转/静交界面处理方法研究及涡轮结构与气动分析
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摘要
本文分两部分,第一部分是转/静交界面处理方法的研究。在对叶轮机械进行数值模拟时,转/静交界面的处理是十分关键的。研究不同的交界面处理方法对计算结果的影响,对于提高叶轮机械数值模拟的精度和效率具有重大意义。过去的二十年里,国内外的学者们提出了一系列交界面的处理方法,并在CFD商用软件中得到了广泛地应用。本文研究的主要目的是,系统地比较不同交界面处理方法对计算结果的影响,为叶轮机数值模拟交界面处理方法的选择提供参考依据。
为了实现上述研究目的,本文的工作从以下几个步骤展开:
1)作为整个研究的理论基础,对混合面法(Mixing Plane)、冻结转子法(Frozen Rotor)、滑移面法(Sliding Plane)几种应用较为广泛的交界面处理方法进行详细的介绍。
2)发挥二维数值计算速度快的优势,对某型冲压涡轮叶中截面叶栅进行数值模拟,比较不同交界面处理方法对计算结果的影响。结果表明,采用混合面处理交界面时,叶栅的气流转角和总压恢复系数都要比滑移面的要大,而且随着周向间距和相对转速的减小,两者的差异越来越大。
3)对冲压涡轮进行三维数值模拟,比较不同交界面处理方法对涡轮的总体性能计算结果的影响。结果表明,不同的交界面处理方法对流量和总压比没有明显的影响,但是对效率有一定的影响。转速越低,效率的差异越大;尤其是当涡轮的工作状态接近不稳定边界时,效率的差异更大。
4)选取NASA STAGE35作为研究对象,分析不同交界面处理方法对压气机总体性能计算结果的影响。不同的交接面处理方法总压比的计算结果差别较小,但是效率的计算结有差异较大。随着转速和流量的减小,不同交界面处理方法所得计算结果的差异越来越大。将数值计算的结果同实验数据进行比较,发现采用滑移面法和冻结转子法处理交界面时,计算结果比混合面法更接近实验值。
通过以上计算,说明在对涡轮一类叶轮机械进行数值模拟时,交界面的处理方法对计算结果的影响不大。采用混合面法处理转静交界面的定常计算,不仅计算精度和非定常计算差别很小,而且计算速度快。在对压气机一类作功的叶轮机械进行数值模拟时,交界面处理方法的选择对计算结果的影响较大。采用冻结转子法处理转/静交界面可以达到同非定常计算同样的精度,而且花费的时间要少。
论文的第二部分是涡轮结构与气动分析。文中提出了一种根据叶型坐标数据,求解叶型的几何参数的算法。首先对测绘数据进行三次样条密集插值,然后求出叶型的中弧线,并通过最小二乘法对中弧线进行修正,最后得出叶型的各项几何参数。通过对冲压涡轮静子和转子叶片上几个型面几何参数的求解,验证了这种算法的可行性。
This paper consists of two parts. The frist part is the investigation on rotor/stator interface processing method. The processing method of the rotor/stator interface is the key in numerical simulation of turbomachinery. To improve the precision and efficiency of turbomachinery simulation, it’s of great important to investigate the influence of different interface processing method to the simulation result. In the past twenty years, researchers gave series of approach to simulate the interface, which was extendly used in various CFD software. This dissertation is aimed towards comparing the computing result of different rotor/stator interface processing method, providing reference for the choice of interface processing method in turbomachinery numerical simulation.
For the sake of realization research purpose above, this dissertation is organized as follow:
1) As the theories foundation of whole dissertation, sever different approaches, such as mixing plane, frozen rotor, sliding plane are introduced in detail.
2) Take advantage of fast speed of 2d numerical simulation, flow field of middle section of turbine blade is simulated, and apply different approaches to simulate the rotor/stator interface. Result show that when apply mixing plane method, flow turning angle and total pressure recovery coefficient are bigger than sliding plane method. The difference of result becomes larger when the gap and translation speed turn small.
3) The detailed numerical simulation on a ram turbine is done, anaysis the influence of different rotor/stator interface processing method to numerical result of the tubine’s overall performance. The result show that interface treatment have no significant effect on flow mass and total pressure ratio, but have certain effect on stage efficiency. The faster the rotation speed, the larger the difference of effciency. Especially when working state is located near the instability boundary, the difference became even larger.
