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激光致声利用高能量脉冲激光击打水面并与水相互作用而产生声波,可以将高能脉冲激光器装载在飞机上构成一个非接触式空中-海洋探测系统(图1)。根据激光脉冲能量强弱和相互作用区域的能量密度与时空分布,激光激发辐射与水相互作用产生声波的机制可分为热膨胀、汽化与光击穿三种,其中热膨胀的光声转换效率低于0.1%,汽化的效率为1%左右,光击穿的效率可达7%~30%[15]。
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当入射激光能量较弱、相互作用能量较低、无法通过水面加热达到沸点温度时,其产声机制为水的不均匀加热引起的热弹性压力(热膨胀)。热膨胀机制所产生的声压强
$p$ 如公式(1)所示[15]:$$p = \frac{{\alpha {c^2}{a_v}{E_0}}}{{{c_p}}}{\rm{e}^{ - \alpha {\textit{z}}}}$$ (1) 式中:
$\alpha $ 为水的吸收系数;$c$ 为水中声速;${E_0}$ 为表面处热能密度;${a_v}$ 为水的膨胀系数;${c_p}$ 为水的比热容。对不同波长的激光,水对其有不同的吸收能力,消光长度越短则吸收能力越强(见图2)。热膨胀致声对实验设备要求低,声信号也相对较弱。
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随着入射激光脉冲能量增大,水面局部温度逐渐升高达到沸点时即产生汽化致声。假设水的初始温度为
${T_0}$ ,使得水面局部温度达到沸点所需要的能量$E$ 为[15]:$$E = \left(\frac{{\rho {c_p}}}{\alpha }\right)({T_{boil}} - {T_0})$$ (2) 式中:
$\rho $ 为水的密度;${T_{boil}}$ 为水的沸点温度;$\alpha $ 为水的吸收系数。与热膨胀致声相比,这种致声方式产生的声信号较强,但对激发激光脉冲的强度要求较高。 -
当激光脉冲强度达到水的介电击穿阈值(约107 W/cm2)时,会产生水的光学击穿。此时水的分子离解并形成等离子体,激光与水的作用变为光与等离子体的作用。发生光击穿的光强超过阈值不大时,击穿区呈点状,可以看作点声源,远场内离击穿区距离为
$r$ 处声脉冲表达式为[16]:$$p(r,t) = \left\{ \begin{array}{l} \dfrac{A}{r}\exp \left[ { - \dfrac{{t - r/c}}{\theta }} \right] \;\;\;\;\;\; t \geqslant (r/c) \\ {\rm{ }}0\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; t < (r/c) \\ \end{array} \right.$$ (3) 式中:
$A$ 为与液体性质有关的函数;$c$ 为液体中声速;${\theta ^{ - 1}}$ 为声脉冲衰减常数。这种致声方式效果最好,但对实验设备的要求比较高。 -
因激光击水点面积微小,则可以把波源当作点波源,产生声波为球面波,分别向空气和水中进行传播。从频谱看,该声波为从几Hz到300 kHz分布的宽频波,但由于在0~20 kHz时受到环境噪声影响较为明显,而且考虑到声波的高频分量在水中衰减速度较快,因此常使用25~40 kHz的分量进行实际应用。
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超声波在液体介质中的传播方程为:
$$\left\{ \begin{array}{l} \dfrac{1}{{\rho {c^2}}}\dfrac{{{\partial ^2}{p_t}}}{{\partial {t^2}}} + \nabla \cdot - \dfrac{1}{p}\left(\nabla {p_t} - {q_d}+\right. \\ \left. \dfrac{1}{{\rho {c^2}}}\left(\dfrac{{(\gamma - 1)k}}{{{C_p}}}\right)\dfrac{{\partial \nabla {p_t}}}{{\partial t}}\right) = {Q_m} \\ {\rm{ }}{p_t} = p + {p_b} \\ \end{array} \right.$$ (4) 式中:
${p_t}$ 为总压力;$c$ 为声速;$ \;\rho $ 为流体的密度;${C_p}$ 为常压热容;$\gamma $ 为比热率;$k$ 为导热系数;${p_b}$ 为背景压力;$p$ 为压力;${Q_m}$ 为偶极源;${q_d}$ 为单极源。在超声波全反射界面采用硬声场边界条件:
