﻿ 潜艇直航操舵水动力尺度效应研究
 舰船科学技术  2023, Vol. 45 Issue (10): 5-11    DOI: 10.3404/j.issn.1672-7649.2023.10.002 PDF

1. 中国船舶科学研究中心 水动力学重点实验室，江苏 无锡 214082;
2. 宁波大学 海运学院，浙江 宁波 315211;
3. 宁波大学 东海战略研究院，浙江 宁波 315211

Research on the scale effect of the steering hydrodynamic forces for a submarine under the straight-ahead condition
QI Jiang-tao1, GUO Hai-peng2,3, ZHANG Qi-min2, LI Guang-nian2,3
1. National Key Laboratory of Science and Technology on Hydrodynamics, China Ship Scientific Research Center, Wuxi 214082, China;
2. Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China;
3. Donghai Academy, Ningbo University, Ningbo 315211, China
Abstract: Scale effect is a key issue in the study of ship hydrodynamics. Most relevant studies focus on the ship resistance performance. Aiming at the requirement of the maneuverability evaluation of the underwater vehicle during navigation, the scale effect of the steering hydrodynamic forces of the underwater vehicle is explored in this study. Taking the typical submarine model SUBOFF as the study object, the steering test under the straight-ahead condition is simulated by using Computational Fluid Dynamics (CFD) method. The effect of grid spacing on the numerical results is analyzed. On this basis, the local flow fields around the submarine model under different scales are analyzed, as well as the variation of hydrodynamic forces and moment acting on the submarine model. Overall, this work can be used as a reference for the study of scale effect of underwater vehicle.
Key words: underwater vehicle     maneuverability     scale effect     CFD method
0 引　言

1 数值方法

 $\left\{ \begin{gathered} \frac{{\partial \left( {\rho k} \right)}}{{\partial t}} + \frac{{\partial \left( {\rho {u_j}k} \right)}}{{\partial {x_j}}} = P - {\beta ^*}\rho \omega k + \\ \qquad\qquad\qquad\qquad\frac{\partial }{{\partial {x_j}}}\left[ {\left( {\mu + {\sigma _k}{\mu _t}} \right)\frac{{\partial k}}{{\partial {x_j}}}}\right]，\\ \frac{{\partial \left( {\rho \omega } \right)}}{{\partial t}} + \frac{{\partial \left( {\rho {u_j}\omega } \right)}}{{\partial {x_j}}} = \frac{{\rho \gamma }}{{{\mu _t}}}P - {\beta ^*}\rho {\omega ^2} + \\ \frac{\partial }{{\partial {x_j}}}\left[ {\left( {\mu + {\sigma _\omega }{\mu _t}} \right)\frac{{\partial \omega }}{{\partial {x_j}}}} \right] + 2\left( {1 - {F_1}} \right)\frac{{\rho {\sigma _{\omega 2}}}}{\omega } \cdot \frac{{\partial k}}{{\partial {x_j}}} \cdot \frac{{\partial \omega }}{{\partial {x_j}}} 。\\ \end{gathered} \right.$ (1)

 ${l_{DES}} = \min \left( {{l_{RANS}},{l_{LES}}} \right)，$ (2)

 ${l_{RANS}} = \frac{{{k^{1/2}}}}{{{\beta ^*}\omega }}，$ (3)

 ${l_{LES}} = {C_{DES}}\Delta 。$ (4)

2 研究对象及工况

 图 1 DARPA潜艇模型SUBOFF-8模型示意图 Fig. 1 Schematic diagram of DARPA submarine model SUBOFF-8 model

 ${X^{'}} = \frac{X}{{0.5\rho {V^2}{L^2}}} ，$ (5)
 ${Y^{'}} = \frac{Y}{{0.5\rho {V^2}{L^2}}}，$ (6)
 ${N^{'}} = \frac{N}{{0.5\rho {V^2}{L^3}}} 。$ (7)
3 计算域与网格生成

