Simulation of Irregular Wave Impact on Horizontal Plate Structures

JIN Feng

(Naval Architecture and Ocean Engineering Department,Jiangsu University of Science and Technology,Zhenjiang 212003,China)

Simulation of Irregular Wave Impact on Horizontal Plate Structures

JIN Feng

(Naval Architecture and Ocean Engineering Department,Jiangsu University of Science and Technology,Zhenjiang 212003,China)

Using numerical simulation method,two-dimensional irregular wave numerical models were established based on the software FLUENT,then the mechanism of wave impact on horizontal plate structures was explored.RANS equations and standard k-ε equations were adopted in the models. VOF method was used to reconstruct the free surface.Through the process of wave slamming on horizontal plate structures,the models were verified by experimental data and the wave impact process could be displayed visually.With calculations and analysis,the characteristics of impact pressure and flow field during the process of wave impact were investigated,and the distribution rules of the impact pressure and flow field were obtained.The parametric studies were carried out for different wave steepness,relative clearances and relative structure widths,and the influences of the three parameters on the impact pressure and flow field were analyzed.Finally,the statistical relationship between the wave impact pressures and corresponding vertical velocities of fluid was analyzed,and the pressure formulas were improved based on the original calculation formulas of Hohai University.The results indicate that the peak impact pressure is proportional to the square of the corresponding vertical velocity and the revised formula is more reasonable and feasible.The work is significant for accurately predicting impact load and mastering more impact mechanism.

irregular wave;horizontal plate structure;wave slamming; numerical simulation;FLUENT

0 Introduction

Determination of wave impact load is the most important issue for coastal and offshore engineering design,which directly affects the elevation of superstructure and further influences the cost and safety.About this problem,many studies were conducted and some wave impact load formulas were developed.Most of them adopted the semi-empirical and semi-theoretical method which was used to establish mathematical model with some basic suppositions to derive the empirical formulas and then to determine the coefficients in the formulas with experiment.Wang(1970)[1]put forward the impact pressure formulas with the momentum and airytheories.China National Harbor and Wharf Design Manual(1975)[2]provided the load formulas in which the pressure correction coefficient was supposed as a constant.Guo and Cai(1980)[3]took relative clearance of structures and wave surface height as the main factors to obtain the formulas.Wang and Ren(2002;2003)[4-5]through physical model tests developed the calculation methods for different plate structures.Bradner(2008)[6]carried out a series of tests and developed the formulas to determine the vertical force and horizontal force impacting on bridge structures.Chen et al(2009;2010)[7-8]studied the impact load on high-pile wharf structures under various situations and obtained corresponding formulas.Due to factors taken into account in each formula were not identical,the results of all existing empirical formulas presented great difference.In addition,the current test equipment and conditions still exist restrictions,for example the sampling frequency is lower so that the peak values during wave action can not be exactly obtained,therefore the results from tests are necessary to be verified and improved with other methods.

With the development of computer and numerical calculation technique,numerical simulation has become another important method to study the problem of wave action.Comparing with physical model test,numerical simulation has many advantages such as the less investment,the short period and the easy changing of parameters.It overcomes a certain limitations of physical model test and gradually is taken as an effective method to study the wave slamming problems.The two methods also can be verified and complemented each other.So we should make full use of advantages of numerical simulation and take further researches to deeply understand the characteristics in the process of the wave slamming on the structures.

This paper mainly used the method of numerical simulation,and combined with physical model test results of Chen et al(2009)[9]in the analysis.Two-dimensional irregular wave numerical models were established based on the software FLUENT and the process of wave slamming on horizontal plate structures was reproduced.In the simulation,the higher sampling frequency was adopted to get the peak values during wave slamming,the fluid vertical velocity under structures was taken as another important parameter into study.At last,the impact pressure formulas in Chen et al(2009)were improved and the statistical relationship between the wave impact pressures and corresponding vertical velocities of fluid was given.The work is significant for accurately predicting impact load and mastering more impact mechanism.

1 Original calculation formulas

In recent years,based on the scientific research projects,Chen et al(2009)carried out physical model tests of wave slamming on different types of high-pile wharves,and developed the formulas of wave peak impact pressures under structures,part of which had been included in the national new standards(2013).During their data analysis,the envelope curve fitting method with 90%assurance was adopted to make structures safe.

