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首页> 外文期刊>International Journal of Heat and Mass Transfer >Effects of Pr and pool curvature on thermocapillary flow instabilities in annular pool
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Effects of Pr and pool curvature on thermocapillary flow instabilities in annular pool

机译：PR和池曲率对环形池热量流量稳定性的影响

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摘要

We linearly analyzed the effect of the Prandtl number (Pr) on the stability of thermocapillary flow in shallow annular pools with an aspect ratio Γ = (R_o - R_i)/d = 20 and two radius ratios Γ_R = R_i/R_o= 0.50 and 0.98039, where d, R_o, and R_i are the liquid depth and the radii of the heated outer wall and the cooled inner wall, respectively. The results for Pr ∈ [0, 10~2] show that the steady axisymmetric thermocapillary flows in these annular pools become unstable against oscillatory instability modes, OSC1, OSC2 and hydrothermal wave (HTW). Two co-dimension-two bifurcations occur at Pr*_1[ and Pr*_2. The critical mode for Pr ≤ Pr*_1 is OSC2 with almost constant critical Reynolds number Re_c, large wave number and high frequency. OSC1 with smaller wave number and lower frequency is the critical mode for Pr*_1 ≤ Pr ≤ Pr*_2 and Re_c slightly decreases with increasing Pr. HTW is the critical mode for Pr ≥ Pr*_2 and Re_c decreases with increasing Pr. The values of (Pr*_1, Pr*_2) are (0.00953, 0.03054) for Γ_R = 0.50, and (0.01919, 0.01946) for Γ_R = 0.98039. Energy-budget analyses reveal that the instabilities in low-Pr range are caused by instabilities in the steady toroidal vortex (or vortices) near the cold wall.
机译：我们线性地分析了Prandtl数（PR）对浅环池中热量流量稳定性的效果，具有纵横比γ=（R_O - r_i）/ d = 20和两个半径比γ_R= R_I / R_O = 0.50和0.98039 ，其中D，R_O和R_I分别是加热的外壁和冷却的内壁的液体深度和半径。 Pr∈[0,10〜2]的结果表明，这些环形池中的稳定轴对称热量流量对振荡不稳定模式，OSC1，OSC2和热热波（HTW）变得不稳定。在Pr * _1 [和Pr * _2，发生两个共尺寸两分的分叉。 PR≤Pr* _1的临界模式是OSC2，具有几乎恒定的关键雷诺数RE_C，大波数和高频。波数和较低频率较小的OSC1是Pr *_1≤Pr≤Pr* _2的临界模式，并且Re_c随着Pr的增加略微降低。 HTW是PR≥Pr* _2的临界模式，并且RE_C随着PR的增加而降低。 （Pr * _1，Pr * _2）的值（0.00953,0.03054），用于γ_R= 0.50，（0.01919,0.01946），用于γ_R= 0.98039。能量预算分析表明，低PR系列的不稳定性是由冷壁附近的稳定环形涡流（或涡流）中的稳定性引起的。

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