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A mathematical method is presented for time-domain simulation of coupled heave, pitch, and roll motions of a planing hull. This method is introduced by using 2D+t theory and employs potential field related to hydrodynamic impact o...
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A mathematical method is presented for time-domain simulation of coupled heave, pitch, and roll motions of a planing hull. This method is introduced by using 2D+t theory and employs potential field related to hydrodynamic impact of an asymmetric wedge with roll speed to solve four relations for the involved added masses in the motion. Momentum variation of the derived added mass terms is used to compute 2D normal force and roll moment. Two-dimensional hydrostatic moment and moment due to hydrodynamic forces are taken into consideration and time derivative of the wetted half-beam is determined by using the roll speed. Three-dimensional forces are computed by integrating the 2D forces over the length of the boat and new added mass terms are derived for the coupled heave, pitch, and roll motions. Ultimately, a nonlinear system of equations for the motion is presented by putting the forces together. Validity of the proposed method is assessed using an extensive set of test cases, which are conducted in four steps. Predicting coupled heave and pitch motions without roll motion, dynamic response of a 2D wedge due to asymmetric impact, computing the hydrodynamic coefficients in coupled heave and roll motions, and predicting roll motion of a planing boat due to a forced pitch motion are involved in the validation steps, respectively. Results of the first three steps are compared against experimental results, while the results of the last step are compared against the results of previously published simulations. Favorable agreement has been displayed between the obtained results and the available data in all of these steps. Finally, the proposed method is used to investigate the effects of the roll motion on the heave and pitch motions of planing hulls. Based on the obtained results, amplitudes of the heave and pitch motions exhibit an increase when the boat is free of roll which is due to an increase in the exciting force, accelerations, and reduction of heave and pitch added masses in this situation.
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Current paper deals with hydroelastic impact of asymmetric and symmetric wedge sections with oblique speed into calm water. It is aimed to provide a better insight regarding fluid–structure interaction of the wedge sections of a ...
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Current paper deals with hydroelastic impact of asymmetric and symmetric wedge sections with oblique speed into calm water. It is aimed to provide a better insight regarding fluid–structure interaction of the wedge sections of a high-speed craft into water in more realistic condition, in the presence of heel angle and oblique speeds. The defined problem is numerically investigated by coupled Finite Volume Method and Finite Element Method under two-way approach consideration. Accuracy of the proposed model is assessed in different steps. The results of current method are compared against previous experimental, numerical and theoretical methods and good agreement is displayed in these comparisons. Subsequently, the method is used in order to examine the fluid and structure behavior during the elastic impact of the wedge into water. Accordingly, four different physical situations are simulated. In the first part, symmetric impact with no oblique speed is simulated. The results of this part show fluctuations in vertical force and pressure of the midpoint during the impact time. Also, the relation of deadrise with deflection and pressure is observed in this part. In the second part, heel angle is also taken into consideration. It is concluded that the pressure and deflections at the right side of the wedge reduce, but these parameters increase at the left side. Moreover, it is observed that, the pressure at the midpoint of the left side of the wedge with deadrise angle of 10°, becomes negative, when the wall of the flexible wedge reaches its largest deflection. It is also observed that, the pressure at left side of the wedge with deadrise angle of 20°, reaches zero. Such behavior does not occur for the wedges of 30° and 45° deadrise angles. In the third part of simulations, oblique water entry of a flexible wedge of 20° deadrise angle is simulated, and no heel angle is considered. Harmonic behavior is observed for the vertical force, horizontal force, pressure of t
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Finite element modeling of one-dimensional Beji and Nadaoka Boussinesq equation is presented. The continuous equations are spatially discretized using standard Galerkin method. Since the extended Boussinesq equations contain high-...
