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Bingham流体双自由面热毛细液层的稳定性分析

王胜 胡开鑫

王胜, 胡开鑫. Bingham流体双自由面热毛细液层的稳定性分析. 力学学报, 2022, 54(12): 1-10 doi: 10.6052/0459-1879-22-364
引用本文: 王胜, 胡开鑫. Bingham流体双自由面热毛细液层的稳定性分析. 力学学报, 2022, 54(12): 1-10 doi: 10.6052/0459-1879-22-364
Wang Sheng, Hu Kaixin. Stability analysis of thermocapillary liquid layers with two free surfaces for a Bingham fluid. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 1-10 doi: 10.6052/0459-1879-22-364
Citation: Wang Sheng, Hu Kaixin. Stability analysis of thermocapillary liquid layers with two free surfaces for a Bingham fluid. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 1-10 doi: 10.6052/0459-1879-22-364

Bingham流体双自由面热毛细液层的稳定性分析

doi: 10.6052/0459-1879-22-364
基金项目: 国家自然科学基金(11872032)和浙江省科学自然基金(Y21A020008)资助项目
详细信息
    作者简介:

    胡开鑫, 教授, 主要研究方向: 非牛顿流体、微重力流体. Email: hukaixin@nbu.edu.cn

  • 中图分类号: O357.1

STABILITY ANALYSIS OF THERMOCAPILLARY LIQUID LAYERS WITH TWO FREE SURFACES FOR A BINGHAM FLUID

  • 摘要: 热毛细对流是流体界面温度分布不均导致的表面张力梯度驱动的流动. 它主要存在于空间等微重力环境或小尺度流动等表面张力占主导的情况中. 在很多工业领域, 如晶体生长、聚合物加工、喷墨打印、微流控, 产品质量都与热毛细对流密切相关. 空间3D打印是太空制造的重要技术, 可以支持空间站的在轨长期有人照料的运行和维护, 实现按需制造. 本文以聚合物流体的空间3D打印为应用背景, 采用线性稳定性理论研究了Bingham流体双自由面热毛细液层的稳定性, 得到了在不同Bingham数(B)下的临界Marangoni数(Mac)与Prandtl数(Pr)的函数关系,分析了临界模态的流场和能量机制. 研究发现: 该流动的临界模态包括流向波和斜波模态, 与B, Bi和两界面垂直方向上的温差(Q)相关. BBi的增加会增强热毛细对流的稳定性. 当Q = 0时, 扰动温度分布分成对称和反对称两种情况. 当Q > 0时, Pr的增加会减弱流动稳定性. 在小Pr情况下, 扰动温度分布在整个流场, 在大Pr情况下, 扰动温度在栓塞区为零. 能量分析表明: 扰动动能的主要能量来源是表面张力做功, 但小Pr数下基本流也有一定贡献.

     

  • 图  1  Bingham流体双自由面热毛细液层示意图

    Figure  1.  The thermocapillary liquid layer with two free surfaces for a Bingham fluid

    图  2  基本流的(a)速度分布和(b)垂直温度分布(Ma = 100, Q = 0)

    Figure  2.  (a) The velocity distribution and (b) vertical temperature distribution at Ma = 100 for the basic flow

    图  3  Q = 0, Bi = 0时, 不同B下, (a) MacPr的变化曲线以及(a)所对应的(b)波数和(c)波传播角. 曲线对应: $a,c,d,e,g,h$为斜波, $b,f,i,j$为流向波

    Figure  3.  (a) The variation of Mac with Pr under different B at when Q = 0 and Bi = 0, (b) wave number and (c) wave propagation angle. The curves correspond to:$a,c,d,e,g,h$ oblique wave and $b,f,i,j$streamwise wave

    图  4  B = 0.2, Ma = 100时垂直方向上的温度分布

    Figure  4.  Vertical temperature distribution at B = 0.2 and Ma = 100

    图  5  Q = 0.05时, (a) MacPr的变化曲线以及(a)所对应的(b)波数和(c)波传播角. 曲线对应: $a,d,g$为斜波, $b,e$为流向波, $c,h,f$为展向稳态模态

    Figure  5.  (a) The variation of Mac with Pr under Q = 0.05, (b) wave number and (c) wave propagation angle. The curves correspond to: $a,d,g$oblique wave,$b,e$streamwise wave, $c,h,f$spanwise stationary mode

    图  6  Q = 0, Bi = 0时不同临界模态所对应的扰动流场: 逆向斜波(B = 0.2, Pr = 0.01)的(a)上屈服面扰动, (b)温度和流线; 逆向斜波(B = 0.4, Pr = 20)的(c)上屈服面扰动, (d)温度和流线

    Figure  6.  The perturbation flow field of the different preferred modes at Q = 0 and Bi = 0: (a) upper yield surface perturbation, (b) temperature and streamlines of the upstream oblique wave (B = 0.2, Pr = 0.01); (c) upper yield surface perturbation, (d) temperature and streamlines of the upstream oblique wave (B = 0.4, Pr = 20)

    图  7  Q = 0, Bi = 5时不同临界模态所对应的扰动流场: 逆向斜波(B = 0.4, Pr = 0.01)的(a)上屈服面扰动, (b)温度和流线; 逆向斜波(B = 0.6, Pr = 0.01)的(c)上屈服面扰动, (d) 温度和流线

    Figure  7.  The perturbation flow field of the different preferred modes at Q = 0 and Bi = 5: (a) upper yield surface perturbation, (b) temperature and streamlines of the upstream oblique wave (B = 0.4, Pr = 0.01); (c) upper yield surface perturbation, (d) temperature and streamlines of the upstream oblique wave (B = 0.6, Pr = 0.01)

    图  8  Q = 0.05, Bi = 0时不同临界模态所对应的扰动流场: 同向流向波(B = 0, Pr = 10)的(a)温度和流线; 同向斜波(B = 0.2, Pr = 0.1)的(b)上屈服面扰动, (c)温度和流线

    Figure  8.  The perturbation flow field of the different preferred modes at Q = 0.05 and Bi = 0: (a) temperature and streamlines of the downstream streamwise wave (B = 0, Pr = 10); (b) upper yield surface perturbation; (c) temperature and streamlines of the downstream oblique wave (B = 0.2, Pr = 0.1)

    表  1  不同参数下各扰动能量变化项的值

    Table  1.   Values of perturbation energy variation terms at different parameters

    QPrBBi$ - N $$ M $$ I $
    00.0100−0.0372530.0372220.000033
    0.20−0.0201730.0171160.002953
    0.40−0.0170030.0147110.001957
    0.60−0.0110050.0095590.001536
    10.25−0.2151730.1693420.045979
    0.45−0.2595660.221430.037879
    1000.25−12.36848712.3728510.002954
    0.45−12.60861612.6115610.001634
    0.050.0100−0.0374810.0374710.000011
    0.100−0.1126110.1125880.000023
    0.10.20−0.0602350.0464190.010708
    下载: 导出CSV
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  • 收稿日期:  2022-08-08
  • 录用日期:  2022-10-12
  • 网络出版日期:  2022-10-13

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