微通道内气体流动换热的理论与实验研究
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摘要
本文以微通道热沉在航空航天载运工具热管理上的应用为背景,从微尺度流体流动与传热基础理论研究作为出发点,从数学模型的构建,关键因素的系统分析为前导,搭建单通道实验台系统分析流动特性；进一步提出新型微通道热沉的设计理念,并进行实验室加工制造,进而进行系列实验研究,验证其流动换热性能。系统的实现从基础理论研究,到数值分析,进一步提出高性能换热系统设计,最终实现实验系统的具体化。即实现了理论——设计——应用一体化。
本文对微尺度下描述流动换热的数学物理模型进行了深入研究,针对不同尺度下流动换热特性,提出了适合不同流区的数学模型,即在滑移流区,采用常规理论的Navier-Stokes方程配合Maxwell一阶滑移模型作为数学模型,可以精确的预测稀薄气体流动。在过渡流区,在合适的选取滑移系数的情况下,采用基于常规理论的Navier-Stokes方程配合二阶滑移模型作为数学模型,可以高效准确的预测稀薄气体流动。引入新的求解非线性方程的同伦分析法(HAM)首次对滑移区流动换热控制方程进行了解析求解,所得结果很好的支撑了所提出的观点。研究发现,在纳米尺度下,截面速度会出现“反转”现象,通过解析求解基于常规理论的Navier-Stokes方程配合二阶滑移模型,对上述现象进行了准确的预测。
基于得到的有关描述微尺度下流动换热的物理模型的研究结论,采用数值计算手段和解析求解的方法,系统分析了可压缩性效应、稀薄效应、入口效应和粘性加热效应。研究表明,可压缩性的影响在微通道中的影响不可忽略。常规的马赫数大于0.3是可压缩性判别条件的标准在微通道流动中不再适用,微通道内可压缩性影响用压力差描述优于用Mach数表述。常规通道的充分发展的概念在微通道中需要重新定义。在滑移流区,考虑可压缩性和稀薄效应的共同作用,针对流动阻力特性进行了专门研究,提出了无量纲滑移长度Ls/Dh这一新概念,用以描述滑移区摩擦特性,得到了该无量纲准则数与摩擦常数的关联式。该关联式对于滑移流动和非滑移流动以及可压缩流动或者不可压缩流动均适用。补充了滑移区考虑可压缩性条件下没有描述摩擦特性的无量纲数的空白,经过与实验数据的对比验证了其适用性。
研究发现矩形微通道中入口段速度分布明显不同于常规通道,截面速度最大值出现在近壁处。导致边界层发展滞后于常规尺寸通道,进而使微通道中入口段长度大于常规理论预测值。计算得到了无量纲流动入口段长度的关联式。微通道中热边界层发展滞后于常规尺寸通道,导致微通道中热入口段长度大于常规理论预测值。微通道入口区换热性能高于常规通道,充分发展区换热弱于常规通道。获得了描述微通道热入口段长度的定量关联式。
采用叠加原理,首次解析求解了考虑粘性加热、速度滑移和温度跳跃条件下的Navier-Stokes方程,针对等热流、上绝热下等热流和任意热流分布的情况进行了研究。粘性加热效应相当于一个内热源可使流体温度沿流动方向线性升高；并且对截面温度分布亦有很大影响,粘性加热效应使得近壁处温度最高,温度梯度加大,所有情况截面温度分布的二阶拐点在距壁面无量纲距离η=1/(?)处。发现对于上下壁面不对称加热边界条件,上下壁面热流密度相等其换热效果最好。
搭建了单微通道流动实验系统平台,并进行了系列实验。获得了摩擦常数与Mach数定量函数关系。实验结果表明,微通道内流动入口段长度大于常规理论预测值；充分发展段的摩擦常数低于常规理论预测值,论证了前述理论结果。还发现,在可压缩性效应的影响较低(Reynolds很小)情况下,粘性加热效应可使流体温度线性增加,在定性上,与前面的理论解析解吻合的较好。
基于前述研究结论,设计了新型结构的高效微通道热沉散热装置。采用干式蚀刻方法在实验室加工了所设计的微通道热沉实验段。在此基础上,搭建了芯片级微通道热沉换热系统实验平台,对其流动与换热性能进行了系列实验研究。通过对多列直通道粘性加热效应的研究进一步论证了前面章节得到的关于粘性加热效应的结论,即流量小时、粘性加热效应占据主导、流体温度升高。随着流量增加,可压缩性效应的影响渐强,流体温度升高值下降。直至最后,可压缩性效应完全占据主导,导致流体温度下降。通过对两级通道Ⅰ和两级通道Ⅱ(100μm-40μm)的实验研究,论证了本文提出的新型散热热沉结构的换热效果。实验结果表明,本文提出的新型散热装置不仅具有很好的换热性能同时压损小耗功少,可以作为高效散热装置应用到实际领域中。实际应用时,还需要要根据具体应用目标,考虑耗能等综合因素进行几何结构的优化设计,以达到强化换热性能和降低耗能的双重效果。
The background of the current investigation is based on the application of micro channel heat sink in the thermal management of the aerospace craft operation system. The research starts from the basic theory of micro scale fluid flow and heat transfer. Then the mathematical models for governing fluid flow and heat transfer in micro scale are proposed.. According to the established mathematical model, key factors, which affect flow and heat transfer characteristic, are systematically analyzed. The single micro-tube experiment platform is set up and a series of experiments have been done for flow characteristic analysis. Inspired by the obtained conclusions, the design concept of the new type micro channel heat sink is proposed and the experiment instruments are fabricated, which verifies a better heat transfer performance than conventional multiple straight micro channel heat sink.
