﻿ 船舶阻力试验实船换算的蒙特卡罗仿真
 舰船科学技术  2023, Vol. 45 Issue (7): 6-9    DOI: 10.3404/j.issn.1672-7649.2023.07.002 PDF

1. 中国特种飞行器研究所，湖北 荆门 448035;
2. 高速水动力航空科学技术重点实验室，湖北 荆门 448035

Monte Carlo simulation for full-scale ship conversion of ship model resistance test
SHI Sheng-zhe1,2, JIANG Ting1,2, LI Xu1,2, ZHENG Xiao-long1,2
1. AVIC Special Vehicle Research Institute, Jingmen 448035, China;
2. Key Aviation Scientific and Technological Laboratory of High Speed Hydrodynamic, Jingmen 448035, China
Abstract: In order to evaluate believable degree of test data, and improve test data quality, Monte Carlo simulation was made for full-scale ship conversion of ship model resistance test based on 1+K method. With full-scale ship velocity increasing, standard uncertainty of full-scale ship resistance and effective power of ship model resistance test increased from 455 N and 1.42 kW to 1 558 N and 10.96 kW, relative standard uncertainty descended from 1.56% and 1.56% to 0.44% and 0.44%. Monte Carlo simulation value of full-scale ship resistance and effective power accorded with bilateral symmetry which is normal distribution.
Key words: Monte Carlo simulation     uncertainty analysis     resistance test     full-scale ship conversion
0 引　言

1 船舶阻力试验实船换算方法

1+ $K$ 方法是目前ITTC推荐的方法。

 ${R_{ts}} = {R_{\upsilon s}} + {R_{ws}} + \Delta {R_s} + {R_{as}} 。$ (1)

 ${R_{\upsilon s}} = \left( {\left( {1{\text{ + }}K} \right){C_{fs}}{\text{ + }}\Delta {C_{fs}}} \right) \cdot \frac{1}{2}{\rho _s} \cdot S{}_s \cdot {V_s}^2 。$ (2)

 ${R_w}_s = {C_{ws}} \cdot \frac{1}{2}{\rho _s} \cdot S{}_s \cdot {V_s}^2 ，$ (3)

 $\Delta {R_s}{\text{ = }}k{}_{ap}({R_{vs}} + {R_{ws}}) ，$ (4)

 ${R_a}_s = {C_{as}} \cdot \frac{1}{2}{\rho _a} \cdot {A_t} \cdot {V_a}^2 。$ (5)

 $\begin{split} {R_t}_s =& (1 + k{}_{ap})(\left( {1{\text{ + }}K} \right){C_{fs}}{\text{ + }}\Delta {C_{fs}} + {C_{ws}}) \times \\ & \frac{1}{2}{\rho _s} \cdot S{}_s \cdot {V_S}^2 + {C_{as}} \cdot \frac{1}{2}{\rho _a} \cdot {A_t} \cdot {V_a}^2 ，\end{split}$ (6)

 ${C_{ts}} = \left( {{\text{1 + K}}} \right){C_{fs}} + \Delta {C_{fs}} + {C_w}_s 。$ (7)

1）摩擦阻力系数

 $\left\{ \begin{gathered}{C_{fs}} = \frac{{0.075}}{{{{(\log {R_e} - 2)}^2}}} ，\\ {C_{sm}} = \frac{{0.075}}{{{{(\log {R_e} - 2)}^2}}}。\end{gathered} \right.$ (8)

2）兴波阻力系数 ${C_w}$

 ${C_w}_s = {C_w}_m= {C_{tm}} - \left( {1{\text{ + }}K} \right){C_{fm}} 。$ (9)

1+ $K$ 方法中 $K$ 系数的取值根据傅汝德数0.1～0.2范围内的试验结果采用Prohaska方法确定，即

 $\frac{{{C_{tm}}}}{{{C_{fm}}}} = (1 + K) + A\frac{{{F_n}^4}}{{{C_{fm}}}} 。$ (10)

 ${C_{tm}} = \frac{{{R_m}}}{{\frac{1}{2}{\rho _m}{S_m}{V_m}^2}}。$ (11)

3） 实船粗糙度补贴 $\Delta {C_{fs}}$

 $\Delta {C_{fs}} = \left\{ 105 \times \left( \frac{{{K_S}}}{{{L_{WLs}}}}\right)^{\frac{1}{3}} - 0.64 \right\} \times {10^{ - 3}} ，$ (12)