$$ - n \cdot \left( - \frac{1}{\rho }(\nabla {p_t} - {q_d})\right) = 0$$ (5) 式中:
$n$ 为边界方向矢量。在材料半无限长边界处为无反射边界,采用平面波辐射边界条件:
$$ - n \cdot \left( - \frac{1}{\rho }(\nabla {p_t} - {q_d})\right) + \frac{1}{\rho }\left(\frac{1}{c}\frac{{\partial p}}{{\partial t}}\right) = {Q_t}$$ (6) 声波在非理想媒质的传播过程中会随着距离的增大而产生衰减,此时声能转变为热能而耗散,这称为媒质中的声衰减。海水中的声吸收与纯水相比非常大。海水中的声吸收由3种效应引起:(1)切变黏滞性效应;(2)体积黏滞性;(3)声波频率低于100 kHz时,海水吸收是由于硫酸镁分子的离子弛豫。综合考虑所有因素,声波在海水中的衰减系数
$\alpha $ 为[17]:$$\alpha \approx 3 \times {10^{ - 4}}{f^2}{\rm{ + }}\frac{{44{f^2}}}{{4100 + {f^2}}} + \frac{{0.11{f^2}}}{{1 + {f^2}}}$$ (7) 式中:
$\alpha $ 为海水声吸收系数(dB/km);$f$ 为水声频率(kHz)。 -
为研究水中光击穿所激发的声场,建立了激光致声模型,由空间能量的径向传播特性,模拟水中光击穿区形成的多个径向等离子体脉冲球源,理论上得到水中光击穿所激发的声场指向特性。等离子体产生辐射声场的方向性函数是[18]:
$$D\left( {\varphi ,\theta } \right) = \frac{{{A_s}}}{{{A_{{s_{\max }}}}}} = \frac{{\left\| {\displaystyle\sum\limits_{i = 0}^N {{A_i}{\rm{e}^{j{\varepsilon _i}}}} } \right\|}}{{\left| {\displaystyle\sum\limits_{i = 0}^N {{A_i}} } \right|}}$$ (8) 式中:
${A_s}$ 为距等离子体形成1 m处合成声波的总振幅;${A_{{s_{\max }}}}$ 是${A_s}$ 在空间方向上的最大值;${A_i}\left( {i = 0,1,2 \cdot \cdot \cdot ,N} \right)$ 为阵源在距其1 m位置所产生的声波振幅。激光致声辐射声场指向性模型如图3所示,其能量主要集中在与激光光束呈0°夹角方向上。 -
为研究水听器接收激光声信号随声距变化的漂移情况,选取了A~D和A~E的实验测量记录过程中各10组典型波形数据进行分析,其中选取的A、D、E位置坐标和移动变化过程如图6所示。绘制了如图11(a)、(b)所示的信号随声距变化而漂移的示意图。通过计算各接收点之间的实际物理距离与实验中计算出理论声距之间的关系可以对声波信号随声距变化的漂移情况进行验证。各接收点声距差
$\Delta S$ 的计算公式为:$$\Delta S = c({t_2} - {t_1})$$ (9) 图 11 A~D与A~E点信号随声距变化而漂移示意图。(a) A~D点信号漂移;(b) A~E点信号漂移
Figure 11. Diagram of signal drift of A-D and A-E with sound distance change. (a) A-D signal drift; (b) A-E signal drift
式中:
$c$ 为纵波在水中的传播速度,大约为1480 m/s;t1和t2分别为在不同坐标处测得的信号峰值时间。在A~D信号变化过程中,测得A点(17,48)处信号峰值时间t1为90 μs,D点(17,30)处信号峰值时间t2为214 μs,根据公式(9)可以计算出A、D两点之间的声距 $\Delta {S_1}$ 约为0.1835 m。A~E的信号变化过程中同理计算出A、E两点之间的声距$\Delta {S_2}$ 约为0.2664 m。其中A、D两点之间测得物理距离约为0.18 m,A、E两点之间测得物理距离约为0.2545 m,因此可以说明实验过程中测得的声信号随着水听器与激光脉冲之间的距离变化是规律且有效的。从A~D点和A~E点的变化过程可以发现,由于水听器逐渐向远离激光脉冲位置移动,其声距也随之变长,在波形图上展现为信号一次波峰出现的时间规律性滞后且波峰幅值明显变小,这与理论预期结果相吻合。为考虑在海洋实际应用中波浪面和斜面等因素对激光致声信号的影响,人为地对水面进行扰动来观察信号时域波形变化。从图12(a~e)表示扰动依次增大)中可以看出,随着扰动幅度变大,激光致声信号一次波峰变小,对信号有较大干扰,在实际应用中应考虑水面扰动带来的影响。
