PSE方法在叶片表面流动稳定性预测中的应用研究
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摘要
针对在叶轮机械内对效率影响显著的边界层转捩问题,本文结合已有的风洞实验数据,通过求解PSE方程,给出了一套可有效分析、预测、评价边界层稳定性的数值求解方法。
本文推导了正交曲线坐标系下稳定性PSE方程,使稳定性方程扩展为适合叶轮机械表面型线的正交曲线坐标系计算,并给出了稳定性方程离散和数值差分求解的方式。在现有叶栅叶片表面静压分布实验数据基础上,结合曲线坐标系下Falkner- Skan- Cooke方程求解叶栅表面边界层的平均流动解。将求解结果作为初值带入到稳定方程中。编制了整个求解过程的计算程序。稳定性方程特征值求解分别采用全局法和区域法方法。应用eN模型作为边界层转捩预测和稳定性比较的数值判据以评定叶栅内边界层流动的稳定性。并将以上算法应用于透平和压气机叶片表面边界层稳定性分析中。
本文计算分析了600Mw超临界汽轮机高压第八级汽轮机动叶及静叶两套叶栅吸力面边界层流动的稳定性及变冲角性能,两套叶栅均采用后部加载叶型。稳定性分析表明,在涡轮叶栅中,叶栅中部流动最为稳定,而两端壁附近的流动相对不稳定。
通过分析后部加载叶栅的变冲角特性,可以发现,当冲角改变后,叶栅两端壁边界层所受的影响最为显著,而叶栅中部边界层几乎不随冲角变化。由此看来,采用后部加载叶型,使叶片吸力面压力点移到60%轴向弦长之后,可有效推迟转捩发生,提高叶栅表面边界层稳定性,以及削弱叶栅的冲角对气流变化的敏感性。
为了研究来流条件变化对调节级喷嘴叶栅边界层稳定性的影响,计算了600Mw超临界汽轮机调节级喷嘴叶栅边界层流动的稳定性。结果表明,外界条件的改变在很大程度上影响叶栅表面边界层流动的稳定性。当来流速度增加时,雷诺数会随之增加,并导致流动稳定性变差。若通过改变叶栅几何尺寸,保持雷诺数不变,只增加马赫数,来流马赫数的增加会在一定程度上提高流动稳定性。另外,来流扰动频率也是影响叶栅边界层稳定性的重要因素。当扰动频率发生变化时,存在一个扰动放大率的最大极值点,在极值点附近扰动最容易放大,边界层也最容易发生转捩。
本文还探讨了在常见叶栅的改型设计中,二次流的变化对边界层流动稳定性影响。在对具有大扩张角外端壁的涡轮静叶栅的流动稳定性计算中发现,在该类涡轮静叶栅中,具有大扩张角的外端会引起叶栅顶部边界层增厚,转捩甚至分离,降低叶顶附近流动的稳定性。在该类涡轮静叶栅中如果叶顶采用前掠叶片,可削弱外端壁大子午扩张角对叶片顶部区域流动产生的不利影响。
本文最后讨论了叶片弯曲对扩压叶栅壁面边界层流动稳定性的影响,分析了直叶片和具有不同弯曲角的弯叶片叶栅的吸力面和压力面边界层流动的稳定性。结果表明在压气机中采用弯叶片,可改善压气机叶栅吸力面两端边界层流动,同时会降低吸力面中部边界层流动的稳定性。只有合理匹配选择弯叶片才能有效提高叶栅的整体性能。
The transition of boundary layer from laminar to turbulent plays an important role in turbine machine. Solving Parabolized Stability Equations(PSE), a numerical method is presented in this dissertation, which is based on wind tunnel experiment date to analyze, predict and estimate the boundary flow stability.
A stability PSE equation is developed in the dissertation. In order to generalize the equation for geometries with curved blade surfaces, an orthogonal curvilinear coordinate system is introduced. The numerical discretization and the finite diffence scheme are both proposed. Based on experiment date of blade surface pressure distribution, the mean parameters of the boundary flow can be solved with the Falkner- skan- Cooke equation in curvilinear coorinate system. The results are then used to be the initial parameters for the stability equations. Numercal solution codes are developed, in which the global and local methods are both used. The eN method is used for the criterion of the boundary flow stability and transition prediction in the blade cascade boundary flow stability problem. All of these methods can be used in stability analysis of both tubine and compressor blades.
