Progress in Efficient Reduced Order Methods for Temporal Periodic Unsteady Flows Within Turbomachinery

doi:10.13675/j.cnki.tjjs.200339

Journal of Propulsion Technology ›› 2021, Vol. 42 ›› Issue (1): 39-52.DOI: 10.13675/j.cnki.tjjs.200339

• Aero-thermodynamics • Previous Articles Next Articles

Progress in Efficient Reduced Order Methods for Temporal Periodic Unsteady Flows Within Turbomachinery

1.School of Power and Energy，Northwestern Polytechnical University，Xi’an 710129，China;2.Key Laboratory of Aeroengine Internal Flows，Northwestern Polytechnical University，Xi’an 710129，China

Online:2021-01-15 Published:2021-01-15

叶轮机周期性非定常流高效降阶数值计算方法研究进展

吴航空¹，王丁喜^1,2，黄秀全^1,2

1.西北工业大学动力与能源学院，陕西西安 710129;2.西北工业大学航空发动机内流重点实验室，陕西西安 710129

作者简介:吴航空，博士生，研究领域为计算流体力学。E-mail：hangkong_wu@qq.com
基金资助:
自然科学基金面上项目（51976172）；国家科技重大专项（2017-II-0009-0023)。

Abstract

Abstract: The paper starts with a brief introduction of the significant influence of unsteady flows on turbomachinery performance， then summarizes the time and space periodicities of turbomachinery unsteady flows arising from blade row interaction and blade vibration. The time and space periodicities can be made use of to develop efficient reduced order numerical methods for analysing these unsteady flows. This paper classifies these reduced order methods based upon their own features and provides detailed discussions about their pros and cons and their applications in turbomachinery aeroelasticity. Finally， the key technologies and the future development prospects of reduced order methods are outlined.

Key words: Reduced order methods;Unsteady flows;Periodicity;Aeroelasticity;Turbomachinery;Review

摘要： 简要介绍了叶轮机内非定常流对叶轮机性能的重要影响，总结了叶轮机内动静相干和叶片振动诱发的非定常流的时空周期性特点，并指出这些时空周期性特点可以加以利用，发展分析这些非定常流的高效降阶数值计算方法。本文根据不同数值降阶方法的特点对其进行了归类，详细分析了各自的优缺点及在气动弹性力学领域的应用，并进一步展望了降阶数值方法在未来的几个关键技术及发展趋势。

关键词: 降阶数值计算方法;非定常流动;周期性;气动弹性力学;叶轮机;综述

WU Hang-kong¹, WANG Ding-xi^1,2, HUANG Xiu-quan^1,2. Progress in Efficient Reduced Order Methods for Temporal Periodic Unsteady Flows Within Turbomachinery[J]. Journal of Propulsion Technology, 2021, 42(1): 39-52.

吴航空，王丁喜，黄秀全. 叶轮机周期性非定常流高效降阶数值计算方法研究进展[J]. 推进技术, 2021, 42(1): 39-52.