4) Take the NASA STAGE35 as study object, anaysis the influence of different rotor/stator interface treatment to numerical result of the compressor’s overall performance. Study imply that when the interface is simulate by frozen rotor or sliding plane method, the numerical result agreed well with experimental test data for overall performance than mixing plane method. When take mixing plane method to simulate interface, the efficiency is biger than test data, and the tatal pressure ratio is smaller than test data. In addition, the difference of numerical result of different interface treatment becomes larger, when the flow mass and rotating speed become low.
Through the above research, we find that the rotor/stator interface treatment have no significant effect on the numerical result of turbine. The steady computation,which uses mixing plane method to simulate the interface, not only can get the precision as unsteady computation, but also calculate fast. On the other hand, the rotor/stator interface treatment has a great influence on the numerical result of the compressor. Making use of frozen rotor model to simulate the interface, the precision is high than mixing plane, and the computation speed is faster than sliding plane.
The second part of thi.s paper is the analysis of configuration and aerodynamic character. In the paper, a new algorithm is applied to calculate the geometric parameters of blade profile according to the surveying data of the blade profile. Fristly, reviews cubic spline curve of interpolation on the surveying data, then obtain the central arced curve of the blade section, correct the central arced curve with least square method, at last calculate various geometric parameters of the blade. By solving the geometric parameters of a ram tubine, feasibility of the algorithm is validated.
为了实现上述研究目的,本文的工作从以下几个步骤展开:
1)作为整个研究的理论基础,对混合面法(Mixing Plane)、冻结转子法(Frozen Rotor)、滑移面法(Sliding Plane)几种应用较为广泛的交界面处理方法进行详细的介绍。
2)发挥二维数值计算速度快的优势,对某型冲压涡轮叶中截面叶栅进行数值模拟,比较不同交界面处理方法对计算结果的影响。结果表明,采用混合面处理交界面时,叶栅的气流转角和总压恢复系数都要比滑移面的要大,而且随着周向间距和相对转速的减小,两者的差异越来越大。
3)对冲压涡轮进行三维数值模拟,比较不同交界面处理方法对涡轮的总体性能计算结果的影响。结果表明,不同的交界面处理方法对流量和总压比没有明显的影响,但是对效率有一定的影响。转速越低,效率的差异越大;尤其是当涡轮的工作状态接近不稳定边界时,效率的差异更大。
4)选取NASA STAGE35作为研究对象,分析不同交界面处理方法对压气机总体性能计算结果的影响。不同的交接面处理方法总压比的计算结果差别较小,但是效率的计算结有差异较大。随着转速和流量的减小,不同交界面处理方法所得计算结果的差异越来越大。将数值计算的结果同实验数据进行比较,发现采用滑移面法和冻结转子法处理交界面时,计算结果比混合面法更接近实验值。
通过以上计算,说明在对涡轮一类叶轮机械进行数值模拟时,交界面的处理方法对计算结果的影响不大。采用混合面法处理转静交界面的定常计算,不仅计算精度和非定常计算差别很小,而且计算速度快。在对压气机一类作功的叶轮机械进行数值模拟时,交界面处理方法的选择对计算结果的影响较大。采用冻结转子法处理转/静交界面可以达到同非定常计算同样的精度,而且花费的时间要少。
论文的第二部分是涡轮结构与气动分析。文中提出了一种根据叶型坐标数据,求解叶型的几何参数的算法。首先对测绘数据进行三次样条密集插值,然后求出叶型的中弧线,并通过最小二乘法对中弧线进行修正,最后得出叶型的各项几何参数。通过对冲压涡轮静子和转子叶片上几个型面几何参数的求解,验证了这种算法的可行性。
This paper consists of two parts. The frist part is the investigation on rotor/stator interface processing method. The processing method of the rotor/stator interface is the key in numerical simulation of turbomachinery. To improve the precision and efficiency of turbomachinery simulation, it’s of great important to investigate the influence of different interface processing method to the simulation result. In the past twenty years, researchers gave series of approach to simulate the interface, which was extendly used in various CFD software. This dissertation is aimed towards comparing the computing result of different rotor/stator interface processing method, providing reference for the choice of interface processing method in turbomachinery numerical simulation.
For the sake of realization research purpose above, this dissertation is organized as follow:
1) As the theories foundation of whole dissertation, sever different approaches, such as mixing plane, frozen rotor, sliding plane are introduced in detail.
2) Take advantage of fast speed of 2d numerical simulation, flow field of middle section of turbine blade is simulated, and apply different approaches to simulate the rotor/stator interface. Result show that when apply mixing plane method, flow turning angle and total pressure recovery coefficient are bigger than sliding plane method. The difference of result becomes larger when the gap and translation speed turn small.
