发散冷却基础问题的理论和实验研究
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摘要
航空航天技术是20世纪以来发展最为迅速、对人类生活影响最大的科学技术之一,因其对军事战略、国民经济和社会生活的重大意义,已成为各发达国家竞相发展的重点项目。目前热防护问题已成为空天技术进一步发展的瓶颈,更加高效的强化冷却技术已成为航空航天领域关注的焦点,其中以多孔介质为载体的发散冷却,因其出色的冷却效果受到越来越多的关注和研究。然而发散冷却在基础理论和实验方法方面值得研究的问题还有很多,如描述多孔介质内流体流动、传热、传质和相变过程的数学模型和边界条件的精确化,对发散冷却系统进行优化设计,确定特定热环境中冷却剂用量等。
本文围绕以上问题展开,以理论分析为基础采用数值模拟和实验验证相结合的方法,对发散冷却基础理论问题进行了研究。主要工作有：
(1)总结和分析了发散冷却过程中所涉及到的多孔介质内单相流和多相流的数学模型。首先详细列举和对比了过去文献中出现的多孔介质单相流的动量方程、实验中获得的各种流动经验公式以及本构关系式,讨论了每个流动模型所适用的学科领域、物理模型以及流动条件。然后在单相流的质量、动量和能量守恒方程的基础上,进一步分析了带有物理相变或化学反应的混溶多相流的数学模型。通过对多孔介质内流体流动、传热和相变过程的数学模型的整理和研究,指出了现有模型的不足,为发散冷却数学模型的修正提供了思路。
(2)在传统模型的基础上,对常温下多孔介质内流体运动方程进行了修正,使其在高温及大温度梯度变化环境中同样具有适用性。在模型的修正中,考虑了多孔骨架内部气体的自然对流和受迫运动,以及流体物性参数随温度和压力的变化,并通过以空气作为冷却剂的发散冷却实验对模型进行了验证。结果表明：对于工作在高温高压环境中的发散冷却系统,环境条件对流动过程的影响不可忽略,要考虑随温度和压力变化的流体物性。最后获得了表观渗透率的表达式,可以在保留Darcy定律的简洁线性形式的前提下,将温度、压力以及高速流动产生的惯性作用通过表观渗透率体现。
(3)从基本物理原理出发建立了描述流体在多孔介质内运动、吸热、相变过程的质量、动量和能量守恒模型。在连续性方程中,考虑流体汽化膨胀后的密度变化,并将可压缩性影响代入动量和能量守恒方程；在动量方程中,增加了液体汽化相变导致的动量迁移项；在能量方程中,考虑混合流体的压力和温度变化。通过使用液态水作为冷却剂的发散冷却实验对模型和数值计算方法进行了验证。并用验证过的模型和方法分析一维稳态情况下的温度、压力和速度分布,讨论冷却剂流量、外界热流密度对液体在微孔里运动、吸热、相变特性的影响。计算结果表明：多孔介质内气液两相共存区的流体温度沿流动方向是增加的,并非恒定不变,且液体汽化相变导致的动量迁移项对流体压力和速度分布有显著影响。因此,本文所得到的具有相变现象的动力学模型和能量方程可以对液体发散冷却过程进行更精确的描述,所提出的数值方法可以进行更精确的求解,使得发散冷却数学模型得到进一步的完善。
(4)对带有液体相变的发散冷却过程中可能出现的流体流动和传热状态进行了数值模拟,就系统优化问题进行了研究,主要包括两部分工作。1)分析了多孔介质平板内两相区厚度和位置、毛细力和驱动力随热流密度和冷却剂流量的变化,并确定了发散冷却的理想工作状态。通过获得的热流密度和冷却剂流量之间的关系曲线,可以估算出发散冷却处于理想工作状态时所能承受的最大外界热流和所需要的最小冷却剂量。由此,可以确定工作在特定热环境中的发散冷却所需的冷却剂流量和驱动力。2)分析了防热材料、冷却剂的选择和工作环境等参数对发散冷却过程的影响,以冷却效率和驱动力大小作为考察发散冷却效果的标准,从多孔材料热导率、孔隙率和粒径以及冷却剂的选择出发,对发散冷却系统提出了优化方案。冷却剂用量和驱动力的研究对发散冷却技术的实际应用非常有意义。另外对热防护材料和结构的分析可以为今后系统优化设计提供有参考价值的借鉴。
Aerospace technology has developed rapidly and influenced human life greatly since twentieth century, and now becomes the key project of all the developed countries for its significant effects on military strategy, national economy and social life. However, the further development of aerospace technology has been limited by existing thermal protection system (TPS), therefore more efficient enhanced cooling technology is the focus of aerospace industry at present. Transpiration cooling, as a potential thermal protection approach, has attracted more and more attention from the researchers due to its excellent cooling efficiency. However there are still many problems in the investigations of experimental methods, theoretical models and numerical approaches, such as more accurate models and boundary conditions to describe the fluid flow, heat and mass transfer and phase change in porous media, the optimal design of transpiration cooling system, the evaluation of coolant consumption under a certain thermal circumstance and so on.
