【作者】 王飞；

【导师】 彭岚；

【作者基本信息】 重庆大学 ， 动力工程及工程热物理， 2015， 博士

【摘要】 温度梯度会导致液层表面张力和密度不均匀,从而驱动流体运动。其中由表面张力不均匀所引起的流动被称为Marangoni或热毛细对流:当温度梯度垂直于自由表面时,这种流动被称为Marangoni对流;当温度梯度平行于自由界面时,这种流动为热毛细对流。而由密度不均匀所引起的流动被称为浮力对流。在重力条件下,Marangoni或热毛细对流和浮力对流同时出现。在微重力条件下,浮力对流消失,而Marangoni或热毛细对流依然存在。目前关于这些对流的研究主要针对单向温差作用下的流动,但是对于水平和垂直温度梯度同时存在时的Marangoni-热毛细对流以及浮力-Marangoni-热毛细对流的研究还很少。在自然界和实际的工业生产过程中这种双向温度梯度往往同时存在,它们共同驱动流体运动,与单向温差作用时相比,流动变得复杂且差异显著。因此,本课题采用数值模拟和实验研究相结合、数值模拟为主的方法研究水平和垂直温度梯度共存时环形浅液池内中等普朗特数流体的Marangoni-热毛细对流以及浮力-Marangoni-热毛细对流,重点探究水平温差和垂直热流在驱动流体运动中各自发挥的作用力,得到了Marangoni-热毛细对流的基本形态及不稳定性的基本特征,并讨论了自由表面换热对基本形态和不稳定性特征的影响,分析了重力对浮力-Marangoni-热毛细对流不稳定性的作用机制。所得结论从理论上可发展液层内复杂流动的耗散结构理论、拓展热毛细对流的研究领域,从工程实践上可为熔体法单晶生长奠定重要的理论基础。主要研究内容及结果如下:首先,通过数值模拟研究了双向温度梯度作用下环形浅液池内0.65cSt硅油的Marangoni-热毛细对流,界定了在驱动流体运动中发挥主导作用的两个热力学势(水平温差和底部热流)在对流中各自发挥的影响:水平温差使得表面温度由内壁向外壁递增,导致表面流体从外壁流向内壁;底部热流使得表面温度由中间区域向两壁递减,导致表面流体从中间区域流向两壁。这两种力的耦合作用驱动流体运动,对流的形态取决于这两种力的强度对比。当水平温差起主导作用时,表面温度由内壁向外壁递增;当底部热流起主导作用时,表面温度由中间区域向两壁递减;当水平温差和底部热流作用力都较为显著时,最高表面温度位于外壁与中间区域之间,并从此处向两壁递减。其次,通过研究水平温差和底部热流对Marangoni-热毛细对流的影响,证明了水平温差和底部热流降低了对流的稳定性。稳态对流为二维轴对称流动,即表面温度无周向波动,对流失稳后出现表面温度周向波动,且不稳定性越强,周向波动越大,同时表面温度径向波动导致的径向流动占主导地位,因此提出了用表面温度径向波动来表征流动的强弱,而用表面温度周向波动来表征流动失稳程度。并根据不稳定性的强弱,对Marangoni-热毛细对流的不稳定性特征进行了基本分类:不稳定性较弱时,表征对流失稳状态的表面温度周向波动主要表现为点状波;不稳定性较强时,底部热流在驱动流动中起绝对主导作用时为双热流体波,水平温差起主导作用时出现热流体波,当水平温差和底部热流作用力都较为显著时为波长较短的热流体波;不稳定性过强时出现紊乱波动。其中,点状波、热流体波和双热流体波不稳定性是一种有序的非平衡态。点状波随时间沿径向正方向扩散,但是在扩散过程中逐渐减弱同时新的波动在内壁处生成然后继续沿径向正方向扩散,以此循环,在整个变化周期中,点状波的基本形态不会发生变化;热流体波和双热流体波随时间沿周向旋转,在整个变化周期中,波动的基本形态同样不会发生变化。然后,研究了Bi数所表征的自由表面换热和Gr数所表征的重力对三种典型的非稳态Marangoni-热毛细对流的影响,结果表明自由表面热损失和重力有利于稳定双向温差作用下的Marangoni-热毛细对流。并分析了重力抑制Marangoni-热毛细对流的物理机制为:在表面张力梯度所导致的Marangoni-热毛细对流中,自由表面上的流体由热端流向冷端同时流体在底部由冷端流向热端形成回流,造成某区域上层流体的温度高于下层流体的温度,流体在此区域沿Z轴负方向流动时为高温流体(低密度流体)向下流,这与浮升力的方向相反,因而使得重力对Marangoni-热毛细对流产生了抑制作用。最后,研究了底部热流和水平温差对浮力-Marangoni-热毛细对流的影响,数值模拟与实验研究的结果表明:水平温差和底部热流在驱动流体运动中各自发挥的作用与其在Marangoni-热毛细对流中的作用类似;水平温差起主导作用或者水平温差与底部热流共同主导时,重力有效抑制了内壁附近的流胞,而对外壁附近的流胞抑制效果较差;底部热流起主导作用时,重力有效抑制了内外壁附近的流胞;当最高表面温度脱离外壁处后,表面温度周向波动主要集中在最高表面温度附近,随着底部热流的增强,最高表面温度向中间区域移动,表面温度周向波动也相应地向中间区域移动;而当自由表面温度沿径向正方向递增时,表面温度周向波动随非平衡热力学力的变化则较为复杂。更多还原