References

[1] Platzer M， Carta F. AGARD Manual on Aeroelasticity in Axial-Flow Turbomachines Volume I： Unsteady Turbomachinery Aerodynamics［R］. AGARD-AG-298， 1987.
[2] Wennerstrom A. Low Aspect Ratio Axial Flow Compressors： Why and What It Means［J］. Journal of Turbomachinery， 1989， 111： 357-365.
[3] 刘永泉，刘太秋，季路成. 航空发动机风扇／压气机技术发展的若干问题与思考［J］. 航空学报， 2015， 36（8）： 2563-2576.
[4] 季路成，陈江，黄海波，等. 关于叶轮机时均（准四维）和非定常（四维）气动设计体系的初步诠释［J］. 工程热物理学报， 2003， 24（4）： 570-574.
[5] Yao J X， Davis R L， Alonso J J， et al. Massively Parallel Simulation of the Unsteady Flow in an Axial Turbine Stage［J］. Journal of Propulsion and Power， 2002， 18（2）： 465-471.
[6] Mayorca M A， De Andrade J A， Vogt D M， et al. Effect of Scaling of Blade Row Sectors on the Prediction of Aerodynamic Forcing in a Highly Loaded Transonic Compressor Stage［J］. Journal of Turbomachinery， 2011， 133（2）.
[7] Erdos J， Alzner E， McNally W. Numerical Solution of Periodic Transonic Flow Through a Fan Stage［J］. AIAA Journal， 1977， 15（11）： 1559-1568.
[8] Erdos J， Alzner E. Computation of Unsteady Transonic Flows Through Rotating and Stationary Cascades I- Method of Analysis［R］. NASA CR-2900， 1997.
[9] He L. An Euler Solution for Unsteady Flows Around Oscillating Blades［J］. Journal of Turbomachinery， 1989， 112： 714-722.
[10] Burgos M A， Corral R. Application of Phase-Lagged Boundary Conditions to Rotor/Stator Interaction［C］. ASME GT 2001-0586.
[11] He L. Method of Simulating Unsteady Turbomachinery Flows with Multiple Perturbations［J］. AIAA Journal， 1992， 30（11）： 2730-2735.
[12] Gerolymos G A， Michon G J， Neubauer J. Analysis and Application of Choro Chronic Periodicity in Turbomachinery Rotor/Stator Interaction Computations［J］. Journal of Propulsion and Power， 2002， 18（6）： 1139-1152.
[13] ANSYS Inc. ANSYS CFX-Solver Theory Guide， Release 14.0［M］. Canonsburg： Springer， 2011.
[14] Dannenhoffer J F， Giles M B. Accelerated Convergence of Euler Solutions Using Time Inclining［J］. AIAA Journal， 1990， 28（8）： 1457-1463.
[15] Hall K C， Crawley E F. Calculation of Unsteady Flows in Turbomachinery Using the Linearized Euler Equations［J］. AIAA Journal， 1989， 27（6）.
[16] Hall K C， Clark W S， Lorence C B. A Linearized Euler Analysis of Unsteady Transonic Flows in Turbomachinery［J］. Journal of Turbomachinery， 1994， 116（3）.
[17] Holmes D G， Chuang H A. 2D Linearized Harmonic Euler Flow Analysis for Flutter and Forced Response［C］. New York： Unsteady Aerodynamics， Aeroacoustic， and Aeroelasticity of Turbomachines and Propellers， 1993.
[18] Marshall J G， Imregun M. A Review of Aeroelasticity Methods with Emphasis on Turbomachinery Applications［J］. Journal of Fluids and Structures， 1996， 10： 237-267.
[19] Clark W S， Hall K C. A Time-Linearized Navier-Stokes Analysis of Stall Flutter［J］. Journal of Turbomachinery， 2000， 122（3）： 467-476.
[20] He L， Ning W. An Efficient Approach for Analysis of Unsteady Viscous Flows in Turbomachines［J］. AIAA Journal， 1998， 36（11）： 2005-2012.
[21] Ning W， He L. Computation of Unsteady Flows Around Oscillating Blades Using Linear and Nonlinear Harmonic Euler Methods［J］. Journal of Turbomachinery， 1997， 120（3）.
[22] 张威. 基于自动微分方法的非线性谐波求解器开发与验证［D］. 西安：西北工业大学， 2020.
[23] Chen T， Vasanthakumar P， He L. Analysis of Unsteady Blade Row Interaction Using Nonlinear Harmonic Approach［J］. Journal of Propulsion and Power， 2001， 17（3）： 651-658.
