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为研究海水温度、密度分层对红外探测距离和反演精度的影响。文中建立了全尺寸、包含舰桥和螺旋桨特征的三维模型,通过有限元方法进行对比和分析。
因为文中研究的是水体与空气的分界面,所以采用的是两相流模型(vof)[10],将区域分成空气和水两部分进行仿真,将海—气交界面处视为海平面,分析潜艇热尾流的浮升和扩散。全尺寸潜艇仿真模型如图1所示。
参照海水物性参数随温度变化数据拟合得计算所用相应物性参数关系式如下[11]:
$$ \rho = 644.895 + 2.612T - 0.005{T^2} $$ (1) $$ {c_p} = 6\;545.302 - 15.377T + 0.025{T^2} $$ (2) $$ k = - 0.666 + 0.007T - 8.669 \times {10^{ - 6}}{T^2} $$ (3) $$ \mu = 0.029\;303 - 0.000\;132T + 4.109 \times {10^{ - 10}}{T^3} $$ (4) 式中:
$ \;\rho $ 为密度(kg/m3);$ {c_p} $ 为定压比热容(J/(kg·K));$ T $ 为温度(K);$ k $ 为导热系数(W/(m·K));$\; \mu $ 为粘性系数(Pa·s)。当有太阳光照射时,海水表层区域接收太阳的热量比海水下层多,使得上层水温高于下层,即海水存在垂直负温度梯度,表层海水到1000 m,水温随深度增加而迅速递减,1000 m以下,水温下降变慢。潜艇的下潜深度一般不超过600 m,文中考虑的深度为50 m,此深度海水温度分布近似为线性,选用海水垂直负温度梯度为−0.1667 K/m。当水面温度为293.15 K时,温度深度关系式为:$$ T = 293.15 - 0.166\;67H $$ (5) -
根据质量守恒方程和动量守恒方程整理得到:
$$ \begin{split} & \frac{{\partial {\boldsymbol{u}}}}{{\partial t}} \cdot \rho - \nabla \cdot (\rho {\boldsymbol{u}}) \cdot {\boldsymbol{u}} - \nabla \left[ {\mu \left( {\nabla {\boldsymbol{u}} + \nabla {{\boldsymbol{u}}^{\rm{T}}}} \right)} \right] + \\ & \qquad \nabla \cdot (\rho {\boldsymbol{uu}}) = - \nabla p + {f_b} + \rho \cdot {\boldsymbol{g}} \\ \end{split} $$ (6) 将潜艇热尾流的初始速度矢量初始温度T代入公式(6)便可求得流体的运动变化,再根据能量守恒方程:
$$ \frac{{\partial \left( {\rho {c_p}T} \right)}}{{\partial t}} + \nabla \cdot \left( {\rho {\boldsymbol{u}}{c_p}T} \right) = \nabla (k\nabla T) $$ (7) 求得温度T的变化。其中,
$ {f_b} $ 为每单位体积的表面张力(N/m3);$ {\boldsymbol{u}} $ 为速度矢量(m/s);$ p $ 为流体静压(Pa);$ {\boldsymbol{g}} $ 为重力加速度矢量(m/s2)将整个系统分割成有限个单元,对每个单元根据上述公式进行求解最终求得海面尾流的温差$\Delta T$ 。 -
对于以面源形式存在的热尾流,在估算红外探测器对其的作用距离时,一般用最小可分辨温差法,即:
$$ \Delta T \geqslant \frac{{\pi }^{2}\cdot SN{R}_{d}\cdot f\cdot NETD\cdot \sqrt{a\cdot b}}{8\cdot \ {\tau_s } \cdot \varepsilon \cdot \tau (R)\cdot MTF(f)\cdot \sqrt{{t}_{0}\cdot {t}_{i}\cdot {f}_{p}\cdot \Delta f\cdot {n}_{e}\cdot {\alpha }_{0}}} $$ (8) 式中:
$ SN{R_d} $ 为观察者能分辨线条的阈值信噪比;$a$ 、$b$ 分别为瞬时视场的水平和垂直张角;$ {t_0} $ 为扫描驻留时间;$ {t_i} $ 为人眼的积分时间;$ f $ 为空间频率;$ {f_p} $ 为帧频;$ \Delta f $ 为等效噪声带宽;$ MTF(f) $ 为调制传递函数;${\tau_s }$ 为光学系统透过率;$ NETD $ 为噪声等效温差;$ {n_e} $ 为某一探测概率对应的等效条带对数;$ {\alpha _0} $ 为目标的长宽比;$ {\alpha _0} $ 可根据热尾流的长度s和宽度b 参数进行计算,要注意到热尾流s可能会超出探测器的视角范围,此时计算目标长度需要根据视场角和观测距离进行修正,即长度变为$R\alpha $ 或$R\beta $ 系统的调制传递函数MTF用以衡量系统如实再现场景的程度。其中,$R$ 为红外辐射源与探测器之间的距离;$ \tau (R) $ 为大气平均透过率;$ \varepsilon $ 为海水的发射率。到达探测器的红外辐射,海面红外辐射并非100%辐射,其辐射量由海水的发射率决定,若用温差关系进行描述[13]。从海面发出的红外辐射需要经过大气作为传输介质最终到达探测器,大气对红外辐射的衰减过程中吸收和散射的影响最为明显[14]。在实际应用中,探测器都有一定的响应波段,一般认为在探测器的响应波长内,大气对红外辐射的透过率与波长无关,可用平均值来近似大气平均透过率。不等式(8)的右边为最小可分辨温差计算模型[15],是以观察者主观视觉为准,用以综合评价红外探测器性能的重要参量,它用来表示红外探测器在不同空间频率下的温度灵敏度。红外探测器的MTF由3个分系统即光学系统、探测器、电路的MTF决定[16]。以圆形孔径的衍射限光学系统为例,其光学系统的 MTF为3个分系统MTF的乘积,即:
$$\begin{split} & MTF = MT{F_o} \times MT{F_d} \times MT{F_e}\\ & MTF = \frac{2}{\pi }\left\{ {\arccos \left( {\frac{f}{{{f_c}}}} \right) - \left( {\frac{f}{{{f_c}}}} \right){{\left[ {1 - {{\left( {\frac{f}{{{f_c}}}} \right)}^2}} \right]}^{\tfrac{1}{2}}}} \right\} \times \\ &\qquad \frac{{\sin \left( {\pi {\omega ^{\tfrac{1}{2}}}f} \right)}}{{\left( {\pi {\omega ^{\tfrac{1}{2}}}f} \right)}} \times {\left[ {1 + {{\left( {2{\omega ^{\tfrac{1}{2}}}f} \right)}^2}} \right]^{ - \tfrac{1}{2}}} \\ \end{split} $$ (9) 式中:
$ {f_c} $ 为光学系统的空间截止频率(c/mrad),且有$ {f_c} = {D_0}/\lambda $ ,$\lambda $ 为平均工作波长;${D_0}$ 为红外探测器的通光孔径;ω为系统的瞬时视场。探测概率与等效条带对数
$ {n_e} $ 的关系由 Johnson准则给出。此外还需要满足:$$ \frac{W}{2{n}_{e}R}\geqslant \frac{1}{2f} $$ (10) 式中:
$W$ 为热尾流的临界宽度。若想求得红外探测器能够探测目标的最大作用距离,只需满足等式条件即可得到唯一对应的$R$ 。通过以上分析,当海面热尾流的红外辐射值传递到探测器并大于探测器的MRTD时,且目标对系统张角大于系统的最小分辨角度即认为探测器可探测到的热尾流。首先需要根据热尾流参数估算模型计算出热尾流的尺寸和温差,然后使用MODTRAN软件对探测器的波段的大气透过率进行拟合求得大气平均透过率
$\tau (R)$ ,然后根据Johnson准则给出得探测率和探测等级确定等效条带对数${n_e}$ 计算出探测器此时的MRTD。若满足公式(8)和公式(10)则可以探测,若不满足则视为无法探测。 -
仿真区域的整体尺寸为600 m×100 m×70 m,其中水深60 m,空气10 m。潜艇模型位于水下50 m。文中所使用的潜艇模型长170 m,最大直径13.5 m,热尾流排水口视为半径为1 m的圆面,从潜艇尾部排出。文中选用的红外探测器参数:F#为1,工作波长8~12
$ {\text{μm}}$ ,探测器分辨率640$ \times $ 512,取临界宽度W=6 m,$ \Delta f $ =49 Hz,$ SN{R_d} $ =4,NETD=0.015 K,$ {f_p} $ =50 Hz,$ {f_c} = 4 $ c/mrad,$ {t_0} $ =0.016 s,$ {t_i} $ =0.2 s,$a = b = 0.425$ mrad,${\tau_s }$ =0.8。文中对潜艇热尾流的浮升过程进行了仿真分析,仿真模型设置航行速度V=1 m/s。热尾流排水口的流速为Vr=1.5 m/s,潜艇的热尾流温度设置为325 K。对水体温度和密度分层的海水进行仿真,水面的温度均取常温293.15 K。仿真得到的水面温度分布图如图3(a)所示。在相同工况下水体的温度和密度不分层的情况下再次进行仿真得到水面分布如图3(b)所示。图 3 (a)水体密度、温度分层条件下水面温度分布图;(b)水体密度、温度不分层条件下水面温度分布图
Figure 3. (a) Temperature distribution map of water surface under conditions of water density and temperature stratification; (b) Temperature distribution map of water surface under conditions of uniform water density and temperature
由图3(a)可知,潜艇的尾流在水面呈现出冷尾迹现象,此时温度异常区域的最低温度要比海平面的平均温度低0.235 K。由于温度分层,在水下50 m处的水温度更低,因此水体密度也随之变大。当排出的热尾流温度、密度相同时,更大的密度差有利于热尾流上浮。当热尾流浮升速度大于热交换速度时,水面下冷水会被尾流排出的热尾流向上一同带到水面。因此,在水面形成了冷尾迹现象。相同工况下,不分层水域潜艇的尾流温度高于水面的平均温度。此时尾流所在温度异常区域的最高温度要比海平面的平均温度高0.083 K。当海水温度密度不分层时,热尾流排出后相比前者密度差更小,在浮升速度上也相对较慢,热尾流在浮升过程中有更长的时间与水体进行热交换,因此,浮升至水面后的温差也相对较小。
使用MODTRAN得到了垂直向下探测情况下热带夏季海洋气溶胶条件下不同距离对应的8~12 μm大气平均透过率, 如表1所示。
表 1 热带夏季海洋气溶胶条件下不同距离对应的 8~12 μm 大气平均透过率
Table 1. Average atmospheric transmittance corres-ponding to different distances under the conditions of tropical summer marine aerosol at 8-12 μm
Distance/km 0 1 2 3 4 5 Atmospheric transmittance 1 0.69 0.58 0.54 0.52 0.51 对曲线进行拟合可以得到大气透过率与距离的拟合关系式,即:
$$ \tau (R) = 0.485\;8{{\text{e}}^{ - 1.008R}} + 0.514 $$ (11) 得到探测距离与
${{{n}}_{{e}}}$ 的关系,如表2所示。表 2 探测距离与等效条带对数关系
Table 2. Relationship between detection distance and equivalent strip logarithm
${ {{n} }_{{e} } }$ 2 8 16 R/km Uniformity 5.832 1.492 0.761 Layered 6.451 1.631 0.824 通过对比可以发现,海水分层条件对尾流的探测影响比较大。在探测概率都为95%的情况下,尾流的发现距离提升了10.61%,尾流的识别距离提升了9.32%,尾流的认清距离提升了8.28%。在分层水情况下,尾迹是以冷尾迹的形式呈现在水面上,冷尾迹与海面温差比不分层水情况下热尾迹与海面温差大了0.152 K。通过尾流的浮升时间可以推算出潜艇距离尾流区域的水平距离,通过计算可知在不分层海水的情况下潜艇向前行进了340 m,而在温度密度分层海水情况下潜艇则航行了101.8 m,相比于海水分层,不分层情况下潜艇的反演误差达到了238.2 m,水面的尾迹温差不但相差了0.152 K,还呈现出了冷尾迹的现象。由此可见,海水分层条件对于潜艇的反演精度存在影响极大,甚至直接导致错误的结果。
