自然空泡流数值模拟方法研究
|
摘要
自然空化是指一定条件下液体介质内部出现蒸汽泡或蒸汽穴的现象。通常高速流动是自然空化发生的原因,它导致液体介质中局部压力低于液体的饱和蒸汽压,液体汽化而形成空泡。
空化对于水利设备的剥蚀、噪声和高速运动物体的水动力特性及其稳定性控制具有极为重要的影响。随着各类水面和水下运载工具航速的大幅度提高,空化的发生不可避免。空泡流动特性及其机理研究仍是目前水动力学研究的前沿课题之一。发展合理的空泡流模型和适用于复杂三维非定常空泡流的数值计算方法,不仅具有重要的理论意义,而且有着广泛的工程应用价值。
本文旨在探索更加合理的自然空泡流模型,发展高效、高精度的数值计算方法,研制具有自主知识产权的三维多相非定常自然空泡流的计算软件,并用于工程实际空泡流动问题的分析。
本文的主要研究内容和创新性成果如下:
1、在自然空泡复杂流场的多相流数学模型方面进行了系统而深入的研究。引入了五种基于正压关系、基于相分数输运方程形式的均质平衡流空化模型,并将五种线性与非线性的涡粘湍流模式与各空化模型相结合,发展了基于求解三维RANS方程系统的自然空泡湍流流动的数值模拟方法。在模型形式和算法实现上进行了改进,成功地模拟了空化数小于0.01条件下以及复杂非定常的自然空泡流问题。本文还提出了一种考虑来流介质可压缩性的高速空泡流模型,模拟了高亚声速来流条件下的自然空泡流问题。
2、在适合于空泡流计算的数值算法方面开展了有特点的工作。针对空泡流问题的特殊性,在以无空泡单相流场作为初始条件进行空泡流计算之前,重置低于饱和蒸汽压区域的压力,并在计算中对压力范围进行限制,以保证得到合理的泡内压力分布。在压力-速度-密度耦合修正方法中,本文采用人工抑制混合介质的压缩性的方法,使得计算中空化区域内被重置的压力快速扩散,空化模型持续保持足够大的相变势,从而能够较快地生成合理的空泡形态。根据计算节点的相分数来设定节点上的可压缩性参数,进而对不可压缩的来流环境和可压缩的空泡区域采用不同的修正量,从而最终得到合理的流场分布。本文还研究了采用TVD的高阶对流格式捕捉空泡面的方法。
3、自行开发了适用于三维非定常自然空泡流的数值模拟软件。该软件采用有限体积法开发,适用于分块结构化网格划分的任意复杂计算域。软件采用基于压力-速度-密度耦合修正算法的分离隐式求解器,求解的方程系统包括:RANS方程、压力修正量方程、能量方程、湍流模式方程、空化模型方程等。空泡流计算部分采用了本文改进和提出的空泡流模型,并结合了十余种线性、二阶、三阶的两方程湍流模式。方程对流项的离散格式采用带延迟修正的一至二阶迎风格式和多种带TVD限制器的高阶对流格式。通过验证表明该软件适用于较广的空化数和雷诺数范围的复杂自然空泡湍流流动。
4、针对存在经典解析解和可靠试验结果的典型问题进行了计算比对,验证了本文数值模拟方法对自然空泡预报的准确性和对工况的广泛适用性。对网格密度、差分格式、模型参数、雷诺数影响等数值计算的基本问题进行了分析,考察了其对计算结果的影响。在较广的空化数范围内,本文计算均得到了稳定光滑的空泡形态,且空泡形状、空泡尺度、压力分布、阻力系数等与解析解和试验数据吻合良好。
基于所提出的可压缩高速空泡流模型,模拟了高亚声速来流条件下的自然空泡流问题。印证了亚声速可压缩势流理论关于空化数固定时空泡长度和阻力系数随马赫数增加而增大的结论,说明了高速条件下考虑来流压缩性影响的必要性。
系统地比较和评价了不同空化模型和湍流模式的组合在计算稳定性、网格依赖性、空泡形态、空泡尺度、泡内流动结构、水动力特性等多方面的差别和优劣,为进一步的空泡流数值模拟工作提供了有价值的参考。
5、运用本文所建立的数值模拟方法,研究了文丘里管内空泡流、绕水翼空泡流与大攻角运行航行体空泡流等工程实际中的自然空泡流动现象与机理。
对于文丘里管内空泡流,在不同的收缩-扩张角下分别计算得到了定常空泡形态和非稳态空泡演化过程。空泡在非稳态演化中呈现周期性的发展、断裂、脱落、下泻与溃灭,与实验现象相符。空泡长度、脱落频率、泡内速度及相分数分布与试验结果接近。入口压力系数的振荡频率与空泡脱落频率一致,表明空泡运动对流场结构产生规律性的影响。
对于绕水翼的非定常空泡流,计算得到的空泡脱落与试验观察到的大块云雾状空泡发展过程一致,空泡脱落频率与升阻系数的振荡频率一致,Strouhal数与理论和试验结果相当接近。分析了空泡非稳态流动结构、特征及其机理,发现空泡周期性脱落现象与回射流发展、流场逆压梯度及涡结构演化之间存在紧密的联系。比较了湍流和层流条件下的计算结果,发现两者在空泡脱落点、脱落方式、副体紊乱度等方面存在较大的差别。
模拟了大攻角运行航行体的自然空泡流,得到的三维空泡形状和压力分布的计算结果与试验数据相符。研究了大攻角下在航行体周向上的空泡形态分布特征,给出了多种空泡尺度与空化数、攻角之间的关系,以及升阻系数与空化数和攻角的关系。通过定量分析发现,空泡的不对称性会导致航行体某些部位受力集中,表明高速带空泡运动的航行体在大攻角运动中其结构将受到巨大的水动力载荷。
Natural cavitation is a kind of phenomenon that vapor bubble or vapor cavity appears in liquid phase at some specific conditions. The general hydrodynamic mechanism of natural cavitation is high-speed flow, where local pressure in liquid falls down under the saturating vapor pressure of liquid, thus the liquid vaporizes to form cavity.
Cavitation has extremely important influence on erosion and noise of hydraulic instruments, hydrodynamic characteristics and stability control of high-speed body. With the great raise of navigating velocity of water-surface or under-water vehicles, cavitation phenomenon becomes unavoidable to appear.
Researches on the property and mechanism of cavitating flow are still one of the leading fields in current studies of hydrodynamics. Therefore, it’s not only of great theoretical significance but also of wide application values on engineering and national defence to develop reasonable cavitation models and numerical methods adaptable for three-dimensional unsteady cavitating flows.
This dissertation is aimed at exploring more sound cavitation models, developing efficient and accurate numerical methods, and creating computer software with independent intellectual property rights, for the simulation of three-dimensional multi-phase unsteady natural cavitating flows, and utilizing them to analyze actual engineering cavitation problems.
The primary researching contents and innovations are as follows:
1. The mathematical model of multi-phase flow for simulating complex natural cavitating flows was researched systematically and profoundly. Five types of Homogenous Equilibrium cavitation Models (HEM) based on barotropic relation or transportation equation of phase fraction were introduced, combining with five kinds of linear or nonlinear eddy viscosity turbulence models, to develop the simulation method for turbulent natural cavitating flows based on solving three-dimensional RANS equations system. By improving these models’form and arithmetic achievement, the flows of cavitation number smaller than 0.01 and complicated unsteady cavitating flows were successfully simulated. A new high-speed cavitation model taking into account the compressibility of incoming flow was also proposed, to simulate high-subsonic cavitating flows.
2. Unique works about the numerical methods suitable for the computation of cavitating flows were carried out. Because of the speciality in the solving of cavitation problems, non-cavitating single phase flow field was used as the initial condition for cavitating flow computation. The pressure below the saturated vapor pressure was reset before computation starts, then the pressure range inside the whole flow field was limited during computation. In the pressure-velocity-density coupling correction method, the compressibility of mixture was artificially restrained to make the reset pressure to diffuse rapidly after computation begins, which guarantees the cavitation model to continuously keep phase transformation potential, so as to grow up reasonable cavity shape. A compressibility parameter emplaced on computational nodes was set according to local phase fraction, to choose different pressure correction modes for the incompressible incoming flow and compressible cavitating region respectively. The cavity interface capturing method by TVD limited High-Order-Convection scheme was studied.
3. A computer code for the numerical simulation of three dimensional natural cavitating flows was developed. This code was developed using Finite-Volume-Method, and is applicable for arbitrarily complicated computational domain divided into multi-block structured grid. A segregated implicit solver based on the pressure-velocity-density coupling correction method was adopted. The equation system includes RANS equation, pressure correction equation, energy equation, turbulence model equations, and phase fraction equation, etc. The cavitation models improved or proposed in this dissertation, combining with over ten kinds of linear or nonlinear turbulence models, were utilized in the software. One-order to two-order upwind scheme with deferred correction and some types of TVD High-Order-Convection schemes were adopted in the convection terms of controlling equations. This software was verified to be applicable to wide ranges of cavitation number and Reynolds number.
4. Calculations and comparisons were carried out for some classic problems which have classical analytic solution or reliable experimental results, to verify the accuracy of the present numerical simulation method in forecasting natural cavitation and the wide applicability for working conditions. Some basic factors for the computation, such as mesh density, convection scheme, model parameter, and Reynolds number’s influence were analyzed, and their effects on computational results were investigated. Stable and smooth cavity profiles were obtained in wide range of cavitation number. The cavity shape, cavity dimensions, pressure distribution and drag-force coefficient agree well with analytic solutions and experimental data.
The compressible subsonic high-speed cavitating flows were simulated based on the model proposed in this dissertation. The present results proved the conclusion derived in the subsonic compressible theory of potential flow that, cavity length and drag-force increase along with the increment of Mach number at fixing cavitation number. This indicates the need to account for the compressibility effect in high-speed flows.
The combinations of cavitation models and turbulence models were compared and reviewed in the aspects of computational stability, grid reliability, cavity profile, cavity size, flow structure inside cavity, hydrodynamic characteristics, etc., to provide valuable references for further numerical simulation works.
5. The phenomenon and mechanism of natural cavitating flows in realistic engineering application, including the cavitating flows in venturi tubes, around hydrofoils, and over an underwater vehicle with large angle of attack, were studied by using the numerical methods established in the dissertation. For the cavitating flows inside the venture tubes at different convergence-divergence degrees, steady cavity shape and unsteady cavity evolution were obtained respectively. The cavity presents periodic growth, breaking, shedding, cascading and collapse during the process, which accords with experimental phenomena. Cavity length, shedding frequency, velocity distribution and phase fraction distribution inside cavity are close to experimental ones. The fluctuation frequency of incoming pressure corresponds with that of cavity shedding, which means the influence of cavity motion on the structure of flow field.
As to the unsteady cavitating flows around hydrofoils, the cavity shedding phenomenon simulated accords with the large cloud cavities observed experimentally, and the shedding frequency was in accordance with the oscillation frequency of lift and drag, and the Strouhal numbers agree well with theoretical and experimental ones. The structure, characters and mechanism of the unstable cavitating flow were analyzed in detail finding that, there are close relations between the periodic cavity shedding process and the development of reentrant jet flow, the adverse pressure near cavity closure, and the vortex structure evolution. The unsteady cavitating flows in turbulent condition and laminar condition were simulated and compared, and obvious distinctions exist in the two cases at the aspects of cavity break position, shedding pattern and flow confusion level.
