可压缩剪切层与边界层流动相互作用的稳定性研究

推进技术 ›› 2017, Vol. 38 ›› Issue (2): 306-314.

可压缩剪切层与边界层流动相互作用的稳定性研究

祁智,刘凤君

北京动力机械研究所高超声速冲压发动机技术重点实验室，北京 100074,北京动力机械研究所高超声速冲压发动机技术重点实验室，北京 100074

发布日期:2021-08-15
作者简介:祁智，硕士生，研究领域为计算流体力学、超燃冲压发动机。E-mail: 1559101306@qq.com 通讯作者:刘凤君，博士，研究员，研究领域为吸气式发动机和计算流体力学。

Linear Stability Studies on Interactional Compressible Shear and Boundary Layers

Science and Technology on Scramjet Laboratory，Beijing Power Machinery Institute，Beijing 100074，China and Science and Technology on Scramjet Laboratory，Beijing Power Machinery Institute，Beijing 100074，China

Published:2021-08-15

摘要/Abstract

摘要： 为了探究可压缩剪切层与边界层组合流动稳定性规律，采用线性稳定性理论对这种组合流动的线性稳定性问题进行研究。平均流动模型取双曲正切函数描述的可压缩剪切层与可压缩相似边界层速度剖面的直接叠加。采用整体数值方法(Global)求解组合流动线性稳定性方程，获得全部不稳定模态。结果表明，在这样的组合流动中，存在两个不稳定模态，一个与剪切层相关的不稳定模态，另一个是与边界层相关的不稳定模态。在此基础上，研究了剪切层与壁面之间的距离、扰动频率、雷诺数、马赫数、速度梯度、温度梯度对这种组合流动稳定性的影响。马赫数增大对不稳定模态起抑制作用，剪切层对边界层的不稳定模态的促进、抑制作用与马赫数、扰动频率有关，边界层对剪切层不稳定模态基本上起抑制作用。

关键词: 可压缩边界层；可压缩剪切层；组合流动；线性稳定性理论

Abstract: In order to explore the stability laws of the confluent compressible shear and boundary layers，the linear stability of this confluent layers was studied through linear stability theory. The base flow model was composed by the hyperbolic tangent function described compressible shear layer and the similar velocity profile of compressible boundary layer directly. The linear stability equations were solved by the global numerical method and obtained all unstable modes eventually. The results indicate that there are two unstable modes in the confluent layers，and each layer has one unstable mode respectively. On this basis，the effects of the distance between the shear layer and the wall，disturbance frequency，Reynolds number，Mach number，velocity gradient and temperature gradient on the stability of the confluent layers were investigated in details. Increasing Mach number can reduce the growth rate of unstable modes，both for shear layer and boundary layer，the influence of shear layer on the unstable mode of boundary layer varies in Mach number and disturbance frequency，boundary layer can reduce the growth rate of the unstable mode in shear layer generally.

Key words: Compressible boundary layer；Compressible shear layer；Confluent layers；Linear stability theory

祁智,刘凤君. 可压缩剪切层与边界层流动相互作用的稳定性研究[J]. 推进技术, 2017, 38(2): 306-314.

QI Zhi ,LIU Feng-jun. Linear Stability Studies on Interactional Compressible Shear and Boundary Layers[J]. Journal of Propulsion Technology, 2017, 38(2): 306-314.

