Research on Simulation and Evaluation of Environmental Adaptability of Ribbon Bridge Based on GMRES Algorithm

This paper focuses on the safety of ribbon bridge navigation at different flow speeds, including bow tilt and stern tilt. By constructing a CAD 3 dimensions simulation model and CFD simulation test model of a ribbon bridge, the Hydrodynamics of the ribbon bridge under different load conditions and flow velocity is simulated and calculated based on the GMRES algorithm.The environmental adaptability assessment was carried out from the aspects of bow tilt, stern tilt and flow velocity adaptability of the ribbon bridge, and the navigation safety and stability of the ribbon bridge in different environments were obtained, which could provide data reference and support for the safe navigation of the ribbon bridge in the actual waters.


Introduction
The ribbon bridge is an important engineering equipment to overcome river obstacles and implement maneuvering, the ribbon bridge's body is a load-bearing structure and bridge deck, and the integrity of the structure is relatively good.Ribbon bridge relies on water propulsion devices or motorboats to provide power for walking on water.The interaction between the ribbon bridge and the flow is different from that of the ship, the linearity of the ribbon bridge is poor, the aspect ratio is small, and its resistance has its characteristics.Therefore, the interaction between the ribbon bridge and the flow is directly related to the hydraulic performance and usage of the ribbon bridge [1].
Because there is no passage between the ribbon bridge to allow water to pass, the resistance of the ribbon bridge is relatively large.When the flow velocity is large, the water level rises seriously due to the obstruction of the water flow in the upflow part, and there is potential safety such as bow tilt, stern tilt and capsizing [2].Wu Zhuo established a three-dimensional structured mesh of the multi-boat model without considering the effect of fluid interference and obtained the time-varying curves of the fluid resistance of each floating boat.Sun Jianqun [3] studied the hydrodynamic response of the hydrodynamic model test to the action of regular waves and obtained the bending moment distribution of the boat bridge.In this paper, the influence of the ribbon bridge on the flow velocity, flow direction and draft is studied, and the relationship between the resistance, torque, draft and inclination angle of the ribbon bridge is analyzed to evaluate the safety and flow rate adaptability of boat bridge equipment during operation [4].

Construction of Ribbon Bridge Simulation Model
In this paper, a CFD simulation test model of the ribbon bridge is constructed on the basis of CAD geometric modeling based on the geometric modeling of a ribbon bridge.Numerical calculations are carried out using multiple structured meshes and unstructured viscous meshes.Unstructured viscous mesh is a prismatic mesh element with a high stretch ratio near the boundary layer of the boat, while the rest of the area is filled with unstructured tetrahedral mesh elements.This not only satisfies the requirements of viscous boundary layer resolution, but also reduces the difficulty of mesh generation [5]. Figure 1 is the schematic diagram of the unstructured viscous mesh of a ribbon bridge.The technical problems related to numerical grids are the key to determine the success rate of numerical solutions.In order to meet the needs of engineering fluid problems, this paper adopts a variety of numerical mesh generation techniques, which should not only consider the accuracy of the numerical solution, but also take into account the practical problems such as the speed, stability, and difficulty of mesh generation.

Simulation Calculation Formula
Assuming that the flow is perpendicular to the length of the ribbon bridge, based on the theoretical formula in Wu Peide's monograph "Ribbon Bridge", the horizontal water resistance of ribbon bridge [6]: Where: C0 is the drag coefficient of the isolated pontoon when the flow is infinitely deep.when the width of the pontoon is 4~5 m, C0 is taken 0.6, and when the width of the pontoon is 8~10 m, C0 is taken 0.5.C1 is the span influence coefficient, for the ribbon bridge, the ratio of the span to the width of the boat is approximately 1, C1 is taken 0.8.Ch is the shallow water influence coefficient.ρ is the density of water, v is the average flow velocity of the river section before the ribbon bridge is erected, Ω is the maximum cross-sectional area of the ribbon bridge flooding area, which is caused by the combination of static load and live load.

Simulation Test Data Verification
For comparison with the test data, the model used for the calculation of the ribbon bridge is the same as that of the test model.The real bridge is similar to the model Fu Rude number, and the length ratio of the real boat to the model is 10:1.The dimensionless parameters of the model and the real boat, Reynolds number and Four-Rude number, cannot be guaranteed to be the same at the same time, so Four-Rude number can only be made the same.The calculation is carried out according to the model, which is divided into two load cases, light load and heavy load [7].
Table 1 shows the relevant performance parameters of the model and the real ribbon bridge under the two working conditions.Among them, L is the length of the ribbon bridge.B is the width of the ribbon bridge, T is the draft for the ribbon bridge, H is the depth of the ribbon bridge, Fb is the free board height of the ribbon bridge, As is the waterline area of the corresponding load condition, Vw is the drainage volume of the ribbon bridge [8].The model calculates the total water resistance and near-field circumference in still water from low speed to high speed, respectively.By searching the literature and specifications, the results of the calculated flow force under the same working condition are quite different.CFD simulations are required to further verify the scope and accuracy of the formula [9].The dimensionless parameters of the heavy-duty belt gate bridge model at different speeds are shown in Table 2.Among them, Um is the velocity of the model, Ur is the velocity of the real bridge, Fr is the number of Fu Rude, Rem is the Reynolds number of the model, and Rer is the Reynolds number of the real bridge.

