Simulation of regular wave impact on beam-plate structure on a slope

In order to study the peculiarities of wave slamming on beam-plate structures on a slope, two-dimensional numerical models of regular waves have been developed on the basis of the FLUENT software. Firstly, the validity of the numerical wave flume was verified. Then, with plentiful simulations, the parametric studies were performed for different wave steepness, structure geometry, and the distance between the underside of the horizontal plate and the still water level. The effects of the three parameters on the impact pressure and vertical velocities were investigated. Lastly, the statistical relationship between the waves’ impact pressures and the corresponding flow velocities was investigated. The results had a certain significance to the further understanding of the mechanism of the impact of the waves.


Introduction
For the engineering design of marine buildings, the determination of wave impact load is the primary problem, which directly affects the height of the building's superstructure.Then, it affects the safety and cost of the project.At present, many scholars at home and abroad have done some research work in physical model tests, numerical simulations, and theoretical research on the problems of wave impact [1][2][3][4][5].However, there are still many problems worth studying, such as the changing properties of the flow field near the structure during wave slamming and the relationships between the flow field and pressure.Due to the limitation of test equipment and conditions, many details of impact action have yet to be discovered and discussed.In addition, the type of structure is relatively simple, mainly horizontal panels, and there are few studies on the wave impact of different structures.
Numerical simulation is an important method of studying the wave action problem [6][7][8][9].It overcomes the limitations of model tests to a certain extent and can be verified and complementary to experimental studies.Therefore, its advantages can be used to carry out more extensive research work.This paper mainly uses numerical simulation methods.Using FLUENT software, a twodimensional mathematical model is established for the interaction between wave and beam-plate structure on a slope to simulate the wave slamming process.The characteristics of the wave impact pressure and the vertical motion speed of the water quality point at the bottom of the plate are discussed.The statistical correlation between the impact pressure of the structure and the vertical motion speed of the corresponding water quality point is analyzed so as to understand the mechanism of wave impact deeply.

Establishment and verification of numerical wave tank
The RANS equation is used as the control equation in the numerical calculation.The VOF method tracks the free liquid level and the  − k model to close the turbulence model.The wave creation boundary method of a given flow velocity and wave height is used to generate a series of regular waves.The porous medium model is used for the numerical wave cancellation [10].
Figure 1 shows the numerical wave flume calculation area.The left side of the wave tank is set as the wave generation boundary, the upper and right parts are symmetrical boundaries, and the lower part is the solid wall boundary.The tank is 45 m long and 0.5 m deep.The 10 m area on the right is used for source term wave elimination, and its length is about 3 representative wavelengths.The plate structure has a thickness of 0.015 m and a length of 1.02 m.The ultra-high height of the plate on static water is denoted by h  .The pressure measuring points are set at the bottom of the plate structure, and the distance from the front end of the plate is 0.035 m.The height of the transverse beam at the bottom part of the plate is 8 cm and 4 cm wide, the transverse beam spacing (middle-middle) is 24.75 cm, the height of the longitudinal beam is 5 cm and 2 cm wide, and the spacing of the longitudinal beam (middle-middle) is 20 cm.The beam size and test sensor arrangement under the plate can be seen in Figure 2.For the plate structure on the slope, the slope is m=2 and non-permeable, which is shown in Figure 3.When generating the numerical tank calculation grid, the grid is encrypted near the free surface in the vertical, so as to accurately calculate the shape and deformation of the surface wave.It is evenly set at 10-20 units in the wave height range and gradually thinning outside.In the horizontal direction, because the flow near the plate is more complex, the physical quantity and gradient may change greatly, so this area is also grid-encrypted.Each unit is about 1.0 cm, and the other set is 60-100 units for one wavelength.The grid division of the numerical wave tank and structures are shown in Figure 4.

The influence of wave steepness
Figure 6 shows the results of numerical simulations of the maximum relative impact pressure with changing wave steepness.The peak maximum relative impact pressure often happens in the smaller wave steepness.For larger wave ultra-height, the impact pressures rise obviously with wave steepness.For smaller ultra-height, the gas layer buffer effect caused by the plate structure sealing will slow the influence of impact angle change on the impact pressure.The corresponding impact pressure with the change of the wave steepness will be gentle.

