Investigation of the aerodynamic characteristics of single-box girders with different aspect ratios

2.1. Numerical method

The aspect ratio of large-span streamlined box girders usually ranges from 5.3 to 11.6, the streamlined box girders with aspect ratios of 7.5, 9.3, and 12.7 were selected to investigate the effects aspect ratios on the force coefficients and three-dimensional flow separation characteristics of streamlined box girders in turbulent field. The dimensions of the model are shown in Fig. 1.

Fig. 1Segmental models with different aspect ratios (Unit: mm)

Numerical simulations are carried out using three-dimensional large-eddy simulations (3D LES) with the SGS model. The computational domain takes into consideration 6$B$ in front, 12$B$ behind, and 6$B$ above/under the surfaces to ensure domain independence. Fig. 2 shows the computational domain and mesh distribution. The dimensions of the computational domain in the $X$, $Y$, and $Z$ directions are 19$B$ × 12$B$ × 3$B$. The computational blocking rate is 0.04 %, which can ensure the independence of the computational domain [12, 13]. The boundary conditions of the computational domain are set as follows: the surface of the main beam is a no-slip wall boundary, the entrance is a velocity-inlet boundary, the exit is an outflow boundary, and the symmetry boundary is used on the top, and bottom, and sides of the computational domain [14, 15].

Fig. 2Details of meshing of the box girder with aspect ratios of 9.3

2.2. Validation

As shown in Fig. 3, the numerical results are validated by the wind tunnel tests in uniform flow. The experimental tests are carried out in a multiple-fan active control wind tunnel at Tongji University, Shanghai, China. It can be found that the lift coefficients obtained by experimental tests and numerical simulations agree well.

Fig. 3Comparisons of lift coefficients obtained by experimental tests and numerical simulations

3.1. Effect of aspect ratio on lift coefficients

The LES method was adapted to simulate the turbulent field $I_u$-2, of which the turbulent intensity is $I_u=$ 7.3 %, turbulent integral scale is $L_u=$ 0.5 m. And the angle of attack was set to ranges from 0° to 12° with an interval of 2°. The details of the numerical simulations are shown in Table 1.

Fig. 4 shows the effect of oscillating amplitude and frequency on the mean velocity distributions around the wake in different sinusoidal oscillating flows. Due to the interference of the box girder, the downstream mean velocity of the wake in the near-wake region ($x\le$ 0.5) is significantly smaller than the mean incoming flow. As the flow distance increases, the mean downstream velocity gradually increases to the mean oncoming flow ($U=$ 8 m/s). The influences of oscillating frequency and amplitude on the changing trend can be ignored.

Fig. 4Effect of the aspect ratios on the aerodynamic coefficients

a) The effect of frequency

b) The effect of amplitude

3.2. Effect of aspect ratios on flow separation characteristics

To investigate the effect of aspect ratio on the streamline distribution of the flow field around the main girder, Fig. 5 shows the streamline distribution of the main girder with different aspect ratios in a turbulent wind field. The picture shows that the aspect ratio of the main beam gradually increases from left to right, and the angle of attack gradually increases from top to bottom.

Fig. 5Streamlines distributions of the box girder with different aspect ratios

a)$\alpha =$ 0°

b)$\alpha =$ 12°

From the figure, it can be seen that, because in the case of small angle of attack $\alpha =$ 0°, the larger the aspect ratio of the main beam, the better the streamline characteristics of the main beam, the smaller the effect on the fluid, all the main beams of the upper and lower surfaces of the flow separation phenomenon does not occur, but only in the leeward side of the main beam appeared in the vortex, and the vortex of the leeward side of the main beam is significantly reduced in the case of the B-3 working conditions. The case of a large angle of attack ($\alpha =$12°) is different, because the height of the flow separation point and the windward area of the main girder are significantly increased in the case of a large angle of attack, so the separation bubble on the upper surface of the main girder becomes thicker gradually with the increase of the width-to-height ratio. Therefore, in the case of a large angle of attack, the increase in aspect ratio will make the separation bubble on the upper surface of the main beam larger.

To investigate the effect of aspect ratio on the wake shedding pattern of the main beams, Fig. 6 illustrates the distribution of wake vorticity for the main beams of conditions B-1, B-2, and B-3 for the angle of attack ranging from 0° to 12°. When $\alpha =$ 0°, the wake streams of the main beams for all the working conditions show a clear phenomenon of alternating shedding of positive and negative vortices. It can be observed that the width of the wake streams of the main beams from working conditions B-1 to B-3 becomes narrower. In all the cases, the wake of the main beam dissipates around $x=$ 0.4 m. The width of the main beam is gradually increasing, so the length of the wake shortens as $B/D$ increases. Therefore, in the case of a small angle of attack, the vortex-shedding phenomenon of the wake stream of the main beam will gradually weaken with the increase of the width-to-height ratio. When $\alpha$ increases to 12°, "2S" vortices reappear on the upper and lower surfaces of the main beam, and the distance between positive and negative vortices increases. As the aspect ratio increases, the distance between the positive and negative vortex generation points becomes longer due to the widening of the main beam, increasing the phase difference between the positive and negative vortices in the wake stream.

Fig. 6Vertex shedding of the box girder with different aspect ratios

a)$\alpha =$ 0°

b)$\alpha =$ 12°