The mathematical models for governing flow and heat transfer in microchannels are proposed for different flow regions. For slip flow region, Navier-Stokes equations, which are based on the conventional theory, with Maxwell slip model are used to describe the flow. Navier-Stokes equations with second-order slip boundary condition can accurately describe the flow in transit flow region by proper choosing of the slip coefficients in slip model. A powerful, easy-to-use analytic technique for non-linear problems, that is, the homotopy analysis method (HAM) was provided for solving these strong non-linear differential equations. By analyzing solutions and comparing with the results of other investigators, the above opinion has been validated. Meanwhile, recent researches show that, at the nano-scale level, an interesting phenomenon, namely "velocity inversion", is obtained by solving the molecular-based model. In the current paper, gas flow in nanochannels is also analytically investigated by using the homotopy analysis method (HAM). It is found that the inverted velocity profile can also be predicted by solving the conventional control equations, which are the Navier-Stokes equations, combined with high-order accurate slip boundary conditions.
Based on the conclusions obtained above about the mathematic models for micro flow and heat transfer, proper equations are chosen to describe the physical process in microchannels. Numerical and analytical analyses were provided to study the effects of compressibility, rarefaction, entrance region and viscous heating on fluid flow and heat transfer characteristics in microchannels. It is indicated that the effect of compressibility can not be neglected in microchannels. The conventional criteria for compressibility effect, that is Mach number larger than 0.3, can not be used as a criteria in micro-scale. The pressure drop is better than Mach number to be used as criteria for compressibility effect. The "developed flow region", which is defined in conventional theory, must be re-defined in microchannel as there is no so-called "developed flow region" in micro-scale. In slip flow region, a new non-dimensional parameter relative slip length Ls/Dh is found to be very useful to describe friction characteristic for compressible flow with slip in micro-scale. The correlation for fRe with this new non-dimensional parameter Ls/Dh is suggested. The suggested correlation for fRe with Ls/Dh is validated by comparing with experimental data. This correlation can be used for both slip and non-slip flow, and for both compressible and incompressible flow.
For entrance effect on fluid flow, it is found that the velocity profile in cross-section in microchannels is different from that in macrochannels, that is, maximum velocity occurs not in the channel core but near the walls due to the surface effect. Meanwhile, another feature of the velocity profiles is the presence of the very large velocity gradients near the walls. These phenomena result in the reduction of the thickness of hydrodynamic boundary layer. So the hydrodynamic entry length in microchannels is much larger than that in conventional channels. The correlation between L/D and Reynolds number and height-to-width ratio, which is useful for designing and optimizing the microchannel heat sinks and other microfluidic devices, is established. For entrance effect on heat transfer, it is found that the temperature gradient near the walls is very large. Thermal entry length in microchannels is much larger than that in conventional channels. Comparing with conventional channels, the heat transfer performance in microchannels is better in entry region and worse in the fully developed region. Also the effects of Reynolds number, hydrodynamic diameter, length diameter ratio, height-to-width ratio and wall temperature on thermal entry length were analyzed. The correlation among these parameters is established.
