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流体运动的复杂性是出于流体本身特性所决定的,流体的惯性、流体的可压缩性、流体的黏性等使得如何描述、测量流体运动变得较为困难。再加上流体运动是否为定常或非定常流动,有旋或无旋流动,层流或湍流流动等,这些流动特点同样导致了流体运动的复杂性。根据流体运动的物理特性,数学家和物理学家们以数学表达的形式建立了流体运动的相关方程组用以描述流体运动[17]。
质量守恒方程可表示为:
$$ \frac{{\partial \rho }}{{\partial t}} + \frac{{\partial \left( {\rho {u_i}} \right)}}{{\partial {x_i}}} = 0 $$ (1) 动量守恒方程可表示为:
$$ \begin{split} & \rho \frac{{\partial {u_i}}}{{\partial t}} + \rho {u_j}\frac{{\partial {u_i}}}{{\partial {x_j}}} + \frac{{\partial p}}{{\partial {x_i}}} - \left( {{\rho _0} - \rho } \right){g_i} =\\ & \frac{\partial }{{\partial {x_j}}}\left[ {\mu \left( {\frac{{\partial {u_i}}}{{\partial {u_j}}} + \frac{{\partial {u_j}}}{{\partial {u_i}}}} \right)} \right] - \frac{2}{3}\frac{\partial }{{\partial {x_i}}}\left( {\mu \frac{{\partial {u_j}}}{{\partial {x_j}}}} \right) \end{split} $$ (2) 式中:ρ0为环境流体密度;
$\;\mu $ 为动力粘性系数;${u_i}\left( {i = 1,2} \right)$ 代表了x、y方向上的速度分量。能量守恒方程可表示为:
$$ \rho {c_p}\frac{{\partial T}}{{\partial t}} + \rho {c_p}{u_j}\frac{{\partial T}}{{\partial {x_j}}} = {u_j}\frac{{\partial p}}{{\partial {x_j}}} + \frac{\partial }{{\partial {x_j}}}\left( {\lambda \frac{{\partial T}}{{\partial {x_j}}}} \right) $$ (3) 受温度影响,环境水体密度状态方程可表示为:
$$ \rho (T) = - 6.71 + 9.119T - 0.026\;45{T^2} + 2.399 \times {10^{ - 5}}{T^3} $$ (4) 选择Realizable k-模型将湍流的脉动值附加项与时均值联系起来。
湍动能k方程可表示为:
$$ \frac{{\partial \left( {\rho k} \right)}}{{\partial t}} + \frac{{\partial \left( {\rho {u_j}k} \right)}}{{\partial {x_j}}} = \frac{\partial }{{\partial {x_j}}}\left[ {\left( {\mu + \frac{{{\mu _t}}}{{{\sigma _{{k}}}}}} \right)\frac{{\partial k}}{{\partial {x_j}}}} \right] + {G_k}{\kern 1pt} {\kern 1pt} + {G_b} - \rho \varepsilon $$ (5) 耗散率ε方程可表示为:
$$ \begin{split} \frac{{\partial \left( {\rho \varepsilon } \right)}}{{\partial t}} +& \frac{{\partial \left( {\rho {u_j}\varepsilon } \right)}}{{\partial {x_j}}} = \frac{\partial }{{\partial {x_j}}}\left[ {\left( {\mu + \frac{{{\mu _t}}}{{{\sigma _{\text{ε}}}}}} \right)\frac{{\partial \varepsilon }}{{\partial {x_j}}}} \right] + \rho {C_1}S\varepsilon - \\ & \rho {{{C}}_{\text{2}}}\frac{{{\varepsilon ^2}}}{{k + \sqrt {\nu \varepsilon } }} + {{{C}}_{{\text{1ε}}}}\frac{\varepsilon }{k}{C_{3\varepsilon }}{G_b} \\ \end{split} $$ (6) 式中:
${G_{{k}}}$ 代表平均速度梯度引起的湍动能;${G_{{b}}}$ 代表浮升影响引起的湍动能;${{{C}}_{{{1ε}}}}{\text{ = 1}}{\text{.44}}$ ;${{{C}}_{\text{2}}}{\text{ = }}1.9$ ;${\sigma _k}{\text{ = }}1.0$ ;${\sigma _{{ε}}}{\text{ = }}1.2$ 。其中
$$ {C_1} = \max \left[ {0.43,\frac{1}{{\eta + 5}}} \right]\text{,} \eta = S\frac{k}{\varepsilon } \text{,} S = \sqrt {2{S_{ij}}{S_{ij}}} {C_{3\varepsilon }} = \tanh \left| {\frac{v}{u}} \right| $$ (7) 式中:v为平行于重力矢量的速度分量;u为垂直于重力矢量的速度分量。
$$ {\mu _t} = \rho {C_\mu }\frac{{{k^2}}}{\varepsilon } $$ (8) 其中
$$ {C_\mu } = \frac{1}{{{A_0} + {A_s}\dfrac{{k{U^*}}}{\varepsilon }}} $$ (9) 其中
