logo

SCIENTIA SINICA Physica, Mechanica & Astronomica, Volume 48 , Issue 9 : 094702(2018) https://doi.org/10.1360/SSPMA2018-00173

Progress in unsteady converging shock reflection and refraction

More info
  • ReceivedMay 3, 2018
  • AcceptedMay 22, 2018
  • PublishedJul 30, 2018
PACS numbers

Abstract


Funding

国家自然科学基金(11772329,U1530103,11625211)


References

[1] Yang Y, Jiang Z L, Hu Z M. Advances in shock wave reflection phenomena (in Chinese). Adv Mech, 2012, 42: 141--161. Google Scholar

[2] Ben-Dor G. Shock Wave Reflection Phenomena. Springer-Verlag Press, Berlin, 2007. Google Scholar

[3] Yang J M, Li Z F, Zhu Y J, et al. Shock wave propagation and interactions (in Chinese). Adv Mech, 2016, 46: 541--587. Google Scholar

[4] Jiang Z L, Teng H H, Liu Y F. Some research progress on gaseous detonation physics (in Chinese). Adv Mech, 2012, 42: 129--140. Google Scholar

[5] Mach E. Uber den Verlauf von Funkenwellen in der Ebene und im Raume. Sitzugsbr Akad Wiss Wien, 1878, 78: 819--838. Google Scholar

[6] von Neumann J. Oblique Reflection of Shocks. Explosion Research Report No. 12, Navy Department, Bureau of Ordinance, Washington, DC, USA, 1943. Google Scholar

[7] von Neumann J. Refraction, Intersection and Reflection of shock Waves. NAVORD Report No. 203-45, Navy Department, Bureau of Ordinance, Washington, DC, USA, 1943. Google Scholar

[8] Courant R, Friedrichs K O. Hypersonic Flow and Shock Waves. New York: Wiley Interscience, 1959. Google Scholar

[9] Emanuel G. Gasdynamics: Theory and Applications. AIAA Education Series. New York: AIAA Inc., 1986. Google Scholar

[10] Ben-Dor G, Takayama K. The phenomena of shock wave reflection - A review of unsolved problems and future research needs. Shock Waves, 1992, 2211-223 CrossRef ADS Google Scholar

[11] Azevedo D J, Liu C S. Engineering approach to the prediction of shock patterns in bounded high-speed flows. AIAA J, 1993, 3183-90 CrossRef ADS Google Scholar

[12] Li H, Ben-dor G. A parametric study of Mach reflection in steady flows. J Fluid Mech, 1997, 341101-125 CrossRef Google Scholar

[13] Gao B, Wu Z N. A study of the flow structure for Mach reflection in steady supersonic flow. J Fluid Mech, 2010, 65629-50 CrossRef ADS Google Scholar

[14] Dewey J M, McMillin D J. Observation and analysis of the Mach reflection of weak uniform plane shock waves. I - Observations. II - Analysis. J Fluid Mech, 1985, 15249-66 CrossRef ADS Google Scholar

[15] Dewey J M, Mcmillin D J. Observation and analysis of the Mach reflection of weak uniform plane shock waves. Part 2. Analysis. J Fluid Mech, 1985, 15267-81 CrossRef ADS Google Scholar

[16] Tan L H, Ren Y X, Wu Z N. Analytical and numerical study of the near flow field and shape of the Mach stem in steady flows. J Fluid Mech, 2006, 546341 CrossRef ADS Google Scholar

[17] Xiang G, Wang C, Teng H. Study on Mach stems induced by interaction of planar shock waves on two intersecting wedges. Acta Mech Sin, 2016, 32362-368 CrossRef ADS Google Scholar

[18] Xiang G X, Wang C, Teng H H. Investigations of Three-Dimensional Shock/Shock Interactions over Symmetrical Intersecting Wedges. AIAA J, 2016, 541472-1481 CrossRef ADS Google Scholar

[19] Law C K, Glass I I. Diffraction of strong shock waves by a sharp compressive corner. CASI Trans, 1971, 4: 2--12. Google Scholar

[20] Ben-dor G. Relation between first and second triple-point trajectory angles in double Mach reflection. AIAA J, 1981, 19531-533 CrossRef ADS Google Scholar

[21] Li H, Ben-Dor G. Reconsideration of pseudo-steady shock wave reflections and the transition criteria between them. Shock Waves, 1995, 559-73 CrossRef ADS Google Scholar

[22] Semenov A N, Berezkina M K, Krasovskaya I V. Classification of shock wave reflections from a wedge. Part 1: Boundaries and domains of existence for different types of reflections. Tech Phys, 2009, 54491-496 CrossRef ADS Google Scholar