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为验证上述实验过程的正确性,利用有限元软件对激光在液体中激励声波并传播的过程进行模拟与仿真,利用边界探针提取声波传播过程中的声压分布信号并进行成像处理,通过对数据进行计算与分析来验证实验结果。
首先在有限元分析软件中建立求解声学问题的相关方程,公式(10)为亥姆霍兹控制方程:
$$\nabla \cdot \left( { - \frac{1}{{{\rho _c}}}(\nabla {p_t} - {q_d})} \right) - \frac{{k_{eq}^2{p_t}}}{{{\rho _c}}} = {Q_m}$$ (10) $${p_t} = p + {p_b}$$ (11) $${k_{eq}} = \frac{\omega }{c}$$ (12) 式中:
${\rho _c}$ 为密度;${p_b}$ 为背景场压力;$p$ 为声压;${p_t}$ 为总压力;$c$ 为声速;${q_d}$ 为偶极声源;$\omega $ 为角频率;${k_{eq}}$ 为波数。声传播损失的计算如公式(13)所示:
$$T{L_p} = - 20\;\lg \left| {\frac{{p(r,\textit{z},\omega )}}{{{p_{ref}}}}} \right|$$ (13) 式中:
$p(r,{\textit{z}},\omega )$ 为声压;${p_{ref}}$ 为参考声压,这里取几何模型中距声源1 m处的声压。对于流体而言,声能流密度在频域上的定义如公式(14)所示:
$$I\left( \omega \right) = \left[ \begin{array}{l} {I_r}\left( \omega \right) \\ 0 \\ {I_{\textit{z}}}\left( \omega \right) \\ \end{array} \right] = \left[ \begin{array}{l} pv_r^* \\ 0 \\ pv_{\textit{z}}^* \\ \end{array} \right]$$ (14) 声能量的强度与传播方向公式为:
$$\left\{ \begin{array}{l} I = \sqrt {{{\left\{ {\operatorname{Re} \left[ {{I_r}\left( \omega \right)} \right]} \right\}}^2} + {{\left\{ {\operatorname{Re} \left[ {{I_{\textit{z}}}\left( \omega \right)} \right]} \right\}}^2}} \\ {\rm{ }}{\theta _I} = \arctan \left\{ {\dfrac{{\operatorname{Re} \left[ {{I_{\textit{z}}}\left( \omega \right)} \right]}}{{\operatorname{Re} \left[ {{I_r}\left( \omega \right)} \right]}}} \right\} \\ \end{array} \right.$$ (15) 式中:
${I_r}(\omega )$ 、${I_{\textit{z}}}\left( \omega \right)$ 分别为水中$r$ 方向和${\textit{z}}$ 方向的声能量强度;${v_r}\left( \omega \right)$ 、${v_{\textit{z}}}\left( \omega \right)$ 分别为水中$r$ 分量和${\textit{z}}$ 分量的声速;$p\left( \omega \right)$ 为水中声压。图13为有限元软件中建立的仿真模型,其中A、B、C三点对应实验过程中(见图6)激光在液体中激励声波的位置,在A点的上方设置用于接收声波信号的边界探针,通过分析探针接收的声压信号对实验结果进行反向验证。这样相当于脉冲激光器在不断地移动并发射激光进行扫查,而接收信号的水听器位置不变。将探针接收到的激光在A、B、C三点所激发出的声波信号进行对比分析,从而验证之前推论的正确性。图14即为分别在A、B、C三点进行激光激励时探针接收到的声压信号对比。
由边界探针所接收的声压信号分布可以分析:A、B、C三点的声压幅值依次大幅减小,验证了距离激光脉冲激励点近信号接收效果较好的分析。而且其声波信号存在明显偏移,信号峰值出现的时间滞后,随之声距变长且信号幅值大幅降低。
在此次实验中设置激光器脉冲重复频率为5 Hz,脉冲宽度10 ns,能量计测得脉冲能量值为50 mJ,由能量密度计算公式得到激光脉冲能量约为1.59×108 W/cm2,已达到水的介电击穿阈值并在实验中实现了对米级探测区域声波传播的成像与分析。在现有激光器可实现的条件下,提升脉冲能量至2.8×1010 W/cm2,仿真计算声波在水中传输400 m经吸收衰减后的声压信号,并与激发点处的声压信号进行对比分析。图15为利用边界探针接收到的激光激发处与接收处声压信号。
