Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-20T18:20:19.692Z Has data issue: false hasContentIssue false
  • English
  • Français

Instability of shock train behaviour with incident shocks

Published online by Cambridge University Press:  01 December 2020

Nan Li ,
Juntao Chang Open the ORCID record for Juntao Chang [Opens in a new window] ,
Kejing Xu ,
Daren Yu  and
Wen Bao
Nan Li
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, PR China
Juntao Chang*
Affiliation:
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin150001, PR China
Kejing Xu
Affiliation:
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin150001, PR China
Daren Yu
Affiliation:
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin150001, PR China
Wen Bao
Affiliation:
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin150001, PR China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In a back pressured duct with incident shocks, the shock train exhibits violent oscillations or even a rapid movement when it passes through a shock-wave–boundary-layer interaction (SWBLI) region. In this study, the dynamics of a shock train system was investigated. Linear stability analysis was used to identify the underlying cause of the unstable behaviour. Results from the eigenvalue analysis indicated that as the shock train enters the SWBLI region, the divergent vibration, which is the outcome of a Hopf bifurcation, emerges. An analysis based on the feedback mechanism identified a criterion for this instability, i.e. the sign of the gradient of the maximal pressure that the boundary layer can sustain. Different unstable motions were also investigated according to the condition of the non-existence of a limit cycle. These motions were associated with the speed of the shock train and the configurations of the flow parameter gradients. It was shown in the controllability matrix that the rapid movement is uncontrollable, which indicates that there is a low correlation between the shock train motion and the flap actuator in the SWBLI region. However, for the remaining part of the unstable motion, a fast-response actuator is required. According to the observability analysis, the shock train movement contributes more to the variation in the pressure behind the first separation shock than the backpressure further downstream, which confirms that monitoring the pressure change along the tunnel is a better method for shock train detection rather than a polynomial model using the backpressure.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models Compressible Flows: Shock waves Boundary Layers: Boundary layer separation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 907 , 25 January 2021 , A40
Check for updates
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ashley, J., Szmuk, M., Clemens, N. T., Akella, M. R., Gogineni, S. & Donbar, J. M. 2014 Closed-loop control of shock location in Mach 1.8 direct connect wind tunnel. AIAA Paper 2014-2935.CrossRefGoogle Scholar
Bruce, P. J. K. & Babinsky, H. 2008 Unsteady shock wave dynamics. J. Fluid Mech. 603, 463–473.CrossRefGoogle Scholar
Bruce, P. J. K., Burton, D. M. F., Titchener, N. A. & Babinsky, H. 2011 Corner effect and separation in transonic channel flows. J. Fluid Mech. 679, 247–262.CrossRefGoogle Scholar
Burton, D. M. F. & Babinsky, H. 2012 Corner separation effects for normal shock wave/turbulent boundary layer interactions in rectangular channels. J. Fluid Mech. 707, 287–306.CrossRefGoogle Scholar
Chapman, D. R., Kuhen, D. M. & Larson, H. K. 1957 Investigation of separated flows in supersonic and subsonic streams with emphasis on the effect of transition. NACA Rep. 1356.Google Scholar
Clemens, N. T. & Narayanaswamy, V. 2014 Low-frequency unsteadiness of shock wave/turbulent boundary layer interactions. Annu. Rev. Fluid Mech. 46, 469–492.CrossRefGoogle Scholar
Cui, T., Wang, Y. & Yu, D. R. 2014 Bistability and hysteresis in a nonlinear dynamic model of shock motion. J. Aircraft 51 (5), 1373–1379.CrossRefGoogle Scholar