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Finite element modeling of one-dimensional Beji and Nadaoka Boussinesq equation is presented. The continuous equations are spatially discretized using standard Galerkin method. Since the extended Boussinesq equations contain high-order derivatives, two different numerical techniques are proposed in this paper in order to simplify the discretization task of the third-order terms. In the first technique, an auxiliary equation is introduced to eliminate the third-order derivatives of the momentum equation while non-overlapping elements with linear interpolating functions are employed to account for the dependent variables. However, in the second method, overlapping elements with quadratic interpolating functions are applied for discretizing the governing equations. Time integration is performed using the Adams-Bashforth-Moulton predictor-corrector method. By considering the truncation error and theoretical analysis for both of the numerical techniques, accuracy and stability of the adopted finite element schemes have been studied. Finally, a computer code is developed based on the proposed schemes. To show the validity as well as the practicality of the developed code, five different test cases are presented, and the results are compared with some analytical solutions and experimental data. Favorable agreements have been achieved in all cases.
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A 3D unsteady computer solver is presented to compute incompressible Navier-Stokes equations combined with the volume of fraction (VOF) method on an arbitrary unstructured domain. This is done to simulate fluid flows in various ap...
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A 3D unsteady computer solver is presented to compute incompressible Navier-Stokes equations combined with the volume of fraction (VOF) method on an arbitrary unstructured domain. This is done to simulate fluid flows in various applications, especially around a marine vessel. The Navier-Stokes solver is based on the fractional steps method coupled with a finite volume scheme and collocated grids by which velocity components and pressure fields are defined at the center of the control volume. However, the fluxes are defined at the midpoint on their corresponding cell faces. On the other hand, the CICSAM (Compressive Interface Capturing Scheme for Arbitrary Meshes) scheme is applied to capture the free surface. In the presented fractional step method, the pressure Poisson equation suffers from poor convergence rate by simple iterative methods like Successive Overrelaxation (SOR), especially in simulating complex geometrics like a ship with appendages. Therefore, to accelerate the convergence rate, an agglomeration multigrid method is applied on arbitrary moving mesh for solving pressure Poisson equation with two well-known cycles, V and W. In order to maintain accuracy, the geometry details should not change in grid coarsening procedure. Therefore, the boundary faces are assumed to be fixed in all grids level. This assumption requires nonstandard cells in coarsening procedures. To investigate the performance of the applied algorithm, various flows including one and two-phase flows are studied in two and three dimensions. It is found that the multigrid method can speed up the convergence rate of fractional step twofold. In most cases (not all), W cycle displays better performance. It is also concluded that the efficiency of the cycle depends on the number of meshes and complexity of the problem and this is mainly due to the data transferring between grids. Therefore, the type of cycle should be selected judiciously and carefully, while considering the mesh size and flow properties.
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Through the use of perturbation theory, Kuo has previously introduced a joint surface roughness/volumetric model in order to characterize bubbly sea surface reverberation based on volumetric wave spectra, surface roughness wave sp...
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Through the use of perturbation theory, Kuo has previously introduced a joint surface roughness/volumetric model in order to characterize bubbly sea surface reverberation based on volumetric wave spectra, surface roughness wave spectrum, and correlation of volumetric wave spectrum and surface roughness wave spectrum. Due to the lack of undetermined volumetric scattered wave number K_v, Kuo obtained backscattering strengths using only Pierson-Moskwitz wave spectrum. In this paper, the reformed integral equation of authentic Helmholtz-Kirchhoff-Fresnel is discussed in which volumetric scattering is involved. By applying the reformed Helmholtz-Kirchhoff-Fresnel, volumetric scattered acoustic pressure field P_v is obtained. Using Helmholtz wave equation and the obtained pressure field P_v, the wave number vector of volumetric scattered field K_v is calculated, and this used to compute the volumetric wave spectrum and the joint surface roughness/volumetric wave spectrum. The obtained spectra are then used to compute scattering strengths. Comparison of the obtained results against the results of experimental Critical Sea Tests shows good agreement. Finally, a parametric study is conducted to examine the effects of wind speeds, grazing angles, and frequencies on the scattering strengths.
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The central problem of strip theory is the calculation of potential flow around 2D sections. One particular method of solutions to this problem is conformal mapping of the body section to the unit circle over which a solution of p...
