Abstract
The primary aim of this study is to analyze the unsteady characteristics of the interaction between a reflected shock wave and a laminar boundary layer in an end-wall shock tube. Our direct numerical simulations at shock Mach numbers of Ms = 1.9, 2.5, and 3.5 using a fifth-order WENO scheme and three-step Runge–Kutta time integration method revealed inhomogeneity and anisotropy in the shock bifurcation. Surprisingly, the upper and lower bifurcated structures maintain a notably asymmetric flow during the forward propagation of the reflected shock bifurcation. The inverse flow in the bifurcation resembles a crooked earthworm structure, exhibiting high-frequency oscillations indicative of instability. However, at higher shock intensities, the earthworm transforms into a stable strip-like configuration, facilitating the entrapment of inverse flow and leading to rapid bifurcation height growth and early convergence. Additionally, isolated islands with high density, temperature, and pressure emerge in the transitional region behind the bifurcated shocks, due to variations in wave propagation speed.
References
1.
Bernardini
, M.
, Della Posta
, G.
, Salvadore
, F.
, and Martelli
, E.
, 2023
, “Unsteadiness Characterisation of Shock Wave/Turbulent Boundary-Layer Interaction at Moderate Reynolds Number
,” J. Fluid Mech.
, 954
, p. A43
.10.1017/jfm.2022.10382.
Gaitonde
, D. V.
, and Adler
, M. C.
, 2023
, “Dynamics of Three-Dimensional Shock-Wave/Boundary-Layer Interactions
,” Annu. Rev. Fluid Mech.
, 55
(1
), pp. 291
–321
.10.1146/annurev-fluid-120720-0225423.
Zuo
, F. Y.
, and Pirozzoli
, S.
, 2024
, “Recent Progress in Conical Shock Wave/Boundary Layer Interaction With Spanwise Pressure Gradient
,” Propul. Power Res.
, 13
(3
), pp. 295
–318
.10.1016/j.jppr.2024.08.0034.
Sabnis
, K.
, and Babinsky
, H.
, 2023
, “A Review of Three-Dimensional Shock Wave–Boundary-Layer Interactions
,” Prog. Aerosp. Sci.
, 143
, p. 100953
.10.1016/j.paerosci.2023.1009535.
Laguarda
, L.
, Hickel
, S.
, Schrijer
, F. F. J.
, and Van Oudheusden
, B. W.
, 2024
, “Reynolds Number Effects in Shock-Wave/Turbulent Boundary-Layer Interactions
,” J. Fluid Mech.
, 989
, p. A20
.10.1017/jfm.2024.3616.
Threadgill
, J. A.
, Little
, J. C.
, and Wernz
, S. H.
, 2021
, “Transitional Shock Boundary Layer Interactions on a Compression Ramp at Mach 4
,” AIAA J.
, 59
(12
), pp. 4824
–4841
.10.2514/1.J0599817.
Ceci
, A.
, Palumbo
, A.
, Larsson
, J.
, and Pirozzoli
, S.
, 2024
, “Low-Frequency Unsteadiness in Hypersonic Swept Shock Wave-Boundary Layer Interactions
,” Phys. Rev. Fluids
, 9
(5
), p. 054603
.10.1103/PhysRevFluids.9.0546038.
Thangadurai
, M.
, Kundu
, A.
, and Biswas
, G.
, 2022
, “Analysis of Shock Wave-Boundary Layer Interaction in a Shock Tube Using Higher Order Scheme
,” Comput. Fluids
, 236
, p. 105305
.10.1016/j.compfluid.2022.1053059.
Kundu
, A.
, Thangadurai
, M.
, and Biswas
, G.
, 2021
, “Investigation on Shear Layer Instabilities and Generation of Vortices During Shock Wave and Boundary Layer Interaction
,” Comput. Fluids
, 224
, p. 104966
.10.1016/j.compfluid.2021.10496610.
Davies
, L.
, and Wilson
, J. L.
, 1969
, “Influence of Reflected Shock and Boundary‐Layer Interaction on Shock‐Tube Flows
,” Phys. Fluids
, 12
(5
), pp. I-37
–I-43
.10.1063/1.169262511.
Mark
, H.
, 1958
, “The Interaction of a Reflected Shock Wave With the Boundary Layer in a Shock Tube
,” No. NACA-TM-1418.12.
Wilson
, G.
, Sharma
, S.
, and Gillespie
, W.
