水下高速航行体非定常空化流场数值计算
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摘要
空化现象是水下高速航行体周围以及高速水轮机械系统中的常见现象。空化现象机理复杂，流体动力环境恶劣，在水轮机械中的空化现象，往往会导致空蚀破坏，而水下高速航行体周围的空化往往又能起到革命性的减阻效果，因而，加强空化现象的机理研究具有广泛的实际意义。
论文参考Rayleigh-Plesset方程，首先针对无限大水域中的单个球形气泡，建立了Rayleigh-W气泡动力学方程。再将Rayleigh-W方程引入到空化相变率中，建立了基于Rayleigh-W方程的空化模型，并对该模型进行了验证和应用。具体研究工作如下：
首先概述了空化流场的基本控制方程，指出了现有空化模型存在的问题，提出了相应的解决办法。其次，在不可压缩流场中，根据单个球形气泡的运动特点，在Rayleigh方程的基础上，重新构建了气泡动力学模型——Rayleigh-W模型。再以理想气体为例，分析了气泡变形过程中，气泡界面上空化相变进行的方向，并将之引入到Rayleigh-W模型中，得到了考虑相变作用的气泡动力学方程。
以Rayleigh-W方程的推导过程为基础，进一步研究了单个球形气泡的扩张过程和收缩过程，估算了气泡内外压差以及泡壁运动速度。通过假设泡内气体经历多方热力学过程，进一步研究了气泡的溃灭频率。通过对Rayleigh-W方程的变分分析，研究了气泡溃灭过程中的泡壁速度与气泡直径之间的关系，同时研究了常温下气泡收缩可达到的极限半径。
根据两相流体的连续性方程，推导并证明了球形气泡变形过程中的空化相变率，并将之推广到任意气泡形态。
结合Rayleigh-W方程、空化相变率以及气泡变形过程中相变的进行方向，建立了基于简化的Rayleigh-W方程的空化模型。以水洞实验结果和文献资料为基准，完成了该空化模型的正确性和有效性验证(V&V验证)。
应用基于Rayleigh-W方程的空化模型，对半球头圆柱体模型的空化流场进行了数值模拟研究。在研究过程中，首先采用枚举的方法，分别对空化模型中的模型系数进行了数值确定，然后分析了半球头圆柱体模型在水下高速航行时，流场内的流体动力布局及相关参数随时间的变化规律，同时分析了由空化模型系数引起的阻力系数的计算误差。
在半球头圆柱体模型的空化流场中，研究了空化模型系数与主空泡形态之间的关系，总结了空化流场中出现的空泡类型及其随空化数变化的规律。分别得到了局部空化流场和弱空化流场中的空化模型系数与空化数之间的关系。
最后，利用空化模型中的模型系数与空化流场主空泡形态之间的关系的推论，间接分析了超空化水下射弹流场中的模型阻力系数和主空泡形态。
论文研究了气泡动力学模型和数值空化模型，实现了空化流场中的非定常细节捕捉，为深入研究气泡运动机理和空化机理，提供了理论基础和依据。
Cavitation often occurs around the high-speed submerged body and in thehigh-speed turbine system and other high-speed motion under water. Cavitation mayoften cause cavitation damage in the turbine system however may show therevolutionary drag reduction effect during the motions of the underwater vehicleenveloped in a supercavity. To strengthen the research of the cavitation mechanismhas a wide range of practical significance. The research began with the analysis ofthe bubble dynamics, the theoretical correction was implemented onRayleigh-Plesset equation and the Rayleigh-W equation was acquired. Then thesimplified Rayleigh-W equation was introduced to establish the cavitation modelwith cavitation mass rate just similar to the process of the derivation of the FullCavitation Model. The main research works are as follows.
The paper first provides an overview of the basic control equations ofcavitation flow, and then points out the defects of the existing cavitation models.Secondly, based on the Rayleigh-W equation, a new bubble dynamics model wasestablished taking into acount the deformation characteristics of the single sphericalbubble in the incompressible flow. Taking ideal gas as an example, the changedirection of the cavitation phase-change during the bubble deformation was studiedand then the result was introduced into the Rayleigh-W model to rebuild the bubbledynamics model.