For the cavitating flows over underwater vehicle with large angle of attack, three-dimensional cavity profiles and pressure distributions calculated are consistent with experiment ones. The cavity shape distribution on the body surface was studied. The dependences of some cavity dimensions on cavitation number and angle of attack were investigated, and also the variation relations of lift and drag coefficients in reference to cavitation number and angle of attack were computed. Quantitative analysis shows that the asymmetry of cavity will cause the nonuniform stress along body, and result in the great hydrodynamic load of vehicle navigating at large angle of attack.
空化对于水利设备的剥蚀、噪声和高速运动物体的水动力特性及其稳定性控制具有极为重要的影响。随着各类水面和水下运载工具航速的大幅度提高,空化的发生不可避免。空泡流动特性及其机理研究仍是目前水动力学研究的前沿课题之一。发展合理的空泡流模型和适用于复杂三维非定常空泡流的数值计算方法,不仅具有重要的理论意义,而且有着广泛的工程应用价值。
本文旨在探索更加合理的自然空泡流模型,发展高效、高精度的数值计算方法,研制具有自主知识产权的三维多相非定常自然空泡流的计算软件,并用于工程实际空泡流动问题的分析。
本文的主要研究内容和创新性成果如下:
1、在自然空泡复杂流场的多相流数学模型方面进行了系统而深入的研究。引入了五种基于正压关系、基于相分数输运方程形式的均质平衡流空化模型,并将五种线性与非线性的涡粘湍流模式与各空化模型相结合,发展了基于求解三维RANS方程系统的自然空泡湍流流动的数值模拟方法。在模型形式和算法实现上进行了改进,成功地模拟了空化数小于0.01条件下以及复杂非定常的自然空泡流问题。本文还提出了一种考虑来流介质可压缩性的高速空泡流模型,模拟了高亚声速来流条件下的自然空泡流问题。
2、在适合于空泡流计算的数值算法方面开展了有特点的工作。针对空泡流问题的特殊性,在以无空泡单相流场作为初始条件进行空泡流计算之前,重置低于饱和蒸汽压区域的压力,并在计算中对压力范围进行限制,以保证得到合理的泡内压力分布。在压力-速度-密度耦合修正方法中,本文采用人工抑制混合介质的压缩性的方法,使得计算中空化区域内被重置的压力快速扩散,空化模型持续保持足够大的相变势,从而能够较快地生成合理的空泡形态。根据计算节点的相分数来设定节点上的可压缩性参数,进而对不可压缩的来流环境和可压缩的空泡区域采用不同的修正量,从而最终得到合理的流场分布。本文还研究了采用TVD的高阶对流格式捕捉空泡面的方法。
3、自行开发了适用于三维非定常自然空泡流的数值模拟软件。该软件采用有限体积法开发,适用于分块结构化网格划分的任意复杂计算域。软件采用基于压力-速度-密度耦合修正算法的分离隐式求解器,求解的方程系统包括:RANS方程、压力修正量方程、能量方程、湍流模式方程、空化模型方程等。空泡流计算部分采用了本文改进和提出的空泡流模型,并结合了十余种线性、二阶、三阶的两方程湍流模式。方程对流项的离散格式采用带延迟修正的一至二阶迎风格式和多种带TVD限制器的高阶对流格式。通过验证表明该软件适用于较广的空化数和雷诺数范围的复杂自然空泡湍流流动。
4、针对存在经典解析解和可靠试验结果的典型问题进行了计算比对,验证了本文数值模拟方法对自然空泡预报的准确性和对工况的广泛适用性。对网格密度、差分格式、模型参数、雷诺数影响等数值计算的基本问题进行了分析,考察了其对计算结果的影响。在较广的空化数范围内,本文计算均得到了稳定光滑的空泡形态,且空泡形状、空泡尺度、压力分布、阻力系数等与解析解和试验数据吻合良好。
基于所提出的可压缩高速空泡流模型,模拟了高亚声速来流条件下的自然空泡流问题。印证了亚声速可压缩势流理论关于空化数固定时空泡长度和阻力系数随马赫数增加而增大的结论,说明了高速条件下考虑来流压缩性影响的必要性。
系统地比较和评价了不同空化模型和湍流模式的组合在计算稳定性、网格依赖性、空泡形态、空泡尺度、泡内流动结构、水动力特性等多方面的差别和优劣,为进一步的空泡流数值模拟工作提供了有价值的参考。
5、运用本文所建立的数值模拟方法,研究了文丘里管内空泡流、绕水翼空泡流与大攻角运行航行体空泡流等工程实际中的自然空泡流动现象与机理。
对于文丘里管内空泡流,在不同的收缩-扩张角下分别计算得到了定常空泡形态和非稳态空泡演化过程。空泡在非稳态演化中呈现周期性的发展、断裂、脱落、下泻与溃灭,与实验现象相符。空泡长度、脱落频率、泡内速度及相分数分布与试验结果接近。入口压力系数的振荡频率与空泡脱落频率一致,表明空泡运动对流场结构产生规律性的影响。
对于绕水翼的非定常空泡流,计算得到的空泡脱落与试验观察到的大块云雾状空泡发展过程一致,空泡脱落频率与升阻系数的振荡频率一致,Strouhal数与理论和试验结果相当接近。分析了空泡非稳态流动结构、特征及其机理,发现空泡周期性脱落现象与回射流发展、流场逆压梯度及涡结构演化之间存在紧密的联系。比较了湍流和层流条件下的计算结果,发现两者在空泡脱落点、脱落方式、副体紊乱度等方面存在较大的差别。
模拟了大攻角运行航行体的自然空泡流,得到的三维空泡形状和压力分布的计算结果与试验数据相符。研究了大攻角下在航行体周向上的空泡形态分布特征,给出了多种空泡尺度与空化数、攻角之间的关系,以及升阻系数与空化数和攻角的关系。通过定量分析发现,空泡的不对称性会导致航行体某些部位受力集中,表明高速带空泡运动的航行体在大攻角运动中其结构将受到巨大的水动力载荷。
Natural cavitation is a kind of phenomenon that vapor bubble or vapor cavity appears in liquid phase at some specific conditions. The general hydrodynamic mechanism of natural cavitation is high-speed flow, where local pressure in liquid falls down under the saturating vapor pressure of liquid, thus the liquid vaporizes to form cavity.
Cavitation has extremely important influence on erosion and noise of hydraulic instruments, hydrodynamic characteristics and stability control of high-speed body. With the great raise of navigating velocity of water-surface or under-water vehicles, cavitation phenomenon becomes unavoidable to appear.
Researches on the property and mechanism of cavitating flow are still one of the leading fields in current studies of hydrodynamics. Therefore, it’s not only of great theoretical significance but also of wide application values on engineering and national defence to develop reasonable cavitation models and numerical methods adaptable for three-dimensional unsteady cavitating flows.
This dissertation is aimed at exploring more sound cavitation models, developing efficient and accurate numerical methods, and creating computer software with independent intellectual property rights, for the simulation of three-dimensional multi-phase unsteady natural cavitating flows, and utilizing them to analyze actual engineering cavitation problems.
The primary researching contents and innovations are as follows:
1. The mathematical model of multi-phase flow for simulating complex natural cavitating flows was researched systematically and profoundly. Five types of Homogenous Equilibrium cavitation Models (HEM) based on barotropic relation or transportation equation of phase fraction were introduced, combining with five kinds of linear or nonlinear eddy viscosity turbulence models, to develop the simulation method for turbulent natural cavitating flows based on solving three-dimensional RANS equations system. By improving these models’form and arithmetic achievement, the flows of cavitation number smaller than 0.01 and complicated unsteady cavitating flows were successfully simulated. A new high-speed cavitation model taking into account the compressibility of incoming flow was also proposed, to simulate high-subsonic cavitating flows.
2. Unique works about the numerical methods suitable for the computation of cavitating flows were carried out. Because of the speciality in the solving of cavitation problems, non-cavitating single phase flow field was used as the initial condition for cavitating flow computation. The pressure below the saturated vapor pressure was reset before computation starts, then the pressure range inside the whole flow field was limited during computation. In the pressure-velocity-density coupling correction method, the compressibility of mixture was artificially restrained to make the reset pressure to diffuse rapidly after computation begins, which guarantees the cavitation model to continuously keep phase transformation potential, so as to grow up reasonable cavity shape. A compressibility parameter emplaced on computational nodes was set according to local phase fraction, to choose different pressure correction modes for the incompressible incoming flow and compressible cavitating region respectively. The cavity interface capturing method by TVD limited High-Order-Convection scheme was studied.
3. A computer code for the numerical simulation of three dimensional natural cavitating flows was developed. This code was developed using Finite-Volume-Method, and is applicable for arbitrarily complicated computational domain divided into multi-block structured grid. A segregated implicit solver based on the pressure-velocity-density coupling correction method was adopted. The equation system includes RANS equation, pressure correction equation, energy equation, turbulence model equations, and phase fraction equation, etc. The cavitation models improved or proposed in this dissertation, combining with over ten kinds of linear or nonlinear turbulence models, were utilized in the software. One-order to two-order upwind scheme with deferred correction and some types of TVD High-Order-Convection schemes were adopted in the convection terms of controlling equations. This software was verified to be applicable to wide ranges of cavitation number and Reynolds number.
4. Calculations and comparisons were carried out for some classic problems which have classical analytic solution or reliable experimental results, to verify the accuracy of the present numerical simulation method in forecasting natural cavitation and the wide applicability for working conditions. Some basic factors for the computation, such as mesh density, convection scheme, model parameter, and Reynolds number’s influence were analyzed, and their effects on computational results were investigated. Stable and smooth cavity profiles were obtained in wide range of cavitation number. The cavity shape, cavity dimensions, pressure distribution and drag-force coefficient agree well with analytic solutions and experimental data.
The compressible subsonic high-speed cavitating flows were simulated based on the model proposed in this dissertation. The present results proved the conclusion derived in the subsonic compressible theory of potential flow that, cavity length and drag-force increase along with the increment of Mach number at fixing cavitation number. This indicates the need to account for the compressibility effect in high-speed flows.
The combinations of cavitation models and turbulence models were compared and reviewed in the aspects of computational stability, grid reliability, cavity profile, cavity size, flow structure inside cavity, hydrodynamic characteristics, etc., to provide valuable references for further numerical simulation works.
5. The phenomenon and mechanism of natural cavitating flows in realistic engineering application, including the cavitating flows in venturi tubes, around hydrofoils, and over an underwater vehicle with large angle of attack, were studied by using the numerical methods established in the dissertation. For the cavitating flows inside the venture tubes at different convergence-divergence degrees, steady cavity shape and unsteady cavity evolution were obtained respectively. The cavity presents periodic growth, breaking, shedding, cascading and collapse during the process, which accords with experimental phenomena. Cavity length, shedding frequency, velocity distribution and phase fraction distribution inside cavity are close to experimental ones. The fluctuation frequency of incoming pressure corresponds with that of cavity shedding, which means the influence of cavity motion on the structure of flow field.
