Study on Mach Stem Shape of the Asymmetric Overall Mach Reflection

2019 ◽  
pp. 725-730
Author(s):  
Y. Tao ◽  
W. D. Liu ◽  
X. Q. Fan
Keyword(s):  
Mach Reflection ◽  
Mach Stem ◽  
Stem Shape

scholarly journals Onset of the Mach Reflection of Zel’dovich–von Neumann–Döring Detonations

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 314
Author(s):  
Tianyu Jing ◽  
Huilan Ren ◽  
Jian Li
Keyword(s):  
Hot Spot ◽  
Mach Reflection ◽  
Near Field ◽  
The Self ◽  
Small Scale ◽  
Mach Stem ◽  
Self Similarity ◽  
Von Neumann ◽  
Similarity Problem ◽  
Self Similar

The present study investigates the similarity problem associated with the onset of the Mach reflection of Zel’dovich–von Neumann–Döring (ZND) detonations in the near field. The results reveal that the self-similarity in the frozen-limit regime is strictly valid only within a small scale, i.e., of the order of the induction length. The Mach reflection becomes non-self-similar during the transition of the Mach stem from “frozen” to “reactive” by coupling with the reaction zone. The triple-point trajectory first rises from the self-similar result due to compressive waves generated by the “hot spot”, and then decays after establishment of the reactive Mach stem. It is also found, by removing the restriction, that the frozen limit can be extended to a much larger distance than expected. The obtained results elucidate the physical origin of the onset of Mach reflection with chemical reactions, which has previously been observed in both experiments and numerical simulations.

A parametric study of Mach reflection in steady flows

1997 ◽  
Vol 341 ◽  
pp. 101-125 ◽  
Author(s):  
H. LI ◽  
G. BEN-DOR
Keyword(s):  
Present Model ◽  
Mach Reflection ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Incoming Flow ◽  
Steady Flows ◽  
Mach Stem ◽  
Stem Height ◽  
Von Neumann ◽  
Set Up

The flow fields associated with Mach reflection wave configurations in steady flows are analysed, and an analytical model for predicting the wave configurations is proposed. It is found that provided the flow field is free of far-field downstream influences, the Mach stem heights are solely determined by the set-up geometry for given incoming-flow Mach numbers. It is shown that the point at which the Mach stem height equals zero is exactly at the von Neumann transition. For some parameters, the flow becomes choked before the Mach stem height approaches zero. It is suggested that the existence of a Mach reflection not only depends on the strength and the orientation of the incident shock wave, as prevails in von Neumann's three-shock theory, but also on the set-up geometry to which the Mach reflection wave configuration is attached. The parameter domain, beyond which the flow gets choked and hence a Mach reflection cannot be established, is calculated. Predictions based on the present model are found to agree well both with experimental and numerical results.

Study of asymmetrical shock wave reflection in steady supersonic flow

2019 ◽  
Vol 864 ◽  
pp. 848-875 ◽  
Author(s):  
Jing Lin ◽  
Chen-Yuan Bai ◽  
Zi-Niu Wu
Keyword(s):  
Cfd Simulation ◽  
Mach Reflection ◽  
Vertical Axis ◽  
Lower Surface ◽  
Mach Stem ◽  
Stem Height ◽  
Horizontal Shift ◽  
Reflection Configuration ◽  
The Asymmetry ◽  
Asymmetrical Model

The asymmetrical Mach reflection configuration is studied analytically in this paper, using an asymmetrical model extended from a recent symmetrical model and accounting for the new features related to asymmetry of the two wedges. It is found that the two sliplines do not turn parallel to the incoming flow at the same horizontal location and the sonic throat locates at the position where the difference of slopes of the two sliplines vanishes. This allows us to define a new sonic throat compatibility condition essential to determine the size of the Mach stem. The present model gives the height of the Mach stem, declined angle of the Mach stem from vertical axis, sonic throat location and shape of all shock waves and sliplines. The accuracy of the model is checked by computational fluid dynamics (CFD) simulation. It is found that the Mach stem height is strongly dependent on asymmetry of the wedge angles and almost linearly dependent on the asymmetry of the wedge lower surface lengths. The Mach stem height is shown to be insensitive to the asymmetry of the horizontal positions of the two wedges. The mechanisms for these observations are explained. For instance, it is demonstrated that the Mach reflection configuration remains closely similar when there is horizontal shift of either wedge.