 ${P_e} = \frac{{{R_{ts}} \times {V_s}}}{{735.{\text{5}}}} 。$ (13)
2 蒙特卡罗仿真 2.1 蒙特卡罗仿真的步骤

2.2 蒙特卡罗仿真的输入量

2.3 蒙特卡罗仿真的输出量

 图 1 实船有效功率的概率密度直方图 Fig. 1 Probability density histogram of full-scale ship effective power
3 结　语

1）随着实船速度的增加，实船阻力和实船有效功率的标准不确定度分别从455 N，1.42 kW逐步增加至1558 N，10.96 kW，实船阻力和实船有效功率的相对标准不确定度却分别从1.56%，1.56%下降至0.44%，0.44%，表明基于1+K法的船舶阻力试验实船换算结果较为精确。

2）实船阻力和实船有效功率的蒙特卡罗仿真值分布左右对称，符合正态分布。

 [1] 周广利, 黄德波, 李凤来. 船模拖曳阻力试验的不确定度分析[J]. 哈尔滨工程大学学报. 2006, 27(3): 377–390. ZHOU Guang-li, HUANG De-bo, LI Feng-lai. Uncertainty analysis of ship model towing resistance test[J]. Journal of Harbin Engineering University. 2006, 27(3): 377–390. [2] 崔健, 陆泽华, 陈涛. 船模阻力自航和螺旋桨敞水试验不确定度分析[J]. 船舶物资与市场. 2020, (9): 5–8. CUI Jian, LU Ze-hua, CHEN Tao. Uncertainty analysis of ship model resistance self navigation and propeller open water test[J]. Ship Materials and Market. 2020, (9): 5–8. [3] 施奇, 杨大明, 尹赘凯. 拖曳水池船模阻力试验不确定度分析[J]. 江苏科技大学学报(自然科学版), 2010, 24(5): 428-433. Shi Qi, Yang Daming, Yin Yunkai. Uncertainty analysis of ship model resistance test in towing tank[J]. Journal of Jiangsu University of Science and Technology (Natural Science Edition), 2010, 24(5): 428-433. [4] 童寿龙, 陈作钢. 循环水槽船模阻力试验不确定度分析[J]. 中国舰船研究, 2020, 15(4): 144-152. Tong Shoulong, Chen Zuogang. Uncertainty analysis of ship model resistance measurement in circulating water channel[J]. Chinese Journal of Ship Research, 2020, 15(4): 144-152. DOI:10.19693/j.issn.1673-3185.01658 [5] 史圣哲, 郑亚雄. 潜艇标模阻力试验的不确定度分析[J]. 实验流体力学, 2015, 29(5): 65-71. Shi Shengzhe, Zheng Yaxiong. Uncertainty analysis in submarine standard model resistance test[J]. Journal of Experiment in Fluid Mechanics, 2015, 29(5): 65-71. DOI:10.11729/syltlx20150002 [6] 丁举, 马向能. 考虑浅水影响的航速测量不确定度分析[J]. 船舶, 2005(4): 1-4. Ding Ju, Ma Xiangneng. Uncertainty analysis of ship velocity measurement with allowance to shallow water influence[J]. Ship & Boat, 2005(4): 1-4. DOI:10.3969/j.issn.1001-9855.2005.04.001 [7] 丁举. 考虑算法的的实船试航船速测量不确定度分析[J]. 中国造船, 2007, 177(2): 143-148. Ding Ju. Uncertainty analysis of ship velocity measurement in sea trial considering ship velocity algorithm[J]. Shipbuilding of China, 2007, 177(2): 143-148. DOI:10.3969/j.issn.1000-4882.2007.02.019 [8] 郑科, 耿卫国, 朱子环. 蒙特卡洛法在发动机推力测量不确定度评估中的应用[J]. 计算机测量与控制, 2021, 29(2): 249-254. Zheng Ke, Geng Weiguo, Zhu Zihuan. Application of Mote Carlo method in uncertainty evaluation of engine thrust measurement[J]. Computer Measurement & Control, 2021, 29(2): 249-254. DOI:10.16526/j.cnki.11-4762/tp.2021.06.048 [9] 刘伟, 张秀凤, 张威. 基于蒙特卡洛法的实船功率性能试验不确定度分析[J]. 船海工程. 2021, 50(1): 25-29, 33. LIU Wei, ZHANG Xiu-feng, ZHANG Wei. Uncertainty analysis for ship powering performance measurement with Monte Carlo method[J]. Ship & Ocean Engineering. 2021, 50(1): 25–29, 33.