Wherein,the irregular wave impact pressure on horizontal plate structures can be calcu-lated as follows:

where H is the wave height,L is the wave length,d is the water depth,ch is the hyperbolic cosine,sh is the hyperbolic sine.

2 Establishment and validation of numerical wave flume

2.1 Governing equations

During wave impact,the fluid is in turbulent motion and the turbulence effect cannot be neglected in wave breaking models.Therefore,the Reynolds Equations are used to solve the fluid flow and a k-ε model is used to close the Reynolds equations.The VOF method is used to track the free surface.

The continuity equation and the RANS equations are as follows:

where i=1,2,j=1,2,uiis the velocity vector of flow,ρ is the fluid density,t is the time,μ is the dynamic viscosity,fiis the volume force of fluid,and Fiis the additional source term.

2.2 Boundary conditions

The tank parameters of numerical model and physical model test are consistent.The computation domain is showed in Fig.1.The left,the right and the downside boundaries of the tank are the wall,the upside is the pressure inlet boundary.The length of the tank is 45 m,the water depth is 0.5 m.After the tank grid setting,the one unit width under static level of the left side is taken as the wave generation zone.The 10 m length of the right side is the wave absorbing zone.The thickness of the horizontal plate structure is 0.015 m and its length is 1.02 m.In the structure,20 measuring points are distributed horizontally,the space between adjacent points is 0.05 m,and the space on one end of the plate is 0.035 m.The test sampling frequency is nearly 300 Hz.The maximum simulation sampling frequency is 2 000 Hz so as to obtain the exact peak values.

Fig.1 Schematic diagram of computation domain

2.2.1 Wave generation

JONSWAP spectrum is chosen as the irregular wave spectrum.Quality source method is used to generate needed wave.In this wave generation method,a kind of source term is added to the continuity equation,and for two-dimensional problems,the continuous equations should be written as:

where S（ x,y,t）is the source term,S（ y,t）is the wave strength at wave generation position x=xs,S（ y,t）=0 outside wave generation position.

Depending on Eq.(5),the momentum equations become

Because the arrangement of wave generation domain is along the water depth direction, two and opposite direction wave propagation would be produced,so

2.2.2 Wave absorbing

Wave absorbing uses the porous media model introduced by Dong(2009)[11].The model dissipates the wave energy by adding an attenuate source in the RANS equations.

The attenuate source can be expressed as:

2.3 Tank grid setting

The mesh created for the computational model is a structured quadrilateral mesh with a higher concentration of cells at the structure’s location and zone of wave height.

The basic mesh structure is shown in Fig.2.In the x-direction the mesh expands 60-100 cells for each wavelength from the left boundary to the right boundary,and a mesh of 30 cells is used at the structure’s location.In the y-direction the mesh expands at a rate of 1.03 to the upper and lower boundary from corresponding borderlines,and a mesh of 10-20 cells is used at the zone of wave height.

Fig.2 Calculation meshes

2.4 Mathematical model validation

Fig.3 Comparison of numerical spectra and theoretical spectra

Using the established mathematical models,a few typical cases of wave slamming on horizontal plate structures are reproduced.Fig.4 shows the impact pressure time history on the structures in one typical case(using the data of leftside measuring-point and the same below). t is the time,p is the impact pressure.It indicates that the simulation and the experiment curves are similar,the peak impact pressure changes irregularly and it is a random process. Tab.1 shows the most comparison results of simulation and experiment.In the table for each case the test repeats one time and the eigen values are calculated through the pressure peak values of successive 12 wave periods.Except the maximum value,the average peak value,the 1/3 average peak value and 1/2 average peak value are relatively stable so the 1/3 average peak value is taken as the eigen value to analyze the characteristics of impact.Hereinafter it refers to as peak impact pressure.

Fig.4 Impact pressure time history of the structures in one typical case

More extensive validation work is carried out.Figs.5 and 6 show the comparison of simulation and experiment results about peak impact pressure and its distribution under situations.Simulation values often present a little larger.The reasons are that the maximum sampling frequencies of simulation and experiment are different,and the simulation’s is much higher so as to catch the accurate instant slamming pressures.Through the comparisons above, it shows that the wave tank can work well to simulate the wave slamming.