【Abstract】 The uneven surface tension and density induced by temperature gradient can drive the fluid. The surface tension driven convection can take two different forms: one is the thermocapillary convection caused by the temperature gradient parallel to the free surface, and the other is the Marangoni convection driven by the temperature gradient perpendicular to the free surface. The flow driven by density gradient is called buoyancy convection. Under gravity condition, Marangoni or thermocapillary convection and buoyancy convection coexist, however, the buoyancy convection disappears while the Marangoni or thermocapillary convection still exists under microgravity. Up to now, most researchers have only studied these convections due to a unidirectional temperature difference. However, the vertical and horizontal temperature differences often coexist in nature and many actual production processes, these two thermodynamic forces drive the fluid system away from equilibrium state together, which makes the result different from the situation with unidirectional temperature difference. In this thesis, the Marangoni-thermocapillary and BuoyancyMarangoni-thermocapillary convections of 0.65 cSt silicon oil with moderate Prandtl number in a shallow annular layer under the combined action of horizontal and vertical temperature gradients were investigated by numerical simulation and experiment, and numerical simulation is adopted as the main method. The study focuses on the respective roles of horizontal temperature difference and vertical bottom heat flux in these convections, the basic pattern and instability characteristic of Marangoni-thermocapillary convection are obtained, the effect of free surface heat transfer on the basic pattern and instability characteristic is discussed, and the action mechanism of gravity for Buoyancy-Marangoni-thermocapillary convection is analyzed. The obtained results are helpful to not only expand the theory on the thermocapillary convection but lay a certain theoretical foundation for many actual production processes. The main works and results are as follows:Firstly, the Marangoni-thermocapillary convection of 0.65 cSt silicon oil in a shallow annular layer under bidirectional temperature gradients is investigated by numerical simulation, the respective roles of horizontal temperature difference and vertical bottom heat flux in convection are identified: horizontal temperature difference makes surface temperature increase from inner wall to outer wall, accordingly the surface fluid flows from the outer wall to inner wall, while bottom heat flux makes surface temperature decrease from the middle region to the inner and outer walls, accordingly the surface fluid flows from the middle region to the two walls. The fluid is driven by these two thermodynamic forces together and the convection pattern depends on their strength relationship. When the horizontal temperature difference plays a leading role in convection, the surface temperature increases from inner wall to outer wall; When the vertical bottom heat flux dominates the convection, the surface temperature decreases from the middle region to the two walls; When both of them act effectively, the highest surface temperature locates at the region between the middle and outer wall.Secondly, horizontal temperature difference and vertical bottom heat flux can destabilize Marangoni-thermocapillary convection, which is proved by studying the effects of horizontal temperature difference and vertical bottom heat flux on the convection. Surface temperature radial fluctuation can characterize the flow strength while the circumferential fluctuation can characterize the instability strength because that the circumferential fluctuation doesn’t exist for steady convection, and the stronger the instability, the stronger the circumferential fluctuation, while the radial flow induced by the radial fluctuation dominates the convection. The instability of Marangoni-thermocapillary convection can be categorized according to the instability strength: the circumferential fluctuation with punctate wave represents the weak instability; For the strong instability, it is a double hydrothermal wave when the vertical bottom heat flux dominates the flow, it is a hydrothermal wave when the horizontal temperature difference plays a leading role, and it is a hydrothermal wave with shorter wavelength when both of horizontal temperature difference and vertical bottom heat flux act effectively; It is a chaos wave for the too strong instability. Here, the punctate, hydrothermal and double hydrothermal waves are a regular instability. Punctate wave moves along the positive radial direction over time and the wave gradually abates during the movement while the new wave appears near the inner wall, this process cycles and the basic wave pattern doesn’t change over the whole period; Hydrothermal and double hydrothermal waves rotate over time and the basic patterns are also consistent.Thirdly, the effects of surface heat exchange characterized by Bi number and gravity characterized by Gr number on three typical unsteady Marangonithermocapillary convections with strong instability are investigated, the results show that the surface heat loss and gravity stabilize the Marangoni-thermocapillary convection with bidirectional temperature differences. The mechanism that gravity suppresses the convection is as following: surface fluid flows from the hot end to the cold end while the bottom fluid flows along the opposite direction, which makes the temperature of upper fluid higher than the temperature of lower fluid somewhere, fluid flows along the negative direction of Z axis in this region, which is against the buoyancy, therefore, gravity suppresses the convection.Finally, the effects of vertical bottom heat flux and horizontal temperature difference on Buoyancy-Marangoni-thermocapillary convection are studied, the results of numerical simulation and experiment show that the roles of vertical bottom heat flux and horizontal temperature difference in Buoyancy-Marangoni-thermocapillary convection are similar to the ones in Marangoni-thermocapillary convection; When both of vertical bottom heat flux and horizontal temperature difference act effectively or horizontal temperature difference dominates the flow, gravity succeeds in suppressing the flow cell near inner wall but fails to weaken the one near outer wall; when the highest surface temperature is away from the outer wall, the surface temperature circumferential fluctuation mainly concentrates in the region where the highest surface temperature locates, with the increase of bottom heat flux, the highest surface temperature moves towards the middle region, accordingly, the fluctuation moves towards the middle region; However, the evolution of surface temperature circumferential fluctuation with the non-equilibrium thermodynamic forces is complicated when the surface temperature increases along the positive radial direction.更多还原