Boundary Element Method For Flow Research Articles

Numerical investigation of the effects of short-crested irregular waves on the performance of a floating power capture platform

This paper presents a novel power capture platform concept consisting of a semi-submersible platform and multiple point-absorber wave energy converters (WECs). The primary objective of the current study is to investigate the dynamic behavior of the power capture platform under short-crested irregular wave conditions. A spreading function is used to modify the JONSWAP spectrum into a wave spectrum that accounts for both frequency and direction. To ensure the reliability of the numerical analysis, three-dimensional potential flow theory and boundary element method (BEM) are utilized to perform mesh convergence analysis and hydrodynamic validation of the platform and WEC models. Time-domain simulations are conducted to evaluate the effects of wave directionality on the platform motion, mooring line tension, and power absorption of the WEC array. In addition, three models, “single WEC”, “WEC array” and “fixed power capture platform” are defined. The influence of hydrodynamic interactions and platform motion are predicted by comparing the power absorption of individual WEC, WEC row, and WEC array among these models. The results show that the effects of wave directionality on the performance of the floating power capture platform cannot be ignored. The findings of this study may provide some insights into the design of power capture platforms. Meanwhile, it is recommended to determine the wave characteristics of the target operational area in advance, in order to find out the optimal design for system stability and power absorption.

Boundary Element Method for Viscous Flow through Out-phase Slip-patterned Microchannel under the Influence of Inclined Magnetic Field

Abstract In this paper, we investigate the impact of an inclined magnetic field of uniform intensity on viscous, incompressible pressure-driven Stokes flow through a slip-patterned, rectangular microchannel using the boundary element method based on the stream function-vorticity variables approach. The present investigation focuses only on the out-phase slip patterning of the microchannel walls. We address two scenarios of slip patterning, specifically large and fine slip patterning, which are determined by the periodicity of the patterning. We utilized the no-slip and Navier’s slip boundary conditions in an alternative manner on the walls. The Stokes equations govern the viscous flow through a microchannel. We assume a very small magnetic Reynold’s number to eliminate the equation of induced magnetic field in the present study. We analyzed the impact of considered dimensionless hydrodynamic parameters, including the Hartman number (Ha), inclination angle (θ) of the magnetic field, and the slip length (ls ) on fluid dynamics. In the case of fine slip, we observed significant variations in both velocity and pressure gradient, in contrast to large slip patterning. Fine slip patterning significantly increases the shear stress at slip regimes, while large slip periodicity significantly reduces it at no-slip regimes. The present investigation has several notable implications, such as regulation and advancement of mixing and heat transmission within microfluidic systems.

Nonlinear buffeting responses of a coastal long-span bridge under the coupled wind, wave and current loads

The buffeting responses of sea-crossing bridges pose significant challenges due to the diverse terrain in the bridge region and intricate coupling effects between the environmental variables and structures. A novel Wind-Wave-Current-Bridge (WWCB) framework is proposed to assess the buffeting responses of coastal long-span bridges under coupled wind, wave, and current loads. By employing measured wind and wave data, the optimized C-vine copula and Ekman drift current theory are utilized to establish correlations among four environmental variables, namely wind speed, wave height, wave period, and current velocity. The nonlinear wave loads acting on the pile-cap foundations are computed using the potential flow theory and boundary element method (BEM). The interactions among wind, wave, current, and bridge involve both aerodynamic and geometric nonlinearity. The dynamic responses of the full bridge finite element model are iteratively solved until structural convergence is achieved using the Newmark-β method. Subsequently, the buffeting responses and the vibration mechanism of bridges are discussed in both the time and frequency domains. The results indicate that the nonlinear and correlation effects of wind, waves, and currents significantly affect the buffeting responses of the example bridge. Furthermore, the influence mechanism of wind and waves on the sea-crossing bridge is also discussed.