 图 2 计算域划分及边界条件 Fig. 2 Division of the computational domain and boundary conditions

 图 3 潜艇表面网格分布情况 Fig. 3 Grid distribution on the submarine surface

 图 4 计算域网格分布 Fig. 4 Grid distribution in the computational domain
4 网格收敛性分析

 ${\varepsilon _{G21}} = {S_{G2}} - {S_{G1}}，$ (8)
 ${\varepsilon _{G32}} = {S_{G3}} - {S_{G2}}，$ (9)
 ${R_G} = \frac{{{\varepsilon _{G21}}}}{{{\varepsilon _{G32}}}}。$ (10)

 ${U_G} = \left| {\frac{1}{2}\left( {{S_U} - S{}_L} \right)} \right|。$ (11)

 $\delta _{R{E_{G1}}}^{*\left( 1 \right)} = \frac{{{\varepsilon _{{G_{21}}}}}}{{r_G^{{p_G}} - 1}} ，$ (12)
 ${p_G} = \dfrac{{\ln \left( {\dfrac{{{\varepsilon _{{G_{32}}}}}}{{{\varepsilon _{{G_{21}}}}}}} \right)}}{{\ln \left( {{r_G}} \right)}} 。$ (13)

 ${C_G} = \frac{{r_G^{{p_G}} - 1}}{{r_G^{{p_{Gest}}} - 1}}，$ (14)

 ${U_G} = \left\{ {\begin{array}{*{20}{c}} {\left( {9.6{{\left( {1 - {C_G}} \right)}^2} + 1.1} \right)\left| {\delta _{R{E_{G1}}}^*} \right|,\left| {1 - {C_G}} \right| < 0.125}，\\ {\left( {2\left| {1 - {C_G}} \right| + 1} \right)\left| {\delta _{R{E_{G1}}}^*} \right|,\left| {1 - {C_G}} \right| \geqslant 0.125} 。\end{array}} \right.$ (15)

5 计算结果 5.1 泄出涡系结构

 图 5 L/LOA=1时艇体及舵附近的泄出涡结构 Fig. 5 Vortex structure around the submarine body and rudder with L/LOA=1

 图 6 L/LOA=2时艇体及舵附近的泄出涡结构 Fig. 6 Vortex structure around the submarine body and rudder with L/LOA=2

 图 7 L/LOA=4时艇体及舵附近的泄出涡结构 Fig. 7 Vortex structure around the submarine body and rudder with L/LOA=4

 图 8 L/LOA=8时艇体及舵附近的泄出涡结构 Fig. 8 Vortex structure around the submarine body and rudder with L/LOA=8

 图 9 L/LOA=16时艇体及舵附近的泄出涡结构 Fig. 9 Vortex structure around the submarine body and rudder with L/LOA=16
5.2 舵面压力分布

 图 10 L/LOA=1时舵中剖面处表面压力分布 Fig. 10 Pressure distribution on the midsection of the rudder with L/LOA=1

 图 14 L/LOA=16时舵中剖面处表面压力分布 Fig. 14 Pressure distribution on the midsection of the rudder with L/LOA=16
5.3 水动力及力矩
 图 11 L/LOA=2时舵中剖面处表面压力分布 Fig. 11 Pressure distribution on the midsection of the rudder with L/LOA=2

 图 12 L/LOA=4时舵中剖面处表面压力分布 Fig. 12 Pressure distribution on the midsection of the rudder with L/LOA=4

 图 13 L/LOA=8时舵中剖面处表面压力分布 Fig. 13 Pressure distribution on the midsection of the rudder with L/LOA=8

 图 15 不同雷诺数下的纵向力 Fig. 15 Longitudinal force under different Reynolds numbers

 图 16 不同雷诺数下的横向力 Fig. 16 Lateral force under different Reynolds numbers

 图 17 不同雷诺数下的转首力矩 Fig. 17 Yaw moment under different Reynolds numbers
6 结　语

1）不同雷诺数下的艇体附近流场存在显著差异。舵面附近的流动分离现象随雷诺数的增大而减弱，流动分离发生位置逐步后移，导致泄出涡系结构也有所减弱，其中雷诺数较小时变化更为明显。舵面压力分布也随之发生改变，舵背风面的负压区逐渐扩大，导致舵剖面压差随雷诺数增大而增大。

