正交分解法:涡流流体动力学应用的正交分解法:英文

本书是一部英文版的应用数学专著。在旋进流形式下产生的流体动力不稳定性，称为涡流，在Francis水轮机尾水管的壁面上产生高压不稳定波动，导致了包括疲劳损坏在内的比较差的涡轮性能.该现象的建模和这个涡流系统的流体动力学不稳定性的数值研究是本书调研的任务.作为经典方法的替代方法，本书呈现了一种新的涡流流体解析法，该方法基于最近的一种具有正交分解的谱配置的数学方法.本书呈现的数学模型可以恢复水轮机特性预测中的信息，而无须计算三维的不稳定流.本书提供了有价值的工具，可以在流道设计的早期阶段评估非设计运行状态下的水轮机性能.本书提供的数学工具为解决现代科学中出现的跨学科问题提供了可转移的知识，这些知识可以应用于许多不同的学科之中。本书共分为10章.第1章采用计算机辅助的并行和分布式计算技术，为研究Francis水轮机涡流的流体动力稳定性提供了动力.第2章概述了涡流流体动力学的线性稳定性分析。第3章为Francis涡轮的涡流顺流而下的数学模型.第4章介绍了谱方法在未来的数值稳定性算法中的应用，还介绍了稳定性特征值问题的计算方法，以及多项式检验函数的新的正交基。第5章介绍了用于非轴对称稳定性研究的一种边界适应的径向光谱近似.第6章提出了一种改进的基于正交分解的L投影方法，用于轴对称和弯曲模式的稳定性研究.第7章提出了一种基于谱描述符技术的并行计算方法，用于分析具有复杂边界条件的旋流流体力学稳定性.第8章通过现有的关于已知速度剖面的旋流系统的稳定性研究验证了新谱算法.第9章展示了在Windows操作系统丛上并行研究和分布式研究涡流模型的结果。第10章为结论，并概述了未来的工作。

   1 Introduction

2 Mathematical issues on hydrodynamic stability of swirling flows

2.1 Linearized disturbance equations

2.2 The method of normal modes analysis

2.3 Definition of temporal and spatial instability

2.4 Studies upon stability of swirling flows cited in literature

3 Mathematical model for a swirling system - a Francis turbine runner case

3.1 Discrete operator formulation of the hydrodynamic model

3.2 Axis and wall boundary conditions

4 Orthngonal decomposition method for stability eigenvalue problems

4.1 Motivation of using the spectral methods in hydrodynamic stability problems

4.1.1 The L2 -Projection method

4.1.2 The collocation method

4.2 0rthogonal polynomial decomposition base

4.2.1 Considerations on shifted Chebyshev polynomials

4.2.2 Orthogonality of the shifted Chebyshev polynomials

4.2.3 Evaluation of the shifted Chebyshev derivatives

4.3 Computational domain and grid setup

5 Numerical approach for non-axisymmetrie stability investigation

5.1 Boundary adapted decomposition

5.1.1 Description of the method

5.1.2 Interpolative derivative matrix

5.1.3 Implementation of the boundary adapted decomposition

5.2 Summary of this chapter

6 Numerical approach for axisymmetric and bending modes stability investigation

6.1 A modified L2-Projection method based on orthogonal decomposition

6.1.1 Description of the method

6.1.2 Implementation of the projection method using symbolic and numeric conversions

6.2 Summary of this chapter

7 Spectral descriptor technique for hydrodynamic stability of swirling flows

7.1 The analytical investigation of the eigenvalue problem

7.2 Numerical approach based on collocation technique

7.2.1 Interpolative derivative operator

7.2.2 Parallel implementation of the spectral collocation algorithm

7.3 Summary of this chapter

8 Validation of the numerical procedures on a Q-vortex problem

8.1 The Q-vortex profile

8.2 Radial boundary adapted method validation and results

8.3 L2 -Projection method validation and results

8.4 Spectral descriptor method validation and results

8.5 Comparative results

9 Parallel and distributed investigation of the vortex rope model

9.1 Considerations about parallel computing

9.2 Theoretical model and computational domain

9.3 Influence of discharge coefficient on hydrodynamic stability

9.3.1 Investigation of axisymmetric mode

9.3.2 Investigation of bending modes

9.4 Study of absolute and convective instability of the swirl system with discrete velocity profiles

9.4.1 Computational aspects

9.4.2 Validations with experimental results

9.5 Accuracy and convergence of the algorithm

9.6 Evaluation of the parallel algorithm performance

9.7 Summary of this chapter

10 Conclusions

10.1 Book summary

10.2 Final remarks

Bibliography and references