[23] Takayama K, Sasaki M. Effects of radius of curvature and initial angle on the shock transition over concave and convex walls. Rep Inst High Speed Mech, 1983, 46: 1--30. Google Scholar

[24] Courant R, Friedrichs K O. Hypersonic Flow and Shock Waves. New York: Wiley Interscience, 1948. Google Scholar

[25] Ben-Dor G, Takayama K. The dynamics of the transition from Mach to regular reflection over concave cylinders. Israel J Tech, 1986, 23: 71--74. Google Scholar

[26] Ben-Dor G, Takayama K. Analytical prediction of the transition from Mach to regular reflection over cylindrical concave wedges. J Fluid Mech, 1985, 158365-380 CrossRef ADS Google Scholar

[27] Ben-Dor G, Takayama K, Dewey J M. Further analytical considerations of weak planar shock wave reflections over a concave wedge. Fluid Dyn Res, 1987, 277-85 CrossRef ADS Google Scholar

[28] Takayama K, Ben-Dor G. A reconsideration of the transition criterion from mach to regular reflection over cylindrical concave surfaces. KSME J, 1989, 36-9 CrossRef Google Scholar

[29] Suzuki T, Adachi T, Kobayashi S. Nonstationary shock reflection over nonstraight surfaces: an approach with a method of multiple steps. Shock Waves, 1997, 755-62 CrossRef ADS Google Scholar

[30] Ames N. Equations, tables and charts for compressible flow. Ames Aeronautical Laboratory, Rep. 1953, 1135. Google Scholar

[31] Gruber S, Skews B. Weak shock wave reflection from concave surfaces. Exp Fluids, 2013, 541571 CrossRef ADS Google Scholar

[32] Heilig W H. Diffraction of a Shock Wave by a Cylinder. Phys Fluids, 1969, 12I-154 CrossRef ADS Google Scholar

[33] Itoh S, Okazaki N, Itaya M. On the transition between regular and Mach reflection in truly non-stationary flows. J Fluid Mech, 1981, 108383-400 CrossRef ADS Google Scholar

[34] Ginzburg I P, Markov Y S. Experimental investigation of the reflection of a shock wave from a two-facet wedge. Fluid Mech-Soviet Res, 1975, 4: 167--172. Google Scholar

[35] Pressure distribution behind a nonstationary reflected-diffracted oblique shock wave. AIAA J, 1984, 22305-306 CrossRef ADS Google Scholar

[36] Ben-Dor G, Dewey J M, Takayama K. The reflection of a plane shock wave over a double wedge. J Fluid Mech, 1987, 176483-520 CrossRef ADS Google Scholar

[37] Geva M, Ram O, Sadot O. The regular reflectionMach reflection transition in unsteady flow over convex surfaces. J Fluid Mech, 2018, 83748-79 CrossRef ADS Google Scholar

[38] Soni V, Hadjadj A, Chaudhuri A. Shock-wave reflections over double-concave cylindrical reflectors. J Fluid Mech, 2017, 81370-84 CrossRef ADS Google Scholar

[39] Dewey J M, Mcmillin D J, Classen D F. Photogrammetry of spherical shocks reflected from real and ideal surfaces. J Fluid Mech, 1977, 81701-717 CrossRef ADS Google Scholar

[40] Dewey J M, McMillin D J. An analysis of the particle trajectories in spherical blast waves reflected from real and ideal surfaces. Can J Phys, 1981, 591380-1390 CrossRef ADS Google Scholar

[41] Jameson A, Mavriplis D. Blast wave reflection trajectories from a height of burst. AIAA J, 1986, 24607-610 CrossRef ADS Google Scholar

[42] Takayama K, Sekiguchi H. Triple-point trajectory of a strong spherical shock wave. AIAA J, 1981, 19815-817 CrossRef ADS Google Scholar

[43] Vignati F, Guardone A. Leading edge reflection patterns for cylindrical converging shock waves over convex obstacles. Phys Fluids, 2016, 28096103 CrossRef ADS Google Scholar

[44] Ndebele B B, Skews B W. The reflection of cylindrical shock wave segments on cylindrical concave wall segments. Shock Waves, 2018, 19https://doi.org/10.1007/s00193-018-0812-6 CrossRef ADS Google Scholar

[45] Taub A H. Refraction of Plane Shock Waves. Phys Rev, 1947, 7251-60 CrossRef ADS Google Scholar