Based on the derivative of the Rayleigh-W equation, the expansion andcontraction of a single bubble were studied, and then the pressure difference insideand outside of a bubble and the velocity of the bubble wall were estimated. Throughthe assumption that the gas inside a cavitation bubble experienced polytrophicprocess, the bubble collapse frequency was further studied. Through the variationalanalysis of the Rayleigh-W equation, the relationship between the bubble wallvelocity and the bubble diameter during the bubble collapse was studied, and theachievable contraction limit radius during the bubble collapse was also studied atnormal temperature.
Based on the two-phase fluid continuity equation, the cavitation phase-changerate during the deformation of the spherical bubble was derived and then proved,and then the conclusions of which were generalized to an arbitrary cavity shape.
Combined the Rayleigh-W equation, the cavitation phase change rate and phasechange direction during the bubble deformation process, a new cavitation modelbased on the simplified Rayleigh-W equations was established for the numerical study of cavitation flow. Taking the water tunnel experiment and literature data forreference, the validation and verification (V&V) were carried out on the newlycreated cavitation model.
Numerical simulations were carried on the cavitation flow generated from theunderwater high-speed hemispherical head cylinder model using the new createdcavitation model. During the study, the calculations to verify the model coefficientswere firstly numerically carried out using enumeration method, and then thehydrokinetic layout and the variations of related parameters over time of thehemispherical head cylinder high-speed sailing underwater were analyzed. Thecalculation errors of the drag coefficients caused by the improper model coefficientswere studied. The relationship between the model coefficients and the cavity shapewas analyzed. The types of the cavities in the cavitation flow field and therelationship with the cavitation number has been summed up. The relationshipsbetween the cavitation number and the cavitation model coefficients in some typesof cavitation flow fields have been acquired.
Indirect analysis was carried out to the relationship between the main cavityshape and the model drag coefficients in the supercavitation flow field using therelationship between the cavitation model coefficients and the shape of the maincavity.
The thesis has studied the bubble dynamics model and numerical cavitationmodel, successfully capture the main unsteady details of the cavitation flow,provides a theoretical basis and foundation for the study of cavitation mechanismin-depth.
论文参考Rayleigh-Plesset方程，首先针对无限大水域中的单个球形气泡，建立了Rayleigh-W气泡动力学方程。再将Rayleigh-W方程引入到空化相变率中，建立了基于Rayleigh-W方程的空化模型，并对该模型进行了验证和应用。具体研究工作如下：
首先概述了空化流场的基本控制方程，指出了现有空化模型存在的问题，提出了相应的解决办法。其次，在不可压缩流场中，根据单个球形气泡的运动特点，在Rayleigh方程的基础上，重新构建了气泡动力学模型——Rayleigh-W模型。再以理想气体为例，分析了气泡变形过程中，气泡界面上空化相变进行的方向，并将之引入到Rayleigh-W模型中，得到了考虑相变作用的气泡动力学方程。
以Rayleigh-W方程的推导过程为基础，进一步研究了单个球形气泡的扩张过程和收缩过程，估算了气泡内外压差以及泡壁运动速度。通过假设泡内气体经历多方热力学过程，进一步研究了气泡的溃灭频率。通过对Rayleigh-W方程的变分分析，研究了气泡溃灭过程中的泡壁速度与气泡直径之间的关系，同时研究了常温下气泡收缩可达到的极限半径。
根据两相流体的连续性方程，推导并证明了球形气泡变形过程中的空化相变率，并将之推广到任意气泡形态。
结合Rayleigh-W方程、空化相变率以及气泡变形过程中相变的进行方向，建立了基于简化的Rayleigh-W方程的空化模型。以水洞实验结果和文献资料为基准，完成了该空化模型的正确性和有效性验证(V&V验证)。
应用基于Rayleigh-W方程的空化模型，对半球头圆柱体模型的空化流场进行了数值模拟研究。在研究过程中，首先采用枚举的方法，分别对空化模型中的模型系数进行了数值确定，然后分析了半球头圆柱体模型在水下高速航行时，流场内的流体动力布局及相关参数随时间的变化规律，同时分析了由空化模型系数引起的阻力系数的计算误差。
在半球头圆柱体模型的空化流场中，研究了空化模型系数与主空泡形态之间的关系，总结了空化流场中出现的空泡类型及其随空化数变化的规律。分别得到了局部空化流场和弱空化流场中的空化模型系数与空化数之间的关系。
最后，利用空化模型中的模型系数与空化流场主空泡形态之间的关系的推论，间接分析了超空化水下射弹流场中的模型阻力系数和主空泡形态。
论文研究了气泡动力学模型和数值空化模型，实现了空化流场中的非定常细节捕捉，为深入研究气泡运动机理和空化机理，提供了理论基础和依据。