Control of Mach Reflection by a Single Laser Pulse

2012 ◽  
Vol 271-272 ◽  
pp. 1516-1520
Author(s):  
Dian Kai Wang ◽  
Yan Ji Hong
Keyword(s):  
Pressure Loss ◽  
Total Pressure ◽  
Free Stream ◽  
Laser Energy ◽  
Mach Reflection ◽  
Pulsed Laser ◽  
Total Pressure Loss ◽  
Mach Stem ◽  
Stem Height ◽  
Free Stream Mach Number

In the supersonic engine inlet, Mach Reflection probably appears when a supersonic flow goes through the symmetric wedges, causing a great total pressure loss. A single pulsed laser energy deposition leads a decrease of the Mach stem height and reduces the total pressure loss. By solving the two-dimensional RANS equations, with the condition of symmetric wedges at 22 degrees, and the free stream Mach number 3.45, influences of the deposition location and the magnitude of pulsed laser energy in Mach Reflection are investigated. The results indicate that when laser energy rises from 70mJ to 270mJ, the height of Mach stem changes and a vale value is obtained. The deposition position is also optimized.

Mach reflection of a large-amplitude solitary wave

1993 ◽  
Vol 248 ◽  
pp. 637-661 ◽  
Author(s):  
Mitsuhiro Tanaka
Keyword(s):  
Solitary Wave ◽  
Water Depth ◽  
Large Amplitude ◽  
Mach Reflection ◽  
Vertical Wall ◽  
Angle Of Incidence ◽  
Mach Stem ◽  
Regular Reflection ◽  
Regular Type ◽  
Numerical Result

Reflection of an obliquely incident solitary wave by a vertical wall is studied numerically by applying the ‘high-order spectral method’ developed by Dommermuth & Yue (1987). According to the analysis by Miles (1977a, b) which is valid when ai [Lt ] 1, the regular type of reflection gives way to ‘Mach reflection’ when ai/(3ai)½ ≤ 1, Where ai is the amplitude of the incident wave divided by the quiescent water depth d and ψi is the angle of incidence. In Mach reflection, the apex of the incident and the reflected waves moves away from the wall at a constant angle (ψ*, say), and is joined to the wall by a third solitary wave called ‘Mach stem’. Miles model predicts that the amplitude of Mach stem, and so the run-up at the wall, is 4ai when ψi = (3ai)½.Our numerical results shows, however, that the effect of large amplitude tends to prevent the Mach reflection to occur. Even when the Mach reflection occurs, it is ‘contaminated’ by regular reflection in the sense that all the important quantities that characterize the reflection pattern, such as the stem angle ψ*, the angle of reflection ψr, and the amplitude of the reflected wave ar, are all shifted from the values predicted by Miles’ theory toward those corresponding to the regular reflection, i.e. ψ* = 0, ψr = ψi, and ar = ai. According to our calculations for ai = 0.3, the changeover from Mach reflection to regular reflection happens at ψi ≈ 37.8°, which is much smaller than (3ai)½ = 54.4°, and the highest Mach stem is observed for ψi = 35° (ψi/(3ai)½ = 0.644). Although the ‘four-fold amplification’ is not observed for any value of ψi considered here, it is found that the Mach stem can become higher than the highest two-dimensional steady solitary wave for the prescribed water depth. The numerical result is also compared with the analysis by Johnson (1982) for the oblique interaction between one large and one small solitary wave, which shows much better agreement with the numerical result than the Miles’ analysis does when ψi is sufficiently small and the Mach reflection occurs.

Time history of regular to Mach reflection transition in steady supersonic flow

2011 ◽  
Vol 682 ◽  
pp. 160-184 ◽  
Author(s):  
S. G. LI ◽  
B. GAO ◽  
Z. N. WU
Keyword(s):  
Triple Point ◽  
Early Stage ◽  
Mach Reflection ◽  
Time History ◽  
Mach Stem ◽  
Interaction Structure ◽  
Reflection Transition ◽  
History Of ◽  
Multiple Interaction ◽  
Mach Waves

