalflows beyond the lateral boundaries of building arrays.To reduce the calculation time in numerical simulations,this study only con-sidered the middle column of the building array and only used half of this column,which is shown surrounded by dash lines in Fig.1a–c.Fig.2a shows the computational domain in the vertical (z)direction and in the stream-wise direction(x).This paper used a no-slip wall boundary condition at all the wall surfaces and a normal zero gradient boundary condition at the domain outlet and the domain top as well as symmetrical boundary conditions at the two lateral boundaries of the domain.This study measured the vertical profile of the velocity(U)and turbulence intensity(I) in the upstream freeflow(see Fig.2b),and used them to provide boundary conditions at the upstream domain inlet(the turbulent kinetic energy k¼1.5(IU)2,and its dissipation rate e¼C m3/4k3/2/l t, C m¼0.09and l t is the turbulent characteristic length scale).The velocity in the upstream freeflow can be approximately described by a power-law profile U(z)E2.9Â(z/B)0.1616as z o6.7B,and a linear profile U(z)E3.91m/s as z46.7B.For the similarity con-siderations,if the velocity at the height of the lower building roof (z¼H¼2B)in the upstream freeflow is defined as the reference velocity U ref E3.35m/s,the reference Reynolds number(Re H ¼r U ref H/m E13760)is much higher than4000,and sufficient to ensure Reynolds number independence(Meroney et al.,1996). There is no roughness element above wind tunnelfloor in the upstream approachingflow.The power law exponent for the measured velocity profile shown in Fig.2b is0.1616.According to Irwin(1979),it corresponds to an approximately stable turbulent boundary-layer at full scale with a surface roughness of z0¼0.1m (i.e.above a cultivated area with regular cover of low crop).The height above which wind speed is nearly a constant is named as ‘the gradient height’.Fig.2b shows the gradient height in wind tunnel freeflow is around0.2m(i.e.6.7B),corresponding to the
x/B
N
o
r
m
a
l
i
z
e
d
v
e
l
o
c
i
t
y
U
*
-3
T
u
r
b
u
l
e
n
c
e
i
n
t
e
n
s
i
t
y
1
2
3
4
5
6
z
/
B
1
2
3
4
5
6
z
/
B
x/B
0369121518
Velocity (m s-1)
Turbulent kinetic energy (m2 s-2)
Fig.3.Validation profiles including numerical results and wind tunnel data:(a)Horizontal profiles of normalised velocity and turbulence intensity along the main street centerline at the height of z¼B in Case[2.67-2.67,1-1,6,0.25].Vertical profiles of velocity and turbulent kinetic energy at(b)Point V1and(c)Point V6in Case[2.67-2.67,1-1,6,0.25].Vertical profiles of velocity and turbulent kinetic energy at(d)Points V0,V1and(e)Points V2,V4in Case[2-2,1-1,6,0.25].The model description is shown in Fig.1a.
J.Hang et al./J.Wind Eng.Ind.Aerodyn.99(2011)1036–1055
1042
height of 200m at full scale.This gradient height is near to that
for a terrain type of open sea (about 213m)and a little less than that for open terrain (about 274m)at full scale (Chen,1997).
In CFD simulations,this paper not only studied the six-row or nine-row arrays in wind tunnel tests,but also some building arrays with more number of rows,to investigate what happens when the street length (L )reaches neighbourhood-scale (i.e.1–2km at full scale).Then six more test cases were numerically studied,i.e.Case [2.67-2.67,1-1,18,0.25](18rows,L ¼35B ,i.e.1.05km at full scale),Case [2.67-2.67,1-1,28,0.25](28rows,L ¼55B ,i.e.1.65km at full scale),Case [2-2,1-1,18,0.25](18rows,L ¼35B ),Case [2-2.67,1-1,18,0.25](18rows,L ¼35B ),Case [2.67-2.67,0.5-0.67,21,0.4](21rows,L ¼34.3B ,1.03km at full scale).All these test cases are summarised in Table 1.This paper used three kinds of grids (coarse,medium and fine)for Case [2.67-2.67,1-1,6,0.25]including the coarse grid (the grid number in x ,y ,z is 225Â21Â87),the medium grid (361Â29Â100)and the fine grid (528Â39Â121)in which the minimum grid size near wall surfaces are 0.7mm (0.023B ),0.4mm (0.013B )and 0.2mm (0.0067B ),respectively.The grid independence study confirmed that numerical results with medium grids change little when the grids become finer.So all other test cases used medium grids and the total grid number is from about 1to 3.5millions with expansion ratio of not more than 1.1for grid size variations (i.e.less than 1.3according to Tominaga et al.(2008)).As an example,Fig.2c shows the medium grid generation in Case [2.67-2.67,1-1,6,0.25].
3.Results and discussion
3.1.Validation of numerical simulations using wind tunnel data This paper first performed a detailed grid independence study for the six-row array of Case [2.67-2.67,1-1,6,0.25](H ¼2.67B ,
l p ¼0.25,W ¼B )using standard k –e turbulence model and also
evaluated numerical results by wind tunnel data.Fig.3a shows horizontal profiles of the velocity and turbulence intensity along the street centreline at the height of z ¼B (x /B ¼0is the windward street entry).To show the velocity reduction,in particular,this paper normalised this velocity profile using the velocity at the same height in the far upstream free flow (i.e.U (z ¼B )¼2.90m/s given in Fig.2b).Fig.3b and c display vertical profiles of the velocity and turbulence (z /B ¼2.67is the canopy roof level)at Point V1and V6in the wake,as two examples.
Obviously both wind tunnel data and numerical results in Fig.3a confirm that,there is a velocity reduction when wind approaches the building array (i.e.x /B o À0.75),an acceleration of the velocity across the windward street entry (i.e.about À0.75o x /B o 0.5)of the main street,and a decreasing velocity deeper into the main street (i.e.x /B 40.5).More importantly,the normalised velocity at the windward entry (x /B ¼0)is about 1,verifying that rural wind flowing into building array is consider-able with a similar strength as that in the far upstream free flow.
In contrast to wind tunnel data,all three grids predicted horizontal profiles of the velocity generally well,however,they overestimated turbulence near the windward street entry (x /B ¼0)which is widely known that RANS standard k Àe turbulence model has significant limitations in predicting magnitudes of turbulence especially near the windward entry where separation flows appear.For vertical profiles at Points V1and V6,the numerical predictions using the medium and fine grids were similarly good,but the prediction using the coarse grid was not as good as the other two.Therefore this paper selected the medium grid in the following numerical simulations,considering both the solution accuracy and the computational time.Fig.3b and c also shows that the velocity profile at Point V1was better predicted than that at Point V6in the wake because RANS standard k –e turbulence model is not good at simulating reattaching flows in
00
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z / B 0.0
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3456z / B
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23456z / B Velocity (m s -1)
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2
34
5
Turbulent kinetic energy (m 2 s -2)
0.40.8 1.2 1.6 2.0 2.41
Velocity (m s -1)
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2Velocity (m s -1)
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Fig.3.(continued )
J.Hang et al./J.Wind Eng.Ind.Aerodyn.99(2011)1036–10551043。