轴流叶轮机械二维叶栅非定常流动数值模拟
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摘要
非定常性是叶轮机械内流动的本质属性，对叶轮机械非定常流动的研究是近
年来叶轮机械气动热力学领域里的难点和热点之一。本文通过数值求解
Navier-Stokes方程来模拟轴流式叶轮机械内多排叶栅通道二维粘性流场的非定
常流动。
本文首先采用双重时间步法将叶轮机械单排叶片定常流场求解程序改编成
非定常时间精确求解程序，非定常现象由叶片通道入口处压力值随时间的周期性
变化带来；在此基础上改编程序使之可以求解多排叶片非定常流场，排间滑移界
面参数传递采用线性插值方式，论文详细介绍了它的实现过程并且对参数传递的
误差进行了分析；为了解决各排叶片通道宽度不相同的叶轮机械非定常流动数值
模拟问题，论文采用相延迟方法实现了具有多排叶片、各排叶片通道宽度不相等
的叶轮机械非定常流动数值模拟，详细介绍了相延迟理论以及具体的实现方法；
最后将所编写的程序应用于对转涡轮非定常流动数值模拟。
论文中进行了七个算例的计算，数值模拟结果表明所采用的方法可以给出正
确的数值计算结果。本文的研究工作可以为叶轮机械的优化设计提供帮助。
Unsteadiness is an essential attribute of the flow in turbomachinery. The related work has been one of the major problems in the research of turbomachinery aerodynamics, and has focused much attention of scholars for many years. In this paper, the unsteady 2D viscious flow field in multi-stage turbomachinery was studied by solving Navier-Stokes equations numerically.
The implicit dual time step algorithm of Jameson is used to simulate the unsteady flow of cascade, the unsteady phenomenon was brought by the simulated upstream wake. The work was developed on more stages, and some details were emphasized such as how to settle the slip interface. The phase-lagged method was adopted to solve the difficulty caused by the different number of vanes in different vane rows, some experiences and some formulas were shown in this paper. Finally, the flow in an counter-rotating turbine was simulated with the program.
The numerical examples show that the code developed in this paper may give accurate numerical result. The work of this paper can provide a useful reference for optimum design in turbomachinery.
年来叶轮机械气动热力学领域里的难点和热点之一。本文通过数值求解
Navier-Stokes方程来模拟轴流式叶轮机械内多排叶栅通道二维粘性流场的非定
常流动。
本文首先采用双重时间步法将叶轮机械单排叶片定常流场求解程序改编成
非定常时间精确求解程序，非定常现象由叶片通道入口处压力值随时间的周期性
变化带来；在此基础上改编程序使之可以求解多排叶片非定常流场，排间滑移界
面参数传递采用线性插值方式，论文详细介绍了它的实现过程并且对参数传递的
误差进行了分析；为了解决各排叶片通道宽度不相同的叶轮机械非定常流动数值
模拟问题，论文采用相延迟方法实现了具有多排叶片、各排叶片通道宽度不相等
的叶轮机械非定常流动数值模拟，详细介绍了相延迟理论以及具体的实现方法；
最后将所编写的程序应用于对转涡轮非定常流动数值模拟。
论文中进行了七个算例的计算，数值模拟结果表明所采用的方法可以给出正
确的数值计算结果。本文的研究工作可以为叶轮机械的优化设计提供帮助。
Unsteadiness is an essential attribute of the flow in turbomachinery. The related work has been one of the major problems in the research of turbomachinery aerodynamics, and has focused much attention of scholars for many years. In this paper, the unsteady 2D viscious flow field in multi-stage turbomachinery was studied by solving Navier-Stokes equations numerically.
The implicit dual time step algorithm of Jameson is used to simulate the unsteady flow of cascade, the unsteady phenomenon was brought by the simulated upstream wake. The work was developed on more stages, and some details were emphasized such as how to settle the slip interface. The phase-lagged method was adopted to solve the difficulty caused by the different number of vanes in different vane rows, some experiences and some formulas were shown in this paper. Finally, the flow in an counter-rotating turbine was simulated with the program.
The numerical examples show that the code developed in this paper may give accurate numerical result. The work of this paper can provide a useful reference for optimum design in turbomachinery.
