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高径比对GaAs熔体液桥热毛细对流失稳的影响

周游 曾忠 刘浩 张良奇

周游, 曾忠, 刘浩, 张良奇. 高径比对GaAs熔体液桥热毛细对流失稳的影响. 力学学报, 2022, 54(1): 1-15 doi: 10.6052/0459-1879-21-227
引用本文: 周游, 曾忠, 刘浩, 张良奇. 高径比对GaAs熔体液桥热毛细对流失稳的影响. 力学学报, 2022, 54(1): 1-15 doi: 10.6052/0459-1879-21-227
Zhou You, Zeng Zhong, Liu Hao, Zhang Liangqi. Effect of aspect ratio on thermocapillary convection instability of gaas meltl iquid bridge. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 1-15 doi: 10.6052/0459-1879-21-227
Citation: Zhou You, Zeng Zhong, Liu Hao, Zhang Liangqi. Effect of aspect ratio on thermocapillary convection instability of gaas meltl iquid bridge. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 1-15 doi: 10.6052/0459-1879-21-227

高径比对GaAs熔体液桥热毛细对流失稳的影响

doi: 10.6052/0459-1879-21-227
基金项目: 国家自然科学基金(No.12172070)国家自然科学基金青年科学基金项目 (No.12102071)中央高校基本科研业务费(No.2021 CDJQY-055)重庆市教委科学技术研究项目(No.KJQN202100706)
详细信息
    作者简介:

    曾忠, 教授, 主要研究方向: 流体力学; 热毛细对流; 多相流. E-mail:zzeng@cqu.edu.cn

  • 中图分类号: O35

EFFECT OF ASPECT RATIO ON THERMOCAPILLARY CONVECTION INSTABILITY OF GAAS MELTL IQUID BRIDGE

  • 摘要: 本文采用基于谱元法线性稳定性分析方法, 研究了高径比对GaAs熔体(Pr = 0.068)液桥热毛细对流失稳的影响, 同时结合能量分析揭示了热毛细对流的失稳机制. 研究结果表明: 与典型低普朗特数(例如Pr = 0.011)熔体静态失稳模式和典型高普朗特数(例如Pr>1)熔体振荡失稳模式不同, GaAs熔体热毛细对流失稳模式依赖于液桥高径比(As). 随高径比的变化, GaAs熔体热毛细对流存在两种失稳模式. 高径比As 在0.4≤As≤1.18范围内, 热毛细对流失稳是从二维轴对称定常对流转变为三维周期性振荡对流(振荡失稳); 高径比在1.20≤As≤2.5范围内, 热毛细对流失稳是从二维轴对称定常流动转变为三维定常流动(静态失稳). 典型的高普朗特数熔体液桥热毛细对流失稳机制是热毛细机制; 典型的低普朗特数液桥热毛细对流失稳机制是水动力学惯性机制. 我们基于扰动能量分析的结果表明: GaAs熔体热毛细对流失稳同时包括水动力学惯性失稳机制和热毛细失稳机制的贡献, 其中水动力学惯性失稳机制占主导作用, 两种机制对热毛细对流失稳能量贡献的占比随高径比的变化而变化.

     

  • 图  1  半浮区液桥模型

    Figure  1.  Floating half-zone model

    图  2  Mac随高径比(As)的变化(Pr = 0.068)

    Figure  2.  The variation of Mac versus the aspect ratio As for Pr = 0.068.

    图  3  扰动能量随高径比As变化(续)

    Figure  3.  The variation of the kinetic energy budgets with respect to the aspect ratio (continued)

    3  扰动能量随高径比As变化

    3.  The variation of the kinetic energy budgets with respect to the aspect ratio

    图  4  高径比As = 0.48, Pr = 0.068的临界状态(Mac = 1936.3)下: (a)扰动能量平衡条状图; (b)局部扰动动能极值图

    Figure  4.  The disturbance energy balance (a) and distribution of the local disturbance kinetic energy extreme value (b) under critical condition(Mac = 1936.3) at As = 0.48, Pr = 0.068.

    图  5  高径比As = 0.48, Pr = 0.068的临界状态(Mac = 1936.3)下: (a) z = 0.51截面扰动温度(云图)和扰动速度矢量(箭头); (b)自由液面扰动温度(云图)和扰动速度矢量(箭头)

    Figure  5.  The disturbance temperature (colored contour) and disturbance velocity vector (arrow): (a) the z = 0.51 cross section; (b) the free surface. under the critical condition (Mac = 1936.3) at As = 0.48, Pr = 0.068.

    图  6  高径比As = 0.77, Pr = 0.068的临界状态(Mac = 1083.9)下: (a)扰动能量平衡条状图; (b)局部扰动动能极值图

    Figure  6.  The disturbance energy balance (a) and distribution of the local disturbance kinetic energy extreme value (b) under critical condition (Mac = 1083.9) at As = 0.77, Pr = 0.068.

