Three-dimensional numerical simulation of obfique wave action on vertical walls

A three-dimensional numerical model based on the potential theory was developed to study the oblique wave action on vertical walls. A source term inside the domain was used to generate incident waves and outgoing waves were dissipated by sponge layers and transmitted by radiation boundaries. The finite difference method was used to solve the governing equations and boundary conditions in the regular transformed domain in σ-coordinate. Satisfactory agreements between the numerical predictions and experimental results of wave force were obtained. It is concluded that the maximum wave force acting on the vertical walls is induced by the obliquely incident waves rather than the normally incident waves.

Impedance Analytical Method of Wave Run-up and Reflection from A Slotted-Wall Caisson Breakwater

An impedance analytical method （IAM） is developed to study the interaction of plane water wave with a slotted-wall caisson breakwater. The non-linear boundary condition at the slotted-wall is expressed in terms of flow resistance. A set of algebraic expressions are obtained for free surface elevation inside and outside chamber, and reflection coefficient. The prediction of the reflection coefficients shows that the relative widths of the chamber inducing the minimum reflection coefficient for a slotted-wall caisson breakwater are in a range of 0.10～0.20, which are smaller than that （0.15～0.25） for a perforated-wall caisson breakwater. The reflection coefficients and free surface elevation obtained by the present model are compared with that of laboratory experiments carried out by previous researchers.

Oblique Wave Motion over Multiple Submerged Porous Bars near a Vertical Wall

This study examines oblique wave motion over multiple submerged porous bars in front of a vertical wall.Based on linear potential theory,an analytical solution for the present problem is developed using matched eigenfunction expansions.A complex dispersion relation is adopted to describe the wave elevation and energy dissipation over submerged porous bars.In the analytical solution,no limitations on the bar number,bar size,and spacing between adjacent bars are set.The convergence of the analytical solution is satisfactory,and the correctness of the analytical solution is confirmed by an independently developed multi-domain BEM(boundary element method) solution.Numerical examples are presented to examine the reflection and transmission coefficients of porous bars,C_R and C_T,respectively,for engineering applications.The calculation results show that when the sum of widths for all the porous bars is fixed,increasing the bar number can significantly improve the sheltering function of the bars.Increasing the bar height can cause more wave energy dissipation and lower C_R and C_T.The spacing between adjacent bars and the spacing between the last bar and the vertical wall are the key parameters affecting C_R and C_T.The proposed analytical method may be used to analyze the hydrodynamic performance of submerged porous bars in preliminary engineering designs.

The theoretical study on diagonal wave interaction with perforated-wall breakwater with rock fill

The interaction of diagonal waves with perforated-wall breakwater partially filled with rock fill is studied using the linear potential theory. By means of the matched eigenfunction expansion method, an analytical method is presented to calculate the reflection coefficient and the wave force coefficient of the breakwater. The calculated results of the reflection coefficient for limiting cases are the same to the existing results. The main effect factors of the reflection coefficient and the wave force coefficient are analyzed by numerical examples. With the increasing of thickness of rock fill, the wave force coefficient on the perforated wall generally decreases, while the reflection coefficient increases. With the increasing of the incident angle of the wave, the reflection coefficient of the breakwater first decreases, reaches its minimum, and then increases monotonously.

Combined stress waves with phase transition in thin-walled tubes

The incremental constitutive relation and governing equations with combined stresses for phase transition wave propagation in a thin-walled tube are established based on the phase transition criterion considering both the hydrostatic pressure and the deviatoric stress. It is found that the centers of the initial and subsequent phase transition ellipses are shifted along the sigma-axis in the sigma tau-plane due to the tension-compression asymmetry induced by the hydrostatic pressure. The wave solution offers the 'fast' and 'slow' phase transition waves under combined longitudinal and torsional stresses in the phase transition region. The results show some new stress paths and wave structures in a thin-walled tube with phase transition, differing from those of conventional elastic-plastic materials.