, 1993
, “Time-Dependent Simulation of Reflected-Shock/Boundary Layer Interaction
,” AIAA
Paper No. 1993-480.10.2514/6.1993-48013.
Petersen
, E. L.
, and Hanson
, R. K.
, 2001
, “Nonideal Effects Behind Reflected Shock Waves in a High-Pressure Shock Tube
,” Shock Waves
, 10
(6
), pp. 405
–420
.10.1007/PL0000405114.
Petersen
, E. L.
, and Hanson
, R. K.
, 2006
, “Measurement of Reflected-Shock Bifurcation Over a Wide Range of Gas Composition and Pressure
,” Shock Waves
, 15
(5
), pp. 333
–340
.10.1007/s00193-006-0032-315.
Zhao
, W.
, Fan
, C.
, Deiterding
, R.
, Li
, X.
, Liang
, J.
, and Yang
, X.
, 2024
, “A New Rapid Deflagration-to-Detonation Transition in a Short Smooth Tube
,” Phys. Fluids
, 36
(3
), p. 036104
.10.1063/5.019150016.
Lai
, S.
, Tang
, S.
, Xu
, C.
, Sekularac
, N.
, and Fang
, X.
, 2023
, “Computational Diagnostics for Flame Acceleration and Transition to Detonation in a Hydrogen/Air Mixture
,” Combust. Flame
, 258
, p. 113054
.10.1016/j.combustflame.2023.11305417.
Gamezo
, V. N.
, Oran
, E. S.
, and Khokhlov
, A. M.
, 2005
, “Three-Dimensional Reactive Shock Bifurcations
,” Proc. Combust. Inst.
, 30
(2
), pp. 1841
–1847
.10.1016/j.proci.2004.08.25918.
Yang
, H.
, and Radulescu
, M. I.
, 2021
, “Enhanced DDT Mechanism From Shock-Flame Interactions in Thin Channels
,” Proc. Combust. Inst.
, 38
(3
), pp. 3481
–3495
.10.1016/j.proci.2020.07.14019.
Zhu
, Y.
, and Gao
, L.
, 2021
, “Effect of Reactive Gas Mixture Distributions on the Flame Evolution in Shock Accelerated Flow
,” Acta Astronaut.
, 179
, pp. 484
–494
.10.1016/j.actaastro.2020.11.02620.
Hargis
, J. W.
, and Petersen
, E. L.
, 2017
, “Shock-Tube Boundary-Layer Effects on Reflected-Shock Conditions With and Without CO2
,” AIAA J.
, 55
(3
), pp. 902
–912
.10.2514/1.J05525321.
Hargis
, J. W.
, and Petersen
, E. L.
, 2015
, “Methane Ignition in a Shock Tube With High Levels of CO2 Dilution: Consideration of the Reflected-Shock Bifurcation
,” Energy Fuels
, 29
(11
), pp. 7712
–7726
.10.1021/acs.energyfuels.5b0176022.
Yamashita
, H.
, Kasahara
, J.
, Sugiyama
, Y.
, and Matsuo
, A.
, 2012
, “Visualization Study of Ignition Modes Behind Bifurcated-Reflected Shock Waves
,” Combust. Flame
, 159
(9
), pp. 2954
–2966
.10.1016/j.combustflame.2012.05.00923.
Grogan
, K. P.
, and Ihme
, M.
, 2017
, “Regimes Describing Shock Boundary Layer Interaction and Ignition in Shock Tubes
,” Proc. Combust. Inst.
, 36
(2
), pp. 2927
–2935
.10.1016/j.proci.2016.06.07824.
Zhu
, K.
, Jiang
, L. X.
, Liu
, W. D.
, Sun
, M. B.
, Wang
, Q. C.
, and Hu
, Z. W.
, 2021
, “Wall Temperature Effects on Shock Wave/Turbulent Boundary Layer Interaction Via Direct Numerical Simulation
,” Acta Astronaut.
, 178
, pp. 499
–510
.10.1016/j.actaastro.2020.08.04225.
Fang
, J.
, Zheltovodov
, A. A.
, Yao
, Y.
, Moulinec
, C.
, and Emerson
, D. R.
, 2020
, “On the Turbulence Amplification in Shock-Wave/Turbulent Boundary Layer Interaction
,” J. Fluid Mech.
, 897
, p. A32
.10.1017/jfm.2020.35026.
Huang
, W.
, Wu
, H.
, Yang
, Y. G.
, Yan
, L.
, and Li
, S. B.