[24] He L， Chen T， Wells R G， et al. Analysis of Rotor-Rotor and Stator-Stator Interferences in Multi-Stage Turbomachines［J］. Journal of Turbomachinery， 2002， 124（4）： 564-571.
[25] Li H D， He L. Blade Aerodynamic Damping Variation with Rotor-Stator Gap： A Computational Study Using Single-Passage Approach［J］. Journal of Turbomachinery， 2005， 127（3）： 573-579.
[26] Stéphane Vilmin， éric Lorrain， Beno?t Tartinville. The Nonlinear Harmonic Method： from Single Stage to Multi-Row Effects［J］. International Journal of Computational Fluid Dynamics， 2013， 27（2）： 88-99.
[27] Hall K C， Ekici K， Thomas J P， et al. Harmonic Balance Methods Applied to Computational Fluid Dynamics Problems［J］. International Journal of Computational Fluid Dynamics， 2013， 27（2）： 52-67.
[28] Hall K C， Thomas J P， Clark W S. Computation of Unsteady Nonlinear Flows in Cascades Using a Harmonic Balance Technique［J］. AIAA Journal， 2002， 40（5）： 879-886.
[29] Ekici K， Hall K C. Nonlinear Analysis of Unsteady Flows in Multistage Turbomachines Using Harmonic Balance［J］. AIAA Journal， 2007， 45（5）： 1047-1057.
[30] Ekici K， Hall K C， Kielb R E. Harmonic Balance Analysis of Blade Row Interactions in a Transonic Compressor［J］. Journal of Propulsion and Power， 2010， 26（2）： 335-343.
[31] Ekici K， Hall K C， Dowell E H. Computationally Fast Harmonic Balance Methods for Unsteady Aerodynamic Predictions of Helicopter Rotors［J］. Journal of Computational Physics， 2008， 227（12）： 6206-6225.
[32] Ekici K， Hall K C. Harmonic Balance Analysis of Limit Cycle Oscillations in Turbomachinery［J］. AIAA Journal， 2011， 49（7）： 1478-1487.
[33] van der Weide E， Gopinath， Jameson A. Turbomachinery Applications with the Time Spectral Method［C］. Toronto： 17th AIAA Computational Fluid Dynamics Conference， 2005.
[34] He L. Harmonic Solution of Unsteady Flow Around Blades with Separation［J］. AIAA Journal， 2008， 46（6）： 1299-1307.
[35] Gopinath A， van der Weide E， Alonso J， et al. Three Dimensional Unsteady Multi-Stage Turbomachinery Simulations Using the Harmonic Balance Technique［C］. Reno： 45th Aerospace Sciences Meeting and Exhibit， 2007.
[36] Sicot F， Dufour G， Gourdain N A. Time-Domain Harmonic Balance Method for Rotor/Stator Interactions［J］. Journal of Turbomachinery， 2012， 134（1）： 1-13.
[37] Huang H， Ekici K. An Efficient Harmonic Balance Method for Unsteady Flows in Cascades［J］. Aerospace Science and Technology， 2013， 29（1）： 144-154.
[38] Gomar A， Bouvy Q， Sicot F， et al. Convergence of Fourier-Based Time Methods for Turbomachinery Wake Passing Problems［J］. Journal of Computational Physics， 2014， 278： 229-256.
[39] Djeddi R， Howison J， Ekici K. A Fully Coupled Turbulent Low-Speed Preconditioner for Harmonic Balance Applications［J］. Aerospace Science and Technology， 2016， 53： 22-37.
[40] Djeddi R， Ekici K. Solution-Based Adaptive Mesh Redistribution Applied to Harmonic Balance Solvers［J］. Aerospace Science and Technology， 2018， 13（39）： 1-22.
[41] 黄秀全，周星海. 利用傅立叶方法求解振荡叶栅非定常流［J］. 西北工业大学学报， 2008， 26（3）： 357-361.
[42] 杜鹏程，宁方飞. 跨声风扇周向畸变流动的谐波平衡法计算，推进技术， 2012， 33（3）： 391-397.
[43] 马灿，苏欣荣，袁新. 用于非定常流动的谐波平衡方法研究［J］. 工程热物理学报， 2015， 36（4）： 739-743.
[44] 刘南，白俊强，华俊，等. 高阶谐波平衡方法中非物理解来源分析及改进方法研究［J］. 力学学报， 2016， 48（4）： 897-906.