    图  7  高径比As = 0.77, Pr = 0.068的临界状态(Mac = 1083.9)下: (a) z = 0.51截面扰动温度(云图)和扰动速度矢量(箭头); (b)自由液面扰动温度(云图)和扰动速度矢量(箭头)

    Figure  7.  The disturbance temperature (colored contour) and disturbance velocity vector (arrow): (a) the z = 0.51 cross section; (b) the free surface. under the critical condition (Mac = 1083.9) at As = 0.77, Pr = 0.068.

    图  8  高径比As = 1.11, Pr = 0.068的临界状态(Mac = 1273.6)下: (a)扰动能量平衡条状图; (b)局部扰动动能极值图

    Figure  8.  The disturbance energy balance (a) and distribution of the local disturbance kinetic energy extreme value (b) under critical condition (Mac = 1273.6) at As = 1.11, Pr = 0.068.

    图  9  高径比 As = 1.11, Pr = 0.068的临界状态(Mac = 1273.6)下扰动温度(云图)和扰动速度矢量(箭头): (a)自由液面; (b) z = 0.20截面; (c) z = 0.51截面; (d) z = 0.74截面

    Figure  9.  The disturbance temperature (colored contour) and disturbance velocity vector (arrow) under the critical condition (Mac = 1273.6) for the case of As = 1.11 and Pr = 0.068 at: (a) the free surface; (b) the z = 0.20 section; (c) the z = 0.51 section; (d) the z = 0.74 section

    图  10  高径比As = 1.43, Pr = 0.068的临界状态(Mac = 531.9)下: (a)扰动能量平衡条状图; (b)局部扰动动能极值图

    Figure  10.  The disturbance energy balance (a) and distribution of the local disturbance kinetic energy extreme value (b) under critical condition (Mac = 531.9) at As = 1.43, Pr = 0.068.

    图  11  高径比As = 1.43, Pr = 0.068的临界状态(Mac = 531.9)下扰动温度(云图)和扰动速度矢量(箭头): (a)自由液面; (b) z = 0.20截面; (c) z = 0.51截面; (d) z = 0.74截面

    Figure  11.  The disturbance temperature (colored contour) and disturbance velocity vector (arrow) under the critical condition (Mac = 531.9) for the case of As = 1.43 and Pr = 0.068 at: (a) the free surface; (b) the z = 0.20 section; (c) the z = 0.51 section; (d) the z = 0.74 section

    图  12  高径比As = 1.43, Pr = 0.009临界状态(Mac = 531.9)下自由液面处扰动温度(云图)和扰动速度矢量(箭头)

    Figure  12.  The disturbance temperature (colored contour) and disturbance velocity vector (arrow) at the free surface under the critical condition (Mac = 531.9) for the case of As = 1.43 and Pr = 0.009

    图  13  高径比 As = 2.00, Pr = 0.068的临界状态(Mac = 234.6)下: (a)扰动能量平衡条状图; (b)局部扰动动能极值图

    Figure  13.  The disturbance energy balance (a) and distribution of the local disturbance kinetic energy extreme value (b) under critical condition (Mac = 234.6) at As = 2.00, Pr=0.068.

    图  14  高径比As = 2.00, Pr = 0.068的临界状态(Mac = 234.6)下扰动温度(云图)和扰动速度矢量(箭头): (a)自由液面; (b) z = 0.20截面; (c) z = 0.51截面; (d) z = 0.74截面

    Figure  14.  The disturbance temperature (colored contour) and disturbance velocity vector (arrow) under the critical condition (Mac = 234.6) for the case of As = 2.00 and Pr = 0.068 at: (a) the free surface; (b) the z = 0.20 section; (c) the z = 0.51 section; (d) the z = 0.74 section

    图  15  As = 2.00 Pr = 0.009时临界状态(Mac = 234.6)下自由液面处扰动温度(云图)和扰动速度矢量(箭头)

    Figure  15.  The disturbance temperature (colored contour) and disturbance velocity vector (arrow) at the free surface under the critical condition (Mac = 234.6) for the case of As = 2.00 and Pr = 0.009

    图  16  失稳模式I在临界状态下的基态流函数(云图)、基态温度场(等值线): (a) As = 0.48, Mac = 1936.3; (b) As = 0.77, Mac = 1083.9; (c) As = 1.11, Mac = 1273.6.

    Figure  16.  The basic flow (colored contour) and temperature (isotherm) of instability mode I under critical condition for case of: (a) As = 0.48, Mac = 1936.3; (b) As = 0.77, Mac = 1083.9; (c) As = 1.11, Mac = 1273.6.

    图  17  失稳模式II在临界状态下的基态流函数(云图)、基态温度场(等值线): (a) As = 1.43, Mac = 531.9; (b) As = 2.00, Mac = 234.6(续)

    Figure  17.  The basic flow (colored contour) and temperature (isotherm) of instability mode II under critical condition at (a) As = 1.43, Mac = 531.9; (b) As = 2.00, Mac = 234.6. (continued)

    17  失稳模式II在临界状态下的基态流函数(云图)、基态温度场(等值线): (a) As=1.43, Mac=531.9; (b) As=2.00, Mac=234.6

    17.  The basic flow (colored contour) and temperature (isotherm) of instability mode II under critical condition at (a) As = 1.43, Mac=531.9; (b) As = 2.00, Mac=234.6.