Wall Effect of Underwater Explosion Load Based on Wave Motion Theories

Owing to the existence of the flow field boundary, the shock wave load near the boundary is different from the freefield shock wave load. In the present paper, the hull plate load subjected to underwater shock wave is investigated based onwave motion theories; in addition, the experimental study of the hull plate load is carried out. According to the theoreticalanalysis of the hull plate pressure, we find that the hull plate pressure oscillates repeatedly and decays rapidly with timepassing, the maximum hull plate pressure is 2/（1＋n） times the maximum free field pressure, where n is the ratio ofimpedance, and the impulse is much smaller than the free field impulse. Compared with the experimental study, thetheoretical results agree well with the experimental data.

Reflection and Transmission of Regular Waves from/Through Single and Double Perforated Thin Walls

In this paper, reflection and transmission coefficients of regular waves from/through perforated thin walls are investigated. Small scale laboratory tests have been performed in a wave flume firstly with single perforated thin Plexiglas plates of various porosities. The plate is placed perpendicular to the flume with the height from the flume bottom to the position above water surface. With this thin wall in the flume wave overtopping is prohibited and incident waves are able to transmit. The porosities of the walls are achieved by perforating the plates with circular holes. Model settings with double perforated walls parallel to each other forming so called chamber system, have been also examined. Several parameters have been used for correlating the laboratory tests’ results. Experimental data are also compared with results from the numerical model by applying the multi-domain boundary element method （MDBEM） with linear wave theory. Wave energy dissipation due to the perforations of the thin wall has been represented by a simple yet effective porosity parameter in the model. The numerical model with the MDBEM has been further validated against the previously published data.

Motion Characteristics of Cavitation Bubble near the Rigid Wall with the Driving of Acoustic Wave

The dynamics of cavitation bubble is analyzed in the compressible fluid by use of the boundary integral equation considering the compressibility. After the vertical incidence of plane wave to the rigid wall, the motion characteristics of single cavitation bubble near the rigid wall with initial equilibrium state are researched with different parameters. The results show that after the driving of acoustic wave, the cavitation bubble near the rigid wall will expand or contract, and generate the jet pointing to the wall. Also, the existence of the wall will elongate time for one oscillation. With the compressible model, the oscillation amplitude is reduced, as well as the peak value of inner pressure and jet tip velocity. The effect of the wall on oscillation amplitude is limited. However with the increment of initial vertical distance, the effect of wall on the jet velocity is from acceleration to limitation, and finally to acceleration again.

Development of a helicon-wave excited plasma facility with high magnetic field for plasma-wall interactions studies

The high magnetic field helicon experiment system is a helicon wave plasma（HWP）source device in a high axial magnetic field（B0）developed for plasma–wall interactions studies for fusion reactors.This HWP was realized at low pressure（5×10^-3-10 Pa）and a RF（radio frequency,13.56 MHz）power（maximum power of 2 k W）using an internal right helical antenna（5 cm in diameter by 18 cm long）with a maximum B0of 6300 G.Ar HWP with electron density～10^18–10^20m^-3 and electron temperature～4–7 e V was produced at high B0 of 5100 G,with an RF power of 1500 W.Maximum Ar^＋ion flux of 7.8×10^23m^-2s^-1 with a bright blue core plasma was obtained at a high B0 of 2700 G and an RF power of 1500 W without bias.Plasma energy and mass spectrometer studies indicate that Ar^＋ ion-beams of 40.1 eV are formed,which are supersonic（～3.1cs）.The effect of Ar HWP discharge cleaning on the wall conditioning are investigated by using the mass spectrometry.And the consequent plasma parameters will result in favorable wall conditioning with a removal rate of 1.1×10^24N2/m^2 h.

FLEXURAL WAVE DISPERSION IN MULTI-WALLED CARBON NANOTUBES CONVEYING FLUIDS

Motivated by the great potential of carbon nanotubes for developing nanofluidic devices, this paper presents a nonlocal elastic, Timoshenko multi-beam model with the second order of strain gradient taken into consideration and derives the corresponding dispersion relation of flexural wave in multi-walled carbon nanotubes conveying fuids. The study shows that the moving flow reduces the phase velocity of flexural wave of the lowest branch in carbon nanotubes. The phase velocity of flexural wave of the lowest branch decreases with an increase of flow velocity. However, the effects of flow velocity on the other branches of the wave dispersion are not obvious. The effect of microstructure characterized by nonlocal elasticity on the dispersion of flexural wave becomes more and more remarkable with an increase in wave number.