Bubble dynamics in a pressure gradient with reentrant jet break through and energy loss

The dynamics of a bubble in a pressure gradient is investigated experimentally and numerically with particular emphasis on the behavior at reentrant jet impact and break through the opposite side of the bubble with corresponding energy loss and vorticity generation. High speed photography observations of a bubble generated by electric spark energy deposit in a low ambient pressure tank are coupled with wavelet based Optical Flow Velocimetry (wOFV) and Boundary Element Method (BEM) numerical analysis to examine the flow field resulting from the reentrant jet formation and break through. We study, as an illustration, the effects of the constant pressure gradient due to gravity on the bubble dynamics. Energy losses between the first and second cycle are measured for the bubbles generated under various conditions characterized by a non-dimensional pressure gradient parameter, and the corresponding measured energy loss is used in the numerical simulations. Good correspondence is seen between the image analysis, the wOFV computations, and the BEM results and insight is gained on the involved physics.

Dynamic response characteristics of the 67-type railway pontoon bridge

In China at present, the 67-type railway pontoon bridge is part of the main reserve standard equipment that can be utilized for traffic emergency of cross-river bridges. Based on the potential flow theory and boundary element method (the three-dimensional source distribution method), this paper studies the dynamic response characteristics of the 67- type railway pontoon bridge under the action of waves and train loads (the live load of the Chinese Standard-18). First of all, the hydrodynamic characteristics based on application of other computation models applied in relation to floating bridges are compared with the results obtained by the present approach. Secondly, the effects of varying the related wave parameters (i.e. wave period and angle of incidence) on the dynamic response of the 67-type emergency railway pontoon bridge (as installed across the Ji Canal within the Beijing-Shanhaiguan line) are investigated. Finally, the load effects in the girder when this bridge is subjected to the action of various wave and train loads are analyzed. The calculation results indicate that the method proposed in this paper has good generality which enables it to perform a better analysis of the hydrodynamic characteristics of this kind of practical emergency pontoon.Article highlightsResearch on dynamic response for the major railway emergency pontoon in China are carried out;The three-dimensional source distribution method and FEM is adopted;Simulate traffic loads with the live load of the Chinese Standard-18.

Comparison of wave diffraction forces on a surface-piercing body for various free-surface grid update schemes

This study analyzed the difference in wave diffraction force of a surface piercing body according to the grid update scheme of free surface nodes in the time integration process. A two-dimensional fully nonlinear numerical wave tank based on potential flow theory and boundary element method was used for numerical analysis. The MEL (mixed Eulerian–Lagrangian) method was used for free surface node treatment. This method was divided into a semi-Lagrangian approach and a full Lagrangian approach (material node approach).The Runge–Kutta 4th-order integration method was used to integrate the free surface boundary condition temporally. In the internal sub-time step of the time integration process, the frozen coefficient scheme and the full update scheme were used according to the node update scheme, respectively. The vertical diffraction forces of each frequency component for node update schemes were compared. The difference in the 2nd-order vertical forces according to wave frequency, wave steepness, time step interval, and node spacing was investigated. A more precise time-domain numerical analysis method was proposed for high-order external forces in the wave-floating body interaction.

Parametric Hull Form Optimization of Containerships for Minimum Resistance in Calm Water and in Waves

This paper described the process of generating the optimal parametric hull shape with a fully parametric modeling method for three containerships of different sizes. The newly created parametric ship hull was applied to another ship with a similar shape, which greatly saved time cost. A process of selecting design variables was developed, and during this process, the influence of these variables on calm water resistance was analyzed. After we obtained the optimal hulls, the wave added resistance and motions of original hulls and optimal hulls in regular head waves were analyzed and compared with experimental results. Computations of the flow around the hulls were obtained from a validated nonlinear potential flow boundary element method. Using the multi-objective optimization algorithm, surrogate-based global optimization (SBGO) reduced the computational effort. Compared with the original hull, wave resistance of the optimal hulls was significantly reduced for the two larger ships at Froude numbers corresponding to their design speeds. Optimizing the hull of the containerships slightly reduced their wave added resistance and total resistance in regular head waves, while optimization of their hulls hardly affected wave-induced motions.