    表  1  基于不同网格分辨率得到的热毛细对流(Pr = 0.068)失稳临界Marangoni数(Mac)和波数kc

    Table  1.   The critical Marangoni number (Mac) and wave number kc for the instability of thermocapillary flow with Pr = 0.068 under different mesh resolution conditions

    mesh resolution41 × 4649 × 5557 × 64
    Mac / kc1179.7 / 31182.4 / 31182.7 / 3
    下载: 导出CSV

    表  2  计算失稳临界参数(Rec、fckc)与文献结果[14]对比

    Table  2.   The critical values(Rec, fc, kc)from the present computations against the reference results [14]

    PrRec / fc /kc(Present)Rec / fc /kc [14]relative error of Rec/ fc
    0.06817379 / 205.3 / 317229 / 206 / 30.87% / 0.36%
    0.18314021/ 409.1/ 314276 /415/ 31.78% / 1.42%
    1.02544/64.9 / 22551 /65/ 20.27% / 0.15%
    下载: 导出CSV

    表  3  计算失稳临界参数(Mackc)与文献结果[15]对比

    Table  3.   The critical values(Mac and kc)from the present computations against the reference results[15]

    AsMac / kc(Present)(LSA)Mac / kc[15](DNS)Mac / kc[15]
    0.632.27 / 332.21 / 334.73 / 3
    0.823.12 / 223.18 / 224.71 / 2
    1.016.76 / 217.00 / 219.77 / 2
    下载: 导出CSV

    表  4  Pr = 0.068时不同高径比下的失稳临界参数

    Table  4.   The critical values at different aspect ratios for Pr = 0.068

    AsMacfckcType
    0.402033.1±490.76



    0.431920.0±493.65
    0.481936.3±507.45
    0.531770.8±504.74
    0.591838.4±536.14
    0.671988.8±233.04
    失稳模式I
    (振荡失稳)

    0.711278.0±200.34
    0.771083.9±201.74
    0.91995.3±155.23
    1.001182.4±205.33
    1.051246.8±63.62

    1.111273.6±62.72
    1.181393.6±36.72
    1.201348.40.02
    1.251058.60.02


    失稳模式II
    1.33691.30.02
    1.43531.90.02
    1.54483.60.02
    1.67350.50.01(静态失稳)



    1.82262.80.01
    2.00234.60.01
    2.22248.40.01
    2.50326.00.01
    下载: 导出CSV

    表  5  Pr = 0.068时不同高径比能量分析结果

    Table  5.   The energy analysis results at different aspect ratios for Pr = 0.068

    AsIV1IV2IV3IV4IV5IV4 + IV5MZMφMZ + Mφ
    0.402.45%-7.90%-1.44%51.69%47.92%99.61%3.54%3.67%7.21%
    0.432.17%-12.31%-1.45%59.63%44.46%104.09%4.04%3.34%7.38%
    0.484.39%-6.12%-1.81%48.98%48.38%97.36%3.11%2.99%6.10%
    0.534.14%-11.26%-1.84%58.69%44.07%102.76%3.55%2.53%6.08%
    0.596.69%-3.11%-2.53%44.19%49.81%94.00%2.59%2.22%4.81%
    0.670.63%9.55%-1.11%18.19%63.87%82.06%2.57%6.17%8.74%
    0.71-0.18%10.44%-2.67%20.40%62.95%83.35%2.49%6.49%8.98%
    0.770.85%12.58%-4.16%19.41%63.65%83.06%1.86%5.75%7.61%
    0.910.33%9.57%-4.29%22.39%59.06%81.45%3.36%6.50%9.86%
    1.007.10%16.23%-5.75%14.43%61.53%75.96%1.48%5.04%6.52%
    1.05-1.95%-23.35%-1.05%71.59%26.65%98.24%18.95%8.40%27.35%
    1.112.49%-16.15%2.00%65.21%23.27%88.48%15.51%7.06%22.57%
    1.189.54%-6.57%6.34%55.90%19.22%75.12%10.95%4.36%15.31%
    1.2010.29%-2.22%7.53%50.60%20.41%71.01%9.73%3.66%13.39%
    1.254.91%1.52%7.66%44.28%27.33%71.61%9.14%4.93%14.07%
    1.33-2.44%1.75%8.78%43.12%29.86%72.98%10.72%8.18%18.90%
    1.43-4.71%1.34%9.22%43.80%28.81%72.61%10.88%10.64%21.52%
    1.54-4.84%2.51%9.18%43.27%27.71%70.98%10.04%12.14%22.18%
    1.675.33%-23.21%-13.15%117.74%8.12%125.86%16.78%-11.67%5.11%
    1.825.42%-19.76%-13.34%118.69%7.33%126.02%15.32%-13.65%1.67%
    2.004.22%-14.91%-12.64%108.46%11.71%120.17%16.04%-12.88%3.16%
    2.222.39%-9.98%-11.03%93.18%17.04%110.22%17.92%-9.51%8.41%
    2.50-0.11%-5.68%-8.57%77.13%19.57%96.70%20.53%-2.87%17.66%
    下载: 导出CSV
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