[45] Wang D， Huang X. A Complete Rotor-Stator Coupling Method for Frequency Domain Analysis of Turbomachinery Unsteady Flow［J］. Aerospace Science and Technology， 2017， 70（11）： 367-377.
[46] Sun H， Wang M， Wang Z， et al. Numerical Investigation of Surge Prediction in a Transonic Axial Compressor with a Hybrid BDF/Harmonic Balance Method［J］. Aerospace Science and Technology， 2019， 90（6）： 401-409.
[47] Zhang S， Huang X， Li Y， et al. Effect of the Condition Number of the Inverse Fourier Transform Matrix on the Solution Behavior of the Time Spectral Equation System［R］. ASME GT 2020-14754.
[48] Ekici K， Hall K C. Nonlinear Frequency-Domain Analysis of Unsteady Flows in Turbomachinery with Multiple Excitation Frequencies［J］. AIAA Journal， 2008， 46（8）： 1912-1920.
[49] Guédeney T， Gomar A， Gallard F， et al. Non-Uniform Time Sampling for Multiple-Frequency Harmonic Balance Computations［J］. Journal of Computational Physics， 2013， 236（2）： 317-345.
[50] Liu L， Thomas J P， Dowell E H， et al. A Comparison of Classical and High Dimensional Harmonic Balance Approaches for Duffing Oscillator［J］. Journal of Computational Physics， 2006， 215（1）： 298-320.
[51] Maple R C， King P I， Orkwis P D， et al. Adaptive Harmonic Balance Method for Nonlinear Time-Periodic Flows［J］. Journal of Computational Physics， 2004， 193（2）： 620-641.
[52] Gentilli N C. Efficient Solution of Unsteady Nonlinear Flows Using a Multiple-Zone Harmonic Balance Technique［D］. Durham： Duke University， 2010
[53] Huang H， Ekici K. Stabilization of High-Dimensional Harmonic Balance Solvers Using Time Spectral Viscosity［J］. AIAA Journal， 2014， 52（8）： 558-574.
[54] Wu H， Wang D， Huang X， et al. Investigation of Spectral Vanishing Viscosity for Stabilizing and Accelerating Solution of Time Spectral Equation System［R］. ASME GT 2018-76011.
[55] Wu H， Wang D， Huang X. Solution Stabilization and Convergence Speedup for Non-Linear Frequency Domain Equation System Using a Time-Space Multigrid Method［C］. Beijing： Global Power and Propulsion Forum， 2019.
[56] Sicot F， Puigt G， Montagnac M. Block-Jacobi Implicit Algorithms for the Time Spectral Method［J］. AIAA Journal， 2008， 46（12）： 3080-3089.
[57] Ma C， Su X， Gou J， et al. Runge-Kutta/Implicit Scheme for the Solution of Time Spectral Method［R］. ASME GT 2014-26474.
[58] Weiss J M， Subramanian V， Hall K C. Simulation of Unsteady Turbomachinery Flows Using an Implicitly Coupled Nonlinear Harmonic Balance Method［R］. ASME GT 2011-46367.
[59] Zhan L， Xiong J， Liu F. A Space-Time Lower-Upper Symmetric Gauss-Seidel Scheme for the Time-Spectral Method［J］. International Journal of Computational Fluid Dynamics， 2016， 30（5）： 337-355.
[60] Wang D， Huang X. Solution Stabilization and Convergence Acceleration for the Harmonic Balance Equation System［J］. Journal of Engineering for Gas Turbines & Power， 2017， 139（9）.
[61] 吴航空，王丁喜，黄秀全，等. 时间谱方法的扩稳与加速技术研究［J］. 工程热物理学报， 2018，（9）： 1929-1934.
[62] Huang X， Wu H， Wang D. Implicit Solution of Harmonic Balance Equation System Using the LU-SGS Method and One-Step Jacobi/Gauss-Seidel Iteration［J］. International Journal of Computational Fluid Dynamics， 2018， 32（5）： 1-15.
[63] Su X， Yuan X. Implicit Solution of Time Spectral Method for Periodic Unsteady Flows［J］. Journal of Engineering Thermo Physics， 2010， 63（7）： 860-876.