Theoretical Model and Random Simulation for Nonlinear Interaction of Irregular Waves with Vertical Wall

According to the theoretical solutions for the nonlinear three-dimensional gravity surface waves and their interactions with vertical wall previously proposed by the lead author, in this paper an exact second-order random model of the unified wave motion process for nonlinear irregular waves and their interactions with vertical wall in uniform current is formulated, the corresponding theoretical nonlinear spectrum is derived, and the digital simulation model suitable to the use of the FFT (Fast Fourier Transform) algorithm is also given. Simulations of wave surface, wave pressure, total wave pressure and its moment are performed. The probability properties and statistical characteristics of these realizations are tested, which include the verifications of normality for linear process and of non-normality for nonlinear process; the consistencies of the theoretical spectra with simulated ones; the probability properties of apparent characteristics, such as amplitudes, periods, and extremes (maximum and minimum, positive and negative extremes). The statistical analysis and comparisons demonstrate that the proposed theoretical and computing models are realistic and effective, and estimated spectra are in good agreement with the theoretical ones, and the probability properties of the simulated waves are similar to those of the sea waves. At the same time, the simulating computation can be completed rapidly and easily.

Laboratory Study on the Interaction Between Regular Obliquely Incident Waves and Vertical Walls

The characteristics of wave forces are studied based on physical model tests with regular waves. The ratio of obliquely incident wave forces to normally incident wave forces on unit length of a vertical wall is related with various factors. A linear reduction of the mean force of obliquely incident waves is confirmed with an increase in the relative caisson length. Also the characteristics of reflection coefficient of diagonal waves are discussed.

Action of Cnoidal Waves on Vertical Walls

Based on the 2nd order cnoidal wave theory, the characters of shallow water standing waves and their action on vertical walls are studied in this paper. The theoretical expressions of the wave surface elevation in front of and the wave pressure on the vertical wall are obtained. In order to verify the theoretical results, model tests were made in the State Key Laboratory of Coastal and Offshore Engineering at DUT. For the wave surface elevation in front of the wall and the wave forces on the wall at the moment when the wave surface at the wall surface goes down to the bottom of the wave trough, the calculated results coincide quite well with the experimental results. For the wave forces on the wall at the moment when the wave surface at the wall surface goes up to the top of the wave crest, the theoretical expressions are modified by the experimental results. For the convenience of practical use, calculations are made for the wave conditions which usually occur in enginering practice by use of the investigated results obtained in this paper. Empirical formulas are fitted with these calculated results for designers to use.

Wave Forces Acting on Vertical Walls

Regular and irregular wave forces acting on vertical walls are studied by a previously developed numerical model. The computed wave forces are compared with the available experimental data to verify the numerical model, and satisfactory agreements are obtained. The variation of wave forces with incident angles and the shape of simultaneous pressure distribution are investigated, and the comparisons between numerical results and Goda＇ s predictions are also carried out. It is concluded that the maximum wave forces acting on the unit length of vertical wall is often induced by the obliquely incident waves instead of normally incident waves, while Goda＇ s formula may be inapplicable for oblique wave incidence. The shape of simultaneous pressure distribution is not significantly influenced by incident angles, and it can be favorably predicted by Goda＇ s formula. When regular wave heights are taken as the same as irregular wave height H1%, the irregular wave forces Ph. 1% are slightly larger than regular wave forces in most cases.

Calculating Method and Verification of Wave Pressure Distribution on the Breast Wall of Mound Breakwater

In this paper, the calculating charts and formulae about wave pressure on the breast wall are derived with seven parameters on the basis of physical model study. The verification shows that the charts agree with the example, and are adopted in the Specifications of Fishery Harbours Breakwater by the Ministry of Agricultures.

