Intermodal exchange and wall temperature effect in a supersonic boundary layer

SU Caihong; SONG Mingzhen

doi:10.7638/kqdlxxb-2019.0048

ACTA AERODYNAMICA SINICA > 2020 > 38(6): 1056-1063. > DOI: 10.7638/kqdlxxb-2019.0048

SU Caihong, SONG Mingzhen. Intermodal exchange and wall temperature effect in a supersonic boundary layer[J]. ACTA AERODYNAMICA SINICA, 2020, 38(6): 1056-1063. DOI: 10.7638/kqdlxxb-2019.0048

Citation:

SU Caihong, SONG Mingzhen. Intermodal exchange and wall temperature effect in a supersonic boundary layer[J]. ACTA AERODYNAMICA SINICA, 2020, 38(6): 1056-1063. DOI: 10.7638/kqdlxxb-2019.0048

Citation:

SU Caihong, SONG Mingzhen. Intermodal exchange and wall temperature effect in a supersonic boundary layer[J]. ACTA AERODYNAMICA SINICA, 2020, 38(6): 1056-1063. DOI: 10.7638/kqdlxxb-2019.0048

PDF (6084 KB)

Intermodal exchange and wall temperature effect in a supersonic boundary layer

Laboratory for High-speed Aerodynamics, School of Mechanical Engineering, Tianjin University, Tianjin 300072, China

More Information

Received Date: April 18, 2019
Revised Date: May 15, 2019
Available Online: January 07, 2021

Graphical Abstract

Abstract

Abstract

At free-stream Mach number larger than 4, the second mode is the dominant instability mode in supersonic boundary layers. According to the findings from receptivity research, one important way to generate the second mode is through intermodal exchange, by which the excited fast mode in the boundary layer synchronizes with the second mode when travels downstream. In this paper, the intermodal exchange between the fast mode and the second mode in a supersonic boundary layer is investigated numerically. Two coefficients, i.e. the amplitude and region of intermodal exchange are defined. Their relations are established with respect to the disturbance frequency. Based on linear stability theory, a new method accounting for the intermodal exchange is developed to compute the evolutions of the disturbances. The parabolized stability equations is used to verify the new method. It is shown that, under a wide range of wall temperature conditions, the newly developed method can accurately predict the evolutions of the disturbance considering the process of intermodal exchange between fast mode and the second mode. With considerations of the initial amplitude of the excited fast mode and a transition criterion, this method can be easily used to predict transition of a boundary layer. Since it considers the generation of the second mode through intermodal exchange, it accounts for more physics than the conventional transition prediction method.
- intermodal exchange,
- second mode,
- receptivity,
- supersonic boundary layer,
- transition prediction

FullText(HTML)

References (27)