Numerical calculation and model experiment of a novel external buoy type wave energy converter for navigation lighted buoys numerical study of a novel wave energy converter

A novel external buoy type wave energy device with hydraulic conversion system used for navigation lighted buoys, named floating external double buoys wave energy device, is put forward and investigated by numerical calculations and model experiments. The hydrodynamic performance of the device under regular waves is numerically calculated based on linear potential flow theory and boundary element method. The generalized modal method is used to solve the hydrodynamic problems of multi-buoy with hinged constraints. The model experiments are carried out in a 2D wave tank with a depth of 0.9 m. The wave height is set to 1/40 of the wavelength. The influence of wave period and damping loads on the hydrodynamic performance of the device is tested. The results of numerical calculations and model experiments have shown that the appropriate selection of hydraulic damping coefficient is of great significance to improve the capture width ratio of the device, and this device has good capture performance in a certain wave range, and it is expected to effectively solve the problem of continuous power supply for middle and small types of navigation lighted buoys.

Added resistance, heave and pitch for the KVLCC2 tanker using a fully nonlinear unsteady potential flow boundary element method

In this paper, a fully nonlinear unsteady potential flow method is used to predict added resistance, heave and pitch for the KVLCC2 hull in regular head waves at design speed. The method presents a nonlinear decomposition of the velocity potential and the wave field and an adaptive grid refinement. A formulation for the acceleration potential is used to obtain the pressure. To improve computational efficiency, a Barnes-Hut algorithm is introduced. A grid dependency study and a study on the impact of different time steps on the solution are performed. Numerical results have been compared with experimental data for the design speed. A general good agreement is found for added resistance, especially for longer waves. Heave and pitch are properly computed for all wave lengths in the range λ/Lpp=0.4 to 1.4.

Numerical analysis of the bubble-particle interaction in an acoustic field

Features of the interaction of a bubble and a solid spherical particle in the presence of an acoustic field in the three-dimensional case are numerically studied using the boundary element method for potential flow. Multiparametric calculations are presented and dependences of the change in the volume of the bubble, dynamics of the mass center of the bubble and particle on the distance between the objects and their sizes are constructed. It is shown that during the bubble expansion, the particle repels from it, and during the bubble shrinkage it is attracted, the size of the particle determines its mobility. On average, over five periods of acoustic field oscillations, the distance between the objects decreases, which is due to the translational motion of the bubble in the compression phase. The features of the deformation of a bubble located near a solid spherical particle with small amplitudes of the acoustic field are studied.

Noise Analysis for Large Silencers of Ships and Off-shore Plants using Energy Flow Analysis

In the study, energy flow analysis is performed to predict the performance of silencers. To date, deterministic approaches such as finite element method have been widely used for silencer analysis. However, they have limitations in analyzing large structures and mid-high frequency ranges due to unreasonable computational costs and errors. However, silencers used for ships and off-shore plants are much larger than those used in other engineering fields. Hence, energy governing equation, which is significantly efficient for systems with high modal density, is solved for silencers in ships and off-shore plants. The silencer is divided into two different acoustic media, air and absorption materials. The discontinuity of energy density at interfaces is solved via hypersingular integrals for the 3-D modified Helmholtz equation to analyze multi-domain problems with the energy flow boundary element method. The method is verified by comparing the measurements and analysis results for ship silencers over mid–high frequency ranges. The comparisons confirm good agreement between the measurement and analysis results. We confirm that the applied analysis method is useful for large silencers in mid-high frequency ranges. With the proven procedures, energy flow analysis can be performed for various types of silencer used in ships and off-shore plants in the first stage of the design.

The steering and course keeping qualities of high-speed craft and the inception of dynamic instabilities in the following sea

Small high-speed craft are the most vulnerable to the severity of the sea: achieving a design which pairs good performance and acceptable levels of safety is not a trivial task. The seakeeping and manoeuvrability of these vessels play a crucial role in following sea conditions: dynamic instabilities, namely broaching-to and surf-riding, are more than a rare eventuality and threaten the survivability of the vessel and the life of the mariners. This study investigates the effects of the steering qualities on the broaching-to behaviour of a high-speed craft when it is sailing in following and stern-quartering waves.The motions and loads of the vessel are simulated by means of a 3D time domain blended potential flow boundary element method (BEM), validated using captive model tests in regular waves carried out at the Seakeeping and Manoeuvring Basin (SMB) of MARIN. The hull directional stability and turning ability of the high-speed craft were artificially modified, showing that an increase in the directional stability as well as in the effectiveness of the steering can be beneficial to avoid the inception of broaching-to, but they have different consequences on the dynamics of the vessel's loss of control.

