2D Wedge Research Articles

2D and 3D Augmented Reality Attention Cueing Comparisons in 3D Target Search

This study compared three attentional cueing types to assist the user/participant in visually searching for a target within a simulated naturalistic scene. Participants had to locate a hostile combatant appearing in one of several building windows on an AR-simulated building. Other non-target windows either contain no people or people dressed in non-hostile clothes. We compare the effectiveness of three commonly used attention cues placed in simulated augmented reality on a head mounted display (Magic Leap 2): a 2D wedge arrow pointing toward the target, a 3D Arrow pointing toward the target, and a 3D gaze guidance line, connecting the center of the momentary field of view to the target. Results revealed that the gaze guidance line significantly supported the most rapid cueing and the 3D arrow was slowest and least accurate. The gaze guidance line also induced the fewest head movements. This pattern of results is explained via three mechanisms: the ambiguity of depth perception and the complexity of the 3D arrow, and the ability of the gaze guidance line to always indicate the direction of the target, even when the latter is not in the initial field of view.

2D calculation method on global stability safety factor of diaphragm wall slurry trench based on minimum potential energy principle

In order to limit the phenomenon that the global stability safety factor (GSF) of the diaphragm wall slurry trench calculated by the two-dimensional (2D) wedge method is too small, the 2D calculation model on global instability of trench wall is established by assuming the whole critical failure surface (CFS) is a quarter elliptic cylindrical surface, and the determination method of CFS is given too. In view of the successful application of the minimum potential energy principle in slope stability checking calculation and on the basis of the new model established, the 2D minimum potential energy method for calculating the GSF is proposed according to the minimum potential energy principle. The correctness of the 2D calculation model built and the rationality of the 2D calculation method proposed are verified based on ten engineering cases, and the sensitivity of the GSF to various parameters is analyzed on the basis of six design examples. Finally, the new calculation method is applied to the global stability checking calculation of trench wall in practical engineering, and the result shows the new calculation method given in this paper is still conservative, so the result calculated by the new calculation method is advised to be multiplied by a modification factor of 1.67 in practical application.

An efficient pressure-based multiphase finite volume method for interaction between compressible aerated water and moving bodies

Maritime structures in heavy seas can experience wave impact events with high loads. The loads can lead to structural failure and even loss of life. Wave breaking in said sea states causes air to be entrained in water as aeration cloads, remaining long enough to be transported and to play a role in the impulsive interaction with the structure. A small amount of air in water already forms a highly compressible mixture. Compressibility influences the magnitude of the impact loads.A new cartesian grid method for compressible multiphase flow is introduced to account for water, air and homogeneous mixtures of air and water. The method is designed to predict the hydrodynamic loads on moving bodies engaging with interfaces between fluids having large density ratios. An equation for conservation of energy is omitted by enforcing pressure-density relations. The interface between fluids is transported using a geometric Volume-of-Fluid method. The interface between fluids and structure is taken care of by a cut-cell method. An additional fraction field for the amount of air in water in combination with a new formulation for the multiphase speed of sound prevent overprediction of compressibility by artificial air entrainment.New experimental data of 2D wedge impacts with aerated water, made available as open data, are presented to demonstrate the validity of the numerical method. For low aeration levels, the simulation results in terms of the impact loads on the wedge and the frequencies of pressure waves generated upon impact are in good agreement with the experimental data. Increasing the level of aeration reduces the maximum impact load on the wedge. Reflected density waves lead to secondary loads on the wedge. The intensity of the secondary loads, relative to the primary load of impact, increases with the aeration level while the density wave frequency decreases.

Study of the water entry and exit problems by coupling the APR and PST within SPH

In this manuscript, the adaptive particle refinement (APR) and particle shifting technique (PST) are coupled and applied to investigate the entire process of water entry and exit. The PST implementation for various types of particles is quantitatively discussed in detail in the coupled APR-PST approach. A comprehensive analysis of different APR-PST coupled schemes is conducted with crucial variables compared and analyzed for the first time. The stability, accuracy and robustness of the developed numerical model are verified by three benchmark tests: 2D wedge water entry, 2D cylinder water exit and 2D cylinder water entry and exit. The obtained results show that the current model can ensure the overall computational precision in the situation of local refinement, which indicates it is a viable way to solve the problems of water entry and exit.

