Linear stability theory with the equivalent spanwise wavenumber correction in 3D boundary layers

doi:10.1007/s10483-019-2450-6

Applied Mathematics and Mechanics (English Edition) ›› 2019, Vol. 40 ›› Issue (3): 407-420.doi: https://doi.org/10.1007/s10483-019-2450-6

• 论文 • 上一篇

Linear stability theory with the equivalent spanwise wavenumber correction in 3D boundary layers

Runjie SONG¹, Shaolong ZHANG², Jianxin LIU¹

1. Laboratory for High-Speed Aerodynamics, Tianjin University, Tianjin 300072, China;
2. Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900, Sichuan Province, China

收稿日期:2018-09-05 修回日期:2018-12-13 出版日期:2019-03-01 发布日期:2019-03-01
通讯作者: Jianxin LIU E-mail:shookware@tju.edu.cn
基金资助:
Project supported by the National Key Research and Development (R & D) Program of China (No. 2016YFA0401200) and the National Natural Science Foundation of China (Nos. 11402167, 11332007, 11672204, 11672205, and 11732011)

Linear stability theory with the equivalent spanwise wavenumber correction in 3D boundary layers

Runjie SONG¹, Shaolong ZHANG², Jianxin LIU¹

1. Laboratory for High-Speed Aerodynamics, Tianjin University, Tianjin 300072, China;
2. Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900, Sichuan Province, China

Received:2018-09-05 Revised:2018-12-13 Online:2019-03-01 Published:2019-03-01
Contact: Jianxin LIU E-mail:shookware@tju.edu.cn
Supported by:
Project supported by the National Key Research and Development (R & D) Program of China (No. 2016YFA0401200) and the National Natural Science Foundation of China (Nos. 11402167, 11332007, 11672204, 11672205, and 11732011)

摘要/Abstract

摘要： The prediction on small disturbance propagation in complex three-dimensional (3D) boundary layers is of great significance in transition prediction methodology, especially in the aircraft design. In this paper, the linear stability theory (LST) with the equivalent spanwise wavenumber correction (ESWC) is proposed in order to accurately predict the linear evolution of a disturbance in a kind of boundary layer flow with a vital variation in the spanwise direction. The LST with the ESWC takes not only the scale of the mean flow with the significant variation but also the wavenumber evolution of the disturbance itself. Compared with the conventional LST, the results obtained by the new method are in excellent agreement with those of the numerical simulations. The LST with the ESWC is an effective method on the prediction of the disturbance evolution in 3D boundary layers, which improves the prediction of the LST in the applications to complex 3D boundary layers greatly.

关键词: dynamic plastic buckling, energy criterion, rigid plastic material, cylindrical shell, prediction of disturbance propagation, numerical simulation, three-dimensional (3D) boundary layer, linear stability theory (LST), equivalent spanwise wavenumber

Abstract: The prediction on small disturbance propagation in complex three-dimensional (3D) boundary layers is of great significance in transition prediction methodology, especially in the aircraft design. In this paper, the linear stability theory (LST) with the equivalent spanwise wavenumber correction (ESWC) is proposed in order to accurately predict the linear evolution of a disturbance in a kind of boundary layer flow with a vital variation in the spanwise direction. The LST with the ESWC takes not only the scale of the mean flow with the significant variation but also the wavenumber evolution of the disturbance itself. Compared with the conventional LST, the results obtained by the new method are in excellent agreement with those of the numerical simulations. The LST with the ESWC is an effective method on the prediction of the disturbance evolution in 3D boundary layers, which improves the prediction of the LST in the applications to complex 3D boundary layers greatly.

Key words: dynamic plastic buckling, energy criterion, rigid plastic material, cylindrical shell, linear stability theory (LST), equivalent spanwise wavenumber, numerical simulation, three-dimensional (3D) boundary layer, prediction of disturbance propagation

中图分类号:

76E09

Runjie SONG, Shaolong ZHANG, Jianxin LIU. Linear stability theory with the equivalent spanwise wavenumber correction in 3D boundary layers[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(3): 407-420.