, 2020
, “Recent Advances in the Shock Wave/Boundary Layer Interaction and Its Control in Internal and External Flows
,” Acta Astronaut.
, 174
, pp. 103
–122
.10.1016/j.actaastro.2020.05.00127.
Tong
, F.
, Duan
, J.
, and Li
, X.
, 2021
, “Shock Wave and Turbulent Boundary Layer Interaction in a Double Compression Ramp
,” Comput. Fluids
, 229
, p. 105087
.10.1016/j.compfluid.2021.10508728.
Weber
, Y. S.
, Oran
, E. S.
, Boris
, J. P.
, and Anderson
, J. D.
, Jr, 1995
, “The Numerical Simulation of Shock Bifurcation Near the End Wall of a Shock Tube
,” Phys. Fluids
, 7
(10
), pp. 2475
–2488
.10.1063/1.86869129.
Arun
, K. R.
, and Kim
, H. D.
, 2013
, “Computational Study of the Unsteady Flow Characteristics of a Micro Shock Tube
,” J. Mech. Sci. Technol.
, 27
(2
), pp. 451
–459
.10.1007/s12206-012-1259-930.
Bulovich
, S. V.
, Vikolaĭnen
, V. É.
, Zverintsev
, S. V.
, and Petrov
, R. L.
, 2007
, “Numerical Simulation of the Interaction Between Reflected Shock Wave and Near-Wall Boundary Layer
,” Tech. Phys. Lett.
, 33
(2
), pp. 173
–175
.10.1134/S106378500702024131.
Amir
, A. F.
, Yusoff
, M. Z.
, Yusaf
, T.
, and Ahmed
, D. I.
, 2012
, “Numerical Investigation of Flow Instability in Shock Tube Due to Shock Wave‐Contact Surface Interactions
,” Int. J. Numer. Methods Heat Fluid Flow
, 22
(3
), pp. 377
–398
.10.1108/0961553121120807932.
Penyazkov
, O.
, and Skilandz
, A.
, 2018
, “Bifurcation Parameters of a Reflected Shock Wave in Cylindrical Channels of Different Roughnesses
,” Shock Waves
, 28
(2
), pp. 299
–309
.10.1007/s00193-017-0739-333.
Daru
, V.
, and Tenaud
, C.
, 2009
, “Numerical Simulation of the Viscous Shock Tube Problem by Using a High Resolution Monotonicity-Preserving Scheme
,” Comput. Fluids
, 38
(3
), pp. 664
–676
.10.1016/j.compfluid.2008.06.00834.
Steger
, J. L.
, and Warming
, R.
, 1981
, “Flux Vector Splitting of the Inviscid Gasdynamic Equations With Application to Finite Difference Methods
,” J. Comput. Phys.
, 40
(2
), pp. 263
–293
.10.1016/0021-9991(81)90210-235.
Jiang
, G. S.
, and Shu
, C. W.
, 1996
, “Efficient Implementation of Weighted ENO Schemes
,” J. Comput. Phys.
, 126
(1
), pp. 202
–228
.10.1006/jcph.1996.013036.
Matsuo
, K.
, Kawagoe
, S.
, and Kage
, K.
, 1974
, “The Interaction of a Reflected Shock Wave With the Boundary Layer in a Shock Tube
,” Bull. JSME
, 17
(110
), pp. 1039
–1046
.10.1299/jsme1958.17.103937.
Mirels
, H.
, 1955
, “Laminar Boundary Layer Behind Shock Advancing Into Stationary Fluid
,” No. NACA-TN-3401.38.
Zhang
, Y.
, Ma
, Z.
, Zou
, J.
, and Zheng
, Y.
, 2019
, “Shock Bifurcation Phenomenon in the Reflected Shock/Boundary Layer Interaction
,” The Proceedings of the 2018 Asia-Pacific International Symposium on Aerospace Technology (APISAT 2018
), 9th ed., Chengdu City, China, Oct. 16–18
, pp. 423
–430
.10.1007/978-981-13-3305-7_3439.
Zhang
, Y.
, Zou
, J.
, Xie
, J.
, Li
, X.
, Ma
, Z.
, and Zheng
, Y.
, 2018
, “Asymmetric Characteristics of the Shock Bifurcation in the Reflected Shock/Boundary Layer Interaction
,” Int. J. Numer. Methods Heat Fluid Flow
, 28
(10
), pp. 2357
–2377
.10.1108/HFF-09-2017-0376