Based on the superposition principle, an analytical solution for steady convective heat transfer in a two-dimensional microchannel in the slip flow region is obtained, including the effects of velocity slip and temperature jump at the wall, which are the main characteristics of flow in the slip flow region, and viscous heating effects in the calculations. The cases of constant heat flux boundary conditions, one wall with adiabatic boundary and the other wall with constant heat flux input and non-symmetric constant heat flux boundary condition are studied. The effect of viscous heating can be seen as a volume energy source, the temperature of fluid increase linearly along the flow direction. In addition, it is noted that the effect of viscous heating distorts the temperature distributions at the cross-sections. The velocity gradient is larger near walls, since the effect of viscous heating is more significant there. According to these calculations, it is found that the position in the inflexion of the temperature profiles does not change with Br and Kn. The position of the inflexion is a constant, given byη= 1/(?). For non-symmetric constant heat flux boundary condition, it is indicated that uniform heating will get better heat transfer performance.
The single micro-tube experiment platform is set up and a series of experiments have been done for flow characteristic analysis. It is found that the friction constant is the function of Mach number, and the correlation is obtained. By analyzing the experimental data, it can be concluded that the entrance length in microtube is larger than that predicted by conventional theory. Also, the value of friction constant in the developed region is smaller than that predicted by conventional theory. These agree with the conclusions obtained in numerical study part. Meanwhile, the theoretical prediction suggested can give reasonable prediction on temperature field under the effect of viscous heating for incompressible (low Re number) flow.
Inspired by the above conclusions, the new type micro channel heat sink with new structures is proposed. The test sections with these new structures are fabricated by using dry etching method. Then, the microchannel heat sink experimental system is established. A series of experiments have been conducted for flow and heat transfer performance analysis. The conclusion on the effect of viscous heating on flow and heat transfer characteristics, which is obtained above, is verified by experimentally investigation about the multiple straight microchannels. That is that temperature change is due to the viscous heating effect and compressibility effect. The relationship of these two effects is competitive. By experimental study on two new type microchannel heat sink——two stage microchannel heat sinkⅠ(250μm-100μm) and two stage microchannel heat sinkⅡ(100μm-40μm), it can be concluded that the new type microchannel heat sink proposed in this paper has better heat transfer performance and lower pressure lose. It can be used as a high efficiency heat exchanger to the real applications. In practice, the geometry parameters of this new type microchannel heat sink can be optimized according to the purpose of the heat exchanger to realize the maximum the heat transfer and minimum the pressure loss to save energy.
本文对微尺度下描述流动换热的数学物理模型进行了深入研究,针对不同尺度下流动换热特性,提出了适合不同流区的数学模型,即在滑移流区,采用常规理论的Navier-Stokes方程配合Maxwell一阶滑移模型作为数学模型,可以精确的预测稀薄气体流动。在过渡流区,在合适的选取滑移系数的情况下,采用基于常规理论的Navier-Stokes方程配合二阶滑移模型作为数学模型,可以高效准确的预测稀薄气体流动。引入新的求解非线性方程的同伦分析法(HAM)首次对滑移区流动换热控制方程进行了解析求解,所得结果很好的支撑了所提出的观点。研究发现,在纳米尺度下,截面速度会出现“反转”现象,通过解析求解基于常规理论的Navier-Stokes方程配合二阶滑移模型,对上述现象进行了准确的预测。
基于得到的有关描述微尺度下流动换热的物理模型的研究结论,采用数值计算手段和解析求解的方法,系统分析了可压缩性效应、稀薄效应、入口效应和粘性加热效应。研究表明,可压缩性的影响在微通道中的影响不可忽略。常规的马赫数大于0.3是可压缩性判别条件的标准在微通道流动中不再适用,微通道内可压缩性影响用压力差描述优于用Mach数表述。常规通道的充分发展的概念在微通道中需要重新定义。在滑移流区,考虑可压缩性和稀薄效应的共同作用,针对流动阻力特性进行了专门研究,提出了无量纲滑移长度Ls/Dh这一新概念,用以描述滑移区摩擦特性,得到了该无量纲准则数与摩擦常数的关联式。该关联式对于滑移流动和非滑移流动以及可压缩流动或者不可压缩流动均适用。补充了滑移区考虑可压缩性条件下没有描述摩擦特性的无量纲数的空白,经过与实验数据的对比验证了其适用性。
研究发现矩形微通道中入口段速度分布明显不同于常规通道,截面速度最大值出现在近壁处。导致边界层发展滞后于常规尺寸通道,进而使微通道中入口段长度大于常规理论预测值。计算得到了无量纲流动入口段长度的关联式。微通道中热边界层发展滞后于常规尺寸通道,导致微通道中热入口段长度大于常规理论预测值。微通道入口区换热性能高于常规通道,充分发展区换热弱于常规通道。获得了描述微通道热入口段长度的定量关联式。