[64] Mundis N L， Mavriplis J D. GMRES Applied to the Time-Spectral and Quasi-Periodic Time Spectral Methods［C］. San Diego： In Proceedings of 21st AIAA Computational Fluid Dynamics Conference， 2013.
[65] Mundis N L， Mavriplis J D. Wave-Number Independent Preconditioning for GMRES Time-Spectral Solvers［C］. Kissimmee： In Proceedings of 53rd AIAA Aerospace Sciences Meeting， 2015.
[66] 贡伊明，刘战合，刘溢浪，等. 时间谱方法中的高效GMRES算法［J］. 航空学报， 2017， 38（7）： 196-204.
[67] Wu H， Wang D， Huang X. Development of a Time-Space Multigrid Method for Efficient Solution of the Time Spectral Equation System［C］. Chongqing： Chinese International Turbomachinery Conference， 2018.
[68] Djeddi R， Ekici K. Resolution of Gibbs Phenomenon Using a Modified Pseudo-Spectral Operator in Harmonic Balance CFD Solvers［J］. International Journal of Computational Fluid Dynamics， 2016， 10（6）： 495-515.
[69] Huang X， Wang D. Time-Space Spectral Method for Rotor-Rotor/Stator-Stator Interactions［J］. Journal of Turbomachinery， 2019， 141（11）： 1-20.
[70] Subramanian V， Custer C H， Weiss J M， et al. Unsteady Simulation of a Two-Stage Cooled High Pressure Turbine Using an Efficient Non-Linear Harmonic Balance Method［R］. ASME GT 2013-94574.
[71] Frey C， Ashcroft G， Kersken H P， et al. A Harmonic Balance Technique for Multistage Turbomachinery Applications［R］. ASME GT 2014-25230.
[72] Frey C， Ashcroft G， Kersken H P， et al. Simulation of Indexing and Clocking with Harmonic Balance［J］. International Journal of Turbomachinery Propulsion and Power， 2018， 3（1）： 1-12.
[73] McMullen M， Jameson A， Alonso J J. Application of a Non-Linear Frequency Domain Solver to the Euler and Navier-Stokes Equation［R］. AIAA 2002-120.
[74] McMullen M， Jameson A， Alonso J J. Demonstration of Nonlinear Frequency Domain Methods［J］. AIAA Journal， 2006， 44（7）： 1428-1435.
[75] Nadarajah S， McMullen M， Jameson A. Optimal Control of Unsteady Flows Using Time Accurate and Non-Linear Frequency Domain Methods［R］. AIAA 2003-3875.
[76] McMullen M， Jameson A. The Computational Efficiency of Non-Linear Frequency Domain Methods［J］. Journal of Computational Physics， 2006， 212（2）： 637-661.
[77] Wu H， Wang D. Comparison of Different Frequency Domain Methods for Efficient Analysis of Temporal Periodic Flow Field［C］. Shanghai： Global Power and Propulsion Forum， 2017.
[78] 杨体浩，白俊强，史亚云，等. 适用于非周期流固耦合问题的时间谱方法［J］. 航空学报， 2018， 39（5）： 1-13.
[79] Du P， Ning F. Simulating Periodic Unsteady Flows Using a Cubic-Spline-Based Time Collocation Method［J］. Journal of Turbomachinery， 2014， 136（4）.
[80] Yi J， He L. Space-Time Gradient Method for Unsteady Blade Row Interaction， Part I： Basic Methodology and Verification［J］. Journal of Turbomachinery， 2015， 137（11）.
[81] He L， Yi J， Adami P， et al. Space-Time Gradient Method for Unsteady Blade Row Interaction， Part II： Further Validation， Clocking， and Multi Disturbance Effect［J］. Journal of Turbomachinery， 2015， 137（12）.
[82] 吴航空，王丁喜，黄秀全. 时间拟合方法与谐波平衡方法的对比研究［C］. 昆明：中国航天第三专业信息网第四十届技术交流会暨第四届空天动力联合会议， 2019.

Progress in Efficient Reduced Order Methods for Temporal Periodic Unsteady Flows Within Turbomachinery

叶轮机周期性非定常流高效降阶数值计算方法研究进展

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 0

Recommended Articles 0

Metrics

Comments