[46] Polachek H, Seeger R J. On Shock-Wave Phenomena. Google Scholar

[47] Jahn R G. The refraction of shock waves at a gaseous interface. J Fluid Mech, 1956, 1457-489 CrossRef ADS Google Scholar

[48] Catherasoo C J, Sturtevant B. Shock dynamics in non-uniform media. J Fluid Mech, 1983, 127539-561 CrossRef ADS Google Scholar

[49] Schwendeman D W. Numerical shock propagation in non-uniform media. J Fluid Mech, 1988, 188383-410 CrossRef ADS Google Scholar

[50] Abd-El-Fattah A M, Henderson L F, Lozzi A. Precursor shock waves at a slow-fast gas interface. J Fluid Mech, 1976, 76157-176 CrossRef ADS Google Scholar

[51] Henderson L F, Colella P, Puckett E G. On the refraction of shock waves at a slow-fast gas interface. J Fluid Mech, 1991, 2241-27 CrossRef ADS Google Scholar

[52] Henderson L F, Puckett E G. The refraction of shock pairs. Shock Waves, 2014, 24553-572 CrossRef ADS Google Scholar

[53] Zhai Z, Liu C, Qin F. Generation of cylindrical converging shock waves based on shock dynamics theory. Phys Fluids, 2010, 22041701 CrossRef ADS Google Scholar

[54] Zhang F, Si T, Zhai Z. Reflection of cylindrical converging shock wave over a plane wedge. Phys Fluids, 2016, 28086101 CrossRef ADS Google Scholar

[55] Wang H, Zhai Z, Luo X. A specially curved wedge for eliminating wedge angle effect in unsteady shock reflection. Phys Fluids, 2017, 29086103 CrossRef ADS Google Scholar

[56] Zhai Z, Li W, Si T. Refraction of cylindrical converging shock wave at an air/helium gaseous interface. Phys Fluids, 2017, 29016102 CrossRef ADS Google Scholar

[57] WenJuan G, ZhiGang Z, JuChun D. Numerical investigation on unsteady refraction of planar shock wave at air/SF$_6$ gas interface (in Chinese). Sci Sin-Phys Mech Astron, 2017, 47124701 CrossRef ADS Google Scholar

[58] Skews B W, Kleine H. Flow features resulting from shock wave impact on a cylindrical cavity. J Fluid Mech, 2007, 580481-493 CrossRef ADS Google Scholar

[59] Henderson L F, Lozzi A. Further experiments on transition to Mach reflexion. J Fluid Mech, 1979, 94541-559 CrossRef ADS Google Scholar

[60] Li H, Ben-Dor G. Analysis of double-Mach-reflection wave configurations with convexly curved Mach stems. Shock Waves, 1999, 9319-326 CrossRef ADS Google Scholar

[61] Shen H, Wen C Y, Zhang D L. A characteristic space-time conservation element and solution element method for conservation laws. J Comput Phys, 2015, 288101-118 CrossRef ADS Google Scholar

[62] Shen H, Wen C Y. A characteristic space-time conservation element and solution element method for conservation laws II. Multidimensional extension. J Comput Phys, 2016, 305775-792 CrossRef ADS Google Scholar

[63] Zeng S, Takayama K. On the refraction of shock wave over a slow-fast gas interface. Acta Astronaut, 1996, 38829-838 CrossRef ADS Google Scholar

[64] Abd-El-Fattah A M, Henderson L F. Shock waves at a slow-fast gas interface. J Fluid Mech, 1978, 8979-95 CrossRef ADS Google Scholar

  • Figure 1

    Schlieren images of a cylindrical shock reflection over a wedge with $\alpha_0$ = 35$^{\circ}$ from experiment (upper) and numerical simulation (lower) [54]. The Mach number of shock wave when encountering the wedge is 1.61. Numbers in the figure indicate the time of the shock impact (similarly hereinafter). IS, incident shock; RS, the reflected shock of the ISfrom wedge; $r_1$, the reflected shock of the ISfrom the focal point; m, Mach stem; s, shear layer.

  • Figure 2

    Schlieren images of a cylindrical shock reflection over a wedge with $\alpha_0$ = 65$^{\circ}$ and $\alpha_0$ = 75$^{\circ}$ from experiment and numerical simulation [54]. The shock Mach number is the same as that in the case of $\alpha_0$ = 35$^{\circ}$. $TP$, triple point; $r_2$, the reflected shock of $m_1$ from the focal point; SRS, the second reflected shock of RSfrom the upper wall; TRS, the third reflected shock from the SRSover the wedge. The dashed arrows indicate the shock moving directions. The other symbols represent the same meaning as those in Figure 1.