In this paper, we study the transition from regular to Mach reflection (RR → MR) in the dual solution domain due to the influence of an upstream disturbance, by considering the transition as an evolutionary rather than an abrupt process. From numerical simulation, we observe for the early stage of transition a multiple interaction structure, composed of a triple-shock structure, a type VI shock interaction and a shock/slipline interaction. In the end, we observe a pure unsteady MR structure. Under self-similar assumption of the triple point for the first stage and including additional Mach waves over the slipline for the last stage, we develop an idealized unsteady model to obtain the evolution of the Mach stem height and the time taken for the Mach stem to stabilize. The triple point is found to move at a nearly constant speed in the multiple interaction stage which occupies about one quarter of the transition time. In the pure unsteady MR stage, which occupies the rest of transition, the speed of the triple point drops nonlinearly until the Mach stem stabilizes.

scholarly journals A Study of the Dependence of the Mach Stem Height on the Trailing Edge Height

Fluids ◽  
2021 ◽  
Vol 6 (9) ◽  
pp. 313
Author(s):  
Chen-Yuan Bai ◽  
Zi-Niu Wu
Keyword(s):  
Linear Trend ◽  
Mach Reflection ◽  
Analytical Models ◽  
Mach Stem ◽  
Stem Height ◽  
Trailing Edge ◽  
The Past ◽  
Wedge Surface ◽  
Future Work ◽  
Single Set

The Mach stem height is an important parameter in the Mach reflection of steady supersonic flow. Various experimental, numerical, and theoretical works have been conducted to study this parameter in the past. However, much of the established work focuses around a single set of trailing edge heights. Here, we perform a study to show the dependence of Mach stem height on the trailing edge height for a wider range of geometry. Through numerical simulation for a set of trailing edge heights, we found that the normalized Mach stem height is almost linear with respect to the normalized wedge trailing edge height. The parameter used for normalization can be either the inlet height or the length of the lower wedge surface. The observation of this linear trend is justified through a simplified analysis, which leads to an expression of the Mach stem height that linearly depends on the trailing edge height. The present study extends our knowledge about how the geometry affects the Mach stem height, and provides a basis for future work to elaborate analytical models for Mach stem height.

scholarly journals WATER WAVE EQUIVALENT OF MACH-REFLECTION

1964 ◽  
Vol 1 (9) ◽  
pp. 6
Author(s):  
R.L. Wiegel
Keyword(s):  
Shallow Water ◽  
Wave Front ◽  
Gravity Waves ◽  
Water Wave ◽  
Mach Reflection ◽  
Blast Waves ◽  
Periodic Waves ◽  
Mach Stem ◽  
Air Blast ◽  
Reflected Wave

Periodic (shallow water and transitional water) and solitary water gravity waves do not reflect from a wall in the manner commonly supposed, when the angle between the direction of wave advance and the wall is less than about 5? to 45 degrees. The wave front bends near the wall, becoming normal to the wall, with a small reflected wave. For angles less than about 20 degrees the reflected wave becomes almost negligible. The portion of the wave near the wall (called the Mach-stem in air blast waves) increases in height as the wave continues to move along the wall. Once the Mach-stem is formed, it will continue to grow even when the wall is bent around through almost 90 degrees; for periodic waves a Machreflected wave also develops. The Mach-stem is insensitive to undulation, of the wall. Results of studies of this phenomenon in the laboratory are presented, together with some observation of its occurrence in the ocean. The importance of this phenomenon to the study of tsunami action at Hilo, Hawaii, is presented.

A study of the asymmetric shock reflection configurations in steady flows

2017 ◽  
Vol 825 ◽  
pp. 1-15 ◽  
Author(s):  
Yuan Tao ◽  
Weidong Liu ◽  
Xiaoqiang Fan ◽  
Bin Xiong ◽  
Jiangfei Yu ◽  
...  
Keyword(s):  
Analytical Model ◽  
Mach Reflection ◽  
Shock Reflection ◽  
Horizontal Distance ◽  
Steady Flows ◽  
Two Dimensional ◽  
Mach Stem ◽  
Stream Tube ◽  
Triple Points ◽  
Asymmetric Shock

In this paper the asymmetric shock reflection configurations in two-dimensional steady flows have been studied theoretically. For an overall Mach reflection, it is found that the horizontal distance between both triple points in the Mach stem is related to the angles of two slip streams. Based on the features of the converging stream tube, several assumptions are put forward to perform better the wave configurations near the slip streams. Therefore, we present an analytical model here to describe the asymmetric overall Mach reflection configurations which agrees well with the computational and experimental results.

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