引文
[1] Oguz Uzol,Yi-Chih Chow, Joseph Katz, Experimental Investigation of Unsteady Flow Field Within a Two-Stage Axial Turbomachine Using Particle Image Velocimetry, ASME Journal of Turbomachinery, Vol. 124,OCTOBER, PP542-552, 2002
[2] Dorney D.J.,Davis R.L.,Steady and Unsteady Boundary Conditions for Numerical Simulations of Flows in Turbomachines,ASME paper, No.94-GT-152,1994
[3] Hodson,H.P,An Inviscid Blade-to-Blade Prediction of a Wake-Generated Unsteady Flow, ASME Journal of Engineering for Gas Turbines and Power, Vol. 107 pp.337(84-GT-43), 1984
[4] Sharma, O.P,Pickett,G. F.,Ni,R.H.,Assessment of Unsteady Flows in Turbines, ASME paper,90-GT-150,1990
[5] Erdos J.I.,Computation of Unsteady Transonic Flows Through Rotating and Stationary Cascades,NASA CR-2900,1977
[6] Giles M.B.,A Numerical Method for Unsteady Inviscid Flow in Turbomachinery, Technical Report 195,MIT Gas Turbine Laboratory, 1988
[7] Adamczyk, J.J.,Simulation of Three-Dimensional Viscous Flow within a Multistage Turbine, ASME paper, 89-GT-152,1989,1989
[8] Giles M.B.,An Approach for Multi-Stage Calculations Incorporating Unsteadiness,ASME paper,92-GT-282,1992
[9] Jameson A.,Time Dependent Calculations Using Multigrid with Applications to Unsteady Flows Past Airfoils and Wimgs,AIAA paper, 91-1596,1991
[10] Andrea Arnone,Michele Marconcini, Roberto Pacciani,Numerical Investigation of Airfoil Clocking in a Three-Stage Low-Pressure Turbine, ASME Journal of Turbomachinery, Vol. 124,JANUARY, PP. 61-68,2002
[11] U.Reinm(?)ller, B.Stephan, S.Schmidt, et, al,Clocking Effects in a 1.5 Stage Axial Turbine—Steady and Usteady Experimental Investigations Supported by Numerical Simulations, ASME Journal of Turbomachinery, Vol. 124,PP. 52-60,JANUARY 2002
[12] Huber, F.W.,Johnson, P.D., Sharma, O.P.,et, al,Performance Improvement Through Indexing Turbine Airfoils Part 1-Experimental Investigation,ASME Paper, No.95-GT-27,1995
[13] Dorney, D.J.Sharma, O.P.,Turbine Performance Increases Through Airfoil Clocking, International Journal of Turbo and Jet Engines, 15,119-127,1998
[14] Jameson,A., Schmidt,W.,Turkel,E.,Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time Stepping Schemes,AIAA paper, 81-1259,1981
[15] Ni,R.H.,et al,Prediction of 3D Multi-Stage Turbine Flow Field Using a Multiple-Grid Euler Solver, AIAA paper 89-0203,1989
[16] 刘建军，蒋洪德，高分辨率有限体积LW格式，工程热物理学报，第14卷第3期，PP．263，1993
[17] 季路成，轴流叶轮机转子／静子干扰非定常流动探索，北京航空航天大学博士学位论文，1998年7月
[18] Denton, The Calculation of Three Dimensional Viscous Flow Through Multistage Turbomachines,ASME paper,90-GT-19,1990
[19] Bj(?)rn Laumert,Hans M(?)rtensson,Torsten H.Fransson, Simulation of Rotor/Stator Interaction With a 4D Finite Volume Method, ASME paper, GT-2002-30601,2002
[20] Rai M.M.,Navier-Stokes Simulations of Rotor-Stator Interactions Using Patched and Overlaid Grids,AIAA paper, 85-1519
[21] 赵晓路，蒋雪辉，E~3对转涡轮设计特点分析(Ⅰ)高压涡轮基元级方案分析，中国工程热物理学会热机气动热力学学术会议论文，中山，2002年11月
[22] 季路成，徐建中，关于1+1／2对转涡轮的基本分析和初步设计，中国工程热物理学会热机气动热力学学术会议论文，南京，2000
[23] P.L.Roe, Some Contributions to the Modelling of Discontinuous Flows,Lectures in Applied Mathmatics, Vol.22,1985
[24] 刘超群，多重网格法及其在计算流体力学中的应用，清华大学出版社，1995
[25] Giles,M.B.Calculation of Unsteady Wake/Rotor Interactions, AIAA Paper NO.87-0006,1987
[26] Dawes,W.N.,Towards Improved Through Flow Capability:The Use of 3D Viscous
Flow Solvers in a Multistage Environment, ASME paper 90-GT-18,1990
[27] 陶文铨，计算传热学，第二版，西安交通大学出版社，2001