Numerical Analysis of Simulation Calculations
The three-dimensional unsteady Navier-Stokes equation is used to determine the flow field governing equation, and the governing equation is discretized by finite difference method.the space is discretized into a three-dimensional rectangular staggered grid, and the scalar is defined at the center of the control body, such as pressure, fluid volume function, density, flow volume fraction.while the velocity and area fractions are defined at the center point of the grid boundary surface, the momentum equation and the continuity equation are discretized and solved by the minimal residual method GMRES [10].
For the heavy model case, the free surface and turbulence effect are quite obvious, which is closely related to the generation of water resistance.the wave resistance is related to the free surface motion, and the viscous resistance and frictional resistance are related to the turbulent motion.In addition, there is a large coupling interaction between the wave resistance, viscous resistance and frictional resistance, which makes the whole physical process quite complicated.The calculation effect of frictional resistance is more closely related to the turbulence simulation, while the calculation of the free surface of the wave depends on the resolving ability of the VOF free surface reconstruction format.Since the total water resistance under light load is definitely smaller than that under heavy load, the comparison of the total water resistance calculated by the heavy-load ribbon bridge model and the test is shown in Table 3. Fig. 2 is the fitting curve.Where: ERRt represents the percentage of relative error, Rtcal represents the calculated value of the total water resistance, and Rtexp represents the test value of the total water resistance.The comparison between the calculated frictional resistance and the estimated value of the heavyduty ribbon bridge model is shown in Table 4, and Figure 3 is the fitting curve.From Figure 3, the error between the calculation of total water resistance and the test is less than 5%, and for the working condition of 1.1 m/s, the model capsized due to excessive bow tilt during the test, so there is no measurement data.Compared with the formula estimate, the average error of calculating 100%

Calculation Estimation
Calculation Estimation frictional resistance is 3.2%, and the maximum error is about 8%.The average error of the total water resistance is less than 1%, and the maximum error is not more than 5%.The calculation results of the above two hydrodynamic parameters meet the engineering accuracy requirements.In particular, it is pointed out that since the resistance component in the calculation can only be divided into frictional resistance and residual resistance, and the total water resistance can only be obtained in the test, the comparison of different standards is carried out.In Figure 4,A is the ratio of estimated frictional resistance to calculated total resistance.B is estimate the ratio of frictional resistance to the total resistance of the test.C is calculate the frictional resistance to calculate the total resistance ratio.D is calculate the ratio of frictional resistance to total test resistance.It can be seen that the proportion of frictional resistance in the total resistance is quite different from that of the light load condition with the increase of speed, and the overall trend is decreasing.with the increase of total resistance, the frictional resistance increases slowly.

Near-field Flow for Overloaded Model Cases
The waveform of the heavy-load ribbon bridge model obtained by numerical calculation is shown in Fig. 6 It can be seen that obstruction of the water flow of the ribbon bridge model.from low speed to high speed, the waveform is gradually obvious, and the navigation wave is also gradually significant.Comparing the two working conditions of light load and heavy load, the waveform of the heavy load condition is larger than that of the light load condition at the same speed.Under light load conditions, when the speed reaches 1.1m/s, there is not much water crossing on the model deck, and the ribbon bridge can continue to maintain safe navigation.When the speed of heavy load is 0.8m/s, the deck begins to be significantly wet by water.When the speed reaches 1.0m/s, the obstruction of the water flow of the ribbon bridge becomes very serious, and a large amount of obstruction of the water flow tries to row from both sides of the boat to the rear.it is still too late, so the obstruction of the water flow has to climb over the deck, causing the bow inclination angle and resistance to increase until the recovery moment of the boat can not resist and leads to capsizing.

Conclusion
Combined with the prototype of a ribbon bridge, a CAD 3 dimensions simulation model and CFD simulation test model of a ribbon bridge are constructed.The hydrodynamics of the ribbon bridge under different load conditions and flow velocities are simulated and calculated based on the GMRES algorithm.The environmental adaptability assessment was carried out from the aspects of bow tilt, stern tilt and flow velocity adaptability of the ribbon bridge.the ribbon bridge navigation under light load and heavy load is obtained, and the research results can provide data reference and support for the safe navigation of the ribbon bridge in the actual waters.

Figure 1 .
Figure 1. the schematic diagram of the unstructured viscous mesh of a ribbon bridge.

Figure 2 .
Figure 2. Comparison of total water resistance with the test value.

Figure 3 .
Figure 3.The heavy-duty model case calculates frictional resistance compared to estimated value.

Figure 4 .
Figure 4. Comparison of friction resistance component analysis under heavy load model.

4. 1 .
Near-field Flow for a Light-load Model Case Fig.5is the waveform of the ribbon bridge model under light load obtained by numerical calculation, and the arrow in the figure indicates the direction of navigation.the numerical calculation simulates the obstruction of the water flow well, and the waveform from low speed to high speed is gradually obvious.The draft of the ribbon bridge model under the light load condition is shallow and the navigation wave is not very significant.the possibility and effectiveness of the CFD numerical calculation method for the near-field flow simulation of the ribbon bridge are verified by using the working condition.

Figure 5 .
Figure 5. Calculation of near-field waveform under the light-load model.

Figure 6 .
Figure 6.Calculation of near-field waveform under the heavy-load model.

Table 1 .
The main parameters of the real boat and the model of the ribbon bridge.

Table 2 .
Dimensionless parameters by the heavy-duty ribbon bridge model at different speeds.

Table 3 .
Comparison of the total water resistance with the experiment.

Table 4 .
The comparison between the calculated frictional resistance and the estimated value of the heavy-duty ribbon bridge model m U m s