Surrounding the above problems and based on the theoretical analysis, this dissertation will present experimental and numerical investigations on the basic problems of transpiration cooling. Main works include:
(1) The present mathematical models of single-phase and multi-phase flows within porous media which during transpiration cooling process are summarized and analyzed. Firstly, the momentum equation, empirical formulas summarized by experimental data and constitutive relations of single-phase flow within porous media are particularized and compared, and the subject area, physical model and flow condition in which those flow models are applicable are discussed. Then based on the mass, momentum and energy conservation equations of single-phase flow, the interactive multi-phase flow with phase change or chemical reaction are further analyzed. By investigating the mathematical models which describe the performances of fluid flow, heat transfer and phase change within porous media, the deficiencies of the previous models are pointed out, which is helpful for the further improvement of the theoretical model of transpiration cooling.
(2) Based on the traditional model, the momentum equation of fluid within porous media at ambient temperature is modified in this work, so that it can be applicable in the circumstance with high temperature or great temperature gradient. Both the natural and forced convection of fluid within porous matrix, and the variation of fluid properties with temperature and pressure are considered in the modified model, and then transpiration cooling experiment using air as coolant is conducted to validate the model. Theoretical analysis and experimental results indicate that the effect of environmental condition on fluid flow is significant when transpiration cooling system works in high temperature and pressure environment, and varied fluid properties should be used. Finally, an expression of apparent permeability is obtained, which can embody the temperature, pressure and inertia effect caused by high speed flow of fluid, and ensure Darcy's law keeps its concise linear form at the same time.
(3) A series of new conservation equations for mass, momentum and energy are presented in this work, to describe the performances of fluid flow, heat absorption and phase change in porous media. The differences from the previous models include, firstly, considering the compressibility of vapor in the momentum and energy equation; secondly, adding a term of momentum transfer caused by liquid phase change into the momentum equations of vapor and liquid phases in two-phase region; finally, in the energy equation of two-phase region, taking the variations of temperature and pressure into account, eliminating the assumptions that the enthalpy is only dependent on temperature, and saturation temperature is constant. Transpiration cooling experiment using liquid water as coolant is conducted to validate the model. The distributions of temperature, pressure and velocity of one-dimension steady-state problem are analyzed by using the verified model and numerical approach, and the effects of coolant volume and external heat flux are discussed. The numerical simulations show that:the temperature of liquid and vapor phases in two-phase region is not constant, but rises in coolant flow direction; the momentum moving from liquid to vapor caused by phase change has a significant effect on the distributions of pressure and velocity in two-phase region. So the new model and numerical approach developed in this work can provide more accurate description and solutions to the phase change process involved in transpiration cooing using liquid as coolant, and improves the present mathematical models.
(4) The states of fluid flow and heat transfer probably occurring during the phase change procedure are numerically investigated, and the optimized design of transpiration cooling system is discussed. The optimization includes two parts:1) The variation of the thickness and location of two-phase region, capillary pressure and driving force with heat flux and coolant volume are analyzed, and a desired case of transpiration cooling is determined. From the relationships between the external heat flux and coolant mass flow rate, an approach is given to estimate the maximal heat flux afforded and the minimal coolant consumption required by the desired case of transpiration cooling. Thus the pressure and coolant consumption required in a certain thermal circumstance can be determined.2) The effects of thermal protection material, coolant and working environment on the transpiration cooling with liquid phase change are numerically investigated. The optimizations from the choice in coolant, and the thermal protection material and structure such as thermal conductivity, porosity and particle diameter, are discussed with the ultimate targets of high cooling efficiency and low driving force. The estimation of coolant consumption and driving force are important in the practical application of transpiration cooling, and the analysis of thermal protection material and structure can provide valuable experience to the optimized design of cooling system in the future.