[28] He, L.,An Euler Solution for Unsteady Flows Around Oscillating Blades,ASME paper 89-GT-279,1989
[2] Dorney D.J.,Davis R.L.,Steady and Unsteady Boundary Conditions for Numerical Simulations of Flows in Turbomachines,ASME paper, No.94-GT-152,1994
[3] Hodson,H.P,An Inviscid Blade-to-Blade Prediction of a Wake-Generated Unsteady Flow, ASME Journal of Engineering for Gas Turbines and Power, Vol. 107 pp.337(84-GT-43), 1984
[4] Sharma, O.P,Pickett,G. F.,Ni,R.H.,Assessment of Unsteady Flows in Turbines, ASME paper,90-GT-150,1990
[5] Erdos J.I.,Computation of Unsteady Transonic Flows Through Rotating and Stationary Cascades,NASA CR-2900,1977
[6] Giles M.B.,A Numerical Method for Unsteady Inviscid Flow in Turbomachinery, Technical Report 195,MIT Gas Turbine Laboratory, 1988
[7] Adamczyk, J.J.,Simulation of Three-Dimensional Viscous Flow within a Multistage Turbine, ASME paper, 89-GT-152,1989,1989
[8] Giles M.B.,An Approach for Multi-Stage Calculations Incorporating Unsteadiness,ASME paper,92-GT-282,1992
[9] Jameson A.,Time Dependent Calculations Using Multigrid with Applications to Unsteady Flows Past Airfoils and Wimgs,AIAA paper, 91-1596,1991
[10] Andrea Arnone,Michele Marconcini, Roberto Pacciani,Numerical Investigation of Airfoil Clocking in a Three-Stage Low-Pressure Turbine, ASME Journal of Turbomachinery, Vol. 124,JANUARY, PP. 61-68,2002
[11] U.Reinm(?)ller, B.Stephan, S.Schmidt, et, al,Clocking Effects in a 1.5 Stage Axial Turbine—Steady and Usteady Experimental Investigations Supported by Numerical Simulations, ASME Journal of Turbomachinery, Vol. 124,PP. 52-60,JANUARY 2002
[12] Huber, F.W.,Johnson, P.D., Sharma, O.P.,et, al,Performance Improvement Through Indexing Turbine Airfoils Part 1-Experimental Investigation,ASME Paper, No.95-GT-27,1995
[13] Dorney, D.J.Sharma, O.P.,Turbine Performance Increases Through Airfoil Clocking, International Journal of Turbo and Jet Engines, 15,119-127,1998
[14] Jameson,A., Schmidt,W.,Turkel,E.,Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time Stepping Schemes,AIAA paper, 81-1259,1981
[15] Ni,R.H.,et al,Prediction of 3D Multi-Stage Turbine Flow Field Using a Multiple-Grid Euler Solver, AIAA paper 89-0203,1989
[16] 刘建军，蒋洪德，高分辨率有限体积LW格式，工程热物理学报，第14卷第3期，PP．263，1993
[17] 季路成，轴流叶轮机转子／静子干扰非定常流动探索，北京航空航天大学博士学位论文，1998年7月
[18] Denton, The Calculation of Three Dimensional Viscous Flow Through Multistage Turbomachines,ASME paper,90-GT-19,1990
[19] Bj(?)rn Laumert,Hans M(?)rtensson,Torsten H.Fransson, Simulation of Rotor/Stator Interaction With a 4D Finite Volume Method, ASME paper, GT-2002-30601,2002
[20] Rai M.M.,Navier-Stokes Simulations of Rotor-Stator Interactions Using Patched and Overlaid Grids,AIAA paper, 85-1519
[21] 赵晓路，蒋雪辉，E~3对转涡轮设计特点分析(Ⅰ)高压涡轮基元级方案分析，中国工程热物理学会热机气动热力学学术会议论文，中山，2002年11月
[22] 季路成，徐建中，关于1+1／2对转涡轮的基本分析和初步设计，中国工程热物理学会热机气动热力学学术会议论文，南京，2000
[23] P.L.Roe, Some Contributions to the Modelling of Discontinuous Flows,Lectures in Applied Mathmatics, Vol.22,1985
[24] 刘超群，多重网格法及其在计算流体力学中的应用，清华大学出版社，1995
[25] Giles,M.B.Calculation of Unsteady Wake/Rotor Interactions, AIAA Paper NO.87-0006,1987
[26] Dawes,W.N.,Towards Improved Through Flow Capability:The Use of 3D Viscous
Flow Solvers in a Multistage Environment, ASME paper 90-GT-18,1990
[27] 陶文铨，计算传热学，第二版，西安交通大学出版社，2001
[28] He, L.,An Euler Solution for Unsteady Flows Around Oscillating Blades,ASME paper 89-GT-279,1989