流体与结构砰击的相似解与时域分析
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摘要
流体与结构砰击问题有十分广泛的应用,包括船舶水动力砰击、波浪砰击海洋平台、翻卷波砰击海岸结构、飞机的海上紧急迫降、航空条件下的超冷大液滴或冰块的砰击及体育运动方面的应用。本文首先综述流体与结构砰击的预报技术,回顾预报方法的技术状况,讨论其难点与关键技术问题。
砰击过程持续的时间短,流体的运动近似无旋,故忽略流体的重力效应、粘性效应。忽略流体的压缩性可以引入速度势理论,流体满足Laplace方程。砰击时自由面的变化是非线性的,且自由面的变形是未知的,其变化是解的一部分,这也是砰击问题求解的一个主要困难。基于以上基本假定,论文建立相应模型、给出数学方程,采用数值方法进行求解。
对于二维楔形刚体与楔形水柱的匀速砰击,由于参数可以无量纲化,空间时间变量可以分离,文章采用相似解求解。相似解的求解以边界元方法解边界值问题实现,并在射流区引入了浅水近似的解析解。文章引入积分形式的自由面边界条件,通过迭代得到收敛的相似解。文中给出了不同底升角楔形垂向或斜向入水的相似解,给出了自由面剖面的变化及对应的压力分布状况。特别讨论了楔形的非对称性和不同斜向速度对砰击的影响,分析了楔形刚体砰击时尖端的负压现象。
砰击发生时,结构物遭受巨大砰击载荷,结构物的运动速度是变化的,该类问题需要采用时域步进的方法分析。本文首先研究了单个楔形和双楔形体的入水问题。首先考虑的是单楔形体和双楔形体的垂向入水,讨论了楔形体的质量、砰击速度及底升角对单楔形体砰击的影响,并讨论了双楔形体砰击时的双体干扰现象。接着进一步研究了单楔形体三自由度的自由入水,特别的考虑了常常被忽略的旋转速度的影响。文章详细而深入的考虑了砰击过程中三自由度运动的耦合。在时域分析中采用相似解作为初始解,在拓展坐标系下进行时域步进分析。在求解物体运动与流体流动的耦合运动时,采用辅助函数法对二者的耦合运动进行分析解耦。文章采用的方法与其他较为简单的数值方法和实验数据进行了对比验证,并进一步进行了质量守恒和能量守恒的验证。
对于三维轴对称的锥形结构与轴对称水柱的砰击问题,本文将其转换到基于轴对称的柱坐标系下,通过边界元来求解该类问题,这给问题的求解带来很大的便利。锥形结构的匀速入水及锥形结构与液柱的匀速砰击也可通过相似解来求解,采用积分形式的自由面边界条件,以迭代的方法进行求解。文中给出了锥形结构入水及锥形结构与液柱砰击的自由面剖面形状及压力分布。特别的文中将三维相似解与二维相似解进行比较,考察三维效应。
文章进一步研究了锥形液柱或椭球大液滴与锥形结构的砰击。研究了锥形结构的自由入水,给出了不同底升角圆锥的不同时刻的自由面剖面形状和压力分布。再次引入辅助函数对流体流动与锥形结构运动的耦合进行解耦分析。经验证,锥形结构与锥形液柱的匀速砰击时域解与相似解比较十分吻合,文章随后分析了二者的耦合运动。最后文章采用时域步进法分析了球形大液滴与锥形结构的匀速砰击及耦合运动,对比分析了二者的差异。
Fluids/structures impact problems have a wide range of important applications, including ship slamming, wave impact on offshore platforms, plunging wave on coastal structures, emergency landing of airplanes on the sea, as well as impact of super-cooled large droplets and ice lumps in the aeronautical settings, and applications in sports. Review and assessment of estimation techniques on fluids/structures impact are presented. The state of the art of prediction method is presented; Difficulties and key technologies are discussed.
Impact usually lasts for a very short period of time and the effects of the viscosity of the liquid are usually ignored. As a result, the velocity potential can be introduced, which satisfies the Laplace equation when the compressibility of the liquid is ignored. A major difficulty is however the boundary conditions on the free surface, which are fully nonlinear and are imposed on a surface which is unknown and is part of the solution itself. The gravity effect on the flow is ignored based on the assumption that the ratio of the incoming speed of the liquid to the acceleration due to gravity is much larger than the time scale of interest. Based on the above assumptions we have developed the corresponding mathematic equations together with the numerical methodology.