Computational Analysis of Surface Pressure Distribution over a 2D Wedge in the Supersonic and Hypersonic Flow Regimes

The complex fluid-dynamic instabilities and shock waves occurring along the surface of a two-dimensional wedge at high values of the Mach number are studied here through numerical solution of the governing equations. Moreover, a regression model is implemented to determine the pressure distribution for various Mach numbers and angles of incidence. The Mach number spans the interval from 1.5 to 12. The wedge angles (θ) are from 5° to 25°. The pressure ratio (P2/P1) is reported at various locations (x/L) along the 2D wedge. The results of the numerical simulations are compared with the regression model showing good agreement.

Numerical Water Impacts of 2D Hull Forms using Dynamic Overset Meshing

The phenomenon of slamming is often the critical design load for high-performance marine craft. Slamming involves the solid-fluid impact of a hull structure, resulting in large forces acting on the structure from the large volume of water displaced in a very short time frame. Due to its importance in the design and operation of marine craft, the impact of ship forms into water has been the focus of a significant body of literature. These studies have primarily focused on rigid shapes, so the effects of hydroelasticity have not been examined in detail. This paper presents a robust and practical methodology for simulating water impacts involving overset meshing and the Volume of Fluid (VOF) method using the Ansys Fluent 2021 R1 Computational Fluid Dynamics (CFD) solver. The framework involves a high resolution dynamic overset mesh attached to the body in a coarse static Cartesian background mesh. Results for a simple 2D wedge impact are compared to experimental and analytical results and a good agreement to the validation material is observed. A 2D transverse section based on the IMOCA60 racing yacht Banque Populaire VIII is then analysed to obtain impact force and pressures. Results capture the peaked pressure distributions characteristic of slamming, with possible effects of air entrapment. The methodology presented is applicable for designers of high-performance sailing craft to improve the prediction of hydrodynamic loading on their hull-form designs. The overset method can quickly and easily be applied to a number of different geometries and impact events with minor changes between models.

Water entry and exit of 2D and axisymmetric bodies

The present paper is dedicated to the development of a numerical model for the water impact of two-dimensional (2D) and axisymmetric bodies with imposed motion. The work is a first step towards the implementation of a 2D+t procedure to be used for the analysis of aircraft ditching. The problem is investigated under the assumptions of an inviscid and incompressible fluid, which is modeled by a potential flow model with fully non-linear boundary conditions at the free-surface. The unsteady boundary value problem with a free-surface is numerically solved through a boundary element method, coupled to a simplified finite element method to describe the thinnest part of the jet. The study is aimed at describing the entry and exit phases. Specific numerical solutions are developed to tackle the exit phase and to improve the stability of the model. Results are presented in terms of free-surface shape, pressure distribution and hydrodynamic load acting on the impacting body. The model is used to study the water entry and exit of a 2D wedge and an axisymmetric cone, for which numerical or experimental results are available in the literature. The numerical investigation shows that the proposed model accurately simulate both the entry and exit phases. For the exit phase, it is shown that the proposed model, being fully non-linear, provides a much better prediction of the loads and the wetted area compared to simplified (analytical) approaches. The effects of the gravity, usually missing in the approaches available in the literature, are also investigated, showing they are rather important, especially, in the exit phase.

Numerical prediction of slamming loads during water entry of a slender hull

The water entry of a slender hull with 5 degrees of freedom (5-DOF), except surge, at a prescribed speed is investigated through a strip theory together with the boundary element method. The hull is cut into a series of slices, the motion of each slice is equivalent to the water entry of a two-dimensional (2D) wedge, which can be solved through the boundary element method in the time domain, with the fully nonlinear boundary conditions imposed on the free surface. In each slice or cross plane, the pressure on the body can be calculated through an auxiliary function method. The total force and moment can then be obtained through an integration scheme along the longitudinal direction of hull. Results are provided for pressure distribution, free surface deformation, the forces and moments, and the influence of the hull velocities is discussed in depth.