Analysis of airborne infrared detection performance of submarine thermal wake in stratified seawater
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摘要: 针对传统机载红外探测潜艇热尾流的计算方法未考虑温度、密度分层海水等实际海况,难以精准分析潜艇热尾流红外探测性能的问题。文中基于有限元分析方法,结合海面红外辐射模型和大气传输模型,构建出尾迹从浮升扩散、大气衰减到传感器探测的全链路数理模型,并应用模型开展全尺寸潜艇模型的仿真,实现在温度、密度分层海水情况下对潜艇热尾流红外探测性能的精准分析。结果表明:海水温度、密度分层条件对于潜艇尾迹的仿真和反演精度至关重要,当其他条件都相同时,海水温度、密度分层与不分层仿真出了截然相反的结果,不分层条件下海面为热尾迹,而分层条件下海面却为冷尾迹,直接影响对潜艇热尾迹反演精度。相比于海水分层,不分层情况下潜艇的反演误差达到了238.2 m,水面的尾迹温差不但相差了0.152 K,还呈现出了冷尾迹的现象。文中的研究对机载红外设备发现潜艇航行尾流特性的高精度识别反演具有重要意义。Abstract:
Objective At present, most of the calculation methods for thermal wake detection by MRTD analysis consider the water body as uniformly distributed seawater. The stratified nature of seawater temperature and density has great influence on the inversion accuracy of submarine thermal wake on the surface temperature distribution, rise time and wake rise distance. However, the research at home and abroad mainly focuses on the improvement of MRTD algorithm of infrared system or derivation of the detection ability of infrared detector based on other parameters of the system, as well as the influence of weather and other factors on wake detection, and has not analyzed the influence of seawater stratification on wake detection and inversion. Therefore, the research on infrared radiation detection of thermal wake under the conditions of stratified seawater temperature and density is of great significance to the infrared detection of submarines. Methods For the lack of infrared detection of submarine thermal wake under the condition of stratified sea water temperature and density, the calculation error of detection distance and inversion accuracy error of submarine are large. Based on the finite element analysis method, the research on submarine infrared radiation characteristics under the condition of seawater stratification is carried out in this paper. Firstly, the finite element analysis method is used to simulate the floating process of submarine thermal wake in stratified seawater by a full-size submarine model with propeller and bridge characteristics. Then, according to the sea surface infrared radiation model and atmospheric transmission model, the full-link mathematical and physical model of the wake from floating diffusion, atmospheric transmission atmospheric attenuation to sensor detection is built, and the detection distance of the infrared detector to the submarine thermal wake under the condition of layered seawater is calculated according to the specific infrared detector performance parameters. Results and Discussions The comparison shows that the stratification condition of seawater has a great influence on the detection of wake. With 95% detection probability, the detection distance of the wake increases by 10.61%, the identification distance of the wake increases by 9.32%, and the recognition distance of the wake increases