参考文献

[1] HERBERT, T. Parabolized stability equations. Annual Review of Fluid Mechanics, 29, 245-283(1997)
[2] CEBECI, T. and STEWARTSON, K. Stability and transition in three-dimensional boundary layer instability. AIAA Journal, 18, 398-405(1980)
[3] CEBECI, T. and STEWARTSON, K. On stability and transition of three-dimensional flows. AIAA Journal, 18, 398-405(1980)
[4] DEYHLE, H., HOHLER, G., and BIPPES, H. Experimental investigation of instability wave propagation in a three dimensional boundary layer flow. AIAA Journal, 31, 637-646(1993)
[5] PRUETT, C. D., CHANG, C. L., and STREETT, C. L. Simulation of crossflow instability on a supersonic highly swept wing. Computers and Fluids, 29, 33-63(2000)
[6] JIANG, X. Y. Revisiting coherent structures in low-speed turbulent boundary layers. Applied Mathematics and Mechanics (English Edition), 40(2), 261-272(2019) https://doi.org/10.1007/s10483-019-2445-8
[7] SPALL, R. E. and MALIK, M. R. Linear stability of three dimensional boundary layers over axisymmetric bodies at incidence. AIAA Journal, 30, 905-914(1992)
[8] MEIER, H. U. and KREPLIN, H. P. Experimental investigation of the boundary layer transition and separation on a body of revolution. Zeitschrift für Flugwissenschaften und Weltraumforschung, 4, 65-71(1980)
[9] CHANG, C. L. LASTRAC.3d:transition prediction in 3D boundary layers. AIAA Paper, 2004-2542, Portland, Oregon (2004)
[10] YU, G. T. Application of e^N Method and Prediction of Disturbances Propagation in ThreeDimensional Hypersonic Boundary Layers (in Chinese), Ph. D. dissertation, Tianjin University, Tianjin (2015)
[11] ZHAO, L., YU, G. T., and LUO, J. S. Extension of eN method to general three-dimensional boundary layers. Applied Mathematics and Mechanics (English Edition), 38(7), 1007-1018(2017) https://doi.org/10.1007/s10483-017-2215-6
[12] PAREDES, P. and THEOFILIS, V. Centerline instabilities on the hypersonic international flight research experimentation HIFiRE-5 elliptic cone model. Journal of Fluids and Structures, 53, 36-49(2015)
[13] PAREDES, P. and THEOFILIS, V. Traveling global instabilities on the HIFiRE-5 elliptic cone model flow. 52nd Aerospace Sciences Meeting, National Harbor, Maryland (2014)
[14] ZHANG, S. L. The Instability and Wave Propagation in the Hypersonic 2:1 Elliptic Cone Boundary Layer (in Chinese), Ph. D. dissertation, Tianjin University, Tianjin (2016)
[15] LIU, J. X. and LUO, J. S. Effect of disturbances at inlet on hypersonic boundary layer transition on a blunt cone at small angle of attack. Applied Mathematics and Mechanics (English Edition), 31(5), 535-544(2010) https://doi.org/10.1007/s10483-010-0501-z
[16] KRIST, S. L., BIEDRON, R. T., and RUMSEY, C. NASA Langley Research Center:Aerodynamic and Acoustic Methods Branch, CFL3D User's Manual (Version 5) (1997)
[17] RUMSEY, C., BIEDRON, R., and THOMAS, J. CFL3D:Its History and Some Recent Applications, NASA Technical Memorandum 112861, Virginia (1997)
[18] LIGHTHILL, J. Waves in Fluids, Cambridge University, Cambridge (1978)
[19] WHITHAM, G. B. A note on group velocity. Journal of Fluid Mechanics, 9, 347-352(1960)

Linear stability theory with the equivalent spanwise wavenumber correction in 3D boundary layers

Linear stability theory with the equivalent spanwise wavenumber correction in 3D boundary layers

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