采用叠加原理,首次解析求解了考虑粘性加热、速度滑移和温度跳跃条件下的Navier-Stokes方程,针对等热流、上绝热下等热流和任意热流分布的情况进行了研究。粘性加热效应相当于一个内热源可使流体温度沿流动方向线性升高；并且对截面温度分布亦有很大影响,粘性加热效应使得近壁处温度最高,温度梯度加大,所有情况截面温度分布的二阶拐点在距壁面无量纲距离η=1/(?)处。发现对于上下壁面不对称加热边界条件,上下壁面热流密度相等其换热效果最好。
搭建了单微通道流动实验系统平台,并进行了系列实验。获得了摩擦常数与Mach数定量函数关系。实验结果表明,微通道内流动入口段长度大于常规理论预测值；充分发展段的摩擦常数低于常规理论预测值,论证了前述理论结果。还发现,在可压缩性效应的影响较低(Reynolds很小)情况下,粘性加热效应可使流体温度线性增加,在定性上,与前面的理论解析解吻合的较好。
基于前述研究结论,设计了新型结构的高效微通道热沉散热装置。采用干式蚀刻方法在实验室加工了所设计的微通道热沉实验段。在此基础上,搭建了芯片级微通道热沉换热系统实验平台,对其流动与换热性能进行了系列实验研究。通过对多列直通道粘性加热效应的研究进一步论证了前面章节得到的关于粘性加热效应的结论,即流量小时、粘性加热效应占据主导、流体温度升高。随着流量增加,可压缩性效应的影响渐强,流体温度升高值下降。直至最后,可压缩性效应完全占据主导,导致流体温度下降。通过对两级通道Ⅰ和两级通道Ⅱ(100μm-40μm)的实验研究,论证了本文提出的新型散热热沉结构的换热效果。实验结果表明,本文提出的新型散热装置不仅具有很好的换热性能同时压损小耗功少,可以作为高效散热装置应用到实际领域中。实际应用时,还需要要根据具体应用目标,考虑耗能等综合因素进行几何结构的优化设计,以达到强化换热性能和降低耗能的双重效果。
The background of the current investigation is based on the application of micro channel heat sink in the thermal management of the aerospace craft operation system. The research starts from the basic theory of micro scale fluid flow and heat transfer. Then the mathematical models for governing fluid flow and heat transfer in micro scale are proposed.. According to the established mathematical model, key factors, which affect flow and heat transfer characteristic, are systematically analyzed. The single micro-tube experiment platform is set up and a series of experiments have been done for flow characteristic analysis. Inspired by the obtained conclusions, the design concept of the new type micro channel heat sink is proposed and the experiment instruments are fabricated, which verifies a better heat transfer performance than conventional multiple straight micro channel heat sink.
The mathematical models for governing flow and heat transfer in microchannels are proposed for different flow regions. For slip flow region, Navier-Stokes equations, which are based on the conventional theory, with Maxwell slip model are used to describe the flow. Navier-Stokes equations with second-order slip boundary condition can accurately describe the flow in transit flow region by proper choosing of the slip coefficients in slip model. A powerful, easy-to-use analytic technique for non-linear problems, that is, the homotopy analysis method (HAM) was provided for solving these strong non-linear differential equations. By analyzing solutions and comparing with the results of other investigators, the above opinion has been validated. Meanwhile, recent researches show that, at the nano-scale level, an interesting phenomenon, namely "velocity inversion", is obtained by solving the molecular-based model. In the current paper, gas flow in nanochannels is also analytically investigated by using the homotopy analysis method (HAM). It is found that the inverted velocity profile can also be predicted by solving the conventional control equations, which are the Navier-Stokes equations, combined with high-order accurate slip boundary conditions.
Based on the conclusions obtained above about the mathematic models for micro flow and heat transfer, proper equations are chosen to describe the physical process in microchannels. Numerical and analytical analyses were provided to study the effects of compressibility, rarefaction, entrance region and viscous heating on fluid flow and heat transfer characteristics in microchannels. It is indicated that the effect of compressibility can not be neglected in microchannels. The conventional criteria for compressibility effect, that is Mach number larger than 0.3, can not be used as a criteria in micro-scale. The pressure drop is better than Mach number to be used as criteria for compressibility effect. The "developed flow region", which is defined in conventional theory, must be re-defined in microchannel as there is no so-called "developed flow region" in micro-scale. In slip flow region, a new non-dimensional parameter relative slip length Ls/Dh is found to be very useful to describe friction characteristic for compressible flow with slip in micro-scale. The correlation for fRe with this new non-dimensional parameter Ls/Dh is suggested. The suggested correlation for fRe with Ls/Dh is validated by comparing with experimental data. This correlation can be used for both slip and non-slip flow, and for both compressible and incompressible flow.
