﻿ 基于三维动网格技术的潜艇热尾流浮升规律及水面温度特征研究
 舰船科学技术  2018, Vol. 40 Issue (3): 8-13 PDF

1. 哈尔滨工业大学（威海）汽车工程学院，山东 威海 264200;
2. 哈尔滨工业大学（威海）信息与电气工程学院，山东 威海 264200

Study of buoyancy trajectory of thermal wake and temperature characteristics on sea surface based on 3-D dynamic meshing technique
LAI Qing-zhi1, WANG Cheng-an1, TAN Jian-yu1, ZHOU Zhi-quan2
1. School of Automobile Engineering Harbin Institute of Technology at Weihai, Weihai 264200, China;
2. School of Information and Electrical Engineering, Harbin Institute of Technology at Weihai, Weihai 264200, China
Abstract: Obtaining accurately the buoyancy trajectory and the temperature characteristics on sea surface is the basis of infrared technology for detecting submarine. In this paper, the navigation process of submarine in the 3-D sea environment is studied numerically. The dynamic meshing technique is employed and both of fixed wall method and VOF method are used to simulate the buoyancy process of thermal wake. The buoyancy trajectory of the thermal wake, the corresponding temperature distribution and infrared characteristics on sea surface are obtained. Furthermore, the variation of temperature distribution characteristics on sea surface with the discharge program of cooling water is analyzed, and the suppression methods are proposed. The paper provide theoretical base for the experimental study in the future.
Key words: thermal wake     buoyancy characteristics     infrared characteristics on sea surface     suppression method
0 引　言

1 数理模型 1.1 计算模型

 图 1 计算模型示意图 Fig. 1 Schematic diagram of simulation model

1.2 网格技术

 图 2 局部网格示意图 Fig. 2 Schematic diagram of local mesh

 图 3 网格无关性验证 Fig. 3 Validation of mesh independence
1.3 流动传热控制方程

 $\frac{{\partial \rho }}{{\partial t}} + \frac{\partial }{{\partial {x_i}}}\left( {\rho {u_i}} \right) = 0,$ (1)

 $\frac{\partial }{{\partial t}}\left( {\rho {u_i}} \right) + \frac{\partial }{{\partial {x_j}}}\left( {\rho {u_i}{u_j}} \right) = \frac{{\partial p}}{{\partial {x_i}}} + \frac{{\partial {\tau _{ij}}}}{{\partial {x_j}}} + \rho {g_i},$ (2)

 $\begin{split}&\frac{\partial }{{\partial t}}\left[ {\rho \left( {{c_p}T + \frac{{{u^2}}}{2}} \right)} \right] + \frac{\partial }{{\partial {x_j}}}\left[ {\rho {u_j}\left( {{c_p}T + \frac{{{u^2}}}{2}} \right)} \right] = \\ & - \frac{\partial }{{\partial {x_j}}}\left( {p{u_j}} \right) + \frac{\partial }{{\partial {x_j}}}\left( {k\frac{{\partial T}}{{\partial {x_j}}}} \right) + \frac{\partial }{{\partial {x_j}}}\left( {{u_j}{\tau _{ij}}} \right){\text{。}}\end{split}$ (3)

 ${\tau _{ij}} = \left[ {\mu \left( {\frac{{\partial {u_i}}}{{\partial {x_j}}} + \frac{{\partial {u_j}}}{{\partial {x_i}}}} \right)} \right] - \frac{2}{3}\mu \frac{{\partial {u_i}}}{{\partial {x_i}}}{\delta _{ij}}。$ (4)

p相的体积分数满足方程：

 $\frac{\partial }{{\partial t}}\left( {{\alpha _p}{\rho _p}} \right) + \frac{\partial }{{\partial {x_i}}}\left( {{\alpha _p}{\rho _p}{u_i}} \right) = 0.$ (5)

VOF法是目前求解分层流动、有自由表面流动等存在2种或多种互不相溶流体的复杂多相流动问题中最常用的方法。它在计算域内对互不相溶流体求解同一个动量方程，并追踪每种流体的体积分数来模拟多相流动。计算单元内各相体积分数之和为1，在单元内，若αp=0，则单元中没有第p相流体；αp=1，单元中充满第p相流体；0<αp<1，单元中有第p相流体与其他相流体的界面。根据局部αp值，计算域内每一控制容积被赋予适当的物性和变量值。湍流流动是非常复杂的流动，在计算湍流流动时需要附加湍流方程，本文研究均采用标准k-ε湍流模型。

1.4 物性参数及边界设置

 $\rho {{ = }}644.895 + 2.612T - 0.005{T^2},$ (6)
 ${c_{{p}}}{{ = }}6\ 545.302 - 15.377T + 0.025{T^2},$ (7)
 $k{{ = }} - 0.666 + 0.007T - 8.699 \times {10^{ - 6}}{T^2},$ (8)
 $\mu = 0.029\ 303{{ - }}0.000\ 132T + 4.109 \times {10^{ - 10}}{T^3}{\text{。}}$ (9)

2 计算结果 2.1 壁面法热尾流浮升扩散规律
 图 4 纵截面温度分布云图 Fig. 4 Temperature distribution in the longitudinal section

 图 5 热尾流中心温度随其水平扩散距离变化曲线 Fig. 5 Variation of central temperature with horizontal diffusion distance of thermal wake

 图 6 热尾流浮升高度随其水平扩散距离变化曲线 Fig. 6 Variation of rising height varied with horizontal diffusion distance of thermal wake

 图 7 海面温度分布云图 Fig. 7 Temperature distribution on sea surface

 图 8 水面红外图像 Fig. 8 Infrared image of sea surface

2.2 VOF法热尾流浮升扩散规律

 图 9 纵截面温度分布云图 Fig. 9 Temperature distribution in the longitudinal section

 图 10 热尾流浮升高度随扩散距离变化曲线 Fig. 10 Variation of rising height with horizontal diffusion distance of thermal wake

 图 11 海面温度分布云图 Fig. 11 Temperature distribution on sea surface

 图 12 温差异常区域的折算尺寸 Fig. 12 Conversion size of temperature abnormal area

 图 13 水面红外图像 Fig. 13 Infrared image of sea surface

2.3 不同排水方案热尾流浮升扩散规律

 ${v_1} = \frac{Q}{{\rho {c_p}s({T_1} - {T_0})}},$ (10)

 图 14 不同排水方案热尾流浮升高度随扩散距离变化曲线 Fig. 14 Variation of the rising height with diffusion distance of thermal wake for different discharge programs

 图 15 温度异常区域的折算尺寸 Fig. 15 Conversion size of temperature abnormal area

3 结　语

1）潜艇热尾流浮升、扩散过程可分为：近尾流快速扩散、浮升区、过渡区、远尾流表面扩散区三部分；当温差大于0.06 K，热尾流具有较为明显红外识别轮廓。

2）海面空气流动及海-气交界面对热尾流浮升过程及其表面温度分布具有重要影响：受空气流动及交界面影响，热尾流浮升速率降低，水下漂浮距离增加约68%，表面温差大于0.06 K区域尺寸减小约55%。仿真研究中可采用VOF法研究海面空气流动及交界面的对热尾流的影响。

3）排水温度对热尾流浮升过程及其表面温度分布具有重要影响，排水温度增加20 K，表面温差大于0.06 K区域尺寸增大约81%。潜艇航行时可通过适当增加冷却水排出流量，降低排出温度，以减弱潜艇尾迹信号强度，增加自身隐身性能。

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