As to the unsteady cavitating flows around hydrofoils, the cavity shedding phenomenon simulated accords with the large cloud cavities observed experimentally, and the shedding frequency was in accordance with the oscillation frequency of lift and drag, and the Strouhal numbers agree well with theoretical and experimental ones. The structure, characters and mechanism of the unstable cavitating flow were analyzed in detail finding that, there are close relations between the periodic cavity shedding process and the development of reentrant jet flow, the adverse pressure near cavity closure, and the vortex structure evolution. The unsteady cavitating flows in turbulent condition and laminar condition were simulated and compared, and obvious distinctions exist in the two cases at the aspects of cavity break position, shedding pattern and flow confusion level.
For the cavitating flows over underwater vehicle with large angle of attack, three-dimensional cavity profiles and pressure distributions calculated are consistent with experiment ones. The cavity shape distribution on the body surface was studied. The dependences of some cavity dimensions on cavitation number and angle of attack were investigated, and also the variation relations of lift and drag coefficients in reference to cavitation number and angle of attack were computed. Quantitative analysis shows that the asymmetry of cavity will cause the nonuniform stress along body, and result in the great hydrodynamic load of vehicle navigating at large angle of attack.
引文
[1] Michel J. M.,“Fundamentals of cavitation”, Wuxi, P. R. of China, 1995.
[2] Yin L. Y.,“Numerical modeling of supercavitating and surface-piercing propellers”, [Dissertation], The University of Texas, 2002.
[3]柯乃普R. T.,戴利J. W.,哈密脱F. G.,“空化与空蚀”,水利出版社,水利水电科学研究院译, 1981.
[4]黄继汤,“空化与空蚀的原理及应用”,清华大学出版社, 1991.
[5] Akihisa K., Hajime Y., Hiroharu K., et al.,“On the collapsing behavior of cavitation bubble clusters”, Fourth International Symposium on Cavitation, California, USA, June, 2001.
[6] Stinebring D. R., Michael L. B., Jules W., et al.,“Developed cavitation-cavity dynamics”, RTO/AVT lecture series on“Supercavitating flows”, RTO-EN-10, No. 5, Brussels, Belgium, 2001.
[7] Levi-Civita T.,“Scie e leggi di resistenzia”, Rend. Circ. Mat. Palermo, 1907, Vol. 18, pp. 1-37.
[8] Villat H.,“Sur la validatédes solutions de certains problèmes d’hydrodynamique”, J. Math., Pures Appl., 1914, Vol. 10, pp. 231-290.
[9] Riabouchinsky D.,“On steady flow motions with free surfaces”, Proc. London Math. Soc., 1920, Vol. 19, pp. 206-215.
[10] Kreisel G.,“Cavitation with finite cavitation numbers”, Admirally Res. Lab. Rep., R1/H36, 1946.
[11] Joukowshy N. E.,“I. A modification of Kirchhoff’s method of determining a two-dimensional motion of a fluid given a constant velocity along an unknown streamline, II. Determination of the motion of a fluid for any condition given on a streamline”, Mat. Sbornik ( Rec. Math.), 1890, Vol. 15, pp. 121-278.
[12] Wu T. Y.,“A wake model for free streamline theory, part 1: Fully and partially developed wake flows and cavity flows past an oblique flat plate”, J. Fluid Mech. 1962, Vol. 13, pp. 161-181.
[13] Apelt D. J.,“Some studies of fluid flow at low Reynolds numbers”, [Thesis], Oxford Univ., 1957.
[14] Tulin M. P.,“Supercavitating flows-small perturbation theory”, J. Ship Res., 1964, Vol. 7, No. 3, pp. 16-37.
[15] Brennen C. E.,“Cavitation and bubble dynamics”, Oxford, New York, 1995.
[16]汤福坤,何友声,“空泡流理论”,上海交通大学, 1986.
[17] Acosta A. J.,“A note on partial cavitation of flat plate hydrofoils”, Calif. Inst. of Tech. Hydro. Lab. Rep., 1955, E-19.9
[18] Acosta A. J.,“Cavitating flow past a cascade of circular arc hydrofoils”. Calif. Inst. of Tech. Hydro. Lab. Rep., 1960, E-79.2
[19] Wu Y. T.,“A free streamline theory for two-dimensional fully cavitated hydrofoil”, J. Math. Phys., 1956, Vol. 35, pp. 236-265.
[20] Wu Y. T.,“A wake model for free streamline theory, part 1: Fully and partially developed wake flows and cavity flows past an oblique flat plate”, J. Fluid Mech. 1962, Vol. 13, pp. 161-181.
[21] Cohen H., Sutherland C. D., Tu Y. O.,“Wall effects in cavitating hydrofoil flow”, J. Ship Res. 1957, Vol. 1, No. 3, pp. 31-39.
[22] Geurst J. A.,“Linearized theory for partially cavitated hydrofoils”, Int. Shipbuilding Prog. 1959, Vol. 6, No. 60, pp. 369-384.
[23] Chen C. F.,“Linearized theory for supercavitating hydrofoils with spoiler flaps”, J. Ship Res., 1962, Vol. 6, No. 3.
[24] Fabula A.,“Thin airfoil theory applied to hydrofoils with single finite cavity and arbitrary streamline detachment”, J. Fluid Mech., 1962, Vol. 12, Part 2.
[25] Kinnas S. A., Fine N. E.,“A numerical non-linear analysis of the flow around two- and three-dimensional partially cavitating hydrofoils”, J. Fluid Mech., 1993, Vol. 254, pp. 151-181.
[26] Chen C. F.,“Second-order supercavitating hydrofoil theory”, J. Fluid Mech., 1962, Vol. 13, Part 3, pp. 331-331.
[27] Yakimov Y. L.,“Asymptotic laws of degeneration of thin cavity shapes”, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 1981, No. 3, pp. 3-10, reprinted in USA.
[28] Martin M.,“Unsteady lift and moment on fully cavitating hydrofoils at zero cavitation number”, J. Ship Res., 1962, Vol. 6, No. 1, pp. 15-25.
[29] Parkin B. R.,“Numerical data on hydrofoil response to non-steady motions at zero cavitation number”, J. Ship Res., 1962, Vol. 6, No. 1, pp. 40-42.
[30] Woods L. C.,“Unsteady plane flow past curved obstacles with infinite wakes”, Proc. Poy. Soc. (London) A–1955, Vol. 229.
[31] Woods L. C., Boxton,“On the insteability of ventilated cavities”, J. Fluid Mech., 1966, Vol. 36, No. 3, pp. 437-457.
[32] Leehey P.,“Supercavitating hydrofoil of finite span”. Proc. IUTAM Symp. on Non-steady Flow of Water at High Speeds, Leningrad, 1971, pp. 277-298.
[33] Uhlman J. S.,“A partially cavitated hydrofoil of finite span”, ASME, J. Fluids Eng., 1978, Vol. 100, No 3, pp. 353-354.
[34] Furuya O.,“Three-dimensional theory on supercavitating hydrofoils near a free surface”, J. Fluid Mech., 1975, Vol. 71, pp. 339-359.
[35] Chou Y. S.,“Axisymmetric cavity flows past slender bodies of revolution”, J. Hydronautics, 1974, Vol. 8, No. 1.
[36] Serebryakov V. V.,“Asymptotic solutions of problems of axisymmetrical supercavitation flow in slender body approximation”, in Hydrodynamics of High Speeds, Chuvash. University Press, Cheboksari, 1990, pp. 99-111, in Russian.
[37] Al’ev G. A.,“Separated subsonic water flow past a circular cone”, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 1983, No. 2, pp. 152-154, reprinted in USA.
[38] Ye Q. Y., Cheng Z.,“Supercavitating flow past a body of revolution at a small angle of attack in a gravity field”, Third International Symposium on Cavitation: Vol. II, Grenoble, France, April, 1998, pp. 15-19.
[39] Petrov A. G.,“Asymptotic expansions for axially symmetric cavities”, Euro. J. Applied Math., 2005, Vol. 16, pp. 1-16.
[40] Plesset, M. S.,“The dynamics of cavitation bubbles”, J. Appl. Mech., 1949, Vol. 16, pp. 277.
[41] Plesset, M. S., Prosperetti A.,“Bubble dynamics and cavitation”, Annu. Rev. Fluid Mech., 1977, Vol. 9, pp. 145-185.
[42] Prosperetti A., Crum L. A., Commander K. W.,“Nonlinear bubble dynamics”, J. Acoust. Soc., 1988,Vol. 83, pp. 502-514.
[43] Tsao, H. K., Koch, D. L.,“Observation of high Reynolds number bubbles interacting with a rigid wall”, Phys. Fluids, 1996, Vol. 9, No. 1, pp. 44-45.
[44]董世汤,“有厚度水翼局部空泡流的理论解”,中国造船, 1983, pp. 15-27.
[45] Yakimov Y. L.,“Thin cavitation cavity in a compressible fluid”, in Problems of Contemporary Mechanics, Pt. 1, Moscow University Press, Moscow, 1983, pp. 63-73.
[46] Serebryakov V. V.,“Asymptotic solutions of axisymmetrical problems of subsonic and supersonic separated water flows with zero numbers of cavitation”, Dokl. Akad. Nauk Ukraine, 1992, No. 9, pp. 66-71, in Russian.
[47] Zigangareeva L. M., Kiselev O. M.,“Calculation of the compressible subsonic cavitation flow past a circular cone”, Prikl. Mat. Mekh., 1994, Vol. 58, No. 4, pp. 93-107, reprinted in USA.
[48] Vasin A. D.,“Thin axisymmetric cavities in subsonic compressible flow”, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 1987, No. 5, pp. 174-177, reprinted in USA.
[49] Vasin A. D.,“Thin axisymmetric cavities in supersonic compressible flow”, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 1989, No. 1, pp. 179-181, reprinted in USA.
[50] Vasin A. D.,“Calculation of axisymmetric cavities downstream of a disk in subsonic compressible fluid flow”, Izv. Rus. Akad. Nauk, Mekh. Zhidk. Gaza, 1996, No. 2, pp. 94-103, reprinted in USA.
[51] Vasin A. D.,“Calculation of axisymmetric cavities downstream of a disk in supersonic flow”, Izv. Rus. Akad. Nauk, Mekh. Zhidk. Gaza, 1997, No. 4, pp. 54-62, reprinted in USA.
[52] Vasin A. D.,“Shock waves and conic flows in supersonic stream of water”, Izv. Rus. Akad. Nauk, Mekh. Zhidk. Gaza, 1998.
[53] Paryshev E. V.,“Mathematical modeling of unsteady cavity flows”, Fifth International Symposium on Cavitation, Osaka, Japan, November, 2003.
[54] Kirschner I. N., Rosenthal B. J., Uhlman J. S.,“Simplified dynamical systems analysis of supercavitating high-speed bodies”, Fifth International Symposium on Cavitation, Osaka, Japan, November, 2003.
[55] Serebryakov V., Schnerr G.,“Some problems of hydrodynamics for sub- and supersonic motion in water with supercavitation”, Fifth International Symposium on Cavitation, Osaka, Japan, November, 2003.
[56] Silberman E., Song C. S.,“Instability of ventilated cavities”. J. Ship Res., 1961, Vol. 5, pp. 13-33.
[57] Song C. S.,“Pulsation of ventilated cavities”. J. Ship Res., 1962, Vol. 5, pp. 8-20.