Hydrodynamic optimisation of a multi-purpose wind offshore supply vessel

ABSTRACTThe aim of this study was to reduce the total resistance of a multi-purpose wind offshore supply vessel by optimising its hull. Resistance was computed using a potential flow boundary element method and a Reynolds-averaged Navier–Stokes equations solver. Optimised hull forms were obtained for the ship advancing at different ship speeds under calm water conditions, employing the two multi-objective optimisation algorithms, Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-Objective Simulated Annealing (MOSA). Using NSGA-II yielded slightly larger reductions of total resistances than MOSA. The greatest reductions were achieved at ship speeds between 11 and 14knots. At these speeds, a thinner and longer bulbous bow reduced resistance. At speeds greater than 15knots, a bloated bulbous bow was more helpful to reduce resistance.

Numerical research on time domain ship motions coupled with sloshing at different liquid levels and forward speeds

In the present study, an reasonable numerical method based on the potential flow theory and boundary element method (BEM) for solving time domain ship motion coupling with sloshing is proposed. Ship motion is solved based on the three dimensional (3D) time domain potential flow theory with forward speed using the BEM. The 3D fully nonlinear time domain potential flow theory and BEM are also adopted to simulate the nonlinear sloshing phenomenon and then numerically coupled with ship motion in a same time step. A corresponding parallel numerical solver is also developed to investigate the coupling effects between 6 degrees of freedom (DOF) ship motion and internal sloshing. To validate the numerical solver and better understand these coupling effects, numerical research on liquid level and forward speed effects is conducted. The developed numerical solver is also validated from previous model experimental results. Computational and experimental results of ship motion response amplitude operators (RAOs) are in reasonable agreement for both 15000 GT and S175 models with liquid tank. The natural frequency of sloshing varies with changes in liquid levels, and coupling effects become more obvious when the natural frequency of sloshing is close to excited frequency of a ship. Our accurate numerical results on the liquid level effects of roll motions indicate that the numerical method proposed can solve the engineering problem related to liquefied natural gas (LNG) and liquefied petroleum gas (LPG) ships traveling through ocean waves. The numerical behavior of a coupling system with forward speed shows that a liquid tank can reduces the resonance frequency of roll motion and has a limited effect on pitch motion. However, as forward speeds increase, such effects follow a gradually increasing trend.

An Improved Numerical Computation of Hull Pressure Fluctuations Due to Unsteady Sheet Cavitation of a Propeller

