高空巡航时高负荷低压涡轮(LPT)雷诺数较低,在逆压梯度作用下叶背极易发生层流分离转捩并恶化LPT的气动性能。重点开展雷诺数扰动对高负荷LPT流动损失的不确定性影响研究。首先通过求解γ-Reθt模型方程对高负荷LPT叶栅进行数值模拟,通过精度分析及对比评估数值模拟的可靠性。之后分析不同湍流度条件下雷诺数对动能损失系数(KELC)的影响并建立KELC的自适应响应模型,计算KELC的统计均值、标准差等并对比分析KELC的不确定性影响规律。最后开展基于蒙特卡罗模拟的流场统计研究,通过分析雷诺数扰动对流动分离和转捩的影响,揭示雷诺数对高负荷LPT流动损失不确定性变化的作用机制。
The Reynolds number of the high-lift Low-Pressure Turbine(LPT) is small when the aircraft is cruising at a high altitude. Under the effect of the adverse pressure gradient, laminar flow separation and transition tend to occur on the suction side, deteriorating the aerodynamic performance of LPTs. The uncertainty impact of Reynolds number variations on the flow losses of high-lift LPTs is investigated in this study. The flow of a high-lift LPT cascade is first numerically simulated by solving the γ-Reθt transition model equations. The computed flow losses are then analyzed, and compared with the experimental results to evaluate the reliability of the numerical results. Then the effects of the Reynolds number on the Kinetic Energy Loss Coefficient(KELC) are studied with different turbulent intensities. An adaptive surrogate model with a high response accuracy is constructed, which is applied to the calculation of the statistical mean and variance of KELC, and the study of the uncertainty impact of the Reynolds number on KELC. Statistical analysis of flow solutions by Monte Carlo simulation is finally presented. The investigation into the influence of Reynolds number variations on flow separation and transition demonstrates the mechanisms of uncertainty impact on the flow losses of high-lift LPTs.
[1] WISLER D. The technical and economic relevance of understanding blade row interactions effects in turbomachinery[R]. Belgium:von Karman Institute for Fluid Dynamics, 1998.
[2] HOWELL R J, RAMESH O N, HODSON H P, et al. High lift and aft-loaded profiles for low-pressure turbines[J]. Journal of Turbomachinery, 2001, 123(2):181-188.
[3] HODSON H P, HOWELL R J. The role of transition in high-lift low-pressure turbines for aeroengines[J]. Progress in Aerospace Sciences, 2005, 41(6):419-454.
[4] STIEGER R D. The effect of wakes on separating boundary layers in low pressure turbines[D]. Cambridge:University of Cambridge, 2002.
[5] ZHANG X F. Separation and transition control on ultra-high-lift low pressure turbine blades in unsteady flow[D]. Cambridge:University of Cambridge, 2006.
[6] 伊进宝,乔渭阳,孙大伟.低压涡轮叶栅流动分离主动控制实验研究[J].航空学报, 2007, 28(5):1055-1061. YI J B, QIAO W Y, SUN D W. Experimental investigation of active control of flow separation at low-pressure turbine cascade[J]. Acta Aeronautica et Astronautica Sinica, 2007, 28(5):1055-1061(in Chinese).
[7] CIORCIARI R, KIRIK I, NIEHUIS R. Effects of unsteady wakes on the secondary flows in the linear T106 turbine cascade[J]. Journal of Turbomachinery, 2014, 136(9):091010.
[8] WINHART B, SINKWITZ M, SCHRAMM A, et al. Experimental and numerical investigation of secondary flow structures in an annular low pressure turbine cascade under periodic wake impact-Part 1:Experimental results[J]. Journal of Turbomachinery, 2019, 141(2):021008.
[9] QU X, ZHANG Y F, LU X G, et al. Effect of periodic wakes and a contoured endwall on secondary flow in a high-lift low-pressure turbine cascade at low Reynolds numbers[J]. Computers&Fluids, 2019, 190:1-14.
[10] MICHÁLEK J, MONALDI M, ARTS T. Aerodynamic performance of a very high lift low pressure turbine airfoil (T106C) at low Reynolds and high Mach number with effect of free stream turbulence intensity[J]. Journal of Turbomachinery, 2012, 134(6):061009.
