螺旋桨性能预报的速度势面元法研究
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摘要
船舶螺旋桨的设计和性能计算一直是流体力学领域中非常重要的课题之一。由于螺旋桨理论设计计算方法具有传统方法无可比拟的灵活性和适应性，同时，通过理论计算方法对螺旋桨的水动力性能进行准确的预报，对于避免不良设计所带来振动和噪声，进一步提高螺旋桨的效率、改善螺旋桨性能有着重要的意义。因此，本文从升力面理论入手，对应用理论方法的螺旋桨性能预报进行了较为深入的研究。文章的重点放在了应用低阶速度势面元法预报螺旋桨性能及压力分布上，并对现有的面元方法进行了改进，提出了考虑局部流场特性的B样条网格面元计算方法，同时改进了现有的尾涡模型。
尾涡模型一直是螺旋桨理论设计和计算方法中最为关键的问题之一，尾涡模型的好坏直接决定了螺旋桨性能预报结果的准确程度。但是由于尾涡问题的复杂性，很难获得精确的尾涡几何形状，基于这个原因，本文对升力面涡格法的传统经验尾涡模型进行了改进，在解析尾涡模式的基础上，提出了一种新的尾涡近似方法。在过渡区，尾涡在选定扇形截面上解析地求出，在其它处通过非线性插值求得，计算中利用了解析尾涡的特点同时减少了计算量。根据流体连续性方程确定尾涡的收缩半径，避免了梢涡半径的不收敛性，为螺旋桨设计和非设计工况下螺旋桨性能计算提供了一种有效的尾涡近似计算方法。
在应用低阶速度势面元法求解螺旋桨正问题的过程中，桨叶和桨毂表面离散为四边形双曲面元，在每个面元上布置强度相等的源汇和偶极子，螺旋桨尾涡面也离散为布置等强度偶极子的四边形双曲面元。在充分考虑了横向流动对三维升力体的影响作用的前提下，对随边压力相等的非线性库塔条件进行了研究，而面元影响系数通过Morino导出的解析公式计算得到。同时，应用新的方法获得尾涡模型，在采用经验尾涡模型的基础上，应用动量矩定理通过数值迭代并对个别尾涡参数进行确定，使其更适合重载螺旋桨的性能。通过大量的计算实例，验证了本文计算方法及程序的有效性和适用性。
传统的面元法均采用等半径的网格划分方式，但是这种处理方法并不能够反应螺旋桨表面的流场特性。因此，本文在考虑螺旋桨表面流场特性的前提下，采用B样条网格划分方法对桨叶表面单元进行剖分。弦向网格线在桨叶导边处与外轮廓线正交，在随边处与流体的速度方向相一致。同时，在考虑流场特性的基础上，对尾涡模型进行了改进，使得尾涡在离开桨叶随边处的方向与当地流动方向基本一致。计算表明，基于流场特性的B样条网格速度势面元法不仅可以减少迭代次数，改善了程序的收敛性，而且在很大程度上提高了螺旋桨导边附近的压力预报精度，具有较好的数值稳定性。
The design and performance calculation of marine propellers have increasingly become fundamental goals for both researchers and designers in the field of fluid mechanics. As the theoretical methods have better flexibility and adaptability for marine propeller design and performance calculation compared with conventional methods, it is significant to predict the hydrodynamic performance accurately in order to avoid vibration and noise brought by poor design, increase propeller efficiency and improve propeller performance. Therefore, how to make an accurate prediction of the hydrodynamic performance for marine propeller is a promising topic. In present paper, the investigation for theoretical methods including lifting surface method and surface panel method is carried out and special attention is paid to the potential-based low order panel method, which is used to predict the hydrodynamic performance and pressure distribution of marine propeller. A new grid arrangement with the local flow characteristics taken into consideration is proposed and a new trailing wake model is applied compared with existing ones.
The trailing wake model is one of the most important issues in the process of propeller design and numerical calculation, and it has great effect on the precision of prediction results to some extent. However, the complexity of the problem retards the determination of the wake geometry accurately. For this reason, an improvement of wake model is made for the numerical procedure by using vortex lattice method. In the transition wake region, wake vortex is determined by aligning the vortex line with streamline. New numerical methods are adopted to reduce the numerical calculations and wake vortex radii are determined on the basis of continuity equation of in-compressible fluid to avoid the divergence of the tip vortex radius. New wake vortex model provides new numerical methods for the propeller design and propeller off-design analysis.