3) The detailed numerical simulation on a ram turbine is done, anaysis the influence of different rotor/stator interface processing method to numerical result of the tubine’s overall performance. The result show that interface treatment have no significant effect on flow mass and total pressure ratio, but have certain effect on stage efficiency. The faster the rotation speed, the larger the difference of effciency. Especially when working state is located near the instability boundary, the difference became even larger.
4) Take the NASA STAGE35 as study object, anaysis the influence of different rotor/stator interface treatment to numerical result of the compressor’s overall performance. Study imply that when the interface is simulate by frozen rotor or sliding plane method, the numerical result agreed well with experimental test data for overall performance than mixing plane method. When take mixing plane method to simulate interface, the efficiency is biger than test data, and the tatal pressure ratio is smaller than test data. In addition, the difference of numerical result of different interface treatment becomes larger, when the flow mass and rotating speed become low.
Through the above research, we find that the rotor/stator interface treatment have no significant effect on the numerical result of turbine. The steady computation,which uses mixing plane method to simulate the interface, not only can get the precision as unsteady computation, but also calculate fast. On the other hand, the rotor/stator interface treatment has a great influence on the numerical result of the compressor. Making use of frozen rotor model to simulate the interface, the precision is high than mixing plane, and the computation speed is faster than sliding plane.
The second part of thi.s paper is the analysis of configuration and aerodynamic character. In the paper, a new algorithm is applied to calculate the geometric parameters of blade profile according to the surveying data of the blade profile. Fristly, reviews cubic spline curve of interpolation on the surveying data, then obtain the central arced curve of the blade section, correct the central arced curve with least square method, at last calculate various geometric parameters of the blade. By solving the geometric parameters of a ram tubine, feasibility of the algorithm is validated.
引文
[1] Wu C.H.,A general theory of Three-Dimensional Flow in Subsonic and Supersonic Turbomachines of Axial, Radial and Mix-Flow Types, NACA TN 2604, 1952
[2] Denton J.D., The Use of a Distributed Body Force to Simulate Viscous Flow in 3D Calculations, ASME Paper 86-GT-144, 1986
[3] Rai M.M., Three Dimensional Navier-Stokes Simulations of Turbine Rotor-Stator Interaction, J.Propulsion, 1989, 5(3)
[4] Dawes W.N., Application of Full Navier-Stokes Turbomachine Flow Problem, VKI Letures Series 2, Numerical Techniques for Viscous Flow Calculation in Turbomachinery Bladings, 1986
[5] Dawes W.N., The Extension of a Solution-Adaptive Three-Dimensional Navier-Stokes Solver Toward Geometries of Arbitrary ComPlexity Transaction of ASME, J.of Turbomaehinery, Vol.115.No.2, 1993, PP:283-295/
[6]陈乃兴,张丰显,应用非正交曲线坐标表示的任意回转流面叶栅粘性气体流动的完全N-S方程求解,中国科学, A辑, vol.8, 1984
[7]蒋滋康,袁新,跨音速叶栅中实际流动的数值试验,中国工程热物理学会第五届会议论文集, No,852066,1985
[8]周新海,朱方元,应用Navier-Stockes方程的叶栅粘性流场数值分析,工程热物理学报, 1988, 9(3):230-235
