﻿ 散货船纵倾阻力研究
 舰船科学技术  2016, Vol. 38 Issue (12): 48-52 PDF

1. 华中科技大学 船舶与海洋工程学院, 湖北 武汉 430074 ;
2. 船舶与海洋工程水动力湖北省重点实验室, 湖北 武汉 430074 ;
3. 高新船舶与深海开发装备协同创新中心, 上海 200240

The effect of trim adjustment on bulk freighter resistance
SONG Lei1, TU Hai-wen1, XIE Wen-xiong1, SUN Jiang-long1,2,3
1. School of Naval Architecture and Ocean Engineering, Wuhan 430074, China ;
2. Hubei Key Laboratory of Naval Architecture & Ocean Engineering Hydrodynamics, Wuhan 430074, China ;
3. Collaboration Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China
Abstract: During the opratation of shipping, in order to achieve energy-saving emission reduction and the maximum economic benefits, people often hope that under the same loading and the same speeds, the ship could cosume less oil. Adjusting the ship trim angle to reduce the sailing state of ship is a good method simple and effective. Based on the 180 000 DWT bulk carrier at design draft as well as design speed on flat floating state, we adjust the ship pitch and stern, and through the fluent numerical simulation and model experiment to study the different trim effects on ship resistance. Using k-ε and k-ω two turbulence models to solving RANS equation in fluent, calculating the resistance and the increase or reduction rate, together with the experiment date and join the conclusion.
Key words: CFD     trim adjustment     ship resistance
0 引 言

Subramani 和 Paterson 等[1]在考虑船舶航态变化的前提下，对 FF1052 和 S60 采用 CFD 求解船舶阻力、姿态，将计算所得结果与实验值对比，整体变化趋势一致，幅值吻合良好。Yang 等[2]采用有限元法求解 Euler 方程，对比了自由模和拘束模的阻力，对 Wigley 和 S60 船的阻力和姿态采用非结构网格计算，结果与试验吻合良好。Gorski，Hino 等[3-4]使用了 RANS 方法计算船舶黏性流场，用于新型舰船的设计和分析，其中数值计算提供了各种球首变化的流场信息以及螺旋桨进流的流动信息，为设计提供了指导。高高等[5]用 Rankine 源面元法数值计算某内河大方形系数双尾船的浅水下沉量及纵倾，计算得出船体纵倾值随航速的变化趋势，并用试验验证计算结果。董文才等[6-7]提出滑行艇纵向运动的基本假设；建立计及浮性和滑行力、滑行力矩影响的滑行艇纵向运动基本方程，提出预报滑行艇纵向运动的实用计算方法（滑航法）并编制了理论预报程序。吴明等[8]同时求解 RANS 和刚体运动方程，计算 S60 躶船模在浅水中的流场，得出其下沉与纵倾值，并用试验验证，结果吻合。

1 控制方程

 $\frac{{\partial \rho }}{{\partial t}} + \frac{{\partial (\rho {u_i})}}{{\partial {x_i}}}{\rm{ = }}0\text{；}$ (1)

 \begin{aligned} & \frac{{\partial \left( {\rho {u_i}} \right)}}{{\partial t}} + \frac{{\partial \left( {\rho {u_i}{u_j}} \right)}}{{\partial {x_j}}} =-\frac{{\partial \rho }}{{\partial {x_i}}} + \\ & \quad \quad \left. {\frac{\partial }{{\partial {x_i}}}\left[ {\mu (\frac{{\partial {u_i}}}{{\partial {x_j}}} + \frac{{\partial {u_j}}}{{\partial {x_i}}})-} \right.\frac{2}{3}\mu \frac{{\partial {u_l}}}{{\partial {x_l}}}{\delta _{ij}}} \right] + \\ & \quad \quad \frac{\partial }{{\partial {x_j}}}\left( {-p\overline {{u_{i'}}{u_{j'}}} } \right) + \rho {f_i}\text{。} \end{aligned} (2)