本文围绕以上问题展开,以理论分析为基础采用数值模拟和实验验证相结合的方法,对发散冷却基础理论问题进行了研究。主要工作有：
(1)总结和分析了发散冷却过程中所涉及到的多孔介质内单相流和多相流的数学模型。首先详细列举和对比了过去文献中出现的多孔介质单相流的动量方程、实验中获得的各种流动经验公式以及本构关系式,讨论了每个流动模型所适用的学科领域、物理模型以及流动条件。然后在单相流的质量、动量和能量守恒方程的基础上,进一步分析了带有物理相变或化学反应的混溶多相流的数学模型。通过对多孔介质内流体流动、传热和相变过程的数学模型的整理和研究,指出了现有模型的不足,为发散冷却数学模型的修正提供了思路。
(2)在传统模型的基础上,对常温下多孔介质内流体运动方程进行了修正,使其在高温及大温度梯度变化环境中同样具有适用性。在模型的修正中,考虑了多孔骨架内部气体的自然对流和受迫运动,以及流体物性参数随温度和压力的变化,并通过以空气作为冷却剂的发散冷却实验对模型进行了验证。结果表明：对于工作在高温高压环境中的发散冷却系统,环境条件对流动过程的影响不可忽略,要考虑随温度和压力变化的流体物性。最后获得了表观渗透率的表达式,可以在保留Darcy定律的简洁线性形式的前提下,将温度、压力以及高速流动产生的惯性作用通过表观渗透率体现。
(3)从基本物理原理出发建立了描述流体在多孔介质内运动、吸热、相变过程的质量、动量和能量守恒模型。在连续性方程中,考虑流体汽化膨胀后的密度变化,并将可压缩性影响代入动量和能量守恒方程；在动量方程中,增加了液体汽化相变导致的动量迁移项；在能量方程中,考虑混合流体的压力和温度变化。通过使用液态水作为冷却剂的发散冷却实验对模型和数值计算方法进行了验证。并用验证过的模型和方法分析一维稳态情况下的温度、压力和速度分布,讨论冷却剂流量、外界热流密度对液体在微孔里运动、吸热、相变特性的影响。计算结果表明：多孔介质内气液两相共存区的流体温度沿流动方向是增加的,并非恒定不变,且液体汽化相变导致的动量迁移项对流体压力和速度分布有显著影响。因此,本文所得到的具有相变现象的动力学模型和能量方程可以对液体发散冷却过程进行更精确的描述,所提出的数值方法可以进行更精确的求解,使得发散冷却数学模型得到进一步的完善。
(4)对带有液体相变的发散冷却过程中可能出现的流体流动和传热状态进行了数值模拟,就系统优化问题进行了研究,主要包括两部分工作。1)分析了多孔介质平板内两相区厚度和位置、毛细力和驱动力随热流密度和冷却剂流量的变化,并确定了发散冷却的理想工作状态。通过获得的热流密度和冷却剂流量之间的关系曲线,可以估算出发散冷却处于理想工作状态时所能承受的最大外界热流和所需要的最小冷却剂量。由此,可以确定工作在特定热环境中的发散冷却所需的冷却剂流量和驱动力。2)分析了防热材料、冷却剂的选择和工作环境等参数对发散冷却过程的影响,以冷却效率和驱动力大小作为考察发散冷却效果的标准,从多孔材料热导率、孔隙率和粒径以及冷却剂的选择出发,对发散冷却系统提出了优化方案。冷却剂用量和驱动力的研究对发散冷却技术的实际应用非常有意义。另外对热防护材料和结构的分析可以为今后系统优化设计提供有参考价值的借鉴。
Aerospace technology has developed rapidly and influenced human life greatly since twentieth century, and now becomes the key project of all the developed countries for its significant effects on military strategy, national economy and social life. However, the further development of aerospace technology has been limited by existing thermal protection system (TPS), therefore more efficient enhanced cooling technology is the focus of aerospace industry at present. Transpiration cooling, as a potential thermal protection approach, has attracted more and more attention from the researchers due to its excellent cooling efficiency. However there are still many problems in the investigations of experimental methods, theoretical models and numerical approaches, such as more accurate models and boundary conditions to describe the fluid flow, heat and mass transfer and phase change in porous media, the optimal design of transpiration cooling system, the evaluation of coolant consumption under a certain thermal circumstance and so on.
