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船舶操纵水动力导数的数值求解及敏感度分析

孙寒冰 肖佳峰 王伟 刘伟杰 郑兴

孙寒冰, 肖佳峰, 王伟, 等. 船舶操纵水动力导数的数值求解及敏感度分析[J]. 中国舰船研究, 2022, 17(1): 60–70 doi: 10.19693/j.issn.1673-3185.02243
引用本文: 孙寒冰, 肖佳峰, 王伟, 等. 船舶操纵水动力导数的数值求解及敏感度分析[J]. 中国舰船研究, 2022, 17(1): 60–70 doi: 10.19693/j.issn.1673-3185.02243
SUN H B, XIAO J F, WANG W, et al. Numerical solution and sensitivity analysis of hydrodynamic force derivatives on maneuverability prediction[J]. Chinese Journal of Ship Research, 2022, 17(1): 60–70 doi: 10.19693/j.issn.1673-3185.02243
Citation: SUN H B, XIAO J F, WANG W, et al. Numerical solution and sensitivity analysis of hydrodynamic force derivatives on maneuverability prediction[J]. Chinese Journal of Ship Research, 2022, 17(1): 60–70 doi: 10.19693/j.issn.1673-3185.02243

船舶操纵水动力导数的数值求解及敏感度分析

doi: 10.19693/j.issn.1673-3185.02243
基金项目: 国家重点研发计划资助项目(2018YFC1508405);国家自然科学基金资助项目(52071100);装备预研基金资助项目(614222303030917);中央高校基本科研业务费专项资金资助项目(3072020CF0102)
详细信息
    作者简介:

    孙寒冰,女,1985年生,博士,副教授。研究方向:船舶操纵性预报及水动力计算方法研究。E-mail: sunhanbing@hrbeu.edu.cn

    肖佳峰,男,1995年生,硕士生。研究方向:船舶操纵性预报及水动力计算。E-mail: xiao3201263@hrbeu.edu.cn

    王伟,男,1991年生,高级工程师

    郑兴,男,1980年生,博士,教授。研究方向:船舶水动力学。E-mail: zhengxing@hrbeu.edu.cn

    通信作者:

    郑兴

  • 中图分类号: U661.33

Numerical solution and sensitivity analysis of hydrodynamic force derivatives on maneuverability prediction

知识共享许可协议
船舶操纵水动力导数的数值求解及敏感度分析孙寒冰,等创作,采用知识共享署名4.0国际许可协议进行许可。
  • 摘要:   目的  为了兼顾船舶操纵运动预报的成本与精度,基于数值计算方法,结合水动力导数敏感度分析,提出一种船舶操纵运动预报方法。  方法  首先,求解RANS方程,应用流体体积(VOF)法捕捉自由液面,采用动态网格方法对DTMB 5415船型进行约束运动的数值计算,并将回归得到的线性水动力导数与试验值进行对比,验证数值方案的有效性;然后,基于MMG分离建模方法建立DTMB 5415船模的操纵数学模型,并利用龙格-库塔算法进行求解,对船舶回转和Z形操纵运动进行仿真;最后,分析水动力导数对这2种操纵运动的敏感度。  结果  结果显示,采用所提方法得到的操纵轨迹和衡准参数仿真结果与试验结果一致,回转运动参数的平均误差为5.1%,Z形操纵运动参数的平均误差为11.7%,较文献使用CFD进行自航船模模拟得到运动参数的精度与计算成本均有所改善;水动力敏感度分析结果也验证了部分非线性水动力导数对操纵性衡准的影响较小,可以使用经验公式进行估算。  结论  研究表明采用所提方法进行船舶操纵性预报方法可行,可在满足工程应用精度的同时大大减少计算成本,尤其适用于船舶设计阶段的操纵性预报及优化。
  • 图  DTMB 5415模型示意图

    Figure  1.  Schematic diagram of DTMB 5415 ship model

    图  DTMB 5415船模在流域中的位置及边界条件示意图

    Figure  2.  Computational domain and boundary conditions of DTMB 5415 ship model

    图  网格划分方案

    Figure  3.  Mesh division schemes

    图  CFD阻力计算值、试验值及拟合曲线

    Figure  4.  The calculated results, experimental data and fitting curve of CFD resistance

    图  纯横荡运动横向力、回转力矩的计算值与试验值比较

    Figure  5.  Comparison of the calculated results and experimental data of sway force and yaw moment in pure sway motion

    图  纯艏摇运动横向力、回转力矩的计算值与试验值比较

    Figure  6.  Comparison of the calculated and experimental data of sway force and yaw moment of pure yaw motion