 \begin{aligned} & \frac{{\partial \left( {\rho k} \right)}}{{\partial t}} + \frac{{\partial \left( {\rho k{u_i}} \right)}}{{\partial {x_i}}} = \frac{\partial }{{\partial {x_j}}}\left[ {{\alpha _k}{\mu _{eff}}\frac{{\partial k}}{{\partial {x_j}}}} \right] + \\ & \quad \quad \,\, \quad {G_k} + {G_b}-\rho \varepsilon \text{，} \end{aligned} (3)
 \begin{aligned} & \frac{{\partial \left( {\rho k} \right)}}{{\partial t}} + \frac{{\partial \left( {\rho k{u_i}} \right)}}{{\partial {x_i}}} = \frac{\partial }{{\partial {x_j}}}\left[ {{\alpha _k}{\mu _{eff}}\frac{{\partial k}}{{\partial {x_j}}}} \right] + \\ & \quad \quad \,\, {C_{1\varepsilon }}\frac{\varepsilon }{k}({G_k} + {C_{3\varepsilon }}{G_b}){G_k}-{C_{2\varepsilon }}\rho \frac{{{\varepsilon ^2}}}{k}-{R_\varepsilon }\text{。} \end{aligned} (4)
 \begin{aligned} {\text{式中：}}\ \ \ \quad\quad\quad\quad\quad\quad\quad& \varepsilon = \frac{\mu }{\rho }\left( {\frac{{\partial {\mu _i}}}{{\partial {x_k}}}} \right)\left( {\frac{{\partial {\mu _i}}} {{\partial {x_k}}}} \right)\text{，}\\ & {\mu _t} = \rho {C_\mu }\frac{{{k^2}}}{\varepsilon }\text{，}\\ & {\mu _{eff}} = \mu + {\mu _t}\text{。} \quad\quad\quad\quad \end{aligned}

Gk 为平均速度梯度引起的湍流能k 的产生项；Gb 为浮力引起的湍动能k 的产生项；C1εC2εC3ε 为经验常数。

 \begin{aligned} & {G_k} = {\mu _t}\left( {\frac{{\partial {\mu _i}}}{{\partial {x_j}}} + \frac{{\partial {\mu _j}}}{{\partial {x_i}}}} \right)\frac{{\partial {\mu _i}}}{{\partial {x_j}}}\text{，}\\ & {G_b} = \beta {g_i}\frac{{{\mu _t}}}{{P{r_t}}}\frac{{\partial T}}{{\partial {x_i}}}\text{。} \end{aligned}

k-ε 模型中，根据 Launder 等的推荐值及后来的实验验证值，模型常数C1ε = 1.45，C2ε = 1.92，Cμ = 0.09。

2 数值计算

2.1 模型的建立

 图 1 模型计算域 Fig. 1 The model of computational domain
2.2 域的离散

 图 2 船体表面网格 Fig. 2 Grid of ship surface

 图 3 船舶模型首尾部网格 Fig. 3 The grid of bow and stern
2.3 边界条件与求解方法设置

 图 4 残差收敛曲线 Fig. 4 The residual convergence curve

 图 5 阻力收敛曲线 Fig. 5 The convergence curves of resistance

2.4 基于 RNGk-ε 湍流模型各倾角下阻力计算结果

 \begin{aligned} & \text{纵倾阻力}\\ & \text{增减比}{\rm{ = }}\frac{{\text{改变纵倾后阻力}{\rm{-}}\text{平浮阻力}}}{\text{平浮阻力}} \times 100{\rm{\% }}\text{。} \end{aligned}

2.5 基于 SSTk-ω 湍流模型各倾角下阻力计算结果

2.6 各倾角下船体表面动压力分布

 图 6 首倾为 0.603 1° 船体表面动压力分布云图 Fig. 6 Hydrodynamic pressure distribution under 0.603 1° trim angle

 图 7 首倾为 0.301 6° 船体表面动压力分布云图 Fig. 7 Hydrodynamic pressure distribution under 0.301 6° trim angle

 图 8 平浮船体表面动压力分布云图 Fig. 8 Hydrodynamic pressure distribution under 0° trim angle

 图 9 尾倾为 0.603 1° 船体表面动压力分布云图 Fig. 9 Hydrodynamic pressure distribution under-0.3016° trim angle

 图 10 尾倾为 0.603 1° 船体表面动压力分布云图 Fig. 10 Hydrodynamic pressure distribution under-0.6031° trim angle

3 模型试验

 图 11 船舶模型 Fig. 11 Ship modle

 图 12 船模试验过程 Fig. 12 Ship modle test
3.1 模型试验结果

3.2 模型试验结果分析

 图 13 不同倾角阻力值对比 Fig. 13 Resistance comparison of different trim angl

 图 14 不同倾角阻力值增减比 Fig. 14 Resistance increase or decrease ration comparison of different trim angl

4 结 语

1）针对本散货船在不改变船舶航速、载重量的前提下，通过纵倾调节可以减少船舶阻力，达到节能减排的作用。

2）针对本散货船设计吃水、设计航速而言，使船舶首倾可以减少船舶行驶的阻力。首倾角在 0.301 6° 时可以减少 1.25% 的阻力，首倾角在 0.603 1° 时可以减少 2.36% 阻力。由此可看出，在设计载重设计航速下，对于节能减阻而言平浮不是最优航态，使船舶首倾能够提高阻力性能。

3）通过k-εk-ω 两种湍流模型的结果与模型试验结果的对比，可以得出对于本肥大型散货船而言，选取k-ω 湍流模型计算更加合理的结论。

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