[58]邓华,“非定常空泡特征的实验研究”, [学士学位论文],上海交通大学, 1988.
[59] Arakeri V. H.,“Viscous effects on the position of cavitation separation from smooth bodies”, J. Fluid Mech., 1975, Vol. 68, pp. 779-799.
[60] Franc J. P., Michel J. M.,“Attached cavitation and the boundary layer: experimental investigation and numerical treatment”, J. Fluid Mech., 1985, Vol. 154, pp. 63-90.
[61] Franc J. P., Michel J. M.,“Unsteady attached cavitation on an oscillating hydrofoil”, J. Fluid Mech., 1988, Vol. 193, pp. 171-189.
[62] Kubota A., Kato H., Yamaguchi H., et al.,“Unsteady structure measurement of cloud cavitation on a foil section using conditional sampling technique”, J. Fluid Eng, 1989, Vol. 111, pp. 204-210.
[63] Hart D. P., Brennen C. E., Acosta A. J.,“Observations of cavitation on a three-dimensional oscillating hydrofoil”, ASME Cavitation and Multiphase Flow Forum, 1990, Vol. 98, pp. 49-52.
[64] Ceccio S.,“Surface dynamics of attached cavities”. ASME Dynamics of Bubbles and Vortices Near a Free Surface, Printed in U.S.A., N. Y. 1991, pp. 9-15.
[65] Le Q., Franc J. P., Michel J. M.,“Partial cavities: Global behavior and mean pressure distribution”, J. Fluids Eng., 1993a, Vol. 115, pp. 243-247.
[66] Le Q., Franc J. P., Michel J. M.,“Partial cavities: pressure pulse distribution around cavity closure”, J. Fluids Eng., 1993b, Vol. 115, pp. 249-254.
[67] Stutz B., Reboud J. L.,“Two-phase flow structure of sheet cavitation”, J. Phys. Fluids, 1996, Vol. 9, No.12, pp. 3678-3686.
[68] Kawanami Y., Kato H., Yamaguchi H., et al.,“Mechanism and control of cloud cavitation”, J. Fluids Eng., 1997, Vol. 119, pp. 788-794.
[69]何友声,刘桦,赵岗,“二维空泡流的脉动性态研究”,力学学报, 1997, Vol. 29, No. 1, pp. 1-7.
[70]刘桦,何友声,赵岗,“轴对称空泡流的脉动性态研究”,上海力学, 1997, Vol. 18, No. 2, pp. 99-105.
[71]顾魏,“非稳定空泡流瞬态和周期现象实验研究”, [博士学位论文],上海交通大学, 1998.
[72]谢正桐,何友声,朱世权,“小攻角带空泡细长体的试验研究”,水动力学研究与进展, A辑, 2001, Vol. 16, No. 3, pp. 374-381.
[73] Feng Xue-mei, Lu Chuan-jing, Hu Tian-qun, et al.,“The fluctuation characteristics of natural and ventilated cavities on an axisymmetric body”, Journal of Hydrodynamics, Ser. B, 2005, Vol. 17, No. 1, pp. 87-91.
[74] Wilczynski L.,“The experimental investigation of the cavitation inception in the flow around NACA 16-018 hydrofoil”, Third International Symposium on Cavitation: Vol. I, Grenoble, France, April, 1998, pp. 167-172.
[75] Kawanami Y., Kato H., Yamaguchi H.,“Three-dimensional characteristics of the cavities formed on a two-dimensional hydrofoil”, Third International Symposium on Cavitation: Vol. I, Grenoble, France, April, 1998, pp. 191-196.
[76] Laberteaux K. R., Ceccio S. L.,“Flow in the closure region of closed partial attached cavitation”, Third International Symposium on Cavitation: Vol. I, Grenoble, France, April, 1998, pp. 197-202.
[77] Stutz B., Reboud J. L.,“Experiments on unsteady cavitation”, Experiments in Fluids, 1997, No. 22, pp. 191-198.
[78] Stutz B., Reboud J. L.,“Measurements within unsteady cavitation”, Experiments in Fluids, 2000, Vol. 29, pp. 545-552.
[79] Lohrberg H., Stoffel B., Fortes-Patella R., et al.,“Numerical and Experimental investigations on the cavitating flow in a cascade of hydrofoils”, Experiments in Fluids, 2002, No. 33, pp. 578-586.
[80] Dular M., Bachert R., Stoffel B., et al.,“Experimental evaluation of numerical simulation of cavitating flows around hydrofoil”, European Journal of Mechanics/ B Fluids, 2005, No. 24, pp. 522-538.
[81] Pham T. M., Larrarte F., Fruman D. H.,“Investigation of unstable cloud cavitation”, Third International Symposium on Cavitation: Vol. I, Grenoble, France, April, 1998, pp. 215-220.
[82] Kawanami Y., Kato H., Yamaguchi H.,“Evaporation rate at sheet cavity interface”, Third International Symposium on Cavitation: Vol. I, Grenoble, France, April, 1998, pp. 221-226.
[83] Kjeldson M., Arndt R. E. A.,“Joint time frequency analysis techniques: a study of transitional dynamics in sheet/cloud cavitation”, Fourth International Symposium on Cavitation, California, USA,June, 2001.
[84] Sakoda M., Yakushiji R., Maeda M., et al.,“Mechanism of cloud cavitation generation on a 2-D hydrofoil”, Fourth International Symposium on Cavitation, California, USA, June, 2001.
[85] Sato K., Shimojo S.,“Detailed observations on a starting mechanism for shedding of cavitation cloud”, Fifth International Symposium on Cavitation, Osaka, Japan, November, 2003.
[86] Vlasenko Y. D.,“Experimental investigations of high-speed unsteady supercavitating flows”, Third International Symposium on Cavitation: Vol. II, Grenoble, France, April, 1998, pp. 39-44.
[87] Wang G. Y., Senocak I., Shyy W., et al.,“Dynamics of attached turbulent cavitating flows”, Progress in Aerospace Sciences, 2001, No. 37, 551-581.
[88] Choi J., Oweis G., Ceccio S.,“Vortex-vortex interactions and cavitation inception”, Fifth International Symposium on Cavitation, Osaka, Japan, November, 2003.
[89] Vlasenko Y. D.,“Experimental investigation of supercavitation flow regimes at subsonic and transonic speeds”, Fifth International Symposium on Cavitation, Osaka, Japan, November, 2003.
[90] Savchenko Y. N., Semenenko V. N., Putilin S. I., et al.,“Some problems of the supercavitating motion management”, Sixth International Symposium on Cavitation, Wageningen, The Netherlands, September, 2006.
[91] Foeth E. J., Terwisga T. V.,“The structure of unsteady cavitation. Part I: Observations of an attached cavity on a three-dimensional hydrofoil”, Sixth International Symposium on Cavitation, Wageningen, The Netherlands, September, 2006.
[92] Foeth E. J., Terwisga T. V.,“The structure of unsteady cavitation. Part II: Applying time-resolved PIV to attached cavitation”, Sixth International Symposium on Cavitation, Wageningen, The Netherlands, September, 2006.
[93] Washio S., Takahashi S., Kikui S., et al.,“Observations of cavitation inception at point of separation using a super-high speed video camera”, Sixth International Symposium on Cavitation, Wageningen, The Netherlands, September, 2006.
[94] Wang G. Y., Li X. B., Zhang M. D., et al.,“Multiphase dynamics of supercavitating flows around a hydrofoil”, Sixth International Symposium on Cavitation, Wageningen, The Netherlands, September, 2006.
[95] Coutier-Delgosha O., Devillers J. F., Pichon T., et al.,“Endoscopic investigation of the internal structure of sheet cavitation”, Sixth International Symposium on Cavitation, Wageningen, The Netherlands, September, 2006.
[96] Coutier-Delgosha O., Stutz B., Vabre A., et al.,“Experimental study of the cavitating flow on a 2D hydrofoil by X-ray absorption”, Sixth International Symposium on Cavitation, Wageningen, The Netherlands, September, 2006.
[97] Christophe S., Yousef A. B., Henda D.,“Effect of cavitation on the structure of the boundary layer in the wake of a partial cavity”, Sixth International Symposium on Cavitation, Wageningen, The Netherlands, September, 2006.
[98] Rankine W. J.,“On the mathematical theory of streamlines especially those with four foci and upwards”, Phil. Trans., 1871, Vol. 161, pp. 267-304.
[99] Reichardt H., Munzner H.,“Rotationally symmetric source-sink bodies with predominantly constant pressure distributions”, Arm. Res. Est. Trans., 1950, No. 1/50.
[100] Lemonnier H., Rowe A.,“Another approach in modelling cavitating flows”, J. Fluid Mech., 1988,Vol. 195, pp. 557-580.
[101] Uhlman J. S.,“The surface singularity method applied to partially cavitating hydrofoils”, J. Ship Res., 1987, Vol. 36, No. 2, pp. 107-124.
[102] Uhlman J. S.,“The surface singularity or boundary integral method applied to supercavitating hydrofoils”, J. Ship Res., 1989, Vol. 33, No. 1, pp. 16-20.
[103] Kinnas S. A., Fine N. E.,“Non-linear analysis of the flow around partially or super-cavitating hydrofoils on a potential based panel method”, Proc. IABEM-90 Symp. Int. Assoc. for Boundary Element Methods, Rome, 1991, pp. 289-300.
[104] De Lange D. F., De Bruin G. J., Van W.,“On the mechanism of cloud cavitation Experiment and modeling”, Second International Symposium on Cavitation, Tokyo, Japan, 1994, pp. 45-49.
[105] Brewer W. H., Kinnas S. A.,“Experiment and viscous flow analysis on a partially cavitating hydrofoil”, J. Ship Res., 1997, Vol. 41, No. 3, pp. 161-171.
[106] Kinnas S. A.,“The prediction of unsteady sheet cavitation”, Third International Symposium on Cavitation, Grenoble, France, April, 1998, pp. 19-36.
[107] Dang J., Kuiper G.,“Re-entrant jet modeling of partial cavity flow on two-dimensional hydrofoils”, Third International Symposium on Cavitation, Grenoble, France, April, 1998.
[108] Kai H., Ikehata M.,“Numerical simulation of cavitation on three-dimensional wings and marine propeller by a surface vortex lattice method”, Third International Symposium on Cavitation, Grenoble, France, April, 1998.
[109] Boulon O., Chahine G. L.,“Numerical simulation of unsteady cavitation on 3D hydrofoil”, Third International Symposium on Cavitation, Grenoble, France, April, 1998.
[110] Deshpande M., Feng J., Merkle C.,“Navier-Stokes analysis of 2-D cavity flows”, Cavitation and Multiphase Flow Forum, ASME, FED, 1993, Vol. 153, pp. 149-155.
[111] Dieval L., Arnaud M., Marcer R.,“Numerical modeling of unsteady cavitating flows by a VOF method”, Third International Symposium on Cavitation, Grenoble, France, April, 1998.
[112] Salvatore F., Esposito P. G.,“An improved boundary element analysis of cavitating three-dimensional hydrofoils”, Fourth International Symposium on Cavitation, California, USA, June, 2001.
[113] Kinnas S. A., Sun H., Lee H.,“Numerical analysis of flow around the cavitating CAV2003 hydrofoil”, Fifth International Symposium on Cavitation, Osaka, Japan, November, 2003.
