Journal of Applied Mathematics and Physics, 2014, 2, 264-268
Published Online May 2014 in SciRes. http://www.scirp.org/journal/jamp
http://dx.doi.org/10.4236/jamp.2014.26031
How to cite this paper: He, W.K. and Yuan, W.B. (2014) Numerical Simulation of Wind Field Characteristics around Two
Adjacent High-Rise Buildings. Journal of Applied Mathematics and Physics, 2, 264-268.
http://dx.doi.org/10.4236/jamp.2014.26031
Numerical Simulation of Wind Field
Characteristics around Two Adjacent
High-Rise Buildings
Wenkai He, Weibin Yuan*
College of Civil Engineering, Zhejiang University of Technolo gy, Hangzhou, China
Received January 2014
Abstract
This paper based on R eynol ds-averaged Navier-Stokes equations standard
k ε −
model [1]; the
surface pressure on the wind field around two adjacent high-rise buildings was numerically simu-
lated with software Fluent. The results show that with the influence of adjacent high-rise building,
numerical simulation is a good way to study the wind field around high-rise building and the dis-
tribution of wind pressure on building’ surface. The pressures on the windward surface are posi-
tive with the maximum at 2/3 H height and have lower values on the top and bottom. The pres-
sures on the leeward surface and two sides were negative. Due to the serious flow separation at
the corner of building’s windward, the wind field has a high turbulent kinetic energy.
Keywords
High-Rise Building, Numerical Simulation, Wind Field Characteristics, Turbulence Model
1. Introduction
Studies on a square or a rectangular cross-section building affected by wind have been made by many research-
ers owing to its importance. However, a single building is a very rare case in the real world [2]-[4]. Shuyong
Tang and Shuifu Chen [5] suggested that building’s wind pressure and surrounding wind field will be affected
by the adjacent building. And when it comes to high-rise building, the influence will be even more serious if
there is another high-rise building beside it.
Nowadays having studied of wind field characteristic on high-rise building we can use both wind tunnel test
and numerical simulation. The wind tunnel test has been widely used to determine the aerodynamic characteris-
tics of buildings for years [6]-[8]. However, wind tunnel test req uires strict conditions of similarity, and it is also
difficult to simulate both atmospheric boundary layer turbulence structure features and inlet wind velocity pro-
file. What’s more, the test conditions have to change in order to adjust to different wind and building environ-
ment. Comparing with the wind tunnel test, numerical simulation has the characteristics of low cost, short cycle
and high efficiency. It can be conveniently by changing various parameters to simulate the flow field characte-
ristics of various kinds of ideal and real conditions. This paper would like to study the wind field characteristics
by using the numerical simulation.
*
Corresponding author.

W. K. He, W. B. Yuan
265
2. Numerical Simulation
2.1. Governing Equations
The governing equation of incompressible turbulent wind flow around building is presented by the Reynolds-
averaged Navier-Stokes equations [1] as follows:
0
i
i
u
x
∂=
∂
, (1)
''
1
j
ii i
j ij
jij ji
u
uu u p
u uu
txpx xxx
η


∂
∂∂ ∂ ∂∂
+=− ++− 


∂∂∂∂∂ ∂



. (2)
where
/ η µρ =
is Kinematic viscosity.
The standard
k ε −
model of the turbulent kinetic energy and turbulent kinetic energy dissipation for the
transport equation of the closed form is:
j
ii t
jt
jjj ijkj
u
uu kk k
u
txxx xxx
η
η ηε
σ
 
∂
∂∂ ∂∂∂ ∂
+ =+−+−
 


∂∂∂∂ ∂∂∂


 
, (3)
2
1
2
j
it
jt
jjj ijj
u
u
Cui
uC
tx kxx xxxk
ε
η
ε εε εε
ηη
σ
 
∂
∂
∂∂∂∂ ∂
+ =+−+−




∂∂∂∂ ∂∂∂


 
(4)
where turbulent kinetic energy is
1
2
ii
k uu=
; Turbulent kinetic energy dissipation is
ii
jj
uu
xx
εη
∂∂
=∂∂
; Turbulent
kinematic viscosity coefficient is
2
t
k
C
µ
ηε =
.
The coefficients of standard
k ε −
model are in Table 1.
2.2. Model and Working Condition
This paper’s study objects are two adjacent high-rise buildings, its length, width and height are 40 m, 40 m and
120 m, respectivel y and are 60 meters apart. Geomorphic types are class C. The buildings are rules, but the in-
fluence effect between two buildings makes it hard to predict the wind field around two buildings. In order to
study the wind field characteristics of two adjacent high-rise buildings, considering sym me try, we only choose
0°
and
90°
two different wind angles as working conditions.
2.3. Computational Domain and Boundary Conditions
2.3.1. Computational Domai n
The upper boundary is 3 H, and the inflow boundaries extend 3 H upstream of the windward face and outflow
boundaries reach 5 H downstream of the leeward face (H is the building height, value 120 m). The domain width
is 2 H from the sideward face. And the setting of flow field meets the requirement of blocking rate that should
be less than 3%. Considering the calculation efficiency, all of the grids we using are unstructured, which are
meshed by software CFD.
2.3.2 Boundary C ond iti on
Although the wind flow around building is totally an open flow wind field, when using numerical simulation, we
should have a bounded 3D computational domain, calculation area and the building wall boundary condition [5].
The entrance to the boundary of the atmospheric boundary layer wind speed profile we usually use speed inlet
conditions, and its average velocity distribution is
Table 1. Co e ffi cients of standard
k ε −
model.
C
µ
k
σ
ε
σ
1
C
2
C
0.09 1.0 1.3 1.44 1.92

W. K. He, W. B. Yuan
266
( )
b
b
vz z
z
v
∂

=

(5)
where
,
bb
zv
are Standard reference height and the average speed of Standard reference height, respectively;
()
,zv z
mean height and the speed value in the height;
∂
is the ground roughness index.
According to the load code for design of building struc tur e [9], the basic wind pressure encounters every 50
years in Hangzhou Zhejiang province is 0.4
2
/kN m
. Based on equation
2
1
2
Pv ρ =
we can get the basic wind speed is 24.9 m/s. And the building landscape types is class C, its ground roughness
index values 0.22. Outlet boundary using pressure outlet boundary conditions, the outlet pressure is 0 Pa. Wa-
tershed top and sides adopt symmetrical boundary condition. Building surface and ground with no slip wall con-
dition.
2.4. Convergence Criteria
Calculation to the parameters relative to iterative residual are less than
5
1 10
−
×
, and observe the building surface
wind pressure coefficient of basic don’t change, then we can say that the calculation of flow field simulation is
stable.
3. Results and Discussion
3.1. Numerical Pressure Coefficients
Wind pressure coefficient is defined as the reference height building surface static pressure to the distance of
measuring points to flow static pressure ratio:
i
si 2
w
1v
2
µ
ρ
=
(6)
where
si
µ
is the average wind pressure coefficient of measuring point i;
i
w
is the net wind pressure of mea-
suring point i;
v
is the average wind speed of reference height;
ρ
is the air d ensi t y,
3
1.225kg / m
.
Figure 1 is the overall building surface wind pressure coefficient contour map at the wind angle
0°
and
90°
,
respectively.
(a) (b)
Fig ure 1. Overall building surface wind pressure coefficients contour map, (a)
0°
; (b)
90
°
.

W. K. He, W. B. Yuan
267
From Figure 1 we can see that at the wind angle of
0
°
, the pressure coefficients on the windward surface are
positive with the maximum at 2/3 H height and have lower values on the top and bottom. In a word, the pressure
coefficients in the middle are larger than that on the top and bottom. And the negative pressures on the channel
wall are larger than that on the other wall.
At the wind angle of
90°
, building on the upstream, its pressure coefficients on the windward surface are
positive. And the circular contour on its leeward surface suggests that the flow field in the vortex structures.
Building on the downstream is in the wake stream of building on the upstream, pressures on its surface are nega-
tive, and the pressure coefficients are irregular.
Form Figure 2 we can see that the pressure coefficients with the maximum at 95 m, which is about 2/3 H
high. And the pressure coefficients with the minimum at the channel between two buildings, which suggests that
wall in the channel with the largest negative pressures. Pressures on leeward and sideward are also negative.
3.2. Distribution of Tur bulent Kinetic Energy
The turbulent kinetic energy means the level of fluid pulsation.
From Fig ure 3 we can see that the turbulence kinetic energy mainly on the windward and channel wall, which
suggests that in these places flow separation is serious.
3.3. Velocity Distribution and Flow Field Analysis
From Figure 4 we can see that flow field on the leeward forms a circular contour, likes a big whirlpool, so as to
cause the suction. Flow field on the sideward forms the separation zone. At the wind angle of
90°
, building on
the downstream is in the wake stream of building on the upstream, the velocity is negative.
(a) (b)
Fig ure 2. Pressure coefficients at the height of 35 m, 65 m, 95 m and 115 m, (a)
0°
; (b)
90
°
.
(a) (b)
Fig ure 3. Turbulence kinetic energy contour map, (a)
0
°
; (b)
90
°
.

W. K. He, W. B. Yuan
268
(a) (b)
Fig ure 4. Velocity distribution contour map, (a)
0
°
; (b)
90
°
.
4. Conclusions
Numerical simulation is a good way to study the wind field around high-rise building and the distribution of
wind pressure on building’s surface. The pressure coefficients in the middle are larger than that on the top and
bottom, and with maximum at the height of 2/3 H. Pressures on leeward and sideward are negative.
Due to the influence of adjacent building, wall in the channel with the minimum negative pressures which
suggest that the channel effect is serious. And the turbulence kinetic energy in the channel has a high level. At
the wind angle of
90°
, building on the downstream is in the wake stream of building on the upstream, the ve-
locity is negative.
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