Culick, F. E. C. & Rogers, T. 1983 The response of normal shocks in diffusers. AIAA J. 21 (10), 1382–1390.CrossRefGoogle Scholar
Do, H., Im, S., Mungal, M. G. & Cappelli, M. A. 2011 a Visualizing supersonic inlet duct unstart using planar laser rayleigh scattering. Exp. Fluids 50 (6), 1651–1657.CrossRefGoogle Scholar
Do, H., Im, S., Mungal, M. G. & Cappelli, M. A. 2011 b The influence of boundary layers on supersonic inlet flow unstart induced by mass injection. Exp. Fluids 51 (3), 679–691.CrossRefGoogle Scholar
Donbar, J. M. 2012 Shock train position control in an axisymmetric scramjet combustor flowpath. AIAA Paper 2012-4145.Google Scholar
Grossman, I. J. & Bruce, P. J. K. 2018 Confinement effects on regular-irregular transition in shock-wave–boundary-layer interactions. J. Fluid Mech. 853, 171–204.CrossRefGoogle Scholar
Handa, T., Mitsuharu, M. & Matsuo, K. 2005 Three-dimensional normal shock-wave/boundary-layer interaction in a rectangular duct. AIAA J. 43 (10), 2182–2187.CrossRefGoogle Scholar
He, Y. B., Chang, J. T., Bao, W., Huang, H. Y. & Yu, D. R. 2016 Numerical investigation of local resistance to backpressure in hypersonic inlet with suction. J. Propul. Power 32 (6), 1531–1543.CrossRefGoogle Scholar
He, Y. B, Huang, H. Y. & Yu, D. R. 2016 Investigation of boundary-layer ejecting for resistance to back pressure in an isolator. Aerosp. Sci. Technol. 56, 1–13.CrossRefGoogle Scholar
Huang, H. X., Tan, H. J., Sun, S. & Wang, Z. 2018 Behavior of shock train in curved isolators with complex background waves. AIAA J. 56 (1), 329–341.Google Scholar
Huang, H. X., Tan, H. J., Wang, J., Sun, S. & Ning, L. 2014 A fluidic control method of shock train in hypersonic inlet/isolator. AIAA Paper 2014-3846.Google Scholar
Hunt, R. L. & Gamba, M. 2019 On the origin and propagation of perturbations that cause shock train inherent unsteadiness. J. Fluid Mech. 861, 815–859.CrossRefGoogle Scholar
Hutchins, K. E., Akella, M. R., Clemens, N. T., Donbar, J. M. & Gogineni, S. 2014 Experimental identification of transient dynamics for supersonic inlet unstart. J. Propul. Power 30 (6), 1605–1612.CrossRefGoogle Scholar
Hutzel, J. R., Decker, D. D., Cobb, R. G., King, P. I., Veth, M. J. & Donbar, J. M. 2011 Scramjet isolator shock train location techniques. AIAA Paper 2011-402.Google Scholar
Ikui, T., Matsuo, K., Nagai, M. & Honjo, M. 1974 Oscillation phenomena of pseudo-shock waves. Bull. JSME 17 (112), 1278–1285.Google Scholar
Im, S., Baccarella, D., McGann, B., Wermer, L. & Do, H. 2016 Unstart phenomena induced by mass addition and heat release in a model scramjet. J. Fluid Mech. 797, 604–629.CrossRefGoogle Scholar
Im, S. & Do, H. 2018 Unstart phenomena induced by flow choking in scramjet inlet-isolators. Prog. Aerosp. Sci. 97, 1–21.CrossRefGoogle Scholar
Klomparens, R., Driscoll, J. F. & Gamba, M. 2016 Response of a shock train to downstream back pressure forcing. AIAA Paper 2016-0078.Google Scholar
Laurence, S. J., Karl, S., Schramm, J. M. & Hannemann, K. 2013 Transient fluid-combustion phenomena in a model scramjet. J. Fluid Mech. 722, 85–120.Google Scholar
Le, D. B., Goyne, C. P. & Krauss, R. H. 2008 Shock train leading-edge detection in a dual-mode scramjet. J. Propul. Power 24 (5), 1035–1041.CrossRefGoogle Scholar
Li, N., Chang, J. T., Xu, K. J., Yu, D. R., Bao, W. & Song, Y. P. 2017 Prediction dynamic model of shock train with complex background waves. Phys. Fluids 29 (11), 116103.CrossRefGoogle Scholar
Li, N., Chang, J. T., Xu, K. J., Yu, D. R., Bao, W. & Song, Y. P. 2018 Oscillation of the shock train in an isolator with incident shocks. Phys. Fluids 30 (11), 116102.CrossRefGoogle Scholar
Li, N., Chang, J. T., Xu, K. J., Yu, D. R. & Song, Y. P. 2019 Closed-loop control of shock train in inlet-isolator with incident shocks. Exp. Therm. Fluid Sci. 103, 355–363.CrossRefGoogle Scholar
MacMartin, D. G. 2004 Dynamics and control of shock motion in a near-isentropic inlet. J. Aircraft 41 (4), 846–853.CrossRefGoogle Scholar
Matheis, J. & Hickel, S. 2015 On the transition between regular and irregular shock patterns of shock-wave/boundary-layer interactions. J. Fluid Mech. 776, 200–234.CrossRefGoogle Scholar
