https://orcid.org/0000-0003-1505-7774
Abstract
The design of supersonic and hypersonic air-breathing vehicles is influenced by the transition between the Mach reflection (MR) and regular reflection (RR) phenomena. The purpose of this study is to investigate the dynamic transition of unsteady supersonic flow from MR to RR over a two-dimensional wedge numerically. The trailing edge of the wedge moves downstream along the x-direction with a velocity, V(t) at a freestream Mach number of 3. An unsteady compressible inviscid flow solver is used to simulate the phenomenon. The Arbitrary Lagrangian–Eulerian (ALE) technique is applied to deform the mesh during the wedge motion. The dynamic transition from MR to RR is defined by two criteria, the sonic and the von Neumann. Moreover, the lag in the dynamic transition from the steady-state condition is studied using various nondimensional angular velocities, κ, in the range of [0.1-2]. The lag effect in the shock system is remarkable at the high values of κ greater than 1.5. Furthermore, the dynamic transition from MR to RR happens below the dual solution domain (DSD) because the shock is upstream curved during the wedge motion.
Issue Section:
Flows in Complex Systems
References
1.
Jagadeesh
,
G.
, 2008
, “
Industrial Applications of Shock Waves
,” Proc. Inst. Mech. Eng., Part G
,
222
(5
), pp. 575
–583
.10.1243/09544100JAERO3062.
Chin
,
C.
,
Li
,
M.
,
Harkin
,
C.
,
Rochwerger
,
T.
,
Chan
,
L.
,
Ooi
,
A.
,
Risborg
,
A.
, and
Soria
,
J.
, 2013
, “
Investigation of the Flow Structures in Supersonic Free and Impinging Jet Flows
,” ASME J. Fluids Eng.
,
135
(3
), p. 031202
.10.1115/1.40231903.
Rita
,
A.
,
Sivakumar
,
A.
, and
Martin Britto Dhas
,
S.
, 2019
, “
Influence of Shock Waves on Structural and Morphological Properties of Copper Oxide Nps for Aerospace Applications
,” J. Nanostruct. Chem.
,
9
(3
), pp. 225
–230
.10.1007/s40097-019-00313-04.
Khan
,
M. R. A.
, and
Hasan
,
A. T.
, 2021
, “
Design and Evaluation of Generic Bump for Flow Control in a Supersonic Inlet Isolator
,” ASME J. Fluids Eng.
,
143
(5
), p. 051207
.10.1115/1.40496775.
Tripathi
,
M.
,
Ganti
,
H.
, and
Khare
,
P.
, 2022
, “
Interactions Between Shock Waves and Liquid Droplet Clusters: Interfacial Physics
,” ASME J. Fluids Eng.
,
144
(10
), p. 101401
.10.1115/1.40541816.
Hamada
,
A.
,
Margha
,
L.
,
Alnemr
,
A. K.
,
Abdelrahman
,
M.
, and
Guaily
,
A.
, 2023
, “
Unsteady Supersonic Flow Over a 2-d Morphing Shock Control Bump Using Different Velocity Profiles
,” AIAA
Paper No. 2023-2117.10.2514/6.2023-21177.
Hamada
,
A. A.
,
Margha
,
L.
,
AbdelRahman
,
M. M.
, and
Guaily
,
A.
, 2022
, “
Shock System Dynamics of a Morphing Bump Over a Flat Plate
,” ASME
Paper No. FEDSM2022-87504.10.1115/FEDSM2022-875048.
Mouton
,
C. A.
, 2007
, “
Transition between regular reflection and mach reflection in the dual-solution domain
,” Ph.D. thesis,
California Institute of Technology, Pasadena, CA
.9.
Hornung
,
H.
, 1986
, “
Regular and Mach Reflection of Shock Waves
,” Annu. Rev. Fluid Mech.
,
18
(1
), pp. 33
–58
.10.1146/annurev.fl.18.010186.00034110.
Ben-Dor
,
G.
, 2007
, Shock Wave Reflection Phenomena
, Vol.
2
,
Springer
, New York.11.
Li
,
H.
, and
Ben-Dor
,
G.
, 1997
, “
A Parametric Study of Mach Reflection in Steady Flows
,” J. Fluid Mech.
,
341
, pp. 101
–125
.10.1017/S002211209700537512.
Azevedo
,
D.
, and
Liu
,
C. S.
, 1993
, “
Engineering Approach to the Prediction of Shock Patterns in Bounded High-Speed Flows
,” AIAA J.
