Double solution and influence of secondary waves on transition criteria for shock interference in pre-Mach reflection with two incident shock waves

2020 ◽  
Vol 887 ◽  
Author(s):  
Xiao-Ke Guan ◽  
Chen-Yuan Bai ◽  
Zi-Niu Wu
Keyword(s):  
Shock Waves ◽  
Mach Reflection ◽  
Incident Shock ◽  
Transition Criteria ◽  
Image Position ◽  
Shock Interference

Transition study for asymmetric reflection between moving incident shock waves

2021 ◽  
Vol 929 ◽  
Author(s):  
Miao-Miao Wang ◽  
Zi-Niu Wu
Keyword(s):  
Shock Waves ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Neumann Condition ◽  
Plane Shock ◽  
Von Neumann ◽  
Transition Criteria ◽  
Shock Motion ◽  
Reduced Problem

The transition criteria seen from the ground frame are studied in this paper for asymmetrical reflection between shock waves moving at constant linear speed. To limit the size of the parameter space, these criteria are considered in detail for the reduced problem where the upper incident shock wave is moving and the lower one is steady, and a method is provided for extension to the general problem where both the upper and lower ones are unsteady. For the reduced problem, we observe that, in the shock angle plane, shock motion lowers or elevates the von Neumann condition in a global way depending on the direction of shock motion, and this change becomes less important for large shock angle. The effect of shock motion on the detachment condition, though small, displays non-monotonicity. The shock motion changes the transition criteria through altering the effective Mach number and shock angle, and these effects add for small shock angle and mutually cancel for large shock angle, so that shock motion has a less important effect for large shock angle. The role of the effective shock angle is not monotonic on the detachment condition, explaining the observed non-monotonicity for the role of shock motion on the detachment condition. Furthermore, it is found that the detachment condition has a wavefunction form that can be approximated as a hybrid of a sinusoidal function and a linear function of the shock angle.

Evaluation of assumptions and criteria in pseudostationary oblique shock-wave reflections

1986 ◽  
Vol 406 (1830) ◽  
pp. 75-92 ◽  
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Mach Reflection ◽  
Wedge Angle ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Oblique Shock ◽  
Oblique Shock Wave ◽  
Reflected Shock ◽  
Wedge Surface

Many experiments in various gases have now been performed on regular and Mach reflection of oblique shock waves in pseudostationary flow. Experimental agreement with the analytical boundaries for such reflec­tions with two- and three-shock theories is reasonable but not precise enough over the entire range of incident shock-wave Mach numbers ( M s ) and compression wedge angle ( θ W ) used in the experiments. In order to improve the agreement, the assumptions and criteria employed in the analysis were critically examined by the use of the experimental data for nitrogen (N 2 ), argon (Ar), carbon-dioxide (CO 2 ), air and sulphurhexa-fluoride (SF 6 ). The assumptions regarding the excitation of the internal degrees of freedom were evaluated based on a relation between the relaxation lengths and a characteristic length of the flow. The ranges in which the frozen-gas and vibrational-equilibrium-gas assumptions can be applied were verified by comparing the experimental and numerical values of δ, the angle between the incident and the reflected shock waves. The deviations of the experimental orientation of the Mach stem at the triple point from a line perpendicular to the wedge surface were considered. A new criterion for the transition from single-Mach to complex-Mach reflection improved the agreement with experiments in the ( M S , θ W )-transition-boundary map. The effects of the shock-induced boundary layer on the wedge surface on the reflected-wave angle and the persistence of regular reflection into the Mach reflection region (‘von Neumann paradox’) were evaluated.

Dynamic effects on the transition between two-dimensional regular and Mach reflection of shock waves in an ideal, steady supersonic free stream

2011 ◽  
Vol 676 ◽  
pp. 432-460 ◽  
Author(s):  
K. NAIDOO ◽  
B. W. SKEWS
Keyword(s):  
Steady State ◽  
Shock Waves ◽  
Experimental Evidence ◽  
High Speed ◽  
Mach Reflection ◽  
Neumann Condition ◽  
Two Dimensional ◽  
Reflection Transition ◽  
Strong Reflection ◽  
Transition Criteria

There have been numerous studies on the steady-state transition criteria between regular and Mach reflection of shock waves generated by a stationary, two-dimensional wedge in a steady supersonic flow, since the original shock-wave reflection research by Ernst Mach in 1878. The steady, two-dimensional transition criteria between regular and Mach reflection are well established. There has been little done to consider the dynamic effect of a rapidly rotating wedge on the transition between regular and Mach reflection. This paper presents the results of an investigation on the effect of rapid wedge rotation on regular to Mach reflection transition in the weak- and strong-reflection ranges with the aid of experiment and computational fluid dynamics. The experimental set-up includes a novel facility to rotate a pair of large aspect ratio wedges in a 450 mm × 450 mm supersonic wind tunnel at wedge rotation speeds up to 11000 deg s−1. High-speed images and measurements are presented. A numerical solution of the inviscid governing flow equations was used to mimic the experimental motion and to extend the investigation beyond the limits of the current facility to explore the influence of variables in the parameter space. There is good agreement between experimental measurements and numerical simulation. This paper includes the first experimental evidence of the regular to Mach reflection transition beyond the steady-state detachment condition in the weak- and strong-reflection ranges. It also presents results of simulations for the dynamic regular to the Mach reflection transition which show a difference between the sonic, length-scale and detachment conditions. This paper includes experimental evidence of the Mach to regular reflection transition below the steady-state von Neumann condition.