Fig.5 Comparison of simulation and experiment results about peak impact pressure distribution

Fig.6 Comparison of simulation and experiment results about peak impact pressure

3 Simulations of wave impact

3.1 Distribution of peak impact pressure

The distributions of peak impact pressure under various wave heights,clearances and periods are presented in Figs.7-9.The ordinate represents the impact pressure or relative impact pressure,the abscissa represents the distance of measuring point away from plane leftside,0 represents the plane leftside.

The figures show that the impact pressure distribution is similar under different wave height conditions.The increasing range of the impact pressure is nearly corresponding to the height values.It is the same to the different clearance conditions,moreover the even distribution generally happens in the middle of the structures.When wave period is relatively small, the maximum impact pressure happens in the foreside of the structures,and when the period gradually increases,the maximum impact pressures will move to the tail.

Fig.7 Influence of wave height on distribution of peak impact pressure

Fig.8 Influence of clearance on distribution of peak impact pressure

Fig.9 Influence of wave period on distribution of peak impact pressure

3.2 Characteristics of peak impact pressure

The influences of wave steepness on peak impact pressure are presented in Fig.10.In most simulation groups,when the wave steepness exceeds a certain value,the relative impact pressure decreases with steepness increasing,when the wave steepness is less than this value,the relative impact pressure decreases with the steepness decrease.

Fig.10 Relationship between peak impact pressure and wave steepness

The influence of relative clearance on peak impact pressure is presented in Fig.11.The relative clearances corresponding to the maximum impact pressures are generally below 0.3.With the same wave period,as the wave height is larger,the relative clearances corresponding to the maximum impact pressures are generally larger.Structure clearance and wave steepness are associated which affect the wave impact angle size.It causes when wave height is very small(H=5 cm),the maximum impact pressure does not appear in the minimum relative clearance,but appears in values 0.1-0.2.

Fig.11 Relationship between peak impact pressure and relative clearance

The influence of relative structure width on peak impact pressure is presented in Fig.12,L is the wave length,B is the longitudinal structure width. With the increase of relative structure width,the relative impact pressure trends to increase.The maximum impact pressures often appear in the middle position(about values 2-3)of curves.

3.3 Peak impact pressure formula

According to the simulation results and experimental data of Hohai University,using the same envelope method shown in Fig.13,the peak impact pressure formula is improved as follows:

Fig.12 Relationship between peak impact pressure and relative structure width

Fig.13 Peak impact pressure enveloping curve

Viewed from above,the maximum relative impact pressure of original envelope curve generally occurs between longitudinal coordinate values 2.0-2.5,the maximum of new envelope curve occurs between values 2.5-3.0 and the corresponding relative clearance occurs between values 0.3-0.4.For original envelope curve, a few data can not be included which indicates the original formula is not completely applicable and its result is less.The new envelope curve contains the majority of physics experiment and numerical data,and the improved formula should be more reasonable.

4 Simulations of fluid flow

4.1 Distribution of vertical velocities

The 1/3 average peak value is also taken as the eigen value to analyze the fluid flow.The distributions of the vertical velocities under various wave heights,clearances and wave periods are presented in Figs.14-16.The vertical velocity distributions are similar under different wave height conditions.The increasing range of vertical velocities is nearly corresponding to the wave height values.Under different clearances,at head and tail ends of structures the velocities increase rapidly.Under different wave period, the maximum velocities happen in the foreside or afterside of the structures,and in the middle the distribution is uniform and wide.

4.2 Characteristics of vertical velocities

Fig.17 shows the characteristics of vertical velocities under various wave steepness. When the wave steepness is greater or less than a certain value,the vertical velocities decrease from this value with the variation of wave steepness.

Fig.14 Distribution of vertical velocities on subface of structure

Fig.15 Distribution of vertical velocities on subface of structure

Fig.16 Distribution of vertical velocities on subface of structure

Fig.17 Relationship between vertical velocities and wave steepness

Fig.18 shows the characteristics of vertical velocities under various relative clearance. For the curves,the relative clearance valuescorresponding to the maximum vertical velocities are generally below 0.3,and mostly locate in 0.2.With the same period,it is often that the higher wave height and the maximum vertical velocity happen at the larger relative clearance.