    图  纯横荡运动兴波

    Figure  7.  The wave-making of pure sway motion

    图  纯艏摇运动兴波

    Figure  8.  The wave-making of pure yaw motion

    图  回转运动中仿真值与试验值的对比

    Figure  9.  Comparison of the simulated results and experimental data for turning motion

    图  10  Z形运动仿真值与试验值的对比

    Figure  10.  Comparison of the simulated results and experimental data for zigzag motion

    表  DTMB 5415船模主要参数

    Table  1.  Main parameters of DTMB 5415 ship model

    主尺度全尺度模型MARIN模型
    缩尺比λ135.48
    垂线间长Lpp /m1424.002
    型宽B/m19.060.538
    吃水T/m6.150.173
    $排水体积 \nabla/{\mathrm{m} }^{3}$8 424.40.189
    湿表面面积S/m22 972.62.361
    螺旋桨直径DP /m6.150.173
    舵面积AR /m215.40.012 2
    下载: 导出CSV

    表  网格收敛性分析

    Table  2.  Grid convergence analysis

    网格类型网格数量总阻力Rf /N误差/%
    计算值试验值
    细网格2.46×10618.41618.410.03
    中等网格1.10×10618.53418.410.67
    粗网格0.56×10618.82118.412.23
    ${R_{\rm{G}}}$0.41
    下载: 导出CSV

    表  DTMB 5415船模的总阻力CFD计算值与试验值比较

    Table  3.  Comparison of the CFD calculated results and experimental data of total resistance for DTMB 5415 ship model

    $F_r= U/\sqrt{gL}$U/(m·s−1)总阻力Rf /N误差/%
    计算值试验值
    0.1380.8644.2864.32−0.79
    0.2101.31510.15
    0.2801.75118.53418.410.67
    0.3302.06727.12
    0.4102.56755.0555.46−0.73
    下载: 导出CSV

    表  纯横荡计算工况

    Table  4.  Calculation conditions of pure sway motion

    Fru/(m·s−1)f /(r·min−1)a/m$ v'_{\text{max}} $
    0.281.75570.083 60.03
    0.281.75570.167 00.07
    0.281.75570.415 80.17
    下载: 导出CSV

    表  纯艏摇计算工况

    Table  5.  Calculation conditions of pure yaw motion

    Fru/(m·s−1)f /(r·min−1)$ {\psi }_{\mathrm{m}\mathrm{a}\mathrm{x}} $/rad$ r'_{\text{max}} $
    0.281.75570.029 910.05
    0.281.75570.179 50.30
    0.281.75570.269 20.45
    0.281.75590.279 20.60
    0.281.75590.349 00.75
    下载: 导出CSV

    表  二次拟合的水动力导数

    Table  6.  Hydrodynamic derivatives obtained by quadratic fitting

    水动力导数计算值试验值误差/%
    $ {Y}_{\nu } $−160.7−190.2−15.51
    $ {Y}_{\dot{\nu }} $−151.6−161.5−6.13
    $ {N}_{\nu } $−431.7−426.31.27
    $ {N}_{\dot{\nu }} $−85.45−86.26−0.94
    $ {Y}_{r} $−181−172.54.93
    $ {Y}_{\dot{r}} $−67.27−63.785.47
    $ {N}_{r} $−551.9−547.60.79
    $ {N}_{\dot{r}} $−203.4−2030.20
    下载: 导出CSV

    表  经验公式计算的水动力导数

    Table  7.  Hydrodynamic derivatives calculated by empirical formulas

    水动力导数数值水动力导数数值
    $ X_{vv}' $−0.086$ Y_{vrr}' $−0.940
    $ X_{rr}' $0.007$ N_{vv}' $0.086
    $ X_{vr}' $−0.052$ N_{rr}' $−0.056
    $ Y_{vv}' $−4.162$ N_{vvr}' $−0.614
    $ Y_{rr}' $−0.015$ N_{vrr}' $−0.016
    $ Y_{vvr}' $−0.407$ X\dot{u} $−0.020
    下载: 导出CSV

    表  回转运动参数仿真值与试验值的对比

    Table  8.  Comparison of the simulated results and experimental data for turning motion parameters

    参数仿真值试验值SB[18]CFDB[5]EMP[20]本文方法与
    试验值间的
    误差/%
    Ad /m382.4385379.14411.8362.1−0.68
    Tr /m237.2215252.76224.36163.310.3
    DT /m548.1518556.64549.54401.865.81
    Do /m544.1519.13555.22381.984.81
    rs /(rad·s−1)0.026 380.024 80.026 746.37
    Us /(m·s−1)7.1476.9457.4085.7412.9
    预报平均
    误差/%
    8.35.819.25.1
    下载: 导出CSV

