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1. 空军工程大学 航空航天工程学院, 西安 710038;
2. 中国人民解放军95889部队, 酒泉 735018

Added mass of trans-media moving object
ZHANG Xiaoqiang1,2, FENG Jinfu1 , LIN Ke1, HU Junhua1
1. Aeronautics and Astronautics Engineering College, Air Force Engineering University, Xi'an 710038, China;
2. PLA 95889, Jiuquan 735018, China
Abstract: Trans-media moving object was equipped with outstanding advantages in multiple fluid media environment. However, its moving characteristics were hard to predict because of the free surface problem and complex stress. Added mass method was common to solve fluid-structure coupling problems in engineering, but the existing conclusions could not be extended to trans-media process with free surface. A new method was proposed aiming to solve the time-varying added mass problems in trans-media process. Changing laws of added mass of some cylinder were studied, which lied in different depths in both separation step and entry step of the trans-media process. It is shown that the two steps have same changing trend and similar depth-varying curve with the depth varying; in the same depth, normal added mass of separation step is near to that of the entry step and both depth-varying curves have linear characteristics; as for axial added mass, added inertia moment, and added static moment, the results of two steps in the same depth are different obviously, so the two steps are irreversible. The proposed method is helpful for design of trans-media structure, and can be extended to other situations of added mass computing with free surface.
Key words: trans-media     added mass     free surface flow     hydrodynamic force     numerical calculation

1 附加质量计算策略

 图 1 倾斜出水过程的坐标系 Fig. 1 Coordinate system of aslant separation

vy=0,ωz=0,物体沿x轴方向运动,方程组可简化为

vx=0,ωz=0,物体沿y轴方向运动,方程组可简化为

vx=0,vy=0,物体绕z轴转动,方程组可简化为

2 流场数值模型

2.1 流动控制方程[18]

2.2 VOF模型[19]

2.3 湍流模型

2.4 动网格方法

smooth根据边界点上的已知位移来光滑调整流域内节点的位置,不改变网格的拓扑结构,能保证网格质量,适用于小位移问题,对于大位移和强切变问题仅靠节点松弛不能保证网格质量,而且有可能出现网格相交的情况,网格的品质会发生改变,需要用到remesh,通过设置网格控制参数如网格的最小、最大长度,网格单元的偏斜度、尺度函数参数可以控制网格移动后的品质。

3 结果验证及分析

 图 2 计算域示意图 Fig. 2 Schematic diagram of computational region
 图 3 网格质量分布 Fig. 3 Mesh quality distribution
 图 4 局部网格示意图 Fig. 4 Schematic diagram of regional mesh

 计算条件 (v,v′,-v′) 理论值 y轴方向 y轴方向相对误差/% z轴方向 z轴方向相对误差/% (1,3,-3) 0.5 0.496 52 0.696 24 0.497 33 0.533 84 (1,10,-10) 0.5 0.496 50 0.700 02 0.497 28 0.543 39 (2,3,-3) 0.5 0.496 64 0.672 06 0.497 36 0.528 48 (2,10,-10) 0.5 0.496 76 0.647 24 0.497 44 0.511 22

 图 5 球体附加质量系数曲线 Fig. 5 Added mass coefficient curves of sphere
4 跨介质过程中的附加质量

 图 6 柱体外形计算域 Fig. 6 Computational region of cylinder shape
 图 7 柱体外形及其局部网格 Fig. 7 Cylinder shape and its regional mesh

 水面/m 无量纲 浸深 附加质量系数 λ11 λ66 λ22 λ26 y=-0.7 0.933 33 0.084 93 0.046 38 0.859 72 0.007 84 y=-0.5 0.800 00 0.075 05 0.036 76 0.724 75 0.042 74 y=-0.2 0.600 00 0.073 84 0.027 87 0.482 60 0.074 58 y=0 0.466 67 0.072 56 0.026 86 0.329 70 0.071 30 y=0.2 0.333 33 0.070 34 0.022 27 0.189 18 0.051 89 y=0.5 0.133 33 0.059 00 0.005 51 0.033 98 0.010 88 y=0.6 0.066 67 0.038 43 0.002 32 0.009 05 0.002 58

 水面/m 无量纲 浸深 附加质量系数 λ11 λ66 λ22 λ26 y=-0.7 0.066 67 0.018 64 0.006 96 0.010 26 0.004 27 y=-0.5 0.200 00 0.042 00 0.016 37 0.070 41 0.027 28 y=-0.2 0.400 00 0.054 00 0.035 17 0.235 44 0.072 06 y=0 0.533 33 0.056 15 0.040 15 0.378 70 0.092 40 y=0.2 0.666 67 0.057 40 0.041 27 0.533 49 0.096 16 y=0.5 0.866 67 0.058 59 0.050 14 0.776 90 0.064 62 y=0.6 0.933 33 0.060 38 0.055 65 0.852 79 0.046 32

 图 8 随浸深变化的轴向附加质量系数 Fig. 8 Depth-varying coefficients of axial added mass
 图 9 随浸深变化的附加转动惯量系数 Fig. 9 Depth-varying coefficients of added inertia moment
 图 10 随浸深变化的法向附加质量系数 Fig. 10 Depth-varying coefficients of normal added mass
 图 11 随浸深变化的附加静矩系数 Fig. 11 Depth-varying coefficients of added static moment

1步计算时物体的浸深反映了真实的自由面,所以严格意义上讲,只有1步计算的结果最能符合物理实际,但1步计算时流场发展不够充分,可能会导致结果偏离真实值,就工程应用而言,还需要考虑外形复杂程度、网格质量以及参数选取等因素对结果的影响。多步计算能够平抑结果的波动,但随着计算步数的增多,物体的浸深位置会发生变化,变化量的大小取决于设定的时间步长和运动速度,从而导致计算误差增大。只要选取适当的计算条件,计算结果就能够反映出实际的运动情况,而且能够降低结果对影响因素的敏感度,所以应用时可以根据情况选择使用。

5 结 论

1) 新的计算策略能够对跨介质运动物体的时变附加质量进行计算,精度符合工程要求。

2) 跨介质运动物体的出水过程和入水过程的附加质量变化趋势相同,规律相近。

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#### 文章信息

ZHANG Xiaoqiang, FENG Jinfu, LIN Ke, HU Junhua

Added mass of trans-media moving object

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(4): 821-828.
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0478