﻿ FLUENTTM求解器在螺旋桨耦合系统水动力分析中的应用
 舰船科学技术  2024, Vol. 46 Issue (12): 178-181    DOI: 10.3404/j.issn.1672-7649.2024.12.032 PDF
FLUENTTM求解器在螺旋桨耦合系统水动力分析中的应用

Application of FLUENTTM solver in hydrodynamic analysis of propeller coupling system
ZHAI Youwen
Department of Mechanical and Electrical Engineering, Kunming University, Kunming 650214, China
Abstract: This article studies numerical calculation methods, focusing on grid partitioning and control equations. It analyzes the numerical model of turbulence, focuses on exploring the mathematical expression of vortex viscosity model, and applies k- ε Model and k- ω Two types of two equation models were analyzed, and the variation curves of wall flow velocity at different positions were provided. Analyzed the characteristics of ship propellers and provided the variation curves of efficiency and thrust under different propulsion coefficients. A simulation was conducted on the coupling system of the ship's propeller, and the hydrodynamic characteristics were analyzed. This study contributes to the rapid development of ship propeller technology in China.
Key words: propeller     coupling system     hydrodynamic force
0 引　言

1 数值计算方法 1.1 网格划分及控制方程

FLUENTTM求解器可生成输入模型所对应的计算网格，并且针对复杂的模型以及流体可对相应部位的网格进行加密处理，进而得到细化程度更高的网格，同时在对模型进行网格划分的过程中可采用自动适应处理，这样能降低模型网格生成所需要的时间[7]。其细化的数学模型为：

 ${2^N} = \frac{{\Delta {X_{init}}}}{{\Delta {X_{targ }}}}\text{，}$ (1)
 $N = \log \left( {\frac{{\Delta {X_{init}}}}{{\Delta {X_{targ }}}}} \right) \text{。}$ (2)

 $y = \max \left( {{y_{\min }},\min \left( {30 + \frac{{\left( {{Re} - 1{e^6}} \right) \times 270}}{{1{e^9}}}} \right),{y_{\max }}} \right)\text{。}$ (3)

 ${Y_{wall}} = 6{\left( {\frac{{{V_{ref}}}}{V}} \right)^{ - \frac{7}{8}}}{\left( {\frac{{{L_{ref}}}}{2}} \right)^{\frac{1}{8}}}{y^ + }\text{。}$ (4)

 $\frac{{{\mathrm{D}}\rho }}{{{\mathrm{D}}t}} + \rho div\left( V \right) = 0\text{。}$ (5)

 $\frac{{{\mathrm{D}}\rho }}{{{\mathrm{D}}t}} = 0\text{，}$ (6)
 $\frac{{\partial u}}{{\partial x}} + \frac{{\partial v}}{{\partial y}} + \frac{{\partial w}}{{\partial z}} = 0\text{。}$ (7)

 $\nabla \cdot v = 0\text{，}$ (8)
 $\frac{{{\mathrm{D}}v}}{{{\mathrm{D}}t}} = {F_b} - \frac{1}{\rho }\nabla p + \upsilon \Delta v + \frac{1}{3}\upsilon \nabla \left( {\nabla \cdot v} \right)\text{，}$ (9)
 $\frac{{\partial {u_i}}}{{\partial t}} + \frac{\partial }{{\partial {x_j}}}\left( {{u_i}{u_j}} \right) = - \frac{1}{\rho }\frac{{\partial p}}{{\partial {x_i}}} + \upsilon \frac{\partial }{{\partial {x_j}}}\left( {\frac{{\partial {u_i}}}{{\partial {x_j}}} + \frac{{\partial {u_j}}}{{\partial {x_i}}}} \right)\text{。}$ (10)
1.2 湍流数值模型

 $- \overline {\rho {{u'}_i}{{u'}_j}} = \left| {{\mu _t}\left( {\frac{{\partial {u_i}}}{{\partial {x_j}}} + \frac{{\partial {u_j}}}{{\partial {x_i}}}} \right) - \frac{2}{3}} \right.\left( {\rho k + \frac{{\partial {u_i}}}{{\partial {x_i}}}} \right){\delta _{ij}}\text{。}$ (11)

 ${\delta _{ij}} = \left\{ {\begin{array}{*{20}{c}} {1}，{i = j}，\\ {0}，{i \ne j}。\end{array}} \right.$ (12)
 $k = \frac{{\overline {{{u'}_i}{{u'}_j}} }}{2}\text{。}$ (13)

 $\varepsilon = \frac{\mu }{\rho }\overline {\left( {\frac{{\partial {{u'}_i}}}{{\partial {x_k}}}} \right)\left( {\frac{{{{u'}_j}}}{{\partial {x_k}}}} \right)} \text{。}$ (14)

 ${\mu _t} = \rho {C_\mu }\frac{{{k^2}}}{\varepsilon }\text{。}$ (15)

k-ω模型中引入了比耗散率和湍动能对湍动粘度进行解算。k-ω模型不但弥补了k-ε模型在解算低雷诺数流动过程中的失真问题，还可对逆压梯度的流动分离现象进行预报。湍流耗散率、湍动能以及比耗散率三者之间的数学关系如下式所示，式中，C为流体特征系数。

 $\omega = \frac{{\varepsilon C}}{k}\text{，}$ (16)

 ${y^ + } = \frac{{\Delta y\rho {u_t}}}{\mu } = \frac{{\Delta y}}{v}\sqrt {\frac{{{\tau _w}}}{\rho }} \text{。}$ (17)
 ${u^ + } = \frac{U}{{{\mu _t}}}\text{。}$ (18)

 图 1 不同位置下的壁面流动速度 Fig. 1 Wall flow velocity at different positions
2 螺旋桨特性分析

 ${K_T} = \frac{T}{{\rho {n^2}{D^4}}}\text{，}$ (19)
 ${\eta _0} = \frac{{{K_T}}}{{{K_Q}}} \cdot \frac{J}{{2{\text{π}} }}\text{。}$ (20)

 图 2 效率随推进系数的变化曲线 Fig. 2 Efficiency variation curve with propulsion coefficient

 图 3 推力随推进系数的变化曲线 Fig. 3 Curve of thrust variation with propulsion coefficient

 ${C_f} = \frac{{{R_f}}}{{0.5\rho {V^2}S}}\text{，}$ (21)
 ${C_t} = \frac{{{R_t}}}{{0.5\rho {V^2}S}}\text{，}$ (22)
 ${C_p} = \frac{{{R_p}}}{{0.5\rho {V^2}S}}\text{。}$ (23)

 图 4 船舶升沉随佛汝德数的变化曲线 Fig. 4 The variation curve of ship's rise and fall with Froude number
3 船体螺旋桨耦合水动力分析

 ${V_x} = - V \times \cos \beta \text{，}$ (24)
 ${V_y} = V \times \sin \beta \text{。}$ (25)

 图 5 扭矩随频率的变化曲线 Fig. 5 Torque variation curve with frequency

 图 6 脉动压强随频率的变化曲线 Fig. 6 The variation curve of pulsating pressure with frequency

 图 7 压力随时间的变化曲线 Fig. 7 Pressure variation curve over time

 图 8 不同频率下功率谱密度的变化曲线 Fig. 8 The variation curve of power spectral density at different frequencies
4 结　语

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