Steady Mach reflection with two incident shock waves

2018 ◽  
Vol 855 ◽  
pp. 882-909 ◽  
Author(s):  
Xiao-Ke Guan ◽  
Chen-Yuan Bai ◽  
Zi-Niu Wu
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Mach Reflection ◽  
Lower Surface ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Neumann Condition ◽  
Mach Stem ◽  
Stem Height ◽  
Reflecting Surface

Mach reflection in steady supersonic flow with two incident shock waves is studied. The second incident shock wave is produced by an additional deflection of the wedge lower surface, at some point ensuring that the two incident shock waves would intersect at the reflecting surface in case of normal reflection. Both theory and computational fluid dynamics (CFD) are used to study the flow structure and the influence of the second incident shock wave. The overall flow configuration, in case of Mach reflection, is shown to be composed of a triple shock structure, a shock/shock interaction structure and a shock/slipline reflection structure. Similar phenomenon, triggered by a high downstream pressure, has been observed before numerically, but not studied theoretically. The second incident shock wave reflects over the slipline to deflect the slipline more towards the reflecting surface, increasing thus the Mach stem height, advancing the transition of regular reflection to Mach reflection of the first incident shock wave, and causing an inverted Mach reflection below the usual von Neumann condition. A Mach stem height model built for a weak second incident shock wave is used to study the influence of the second incident shock wave on the Mach stem height. Both theory and CFD predict a maximum of the Mach stem height at some additional wedge deflection angle.

IMPROVEMENT OF FLAMEHOLDING CHARACTERISTICS BY INCIDENT SHOCK WAVES IN SUPERSONIC FLOW

2002 ◽  
Vol 5 (1-6) ◽  
pp. 330-339 ◽  
Author(s):  
T. Fujimori ◽  
M. Murayama ◽  
J. Sato ◽  
H. Kobayashi ◽  
S. Hasegawa ◽  
...  
Keyword(s):  
Supersonic Flow ◽  
Shock Waves ◽  
Incident Shock

Flow patterns of dual-incident shock waves/turbulent boundary layer interaction

2020 ◽  
Vol 23 (6) ◽  
pp. 931-935
Author(s):  
Xin Li ◽  
Hui-jun Tan ◽  
Yue Zhang ◽  
He-xia Huang ◽  
Yun-jie Guo ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Shock Waves ◽  
Turbulent Boundary Layer ◽  
Flow Patterns ◽  
Incident Shock ◽  
Layer Interaction ◽  
Boundary Layer Interaction

Observation and analysis of the Mach reflection of weak uniform plane shock waves. Part 1. Observations

1985 ◽  
Vol 152 ◽  
pp. 49-66 ◽  
Author(s):  
J. M. Dewey ◽  
D. J. McMillin
Keyword(s):  
Cross Sections ◽  
Mach Reflection ◽  
Incident Shock ◽  
Wave Flow ◽  
Plane Shock ◽  
Wedge Surface ◽  
Point Trajectories ◽  
Particle Velocities ◽  
High Degree ◽  
Shock Fronts

Shock fronts and fluid-particle trajectories throughout a two-dimensional shock wave flow have been measured by multiple schlieren photography in a detailed study of the Mach reflection from a 10° wedge of plane uniform shocks with Mach numbers of 1.105, 1.240 and 1.415. Correction of optical distortions throughout the field of view permitted the positions and shapes of the shock fronts and the magnitudes and directions of the particle velocities to be measured with a high degree of accuracy. No departure from self-similarity of the flow fields could be detected. The cross-sections of the reflected shocks were found to be circular and centred on a point which moved with the velocity of the flow behind the incident shock. The triple-point trajectories were linear. The velocity of the curved Mach stem shock was found to be constant at any one height above the wedge surface and to decrease monotonically with height. A deviation from perpendicularity was noticed where the Mach stems met the surface of the wedge, the shocks having a slight forward inclination of as much as 1°. The experimental results cannot be completely explained using the classical three-shock theory and an alternative model for weak Mach reflection is developed in Part 2 of this paper.

Transition from regular to Mach reflection of shock waves Part 2. The steady-flow criterion

1982 ◽  
Vol 123 ◽  
pp. 155-164 ◽  
Author(s):  
H. G. Hornung ◽  
M. L. Robinson
Keyword(s):  
Shock Waves ◽  
Steady Flow ◽  
Mach Reflection ◽  
Strong Shock ◽  
Hysteresis Effect ◽  
Neumann Condition ◽  
Flow Transition ◽  
Von Neumann ◽  
Mach Numbers ◽  
Flow Criterion

It is shown experimentally that, in steady flow, transition to Mach reflection occurs at the von Neumann condition in the strong shock range (Mach numbers from 2.8 to 5). This criterion applies with both increasing and decreasing shock angle, so that the hysteresis effect predicted by Hornung, Oertel & Sandeman (1979) could not be observed. However, evidence of the effect is shown to be displayed in an unsteady experiment of Henderson & Lozzi (1979).

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