Optimal Sobolev regularity for the Stokes equations on a 2D wedge domain

In this note we prove that the solution of the stationary and the instationary Stokes equations subject to perfect slip boundary conditions on a 2D wedge domain admits optimal regularity in the $$L^p$$ -setting, in particular it is $$W^{2,p}$$ in space. This improves known results in the literature to a large extend. For instance, in Maier and Saal (Discrete Contain Dyn Syst Ser S 7(5):1045–1063, 2014) [Theorem 1.1 and Corollary 3] it is proved that the Laplace and the Stokes operator in the underlying setting have maximal regularity. In that result the range of p admitting $$W^{2,p}$$ regularity, however, is restricted to the interval $$1<p<1+\delta $$ for small $$\delta >0$$ , depending on the opening angle of the wedge. This note gives a detailed answer to the question, whether the optimal Sobolev regularity extends to the full range $$1<p<\infty $$ . We will show that for the Laplacian this does only hold on a suitable subspace, but, depending on the opening angle of the wedge domain, not for every $$p\in (1,\infty )$$ on the entire $$L^p$$ -space. On the other hand, for the Stokes operator in the space of solenoidal fields $$L^p_\sigma $$ we obtain optimal Sobolev regularity for the full range $$1<p<\infty $$ and for all opening angles less than $$\pi $$ . Roughly speaking, this relies on the fact that an existing “bad” part of $$L^p$$ for the Laplacian is complemented to the space of solenoidal vector fields.

Development of Empirical Formulation for Bow Flare Slamming and Deck Wetness for Displacement Vessels

The paper presents an empirical method to calculate bow flare slamming pressure and the green water load. Many empirical formulae for various types of vessels have been provided by rules of ship classification societies. In the present work, attempt is made to develop generalized formulations for all types of displacement vessels. Extreme sea conditions are considered. Bow flare pressure is derived in terms of flare and waterline angles. Specific condition for limiting waterline angle is derived based on 2D numerical simulations. Deck wetness is derived in terms of static and dynamic swell-up and the relative motion. Variation of static swell along the length is determined based on potential solution based analyses considering variation in vessels’ hull. 2D wedge simulations are carried out to validate the formulation of dynamic swell-up. Results of the calculated bow flare and deck pressures are compared with various ship classification society formulations and the trends are found to be in good agreement in general barring at bow flare where lower pressure is found in most of the presented cases. Also IACS UR S21A (2018) governing minimum pressure for deck scantlings is found to be conservative in few of the presented cases. Although scantlings assessment is not performed, the presented new formulations may help in realistic assessment of scantlings.

Numerical Analysis of the Pressure Peak Position Shift With Deadrise Angle in Two-Dimensional Wedge Water Entry

This study deals with the pressure peak position shift with deadrise angle during the initial phase of a two-dimensional (2D) wedge water entry. The finite volume method with volume of fluid (VOF) and dynamic mesh technique is used to simulate the water entry process of the 2D wedges with the moderate deadrise angles within the range α = 20 deg–60 deg. The results show that with the increasing deadrise angle, the pressure peak position shifts from the spray root to the wedge apex. And, the critical deadrise angle of pressure peak position shift is identified in the range between 40.8 deg and 41 deg, which is more precise than previous studies. In the initial stage of water entry of a 2D wedge, the pressure on wedge side is determined by the dynamic pressure term and unsteady term simultaneously. For the spray root position, at small deadrise angles, the unsteady term is stronger than the dynamic pressure term; at large deadrise angles, the former is weaker than the later.

Experimental Investigations of the Characteristics of Pressure Sensors for 2D Wedge Drop

Experimental Investigations of the Characteristics of Pressure Sensors for 2D Wedge Drop

A nonlinear mathematical model for coupled heave, pitch, and roll motions of a high-speed planing hull

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.

Exact solution and high frequency asymptotic methods in the wedge diffraction problem

AbstractThe Sommerfeld exact solution for canonical 2D wedge diffraction problem with perfectly conducting surfaces is presented. From the integral formulation of the problem, the Malyuzhinets solution is obtained and this result is extended to obtain the general impedance solution of canonical 2D wedge problem. Keller’s asymptotic solution is developed and the general formulation of exact solution it’s used to obtain general asymptotic methods for approximate solutions useful from the computational point of view. A simulation tool is used to compare numerical calculations of exact and asymptotic solutions. The numerical simulation of exact solution is compared to numerical simulation of an asymptoticmethod, and a satisfactory agreement found. Accuracy dependence with frequency is verified.

