Numerical and theoretical investigation on three-dimensional trajectory characteristics of skipping stones  

打水漂运动轨迹特性的数值模拟与理论研究

作　　者：Cong-Hui Li Cong Wang Ying-Jie Wei 李聪慧;王聪;魏英杰(School of Astronautics,Harbin Institute of Technology,Harbin,150001,China)

机构地区：[1]School of Astronautics,Harbin Institute of Technology,Harbin,150001,China

出　　处：《Acta Mechanica Sinica》2022年第7期53-64,I0001,共13页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.11972138).

摘　　要：An in-depth study of the complicated trajectory characteristics of skipping stones is carried out in the present work.A three-dimensional numerical simulation validated by acquiring good agreement with experimental results is established.It is devoted to illustrating five different types of motion responses after the stone impacts the water surface in the o-xy plane,including“dive”,“hydroplaning trout”,“hydroplaning skip”,“stable skip”,and“skipping trout”.Then,the lateral deviations are investigated quantitatively based on dimensionless parameter sin(α+β)cosαin the o-yz plane.Steady interval and linear interval are divided for lateral deviation Z1/D and Z2/D based on the values of(α+β)andα,respectively.The results reveal that(1)Z1/D increases almost linearly with the increasing sin(α+β)cosαat different slopes in different(α+β)intervals;(2)Z2/D increases almost linearly with the increasing sin(α+β)cosαat different slopes in differentαintervals;(3)in linear interval,numerical lateral deviations are much larger than the fitting values at pointsβ/α≥4.5,and much smaller than the fitting values at points 2.3≤β/α<4.3.Finally,a theoretical approach is proposed to predict the maximum immersion depth of trailing edge point P.本文对打水漂运动复杂的轨迹特性进行了深入研究,建立了与实验结果吻合度很高的三维数值计算模型.重点描述了圆盘触水之后纵平面o-xy平面五种不同的运动模式,包括潜水、滑水鳟鱼、滑水跳跃、稳定跳跃和稳定鳟鱼.之后,利用无量纲参数sin(α+β)cosα定量分析了o-yz平面的横向偏移量,并分别根据(α+β)和α的值划分了横向偏移Z1/D和Z2/D的稳定区间和线性区间.结果表明:(1)在不同的区间内,Z1/D随sin(α+β)cosα以不同的斜率线性增长;(2)Z2/D在不同区间随sin(α+β)cosα以不同的斜率线性增加;(3)在线性区间内,横向偏移量数值计算结果在β/α≥4.5时明显大于拟合值,在2.3≤β/α<4.3时明显小于拟合值.最后,提出了一种预测尾缘最低点最大入水深度的理论方法.

关 键 词：Continuous skips TRAJECTORY Lateral deviation Theoretical model Immersed depth 

分 类 号：O311[理学—一般力学与力学基础]