基于定涡黏性连续伴随的叶栅气热优化方法研究
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摘要
本文基于网格节点位置坐标变分技术及流动通量雅克比矩阵,在定涡黏性假设下推导了适用于透平叶栅的连续伴随优化系统,降低了RANS方程下伴随系统的推导难度。针对透平叶栅气动换热优化问题,从质熵流和热熵流的角度定义了熵增目标函数,以综合衡量叶栅的气动和换热性能,其中质熵流对应流动损失,热熵流对应叶片表面换热损失。与定涡黏性假设下的连续伴随系统结合,详细推导了伴随方程及边界条件,建立了气动换热伴随优化系统。选取SST k-ω湍流模型及Gamma-Theta转捩模型进行流场和温度场模拟,配合伴随梯度值,使用最速下降法对无冷却结构的MarkⅡ叶栅和GE-E~3静叶进行了气动换热伴随优化分析。优化后总目标函数分别下降了32.95%和8.81%,验证了连续伴随优化系统的有效性。
In this paper, the continuous adjoint system for turbine cascade aero-thermal optimization based on the constant eddy viscosity(CEV) assumption was established by using the variation technique in the grid node coordinates combined with Jacobian Matrics of flow fluxes, which reduced the derivation difficulty of the RANS equations. For turbine cascade aerodynamic and heat transfer optimization problem, the aerodynamic and heat transfer performances were evaluated comprehensively through the objective of system entropy generation, in which the mass entropy flow represents the flow loss and the heat entropy flow corresponds to the heat transfer loss on the blade surface. Combined with the continuous adjoint method under the CEV assumption, the specific adjoint equations and relative boundary conditions were deduced in detail, and the corresponding aerodynamic heat exchange optimization system was established. The SST κ-ω turbulence model and Gamma-Theta transition model were selected to simulate the internal flow and temperature field.Then the flow and heat transfer performance analysis of Mark II cascade without cooling structure and the GE-E~3 vane were calculated using the adjoint gradients and steepest descent method. The total objective function after optimization was decreased by 32.95% and 8.81% respectively. The effectiveness of the continuous adjoint optimization system was verified.
In this paper, the continuous adjoint system for turbine cascade aero-thermal optimization based on the constant eddy viscosity(CEV) assumption was established by using the variation technique in the grid node coordinates combined with Jacobian Matrics of flow fluxes, which reduced the derivation difficulty of the RANS equations. For turbine cascade aerodynamic and heat transfer optimization problem, the aerodynamic and heat transfer performances were evaluated comprehensively through the objective of system entropy generation, in which the mass entropy flow represents the flow loss and the heat entropy flow corresponds to the heat transfer loss on the blade surface. Combined with the continuous adjoint method under the CEV assumption, the specific adjoint equations and relative boundary conditions were deduced in detail, and the corresponding aerodynamic heat exchange optimization system was established. The SST κ-ω turbulence model and Gamma-Theta transition model were selected to simulate the internal flow and temperature field.Then the flow and heat transfer performance analysis of Mark II cascade without cooling structure and the GE-E~3 vane were calculated using the adjoint gradients and steepest descent method. The total objective function after optimization was decreased by 32.95% and 8.81% respectively. The effectiveness of the continuous adjoint optimization system was verified.
引文
[1]张鹏飞.复杂黏性流动环境下基于连续伴随方法的轴流式透平叶栅优化设计研究[D].西安交通大学,2015ZHANG Pengfei. Study on Optimization Design for Axial Turbine Cascades with Complex Viscous PhD Dissertation, Xi'an Jiaotong University, 2015
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[5]丰镇平,厉海涛,宋立明,李颖晨.基于控制理论的透平叶栅气动反设计优化[J].中国科学:技术科学,2013, 43(3):257-273Feng Z P, Li H T, Song L M, et al. Aerodynamic Inverse Design Optimization for Turbine Cascades Based on Control Theory[J]. Sci China Tech Sci, 2013, 56:308-323
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[7] Chung H, Alonso J. Using Gradients to Construct Response Surface Models for High-Dimensional Design Optimization Problems[R]. AIAA-2001-0922, 2001
[8] Martins J R, Alonso J, Reuther J. High-Fidelity Aerostructural Design Optimization of a Supersonic Business Jet[J]. Journal of Aircraft, 2004, 41:523-530
[9] Mani K, Mavriplis D J. Adjoint-Based Sensitity Formulation for Fully Coupled Unsteady Aeroelasticity Problems[J]. AIAA Journal, 2009, 47:1902-1915
[10] Ferlauto M. Inverse Design of Internally Cooled Turbine Blades Based on the Heat Adjoint Equation[J]. Inverse Problem in Science and Engineering, 2013, 21(2):269-282