[114] Cheng Xiao-jun, Lu Chuan-jing,“On the partially cavitating flow around two-dimensional hydrofoils”, Applied Mathematics and Mechanics, 2000, Vol. 21, No. 12, pp. 1450-1459.
[115]程晓俊,鲁传敬,“二维水翼的局部空泡流研究”,应用数学和力学, 2002, Vol. 21, No. 12, pp. 1310-1318.
[116]冷海军,鲁传敬,“轴对称体的局部空泡流研究”,上海交通大学学报, 2002, Vol. 36, No. 3, pp. 395-398.
[117]戚定满,鲁传敬,“空泡噪声的数值研究”,水动力学研究与进展, A辑, Vol. 16, No. 1, pp. 9-17.
[118] Noh W. F., Woodward P.,“SLIC(Simple Line Interface Calculations)”, Lecture Notes in Physics, 1976, Vol. 59, 330-340.
[119] Nichols B. D., Hirt C. W., Hotchkiss R. S.,“SOLA-VOF: A solution algorithm for transient fluid flow with multiple free boundaries”, Tech. Rep. LA-8355, Los Alamos Nat. Lab., 1980.
[120] Torrey M. D., Cloutman L. D., Mjolsness R. C., et al.,“NASA-VOF2D: A computer program for incompressible flow with free surfaces”, Tech. Rep. LA-101612-MS, Los Alamos Nat. Lab., 1985.
[121] Torrey M. D., Mjolsness R. C., Stein L. R.,“NASA-VOF3D: a three-dimensional computer program for incompressible flow with free surface”, Tech. Rep. LA-11009-MS, Los Alamos Nat. Lab., 1987.
[122] Kothe D. B., Mjolsness R. C.,“RIPPLE: a new model for incompressible flows with free surface,”AIAA J. 1992, Vol. 30, pp. 2694-2700.
[123] Hirt C. W., Nichols B. D.,“Flow-3D users manual”, Tech. Rep. Flow Science Inc., 1988.
[124] Lafaurie B., Nardone C., Scardovelli R., et al.,“Modelling merging and fragmentation in multiphase flows with SURFER”, J. Comp. Phys., 1994, Vol. 113, pp. 134-147.
[125] Markatos N. C.,“Modeling of two-phase transient flow and combustion of granular propellants”, Int. J. Multiphase Flow, 1986, Vol. 12, pp. 913-933.
[126] Kubota A., Kato H., Yamaguchi H.,“A new modeling of cavitating flows: a numerical study of unsteady cavitation on a hydrofoil section”, J. Fluid Mech., 1992, Vol. 240, pp. 59-96.
[127] Delannoy Y., Kueny J. L.,“Two-phase flow approach in unsteady cavitation modeling”, ASME Cavitation and Multiphase Flow Forum, Toronto, June, 1990.
[128] Song C., He J.,“Numerical simulation of cavitating flows by single-phase flow approach”, Third International Symposium on Cavitation, Grenoble, France, April, 1998, pp. 295–300.
[129] Merkle C. L., Feng J. Z., Buelow P. E. O.,“Computational modeling of the dynamics of sheet cavitation”, Third International Symposium on Cavitation, Grenoble, France, April, 1998, pp. 307–313.
[130] Reboud J. C., Delannoy Y.,“Two-phase flow modeling of unsteady cavitation”, Second International Symposium on Cavitation, Tokyo, Japan, April, 1994, pp. 39-44.
[131] Chen Y., Heister S.,“Two-phase modeling of cavitating flows”, Computers and fluids, 1995, Vol. 24, No. 7, pp. 799-809.
[132] Hoeijmakers H. W. M., Janssens M. E., Kwan W.,“Numerical simulation of sheet cavitation”, Third International Symposium on Cavitation, Grenoble, France, 1998, pp. 257-262.
[133] Coutier-Delgosha O., Fortes-Patella R., Reboud J. L.,“Evaluation of the turbulence model influence on the numerical simulations of unsteady cavitation”, J. Fluids Eng., 2003, Vol. 125, No. 1, pp. 38-45.
[134] Qin Q., Song C. C. S., Arndt R. E. A.,“A numerical study of an unsteady turbulent wake behind a cavitating hydrofoil”, Fifth International Symposium on Cavitation, Osaka, Japan, November, 2003.
[135] Ventikos Y., Tzabiras G.,“A numerical method for the simulation of steady and unsteady cavitating flows”, Computer & Fluids, 2000, Vol. 29, pp. 63-88.
[136] Hosangadi A., Ahuja V., Arunajatesan S.,“A generalized compressible cavitation model”, Fourth International Symposium on Cavitation, California, USA, June, 2001.
[137] Kunz R. F, Chyczewski T. S, Boger D. A.,“Multiphase CFD analysis of natural and ventilated cavitation about submerged bodies”, Third ASME/JSME Joint Fluids Engineering Conference, San Francisco, USA, 1999.
[138] Kunz R. F, Boger D. A., Stinebring D. R. A,“Preconditioned Navier-Stokes method for two-phase flows with application to cavitation prediction”, Computers & Fluids, 2000, Vol. 29, pp. 849-875.
[139] Vaidyanathan R., Senocak I., Wu J. Y.,“Sensitivity evaluation of a transport-based turbulent cavitation model”, J. Fluids Eng., 2003, Vol. 125, No. 5, pp. 447-458.
[140] Kinzel M. P., Lindau J. W., Paterson E. G., et al.,“The effects of a free-surface on computed turbulent, super and partially cavitating flows”, Sixth International Symposium on Cavitation,Wageningen, The Netherlands, September, 2006.
[141] Singhal A. K., Athavale M. M., Li H. Y., et al.,“Mathematical basis and validation of the full cavitation model”, J. Fluids Eng., 2002, Vol. 124, pp. 617-624.
[142] Xiong Y. L., Gao Y., An W. G.,“Comparisons of turbulence models in predicting unsteady supercavitating flow”, Sixth International Symposium on Cavitation, Wageningen, The Netherlands, September, 2006.
[143] Yuan W. X., Sauer J., Schnerr G. H.,“Modeling and computation of unsteady cavitation flows in injection nozzles”, Mec. Ind., 2001, No. 2, 383-394.
[144] Senocak I., Shyy W.,“A pressure-based method for turbulent cavitating flow computations”, J. Comp. Physics, 2002, Vol. 176, pp. 363-383.
[145] Saito Y., Nakamori I., Ikohagi T.,“Numerical analysis of unsteady vaporous cavitating flow around hydrofoil”, Fifth International Symposium on Cavitation, Osaka, Japan, November, 2003.
[146] Owis F. M., Nayfeh A. H.,“Computation of the compressible multiphase flow over the cavitating high-speed torpedo”, J. Fluids Eng., 2003, Vol. 125, No. 5, 459-468.
[147] Peng G. Y., Fujikawa S.,“Numerical study of cavitating turbulent flows in a starting submerged water jet”, Sixth International Symposium on Cavitation, Wageningen, The Netherlands, September, 2006.
[148] Sakai H., Ohta T., Kajishima T.,“Direct numerical simulation of vortex cavitation in turbulent shear layer”, Sixth International Symposium on Cavitation, Wageningen, The Netherlands, September, 2006.
[149] Jones W. P., Launder B. E.,“The calculation of low-Reynolds-number phenomena with a two-equation model of turbulence”, International Journal of Heat and Mass Transfer, 1973, Vol. 16, pp. 1119-1130.
[150] Wilcox D. C., Rubesin M. W.,“Progress in turbulence modeling for complex flow fields including effects of compressibility”, 1980, NASA, TP-1517.
[151] Myong H. K., Kasagi N.,“Prediction of anisotropy of the near wall turbulence with an anisotropic low-Reynolds number k-e turbulence model”, J. Fluids Eng., 1990, Vol. 112, pp. 521-524.
[152] Rung T., Thiele F.,“Computational modeling of complex boundary-layer flows”, Proc. Ninth International Symposium on Transport Phenomena in Thermal-Fluid Engineering, Singapore, 1996, pp. 321-326.
[153] Craft T. J., Launder B. E., Suga K.,“Development and application of a cubic eddy-viscosity model of turbulence”, Int. J. Heat Fluid Flow, 1996, Vol. 17, pp. 108-115.
[154] Shin B. R., Iwata Y., Ikohagi T.,“Numerical simulation of unsteady cavitating flows using a homogeneous equilibrium model”, Computational Mechanics, 2003, Vol. 30, pp. 388-395.
[155]童景山,“流体的热物理性质”,北京,中国石化出版社, 1996, pp. 24-25.
[156] Lyons C. G.,“A simple equation of state for dense fluids”, Journal of Molecular liquids, 1996, Vol. 69, pp. 269-281.
[157]孔珑,“工程流体力学”,北京,水利电力出版社, 1995, pp. 12.
[158] Van Leer B.,“Towards the ultimate conservative difference scheme. V. A second order sequel to Godunov’s method”, J. Comp. Physics, 1979, Vol. 32, pp. 101-136.
[159] Caretto L. S., Gosman A. D., Patankar S. V., et al.,“Two calculation procedures for steady, three-dimensional flows with recirculation”, Proc. Third Int. Conf. Numer. Methods Fluid Dyn., Paris, 1972.
[160] Stone H. L.,“Iterative solution of implicit approximations of multidimensional partial differential equations”, SIAM J. Numer. Anal., Vol. 5, No. 3, pp. 530-558.
[161] Wesseling P.,“Multigrid methods in computational fluid dynamics”, ZAMMZ, Angew. Math. Mech., Vol. 70, T337-T347.
[162] Xue L. P.,“Entwicklung eines effizienten parallelen L?sungsalgorithmus zur dreidimensionalen Simulation komplexer turbulenter Str?mungen”, Ph. D Dissertation, Berlin: Technischen Universit?t Berlin, 1998.
[163] Garabediant P.,“Calculation of axially symmetric cavities and jets”, Pac. J. Math., 1956, Vol. 6, No. 4, pp. 611-684.
[164] Logvi-novich G. V.,“Hydrodynamics of flows with free boundaries”, Halsted Press, 1973.
[165] Gurevich M.,“Half-body with finite drag in subsonic flow”, Tr, TsAG1, #653, 1947, 1-12. (in Russian)
[166] De Lange D. F., De Bruin G. J.,“Sheet cavitation and cloud cavitation, re-entrant jet and three-dimensionality”, Applied Scientific Research, 1998, Vol. 58, pp. 91-114.
[167] Kjeldsen M., Arndt R. E. A., Effertz M.,“Spectral characteristics of sheet/cloud cavitation”, J. Fluids Eng., 2000, Vol. 122, pp. 481-487.
[168] Watanabe S., Tsujimoto Y., Furukawa A.,“Theoretical analysis of transitional and partial cavity instabilities”, J. Fluids Eng., 2001, Vol. 123, pp. 692–697.
[169] Fujii A., Kawakami D. T., Tsujimoto Y., et al.,“Effect of hydrofoil shape on cavity oscillation”, J. Fluids Eng., 2007, Vol. 129, No. 6, pp. 669-674.
[170] Kawakami D. T., Fujii A., Tsujimoto Y., et al.,“An assessment of the influence of environmental factors on cavitation instabilities”, J. Fluids Eng., 2008, Vol. 130, 031303.
