This article presents a simple mathematical model for predicting the running attitude of warped planing boats fixed in a heel angle and free to trim and sinkage. The proposed model is based on asymmetric 2D + T theory utilizing a pressure equation which is previously introduced in the literature to compute the hydrodynamic force acting on a heeled planing hull. Integration of pressure distribution on the asymmetric wedge sections enables the suggested model to compute trim angle, center of gravity rise, resistance, and heeling moment acting on the heeled planing boat in calm water. The hydrostatic force in addition to two drag forces acting on the pressure area and spray area are also taken into account. Finally, a computational algorithm is introduced to find the running attitude of the heeled planing boats. The validity of the proposed model is examined by comparing the obtained running attitudes for two planing hulls series with zero heel angle and computed lift force and heeling moment of a heeled planing boat against available experimental data. Based on the comparisons, favorable accuracy is observed for both symmetrical and asymmetrical conditions. Moreover, it is shown that existence of a heel angle can lead to a decrease in trim angle and resistance, while it intensifies the center of gravity rise of planing boats. It is also observed that as the beam Froude number increases, the heeling moment of the heeled boat reduces.

This article presents a study based on the smoothed particles hydrodynamics method, aiming at a numerical simulation of solid-fluid coupling in a free surface flow. Smoothed Particle Hydrodynamics method (SPH) represents a very interesting alternative method to classical mesh-based methods such as Finite-Volume, Finite-Difference or FiniteElement Methods. The SPH scheme is first described and discussed through its formulations. Two test cases of wedge water entry are presented. To accomplish this, 2D-SPH models in conjunction with turbulence model are implemented and MLS density filter is utilized to remove pressure fluctuations. Pressure distribution, time history of pressure and free surface level are provided. In order to validate the obtained free surface, free surface of dam break problem is simulated and compared with experimental result. Also, the obtained pressure distribution is compared with the analytical result of similarity solution.

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A numerical modeling of a 2D Navier-Stokes equation by a particular vertex centered control volume framework on an unstructured grid is presented in this paper. Triangular elements are applied with an effective high performance fully coupled algorithm, to simulate incompressible laminar flow over a circular cylinder. The cell face velocities in the discretization of the continuity and momentum equations are calculated by a combined linear and momentum interpolation scheme, respectively, and their performances are compared. Flow analyses have been conducted based on various Reynolds numbers up to 200 for the steady and unsteady flows using structured and unstructured grids. The robustness and accuracy of the scheme in the unstructured mesh are proved using the benchmark problems of incompressible laminar flow over a circular cylinder at low and medium Reynolds numbers. Results have been compared with the structured grid results, both cases with equal cell numbers and same strategy for the mesh refinement. Current results display good agreement with the experimental values. Overall, it is shown that, using the suggested method for the current problem, unstructured grids are highly competitive with the structured grids.

It is the traditional belief that sound transmission from water to the air is very weak due to a large contrast between air and water impedances. Recently, the enhanced sound transmission and anomalous transparency of air-water interface have been introduced. Anomalous transparency of air-water interface states that the sound generated by a submerged shallow depth monopole point source localized at depths less than 1/10 sound wavelength, can be transmitted into the air with omni-directional pattern. The generated sound has 35 times higher power compared to the classical ray theory prediction. In this paper, sound transmission through air-water interface for a localized underwater shallow depth source is examined. To accomplish this, two-phase coupled Helmholtz wave equations in two-phase media of air-water are solved by the commercial finite element based COMSOL Multiphysics software. Ratios of pressure amplitudes of different sound sources in two different underwater and air coordinates are computed and analyzed against non-dimensional ratio of the source depth (D) to the sound wavelength (λ). The obtained results are compared with the experimental data and good agreement is displayed.