,
31
(1
), pp. 83
–90
.10.2514/3.1132213.
Mach
,
E.
, 1878
, Über Den Verlauf Der Funkenwellen in Der Ebene Und im Raume
,
kk Hof-Und Staatsdruckerei
.14.
Von Neumann
,
J.
, 1943
, “
Oblique Reflection of Shocks
,” Bureau Ordinance, Explosive Research Report No. 12, WA
.15.
Hornung
,
H.
, and
Robinson
,
M.
, 1982
, “
Transition From Regular to Mach Reflection of Shock Waves Part 2. the Steady-Flow Criterion
,” J. Fluid Mech.
,
123
, pp. 155
–164
.10.1017/S002211208200300016.
Chpoun
,
A.
,
Passerel
,
D.
,
Li
,
H.
, and
Ben-Dor
,
G.
, 1995
, “
Reconsideration of Oblique Shock Wave Reflections in Steady Flows. Part 1: Experimental Investigation
,” J. Fluid Mech.
,
301
, pp. 19
–35
.10.1017/S002211209500377617.
Ivanov
,
M.
,
Kudryavtsev
,
A.
,
Nikiforov
,
S.
,
Khotyanovsky
,
D.
, and
Pavlov
,
A.
, 2003
, “
Experiments on Shock Wave Reflection Transition and Hysteresis in Low-Noise Wind Tunnel
,” Phys. Fluids
,
15
(6
), pp. 1807
–1810
.10.1063/1.157287418.
Tao
,
Y.
,
Fan
,
X.
, and
Zhao
,
Y.
, 2014
, “
Viscous Effects of Shock Reflection Hysteresis in Steady Supersonic Flows
,” J. Fluid Mech.
,
759
, pp. 134
–148
.10.1017/jfm.2014.57419.
Hu
,
Y.-C.
,
Zhou
,
W.-F.
,
Tang
,
Z.-G.
,
Yang
,
Y.-G.
, and
Qin
,
Z.-H.
, 2021
, “
Mechanism of Hysteresis in Shock Wave Reflection
,” Phys. Rev. E
,
103
(2
), p. 023103
.10.1103/PhysRevE.103.02310320.
Chpoun
,
A.
, and
Ben-Dor
,
G.
, 1995
, “
Numerical Confirmation of the Hysteresis Phenomenon in the Regular to the Mach Reflection Transition in Steady Flows
,” Shock Waves
,
5
(4
), pp. 199
–203
.10.1007/BF0141900121.
Ivanov
,
M.
,
Gimelshein
,
S.
, and
Beylich
,
A.
, 1995
, “
Hysteresis Effect in Stationary Reflection of Shock Waves
,” Phys. Fluids
,
7
(4
), pp. 685
–687
.10.1063/1.86859122.
Ivanov
,
M.
,
Zeitoun
,
D.
,
Vuillon
,
J.
,
Gimelshein
,
S.
, and
Markelov
,
G.
, 1996
, “
Investigation of the Hysteresis Phenomena in Steady Shock Reflection Using Kinetic and Continuum Methods
,” Shock Waves
,
5
(6
), pp. 341
–346
.10.1007/BF0243400923.
Ivanov
,
M.
,
Markelov
,
G.
,
Kudryavtsev
,
A.
, and
Gimelshein
,
S.
, 1998
, “
Numerical Analysis of Shock Wave Reflection Transition in Steady Flows
,” AIAA J.
,
36
(11
), pp. 2079
–2086
.10.2514/2.30924.
Mouton
,
C. A.
, and
Hornung
,
H. G.
, 2008
, “
Experiments on the Mechanism of Inducing Transition Between Regular and Mach Reflection
,” Phys. Fluids
,
20
(12
), p. 126103
.10.1063/1.304226125.
Gao
,
B.
, and
Wu
,
Z.
, 2010
, “
A Study of the Flow Structure for Mach Reflection in Steady Supersonic Flow
,” J. Fluid Mech.
,
656
, pp. 29
–50
.10.1017/S002211201000101126.
Bai
,
C.-Y.
, and
Wu
,
Z.-N.
, 2017
, “
Size and Shape of Shock Waves and Slipline for Mach Reflection in Steady Flow
,” J. Fluid Mech.
,
818
, pp. 116
–140
.10.1017/jfm.2017.13927.
Tao
,
Y.
,
Liu
,
W.
,
Fan
,
X.
,
Xiong
,
B.
,
Yu
,
J.
, and
Sun
,
M.
, 2017
, “
A Study of the Asymmetric Shock Reflection Configurations in Steady Flows
,” J. Fluid Mech.