For a two dimensional rigid wedge colliding with water wedge at constant speed, similarity solution method is used, because there is no length scale. In other words, the spatial variables and the time variable could be combined. The problem of this similarity flow is solved by the boundary element method together with an analytical solution in the jet zone based on the shallow water approximation. Especially the convergent results are achieved through iteration for the integral form of the free surface boundary conditions. Various results are provided for the wave elevation, pressure distribution and force at different deadrise angles and at different direction of oblique entry. The effects of asymmetry and horizontal speed on these results are investigated. In particular, negative pressure near the tip of the solid wedge is observed and discussed.
The water entry problem of single wedge or twin-wedges through free fall is then studied. Firstly the vertical entry of single or twin-wedges are considered, where the effects of mass, entry speed and deadrise angle of a single wedge have been discussed, and the interaction between twin-wedges has been observed. Furthermore the water entry problem of a wedge through free fall in three degrees of freedom is studied; In particular, the effect of the rotational velocity is taken into account, which seems to have been neglected so far. Extensive investigation has been made on the coupling of motions in three degrees of freedom. Similarity solution has been adopted as the initial flow pattern, and these problems are solved in a stretched coordinate system and the impact process is simulated based on the time stepping method. Auxiliary function method has been used to decouple the mutual dependence between the body motion and the fluid flow. The developed method is verified through results from other simulation and experimental data for some simplified cases and further validation are made through mass conservation and energy conservation.
For the three dimensional axisymmetric hydrodynamic impact of cone structures and axisymmetric liquid columns, the problem is converted to quasi two-dimensional one and is solved by axisymmetric boundary element method in the axisymmetric coordinate system. This has simplified the solution procedure significantly. The constant water entry of a cone has been studied through similarity solution similar to the two-dimensional wedge, the integral free surface conditions have been adopted and the results are achieved through iteration. Various results of free surface profile and pressure distribution with different deadrise angle are presented. In particular comparisons with two dimensional wedges are presented to investigate the three dimensional effect.
Then further researches are made on the coupled motion of the collision between cone structures and a liquid cone column or ellipsoid droplet. The free fall motion of cone structures is also studied, and various results on free surface profile and pressure distribution plus the acceleration and velocity at different entry distance are presented. Again the auxiliary function has been introduced to decouple the motion of the cone structures and the fluid flow. Then numerical simulations are made on the impact of liquid cone columns or sphere droplet. The results of the collision of liquid cone column at constant velocity are compared with those obtained from similarity solution and good agreement is found. The collisions of liquid column or sphere have been investigated at either constant velocity or through coupling analysis through time stepping method.
砰击过程持续的时间短,流体的运动近似无旋,故忽略流体的重力效应、粘性效应。忽略流体的压缩性可以引入速度势理论,流体满足Laplace方程。砰击时自由面的变化是非线性的,且自由面的变形是未知的,其变化是解的一部分,这也是砰击问题求解的一个主要困难。基于以上基本假定,论文建立相应模型、给出数学方程,采用数值方法进行求解。
对于二维楔形刚体与楔形水柱的匀速砰击,由于参数可以无量纲化,空间时间变量可以分离,文章采用相似解求解。相似解的求解以边界元方法解边界值问题实现,并在射流区引入了浅水近似的解析解。文章引入积分形式的自由面边界条件,通过迭代得到收敛的相似解。文中给出了不同底升角楔形垂向或斜向入水的相似解,给出了自由面剖面的变化及对应的压力分布状况。特别讨论了楔形的非对称性和不同斜向速度对砰击的影响,分析了楔形刚体砰击时尖端的负压现象。
砰击发生时,结构物遭受巨大砰击载荷,结构物的运动速度是变化的,该类问题需要采用时域步进的方法分析。本文首先研究了单个楔形和双楔形体的入水问题。首先考虑的是单楔形体和双楔形体的垂向入水,讨论了楔形体的质量、砰击速度及底升角对单楔形体砰击的影响,并讨论了双楔形体砰击时的双体干扰现象。接着进一步研究了单楔形体三自由度的自由入水,特别的考虑了常常被忽略的旋转速度的影响。文章详细而深入的考虑了砰击过程中三自由度运动的耦合。在时域分析中采用相似解作为初始解,在拓展坐标系下进行时域步进分析。在求解物体运动与流体流动的耦合运动时,采用辅助函数法对二者的耦合运动进行分析解耦。文章采用的方法与其他较为简单的数值方法和实验数据进行了对比验证,并进一步进行了质量守恒和能量守恒的验证。
对于三维轴对称的锥形结构与轴对称水柱的砰击问题,本文将其转换到基于轴对称的柱坐标系下,通过边界元来求解该类问题,这给问题的求解带来很大的便利。锥形结构的匀速入水及锥形结构与液柱的匀速砰击也可通过相似解来求解,采用积分形式的自由面边界条件,以迭代的方法进行求解。文中给出了锥形结构入水及锥形结构与液柱砰击的自由面剖面形状及压力分布。特别的文中将三维相似解与二维相似解进行比较,考察三维效应。
文章进一步研究了锥形液柱或椭球大液滴与锥形结构的砰击。研究了锥形结构的自由入水,给出了不同底升角圆锥的不同时刻的自由面剖面形状和压力分布。再次引入辅助函数对流体流动与锥形结构运动的耦合进行解耦分析。经验证,锥形结构与锥形液柱的匀速砰击时域解与相似解比较十分吻合,文章随后分析了二者的耦合运动。最后文章采用时域步进法分析了球形大液滴与锥形结构的匀速砰击及耦合运动,对比分析了二者的差异。