When the low order surface panel method is used to solve the direct problem of propeller, both the propeller blades and hub are approximated by a number of hyperbolical quadrilateral panels with constant source and dipole distribution, while the trailing wake surface is represented by hyperbolical quadrilateral panels with only constant dipoles on them. Special emphasis has been considered to meet Kutta condition, which is used to ensure pressure equivalency on the panels at trailing edges and the cross flow component is taken into account for its significant effect on three dimensional problems. The influence coefficients are
尾涡模型一直是螺旋桨理论设计和计算方法中最为关键的问题之一，尾涡模型的好坏直接决定了螺旋桨性能预报结果的准确程度。但是由于尾涡问题的复杂性，很难获得精确的尾涡几何形状，基于这个原因，本文对升力面涡格法的传统经验尾涡模型进行了改进，在解析尾涡模式的基础上，提出了一种新的尾涡近似方法。在过渡区，尾涡在选定扇形截面上解析地求出，在其它处通过非线性插值求得，计算中利用了解析尾涡的特点同时减少了计算量。根据流体连续性方程确定尾涡的收缩半径，避免了梢涡半径的不收敛性，为螺旋桨设计和非设计工况下螺旋桨性能计算提供了一种有效的尾涡近似计算方法。
在应用低阶速度势面元法求解螺旋桨正问题的过程中，桨叶和桨毂表面离散为四边形双曲面元，在每个面元上布置强度相等的源汇和偶极子，螺旋桨尾涡面也离散为布置等强度偶极子的四边形双曲面元。在充分考虑了横向流动对三维升力体的影响作用的前提下，对随边压力相等的非线性库塔条件进行了研究，而面元影响系数通过Morino导出的解析公式计算得到。同时，应用新的方法获得尾涡模型，在采用经验尾涡模型的基础上，应用动量矩定理通过数值迭代并对个别尾涡参数进行确定，使其更适合重载螺旋桨的性能。通过大量的计算实例，验证了本文计算方法及程序的有效性和适用性。
传统的面元法均采用等半径的网格划分方式，但是这种处理方法并不能够反应螺旋桨表面的流场特性。因此，本文在考虑螺旋桨表面流场特性的前提下，采用B样条网格划分方法对桨叶表面单元进行剖分。弦向网格线在桨叶导边处与外轮廓线正交，在随边处与流体的速度方向相一致。同时，在考虑流场特性的基础上，对尾涡模型进行了改进，使得尾涡在离开桨叶随边处的方向与当地流动方向基本一致。计算表明，基于流场特性的B样条网格速度势面元法不仅可以减少迭代次数，改善了程序的收敛性，而且在很大程度上提高了螺旋桨导边附近的压力预报精度，具有较好的数值稳定性。
The design and performance calculation of marine propellers have increasingly become fundamental goals for both researchers and designers in the field of fluid mechanics. As the theoretical methods have better flexibility and adaptability for marine propeller design and performance calculation compared with conventional methods, it is significant to predict the hydrodynamic performance accurately in order to avoid vibration and noise brought by poor design, increase propeller efficiency and improve propeller performance. Therefore, how to make an accurate prediction of the hydrodynamic performance for marine propeller is a promising topic. In present paper, the investigation for theoretical methods including lifting surface method and surface panel method is carried out and special attention is paid to the potential-based low order panel method, which is used to predict the hydrodynamic performance and pressure distribution of marine propeller. A new grid arrangement with the local flow characteristics taken into consideration is proposed and a new trailing wake model is applied compared with existing ones.
The trailing wake model is one of the most important issues in the process of propeller design and numerical calculation, and it has great effect on the precision of prediction results to some extent. However, the complexity of the problem retards the determination of the wake geometry accurately. For this reason, an improvement of wake model is made for the numerical procedure by using vortex lattice method. In the transition wake region, wake vortex is determined by aligning the vortex line with streamline. New numerical methods are adopted to reduce the numerical calculations and wake vortex radii are determined on the basis of continuity equation of in-compressible fluid to avoid the divergence of the tip vortex radius. New wake vortex model provides new numerical methods for the propeller design and propeller off-design analysis.
When the low order surface panel method is used to solve the direct problem of propeller, both the propeller blades and hub are approximated by a number of hyperbolical quadrilateral panels with constant source and dipole distribution, while the trailing wake surface is represented by hyperbolical quadrilateral panels with only constant dipoles on them. Special emphasis has been considered to meet Kutta condition, which is used to ensure pressure equivalency on the panels at trailing edges and the cross flow component is taken into account for its significant effect on three dimensional problems. The influence coefficients are
引文
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