Surrounding the above problems and based on the theoretical analysis, this dissertation will present experimental and numerical investigations on the basic problems of transpiration cooling. Main works include:
(1) The present mathematical models of single-phase and multi-phase flows within porous media which during transpiration cooling process are summarized and analyzed. Firstly, the momentum equation, empirical formulas summarized by experimental data and constitutive relations of single-phase flow within porous media are particularized and compared, and the subject area, physical model and flow condition in which those flow models are applicable are discussed. Then based on the mass, momentum and energy conservation equations of single-phase flow, the interactive multi-phase flow with phase change or chemical reaction are further analyzed. By investigating the mathematical models which describe the performances of fluid flow, heat transfer and phase change within porous media, the deficiencies of the previous models are pointed out, which is helpful for the further improvement of the theoretical model of transpiration cooling.
(2) Based on the traditional model, the momentum equation of fluid within porous media at ambient temperature is modified in this work, so that it can be applicable in the circumstance with high temperature or great temperature gradient. Both the natural and forced convection of fluid within porous matrix, and the variation of fluid properties with temperature and pressure are considered in the modified model, and then transpiration cooling experiment using air as coolant is conducted to validate the model. Theoretical analysis and experimental results indicate that the effect of environmental condition on fluid flow is significant when transpiration cooling system works in high temperature and pressure environment, and varied fluid properties should be used. Finally, an expression of apparent permeability is obtained, which can embody the temperature, pressure and inertia effect caused by high speed flow of fluid, and ensure Darcy's law keeps its concise linear form at the same time.
(3) A series of new conservation equations for mass, momentum and energy are presented in this work, to describe the performances of fluid flow, heat absorption and phase change in porous media. The differences from the previous models include, firstly, considering the compressibility of vapor in the momentum and energy equation; secondly, adding a term of momentum transfer caused by liquid phase change into the momentum equations of vapor and liquid phases in two-phase region; finally, in the energy equation of two-phase region, taking the variations of temperature and pressure into account, eliminating the assumptions that the enthalpy is only dependent on temperature, and saturation temperature is constant. Transpiration cooling experiment using liquid water as coolant is conducted to validate the model. The distributions of temperature, pressure and velocity of one-dimension steady-state problem are analyzed by using the verified model and numerical approach, and the effects of coolant volume and external heat flux are discussed. The numerical simulations show that:the temperature of liquid and vapor phases in two-phase region is not constant, but rises in coolant flow direction; the momentum moving from liquid to vapor caused by phase change has a significant effect on the distributions of pressure and velocity in two-phase region. So the new model and numerical approach developed in this work can provide more accurate description and solutions to the phase change process involved in transpiration cooing using liquid as coolant, and improves the present mathematical models.
(4) The states of fluid flow and heat transfer probably occurring during the phase change procedure are numerically investigated, and the optimized design of transpiration cooling system is discussed. The optimization includes two parts:1) The variation of the thickness and location of two-phase region, capillary pressure and driving force with heat flux and coolant volume are analyzed, and a desired case of transpiration cooling is determined. From the relationships between the external heat flux and coolant mass flow rate, an approach is given to estimate the maximal heat flux afforded and the minimal coolant consumption required by the desired case of transpiration cooling. Thus the pressure and coolant consumption required in a certain thermal circumstance can be determined.2) The effects of thermal protection material, coolant and working environment on the transpiration cooling with liquid phase change are numerically investigated. The optimizations from the choice in coolant, and the thermal protection material and structure such as thermal conductivity, porosity and particle diameter, are discussed with the ultimate targets of high cooling efficiency and low driving force. The estimation of coolant consumption and driving force are important in the practical application of transpiration cooling, and the analysis of thermal protection material and structure can provide valuable experience to the optimized design of cooling system in the future.
引文
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