$$ {{{A}}_{\text{0}}} = 4.04\text{,} {A_s} = \sqrt 6 \cos \varphi \text{,}{U^*} \equiv \sqrt {{s_{ij}}{s_{ij}} + {{\tilde \varOmega }_{ij}}{{\tilde \varOmega }_{ij}}} $$ $$ \begin{split} & \varphi = \frac{1}{3}{\arccos }\left( {\sqrt 6 W} \right)\text{,} W = \frac{{{s_{ij}} + {s_{jk}} + {s_{ki}}}}{{{{\tilde s}^3}}}\text{,} W = \frac{{{s_{ij}} + {s_{jk}} + {s_{ki}}}}{{{{\tilde s}^3}}}\text{,}\\ & {s_{ij}} = \frac{1}{2}\left( {\frac{{\partial {u_j}}}{{\partial {x_i}}} + \frac{{\partial {u_i}}}{{\partial {x_j}}}} \right) \end{split} $$ 式中:
${\tilde \varOmega _{{{ij}}}}$ 在角速度为$\omega $ 的移动参考系中的平均旋转速率张量。 -
在空间维度中,以排放口中心为坐标原点,环境流体流动方向为X轴负方向,热射流排出方向为Y轴正方向,重力方向为Z轴负方向建立三维直角坐标系。各结构椭圆形排放口长短半径分别沿X轴及Z轴方向分布。定义Z轴上椭圆形排放口半径与X轴上椭圆形排放口半径之比为半径比。表1为不同半径比椭圆形排放口结构参数。各结构椭圆形排放口如图3所示。
从图4中热射流流迹可以看出,受环境水体运动影响,冷却水排出后出现分流现象,形成两股热射流。其中一股热射流在Z轴方向上浮升较快,但在Y轴方向上运动距离较小;另一股热射流浮升高度较低,但排出的距离较远。由于出口速度较大,热射流在射出一段距离后才开始向后运动,运动状态受航行器壁面影响较小。
表 1 不同半径比椭圆形排放口结构参数
Table 1. Structure parameters of different radius ratio oval discharge ports
Number Radius in Z-axis/m Radius in X-axis/m Radius ratio Str 1 0.004 0.025 4∶25 Str 2 0.005 0.02 1∶4 Str 3 0.008 0.0125 16∶25 Str 4 0.01 0.01 1∶1 Str 5 0.0125 0.008 25∶16 Str 6 0.02 0.005 4∶1 Str 7 0.025 0.004 25∶4 从图5中排放口附近流体运动可以发现,来流与冷却水掺混时在排放口后方形成了涡旋运动。由于热射流温度高、速度快,流体压力较小,与排放口后方环境水体产生压力差,由此形成了排放口后方与来流方向完全相反的流体运动。因此,受环境水体逆流运动影响,冷却水在排出后形成两股运动状态不同的热射流。环境水体与热射流之间充分接触掺混,接触面周长即为圆形排放口周长,约62.832 mm。
图 5 圆形排放口热射流局部速度矢量图
Figure 5. Local velocity vector diagram of thermal jet from circle discharge port
图6为热射流排放20 s时水面温度云图,受热射流温度影响,环境水体自由液面形成了部分温度升高区域,温升区域以某一点为中心向四周扩散。由于热射流分流现象的出现,导致水面温升区域存在两个温度中心,水面温度扩散区域以X轴方向上横向扩散为主。水面温升区域在X轴方向上的最大扩散距离为2.138 m,在Y轴方向上的最大扩散距离为0.794 m。
按照相同的模型、相同的网格划分、相同的计算参数设置对不同半径比椭圆形排放口排出热射流过程进行计算。对计算结果进行分析后得到不同半径比椭圆形排放口作用下热射流水面温升区域特征数值。
表2为各半径比椭圆形排放口热射流排放20 s时在水面形成的温度扩散区域相关特征的数值。以圆形(结构4)排放口特征值为标准值,当排放口半径比小于1时,水面最高峰值温度下降,与标准值相比,最大降幅为52.03%。当排放口半径比发生变化,热射流水面温度扩散区域横向扩散最大距离变化不大,纵向扩散最大距离减少25.82%~34.38%。
虽然不同半径比椭圆形排放口面积相同,但是排放口周长不同。其中,结构1与结构7排放口周长最大为241.080 mm,而圆形(结构4)排放口周长最小为62.832 mm。排放口周长越大,热射流在排放口出口处与环境水体的接触面越大,掺混换热效果越好。
从图7中半径比4∶25和25∶4的椭圆形排放口热射流流迹来看,半径比越小,热射流在出口处宽度越小,热射流温度衰减越快,浮升较快的一股热射流流量也越小。半径比小于1的椭圆形排放口作用下热射流分流现象更加明显,半径比为4∶25时,热射流对水面温升扩散区域的影响小于半径比为25∶4的椭圆形排放口作用。
表 2 不同半径比椭圆形排放口热射流水面温度场特征值
Table 2. Surface temperature value of thermal jet from different radius ratio oval discharge ports
Number Peak temperature/
KDiffusion distance
in X-axis/mDiffusion distance in
Y-axis/mStr 1 293.071 2.152 0.521 Str 2 293.109 2.140 0.580 Str 3 293.101 2.119 0.539 Str 4 293.148 2.138 0.794 Str 5 293.100 2.129 0.541 Str 6 293.152 2.213 0.586 Str 7 293.196 2.333 0.589
Influence of the discharge port structure on infrared characteristics of underwater vehicle thermal jet