[11] 李维,邹正平,赵晓路.雷诺数对涡轮部件性能的影响[J].航空动力学报, 2004, 19(6):822-827. LI W, ZOU Z P, ZHAO X L. The effects of Reynolds number on the characteristics of the low pressure turbine[J]. Journal of Aerospace Power, 2004, 19(6):822-827(in Chinese).
[12] HURA H S, JOSEPH J, HALSTEAD D E. Reynolds number effects in a low pressure turbine:GT2012-68501[R]. New York:ASME, 2012.
[13] BROSSMAN J R, BALL P R, SMITH N R, et al. Sensitivity of multistage compressor performance to inlet boundary conditions[J]. Journal of Propulsion and Power, 2014, 30(2):407-415.
[14] SALVADORI S, MONTOMOLI F, MARTELLI F, et al. Analysis on the effect of a nonuniform inlet profile on heat transfer and fluid flow in turbine stages[J]. Journal of Turbomachinery, 2012, 134(1):011012.
[15] 夏志恒,罗佳奇.考虑来流角变化影响的叶栅稳健性优化设计[J].工程热物理学报, 2021, 42(1):121-129. XIA Z H, LUO J Q. Robust design optimization of a turbine cascade considering the uncertain changes of inlet flow angle[J]. Journal of Engineering Thermophysics, 2021, 42(1):121-129(in Chinese).
[16] 夏志恒.基于混沌模型的叶轮机械气动不确定性研究及稳健性设计优化[D].北京:北京大学, 2020. XIA Z H. Aerodynamic uncertainty quantification by polynomial chaos and robust design optimization of turbomachinery blades[D]. Beijing:Peking University, 2020(in Chinese).
[17] CUI J, TUCKER P G. Numerical study of purge and secondary flows in a low pressure turbine:GT2016-56789[R]. New York:ASME, 2016.
[18] HU S T, ZHOU C, XIA Z H, et al. Large eddy simulation and CDNS investigation of T106C low-pressure turbine[J]. Journal of Fluids Engineering, 2018, 140(1):011108.
[19] MENTER F R. Two-equation eddy-viscosity turbulence models for engineering applications[J]. AIAA Journal, 1994, 32(8):1598-1605.
[20] LANGTRY R B, MENTER F R. Correlation-based transition modeling for unstructured parallelized computational fluid dynamics codes[J]. AIAA Journal, 2009, 47(12):2894-2906.
[21] MENTER F R, SMIRNOV P E, LIU T, et al. A one-equation local correlation-based transition model[J]. Flow, Turbulence and Combustion, 2015, 95(4):583-619.
[22] 罗天培,柳阳威,陆利蓬.低压涡轮叶栅流动中转捩模型的校验及改进[J].航空学报, 2013, 34(7):1548-1562. LUO T P, LIU Y W, LU L P. Transition model assessment and modification in low-pressure turbine cascade[J]. Acta Aeronautica et Astronautica Sinica, 2013, 34(7):1548-1562(in Chinese).
[23] 杨林,乔渭阳,罗华玲,等.低雷诺数高负荷低压涡轮叶型的气动设计[J].航空动力学报, 2013, 28(5):1019-1028. YANG L, QIAO W Y, LUO H L, et al. Aerodynamic design of highly-loaded blade in low-pressure turbine with low Reynolds number[J]. Journal of Aerospace Power, 2013, 28(5):1019-1028(in Chinese).
[24] BAI T, LIU J Y, ZHANG W H, et al. Effect of surface roughness on the aerodynamic performance of turbine blade cascade[J]. Propulsion and Power Research, 2014, 3(2):82-89.
[25] QU X, ZHANG Y F, LU X G, et al. The effect of endwall boundary layer and incoming wakes on secondary flow in a high-lift low-pressure turbine cascade at low Reynolds number[J]. Proceedings of the Institution of Mechanical Engineers, Part G:Journal of Aerospace Engineering, 2019, 233(15):5637-5649.
[26] ROACH P E. The generation of nearly isotropic turbulence by means of grids[J]. International Journal of Heat and Fluid Flow, 1987, 8(2):82-92.
[27] SAMMUT C, WEBB G. Encyclopedia of machine learning[M]. Boston:Springer, 2010.
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