[171]吴磊,空泡流数值模拟, [博士学位论文],上海:上海交通大学, 2002.
[172] Qin Q., Song C. C. S., Arndt R. E. A.,“An numerical study of an unsteady turbulent wake behind a cavitating hydrofoil”, Fifth International Symposium on Cavitation, Osaka, Japan, November, 2003.
[173]权晓波,李岩,魏海鹏等,“大攻角下轴对称航行体空化流动特性试验研究”,水动力学研究与进展, A辑, 2008, Vol. 23, No. 6, pp. 662-667.
[2] Yin L. Y.,“Numerical modeling of supercavitating and surface-piercing propellers”, [Dissertation], The University of Texas, 2002.
[3]柯乃普R. T.,戴利J. W.,哈密脱F. G.,“空化与空蚀”,水利出版社,水利水电科学研究院译, 1981.
[4]黄继汤,“空化与空蚀的原理及应用”,清华大学出版社, 1991.
[5] Akihisa K., Hajime Y., Hiroharu K., et al.,“On the collapsing behavior of cavitation bubble clusters”, Fourth International Symposium on Cavitation, California, USA, June, 2001.
[6] Stinebring D. R., Michael L. B., Jules W., et al.,“Developed cavitation-cavity dynamics”, RTO/AVT lecture series on“Supercavitating flows”, RTO-EN-10, No. 5, Brussels, Belgium, 2001.
[7] Levi-Civita T.,“Scie e leggi di resistenzia”, Rend. Circ. Mat. Palermo, 1907, Vol. 18, pp. 1-37.
[8] Villat H.,“Sur la validatédes solutions de certains problèmes d’hydrodynamique”, J. Math., Pures Appl., 1914, Vol. 10, pp. 231-290.
[9] Riabouchinsky D.,“On steady flow motions with free surfaces”, Proc. London Math. Soc., 1920, Vol. 19, pp. 206-215.
[10] Kreisel G.,“Cavitation with finite cavitation numbers”, Admirally Res. Lab. Rep., R1/H36, 1946.
[11] Joukowshy N. E.,“I. A modification of Kirchhoff’s method of determining a two-dimensional motion of a fluid given a constant velocity along an unknown streamline, II. Determination of the motion of a fluid for any condition given on a streamline”, Mat. Sbornik ( Rec. Math.), 1890, Vol. 15, pp. 121-278.
[12] Wu T. Y.,“A wake model for free streamline theory, part 1: Fully and partially developed wake flows and cavity flows past an oblique flat plate”, J. Fluid Mech. 1962, Vol. 13, pp. 161-181.
[13] Apelt D. J.,“Some studies of fluid flow at low Reynolds numbers”, [Thesis], Oxford Univ., 1957.
[14] Tulin M. P.,“Supercavitating flows-small perturbation theory”, J. Ship Res., 1964, Vol. 7, No. 3, pp. 16-37.
[15] Brennen C. E.,“Cavitation and bubble dynamics”, Oxford, New York, 1995.
[16]汤福坤,何友声,“空泡流理论”,上海交通大学, 1986.
[17] Acosta A. J.,“A note on partial cavitation of flat plate hydrofoils”, Calif. Inst. of Tech. Hydro. Lab. Rep., 1955, E-19.9
[18] Acosta A. J.,“Cavitating flow past a cascade of circular arc hydrofoils”. Calif. Inst. of Tech. Hydro. Lab. Rep., 1960, E-79.2
[19] Wu Y. T.,“A free streamline theory for two-dimensional fully cavitated hydrofoil”, J. Math. Phys., 1956, Vol. 35, pp. 236-265.
[20] Wu Y. T.,“A wake model for free streamline theory, part 1: Fully and partially developed wake flows and cavity flows past an oblique flat plate”, J. Fluid Mech. 1962, Vol. 13, pp. 161-181.
[21] Cohen H., Sutherland C. D., Tu Y. O.,“Wall effects in cavitating hydrofoil flow”, J. Ship Res. 1957, Vol. 1, No. 3, pp. 31-39.
[22] Geurst J. A.,“Linearized theory for partially cavitated hydrofoils”, Int. Shipbuilding Prog. 1959, Vol. 6, No. 60, pp. 369-384.
[23] Chen C. F.,“Linearized theory for supercavitating hydrofoils with spoiler flaps”, J. Ship Res., 1962, Vol. 6, No. 3.
[24] Fabula A.,“Thin airfoil theory applied to hydrofoils with single finite cavity and arbitrary streamline detachment”, J. Fluid Mech., 1962, Vol. 12, Part 2.
[25] Kinnas S. A., Fine N. E.,“A numerical non-linear analysis of the flow around two- and three-dimensional partially cavitating hydrofoils”, J. Fluid Mech., 1993, Vol. 254, pp. 151-181.
[26] Chen C. F.,“Second-order supercavitating hydrofoil theory”, J. Fluid Mech., 1962, Vol. 13, Part 3, pp. 331-331.
[27] Yakimov Y. L.,“Asymptotic laws of degeneration of thin cavity shapes”, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 1981, No. 3, pp. 3-10, reprinted in USA.
[28] Martin M.,“Unsteady lift and moment on fully cavitating hydrofoils at zero cavitation number”, J. Ship Res., 1962, Vol. 6, No. 1, pp. 15-25.
[29] Parkin B. R.,“Numerical data on hydrofoil response to non-steady motions at zero cavitation number”, J. Ship Res., 1962, Vol. 6, No. 1, pp. 40-42.
[30] Woods L. C.,“Unsteady plane flow past curved obstacles with infinite wakes”, Proc. Poy. Soc. (London) A–1955, Vol. 229.
[31] Woods L. C., Boxton,“On the insteability of ventilated cavities”, J. Fluid Mech., 1966, Vol. 36, No. 3, pp. 437-457.
[32] Leehey P.,“Supercavitating hydrofoil of finite span”. Proc. IUTAM Symp. on Non-steady Flow of Water at High Speeds, Leningrad, 1971, pp. 277-298.
[33] Uhlman J. S.,“A partially cavitated hydrofoil of finite span”, ASME, J. Fluids Eng., 1978, Vol. 100, No 3, pp. 353-354.
[34] Furuya O.,“Three-dimensional theory on supercavitating hydrofoils near a free surface”, J. Fluid Mech., 1975, Vol. 71, pp. 339-359.
[35] Chou Y. S.,“Axisymmetric cavity flows past slender bodies of revolution”, J. Hydronautics, 1974, Vol. 8, No. 1.
[36] Serebryakov V. V.,“Asymptotic solutions of problems of axisymmetrical supercavitation flow in slender body approximation”, in Hydrodynamics of High Speeds, Chuvash. University Press, Cheboksari, 1990, pp. 99-111, in Russian.
[37] Al’ev G. A.,“Separated subsonic water flow past a circular cone”, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 1983, No. 2, pp. 152-154, reprinted in USA.
[38] Ye Q. Y., Cheng Z.,“Supercavitating flow past a body of revolution at a small angle of attack in a gravity field”, Third International Symposium on Cavitation: Vol. II, Grenoble, France, April, 1998, pp. 15-19.
[39] Petrov A. G.,“Asymptotic expansions for axially symmetric cavities”, Euro. J. Applied Math., 2005, Vol. 16, pp. 1-16.
[40] Plesset, M. S.,“The dynamics of cavitation bubbles”, J. Appl. Mech., 1949, Vol. 16, pp. 277.
[41] Plesset, M. S., Prosperetti A.,“Bubble dynamics and cavitation”, Annu. Rev. Fluid Mech., 1977, Vol. 9, pp. 145-185.
[42] Prosperetti A., Crum L. A., Commander K. W.,“Nonlinear bubble dynamics”, J. Acoust. Soc., 1988,Vol. 83, pp. 502-514.
[43] Tsao, H. K., Koch, D. L.,“Observation of high Reynolds number bubbles interacting with a rigid wall”, Phys. Fluids, 1996, Vol. 9, No. 1, pp. 44-45.
[44]董世汤,“有厚度水翼局部空泡流的理论解”,中国造船, 1983, pp. 15-27.
[45] Yakimov Y. L.,“Thin cavitation cavity in a compressible fluid”, in Problems of Contemporary Mechanics, Pt. 1, Moscow University Press, Moscow, 1983, pp. 63-73.
[46] Serebryakov V. V.,“Asymptotic solutions of axisymmetrical problems of subsonic and supersonic separated water flows with zero numbers of cavitation”, Dokl. Akad. Nauk Ukraine, 1992, No. 9, pp. 66-71, in Russian.
[47] Zigangareeva L. M., Kiselev O. M.,“Calculation of the compressible subsonic cavitation flow past a circular cone”, Prikl. Mat. Mekh., 1994, Vol. 58, No. 4, pp. 93-107, reprinted in USA.
[48] Vasin A. D.,“Thin axisymmetric cavities in subsonic compressible flow”, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 1987, No. 5, pp. 174-177, reprinted in USA.
[49] Vasin A. D.,“Thin axisymmetric cavities in supersonic compressible flow”, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 1989, No. 1, pp. 179-181, reprinted in USA.
[50] Vasin A. D.,“Calculation of axisymmetric cavities downstream of a disk in subsonic compressible fluid flow”, Izv. Rus. Akad. Nauk, Mekh. Zhidk. Gaza, 1996, No. 2, pp. 94-103, reprinted in USA.
[51] Vasin A. D.,“Calculation of axisymmetric cavities downstream of a disk in supersonic flow”, Izv. Rus. Akad. Nauk, Mekh. Zhidk. Gaza, 1997, No. 4, pp. 54-62, reprinted in USA.
[52] Vasin A. D.,“Shock waves and conic flows in supersonic stream of water”, Izv. Rus. Akad. Nauk, Mekh. Zhidk. Gaza, 1998.
[53] Paryshev E. V.,“Mathematical modeling of unsteady cavity flows”, Fifth International Symposium on Cavitation, Osaka, Japan, November, 2003.
[54] Kirschner I. N., Rosenthal B. J., Uhlman J. S.,“Simplified dynamical systems analysis of supercavitating high-speed bodies”, Fifth International Symposium on Cavitation, Osaka, Japan, November, 2003.
[55] Serebryakov V., Schnerr G.,“Some problems of hydrodynamics for sub- and supersonic motion in water with supercavitation”, Fifth International Symposium on Cavitation, Osaka, Japan, November, 2003.
[56] Silberman E., Song C. S.,“Instability of ventilated cavities”. J. Ship Res., 1961, Vol. 5, pp. 13-33.
[57] Song C. S.,“Pulsation of ventilated cavities”. J. Ship Res., 1962, Vol. 5, pp. 8-20.
[58]邓华,“非定常空泡特征的实验研究”, [学士学位论文],上海交通大学, 1988.
[59] Arakeri V. H.,“Viscous effects on the position of cavitation separation from smooth bodies”, J. Fluid Mech., 1975, Vol. 68, pp. 779-799.
[60] Franc J. P., Michel J. M.,“Attached cavitation and the boundary layer: experimental investigation and numerical treatment”, J. Fluid Mech., 1985, Vol. 154, pp. 63-90.
[61] Franc J. P., Michel J. M.,“Unsteady attached cavitation on an oscillating hydrofoil”, J. Fluid Mech., 1988, Vol. 193, pp. 171-189.