References

[1]	REED H L, PEREZ E, KUEHL J, et al. Verification and validation issues in hypersonic stability and transition prediction[J]. Journal of Spacecraft and Rockets, 2015, 52(1):29-37. DOI: 10.2514/1.a32825
[2]	陈坚强, 涂国华, 张毅锋, 等.高超声速边界层转捩研究现状与发展趋势[J].空气动力学学报, 2017, 35(3):311-337. doi: 10.7638/kqdlxxb-2017.0030 CHEN J Q, TU G H, ZHANG Y F, et al. Hypersonic boundary layer transition:what we know, where shall we go[J]. Acta Aerodynamica Sinica, 2017, 35(3):311-337.(in Chinese) DOI: 10.7638/kqdlxxb-2017.0030
[3]	罗纪生.高超声速边界层的转捩及预测[J].航空学报, 2015, 36(1):357-372. doi: 10.7527/S1000-6893.2014.0244 LUO J S. Transition and prediction for hypersonic boundary layers[J].Acta Aeronautica et Astronautica Sinica, 2015, 36(1):357-372.(in Chinese) DOI: 10.7527/S1000-6893.2014.0244
[4]	SU C H. The reliability of the improved eN method for the transition prediction of boundary layers on a flat plate[J]. Science China Physics, Mechanics and Astronomy, 2012, 55(5):837-843. doi: 10.1007/s11433-012-4692-y
[5]	MACK L M. Boundary-layer linear stability theory[R]. AGARD Rep.709. California: Jet Propulsion Laboratory, California Institute of Technology, 1984.
[6]	SU C H, ZHOU H. Transition prediction of a hypersonic boundary layer over a cone at small angle of attack:with the improvement of e-N method[J]. Science in China Series G:Physics, Mechanics and Astronomy, 2009, 52(1):115-123. DOI: 10.1007/s11433-009-0006-4
[7]	SU C H, ZHOU H. Transition prediction for supersonic and hypersonic boundary layers on a cone with angle of attack[J]. Science in China Series G:Physics, Mechanics and Astronomy, 2009, 52(8):1223-1232. DOI: 10.1007/s11433-009-0162-6
[8]	SU C H, ZHOU H. Transition prediction of the supersonic boundary layer on a cone under the consideration of receptivity to slow acoustic waves[J]. Science China Physics, Mechanics and Astronomy, 2011, 54(10):1875-1882. DOI: 10.1007/s11433-011-4472-0
[9]	KING R A. Three-dimensional boundary-layer transition on a cone at Mach 3.5[J]. Experiments in Fluids, 1992, 13(5): 305-314. DOI: 10.1007/BF00209502
[10]	GOLDSTEIN M E. The evolution of Tollmien-Sclichting waves near a leading edge[J]. Journal of Fluid Mechanics, 1983, 127:59-81. DOI: 10.1017/s002211208300261x
[11]	GOLDSTEIN M E. Scattering of acoustic waves into Tollmien-Schlichting waves by small streamwise variations in surface geometry[J]. Journal of Fluid Mechanics, 1985, 154:509-529. DOI: 10.1017/s0022112085001641
[12]	RUBAN A I. On the generation of Tollmien-Schlichting waves by sound[J]. Fluid Dynamics, 1985, 19(5):709-717. DOI: 10.1007/bf01093536
[13]	FEDOROV A V, KHOKHLOV A P. Prehistory of instability in a hypersonic boundary layer[J]. Theoretical and Computational Fluid Dynamics, 2001, 14(6):359-375. DOI: 10.1007/s001620100038
[14]	FEDOROV A V. Receptivity of a high-speed boundary layer to acoustic disturbances[J]. Journal of Fluid Mechanics, 2003, 491:101-129. DOI: 10.1017/s0022112003005263
[15]	FEDOROV A. Transition and stability of high-speed boundary layers[J]. Annual Review of Fluid Mechanics, 2011, 43(1):79-95. DOI: 10.1146/annurev-fluid-122109-160750
[16]	MA Y B, ZHONG X L. Receptivity of a supersonic boundary layer over a flat plate. Part 1. Wave structures and interactions[J]. Journal of Fluid Mechanics, 2003, 488: 31-78. DOI: 10.1017/s0022112003004786
[17]	MA Y B, ZHONG X L. Receptivity of a supersonic boundary layer over a flat plate. Part 2. Receptivity to free-stream sound[J]. Journal of Fluid Mechanics, 2003, 488: 79-121. DOI: 10.1017/s0022112003004798
[18]	GAO J, LUO J S, WU X S. Receptivity of hypersonic boundary layer due to fast-slow acoustics interaction[J]. Acta Mechanica Sinica, 2015, 31(6):899-909. DOI: 10.1007/s10409-015-0504-8
[19]	WAN BB, LUO J S, SU C H. Response of a hypersonic blunt cone boundary layer to slow acoustic waves with assessment of various routes of receptivity[J]. Applied Mathematics and Mechanics, 2018, 39(11):1643-1660. DOI: 10.1007/s10483-018-2391-6
[20]	MA Y B, ZHONG X L. Receptivity of a supersonic boundary layer over a flat plate. Part 3. Effects of different types of free-stream disturbances[J]. Journal of Fluid Mechanics, 2005, 532:63-109. DOI: 10.1017/s0022112005003836
[21]	BALAKUMAR P. Receptivity of hypersonic boundary layers to acoustic andvortical disturbances (invited)[C]//Proc of the 45th AIAA Fluid Dynamics Conference, Dallas, TX. Reston, Virginia: AIAA, 2015. DOI: 10.2514/6.2015-2473
[22]	高军.超声速边界层的稳定性分析方法及声波感受性[D].天津: 天津大学, 2014. GAO J. The method of the stability analysis and receptivity to acoustics in supersonic boundary layers[D]. Tianjin: Tianjin University, 2014.(in Chinese)
[23]	张永明. PSE在可压缩边界层中扰动演化和超音速边界层二次失稳中的应用[D].天津: 天津大学, 2008. ZHANG Y M. Applications of PSE to evolution of disturbances in compressible boundary layers and to secondary instability in supersonic boundary layers[D]. Tianjin: Tianjin University, 2008.(in Chinese)
[24]	ZHANG Y M, ZHOU H. Verification of parabolized stability equations for its application to compressible boundary layers[J]. Applied Mathematics and Mechanics, 2007, 28(8):987-998. DOI: 10.1007/s10483-007-0801-3
[25]	ZHANG Y M, ZHOU H. PSE as applied to problems of transition in compressible boundary layers[J]. Applied Mathematics and Mechanics, 2008, 29(7):833-840. DOI: 10.1007/s10483-008-0701-8
[26]	ZANG T A, CHANG C L, NG L L. The transition prediction toolkit: LST, SIT, PSE, DNS, and LES[C]//Fifth Symposium on Numerical and Physical Aspects of Aerodynamic Flows, 1992.
[27]	LIU J X, ZHANG S L, FU S. Linear spatial instability analysis in 3D boundary layers using plane-marching 3D-LPSE[J]. Applied Mathematics and Mechanics, 2016, 37(8):1013-1030. DOI: 10.1007/s10483-016-2114-8

Cited By

Get Citation

PDF

XML

Article views (195) PDF downloads (37)

Turn off MathJax

Article Contents

Abstract

References

Intermodal exchange and wall temperature effect in a supersonic boundary layer

Abstract

References

Catalog

Export File

Citation

Format

Content