,
825
, pp. 1
–15
.10.1017/jfm.2017.28028.
Roy
,
S.
, and
Gopalapillai
,
R.
, 2019
, “
An Analytical Model for Asymmetric Mach Reflection Configuration in Steady Flows
,” J. Fluid Mech.
,
863
, pp. 242
–268
.10.1017/jfm.2018.94529.
Naidoo
,
K.
, and
Skews
,
B. W.
, 2011
, “
Dynamic Effects on the Transition Between Two-Dimensional Regular and Mach Reflection of Shock Waves in an Ideal, Steady Supersonic Free Stream
,” J. Fluid Mech.
,
676
, pp. 432
–460
.10.1017/jfm.2011.5830.
Naidoo
,
K.
, and
Skews
,
B.
, 2014
, “
Dynamic Transition From Mach to Regular Reflection of Shock Waves in a Steady Flow
,” J. Fluid Mech.
,
750
, pp. 385
–400
.10.1017/jfm.2014.28831.
Goyal
,
R.
,
Sameen
,
A.
,
Jayachandran
,
T.
, and
Rajesh
,
G.
, 2021
, “
Dynamic Effects in Transition From Regular to Mach Reflection in Steady Supersonic Flows
,” Phys. Rev. E
,
104
(5
), p. 055101
.10.1103/PhysRevE.104.05510132.
Felthun
,
L. T.
, and
Skews
,
B. W.
, 2004
, “
Dynamic Shock Wave Reflection
,” AIAA Journal
,
42
(8
), pp. 1633
–1639
.10.2514/1.81033.
Laguarda
,
L.
,
Hickel
,
S.
,
Schrijer
,
F.
, and
Van Oudheusden
,
B.
, 2020
, “
Dynamics of Unsteady Asymmetric Shock Interactions
,” J. Fluid Mech.
,
888
, p. A18.10.1017/jfm.2020.2834.
Margha
,
L.
,
Hamada
,
A. A.
,
Ahmed
,
O.
, and
Eltaweel
,
A.
, 2022
, “
Numerical Investigation of a Rotating Double Compression Ramp Intake
,” ASME
Paper No. FEDSM2022-87753.10.1115/FEDSM2022-8775335.
Margha
,
L.
,
Hamada
,
A. A.
,
Knight
,
D. D.
, and
Eltaweel
,
A.
, 2021
, “
Dynamic Transition From Regular to Mach Reflection Over a Moving Wedge
,” ASME
Paper No. IMECE2021-69625.10.1115/IMECE2021-6962536.
Margha
,
L.
,
Hamada
,
A. A.
, and
Eltaweel
,
A.
, 2022
, “
Dynamic Transition From Mach to Regular Reflection Over a Moving Wedge
,” ASME
Paper No.FEDSM2022-87754.10.1115/FEDSM2022-8775437.
Margha
,
L.
,
Hamada
,
A.
, and
Eltaweel
,
A.
, 2023
, “
RR to MR Over a Moving Wedge at a High Supersonic Flow
,” AIAA
Paper No. AIAA-2023-1649.10.2514/6.AIAA-2023-164938.
Kurganov
,
A.
, and
Tadmor
,
E.
, 2000
, “
New High-Resolution Semi-Discrete Central Schemes for Hamilton–Jacobi Equations
,” J. Comput. Phys.
,
160
(2
), pp. 720
–742
.10.1006/jcph.2000.648539.
Kurganov
,
A.
,
Noelle
,
S.
, and
Petrova
,
G.
, 2001
, “
Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton–Jacobi Equations
,” SIAM J. Sci. Comput.
,
23
(3
), pp. 707
–740
.10.1137/S106482750037341340.
Greenshields
,
C. J.
,
Weller
,
H. G.
,
Gasparini
,
L.
, and
Reese
,
J. M.
, 2010
, “
Implementation of Semi-Discrete, Non-Staggered Central Schemes in a Colocated, Polyhedral, Finite Volume Framework, for High-Speed Viscous Flows
,” Int. J. Numer. Methods Fluids
,
63
(1
), pp. 1
–21
.10.1002/fld.206941.
Hirt
,
C. W.
,
Amsden
,
A. A.
, and
Cook
,
J.
, 1974
, “
An Arbitrary Lagrangian–Eulerian Computing Method for All Flow Speeds
,” J. Comput. Phys.
,
14
(3
), pp. 227
–253
.10.1016/0021-9991(74)90051-5Copyright © 2023 by ASME
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