Exploration of the hydrodynamics and mechanism of plate skipping is of significant reference value for the research on aircraft landing problem. Based on the finite volume method and k-ε RNG turbulence model, the Unsteady Reynolds Averaged Navier-Stokes (URANS) equations are solved and a numerical tank is constructed by the velocity-inlet boundary wave maker combined with the Volume of Fluid (VOF) model. Coupled with the global dynamic mesh method, the numerical simulation of two-dimensional plate skipping on both calm and wavy water is carried out. Based on the comparison with experimental and theoretical values, the effects of the initial attitude angle, throwing angle and throwing speed on plate skipping are discussed. Furthermore, the influence of different wave parameters and wave positions is studied and analyzed from the perspective of energy conservation. It is shown that the plate with 20° attitude angle can achieve stone skipping at the minimum throwing speed, and the relative energy loss of the plate is less affected by the initial throwing speed, but mainly affected by the throwing angle and attitude angle, and rises with the increase of the throwing angle or attitude angle. In the case of waves, the plate touching the water at the balance position (up speed) can obtain larger contact area, while the longer contact time occurs at the trough. Therefore, the relative energy loss of the plate contacting the water at these two positions is serious, and the numerical change is about 5% larger than that at the peak position; in the case of touching the water at the balance position (up speed), a rise of the attenuation of velocity and energy loss appears with the increase of wave height, contrary to that at the crest position.
[1] JOHNSON W. The ricochet of spinning and non-spinning spherical projectiles, mainly form water. Part II:an outline of theory and warlike[J]. International Journal of Impact Engineering, 1998, 21(1/2):25-34.
[2] 方方, 周璐, 李志辉. 航天器返回地球的气动特性综述[J]. 航空学报, 2015, 36(1):24-38. FANG F, ZHOU L, LI Z H. A comprehensive analysis of aerodynamics for spacecraft re-entry Earth's atmosphere surroundings[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(1):24-38(in Chinese).
[3] 申蒸洋,陈孝明,黄领才.大型水陆两栖飞机特殊任务模式对总体设计的挑战[J].航空学报, 2019, 40(1):522400. SHENG Z Y, CHEN X M, HUANG L C. Challenges for aircraft design due to special mission models of large-scale amphibious aircraft[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(1):522400(in Chinese).
[4] 黄领才, 雍明培. 水陆两栖飞机的关键技术和产业应用前景[J]. 航空学报, 2019, 40(1):522708. HUANG L C,YONG M P. Key technologies and industrial application prospects of amphibious aircraft[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(1):522708(in Chinese).
[5] 黄淼, 褚林塘, 李成华, 等. 大型水陆两栖飞机抗浪能力研究[J]. 航空学报, 2019, 40(1):522335. HUANG M, CHU L T, LI C H, et al. Seakeeping performance research of large amphibious aircraft[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(1):522335(in Chinese).
[6] 郭保东,屈秋林,刘沛清,等.混合翼身布局客机SAX-40水上迫降力学性能数值研究[J]. 航空学报, 2013, 34(11):2443-2451. GUO B D, QU Q L, LIU P Q, et al. Ditching performance of silent aircraft SAX-40 in hybrid wing-body configuration[J]. Acta Aeronautica et Astronautica Sinica, 2013, 34(11):2443-2451(in Chinese).
[7] ROSELLINI L, HERSEN F, CLANET C, et al. Skipping stones[J]. Journal of Fluid Mechanics, 2005, 543(1):137-146.
[8] LYDERIC B,CHRISTOPHE C. The mystery of the skipping stone[J]. Physics World, 2006, 19(2):29-31.
[9] CLANET C, HERSEN F, BOCQUET L. Secrets of successful stone-skipping[J]. Nature, 2004, 427(6969):29.
[10] LYDERIC B. The physics of stone skipping[J]. American Journal of Physics, 2003, 71(2):150-155.
[11] DO J, LEE N, RYU K W. Realtime simulation of stone skipping[J]. International Journal of Computer, 2007, 4(1):251-254.
[12] Hale J K. Ordinary differential equations[J]. American Mathematical Monthly, 1969, 23(10):82-122.
[13] HARTMAN P. Ordinary differential equations[J]. Mathematics of Computation, 1982, 20:82-122.
[14] NAGAHIRO S I, HAYAKAWA Y. Theoretical and numerical approach to "Magic Angle" of stone skipping[J]. Physical Review Letters, 2005, 94(17):174501.
[15] 戴岩伟. 水漂运动与物理学规律[J].大学物理, 2009, 28(12):16-18. DAI Y W. Stone skipping and physics[J]. College Physics, 2009, 28(12):16-18(in Chinese).
[16] YAN R, MONAGHAN J J. SPH simulation of skipping stones[J]. European Journal of Mechanics/B Fluids, 2017, 61:61-71.
[17] 邬明. LS-DYNA的ALE方法在圆盘击水滑跳中的应用[J]. 科学技术与工程, 2011, 11(33):8247-8251. WU M. Numerical simulation research on bounce of circular disks base on the ALE of LS-DYNA[J]. Science Technology and Engineering, 2011, 11(33):8247-8251(in Chinese).
[18] 陈诗伟. 基于ANSYS/LS-DYNA的圆盘击水弹跳研究[J]. 舰船电子工程, 2013, 33(1):122-124. CHEN S W. Research on the skipping disk based on the ALE method in ANSYS/LS-DYNA[J]. Ship Electronic Engineering, 2013, 33(1):122-124(in Chinese).
[19] HIRT C W, NICHOLS B D. Volume of fluid (VOF) method for the dynamics of free boundaries[J]. Journal of Computational Physics, 1981, 39(1):201-225.
[20] LONGUET-HIGGINS M S, COKELET E D. The deformation of steep surface waves on water. I. a numerical method of computation[J]. Proceedings of the Royal Society A:Mathematical Physical & Engineering Sciences, 1976, 350(1660):1-26.
[21] BOO S Y. Linear and nonlinear irregular waves and forces in a numerical wave tank[J]. Ocean Engineering, 2002, 29(5):475-493.
[22] 金禹彤, 陈吉昌, 卢昱锦, 等. 楔形体入波浪水面数值模拟[J]. 航空学报, 2019, 40(10):122854. JIN Y T, CHEN J C, LU Y J, et al. Numerical simulation of wedge impacting on wavy water[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(10):122854(in Chinese).
[23] 卢昱锦, 肖天航, 李正洲. 高速平板着水数值模拟[J]. 航空学报, 2017, 38(S1):6-14. LU Y J, XIAO T H, LI Z Z. Numerical simulation of high speed plate ditching[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(S1):6-14(in Chinese).
[24] QU Q, HU M, GUO H, et al. Study of ditching characteristics of transport aircraft by global moving mesh method[J]. Journal of Aircraft, 2015, 52(5):1550-1558.
[25] 陈震, 肖熙. 空气垫在平底结构入水砰击中作用的仿真分析[J]. 上海交通大学学报, 2005, 39(5):670-673. CHEN Z, XIAO X. Simulation analysis on the role of air cushion in the slamming of a flat-bottom structure[J]. Journal of Shanghai Jiao Tong University, 2005, 39(5):670-673(in Chinese).
[26] CARPENTER R G. Principles and procedures of statistics, with special reference to the biological sciences[J]. The Eugenics Review, 1960, 52(3):172.
[27] DRAPER N R, SMITH H. Applied regression analysis[M]. New York:John Wiley & Sons, 1998.
[28] GLANTZ S A, SLINKER B K, NEILANDS T B. Primer of applied regression & analysis of variance[M]. New York:McGraw-Hill, Inc., 2001.
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