参考文献

[1] Rumsey C L, Lee-Rasusch E M. Three-Dimensional Effects on Multi-Element High Lift Computations[R]. AIAA 2002-0845.
[2] 王一帆, 刘凤君, 朴英. 剪切层与边界层组合流动的线性不稳定性分析[J]. 航空动力学报, 2016, 31(7): 1649-1657.
[3] Rust B, Gerlinger P, Lourier J, et al. Numerical Simulation of the Internal and External Flowfields of a Scramjet Fuel Strut Injector Including Conjugate Heat Transfer[R]. AIAA 2011-2207.
[4] Sato S, Munakata T, Fukui M. Application of 3-Dimensional Effects of Shock Waves Caused by a Strut-Cowl System in a Scramjet Engine [R]. AIAA 2011-2314.
[5] Joslin R D, Streett C L, Chang C L. Spatial Direct Numerical Simulation of Boundary Layer Transition Mechanisms: Validation of PSE Theory[J]. Theoretical and Computational Fluid Dynamics, 1993, 4(6): 271-288.
[6] Joslin R D, Streett C L. The Role of Stationary Cross-Flow Vortices in Boundary Layer Transition on Swept Wings[J]. Physics of Fluids, 1994, 6(10): 3442-3453.
[7] H 史里希廷. 边界层理论[M]. 徐燕侯, 徐书轩, 马晖扬, 等译. 北京:科学出版社, 1991.
[8] Jordinson R. The Flat Boundary Layer, Part 1: Numerical Integration of the Orr-Sommerfeld Equation[J]. Journal of Fluid Mechanics, 1970, 43(4): 801-811.
[9] 陈懋章. 粘性流体动力学基础 [M]. 北京:高等教育出版社, 2002.
[10] Mack L M. Boundary Layer Linear Stability Theory [R]. AGARD, 1984-709.
[11] Liou W W, Liu F J. Spatial Linear Instability of Conluent Wake/Boundary Layers[J]. AIAA Journal, 2001, 11(11): 2076-2081.
[12] 张红军, 袁湘江, 沈清. 高超声速楔面边界层流动稳定性分析[J]. 推进技术, 2012, 33(5): 671-675. (ZHANG Hong-jun, YUAN Xiang-jiang, SHEN Qing. Analysis of the Stability of Hypersonic Wedge Boundary Layer[J]. Journal of Propulsion Technology, 2012, 33(5): 671-675.)
[13] W W Liou, Fengjun Liou. Compressible Linear Stability of Confluent Wake/Boundary Layers[J]. AIAA Journal, 2003, 41(12).
[14] Michalke A. On Spatially Growing Disturbances in an Inviscid Shear Layer[J]. Journal of Fluid Mechanics, 1965, 23(3): 521-544.
[15] Cebeci T, Smith A M O. Analysis of Turbulent Boundary Layers[M]. New York: Academic Press New York, 1974
[16] 周恒, 赵耕夫. 流动稳定性[M]. 北京:国防工业出版社2004.
[17] Joslin R D, Craig L Streett. A Comparison with Linear Stability and Parabolic Stability Equation Theories for Boundary-Layer Transition on a Flat Plate[R]. NASA Technical-3205, 1992.
[18] Bridges T J, Morris PJ. Differential Eigenvalue Problems in Which the Parameter Appears Nonlinearly[J]. Journal of Computational Physics, 1984, 55: 437-460.
[19] 董平, 颜培刚, 黄洪雁, 等. 温度梯度对平板边界层转捩影响的数值模拟[J]. 推进技术, 2008, 29(5):527-532. (DONG Ping, YAN Pei-gang, HUANG Hong-yan. The Numerical Simulation of the Effect of Temperature Gradient on Transition of the Flat-Plat Boundary Layer[J]. Journal of Propulsion Technology, 2008, 29 (5): 527-532.)
[20] M R. Numerical Methods for Hypersonic Boundary Layers Stability[J]. Journal of Computational Physics, 1990, 86: 376-413.
[21] Bridges T J, Morris P J. Boundary Layer Stability Calculations[J]. Physics of Fluids, 1987, 30(11): 3351-3358.
[22] Liou W W, Fang Y. Bursting Frequency Predictions for Compressible Turbulent Boundary Layers[J]. AIAA Journal, 2003, 41(6): 1022-1028.
[23] Zurigat Y H, Nayfeh A H, Masad J A. Effect of Pressure Gradient on the Stability of Compressible Boundary Layers[J]. AIAA Journal, 1992, 30(9): 2204-2211.
[24] Ching Y Loh. Wave Computation in Compressible Flow Using Space-Time Conservation Element and Solution Element Method[J]. AIAA Journal, 2001, 39(5): 794-801.　收稿日期:2016-09-27；修订日期:2016-10-14。作者简介:祁智,硕士生,研究领域为计算流体力学、超燃冲压发动机。E-mail: 1559101306@qq.com通讯作者:刘凤君,博士,研究员,研究领域为吸气式发动机和计算流体力学。E-mail: liu8024@126.com(编辑:张荣莉)