A two-dimensional mathematical model is used to simulate the influence of water flow on the piers of a bridge for different incidence angles. In particular, a finite volume method is used to discretize the Navier-Stokes control equations and calculate the circumferential pressure coefficient distribution on the bridge piers’ surface. The results show that the deflection of the flow is non-monotonic. It first increases and then decreases with an increase in the skew angle.

After the bridge is built in a natural river, due to the compression and interference of the bridge piers on the water flow, a series of changes near the bridge location can occur. Due to the partial water blocking effect of the pier, the flow velocity upstream of the dock slows down, and the water level is high as a result. Its impact on the upstream and downstream involves the flood control safety of the dams on both sides of the bank, nearby cities, as well as factories and mines. The water flow structure at the bridge pier is more complicated [

The content includes:

The compression ratio.

The flow velocity of the upstream of the river.

The shape of the bridge piers.

However, despite that many studies on the flow structure near the bridge piers exist, there is no ideal result yet due to the complexity of the problem [

Continuity equation

Incompressible fluid has

Momentum equation

Taking the average of both sides of the N-S equation, the Reynolds average equation is

The emergence of Reynolds stress

We simulate the water flow near the pier in the case of a single pier. We then calculate the length, width, and height of the water tank to be 8 m × 1.2 m × 0.18 m. The side length of the pier is 0.2 m, and the height of the pier is 0.18 m. The quality of grid generation directly affects the calculation accuracy and convergence. We can use grid segmentation technology to generate grids for different calculation areas to calculate the water flow near the bridge piers. The complex three-dimensional area can be deconstructed into a series of three-dimensional sub-blocks through block division. In each sub-block, different grid densities can be arranged conveniently according to the characteristics of the flow field [

The numerical calculation method used by the author is the finite volume method. The discrete format we chose is the upwind difference format [

We use three

Criterion ^{3}/h, and the outlet water depth is 15 cm, the contour map of the free surface water level is shown in

In addition, a significant drop in the water level can also be observed in the corresponding range of the downstream rear end of the bridge pier, and the drop in the water level is generally in the range of 0.1 cm. When the flow rate is 288 m^{3}/h, and the outlet water depth is 15 cm, the contour map of the free surface water level is shown in ^{3}/h under the same model. The water level decreases downstream and on both sides of the pier, and the maximum decrease is 0.9 cm. Under this condition, the water level decrease in most areas downstream of the pier exceeding 0.3 cm.

The change of the average flow rate: In the case of a flow rate of 144 m^{3}/h and an outlet depth of 15 cm, the vertical average flow velocity contour diagram is shown in ^{3}/h, and the outlet water depth is 15 cm, the vertical average flow velocity contour diagram is shown in ^{3}/h under the same model [

Free surface water level analysis: When the flow rate is 144 m^{3}/h, and the outlet water depth is 15 cm, the contour map of the free surface water level is shown in ^{3}/h, and the outlet water depth is 15 cm, the contour map of the free surface water level is shown in ^{3}/h under the same model [

Analysis of average flow rate: When the flow rate is 144 m^{3}/h, and the outlet water depth is 15 cm, the vertical average flow velocity contour diagram is shown in ^{3}/h, and the outlet water depth is 15 cm, the vertical average flow velocity contour diagram is shown in ^{3}/h under the same model, but the maximum value of the flow velocity reduction reaches 0.34 m/s. This is greater than the flow rate of 144 m^{3}/h under the same model. When the maximum increase in flow velocity is 0.11 m/s, it appears in the downstream area on both sides of the pier. The maximum reduction is 0.42 m/s. This are is mainly located at the end of the middle pier. The velocity reduction value in other areas is between 0.04 and 0.39 m/s.

Free surface water level analysis: When the flow rate is 144 m^{3}/h, and the outlet water depth is 15 cm, the contour map of the free surface water level is shown in ^{3}/h, and the outlet water depth is 15 cm, the contour map of the free surface water level is shown in ^{3}/h under the same model. The water level downstream of the bridge piers generally decreases, and the decrease range is between 0.2∼0.9 cm.

Analysis of average flow rate: When the flow rate is 144 m^{3}/h, and the outlet water depth is 15 cm, the vertical average flow velocity contour diagram is shown in ^{3}/h, and the outlet water depth is 15 cm, the vertical average flow velocity contour diagram is shown in

Based on some hydraulic characteristics of the water movement near the bridge piers, we compared the calculation results mainly from the free surface water level change, the average flow velocity, the wake vortex shape, and the upstream cross-sectional water level change with the measured data [

^{3}/s. We use three turbulence models to simulate the water level of the cross-section near the single pier and the comparison chart of the measured water level. It can be seen from

^{3}/s and the actual measured velocity [

Under the same model, with the flow rate increase, the maximum value of the decrease of the flow velocity presents the same change law as the maximum height of the backwater. There is an unstable flow state at the end of the pier [

The flow rate of the stagnant water upstream of the bridge pier decreases. The squeezing water flow on both sides of the bridge piers and between the bridge piers causes the flow velocity to increase. Due to the water blocking effect of the bridge piers, the flow velocity at the end of the bridge piers decreases more. In the same model, with the flow rate increase, the maximum value of the flow rate decrease shows the same change law as the maximum height of the backwater.

The author would like to extend his(her) thanks to the learning and research platform, as well as the generous financial support provided by the company and the school.