The off-design performances of stator and rotor blades in the 8th stage of 600Mw supercritical steam turbine and their boundary flow stabilities are all analyzed in this dissertation. Two sets of blades are both aft-loaded profile. It is shown in the result that the flow at the mid span of blade is relatively steady, while the flow near the endwall is relatively unstable.
To analyze the influence of incoming flow on the boundary layer stability, computation is performed in the governing-stage guide vane of 600Mw super-critical steam. It is shown that when the incidence is changed, the boundary flow near the endwall is remarkably affected, but the flow at the mid span is not changed conspicuously. These results indicate that using aft-loaded cascade, the lowest pressure point on blade suction surface is moved to be about 60% axial chord, the transition is put off, the stability of cascade surface is enhanced and the incidence sensitivity is weakend effectively.
In order to investigate the influence of external flow parameter on the boundary flow stability, the blade surface boundary flow stability of the governing-stage guide vane in 600Mw supercritical steam turbine is computated. It is shown in the result that the disturbance of external flow patameter clearly affects the stability of the blade surface flow. When inlet flow velocities are increased, the Reynold number is increased also. The increase of the Reynold number leads to the decrease of the flow stability. If increasing the inlet Mach number and keeping the Reynold number constant, the stability should be increased with the Mach number. Furthermore, the external disturbing frequency is important influencing factors of stability. When the disturbing frequency is changed, there exists a local maximal disturbing magnification. Near this point the disturbance is easily magnified, so the flow transition is easy to occur.
The influence of the second flow on the boundary flow stability in general designed blade is also discussed in this dissertation. From the computation of the boundary flow stability in the diffused meridional flow passage, it is found that the difussed meridional passage thickens the boundary flow in the blade tip and discreases the flow stability there. If the forwardly swept blade is used, the negative effect on stability in blade tip is able to be descreased.
Finally, the effect of boundary flow stability in a diffuser cascade with bowed blade is discussed. The boundary flow stabilities on the suction and pressure surfaces in both the straight and bowed blades are solved. It is shown that the boundary flow stability near the endwall of the bowed blade suction surface is enhanced, but that at the mid span is reduced. So the performence of cascade can be enhanced by selecting appropriate bowed angles.
本文推导了正交曲线坐标系下稳定性PSE方程,使稳定性方程扩展为适合叶轮机械表面型线的正交曲线坐标系计算,并给出了稳定性方程离散和数值差分求解的方式。在现有叶栅叶片表面静压分布实验数据基础上,结合曲线坐标系下Falkner- Skan- Cooke方程求解叶栅表面边界层的平均流动解。将求解结果作为初值带入到稳定方程中。编制了整个求解过程的计算程序。稳定性方程特征值求解分别采用全局法和区域法方法。应用eN模型作为边界层转捩预测和稳定性比较的数值判据以评定叶栅内边界层流动的稳定性。并将以上算法应用于透平和压气机叶片表面边界层稳定性分析中。
本文计算分析了600Mw超临界汽轮机高压第八级汽轮机动叶及静叶两套叶栅吸力面边界层流动的稳定性及变冲角性能,两套叶栅均采用后部加载叶型。稳定性分析表明,在涡轮叶栅中,叶栅中部流动最为稳定,而两端壁附近的流动相对不稳定。
通过分析后部加载叶栅的变冲角特性,可以发现,当冲角改变后,叶栅两端壁边界层所受的影响最为显著,而叶栅中部边界层几乎不随冲角变化。由此看来,采用后部加载叶型,使叶片吸力面压力点移到60%轴向弦长之后,可有效推迟转捩发生,提高叶栅表面边界层稳定性,以及削弱叶栅的冲角对气流变化的敏感性。
为了研究来流条件变化对调节级喷嘴叶栅边界层稳定性的影响,计算了600Mw超临界汽轮机调节级喷嘴叶栅边界层流动的稳定性。结果表明,外界条件的改变在很大程度上影响叶栅表面边界层流动的稳定性。当来流速度增加时,雷诺数会随之增加,并导致流动稳定性变差。若通过改变叶栅几何尺寸,保持雷诺数不变,只增加马赫数,来流马赫数的增加会在一定程度上提高流动稳定性。另外,来流扰动频率也是影响叶栅边界层稳定性的重要因素。当扰动频率发生变化时,存在一个扰动放大率的最大极值点,在极值点附近扰动最容易放大,边界层也最容易发生转捩。
本文还探讨了在常见叶栅的改型设计中,二次流的变化对边界层流动稳定性影响。在对具有大扩张角外端壁的涡轮静叶栅的流动稳定性计算中发现,在该类涡轮静叶栅中,具有大扩张角的外端会引起叶栅顶部边界层增厚,转捩甚至分离,降低叶顶附近流动的稳定性。在该类涡轮静叶栅中如果叶顶采用前掠叶片,可削弱外端壁大子午扩张角对叶片顶部区域流动产生的不利影响。
本文最后讨论了叶片弯曲对扩压叶栅壁面边界层流动稳定性的影响,分析了直叶片和具有不同弯曲角的弯叶片叶栅的吸力面和压力面边界层流动的稳定性。结果表明在压气机中采用弯叶片,可改善压气机叶栅吸力面两端边界层流动,同时会降低吸力面中部边界层流动的稳定性。只有合理匹配选择弯叶片才能有效提高叶栅的整体性能。