  • Figure 3

    (Color online) Variations of the Mach stem length (a) and the velocity components parallel and perpendicular to the wedge of the $TP_1$ for $\alpha_0$ = 65$^{\circ}$ and 75$^{\circ}$ [54].

  • Figure 4

    (Color online) Variations of incident angle and detachment angle for $\alpha_0$ = 65$^{\circ}$, 75$^{\circ}$ and $\alpha_0$ = 48$^{\circ}$.

  • Figure 5

    (Color online) Schlieren images of a cylindrical shock reflection over a wedge with $\alpha_0$ = 48$^{\circ}$ from experiment (upper) and numerical simulation (lower) [54]. The shock Mach number is the same as that in the case of $\alpha_0$ = 35$^{\circ}$.

  • Figure 6

    (Color online) Comparison among the incident angle and the detachment angle and von Neumann angle when the InMR terminates and the TRR forms [54].

  • Figure 7

    The shock Mach number is the same as that in the case of $\alpha_0$ = 35$^{\circ}$ [55]. FRS, the fourth reflected shock of TRSfrom the upper wall; FIRS, the fifth reflected shock of FRSfrom the curved wedge; RW, rarefaction waves. Other symbols are the same as those in Figures 1and 2.

  • Figure 8

    (Color online) (a) Variation of shock Mach number during the shock propagating along the wedge for four cases. (b) History of trajectory angle during the shock convergence from three-shock theory predictions and pseudo-steady computations [55]. The solid and hollow symbols represent the results from pseudo-steady computations and three-shock theory predictions, respectively.

  • Figure 9

    (Color online) Comparison of trajectory of triple point from the present numerical and experimental results, and predictions by three-shock theory and pseudo-steady computation for $\alpha_0$=55$^{\circ}$ and 60$^{\circ}$ (a) and for $\alpha_0$=65$^{\circ}$ and 70$^{\circ}$ (b) [55]. Exp, the present experimental results; Num, the present numerical results; PSS, the results from pseudo-steady computation; TSS, the results from three-shock theory.

  • Figure 10

    (Color online) Variation of length of disturbed shock front for four cases [55]. The lines denote the theoretical results, the solid and hollow symbols denote the experimental and numerical results, respectively.

  • Figure 11

    (Color online) Comparison of variation of the Mach stem length [55]. SW and CW mean straight wedge and curved wedge, respectively. The dashed straight line shows the variation of the Mach stem length in the pseudo-steady shock reflection.

  • Figure 12

    Sequences of experimental and numerical schlieren frames showing the evolution of a converging shock wave refracting at a tilted interface with $\alpha_0$ = 45$^{\circ}$ [56]. The shock Mach number when encountering the interface is about 1.6. i, incident shock; ts, transmitted shock; m, undisturbed material interface.

  • Figure 13

    Schematics of the wave patterns of a cylindrical converging shock wave refracting at a tilted interface with $\alpha_0$ = 45$^{\circ}$ [56]. $m^{'}$, disturbed material interface; r, reflected shock; $r_1$, first reflected shock; $r_2$, second reflected shock; $\alpha_i$, incident angle; $\alpha_t$, angle of transmitted shock with gaseous interface; $v_i$, velocity of incident shock; $v_t$, velocity of transmitted shock; e, expansion waves. Other symbols are the same as those indicated in Figure 12.

  • Figure 14

    (Color online) Comparison of the displacements of some typical points on the transmitted and incident shocks for $\alpha_0$ = 45$^{\circ}$.

  • Figure 15

    (Color online) Comparison of relative displacements ($d-d_0$) of typical points on tsfor $\alpha_0$ = 45$^{\circ}$ [56]. $d_0$ is the displacement under quasi-steady condition of a planar shock refracting at a planar interface.

  • Figure 16

    Sequences of experimental and numerical schlieren frames showing the evolution of a converging shock wave refracting at a tilted interface with $\alpha_0$ = 60$^{\circ}$ [56]. The symbols have the same meaning as those indicated in Figure 12.

  • Figure 17

    Schematics of the wave patterns of a cylindrical converging shock wave refracting at a tilted interface with 60$^{\circ}$ [56]. $tp_1$, the first triple point; $tp_2$, the second triple point; qp, the quadruple point. Other symbols are the same as those indicated in Figure 13.

  • Figure 18

    (Color online) Comparison of displacements of some typical points on the incident and transmitted shocks for $\alpha_0$ = 60$^{\circ}$ [56].

qqqq

Contact and support