2）潜艇纵向力、横向力及转首力矩系数随雷诺数的变化而发生显著变化。随雷诺数增大，尺度效应对潜艇纵向力的影响虽有所下降但依然显著，而对横向力和转首力矩的影响显著减弱。

 [1] 苏玉民, 林健峰, 赵大刚, 等. 实尺度船舶快速性数值模拟方法综述[J]. 中国造船, 2020, 61(2): 229-239. SU Y M, LIN J F, ZHAO D G, et al. Review of numerical simulation methods for full-scale ship resistance and propulsion performance[J]. Shipbuilding of China, 2020, 61(2): 229-239. DOI:10.3969/j.issn.1000-4882.2020.02.022 [2] 操盛文, 吴方良. 尺度效应对全附体潜艇阻力数值计算结果的影响[J]. 中国舰船研究, 2009, 4(1): 33-37+42. CAO S W, WU F L. Investigation of scaling effects on numerical computation of submarine resistance[J]. Chinese Journal of Ship Research, 2009, 4(1): 33-37+42. DOI:10.3969/j.issn.1673-3185.2009.01.007 [3] 吴方良, 吴晓光, 马运义, 等. 潜艇实艇阻力预报方法研究[J]. 中国舰船研究, 2009, 4(3): 28-32. DOI:10.3969/j.issn.1673-3185.2009.03.006 [4] 司朝善, 姚惠之, 张楠. 大尺度高雷诺数下水下航行体的数值模拟分析研究[C]// 第十一届全国水动力学学术会议暨第二十四届全国水动力学研讨会并周培源诞辰110周年纪念大会文集(上册), 2012: 411-420. [5] 王展智, 熊鹰, 孙海涛, 等. 双桨船附体阻力尺度效应[J]. 上海交通大学学报, 2015, 49(2): 255-261. DOI:10.16183/j.cnki.jsjtu.2015.02.020 [6] 张恒, 詹成胜. 基于CFD的船舶阻力尺度效应研究[J]. 武汉理工大学学报(交通科学与工程版), 2015, 39(2): 329-332. [7] 蔡博奥, 秦江涛, 毛筱菲, 等. 尺度效应对三体船各阻力成分的影响[J]. 武汉理工大学学报(交通科学与工程版), 2018, 42(3): 487-491+496. [8] 师超, 韩阳, 邱耿耀. 基于CFD技术船体尺度对操纵运动的影响研究[C]// 第三十一届全国水动力学研讨会论文集(下册), 2020: 648−655. [9] DOGRUL A, SONG S, DEMIREL Y K. Scale effect on ship resistance components and form factor[J]. Ocean Engineering, 2020, 209: 107428. DOI:10.1016/j.oceaneng.2020.107428 [10] 宋科委, 郭春雨, 孙聪, 等. 实尺度船舶阻力计算及尺度效应研究[J]. 华中科技大学学报(自然科学版), 2021, 49(6): 74-80. [11] SEZEN S, DELEN C, DOGRUL A, et al. An investigation of scale effects on the self-propulsion characteristics of a submarine[J]. Applied Ocean Research, 2021, 113: 102728. DOI:10.1016/j.apor.2021.102728 [12] MENTER F R, KUNTZ M, LANGTRY R. Ten years of industrial experience with the SST turbulence model[J]. Turbulence, Heat and Mass Transfer, 2003, 4: 625-632. [13] STERN F, WILSON R V, COLEMAN H W, et al. Verification and validation of CFD simulations[R]. IIHR Report No. 407, Iowa Institute of Hydraulic Research, The University of Iowa, 1999.