The transition of boundary layer from laminar to turbulent plays an important role in turbine machine. Solving Parabolized Stability Equations(PSE), a numerical method is presented in this dissertation, which is based on wind tunnel experiment date to analyze, predict and estimate the boundary flow stability.
A stability PSE equation is developed in the dissertation. In order to generalize the equation for geometries with curved blade surfaces, an orthogonal curvilinear coordinate system is introduced. The numerical discretization and the finite diffence scheme are both proposed. Based on experiment date of blade surface pressure distribution, the mean parameters of the boundary flow can be solved with the Falkner- skan- Cooke equation in curvilinear coorinate system. The results are then used to be the initial parameters for the stability equations. Numercal solution codes are developed, in which the global and local methods are both used. The eN method is used for the criterion of the boundary flow stability and transition prediction in the blade cascade boundary flow stability problem. All of these methods can be used in stability analysis of both tubine and compressor blades.
The off-design performances of stator and rotor blades in the 8th stage of 600Mw supercritical steam turbine and their boundary flow stabilities are all analyzed in this dissertation. Two sets of blades are both aft-loaded profile. It is shown in the result that the flow at the mid span of blade is relatively steady, while the flow near the endwall is relatively unstable.
To analyze the influence of incoming flow on the boundary layer stability, computation is performed in the governing-stage guide vane of 600Mw super-critical steam. It is shown that when the incidence is changed, the boundary flow near the endwall is remarkably affected, but the flow at the mid span is not changed conspicuously. These results indicate that using aft-loaded cascade, the lowest pressure point on blade suction surface is moved to be about 60% axial chord, the transition is put off, the stability of cascade surface is enhanced and the incidence sensitivity is weakend effectively.
In order to investigate the influence of external flow parameter on the boundary flow stability, the blade surface boundary flow stability of the governing-stage guide vane in 600Mw supercritical steam turbine is computated. It is shown in the result that the disturbance of external flow patameter clearly affects the stability of the blade surface flow. When inlet flow velocities are increased, the Reynold number is increased also. The increase of the Reynold number leads to the decrease of the flow stability. If increasing the inlet Mach number and keeping the Reynold number constant, the stability should be increased with the Mach number. Furthermore, the external disturbing frequency is important influencing factors of stability. When the disturbing frequency is changed, there exists a local maximal disturbing magnification. Near this point the disturbance is easily magnified, so the flow transition is easy to occur.
The influence of the second flow on the boundary flow stability in general designed blade is also discussed in this dissertation. From the computation of the boundary flow stability in the diffused meridional flow passage, it is found that the difussed meridional passage thickens the boundary flow in the blade tip and discreases the flow stability there. If the forwardly swept blade is used, the negative effect on stability in blade tip is able to be descreased.
Finally, the effect of boundary flow stability in a diffuser cascade with bowed blade is discussed. The boundary flow stabilities on the suction and pressure surfaces in both the straight and bowed blades are solved. It is shown that the boundary flow stability near the endwall of the bowed blade suction surface is enhanced, but that at the mid span is reduced. So the performence of cascade can be enhanced by selecting appropriate bowed angles.
引文
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