[62] Kubota A., Kato H., Yamaguchi H., et al.,“Unsteady structure measurement of cloud cavitation on a foil section using conditional sampling technique”, J. Fluid Eng, 1989, Vol. 111, pp. 204-210.
[63] Hart D. P., Brennen C. E., Acosta A. J.,“Observations of cavitation on a three-dimensional oscillating hydrofoil”, ASME Cavitation and Multiphase Flow Forum, 1990, Vol. 98, pp. 49-52.
[64] Ceccio S.,“Surface dynamics of attached cavities”. ASME Dynamics of Bubbles and Vortices Near a Free Surface, Printed in U.S.A., N. Y. 1991, pp. 9-15.
[65] Le Q., Franc J. P., Michel J. M.,“Partial cavities: Global behavior and mean pressure distribution”, J. Fluids Eng., 1993a, Vol. 115, pp. 243-247.
[66] Le Q., Franc J. P., Michel J. M.,“Partial cavities: pressure pulse distribution around cavity closure”, J. Fluids Eng., 1993b, Vol. 115, pp. 249-254.
[67] Stutz B., Reboud J. L.,“Two-phase flow structure of sheet cavitation”, J. Phys. Fluids, 1996, Vol. 9, No.12, pp. 3678-3686.
[68] Kawanami Y., Kato H., Yamaguchi H., et al.,“Mechanism and control of cloud cavitation”, J. Fluids Eng., 1997, Vol. 119, pp. 788-794.
[69]何友声,刘桦,赵岗,“二维空泡流的脉动性态研究”,力学学报, 1997, Vol. 29, No. 1, pp. 1-7.
[70]刘桦,何友声,赵岗,“轴对称空泡流的脉动性态研究”,上海力学, 1997, Vol. 18, No. 2, pp. 99-105.
[71]顾魏,“非稳定空泡流瞬态和周期现象实验研究”, [博士学位论文],上海交通大学, 1998.
[72]谢正桐,何友声,朱世权,“小攻角带空泡细长体的试验研究”,水动力学研究与进展, A辑, 2001, Vol. 16, No. 3, pp. 374-381.
[73] Feng Xue-mei, Lu Chuan-jing, Hu Tian-qun, et al.,“The fluctuation characteristics of natural and ventilated cavities on an axisymmetric body”, Journal of Hydrodynamics, Ser. B, 2005, Vol. 17, No. 1, pp. 87-91.
[74] Wilczynski L.,“The experimental investigation of the cavitation inception in the flow around NACA 16-018 hydrofoil”, Third International Symposium on Cavitation: Vol. I, Grenoble, France, April, 1998, pp. 167-172.
[75] Kawanami Y., Kato H., Yamaguchi H.,“Three-dimensional characteristics of the cavities formed on a two-dimensional hydrofoil”, Third International Symposium on Cavitation: Vol. I, Grenoble, France, April, 1998, pp. 191-196.
[76] Laberteaux K. R., Ceccio S. L.,“Flow in the closure region of closed partial attached cavitation”, Third International Symposium on Cavitation: Vol. I, Grenoble, France, April, 1998, pp. 197-202.
[77] Stutz B., Reboud J. L.,“Experiments on unsteady cavitation”, Experiments in Fluids, 1997, No. 22, pp. 191-198.
[78] Stutz B., Reboud J. L.,“Measurements within unsteady cavitation”, Experiments in Fluids, 2000, Vol. 29, pp. 545-552.
[79] Lohrberg H., Stoffel B., Fortes-Patella R., et al.,“Numerical and Experimental investigations on the cavitating flow in a cascade of hydrofoils”, Experiments in Fluids, 2002, No. 33, pp. 578-586.
[80] Dular M., Bachert R., Stoffel B., et al.,“Experimental evaluation of numerical simulation of cavitating flows around hydrofoil”, European Journal of Mechanics/ B Fluids, 2005, No. 24, pp. 522-538.
[81] Pham T. M., Larrarte F., Fruman D. H.,“Investigation of unstable cloud cavitation”, Third International Symposium on Cavitation: Vol. I, Grenoble, France, April, 1998, pp. 215-220.
[82] Kawanami Y., Kato H., Yamaguchi H.,“Evaporation rate at sheet cavity interface”, Third International Symposium on Cavitation: Vol. I, Grenoble, France, April, 1998, pp. 221-226.
[83] Kjeldson M., Arndt R. E. A.,“Joint time frequency analysis techniques: a study of transitional dynamics in sheet/cloud cavitation”, Fourth International Symposium on Cavitation, California, USA,June, 2001.
[84] Sakoda M., Yakushiji R., Maeda M., et al.,“Mechanism of cloud cavitation generation on a 2-D hydrofoil”, Fourth International Symposium on Cavitation, California, USA, June, 2001.
[85] Sato K., Shimojo S.,“Detailed observations on a starting mechanism for shedding of cavitation cloud”, Fifth International Symposium on Cavitation, Osaka, Japan, November, 2003.
[86] Vlasenko Y. D.,“Experimental investigations of high-speed unsteady supercavitating flows”, Third International Symposium on Cavitation: Vol. II, Grenoble, France, April, 1998, pp. 39-44.
[87] Wang G. Y., Senocak I., Shyy W., et al.,“Dynamics of attached turbulent cavitating flows”, Progress in Aerospace Sciences, 2001, No. 37, 551-581.
[88] Choi J., Oweis G., Ceccio S.,“Vortex-vortex interactions and cavitation inception”, Fifth International Symposium on Cavitation, Osaka, Japan, November, 2003.
[89] Vlasenko Y. D.,“Experimental investigation of supercavitation flow regimes at subsonic and transonic speeds”, Fifth International Symposium on Cavitation, Osaka, Japan, November, 2003.
[90] Savchenko Y. N., Semenenko V. N., Putilin S. I., et al.,“Some problems of the supercavitating motion management”, Sixth International Symposium on Cavitation, Wageningen, The Netherlands, September, 2006.
[91] Foeth E. J., Terwisga T. V.,“The structure of unsteady cavitation. Part I: Observations of an attached cavity on a three-dimensional hydrofoil”, Sixth International Symposium on Cavitation, Wageningen, The Netherlands, September, 2006.
[92] Foeth E. J., Terwisga T. V.,“The structure of unsteady cavitation. Part II: Applying time-resolved PIV to attached cavitation”, Sixth International Symposium on Cavitation, Wageningen, The Netherlands, September, 2006.
[93] Washio S., Takahashi S., Kikui S., et al.,“Observations of cavitation inception at point of separation using a super-high speed video camera”, Sixth International Symposium on Cavitation, Wageningen, The Netherlands, September, 2006.
[94] Wang G. Y., Li X. B., Zhang M. D., et al.,“Multiphase dynamics of supercavitating flows around a hydrofoil”, Sixth International Symposium on Cavitation, Wageningen, The Netherlands, September, 2006.
[95] Coutier-Delgosha O., Devillers J. F., Pichon T., et al.,“Endoscopic investigation of the internal structure of sheet cavitation”, Sixth International Symposium on Cavitation, Wageningen, The Netherlands, September, 2006.
[96] Coutier-Delgosha O., Stutz B., Vabre A., et al.,“Experimental study of the cavitating flow on a 2D hydrofoil by X-ray absorption”, Sixth International Symposium on Cavitation, Wageningen, The Netherlands, September, 2006.
[97] Christophe S., Yousef A. B., Henda D.,“Effect of cavitation on the structure of the boundary layer in the wake of a partial cavity”, Sixth International Symposium on Cavitation, Wageningen, The Netherlands, September, 2006.
[98] Rankine W. J.,“On the mathematical theory of streamlines especially those with four foci and upwards”, Phil. Trans., 1871, Vol. 161, pp. 267-304.
[99] Reichardt H., Munzner H.,“Rotationally symmetric source-sink bodies with predominantly constant pressure distributions”, Arm. Res. Est. Trans., 1950, No. 1/50.
[100] Lemonnier H., Rowe A.,“Another approach in modelling cavitating flows”, J. Fluid Mech., 1988,Vol. 195, pp. 557-580.
[101] Uhlman J. S.,“The surface singularity method applied to partially cavitating hydrofoils”, J. Ship Res., 1987, Vol. 36, No. 2, pp. 107-124.
[102] Uhlman J. S.,“The surface singularity or boundary integral method applied to supercavitating hydrofoils”, J. Ship Res., 1989, Vol. 33, No. 1, pp. 16-20.
[103] Kinnas S. A., Fine N. E.,“Non-linear analysis of the flow around partially or super-cavitating hydrofoils on a potential based panel method”, Proc. IABEM-90 Symp. Int. Assoc. for Boundary Element Methods, Rome, 1991, pp. 289-300.
[104] De Lange D. F., De Bruin G. J., Van W.,“On the mechanism of cloud cavitation Experiment and modeling”, Second International Symposium on Cavitation, Tokyo, Japan, 1994, pp. 45-49.
[105] Brewer W. H., Kinnas S. A.,“Experiment and viscous flow analysis on a partially cavitating hydrofoil”, J. Ship Res., 1997, Vol. 41, No. 3, pp. 161-171.
[106] Kinnas S. A.,“The prediction of unsteady sheet cavitation”, Third International Symposium on Cavitation, Grenoble, France, April, 1998, pp. 19-36.
[107] Dang J., Kuiper G.,“Re-entrant jet modeling of partial cavity flow on two-dimensional hydrofoils”, Third International Symposium on Cavitation, Grenoble, France, April, 1998.
[108] Kai H., Ikehata M.,“Numerical simulation of cavitation on three-dimensional wings and marine propeller by a surface vortex lattice method”, Third International Symposium on Cavitation, Grenoble, France, April, 1998.
[109] Boulon O., Chahine G. L.,“Numerical simulation of unsteady cavitation on 3D hydrofoil”, Third International Symposium on Cavitation, Grenoble, France, April, 1998.
[110] Deshpande M., Feng J., Merkle C.,“Navier-Stokes analysis of 2-D cavity flows”, Cavitation and Multiphase Flow Forum, ASME, FED, 1993, Vol. 153, pp. 149-155.
[111] Dieval L., Arnaud M., Marcer R.,“Numerical modeling of unsteady cavitating flows by a VOF method”, Third International Symposium on Cavitation, Grenoble, France, April, 1998.
[112] Salvatore F., Esposito P. G.,“An improved boundary element analysis of cavitating three-dimensional hydrofoils”, Fourth International Symposium on Cavitation, California, USA, June, 2001.
[113] Kinnas S. A., Sun H., Lee H.,“Numerical analysis of flow around the cavitating CAV2003 hydrofoil”, Fifth International Symposium on Cavitation, Osaka, Japan, November, 2003.
[114] Cheng Xiao-jun, Lu Chuan-jing,“On the partially cavitating flow around two-dimensional hydrofoils”, Applied Mathematics and Mechanics, 2000, Vol. 21, No. 12, pp. 1450-1459.
[115]程晓俊,鲁传敬,“二维水翼的局部空泡流研究”,应用数学和力学, 2002, Vol. 21, No. 12, pp. 1310-1318.
[116]冷海军,鲁传敬,“轴对称体的局部空泡流研究”,上海交通大学学报, 2002, Vol. 36, No. 3, pp. 395-398.