Effects of 2D wedge design as a wayfinding facilitator in a 3D virtual environment

AbstractThe purpose of this study is to investigate users' wayfinding task performance and subjective preference in a three‐dimensional (3D) virtual environment. The research variables are interaction mode (touch sensitive vs body movement modes), viewing perspective [first‐person perspective (1PP) versus third‐person perspective (3PP)], and gender (man versus woman). Three difficult levels of tasks were conducted, i.e., A, A‐P, and A‐A types. The experiment is 2 × 2 × 2 between‐subject design. Participants needed to complete three wayfinding tasks and fill out subjective preference questionnaires regarding task fluency, satisfaction, system usability scale, and NASA Task Load Index (NASA‐TLX). Fifty‐six participants (28 men and 28 women) were invited using convenient sampling method. The results are as follows: (1) Participants adopting touch‐sensitive mode performed better than body movement mode. (2) Participants using touch‐sensitive mode could have better task fluency and higher SUS score, and with less effort and frustration. (3) Participants adopting 3PP had better wayfinding task performance than first‐person perspective. They also had higher system usability scale score and spent less effort for having wider viewing perspective. (4) The gender variable only showed significant effect in A‐P type of wayfinding task. Men performed better than women. It is concluded that adopting touch‐sensitive interaction and 3PP designs can better facilitate users' wayfinding tasks.

Double Tip Diffraction Modeling: Finite Difference Time Domain vs. Method of Moments

Discontinuitiessuchastipsandedgescausediffracted fields when electromagnetic waves interact with objects. Two-di- mensional (2D) wedge with non-penetrable boundaries is a canon- icalstructurewhichhaslongbeeninvestigatedanalyticallyandnu- mericallyfortheunderstandingandextractionofdiffractedwaves. Multiple-diffraction has also been investigated. Here, double tip diffraction is modeled with both finite-difference time-domain and method of moments and reference data are generated. Index Terms—Diffraction, double diffraction, double tips, fi- nite difference time domain (FDTD), high frequency asymtotics, method of moments (MoM).

Numerical Simulation of Water Impact of 2D Wedge with Different Density

It remains unresolved to study the relation between the density of wedge and its impact. Fluent is applied to simulate its mechanism with 6DOF model. After the comparison of numerical result and the theoretical, it matches good and then the transient free surface scene is observed. Thus Fluent is able to solve this kind of non-linear problem. And the effect of density of wedge on the slamming character is also studied.

Incompressible impulsive wall impact of liquid bodies

Analytical leading-order solutions are given for various liquid bodies in translational motion that hit a plane wall in impulsive impact at constant velocity. The initial velocity field and the associated virtual masses are calculated for selected liquid bodies of uniform density. We consider 2D and 3D wedges, a cone, the semi-circle and the hemisphere. Sideways force impulses are obtained for 2D bodies. The loss of mechanical energy during impact is calculated for a 2D wedge.

Numerical simulation of 2D hydrodynamic impact of wedge and ship section at variable velocity

A commercial CFD code Fluent 6.3® is used to simulate non-linear free surface flow and compute the impact load during variable velocity water entry of 2D wedge and ship section. The code uses the finite volume method to solve the conservation of mass and momentum equations to obtain simulated flow field. The interface between water and air was modeled using volume of fluid (VOF) method. Wedge section with 30 degree dead-rise angle and a ship section are numerically simulated. Time history of impact force and pressures at distinct locations are predicted; and compared with existing experimental results and other numerical methods. Present numerical results compare well with experimental measurements.DOI: http://dx.doi.org/10.3329/jname.v10i1.14383

Simulation of 2D wedge impacts on water using the SPH–ALE method

Prediction of the forces on pitching boat hulls is a subtle issue, since the underlying phenomena are highly dynamic and unsteady. The solution of a full 3D model of the hull is possible, but comes with a high computational cost; alternatively, it might be simpler to assume the hull as consecutive 2D slices. The traditional CFD approach, with mesh-based algorithms, introduces additional complexity due to mesh motion and interface tracking. By adopting a Lagrangian point of view, the computational algorithm would be substantially simpler, since free surface and moving geometries would be handled easily. In the current work, the smoothed particle hydrodynamics meshless method is used within an arbitrary Lagrangian–Eulerian framework (SPH–ALE), in order to predict the force and motion of a wedge during high-velocity water entry. Various impacts have been simulated, using wedges of different shapes and masses. Two methods of particle refinement have also been examined, in order to increase the accuracy near the point of impact. Results of the method are compared with experimental and numerical results from literature, showing good agreement.