[9] Gallus H.E., Grollius H.W., Lambertz J.,The Influence of Blade Number Ratio and Blade Row Spacing on Axial-Flow Compressor Stator Blade Dynamic Load and Stage Sound Pressure Level, ASME Paper 81-GT-165, Houston, 1981
[10] Evans R.J., Boundary Layer Development on Axis-Flow Turbomachinery Blading, Pumps:Analysis,design and application, Volume 1, Worthington Pump, Inc,1978:1-15
[11] Denton J.D., The Calculation of Three-Dimensional Viscous Flow Through Multistage Turbomachines, Journal of Turbomachinery, 1992, January, Vol.114
[12] Dawes W.N., Unsteady Flow and Loss Production in Centrifugal and Axial Compressor Stages, Von Karmaa Institute for Fluid Mechanics Lecture Series, 1994, June
[13] Rai M.M., Applications of Domain Decomposition Methods To Turbomachiner Flows. ASME Advances and Applications in Computational Fluid Dynamics, 1988, January,Vol.66
[14] Erdos J.L., Ahner E., McNally W., Numerlcal Solution of Periodic Transonic Flow Through a Fan Stage. AIAA Journal,1977,15,11,1559-1568
[15] Giles M., A Numerical Method for Unsteady Inviscid Flow in Turbomachinery,GTL Report# 193,1988
[16] Rai M.M., Unsteady Three-Dimensional Navier-Stokes Simulations of Turbomachine Rotor/Stator Interaction ,AIAA Paper 87-2058
[17] Rai M.M., Three-Dimensional Navier-Stokes Simulation of Turbine Rotor-Staor Interaction, NASA Technical Memorandum, 1988, March
[18] Brost V., Ruprecht A., Maih?fer M., Rotor/Stator Interactions in an Axial Turbine,A Comparion of Transient And Steady State Frozen Rotor Simuations, Institute for Fluid Mechanics and Hydraulic Machinery, University of Stuttgart, Germany
[19] Hall E.J., Aerodynamic Modelling of Multistage CompressorFlow Fields, MechEngrs, Vol 212, Part G
[20] Ruprecht A., Bauer C., Gentner C., Lein G., Parallel Computation of Stator-Rotor Interaction in an Axial Turbine, ASME PVP Conference, CFD Symposium, Boston, 1999
[21] Thomas W.V., Bernard B., Heinz E.G., Time-Accurate Three-Dimensional Navier-Stokes Analysis of One-and-One-Half Stage Axial-Flow Turbine, Journal of Proulsion and Power, 2000, March-April, Vol.16
[22]姚征,多级叶轮机三维流动的级间混合方法分析,工程热物理学报,第17卷,第四期,1996年11月
[23]党政,席光,王尚锦,应用滑移界面方法求解动/静相干叶排内非定常流动,西安交通大学学报,第33卷,第7期,1999年7月
[24]董素艳,刘松龄,朱惠人,二维涡轮级的定常/非定常数值模拟,推进技术,第22卷,第5期,2001年10月
[25]钟光辉,刘建军,多排叶片间交界面处理方法分析,燃气轮机技术,第16卷,第3期,2003年9月
[26]任玉新,沈孟育,刘秋生,跨音速压气机在非设计工况下动静叶相互作用的数值模拟,航空动力学报,第14卷,第三期,1999年7月
[27]宁卫,刘前智,姚吉先,周新海,跨音速压气机动静叶栅相干的三维非定常流动数值分析,航空动力学报,第11卷,第二期,1996年4月、
[28]邹正平,徐力平,双重时间步方法在非定常流场模拟中的应用,航空学报,第21卷,第四期,2000年7月
[29]季路成,周盛,一个跨音风扇级转/静干扰流动的时间精确模拟,工程物理学报,第20卷,第四期,1999年7月
[30]于海力,闫朝,季路成,徐建中,探讨一种叶轮机非定常流数值模拟的方法,工程物理学报,第21卷,第4期,2003年1月
[31]徐朝晖,吴玉林,陈及祥,基于滑移网格与RNG湍流模型计算动静干扰,工程物理学报,第26卷,第一期,2005年1月
[32]葛宁,二维轴流压气机转/静非定常方程数值计算,航空动力学报,第15卷,第1期,2000年1月
[33] Reid L., Moore R.D., Design and Overall Performance of Four Highly Loaded, High-Speed Inlet Stage for an Advanced High-Pressure-Ratio Core Compressor, NASA Technical Paper 1337,1978
[34]张韶华,奚梅成,陈效群,数值计算方法与算法,科学出版社, 2006年5月
[35]何渝,计算机常用数值算法与程序,人民邮电出版社,2003年7月
[2] Denton J.D., The Use of a Distributed Body Force to Simulate Viscous Flow in 3D Calculations, ASME Paper 86-GT-144, 1986
[3] Rai M.M., Three Dimensional Navier-Stokes Simulations of Turbine Rotor-Stator Interaction, J.Propulsion, 1989, 5(3)
[4] Dawes W.N., Application of Full Navier-Stokes Turbomachine Flow Problem, VKI Letures Series 2, Numerical Techniques for Viscous Flow Calculation in Turbomachinery Bladings, 1986