Fig.18 Relationship between vertical velocities and relative clearance

Fig.19 shows the characteristics of vertical velocities under various structure width.For different relative clearances,the influence of relative structure width on the vertical velocities is less.In general,with the increasing of relative structure width,the curves of the vertical velocities have a certain trend to increase.

Fig.19 Relationship between vertical velocities and relative structure width

4.3 Statistical relationship between peak impact pressures and corresponding vertical velocities

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Based on numerical simulation results,the relationship between the peak impact pressure P and the square of corresponding vertical velocity V2can be statistic.Fig.20 shows the value histograms of P/ρV2appearance frequency,wherein kPa is the pressure unit, m/s is the unit of speed,ρ is the density of water.The longitudinal coordinate shows the statistical appearance amount.Through analysis the maximum appearance frequency is about value 0.1,the probability that P/ρV2value is located between 0.05-0.15 is greater than 0.75.It shows that in most cases the peak impact pressure P under structures can be counted as 0.05-0.15ρV2.

Fig.20 Statistical distribution histogram for P/ρV2

5 Conclusions

Numerical simulation method was mainly used,and combined with physical experiment data,the irregular waves impacting on Horizontal Plate Structures were studied.The distribution of peak impact pressure and vertical velocities under structures were analyzed.The influence of each factor including wave steepness,clearance and structure width on peak impact pressure and vertical velocities was studied.The statistical relationship between peak impact pressure and vertical velocities was proposed.The improved formula of the peak impact pressure was put forward.The main conclusions are as follows:

(1)Under different wave heights,the increasing range of peak impact pressure and vertical velocities is nearly corresponding to the wave height values.Under different clearances,the even distribution generally happens in the middle of the structures.Under different wave periods,the maximum values often happen in the foreside or afterside of the structures.

(2)When the wave steepness is greater or less than a certain value,the peak impact pressures and vertical velocities decrease from this value with the variation of wave steepness. The relative clearances corresponding to the peak impact pressures and vertical velocities are generally below 0.3.With the increase of relative structure width,the relative impact pressures and vertical velocities trend to increase.

(3)Combined with numerical simulation and experimental results,the original peak impact pressure formula of Hohai University was revised.The calculated value with the original formula was smaller in some cases so it was not fully applicable,and the revised formula was proved more reasonable and feasible.

(4)The characteristics of peak impact pressure and flow field were explored,the relationship between the peak impact pressure and the flow field was presented.For irregular wave, the peak impact pressure P was about 0.05-0.15 ρV2.

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不规则波对平板冲击作用数值模拟研究

金凤
（江苏科技大学船舶与海洋工程学院，江苏镇江212003）

文章采用数值模拟方法，建立了基于FLUENT软件的二维不规则波浪数值模型，探讨了波浪对水平板结构的作用机理。模型中采用RANS方程和标准k-ε方程，采用VOF方法重建自由液面。通过数值模拟复演了波浪冲击水平板结构的过程，将数值模拟结果与实验数据进行比较，验证了模型的可靠性。经过计算和分析，研究了波浪冲击平板过程中的冲击压力和流场特性，得到了冲击压力和流场的分布规律。分析了波陡，净空及板宽等参数对冲击压力和流场的影响。最后，给出了波浪冲击压力与相应水质点垂直速度间的统计关系，并对河海大学原有冲击压力的计算公式进行了改进，提出了新的冲击压力公式。研究结果表明：冲击压力峰值与相应的水质点垂直速度的平方成正比，修正后的冲击压力公式更为合理、可行。论文工作将对准确预测冲击载荷，掌握更多的冲击机理具有重要意义。

不规则波；平板结构；波浪冲击；数值模拟；FLUENT

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金凤（1980-），女，博士，江苏科技大学船舶与海洋工程学院副教授。

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10.3969/j.issn.1007-7294.2017.06.005

1007-7294（2017）06-0698-13

date：2017-03-22

Supported by the Doctor Science Foundation of Jiangsu University of Science and Technology(Grant No.1012921415)

Biography：JIN Feng(1980-),female,lecturer,E-mail:jflook@126.com.