The influence of ultra-height
Figure 7 shows the variation rule of the maximum slamming load with the ultra-height.The impact pressure appears at two peak points with the increase of ultra-height.The first peak point occurs at the smaller ultra-height, and mostly, the ultra-height is 0 or 0.2.The second peak point appears when the ultra-height is relatively large, and mostly the ultra-height is 0.4 or 0.6.At this time, the obstruction of the plate is small, the effect of the frame beam is enhanced, the buffer effect of the air layer is weakened, the wave power is large, and the wave impact angle decreases with the increase of the ultraheight.Thus, the second peak value is sometimes larger than the first peak point.

The influence of plate width
Figure 8 shows the numerical simulation results of the maximum slamming force change with relative plate width.It is visible from the figure that the width has a certain impact on the maximum slamming force for the beam-plate structure on a slope.As a whole, the maximum impact pressure increases as the plate width decreases.As the relative width of the plate increases to a certain value or decreases to a certain range, the influence of the relative width is gradually becoming smaller.

The influence of wave steepness
The relationship between the maximum vertical motion speed of the water quality point and the wave steepness is shown in Figure 9.For large periods and small wave steepness, the wave impact angle is small, and the vertical motion velocity has a peak point at the wave steepness of 0.037.After this peak point, the vertical velocity decreases with the increase in steepness.In the case of large wave steepness, wave height, and ultra-height, the wave power is greater, and the peak vertical velocity will increase at this time, so there is a peak point at the wave steepness of 0.099.

The influence of ultra-height
Figure 10 shows when the ultra-height is relatively large, the structure has relatively little obstruction to the wave, and the influence of slope is relatively small.Due to the overlapping effect of the frame beam on the wave and the weakening of the air layer under the plate, the vertical motion speed may still be large or even peak when the ultra-height is 0.6.The vertical velocity usually peaks twice with the increase of the ultra-height.The first peak point occurs at the small ultra-height (0 or 0.2).The second peak point appears when the ultra-height is relatively large (0.4 or 0.6).In addition, when the period is large and the ultra-height is large, the plate hinders less to the waves, and the wave propagation is mainly affected by the slope.As the water depth becomes smaller, the wave height becomes larger.The wavelength becomes smaller, the wave steepness increases and the vertical velocity gradually becomes larger.
Figure 10.The influence of ultra-height.

The influence of plate width
According to Figure 11, when the plate width is small, and the ultra-height is large, it means that the wave steepness is small, the impact angle is small, and the vertical motion velocity will be increased.When the ultra-high is small, this effect is reduced by the air cushion under the frame structure, so some curves are relatively flat.In general, for the beam-plate structure on a slope, the plate width has a certain influence on the maximum vertical motion speed.As the ultra-height increases, the value of the relative plate width, which corresponds to the peak of the vertical velocity, has the tendency to become smaller.

Statistical relationship between vertical velocity and peak impact pressure
According to the results of numerical simulation, the correlation between the peak impacting P at the bottom of the plate structure and the square 2 V of the vertical velocity of the corresponding measuring point under the action of the regular wave is analyzed.Figure 12 shows the histogram of the statistical distribution given by the frequency of is not very strong.As can be seen from the figure, there is a wide 2 / V P  range of beam-plate structures on a slope, and although there are peaks, they are not very prominent.

Conclusion 1)
The relationship between impact pressure (vertical velocity) and wave steepness is such that the maximum impact pressure peak occurs at low wave steepness.The impact pressure increases significantly with decreasing wave steepness at higher ultra-height, while the corresponding impact pressure changes more slowly with wave steepness at smaller ultra-height.Impact pressure and vertical velocity generally have two peak values.The first peak occurs at a relatively smaller ultraheight.The second peak occurs at higher ultra-height, which is generally larger than the first.The effect of plate width is more pronounced for beam-plate structures on a slope.
2) For the beam-plate structure on a slope, the 2 / V P  distribution range is wide, and the probability of the 2 / V P  statistical value being within 5.0 is greater than 0.60, indicating that the linear correlation between P and 2 V is not strong.

Figure 3 .
Figure 3. Test arrangement of the beam-plate structure on a slope.

Figure 4 .
Figure 4. Calculation meshes of the numerical wave flume and structure.

Figure 5 .
Figure 5.Comparison between calculation and theoretical waveforms.

Figure 6 .
Figure 6.The influence of wave steepness.Figure 7. The influence of ultra-height.

Figure 7 .
Figure 6.The influence of wave steepness.Figure 7. The influence of ultra-height.

Figure 8 .Figure 9 .
Figure 8.The influence of plate width.Figure 9.The influence of wave steepness.

2 V
5.0 is greater than 0.60, indicating that the linear correlation between P and