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The central problem of strip theory is the calculation of potential flow around 2D sections. One particular method of solutions to this problem is conformal mapping of the body section to the unit circle over which a solution of potential flow is available. Here, a new multiparameter conformal mapping method is presented that can map any arbitrary section onto a unit circle with good accuracy. The procedure for finding the corresponding mapping coefficients is iterative. The suggested mapping technique is shown to be capable of appropriately mapping any chined, bulbous, and large and fine sections. Several examples of mapping symmetric and nonsymmetric sections are demonstrated. For symmetric and nonsymmetric sections, the results of the current method are compared against other mapping techniques, and the currently produced geometries display good agreement with the actual geometries.
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In this article, a mathematical model is presented for simulation of the coupled roll and heave motions of the asymmetric impact of a two-dimensional wedge body. This model is developed based on the added mass theory and momentum ...
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In this article, a mathematical model is presented for simulation of the coupled roll and heave motions of the asymmetric impact of a two-dimensional wedge body. This model is developed based on the added mass theory and momentum variation. To this end, new formulations are introduced which are related to the added mass caused by heave and roll motions of the wedge. These relations are developed by including the asymmetrical effects and roll speed. In addition, by considering the roll speed, a particular method is presented for the time derivative of half-wetted beam of an asymmetric wedge. Furthermore, two equations are derived for the roll and heave motions in which damping terms appear. Validity of the proposed method is verified by comparing the predicted results against available experimental data in two conditions of roll motion and no roll motion. Favorable agreement is observed between the predicted results and experimental data. The pressure and hydrodynamic load are computed, and the differences between the results associated with the considered conditions are explored. Subsequently, the effects of different physical parameters including deadrise angle, initial roll angle, and initial velocity on the dynamic response of a two-dimensional wedge section are investigated. Ultimately, time histories of hydrodynamic coefficients are determined in order to provide a better understanding of the derived equations.
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Transmission of a sound generated by a localized point source in the air through a realistic sea surface is studied by the use of the Kirchhoff-Helmholtz integral. An earlier approach had been based on the Kirchhoff-Helmholtz inte...
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Transmission of a sound generated by a localized point source in the air through a realistic sea surface is studied by the use of the Kirchhoff-Helmholtz integral. An earlier approach had been based on the Kirchhoff-Helmholtz integral which only considered the effects of rough surface. In the current study, not only the effect of the rough surface is taken into account but also the effects of subsurface bubbles are included in modeling the real phenomenon more accurately. In order to include the effects of subsurface bubble population, the classic relations of the Kirchhoff-Helmholtz integral are reformulated. Accordingly, a three-phase region of air, water, and bubbly water at the sea surface is analyzed, and the rough interface of bubbly water-air is discretized. Through considering an element area A_i, the transmission coefficient T_i, incident angle _(li), transmitted angle _(3i), and local surface acoustical roughness R_i are investigated for each individual element. Also, the effects of subsurface bubbles, transmission change as a function of frequency f, wind speed W, incident angle , source/receiver position ratio (D/H), surface acoustical roughness, and subsurface bubble population are examined. Results of the modified Kirchhoff-Helmholtz integral method display good agreement against available experimental data.
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A numerical model based on two-dimensional shallow water equations is presented. The depth-averaged velocity components with free-surface elevation have been used as independent variables in the model. The finite element technique...
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A numerical model based on two-dimensional shallow water equations is presented. The depth-averaged velocity components with free-surface elevation have been used as independent variables in the model. The finite element technique is applied to discretize the spatial derivatives. Triangular elements with quadratic and linear interpolating functions are employed for two horizontal velocity components and the free-surface elevation, respectively. The standard Galerkin method is applied for discretization of the governing equations. Time discretization is performed using an implicit scheme. The resulting linear system of equations is solved by the GMRES method. The model is validated using three test cases and the results are compared with an analytical solution, the result of numerical work and experimental data, respectively. Favorable agreement was achieved in all three cases. Subsequently, the developed model is applied to simulate free-surface elevation through a channel contraction. The effects of width of the narrow section as well as the profile of the cross section of the channel on the wave forces exerted on a circular cylinder were studied. This was done in a channel with a quartic narrow section. Plots of time histories of the drag coefficient on the cylinder were produced, demonstrating the effects of the mentioned oarameters.
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