4.1 Wind environment above the decks
Flow field characteristics around the girder are not only related to the aerodynamic performance of the bridge itself, but also related to the safety of the vehicles travelling over the bridge. Taking the null angle of attack as the example, the wind environment above the six lanes of the upper box and the six lanes of the lower box, as shown in Fig. 12, is focused.
The wind profiles along the central lines of all lanes are shown in Fig. 13 where V is the mean streamwise velocity at the prototype height y above the deck surface and normalized by the inflow velocity U. The height y is also normalized by the height of the upper box D1 and the lower box D2, respectively. With the increase in distance between the two boxes, the wind profiles for the six lanes above the upper box keep similar, indicating that the aerodynamic interference has small effects on the wind environment above the upper deck surface. Near the deck surface, the wind velocity becomes small within a certain height which is called the affected height. The affected height increases along the flow direction from lane 1 to lane 6.
However, the aerodynamic interference has significant effects on the wind environment above the lower deck surface. The wind profiles for the six lanes are different from those above the single box girder. For lanes 1-3 on the windward side, the wind velocities within the affected heights increase while the wind velocities above the affected heights decrease. For lanes 4-6 on the leeward side, as the affected heights become higher, the wind velocities within the computed heights increase.
4.2 Aerodynamic forces on vehicles
The increasing wind velocities between the two boxes is unfavorable to the safety of vehicles travlling through the bridge. In this section, vehicles are considered in the CFD simulations in order to extract the aerodynamic forces. As discussed in introduction, the container car is easier to affect by strong winds which is taken as the target here. The simulated size of the container car is shown in Fig. 14(a). In the three-dimensional CFD simulations, the vehicle is static, and the secondary elements of the bridge are not considered, such as crash barriers and railings. The scale ratio of 1:50 is adopted in the simulations. When the vehicle is located in lane1 above the upper box girder, local computational mesh is shown in Fig. 15. The computational domain is discretized by hexahedral cells. Both in the xy plane and yz plane, that is, in the transverse and longitudinal directions, more cells were generated around the vehicle. The total cell number in the computation domain is 3,244,353, and the quality of cell is relatively good as the maximum equisize skew value is 0.679. The windward and leeward faces are set as velocity-inlet and pressure-outlet boundaries, respectively. The vehicle and the girders are set as smooth walls.
The aerodynamic forces acting on the vehicle include lateral force Fx, lift force Fy, drag force Fz, deflection moment My, overturning moment Mz, and pitching moment Mx. For what concerns the running safety of vehicles, lateral force Fx, lift force Fy, and overturning moment Mz should be carefully studied. The lateral force, lift, and overturning moment coefficients are defined by the following equations.
$${C}_d={F}_x/\left(0.5\rho {U}^2 hl\right)$$
(4)
$${C}_l={F}_y/\left(0.5\rho {U}^2 bl\right)$$
(5)
$${C}_m={M}_z/\left(0.5\rho {U}^2{b}^2l\right)$$
(6)
where, Cd, Cl and Cm are the lateral force coefficient, lift coefficient and overturning moment coefficient respectively; h, b and l are the vehicle height, width, and length, respectively; U is the mean wind velocity and is set as 15 m/s here. The positive directions of forces are shown in Fig. 14(b).
The aerodynamic forces on the static vehicle were extracted by CFD simulations. When the vehicle is placed on lanes 1-3 above the upper and lower deck surfaces, respectively, the aerodynamic forces are shown in Fig. 16 where the abscissa is represented by the lateral position which is the distance from the vehicle to the windward sides of box girders.
From lane 1 to lane 3, the lateral force coefficient, lift coefficient and overturning moment coefficient of the vehicle decrease. Comparing the upper and lower lanes, the aerodynamic coefficients of the vehicle are larger when it is placed above the lower deck surface. The variations in aerodynamic coefficients are relatively significant as well.
When the vehicle is placed on lanes 1-3, respectively, the counters of the mean velocity are compared. Taking different cross sections of the vehicle as examples, the counters are shown in Figs. 17, 18 and 19. Blocked by the vehicle, the wind velocity in the wake decreases significantly, especially for 1/4, 1/2, and 3/4 positions. When the vehicle is placed above the upper deck surface, the flow could pass through the vehicle from its upper side as the space is large enough, so the acceleration effect is not significant. When the vehicle is placed above the lower deck surface, however, the space of the upper side is limited due to the existence of the upper box, so the flow acceleration becomes significant. Therefore, the aerodynamic forces on the vehicle are larger when it is placed above the lower deck surface. From lane 1 to lane 3, the acceleration effect above the vehicle gradually weakens.
The counters of the static pressure on the vehicle are further shown in Fig. 20. Comparing the two cases when the vehicle is placed on the upper and lower deck surfaces, the positive pressure on the windward surface of the vehicle is similar, while the negative pressure on the upper and leeward surfaces is different due to the wake flow.