For entrance effect on fluid flow, it is found that the velocity profile in cross-section in microchannels is different from that in macrochannels, that is, maximum velocity occurs not in the channel core but near the walls due to the surface effect. Meanwhile, another feature of the velocity profiles is the presence of the very large velocity gradients near the walls. These phenomena result in the reduction of the thickness of hydrodynamic boundary layer. So the hydrodynamic entry length in microchannels is much larger than that in conventional channels. The correlation between L/D and Reynolds number and height-to-width ratio, which is useful for designing and optimizing the microchannel heat sinks and other microfluidic devices, is established. For entrance effect on heat transfer, it is found that the temperature gradient near the walls is very large. Thermal entry length in microchannels is much larger than that in conventional channels. Comparing with conventional channels, the heat transfer performance in microchannels is better in entry region and worse in the fully developed region. Also the effects of Reynolds number, hydrodynamic diameter, length diameter ratio, height-to-width ratio and wall temperature on thermal entry length were analyzed. The correlation among these parameters is established.
Based on the superposition principle, an analytical solution for steady convective heat transfer in a two-dimensional microchannel in the slip flow region is obtained, including the effects of velocity slip and temperature jump at the wall, which are the main characteristics of flow in the slip flow region, and viscous heating effects in the calculations. The cases of constant heat flux boundary conditions, one wall with adiabatic boundary and the other wall with constant heat flux input and non-symmetric constant heat flux boundary condition are studied. The effect of viscous heating can be seen as a volume energy source, the temperature of fluid increase linearly along the flow direction. In addition, it is noted that the effect of viscous heating distorts the temperature distributions at the cross-sections. The velocity gradient is larger near walls, since the effect of viscous heating is more significant there. According to these calculations, it is found that the position in the inflexion of the temperature profiles does not change with Br and Kn. The position of the inflexion is a constant, given byη= 1/(?). For non-symmetric constant heat flux boundary condition, it is indicated that uniform heating will get better heat transfer performance.
The single micro-tube experiment platform is set up and a series of experiments have been done for flow characteristic analysis. It is found that the friction constant is the function of Mach number, and the correlation is obtained. By analyzing the experimental data, it can be concluded that the entrance length in microtube is larger than that predicted by conventional theory. Also, the value of friction constant in the developed region is smaller than that predicted by conventional theory. These agree with the conclusions obtained in numerical study part. Meanwhile, the theoretical prediction suggested can give reasonable prediction on temperature field under the effect of viscous heating for incompressible (low Re number) flow.
Inspired by the above conclusions, the new type micro channel heat sink with new structures is proposed. The test sections with these new structures are fabricated by using dry etching method. Then, the microchannel heat sink experimental system is established. A series of experiments have been conducted for flow and heat transfer performance analysis. The conclusion on the effect of viscous heating on flow and heat transfer characteristics, which is obtained above, is verified by experimentally investigation about the multiple straight microchannels. That is that temperature change is due to the viscous heating effect and compressibility effect. The relationship of these two effects is competitive. By experimental study on two new type microchannel heat sink——two stage microchannel heat sinkⅠ(250μm-100μm) and two stage microchannel heat sinkⅡ(100μm-40μm), it can be concluded that the new type microchannel heat sink proposed in this paper has better heat transfer performance and lower pressure lose. It can be used as a high efficiency heat exchanger to the real applications. In practice, the geometry parameters of this new type microchannel heat sink can be optimized according to the purpose of the heat exchanger to realize the maximum the heat transfer and minimum the pressure loss to save energy.
引文
[1]A. P. Shlosinger, W. Woo, Feasibility study of integral heat sink space suit concept, NASA Report, NSL 65-87-2.
[2]T. D. Swanson, G. C. Birur, NASA Thermal Control Technologies for Robotic Spacecraft, NASA-20030031332,2003.
[3]T. Swanson, NASA/Goddard thermal control technology roadmap-2002,13th Annual Spacecraft Thermal Control Workshop, Aerospace Corporation, El Segundo, CA,2002.
[4]G. Birur, JPL advanced thermal control technology roadmap,13th Annual Spacecraft Thermal Control Workshop, Aerospace Corporation, El Segundo, CA,2002.
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