Cavitation often occurs around the high-speed submerged body and in thehigh-speed turbine system and other high-speed motion under water. Cavitation mayoften cause cavitation damage in the turbine system however may show therevolutionary drag reduction effect during the motions of the underwater vehicleenveloped in a supercavity. To strengthen the research of the cavitation mechanismhas a wide range of practical significance. The research began with the analysis ofthe bubble dynamics, the theoretical correction was implemented onRayleigh-Plesset equation and the Rayleigh-W equation was acquired. Then thesimplified Rayleigh-W equation was introduced to establish the cavitation modelwith cavitation mass rate just similar to the process of the derivation of the FullCavitation Model. The main research works are as follows.
The paper first provides an overview of the basic control equations ofcavitation flow, and then points out the defects of the existing cavitation models.Secondly, based on the Rayleigh-W equation, a new bubble dynamics model wasestablished taking into acount the deformation characteristics of the single sphericalbubble in the incompressible flow. Taking ideal gas as an example, the changedirection of the cavitation phase-change during the bubble deformation was studiedand then the result was introduced into the Rayleigh-W model to rebuild the bubbledynamics model.
Based on the derivative of the Rayleigh-W equation, the expansion andcontraction of a single bubble were studied, and then the pressure difference insideand outside of a bubble and the velocity of the bubble wall were estimated. Throughthe assumption that the gas inside a cavitation bubble experienced polytrophicprocess, the bubble collapse frequency was further studied. Through the variationalanalysis of the Rayleigh-W equation, the relationship between the bubble wallvelocity and the bubble diameter during the bubble collapse was studied, and theachievable contraction limit radius during the bubble collapse was also studied atnormal temperature.
Based on the two-phase fluid continuity equation, the cavitation phase-changerate during the deformation of the spherical bubble was derived and then proved,and then the conclusions of which were generalized to an arbitrary cavity shape.
Combined the Rayleigh-W equation, the cavitation phase change rate and phasechange direction during the bubble deformation process, a new cavitation modelbased on the simplified Rayleigh-W equations was established for the numerical study of cavitation flow. Taking the water tunnel experiment and literature data forreference, the validation and verification (V&V) were carried out on the newlycreated cavitation model.
Numerical simulations were carried on the cavitation flow generated from theunderwater high-speed hemispherical head cylinder model using the new createdcavitation model. During the study, the calculations to verify the model coefficientswere firstly numerically carried out using enumeration method, and then thehydrokinetic layout and the variations of related parameters over time of thehemispherical head cylinder high-speed sailing underwater were analyzed. Thecalculation errors of the drag coefficients caused by the improper model coefficientswere studied. The relationship between the model coefficients and the cavity shapewas analyzed. The types of the cavities in the cavitation flow field and therelationship with the cavitation number has been summed up. The relationshipsbetween the cavitation number and the cavitation model coefficients in some typesof cavitation flow fields have been acquired.
Indirect analysis was carried out to the relationship between the main cavityshape and the model drag coefficients in the supercavitation flow field using therelationship between the cavitation model coefficients and the shape of the maincavity.
The thesis has studied the bubble dynamics model and numerical cavitationmodel, successfully capture the main unsteady details of the cavitation flow,provides a theoretical basis and foundation for the study of cavitation mechanismin-depth.
引文
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