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摘要: 水下航行器动力系统循环冷却水经由排放口排出,与环境水体掺混换热形成热射流。热射流在环境水体中扩散、浮升并在水体表面形成红外特征。为探究排放口结构对水下航行器热射流红外特征的影响,文中采用仿真分析结合实验验证的方法进行研究。依托CFD计算软件平台建立水下航行器运动模型,设计不同半径比椭圆形排放口结构并对比热射流红外特征差异。通过缩比水池实验验证椭圆形排放口半径比对热射流红外特征的影响,同时验证仿真计算方法及设计参数的有效性。在椭圆形排放口的基础上,进一步设计排放口数量及分布位置,抑制热射流红外特征,提升水下航行器热隐身性能。根据仿真计算及实验结果可知,在排放流量相同的条件下,半径比越小的椭圆形排放口热射流掺混换热效果越好,红外特征越不明显。同时,增加排放口数量以及排放口分布位置采用两翼排列方式可以进一步加强热射流温度衰减,降低水面最高峰值温度。Abstract: The circulating cooling water of the underwater vehicle power system discharged from the discharge port, mixed with the environmental water for heat exchange and formed the thermal jet. The thermal jet diffused and floated in the environmental water and forms infrared characteristics on the surface of the water. In order to explore the influence of the structure of the discharge port on the infrared characteristics of the underwater vehicle thermal jet, this paper used the method of simulation analysis and experimental verification. Based on the CFD calculation software platform, the motion model of underwater vehicle was established, the structure of different radius-ratio oval discharge ports was designed, and the infrared characteristics of thermal jet were compared. The influence of the radius ratio of the oval discharge port on the infrared characteristics of the thermal jet was verified by the scale tank experiment, and the authenticity of the simulation calculation method and design parameters was verified at the same time. On the basis of oval discharge ports, the number and distribution position of discharge ports were further designed to suppress the infrared characteristics of thermal jet and improve the thermal stealth performance of underwater vehicles. According to the simulation calculation and experimental results, under the condition of the same discharge flow, the smaller the radius ratio was, the better the mixed heat transfer effect of the oval discharge port was, and the less obvious the infrared characteristics were. At the same time, increasing the number of discharge ports and adopting the symmetrical arrangement of discharge ports could further strengthen the temperature attenuation of thermal jet and reduce the surface maximum temperature.
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Key words:
- underwater vehicle /
- thermal jet /
- discharge port /
- structure design /
- infrared characteristics
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表 1 不同半径比椭圆形排放口结构参数
Table 1. Structure parameters of different radius ratio oval discharge ports
Number Radius in Z-axis/m Radius in X-axis/m Radius ratio Str 1 0.004 0.025 4∶25 Str 2 0.005 0.02 1∶4 Str 3 0.008 0.0125 16∶25 Str 4 0.01 0.01 1∶1 Str 5 0.0125 0.008 25∶16 Str 6 0.02 0.005 4∶1 Str 7 0.025 0.004 25∶4 表 2 不同半径比椭圆形排放口热射流水面温度场特征值
Table 2. Surface temperature value of thermal jet from different radius ratio oval discharge ports
Number Peak temperature/
KDiffusion distance
in X-axis/mDiffusion distance in
Y-axis/mStr 1 293.071 2.152 0.521 Str 2 293.109 2.140 0.580 Str 3 293.101 2.119 0.539 Str 4 293.148 2.138 0.794 Str 5 293.100 2.129 0.541 Str 6 293.152 2.213 0.586 Str 7 293.196 2.333 0.589 -
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