An operating propeller is the main source of vibration on the ship hull, especially on the stern. In this article, an improved numerical scheme is presented to predict the pressure fluctuations on the ship hull due to the unsteady sheet cavitation of a propeller. The calculated results are compared with the published results and experimental data carried out in the hydrodynamics and cavitation tunnel of Hamburgische Schiffbau-Versuchsanstalt to verify the improvement. The present method is based on a two-cycle iterating scheme which satisfies the boundary integral equation in time domain. The hull pressure fluctuations calculated by the first-cycle iterations are treated as the initial values for the second-cycle iterations. The solid angles of the elements will deviate from the standard value, .5, as the dramatic variation in geometry appears, and accumulate numerical errors in the calculating process. During the second-cycle iterations, a filter based on the solid angles on hull elements is proposed to minimize the iterating error. A container ship is treated as the computing sample in this study, and evidence is offered regarding the 16% improvement achieved by the present method. 1. Introduction A propeller operating in a nonuniform wake field in the ocean is one of the prime sources of vibration and noise affecting the ship. The prediction of hull pressure fluctuations caused by propellers is an important consideration for many vessels and worthy of being researched. Hull pressure fluctuation caused by the marine propeller has been widely investigated since the 1980s. Huse and Guoqiang (1982) developed a semi-empirical prediction method, in which the cavitation volume on the propeller blade surface can be estimated using experimental data. Breslin et al. (1982) proposed a model based on the potential flow theory, which simulates the ship hull by means of a simple panel method and the propeller by means of a lifting surface vortex lattice method. Kinns and Bloor (2004) used an acoustic boundary element (BE) model to simplify the problem of hull vibration excitation due to propeller sources and dipoles. The convergence of results for a cruise liner model was demonstrated with different element distributions. Kehr and Kao (2004) derived the incident blade rate pressure induced by unsteady sheet cavitation (monopole) and unsteady forces (dipole) of an operating propeller, for calculating the hull pressure fluctuations. Brouwer (2005) applied a stationary set of rings of monopole and dipole sources in the frequency domain to solve the propeller-induced noise and vibrations. Lee et al. (2006) integrated computational fluid dynamics (CFD) and the finite difference method for the computation of propeller-induced hull vibration. It was recommended that the phase difference of the propeller-induced pressure should be considered for preventing overprediction. Kao and Kehr (2006) developed a time domain iteration method to calculate the hull pressure fluctuations induced by the operating propeller. The phase difference is included in the iterating scheme, and the computation is robustly convergent. Seol and Moon (2009) derived the governing equation of pressure fluctuation induced by sheet cavitation according to the Ffowcs Williams approach. In the study by van Wijngaarden (2011), a potential flow boundary element method (BEM) with measured hull pressure data as input was applied to solve the hull pressure fluctuations, and the model experiments were also carried out. It was concluded that the computed hull pressure fluctuations due to non-cavitating propellers is reasonably accurate compared with the experimental data. Kehr and Kao (2011) calculated the pressure fluctuations on ship hull due to propeller sheet cavitation by using the method presented in Kao and Kehr (2006). The numerical result is higher than the experimental data provided by the hydrodynamics and cavitation tunnel (HYKAT) of HSVA (Wiemer 1999) by approximately 27%. The pressure fluctuations on ship stern induced by cavitating propellers were solved by Kanemaru and Ando (2011) with a surface panel method. The maximum amplitude appears in the first blade frequency and overestimates the experimental data by about 30%. Kim et al. (2012) predicted the hull pressure fluctuations induced by marine propeller sheet cavitation, and the Doppler effect was considered at the same time. Wei and Wang (2013) employed CFD to simulate the propulsion of a submarine. The finite element method and BEM were then combined to solve the submarine's structure and acoustic responses under the propeller excitations. The matched-field inversion technique applied in Lee et al. (2014) uses the fluctuating hull pressure field measured by receivers and the acoustic field calculated by BEM to define the sheet cavitation noise, source strengths, source positions, and number of sources. The equivalent source model for the propeller can result in more accurately extrapolated hull pressure distribution. In Wei et al. (2016), the unsteady forces of a submarine propeller were predicted by CFD, and the hull pressure fluctuations due to the non-cavitation propeller were calculated by the method proposed in Kao and Kehr (2006).

Hydrodynamic Coefficients for a 3-D Uniform Flexible Barge Using Weakly Compressible Smoothed Particle Hydrodynamics

The numerical modelling of the interactions between water waves and floating structures is significant for different areas of the marine sector, especially seakeeping and prediction of wave-induced loads. Seakeeping analysis involving severe flow fluctuations is still quite challenging even for the conventional RANS method. Particle method has been viewed as alternative for such analysis especially those involving deformable boundary, wave breaking and fluid fragmentation around hull shapes. In this paper, the weakly compressible smoothed particle hydrodynamics (WCSPH), a fully Lagrangian particle method, is applied to simulate the symmetric radiation problem for a stationary barge treated as a flexible body. This is carried out by imposing prescribed forced simple harmonic oscillations in heave, pitch and the two- and three-node distortion modes. The resultant, radiation force predictions, namely added mass and fluid damping coefficients, are compared with results from 3-D potential flow boundary element method and 3-D RANS CFD predictions, in order to verify the adopted modelling techniques for WCSPH. WCSPH were found to be in agreement with most results and could predict the fluid actions equally well in most cases.

