Races using kitefoil and windfoil surfboards have been in the Olympic Games for the first time in Paris 2024,signalling their relevance in sailing sports.However,the dynamics of these devices is yet not well understoo...Races using kitefoil and windfoil surfboards have been in the Olympic Games for the first time in Paris 2024,signalling their relevance in sailing sports.However,the dynamics of these devices is yet not well understood,in particular the influence on the hydrodynamic forces and moments of the distance of the foil to the free surface.Considering this,the present paper documents an experimental investigation in which forces and torque produced,under uniform flow,by a full-scale state-of-the-art hydrofoil(suitable both for kitesurf and windsurf)were measured.A range of velocities,angles of attack,and submergences were tested,leading to Froude numbers based on submergence with maximum values around five,a typical range in actual sailing conditions.From these tests,formulae for the hydrodynamic coefficients have been proposed.They can be used for developing Velocity Prediction Programs(VPP)for this kind of craft,a necessary tool to plan racing configurations and to analyze their racing performance.With the aim of making the experimental data useful for benchmarking numerical models and for future research on related topics such as foil ventilation and transition to turbulence,the specimen’s 3D file is provided as supplementary material to this paper.展开更多
The aim of this work is to study the solution of the smoothed particle hydrodynamics(SPH)discrete formulation of the hydrostatic problem with a free surface.This problem,in which no time dependency is considered,takes...The aim of this work is to study the solution of the smoothed particle hydrodynamics(SPH)discrete formulation of the hydrostatic problem with a free surface.This problem,in which no time dependency is considered,takes the form of a system of linear equations.In particular,the problem in one dimension is addressed.The focus is set on the convergence when both the particle spacing and the smoothing length tend to zero by keeping constant their ratio.Values of this ratio of the order of one,corresponding to a limited number of neighbors,are of practical interest.First,the problem in which each particle has one single neighbor at each side is studied.The explicit expressions of the numerical solution and the quadratic error are provided in this case.The expression of the quadratic error demonstrates that the SPH solution does not converge to the exact one in general under the specified conditions.In this case,the error converges to a residue,which is in general large compared to the norm of the exact solution.The cases with two and three neighbors are also studied.An analytical study in the case of two neighbors is performed,showing how the kernel influences the accuracy of the solution through modifying the condition number of the referred system of linear equations.In addition to that,a numerical investigation is carried out using several Wendland kernel formulas.When two and three neighbors are involved it is found that the error tends in most cases to a small limiting value,different from zero,while divergent solutions are also found in the case of two neighbors with the Wendland Kernel C2.Other cases with more neighbors are also considered.In general,the Wendland Kernel C2 turns out to be the worst choice,as the solution is divergent for certain values of the ratio between the particle spacing and the smoothing length,associated with an ill-conditioned matrix.展开更多
The study of hyperbolic graphs is an interesting topic since the hyperbolicity of a geodesic metric space is equivalent to the hyperbolicity of a graph related to it.The main result in this paper is a very simple char...The study of hyperbolic graphs is an interesting topic since the hyperbolicity of a geodesic metric space is equivalent to the hyperbolicity of a graph related to it.The main result in this paper is a very simple characterization of the hyperbolicity of a large class of periodic planar graphs.展开更多
文摘Races using kitefoil and windfoil surfboards have been in the Olympic Games for the first time in Paris 2024,signalling their relevance in sailing sports.However,the dynamics of these devices is yet not well understood,in particular the influence on the hydrodynamic forces and moments of the distance of the foil to the free surface.Considering this,the present paper documents an experimental investigation in which forces and torque produced,under uniform flow,by a full-scale state-of-the-art hydrofoil(suitable both for kitesurf and windsurf)were measured.A range of velocities,angles of attack,and submergences were tested,leading to Froude numbers based on submergence with maximum values around five,a typical range in actual sailing conditions.From these tests,formulae for the hydrodynamic coefficients have been proposed.They can be used for developing Velocity Prediction Programs(VPP)for this kind of craft,a necessary tool to plan racing configurations and to analyze their racing performance.With the aim of making the experimental data useful for benchmarking numerical models and for future research on related topics such as foil ventilation and transition to turbulence,the specimen’s 3D file is provided as supplementary material to this paper.
基金Supported by the Spanish ministry of Innovation and Universities(MCIU)(Grants Nos.MTM2017-85934-C3-3-P,RTI2018-096791-B-C21"Hidrodinamica de elementos de amortiguamiento del movimiento de aerogeneradores flotantes"),P.E.Merino-Alonso is supported during the completion of his Ph.D.Thesis by MeyFP(Grant No.FPU 17/05433).
文摘The aim of this work is to study the solution of the smoothed particle hydrodynamics(SPH)discrete formulation of the hydrostatic problem with a free surface.This problem,in which no time dependency is considered,takes the form of a system of linear equations.In particular,the problem in one dimension is addressed.The focus is set on the convergence when both the particle spacing and the smoothing length tend to zero by keeping constant their ratio.Values of this ratio of the order of one,corresponding to a limited number of neighbors,are of practical interest.First,the problem in which each particle has one single neighbor at each side is studied.The explicit expressions of the numerical solution and the quadratic error are provided in this case.The expression of the quadratic error demonstrates that the SPH solution does not converge to the exact one in general under the specified conditions.In this case,the error converges to a residue,which is in general large compared to the norm of the exact solution.The cases with two and three neighbors are also studied.An analytical study in the case of two neighbors is performed,showing how the kernel influences the accuracy of the solution through modifying the condition number of the referred system of linear equations.In addition to that,a numerical investigation is carried out using several Wendland kernel formulas.When two and three neighbors are involved it is found that the error tends in most cases to a small limiting value,different from zero,while divergent solutions are also found in the case of two neighbors with the Wendland Kernel C2.Other cases with more neighbors are also considered.In general,the Wendland Kernel C2 turns out to be the worst choice,as the solution is divergent for certain values of the ratio between the particle spacing and the smoothing length,associated with an ill-conditioned matrix.
基金Supported by Ministerio de Ciencia e Innovaci'on of Spain(Grant No.MTM 2009-07800)the last author also by a grant from CONACY of TM'exico(Grant No.CONACYT-UAG I0110/62/10)
文摘The study of hyperbolic graphs is an interesting topic since the hyperbolicity of a geodesic metric space is equivalent to the hyperbolicity of a graph related to it.The main result in this paper is a very simple characterization of the hyperbolicity of a large class of periodic planar graphs.
