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SBS激光增益系统如图1(a)所示。由于重氟碳系列的电子氟化液具有较好的热稳定性和化学稳定性,其在常见的1 064 nm波段具有较低的吸收系数和较高的布里渊增益系数,因此采用目前广泛应用的FC-770作为SBS介质,如表1所示,其被封装于长为1 000 mm、内径为16 mm的介质池内。当高功率泵浦脉冲进入SBS-PCM介质池后,在声场作用下与Stokes脉冲发生耦合,峰值功率迅速提升,实现激光增益。由于介质内声波场的热耗散,光路附近的介质吸收热量,温度升高并形成不均匀的温度场,进而造成不同区域的介质出现密度差。不同密度的介质在重力的作用下形成浮升力,在浮升力的驱动下介质形成自然对流。由于焦点处激光能量强度最高,此处热效应最为明显,因此文中仅选取焦点所在截面作为研究对象,如图1(b)所示。此外,泵浦光源单脉冲能量采用25 mJ,重复频率采用10、50、100、250 Hz,脉冲宽度为7 ns。
图 1 (a) SBS-PCM激光增益系统;(b) 焦点截面示意图
Figure 1. (a) SBS-PCM laser gain system; (b) Schematic of focus section
表 1 介质物理性质
Table 1. Physical properties of medium
Medium Density/
kg·m−3Thermal conductivity/
W·m−1·K−1Specific heat capacity at constant pressure/
J·kg−1·K−1Dynamic viscosity/
Pa·sAbsorption coefficient/
cm−1FC-770 1789 0.063 1 038 0.001 3 0.001 1 -
描述焦点截面处介质自然对流换热过程的控制方程包括连续性方程、动量方程和能量方程。
连续性方程:
$$ \frac{{\partial (\rho u)}}{{\partial x}} + \frac{{\partial (\rho v)}}{{\partial y}} = 0 $$ (1) 式中:u、v分别为x、y两个方向上的速度;ρ为流体密度。
动量方程:
$$ \rho \left(\frac{{\partial u}}{{\partial \tau }} + u\frac{{\partial u}}{{\partial x}} + v\frac{{\partial u}}{{\partial y}}\right) = \eta \left(\frac{{{\partial ^2}u}}{{\partial {x^2}}} + \frac{{{\partial ^2}u}}{{\partial {y^2}}}\right) - \frac{{\partial p}}{{\partial x}} $$ (2) $$ \rho \left(\frac{{\partial v}}{{\partial \tau }} + u\frac{{\partial v}}{{\partial x}} + v\frac{{\partial v}}{{\partial y}}\right) = \eta \left(\frac{{{\partial ^2}v}}{{\partial {x^2}}} + \frac{{{\partial ^2}v}}{{\partial {y^2}}}\right) - \frac{{\partial p}}{{\partial y}} - \rho g $$ (3) 式中:τ为时间;η为动力粘度。
能量方程:
$$ \rho {c_p}\left(\frac{{\partial T}}{{\partial \tau }} + u\frac{{\partial T}}{{\partial x}} + v\frac{{\partial T}}{y}\right) = \lambda \left(\frac{{{\partial ^2}T}}{{\partial {x^2}}} + \frac{{{\partial ^2}T}}{{\partial {y^2}}}\right) + {{\dot \varPhi }}(x,y) $$ (4) 式中:cp为流体定压比热容;T为热力学温度;λ为导热系数;$ {{\dot \varPhi }}(x,y) $为内热源强度。
文中用内热源模拟空间强度分布为高斯分布的泵浦光,实验中采集的焦点处光斑为明显的椭圆形高斯光斑,如图2(a)所示。因此,数值模拟中的内热源强度分布为接近泵浦光的高斯分布,如图2(b)所示,且内热源的加载频率与泵浦光频率保持一致。内热源强度分布$ {{\dot \varPhi }}(x,y) $的表达式如下:
$$ {{\dot \varPhi }}(x,y) = \iint {\frac{P}{{\pi {r^2}(1 - {{\rm{{e}}}^{ - 1}})}} \cdot \exp \left[ { - \left(\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}}\right)} \right]{\rm{d}}x{\rm{d}}y} $$ (5) 式中:P为泵浦脉冲平均功率;a=0.020 8 mm与b=0.029 4 mm分别为椭圆形高斯光斑短轴与长轴;r=0.029 4 mm为椭圆形高斯光斑平均直径。
设定计算域初始条件为300 K,边界条件为绝热壁面。由于介质池外壁面裸露在空气中,理论上与外界空气存在对流换热与辐射换热。随着泵浦光的载入,虽然焦点处温度上升,但内壁面周围介质温升较小,且玻璃的导热性较差,导致介质池外壁面温度基本接近外界环境温度,此时对流换热与辐射换热量很小,故在此忽略外壁面换热,将外壁面简化为绝热壁面,此时计算域与外界没有热量交换。
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引入无量纲数Se数计算涡通量来量化介质池内热对流强度。涡通量的强弱反映了介质池中热对流的强度,其表达式如下:
$$ S e = \frac{{\rho {D^2}_{{\text{in}}}{J^n}_{{\text{ABS}}}}}{\eta } $$ (6) $$ {J^n}_{{\rm{ABS}}} = \frac{1}{A}\iint\limits_A {\left| {{\omega _n}} \right|}{\rm{d}}A $$ (7) $$ {\omega _{{n}}} = \frac{{\partial u}}{{\partial z}} - \frac{{\partial w}}{{\partial x}} $$ (8) 式中:${D_{{\text{in}}}}$为介质池内径;${J^n}_{{\text{ABS}}}$为绝对涡通量;$A$为介质池截面积;${\omega _{{n}}}$为沿主流方向涡通量的分量。
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采用有限体积法对上述控制方程等进行计算求解,计算至物理时间40 s。为排除网格数量引起的误差,将模型分为6组网格,使用FC-770介质在25 mJ,10 Hz工况下计算介质池内的Se数。得到Se数随网格数的变化,如图3所示。当网格数为7万时,Se数基本不随网格数明显变化,因此选择网格数量为7万进行后续的数值模拟研究。
Effect of pump light repetition rate on thermal convection characteristics in liquid SBS-PCM (invited)
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摘要: 受激布里渊散射相位共轭镜(SBS-PCM)因能实时补偿静态和动态波前畸变、提高光束质量,在激光领域受到广泛关注,但仍存在高功率泵浦下引发损伤和输出光束质量下降的问题。液体增益介质具有高增益、高抗损伤阈值和尺寸拓展性强的特点,目前是高能高功率激光领域最广泛应用的SBS介质,但随着注入功率的提升,热效应引发的液体介质热对流会导致反射Stokes光中出现波前畸变,降低了其光束质量补偿效果。文中发展了高功率泵浦下介质池内热对流的数值模型,定量分析了热对流强度随相互作用时间的变化规律,着重探讨了泵浦光重复频率对热对流强度分布的影响,并结合热对流强度解释了光斑畸变程度。研究结果表明:泵浦光注入初期,热对流强度在达到极值后小幅下降最后趋于稳定;泵浦光重复频率是影响热对流强度的重要因素,热对流强度与重复频率呈正相关;随着热对流强度的增强,光斑偏移程度逐渐增大。文中从液体介质流动性角度分析了泵浦光重复频率与介质热对流的关系,对完善光热效应模型提供了新的研究方向。Abstract:
Objective The stimulated Brillouin scattering phase conjugated mirror (SBS-PCM) has garnered significant attention in the laser field due to its ability to compensate for both static and dynamic wavefront distortion in real time and enhance beam quality. However, there remain concerns regarding optical breakdown and degradation of output beam quality under high power pumping. Liquid gain medium is currently the most widely used SBS medium due to its characteristics of high gain, high damage threshold resistance and strong size expansion. However, with the increase of injection power, thermal convection caused by absorption of liquid medium will cause wavefront distortion in reflected Stokes light, resulting in reductions of beam quality. Methods The finite element method was involved, and the 2-dimentional thermal convection at the focus section was solved by coupling the continuity equation, momentum equation, energy equation and the internal heat source equation. The boundary condition was adiabatic, and the numerical model of thermal convection in the medium cell under high power pump was developed. The dimensionless Se number is introduced to calculate the eddy flux to quantify the thermal convection intensity in the medium cell. Results and Discussions The variation of the Se number with the interaction time is quantitatively analyzed, and the influence of the pump light repetition rate on the thermal convection intensity distribution is emphatically discussed. The results show that, starting from the pump light injection medium, the Se number firstly increases and then decreases, and finally tends to be stable. In addition, when the repetition rate increases from 10 Hz to 250 Hz,the maximum Se number increases from 10 to 49, and the stable Se number increases from 6 to 31, but the time taken for the Se number to reach the maximum value decreases from 9 s to 3 s. The time taken to reach the stable value is reduced from 37 s to 19 s (Fig.4). The contour of thermal convection velocity and density distribution and corresponding experimental observed spatial profiles at different repetition rates were shown (Fig.5-8). With the increase of repetition rate, the intensity of thermal convection increases, and the distribution of low-density areas in the medium cell expands, leading to the increase of the horizontal and vertical deformation of light spots. Conclusions The relationship between pump light repetition rate and thermal convection in liquid medium is analyzed from liquid medium flow. The pump light repetition rate is an important factor affecting the thermal convection intensity, the thermal convection intensity is positively correlated to the repetition rate, and the time for the thermal convection intensity to reach the extreme value and the stable value is negatively correlated with the repetition frequency. With the increase of thermal convection intensity, the degree of spot migration increases gradually. This study provides a new perspective for perfecting the model of photothermal effect. -
表 1 介质物理性质
Table 1. Physical properties of medium
Medium Density/
kg·m−3Thermal conductivity/
W·m−1·K−1Specific heat capacity at constant pressure/
J·kg−1·K−1Dynamic viscosity/
Pa·sAbsorption coefficient/
cm−1FC-770 1789 0.063 1 038 0.001 3 0.001 1 -
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