[5] Dawes W.N., The Extension of a Solution-Adaptive Three-Dimensional Navier-Stokes Solver Toward Geometries of Arbitrary ComPlexity Transaction of ASME, J.of Turbomaehinery, Vol.115.No.2, 1993, PP:283-295/
[6]陈乃兴,张丰显,应用非正交曲线坐标表示的任意回转流面叶栅粘性气体流动的完全N-S方程求解,中国科学, A辑, vol.8, 1984
[7]蒋滋康,袁新,跨音速叶栅中实际流动的数值试验,中国工程热物理学会第五届会议论文集, No,852066,1985
[8]周新海,朱方元,应用Navier-Stockes方程的叶栅粘性流场数值分析,工程热物理学报, 1988, 9(3):230-235
[9] Gallus H.E., Grollius H.W., Lambertz J.,The Influence of Blade Number Ratio and Blade Row Spacing on Axial-Flow Compressor Stator Blade Dynamic Load and Stage Sound Pressure Level, ASME Paper 81-GT-165, Houston, 1981
[10] Evans R.J., Boundary Layer Development on Axis-Flow Turbomachinery Blading, Pumps:Analysis,design and application, Volume 1, Worthington Pump, Inc,1978:1-15
[11] Denton J.D., The Calculation of Three-Dimensional Viscous Flow Through Multistage Turbomachines, Journal of Turbomachinery, 1992, January, Vol.114
[12] Dawes W.N., Unsteady Flow and Loss Production in Centrifugal and Axial Compressor Stages, Von Karmaa Institute for Fluid Mechanics Lecture Series, 1994, June
[13] Rai M.M., Applications of Domain Decomposition Methods To Turbomachiner Flows. ASME Advances and Applications in Computational Fluid Dynamics, 1988, January,Vol.66
[14] Erdos J.L., Ahner E., McNally W., Numerlcal Solution of Periodic Transonic Flow Through a Fan Stage. AIAA Journal,1977,15,11,1559-1568
[15] Giles M., A Numerical Method for Unsteady Inviscid Flow in Turbomachinery,GTL Report# 193,1988
[16] Rai M.M., Unsteady Three-Dimensional Navier-Stokes Simulations of Turbomachine Rotor/Stator Interaction ,AIAA Paper 87-2058
[17] Rai M.M., Three-Dimensional Navier-Stokes Simulation of Turbine Rotor-Staor Interaction, NASA Technical Memorandum, 1988, March
[18] Brost V., Ruprecht A., Maih?fer M., Rotor/Stator Interactions in an Axial Turbine,A Comparion of Transient And Steady State Frozen Rotor Simuations, Institute for Fluid Mechanics and Hydraulic Machinery, University of Stuttgart, Germany
[19] Hall E.J., Aerodynamic Modelling of Multistage CompressorFlow Fields, MechEngrs, Vol 212, Part G
[20] Ruprecht A., Bauer C., Gentner C., Lein G., Parallel Computation of Stator-Rotor Interaction in an Axial Turbine, ASME PVP Conference, CFD Symposium, Boston, 1999
[21] Thomas W.V., Bernard B., Heinz E.G., Time-Accurate Three-Dimensional Navier-Stokes Analysis of One-and-One-Half Stage Axial-Flow Turbine, Journal of Proulsion and Power, 2000, March-April, Vol.16
[22]姚征,多级叶轮机三维流动的级间混合方法分析,工程热物理学报,第17卷,第四期,1996年11月
[23]党政,席光,王尚锦,应用滑移界面方法求解动/静相干叶排内非定常流动,西安交通大学学报,第33卷,第7期,1999年7月
[24]董素艳,刘松龄,朱惠人,二维涡轮级的定常/非定常数值模拟,推进技术,第22卷,第5期,2001年10月
[25]钟光辉,刘建军,多排叶片间交界面处理方法分析,燃气轮机技术,第16卷,第3期,2003年9月
[26]任玉新,沈孟育,刘秋生,跨音速压气机在非设计工况下动静叶相互作用的数值模拟,航空动力学报,第14卷,第三期,1999年7月
[27]宁卫,刘前智,姚吉先,周新海,跨音速压气机动静叶栅相干的三维非定常流动数值分析,航空动力学报,第11卷,第二期,1996年4月、
[28]邹正平,徐力平,双重时间步方法在非定常流场模拟中的应用,航空学报,第21卷,第四期,2000年7月
[29]季路成,周盛,一个跨音风扇级转/静干扰流动的时间精确模拟,工程物理学报,第20卷,第四期,1999年7月
[30]于海力,闫朝,季路成,徐建中,探讨一种叶轮机非定常流数值模拟的方法,工程物理学报,第21卷,第4期,2003年1月
[31]徐朝晖,吴玉林,陈及祥,基于滑移网格与RNG湍流模型计算动静干扰,工程物理学报,第26卷,第一期,2005年1月
[32]葛宁,二维轴流压气机转/静非定常方程数值计算,航空动力学报,第15卷,第1期,2000年1月
[33] Reid L., Moore R.D., Design and Overall Performance of Four Highly Loaded, High-Speed Inlet Stage for an Advanced High-Pressure-Ratio Core Compressor, NASA Technical Paper 1337,1978
[34]张韶华,奚梅成,陈效群,数值计算方法与算法,科学出版社, 2006年5月
[35]何渝,计算机常用数值算法与程序,人民邮电出版社,2003年7月