Formulae for predicting non-acoustical parameters of deformed fibrous porous materials.

Formulae to predict non-acoustical parameters (i.e., flow resistivity, tortuosity, and viscous and thermal characteristic lengths) of deformed fibrous porous materials are proposed provided that the original values of these parameters are known in advance. These formulae are developed using numerical fluid analyses. The flow resistivity was calculated by using the finite element method for a two-dimensional incompressible viscous fluid approximated by Oseen flow. The tortuosity and characteristic lengths were calculated by using the complex variable boundary element method for a two-dimensional potential flow. These calculations showed that the flow resistivity was inversely proportional to the porosity multiplied by the three-halves power of the compression ratio, that the tortuosity can be represented by a linear expression of the porosity, and that both characteristic lengths changed in the same manner with respect to the porosity. These tendencies agreed well with measurements of real glass wools of various bulk densities. The proposed prediction formulae for the parameters were then derived from the tendencies obtained from the numerical analyses. The predicted parameter values were compared with the calculated parameters and good agreement was obtained, confirming the validity of the proposed formulae.

The Galerkin boundary element method for transient Stokes flow

Since the fundamental solution for transient Stokes flow in three dimensions is complicated it is difficult to implement discretization methods for boundary integral formulations. We derive a representation of the Stokeslet and stresslet in terms of incomplete gamma functions and investigate the nature of the singularity of the single- and double layer potentials. Further, we give analytical formulas for the time integration and develop Galerkin schemes with tensor product piecewise polynomial ansatz functions. Numerical results demonstrate optimal convergence rates.

Energy flow models for underwater radiation noise prediction in medium-to-high-frequency ranges

Energy flow analysis is studied as a promising tool for the noise and vibration analysis of system structures in medium-to-high-frequency ranges. The energy flow finite element method, combining energy flow analysis with the finite element method, is efficient for the vibration analysis of a built-up structure, and the energy flow boundary element method, combining energy flow analysis with the boundary element method, is useful for predicting the noise level of a vibrating complex structure. In this article, the energy flow finite element/energy flow boundary element method and semi-coupling relationships are used to investigate the vibration and radiation noise of a reinforced cylindrical structure in water. Energy flow finite element method is employed to analyze the vibrational responses of the reinforced cylindrical structure, considering fluid loading effects, and energy flow boundary element method is applied to analyze the underwater radiation noise. Therefore, the energy flow coupling relationship of structure-to-acoustic space is used to link the energy flow finite element/energy flow boundary element methods together. The vibrational energy of the structure is treated as an acoustic intensity boundary condition of energy flow boundary element method to calculate underwater radiation noise. Numerical simulations are presented and the results are compared with experimental measurements for the reinforced cylindrical structure in water.

Development of a noise prediction software NASEFA and its application in medium-to-high frequency ranges

For the analysis of noise problems in medium-to-high frequency ranges, the energy flow boundary element method (EFBEM) has been studied. EFBEM is numerical analysis method of energy flow analysis (EFA), and solves energy governing equations using a boundary element method in complex structures. Based on EFBEM, a noise prediction software, “noise analysis system by energy flow analysis” (NASEFA), was developed. For effective maintenance, NASEFA is composed of three main modules: the translator, the model converter, and the main solver. The translator changes the FE model to the NASEFA BE model, and the model converter changes the BE model to an EFBE model, including various data, such as structural materials, medium properties, sources, and boundary conditions. NASEFA then solves the acoustic energy density and intensity on boundary and in the field. Moreover, it analyzes interior and exterior noise problems for single and multiple domains in two and three dimensions. Finally, for the validation of the software developed, interior and exterior noise predictions of various structures were performed. The results obtained with NASEFA were compared with those of the commercial SEA program and experiment. From these comparative studies, the usefulness of NASEFA was established.