本文用VOF(Volume of Fluid)方法数值模拟了三维涡环与自由表面的粘性相互作用.重点考察了Froude数、Weber数、初始扰动及密度分层对涡环与自由表面相互作用的影响.结果表明:由于粘性的存在,使得涡环与自由表面的相互作用与无粘情形相...本文用VOF(Volume of Fluid)方法数值模拟了三维涡环与自由表面的粘性相互作用.重点考察了Froude数、Weber数、初始扰动及密度分层对涡环与自由表面相互作用的影响.结果表明:由于粘性的存在,使得涡环与自由表面的相互作用与无粘情形相比有许多不同.粘性的作用主要体现在涡量的耗散和新的二次涡环的产生;对自由表面变形而言,Froude数是主要的控制参数,Froude数越大,自由表面变形越显著,而Weber数的影响作用则不大;在Froude数较大时,涡环与自由表面相互作用会使得自由表面上出现轴对称的快速发展的行波,而当Froude数较小时,自由表面的变形形式较为复杂;当存在初始周向扰动时,水下涡环环量的非均匀分布会在自由表面上留下与实验中观察到的纵向沟槽相对应的水面痕迹.这些非轴对称、短波的表面痕迹正是综合孔径雷达(SAR)所能探测到的;自由表面的存在可削弱流场中的扰动,对流场中的涡环的不稳定性有抑制作用;在密度分层的流体中,水下涡环演化规律仍与均质流体中的定性大致相同,仅在定量数值上有所不同.在密度分层流中,自由表面的存在抑制了内波的发展,因而亦抑制了内波对自由表面的影响,使得密度分层对涡环与自由表面的相互作用影响不大.展开更多
Applications of a novel curve-fitting technique are presented to efficiently predict the motion of the vortex filament, which is trailed from a rigid body such as wings and rotors. The gov- erning equations of the mot...Applications of a novel curve-fitting technique are presented to efficiently predict the motion of the vortex filament, which is trailed from a rigid body such as wings and rotors. The gov- erning equations of the motion, when a Lagrangian approach with the present curve-fitting method is applied, can be transformed into an easily solvable form of the system of nonlinear ordinary dif- ferential equations. The applicability of Bezier curves, B-spline, and Lagrange interpolating polyno- mials is investigated. Local Lagrange interpolating polynomials with a shift operator are proposed as the best selection for applications, since it provides superior system characteristics with minimum computing time, compared to other methods. In addition, the Gauss quadrature formula with local refinement strategy has been developed for an accurate prediction of the induced velocity computed with the line integration of the Biot-Savart law. Rotary-wing problems including a vortex ring problem are analyzed to show the efficiency, accuracy, and flexibility in the applications of the pro- posed method.展开更多
文摘本文用VOF(Volume of Fluid)方法数值模拟了三维涡环与自由表面的粘性相互作用.重点考察了Froude数、Weber数、初始扰动及密度分层对涡环与自由表面相互作用的影响.结果表明:由于粘性的存在,使得涡环与自由表面的相互作用与无粘情形相比有许多不同.粘性的作用主要体现在涡量的耗散和新的二次涡环的产生;对自由表面变形而言,Froude数是主要的控制参数,Froude数越大,自由表面变形越显著,而Weber数的影响作用则不大;在Froude数较大时,涡环与自由表面相互作用会使得自由表面上出现轴对称的快速发展的行波,而当Froude数较小时,自由表面的变形形式较为复杂;当存在初始周向扰动时,水下涡环环量的非均匀分布会在自由表面上留下与实验中观察到的纵向沟槽相对应的水面痕迹.这些非轴对称、短波的表面痕迹正是综合孔径雷达(SAR)所能探测到的;自由表面的存在可削弱流场中的扰动,对流场中的涡环的不稳定性有抑制作用;在密度分层的流体中,水下涡环演化规律仍与均质流体中的定性大致相同,仅在定量数值上有所不同.在密度分层流中,自由表面的存在抑制了内波的发展,因而亦抑制了内波对自由表面的影响,使得密度分层对涡环与自由表面的相互作用影响不大.
基金supported by the EDISON Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Science,ICT and Future Planning(No.2011-0020560)
文摘Applications of a novel curve-fitting technique are presented to efficiently predict the motion of the vortex filament, which is trailed from a rigid body such as wings and rotors. The gov- erning equations of the motion, when a Lagrangian approach with the present curve-fitting method is applied, can be transformed into an easily solvable form of the system of nonlinear ordinary dif- ferential equations. The applicability of Bezier curves, B-spline, and Lagrange interpolating polyno- mials is investigated. Local Lagrange interpolating polynomials with a shift operator are proposed as the best selection for applications, since it provides superior system characteristics with minimum computing time, compared to other methods. In addition, the Gauss quadrature formula with local refinement strategy has been developed for an accurate prediction of the induced velocity computed with the line integration of the Biot-Savart law. Rotary-wing problems including a vortex ring problem are analyzed to show the efficiency, accuracy, and flexibility in the applications of the pro- posed method.