Wave Pressure Distribution over the Breast Wall of Mound Breakwater of Small Ports

In this paper, the mechanism of the interaction between the breast wall of mound breakwater and waves is expounded, then some new views and the law of variation of horizontal and vertical wave pressure over the breast wall are put forward. The results of this study have been adopted in the Specifications of Fishery Harbour Breakwater by the Ministry of Agricultures.

Experimental Study of Sand Bed Configurations in Front of a Vertical Wall Under Wave Action

When a 2-D progressive wave train normally or obliquely approaches a vertical wall and then is normally or obliquely reflected from it, the combination of the approaching and reflected waves may result in a standing wave or a short-crested wave in front of the wall. This paper presents the experimental observations of sand bed configurations under the action of these water waves in front of the wall. The geometry of sand ripples under these water waves in front of the vertical wall is presented as a function of flow parameters, such as the water particle semi-excursion and the mobility number.

Numerical evaluation of passive control of shock wave/boundary layer interaction on NACA0012 airfoil using jagged wall

Shock formation due to flow compressibility and its interaction with boundary layers has adverse effects on aerodynamic characteristics, such as drag increase and flow separation. The objective of this paper is to appraise the practicability of weakening shock waves and, hence, reducing the wave drag in transonic flight regime using a two-dimensional jagged wall and thereby to gain an appropriate jagged wall shape for future empirical study. Different shapes of the jagged wall, including rectangular, circular, and triangular shapes, were employed. The numerical method was validated by experimental and numerical studies involving transonic flow over the NACA0012 airfoil, and the results presented here closely match previous experimental and numerical results. The impact of parameters, including shape and the length-to-spacing ratio of a jagged wall, was studied on aerodynamic forces and flow field. The results revealed that applying a jagged wall method on the upper surface of an airfoil changes the shock structure significantly and disintegrates it, which in turn leads to a decrease in wave drag. It was also found that the maximum drag coefficient decrease of around 17 % occurs with a triangular shape, while the maximum increase in aerodynamic efficiency（lift-to-drag ratio）of around 10 % happens with a rectangular shape at an angle of attack of 2.26？.

Effect of Shock Wave on Fabricated Anti-Blast Wall and Distribution Law Around the Wall Under Near Surface Explosion

The loads of shock wave effect on fabricated anti-blast wall and distribution law around the wall were investigated by using near surface explosion test method and FEM. The pressure-time histories and variety law on the foreside and backside of the anti-blast wall were adopted in the tests of variety of different explosion distances and dynamites, as well as in the comparison between the test and numeri-cal calculation. The test results show that the loads of shock wave effect on the anti-blast wall were es-sen-tially consistent with calculation results using criterion under surface explosion when explosion dis-tances exceed 2 m, the distribution of overpressure behind wall was gained according to variety law based on small-large-small. It is also demonstrated that the peak overpressure behind wall had com-monly appeared in wall height by 1.5—2.5 multiples, and the peak overpressures of protective building behind wall could be reduced effectively by using the fabricated anti-blast wall.

A STUDY ON THE EFFECT OF RADIAL INERTIA ON THE ELASTO-PLASTIC COMBINED STRESS WAVE PROPAGATION IN THIN-WALLED TUBES

An in-depth analysis of propagation characteristics ofelasto-plastic combined stress waves in circular thin-walled tubeshas been made. In obtaining the simple-wave solution, however, mostresearches have ignored the influence of the circumferential stressrelated to the radial inertial ef- fect in the tubes. In this paperthe incremental elasto-plastic constitutive relations which areconve- nient for dynamic numerical analysis are adopted, and thefinite-difference method is used to study the evolution adpropagation of elasto-plastic combined stress waves in a thin-walledtube with the radial inertial effect of the tube considered. Thecalculation results are compared with those obtained when the radialinertial effect is not considered. The calculation results show thatthe radial inertial effect of a tube has a fairly great influence onthe propagation of elasto-plastic combined stress waves.