声波在传输400 m后仍能检测到明显的声压信号,计算其信噪比约为11.3 dB,证明了实现百米级传输及探测的可能性。当激光能量继续提升,传输距离继续增大时,激光声信号能量主要集中于低频段,声波激励的能量增强不明显而且可能导致更复杂的激励机制,因此文中仅作如上分析。
Research on laser induced acoustic detection of trans-media aerial-underwater
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摘要: 跨空水介质间的探测技术是世界主要海洋国家的热点研究问题。为研究空中平台与水下的激光致声探测技术,文中在光击穿机制下采用纳秒脉冲激光与水听器之间的光声信号转换来进行空-水跨介质探测模拟实验研究及验证工作。搭建了激光致声空气-水下实验测试系统,采集了激光声扫描探测数据,对典型实验数据在时域内进行分析得出了激光激励声波的传播特性,根据时间互易原理实现了水下激光声信号的三维探测成像。利用有限元法进行激光在水下激发声波及传播的数值仿真,据此对实验进行了验证。此外,从仿真中发现通过提高脉冲能量至2.8×1010 W/cm2所激励的声波在传播400 m后仍能观测出明显的信号,信噪比约为11.3 dB,证明了百米级传输及探测的可能性。此研究结果为采用激光致声技术进行跨空-水介质探测提供了依据。Abstract: Remote detection technology between air platform and underwater is a hot research issue in the marine countries. The aim of the present work is to study the laser induced acoustic (LIA) technology used for the detection from air to underwater. The experiment and simulation of LIA detection based on the mechanism of laser-induced breakdown were mainly described. Nanosecond pulse laser was used to generate acoustic wave by the photoacoustic conversion, and the hydrophone was used to receive the waves. LIA scanning data was collected to analyze the character of acoustic source underwater by using the setup above. Then 3D imaging of LIA underwater was carried out based on the time reciprocity principle. Simulations of the sound waves generation and propagate underwater was performed by finite element method. Furthermore, it is observed from the simulation that sound signal can be still obtained after it propagates 400 m, when the laser energy increases to 2.8×1010 W/cm2. The signal to noise ratio is about 11.3 dB. The simulation shows the possibility of detection by LIA underwater in hundred meters-level. The present study provides a method for the remote detection underwater across air-water media by using LIA technology.
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Key words:
- laser induced acoustic /
- 3D imaging /
- time domain analysis /
- finite element simulation
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