[11] Ferlauto M. An Inverse Method of Designing the Cooling Passages of Turbine Blades Based on the Heat Adjoint Equation[J]. Journal of Power and Energy, 2014, 228(3):328-339
[12] Mousavi A, Nadarajah S. An Adjoint-Based Shape Optimization of Gas Turbine Blades[R]. AIAA-2010-1421,2010
[13] Mousavi A, Nadarajah S. Adjoint-Based Multidisciplinary Design Optimization of Cooled Gas Turbine Blades[R].AIAA-2011-1131, 2011
[14] Zeinalpour M, Mazaheri K. Entropy Minization in Turbine Cascade Using Continuous Adjoint Formulation[J].Engineering Optimization, 2015, 48(2):213-230
[15] Zeinalpour M, Mazaheri K. A Coupled Adjoint Formulation for Non-Cooled and Internally Cooled Turbine Blade Optimization[J]. Applied Thermal Engineering, 2016,105:327-335
[16] Papadimitriou D I, Giannakoglou K C. A Continuous Adjoint Method with Objective Function Derivatives Based on Boundary Integrals, for Inviscid and Viscous Flows[J].Computers&Fluids, 2007, 36:325-341
[17] Zhang P F, Lu J, Song L M, et al. Study on Continuous Adjoint Optimization with Turbulence Models for Aerodynamic Performance and Heat Transfer in Turbomachinery Cascades[J]. International Journal of Heat and Mass Transfer, 2017, 104:1069-1082
[18] Nielsen E J, Lu J, Park M A, et al. An Implicit Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids[J]. Comput Fluids, 2004, 33:1131-1155
[19] Menter F R. Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications[J]. AIAA Journal,1994, 32(8):1598-1605
[2] Reuther J, Jameson A. Control Based Airfoil Design Using the Euler Equations[R]. AIAA-1994-4272, 1994
[3] Li Y C, Yang D L, Feng Z P. Inverse Problem in Aerodynamic Shape Design of Turbomachinery Blades[R].ASME Paper, No. GT2006-91135, 2006
[4]厉海涛.基于连续伴随方法的轴流式叶栅气动优化理论及系统的研究[D].西安交通大学,2012LI Haitao. Study on Aerodynamic Optimization Theory and System for Axial Turbomachinery Cascades Based on Continuous Adjoint Method[D]. Xi'an Jiaotong University, 2012
[5]丰镇平,厉海涛,宋立明,李颖晨.基于控制理论的透平叶栅气动反设计优化[J].中国科学:技术科学,2013, 43(3):257-273Feng Z P, Li H T, Song L M, et al. Aerodynamic Inverse Design Optimization for Turbine Cascades Based on Control Theory[J]. Sci China Tech Sci, 2013, 56:308-323
[6]张鹏飞,卢娟,丰镇平.基于定涡黏性假设的连续伴随优化方法研究[J].中国工程热物理学报,2016, 37(1):42-45ZHANG Pengfei, LU Juan, FENG Zhenping. Study on Continuous Adjoint Optimization Method Based on Constant Eddy Viscosity Assumption[J]. Journal of Engineering Thermophysics, 2016, 37(1):42-45
[7] Chung H, Alonso J. Using Gradients to Construct Response Surface Models for High-Dimensional Design Optimization Problems[R]. AIAA-2001-0922, 2001
[8] Martins J R, Alonso J, Reuther J. High-Fidelity Aerostructural Design Optimization of a Supersonic Business Jet[J]. Journal of Aircraft, 2004, 41:523-530
[9] Mani K, Mavriplis D J. Adjoint-Based Sensitity Formulation for Fully Coupled Unsteady Aeroelasticity Problems[J]. AIAA Journal, 2009, 47:1902-1915
[10] Ferlauto M. Inverse Design of Internally Cooled Turbine Blades Based on the Heat Adjoint Equation[J]. Inverse Problem in Science and Engineering, 2013, 21(2):269-282
[11] Ferlauto M. An Inverse Method of Designing the Cooling Passages of Turbine Blades Based on the Heat Adjoint Equation[J]. Journal of Power and Energy, 2014, 228(3):328-339
[12] Mousavi A, Nadarajah S. An Adjoint-Based Shape Optimization of Gas Turbine Blades[R]. AIAA-2010-1421,2010
[13] Mousavi A, Nadarajah S. Adjoint-Based Multidisciplinary Design Optimization of Cooled Gas Turbine Blades[R].AIAA-2011-1131, 2011
[14] Zeinalpour M, Mazaheri K. Entropy Minization in Turbine Cascade Using Continuous Adjoint Formulation[J].Engineering Optimization, 2015, 48(2):213-230
[15] Zeinalpour M, Mazaheri K. A Coupled Adjoint Formulation for Non-Cooled and Internally Cooled Turbine Blade Optimization[J]. Applied Thermal Engineering, 2016,105:327-335
[16] Papadimitriou D I, Giannakoglou K C. A Continuous Adjoint Method with Objective Function Derivatives Based on Boundary Integrals, for Inviscid and Viscous Flows[J].Computers&Fluids, 2007, 36:325-341
[17] Zhang P F, Lu J, Song L M, et al. Study on Continuous Adjoint Optimization with Turbulence Models for Aerodynamic Performance and Heat Transfer in Turbomachinery Cascades[J]. International Journal of Heat and Mass Transfer, 2017, 104:1069-1082
[18] Nielsen E J, Lu J, Park M A, et al. An Implicit Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids[J]. Comput Fluids, 2004, 33:1131-1155
[19] Menter F R. Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications[J]. AIAA Journal,1994, 32(8):1598-1605
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