Fluids/structures impact problems have a wide range of important applications, including ship slamming, wave impact on offshore platforms, plunging wave on coastal structures, emergency landing of airplanes on the sea, as well as impact of super-cooled large droplets and ice lumps in the aeronautical settings, and applications in sports. Review and assessment of estimation techniques on fluids/structures impact are presented. The state of the art of prediction method is presented; Difficulties and key technologies are discussed.
Impact usually lasts for a very short period of time and the effects of the viscosity of the liquid are usually ignored. As a result, the velocity potential can be introduced, which satisfies the Laplace equation when the compressibility of the liquid is ignored. A major difficulty is however the boundary conditions on the free surface, which are fully nonlinear and are imposed on a surface which is unknown and is part of the solution itself. The gravity effect on the flow is ignored based on the assumption that the ratio of the incoming speed of the liquid to the acceleration due to gravity is much larger than the time scale of interest. Based on the above assumptions we have developed the corresponding mathematic equations together with the numerical methodology.
For a two dimensional rigid wedge colliding with water wedge at constant speed, similarity solution method is used, because there is no length scale. In other words, the spatial variables and the time variable could be combined. The problem of this similarity flow is solved by the boundary element method together with an analytical solution in the jet zone based on the shallow water approximation. Especially the convergent results are achieved through iteration for the integral form of the free surface boundary conditions. Various results are provided for the wave elevation, pressure distribution and force at different deadrise angles and at different direction of oblique entry. The effects of asymmetry and horizontal speed on these results are investigated. In particular, negative pressure near the tip of the solid wedge is observed and discussed.
The water entry problem of single wedge or twin-wedges through free fall is then studied. Firstly the vertical entry of single or twin-wedges are considered, where the effects of mass, entry speed and deadrise angle of a single wedge have been discussed, and the interaction between twin-wedges has been observed. Furthermore the water entry problem of a wedge through free fall in three degrees of freedom is studied; In particular, the effect of the rotational velocity is taken into account, which seems to have been neglected so far. Extensive investigation has been made on the coupling of motions in three degrees of freedom. Similarity solution has been adopted as the initial flow pattern, and these problems are solved in a stretched coordinate system and the impact process is simulated based on the time stepping method. Auxiliary function method has been used to decouple the mutual dependence between the body motion and the fluid flow. The developed method is verified through results from other simulation and experimental data for some simplified cases and further validation are made through mass conservation and energy conservation.
For the three dimensional axisymmetric hydrodynamic impact of cone structures and axisymmetric liquid columns, the problem is converted to quasi two-dimensional one and is solved by axisymmetric boundary element method in the axisymmetric coordinate system. This has simplified the solution procedure significantly. The constant water entry of a cone has been studied through similarity solution similar to the two-dimensional wedge, the integral free surface conditions have been adopted and the results are achieved through iteration. Various results of free surface profile and pressure distribution with different deadrise angle are presented. In particular comparisons with two dimensional wedges are presented to investigate the three dimensional effect.
Then further researches are made on the coupled motion of the collision between cone structures and a liquid cone column or ellipsoid droplet. The free fall motion of cone structures is also studied, and various results on free surface profile and pressure distribution plus the acceleration and velocity at different entry distance are presented. Again the auxiliary function has been introduced to decouple the motion of the cone structures and the fluid flow. Then numerical simulations are made on the impact of liquid cone columns or sphere droplet. The results of the collision of liquid cone column at constant velocity are compared with those obtained from similarity solution and good agreement is found. The collisions of liquid column or sphere have been investigated at either constant velocity or through coupling analysis through time stepping method.
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