    表  Z形操纵运动参数仿真值与试验值的对比

    Table  9.  Comparison of simulated results and experiment data for zigzag motion parameters

    参数仿真值试验值SB[18]CFDB[5]本文方法与
    试验值的误差/%
    $ {\psi }_{\mathrm{m}\mathrm{a}\mathrm{x}1}/ $(°)25.8224.6124.1526.384.9
    $ {\psi }_{\mathrm{m}\mathrm{a}\mathrm{x}2}/ $(°)25.8424.9624.6927.023.5
    $ {\psi }_{\mathrm{O}\mathrm{V}1}/ $(°)5.824.614.156.3826.2
    $ {\psi }_{\mathrm{O}\mathrm{V}2}/ $(°)5.844.964.697.0217.7
    $ {t}_{\alpha }/ $s21.825.1−13.1
    $ {t}_{\mathrm{l}}/ $s3.5563.44.6
    预报平均误差/%4.623.811.7
    下载: 导出CSV

    表  10  水动力导数对回转运动参数的敏感度

    Table  10.  Sensitivity of hydrodynamic derivatives to turning motion parameters

    水动力导数敏感度/%敏感度
    平均值/%
    AdTrDTDorsUs
    Yv 1.75 7.59 4.53 4.15 −1.76 2.78 3.76
    $ {Y}_{\dot{\nu }} $ −0.27 −2.63 −3.12 −3.73 −2.61 −6.38 3.13
    Yr −1.73 −7.47 −4.36 −4.06 1.77 −2.65 3.67
    Nv −31.01 −36.09 −35.72 −35.50 32.60 0.40 28.55
    Nr 30.32 34.97 34.76 34.69 −36.94 −0.65 28.72
    $ {N}_{\dot{r}} $ 2.80 −0.31 −0.23 0.00 0.00 0.00 0.56
    Xvr 0.84 1.85 1.67 1.77 1.22 3.04 1.73
    Xvv −0.39 −0.63 −0.80 −0.86 −0.61 −0.27 0.59
    Xrr 0.40 1.08 0.76 0.79 0.55 1.37 0.82
    Yvv 2.14 12.28 7.47 7.19 −2.96 4.89 6.15
    Yrr −0.11 −0.59 −0.43 −0.41 0.18 −0.27 0.33
    Yvrr 0.95 6.48 3.99 4.08 −1.72 2.79 3.34
    Yvvr −0.11 −0.67 −0.52 −0.52 0.23 −0.35 0.40
    Nvv 1.89 2.41 2.40 2.41 −2.44 −0.03 1.93
    Nrr 14.18 18.25 18.46 18.60 −20.13 −0.32 14.99
    Nvrr −0.56 −0.71 −0.79 −0.81 0.82 0.01 0.62
    Nvvr 6.52 8.80 8.99 9.08 −9.23 −0.12 7.12
    下载: 导出CSV

    表  11  水动力导数对Z形操纵运动参数的敏感度

    Table  11.  Sensitivity of hydrodynamic derivatives to zigzag motion parameters

    水动力导数敏感度/%敏感度
    平均值/%
    $ {\psi }_{\mathrm{O}\mathrm{V}1} $$ {\psi }_{\mathrm{O}\mathrm{V}2} $$ {t}_{\alpha } $$ {t}_{\mathrm{l}} $
    Yv −3.45 −3.22 4.36 −33.75 11.19
    $ {Y}_{\dot{\nu }} $ 0.19 0.16 4.13 16.87 5.34
    Yr 2.63 2.62 −4.36 22.63 8.06
    Nv 16.55 16.03 −32.80 88.59 38.49
    Nr −17.20 −16.09 29.36 −66.09 32.18
    $ {N}_{\dot{r}} $ 4.43 4.27 6.88 50.62 16.55
    Xvr 0.27 0.38 0.00 1.41 0.51
    Xvv −0.14 −0.47 0.00 0.00 0.15
    Xrr 0.12 0.36 0.00 0.00 0.12
    Yvv −4.53 −3.97 3.90 −39.37 12.94
    Yrr 0.42 0.06 0.00 1.41 0.47
    Yvrr −1.23 −0.96 1.38 −11.25 3.71
    Yvvr 0.39 0.07 0.00 1.41 0.47
    Nvv −0.53 −0.77 1.61 −4.22 1.78
    Nrr −4.60 −5.08 8.94 −16.87 8.87
    Nvrr 0.42 0.45 0.00 0.00 0.22
    Nvvr −2.30 −1.80 2.75 −5.62 3.12
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-12-30
  • 录用日期:  2022-01-28
  • 修回日期:  2021-03-23
  • 网络出版日期:  2022-01-28
  • 刊出日期:  2022-03-02

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