[117]戚定满,鲁传敬,“空泡噪声的数值研究”,水动力学研究与进展, A辑, Vol. 16, No. 1, pp. 9-17.
[118] Noh W. F., Woodward P.,“SLIC(Simple Line Interface Calculations)”, Lecture Notes in Physics, 1976, Vol. 59, 330-340.
[119] Nichols B. D., Hirt C. W., Hotchkiss R. S.,“SOLA-VOF: A solution algorithm for transient fluid flow with multiple free boundaries”, Tech. Rep. LA-8355, Los Alamos Nat. Lab., 1980.
[120] Torrey M. D., Cloutman L. D., Mjolsness R. C., et al.,“NASA-VOF2D: A computer program for incompressible flow with free surfaces”, Tech. Rep. LA-101612-MS, Los Alamos Nat. Lab., 1985.
[121] Torrey M. D., Mjolsness R. C., Stein L. R.,“NASA-VOF3D: a three-dimensional computer program for incompressible flow with free surface”, Tech. Rep. LA-11009-MS, Los Alamos Nat. Lab., 1987.
[122] Kothe D. B., Mjolsness R. C.,“RIPPLE: a new model for incompressible flows with free surface,”AIAA J. 1992, Vol. 30, pp. 2694-2700.
[123] Hirt C. W., Nichols B. D.,“Flow-3D users manual”, Tech. Rep. Flow Science Inc., 1988.
[124] Lafaurie B., Nardone C., Scardovelli R., et al.,“Modelling merging and fragmentation in multiphase flows with SURFER”, J. Comp. Phys., 1994, Vol. 113, pp. 134-147.
[125] Markatos N. C.,“Modeling of two-phase transient flow and combustion of granular propellants”, Int. J. Multiphase Flow, 1986, Vol. 12, pp. 913-933.
[126] Kubota A., Kato H., Yamaguchi H.,“A new modeling of cavitating flows: a numerical study of unsteady cavitation on a hydrofoil section”, J. Fluid Mech., 1992, Vol. 240, pp. 59-96.
[127] Delannoy Y., Kueny J. L.,“Two-phase flow approach in unsteady cavitation modeling”, ASME Cavitation and Multiphase Flow Forum, Toronto, June, 1990.
[128] Song C., He J.,“Numerical simulation of cavitating flows by single-phase flow approach”, Third International Symposium on Cavitation, Grenoble, France, April, 1998, pp. 295–300.
[129] Merkle C. L., Feng J. Z., Buelow P. E. O.,“Computational modeling of the dynamics of sheet cavitation”, Third International Symposium on Cavitation, Grenoble, France, April, 1998, pp. 307–313.
[130] Reboud J. C., Delannoy Y.,“Two-phase flow modeling of unsteady cavitation”, Second International Symposium on Cavitation, Tokyo, Japan, April, 1994, pp. 39-44.
[131] Chen Y., Heister S.,“Two-phase modeling of cavitating flows”, Computers and fluids, 1995, Vol. 24, No. 7, pp. 799-809.
[132] Hoeijmakers H. W. M., Janssens M. E., Kwan W.,“Numerical simulation of sheet cavitation”, Third International Symposium on Cavitation, Grenoble, France, 1998, pp. 257-262.
[133] Coutier-Delgosha O., Fortes-Patella R., Reboud J. L.,“Evaluation of the turbulence model influence on the numerical simulations of unsteady cavitation”, J. Fluids Eng., 2003, Vol. 125, No. 1, pp. 38-45.
[134] Qin Q., Song C. C. S., Arndt R. E. A.,“A numerical study of an unsteady turbulent wake behind a cavitating hydrofoil”, Fifth International Symposium on Cavitation, Osaka, Japan, November, 2003.
[135] Ventikos Y., Tzabiras G.,“A numerical method for the simulation of steady and unsteady cavitating flows”, Computer & Fluids, 2000, Vol. 29, pp. 63-88.
[136] Hosangadi A., Ahuja V., Arunajatesan S.,“A generalized compressible cavitation model”, Fourth International Symposium on Cavitation, California, USA, June, 2001.
[137] Kunz R. F, Chyczewski T. S, Boger D. A.,“Multiphase CFD analysis of natural and ventilated cavitation about submerged bodies”, Third ASME/JSME Joint Fluids Engineering Conference, San Francisco, USA, 1999.
[138] Kunz R. F, Boger D. A., Stinebring D. R. A,“Preconditioned Navier-Stokes method for two-phase flows with application to cavitation prediction”, Computers & Fluids, 2000, Vol. 29, pp. 849-875.
[139] Vaidyanathan R., Senocak I., Wu J. Y.,“Sensitivity evaluation of a transport-based turbulent cavitation model”, J. Fluids Eng., 2003, Vol. 125, No. 5, pp. 447-458.
[140] Kinzel M. P., Lindau J. W., Paterson E. G., et al.,“The effects of a free-surface on computed turbulent, super and partially cavitating flows”, Sixth International Symposium on Cavitation,Wageningen, The Netherlands, September, 2006.
[141] Singhal A. K., Athavale M. M., Li H. Y., et al.,“Mathematical basis and validation of the full cavitation model”, J. Fluids Eng., 2002, Vol. 124, pp. 617-624.
[142] Xiong Y. L., Gao Y., An W. G.,“Comparisons of turbulence models in predicting unsteady supercavitating flow”, Sixth International Symposium on Cavitation, Wageningen, The Netherlands, September, 2006.
[143] Yuan W. X., Sauer J., Schnerr G. H.,“Modeling and computation of unsteady cavitation flows in injection nozzles”, Mec. Ind., 2001, No. 2, 383-394.
[144] Senocak I., Shyy W.,“A pressure-based method for turbulent cavitating flow computations”, J. Comp. Physics, 2002, Vol. 176, pp. 363-383.
[145] Saito Y., Nakamori I., Ikohagi T.,“Numerical analysis of unsteady vaporous cavitating flow around hydrofoil”, Fifth International Symposium on Cavitation, Osaka, Japan, November, 2003.
[146] Owis F. M., Nayfeh A. H.,“Computation of the compressible multiphase flow over the cavitating high-speed torpedo”, J. Fluids Eng., 2003, Vol. 125, No. 5, 459-468.
[147] Peng G. Y., Fujikawa S.,“Numerical study of cavitating turbulent flows in a starting submerged water jet”, Sixth International Symposium on Cavitation, Wageningen, The Netherlands, September, 2006.
[148] Sakai H., Ohta T., Kajishima T.,“Direct numerical simulation of vortex cavitation in turbulent shear layer”, Sixth International Symposium on Cavitation, Wageningen, The Netherlands, September, 2006.
[149] Jones W. P., Launder B. E.,“The calculation of low-Reynolds-number phenomena with a two-equation model of turbulence”, International Journal of Heat and Mass Transfer, 1973, Vol. 16, pp. 1119-1130.
[150] Wilcox D. C., Rubesin M. W.,“Progress in turbulence modeling for complex flow fields including effects of compressibility”, 1980, NASA, TP-1517.
[151] Myong H. K., Kasagi N.,“Prediction of anisotropy of the near wall turbulence with an anisotropic low-Reynolds number k-e turbulence model”, J. Fluids Eng., 1990, Vol. 112, pp. 521-524.
[152] Rung T., Thiele F.,“Computational modeling of complex boundary-layer flows”, Proc. Ninth International Symposium on Transport Phenomena in Thermal-Fluid Engineering, Singapore, 1996, pp. 321-326.
[153] Craft T. J., Launder B. E., Suga K.,“Development and application of a cubic eddy-viscosity model of turbulence”, Int. J. Heat Fluid Flow, 1996, Vol. 17, pp. 108-115.
[154] Shin B. R., Iwata Y., Ikohagi T.,“Numerical simulation of unsteady cavitating flows using a homogeneous equilibrium model”, Computational Mechanics, 2003, Vol. 30, pp. 388-395.
[155]童景山,“流体的热物理性质”,北京,中国石化出版社, 1996, pp. 24-25.
[156] Lyons C. G.,“A simple equation of state for dense fluids”, Journal of Molecular liquids, 1996, Vol. 69, pp. 269-281.
[157]孔珑,“工程流体力学”,北京,水利电力出版社, 1995, pp. 12.
[158] Van Leer B.,“Towards the ultimate conservative difference scheme. V. A second order sequel to Godunov’s method”, J. Comp. Physics, 1979, Vol. 32, pp. 101-136.
[159] Caretto L. S., Gosman A. D., Patankar S. V., et al.,“Two calculation procedures for steady, three-dimensional flows with recirculation”, Proc. Third Int. Conf. Numer. Methods Fluid Dyn., Paris, 1972.
[160] Stone H. L.,“Iterative solution of implicit approximations of multidimensional partial differential equations”, SIAM J. Numer. Anal., Vol. 5, No. 3, pp. 530-558.
[161] Wesseling P.,“Multigrid methods in computational fluid dynamics”, ZAMMZ, Angew. Math. Mech., Vol. 70, T337-T347.
[162] Xue L. P.,“Entwicklung eines effizienten parallelen L?sungsalgorithmus zur dreidimensionalen Simulation komplexer turbulenter Str?mungen”, Ph. D Dissertation, Berlin: Technischen Universit?t Berlin, 1998.
[163] Garabediant P.,“Calculation of axially symmetric cavities and jets”, Pac. J. Math., 1956, Vol. 6, No. 4, pp. 611-684.
[164] Logvi-novich G. V.,“Hydrodynamics of flows with free boundaries”, Halsted Press, 1973.
[165] Gurevich M.,“Half-body with finite drag in subsonic flow”, Tr, TsAG1, #653, 1947, 1-12. (in Russian)
[166] De Lange D. F., De Bruin G. J.,“Sheet cavitation and cloud cavitation, re-entrant jet and three-dimensionality”, Applied Scientific Research, 1998, Vol. 58, pp. 91-114.
[167] Kjeldsen M., Arndt R. E. A., Effertz M.,“Spectral characteristics of sheet/cloud cavitation”, J. Fluids Eng., 2000, Vol. 122, pp. 481-487.
[168] Watanabe S., Tsujimoto Y., Furukawa A.,“Theoretical analysis of transitional and partial cavity instabilities”, J. Fluids Eng., 2001, Vol. 123, pp. 692–697.
[169] Fujii A., Kawakami D. T., Tsujimoto Y., et al.,“Effect of hydrofoil shape on cavity oscillation”, J. Fluids Eng., 2007, Vol. 129, No. 6, pp. 669-674.
[170] Kawakami D. T., Fujii A., Tsujimoto Y., et al.,“An assessment of the influence of environmental factors on cavitation instabilities”, J. Fluids Eng., 2008, Vol. 130, 031303.
[171]吴磊,空泡流数值模拟, [博士学位论文],上海:上海交通大学, 2002.
[172] Qin Q., Song C. C. S., Arndt R. E. A.,“An numerical study of an unsteady turbulent wake behind a cavitating hydrofoil”, Fifth International Symposium on Cavitation, Osaka, Japan, November, 2003.
[173]权晓波,李岩,魏海鹏等,“大攻角下轴对称航行体空化流动特性试验研究”,水动力学研究与进展, A辑, 2008, Vol. 23, No. 6, pp. 662-667.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |