Fig. 7 Measured (top) and simulated vertical accelerations
Fig. 6 Measured (top) and simulated vertical accelerations
Fig. 8 The two-dimensional computational domain
Szabó et al.
Period. Polytech. Civ. Eng.
The geometry size was downscaled with a scaling factor
of 1:40 in order to reduce the computational efforts, which
was done based on the assumption that the Reynolds num-
ber has minor effects on the aerodynamic parameters in
case of an edgy bridge deck shape. At the inlet U = 20 m/s
uniform wind velocity was defined. The turbulent kinetic
energy and its dissipation rate were set uniformly accord-
ing to the turbulence intensity I and the length scale L. Low
(I = 1% and L = 0.001 m) and high (I = 5% and L = 0.01 m)
turbulence conditions were considered in order to study its
effects. The pressure gradient was set to zero. At the out-
let the velocity gradient and the pressure was set to zero.
On the bridge deck no slip, on the sides free slip boundary
condition was defined for the wind velocity.
Besides the k–ε model, DES (Detached Eddy Simulation)
model was also utilized, applied in [11, 12]. This model is the
combination of RANS and LES (Large Eddy Simulation).
The latter is based on filtering, instead of averaging of the
Navier-Stokes equation. The filtering operation leads to the
sub-grid stress tensor (SGS), which needs to be modelled.
The RANS model for DES was Spallart–Allmaras (S–A),
which is a one-equation model for the (modified) turbulent
viscosity (ῦ t ). The switch from RANS to LES is based on
the distance from the closest wall (d) and the grid spac-
ing (Δ) shown in Eq. (5). The DES constants of C DES = 0.65
is offered for a wide range of applications.
d d c DES DES
The DES approach has a weak point of switching from
RANS to LES mode too early near the wall boundary;
therefore, predicts the flow separation in case of aero-
foils inaccurately. In order to circumvent this problem, the
length scale d DES is modified considering the molecular and
turbulent viscosity, leading to the delayed version of DES
(DDES). At the inlet wind velocity U = 5 m/s, ν t = 10
turbulent viscosity were defined for low turbulence inten-
sity (I = 1%). In case of the k–ε model, coarse (mesh#1),
medium (mesh#2) and fine (mesh#3) two-dimensional
meshes were used. The cell numbers are approximately
25.000, 51.000 and 65.000 for the construction stage,
and 38.000, 60.000 and 75.000 for the completed bridge.
In case of DES the two-dimensional mesh was extruded
with a length of L = 0.60 m and division number of N = 60,
which is mesh#4. The total cell number for the two cross
section configurations (see Fig. 9) are around 2.3 and 4.0
million, respectively. The mesh#2 around the bridge deck
is shown for the completed cross section in Fig. 10.
In case of three-dimensional mesh#4 the vertical ele-
ment of the handrails and curbs were replaced by longi-
tudinal elements with equivalent drag force. The average
values near the wall boundary for mesh#1, mesh#2 and
mesh#3 were over 20. In case of DES, the y
kept below 1 by using properly small cells near the wall
boundary and setting wind velocity U of 5 m/s, lower than
in case of the k–ε model. The time step size Δt for mesh#1
was 5 × 10
s, for mesh#2 and mesh#3 was 2.5 × 10
mesh#4 was 2 × 10
s. The velocity contour plots around
the uncomplete and complete cross sections with k–ε model
can be seen in Fig. 11 and Fig. 12, respectively. The simu-
lations were performed in case of the two-cross sections,
with the four meshes in both cases. Low and high turbu-
lence intensity was considered in case of the k–ε model,
and low turbulence intensity only for the DDES.
In Table 1 and Table 2 c d , c y ' and St are the simulated
static drag coefficient, the dynamic lift force coefficient
(RMS of lift) and the Strouhal-number, respectively.
The mesh sensitivity study of the k–ε model showed that
the accuracy of mesh#2 was acceptable expect for the