by 8.28% (Tab.2). In the case of stratified water, the wake is presented as a cold wake on the water surface. The temperature difference between the cold wake and the sea surface is 0.152 K larger than that between the hot wake and the sea surface in the case of non-stratified water. The submarine travels 340 m forward without stratified seawater and 101.8 m under stratified seawater temperature and density. Compared with seawater stratification, the inversion error of submarine without stratification reaches 238.2 m, and the wake temperature difference on the surface is not only 0.152 K, but also cold wake phenomenon. It can be seen that the seawater stratification condition has a great influence on the submarine's inversion accuracy, and even directly leads to incorrect results. Conclusions The mathematical and physical model of the wake from floating diffusion, atmospheric decay to full link of sensor detection under the condition of seawater temperature and density stratification is established. The influence of seawater temperature and density stratification on the wake floating speed, the detection distance of the infrared detection system to the wake and the inversion error of the wake are obtained by simulation calculation. That is, it takes 101.8 s for the wake to rise to the surface at 50 m under the condition of stratified seawater temperature and density. Under the same conditions, when the seawater is not stratified, the time taken for the wake to rise to the surface is 340 s, which is much longer than that for the stratified seawater. This is due to the lower underwater temperature of the stratified seawater and the large density difference conducive to the floating of the hot wake. The discovery distance of the delaminated water body wake is 6.451 km, the identification distance of the wake is 1.631 km, and the recognition distance of the wake is 0.824 km. The unclassified detection distance, identification distance and recognition distance are 5.832 km, 1.492 km and 0.761 km, respectively. Compared with seawater delamination, the inversion error of submarine wake is 238.2 m without delamination, the temperature difference of wake on water surface is 0.152 K, and the cold and hot wakes on sea surface are different. -
Key words:
- submarine /
- temperature stratification /
- thermal wake /
- infrared detection
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表 1 热带夏季海洋气溶胶条件下不同距离对应的 8~12 μm 大气平均透过率
Table 1. Average atmospheric transmittance corres-ponding to different distances under the conditions of tropical summer marine aerosol at 8-12 μm
Distance/km 0 1 2 3 4 5 Atmospheric transmittance 1 0.69 0.58 0.54 0.52 0.51 表 2 探测距离与等效条带对数关系
Table 2. Relationship between detection distance and equivalent strip logarithm
${ {{n} }_{{e} } }$ 2 8 16 R/km Uniformity 5.832 1.492 0.761 Layered 6.451 1.631 0.824 -
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