Matsuo, K., Mochizuki, H., Miyazato, Y. & Gohya, M. 1993 Oscillatory characteristics of a pseudo-shock wave in a rectangular straight duct. JSME Intl J. 36 (2), 222–229.Google Scholar
Riley, L. P., Gaitonde, D. V., Hagenmaier, M. A. & Donbar, M. 2018 Isolator dynamics during unstart of a dual-mode scramjet. J. Propul. Power 34 (6), 1–19.CrossRefGoogle Scholar
Sansica, A., Robinet, J. C., Alizard, F. & Goncalves, E. 2018 Three-dimensional instability of a flow past a sphere: Mach evolution of the regular and Hopf bifurcations. J. Fluid Mech. 855, 1088–1115.CrossRefGoogle Scholar
Sipp, D., Marquet, O., Meliga, P. & Barbagallo, A. 2010 Dynamics and control of global instabilities in open-flows: a linearized approach. Appl. Mech. Rev. 63 (3), 030801.Google Scholar
Smart, M. K. 2015 Flow modeling of pseudoshocks in backpressured ducts. AIAA J. 53 (12), 3577–3588.CrossRefGoogle Scholar
Su, W. Y., Ji, Y. X. & Chen, Y. 2016 Effects of dynamic backpressure on pseudoshock oscillations in scramjet inlet-isolator. J. Propul. Power 32 (2), 516–528.CrossRefGoogle Scholar
Sugiyama, H., Takeda, H., Zhang, J., Okuda, K. & Yamagishi, H. 1988 Locations and oscillation phenomena of pseudo-shock waves in a straight rectangular duct. JSME Intl J. 31 (1), 9–15.Google Scholar
Sullins, G. & Mclafferty, G. 1992 Experimental results of shock trains in rectangular ducts. AIAA Paper 1992-5103.Google Scholar
Tan, H. J., Sun, S. & Huang, H. X. 2012 Behavior of shock trains in a hypersonic inlet/isolator model with complex background waves. Exp. Fluids 53 (6), 1647–1661.CrossRefGoogle Scholar
Valdivia, A., Yuceil, K. B., Wagner, J. L., Clemens, N. T. & Dolling, D. S. 2014 Control of supersonic inlet-isolator unstart using active and passive vortex generators. AIAA J. 52 (1), 1207–1218.Google Scholar
Vanstone, L., Hashemi, K. E., Lingren, J., Akella, M. R., Clemens, N. T., Donbar, J. & Gogineni, S. 2018 Closed-loop control of shock-train location in a combusting scramjet. J. Propul. Power 34 (3), 660–667.CrossRefGoogle Scholar
Vanstone, L., Lingren, J. & Clemens, N. T. 2018 Supersonic isolator shock-train dynamics: simple physics-based model for closed-loop control of shock-train location. AIAA Paper 2018-1618.Google Scholar
Wagner, J. L., Yuceil, K. B. & Clemens, N. T. 2010 Velocimetry measurements of unstart of an inlet-isolator model in Mach 5 flow. AIAA J. 48 (9), 1875–1888.CrossRefGoogle Scholar
Wagner, J. L., Yuceil, K. B., Valdavia, A., Clemens, N. T. & Dolling, D. S. 2009 Experimental investigation of unstart in an inlet/isolator model in Mach 5 flow. AIAA J. 47 (6), 1528–1542.Google Scholar
Wang, B., Sandham, D. N., Hu, Z. W. & Liu, W. D. 2015 Numerical study of oblique shock-wave/boundary-layer interaction considering sidewall effects. J. Fluid Mech. 767, 526–561.Google Scholar
Wang, C. P., Cheng, C., Cheng, K. M. & Xue, L. S. 2018 Unsteady behavior of oblique shock train and boundary layer interactions. Aerosp. Sci. Technol. 79, 212–222.Google Scholar
Xiong, B., Fan, X. Q., Wang, Z. G. & Tao, Y. 2018 Analysis and modelling of unsteady shock train motions. J. Fluid Mech. 846, 240–262.CrossRefGoogle Scholar
Xu, K. J., Chang, J. T., Zhou, W. X. & Yu, D. R. 2015 Mechanism and prediction for occurrence of shock-train sharp forward movement. AIAA Paper 2015-3747.Google Scholar
Yamane, R., Kondo, E., Tomita, Y. & Sakae, N. 1984 a Vibration of pseudo-shock in straight duct, 1st report, fluctuation of static pressure. Bull. JSME 27 (229), 1385–1392.Google Scholar
Yamane, R., Takahashi, M. & Saito, H. 1984 b Vibration of pseudo-shock in straight duct, 2nd report, correlation of static pressure fluctuation. Bull. JSME 27 (229), 1393–1398.Google Scholar

Li et al. supplementary movie 1

The entire movement of the shock train at Mach 1.85 shown in figure 2.

Download Li et al. supplementary movie 1(Video)
Video 8.6 MB

Li et al. supplementary movie 2

The entire movement of the shock train at Mach 2.70 shown in figure 2.

Download Li et al. supplementary movie 2(Video)
Video 9 MB