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.

An analytical model for asymmetric Mach reflection configuration in steady flows

2019 ◽  
Vol 863 ◽  
pp. 242-268
Author(s):  
Shobhan Roy ◽  
Rajesh Gopalapillai
Keyword(s):  
Analytical Model ◽  
Mach Reflection ◽  
Wedge Angle ◽  
Steady Flows ◽  
Mach Stem ◽  
Stem Height ◽  
Von Neumann ◽  
Reflection Configuration ◽  
Symmetric Reflection ◽  
Subsonic Region

An analytical model is presented for the configuration of Mach reflection (MR) due to the interaction of two-dimensional steady supersonic flow over asymmetric wedges. The present asymmetric MR model is an extension of an earlier model for the symmetric MR configuration. The overall Mach reflection (oMR) in the asymmetric wedge configuration is analysed as a combination of upper and lower half-domains of symmetric reflection configurations. Suitable assumptions are made to close the combined set of equations. The subsonic pocket downstream of the Mach stem is taken to be oriented along an average inclination, based on the streamline deflections by the Mach stem at the triple points. This assumption is found to give satisfactory results for all types of oMR configurations. The oMR configuration is predicted for all types of reflections such as direct Mach reflection (DiMR), stationary Mach reflection (StMR) and inverse Mach reflection (InMR). The reflection configuration and Mach stem shape given by the model for various sets of wedge angles, especially those giving rise to InMR, have been predicted and validated with the available numerical and experimental data. The von Neumann criterion for oMR is accurately predicted by this model. The asymmetric Mach stem profile is well captured. The variation of Mach stem height with wedge angle is also analysed and it is found that simplification of an asymmetric MR to a symmetric MR leads to over-prediction of the Mach stem height and hence the extent of the subsonic region.

A method for predicting Mach stem height in steady flows

2021 ◽  
pp. 095441002110015
Author(s):  
Song-Guk Choe
Keyword(s):  
Analytical Model ◽  
Slip Line ◽  
Flow Region ◽  
Rocket Engines ◽  
Steady Flows ◽  
Mach Stem ◽  
Stem Height ◽  
Mach Numbers ◽  
Relative Errors ◽  
Cfd Method

The prediction of Mach stem height can be important in the design of supersonic intake in supersonic and hypersonic flows. It is also important because of the progress in aircraft and rocket engines. An analytical method of predicting the Mach stem height is necessary in theoretical field of shock reflection and is the basis of the comparable computational fluid dynamics (CFD) method. A method for predicting the Mach stem height in steady flows is performed based on the earlier models. In this article, an analytical model for predicting the Mach stem height is improved based on two main assumptions: one is the calculation of the triple point deflection angle when the Mach stem is an oblique shock and the other is about the shape of the free part of the slip line. Under these assumptions, the relations predicting of Mach stem height in two-dimensional steady flow are derived based on the advanced averaging method of the subsonic flow region. The Mach stem heights are decided solely for the incoming flow Mach numbers and the wedge angles by the improved analytical model. As a result, the Mach stem heights by the model of this article are found to agree well with experimental results at lower Mach numbers, but there are relative errors at higher Mach numbers. The convexity of the slip line is also considered.

Analytical and experimental investigations of the reflection of asymmetric shock waves in steady flows

1999 ◽  
Vol 390 ◽  
pp. 25-43 ◽  
Author(s):  
H. LI ◽  
A. CHPOUN ◽  
G. BEN-DOR
Keyword(s):  
Shock Waves ◽  
Wave Reflection ◽  
Mach Reflection ◽  
Three Dimensional ◽  
Experimental Investigations ◽  
Hysteresis Phenomenon ◽  
Steady Flows ◽  
Shock Wave Reflection ◽  
Asymmetric Shock ◽  
The One

The reflection of asymmetric shock waves in steady flows is studied both theoretically and experimentally. While the analytical model was two-dimensional, three-dimensional edge effects influenced the experiments. In addition to regular and Mach reflection wave configurations, an inverse-Mach reflection wave configuration, which has been observed so far only in unsteady flows (e.g. shock wave reflection over concave surfaces or over double wedges) has been recorded. A hysteresis phenomenon similar to the one that exists in the reflection of symmetric shock waves has been found to also exist in the reflection of asymmetric shock waves. The domains and transition boundaries of the various types of overall reflection wave configurations are analytically predicted.

Downstream flow condition effects on the RR → MR transition of asymmetric shock waves in steady flows

2009 ◽  
Vol 620 ◽  
pp. 43-62 ◽  
Author(s):  
Z. M. HU ◽  
R. S. MYONG ◽  
M. S. KIM ◽  
T. H. CHO
Keyword(s):  
Shock Waves ◽  
Mach Reflection ◽  
Flow Structures ◽  
Steady Flows ◽  
Regular Reflection ◽  
Double Wedge ◽  
Asymmetric Reflection ◽  
Asymmetric Shock ◽  
Downstream Flow ◽  
Good Agreement

In this paper, the regular reflection (RR) to Mach reflection (MR) transition of asymmetric shock waves is theoretically studied by employing the classical two- and three-shock theories. Computations are conducted to evaluate the effects of expansion fans, which are inherent flow structures in asymmetric reflection of shock waves, on the RR → MR transition. Comparison shows good agreement among the theoretical, numerical and experimental results. Some discrepancies between experiment and theory reported in previous studies are also explained based on the present theoretical analysis. The advanced RR → MR transition triggered by a transverse wave is also discussed for the interaction of a hypersonic flow and a double-wedge-like geometry.

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.

The reflection of asymmetric shock waves in steady flows: a numerical investigation

2002 ◽  
Vol 469 ◽  
pp. 71-87 ◽  
Author(s):  
M. S. IVANOV ◽  
G. BEN-DOR ◽  
T. ELPERIN ◽  
A. N. KUDRYAVTSEV ◽  
D. V. KHOTYANOVSKY
Keyword(s):  
Numerical Simulation ◽  
Experimental Investigation ◽  
Shock Waves ◽  
Numerical Investigation ◽  
Theoretical Study ◽  
Mach Reflection ◽  
Hysteresis Phenomenon ◽  
Steady Flows ◽  
Regular Reflection ◽  
Asymmetric Shock

The theoretical study and experimental investigation of the reflection of asymmetric shock waves in steady flows reported by Li et al. (1999) are complemented by a numerical simulation. All the findings reported in both the theoretical study and the experimental investigation were also evident in the numerical simulation. In addition to weak regular reflection and Mach reflection wave configurations, strong regular reflection and inverse-Mach reflection wave configurations were recorded numerically. The hysteresis phenomenon, which was hypothesized in the course of the theoretical study and then verified in the experimental investigation, was also observed in the numerical simulation.

Two-dimensional centered wave flow patches to the Guderley Mach reflection configurations for steady flows in gas dynamics

2016 ◽  
Vol 13 (01) ◽  
pp. 107-128 ◽  
Author(s):  
Geng Lai ◽  
Wancheng Sheng
Keyword(s):  
Triple Point ◽  
Mach Reflection ◽  
Wave Flow ◽  
Steady Flows ◽  
Two Dimensional ◽  
Wave Problem ◽  
Von Neumann ◽  
Physical Experiments ◽  
Expansion Fan ◽  
Reflection Configuration

In an attempt to resolve the von Neumann triple point paradox in shock reflection phenomenon, a new type of reflection configuration, called Guderley Mach reflection, was observed both in numerical simulations and physical experiments recently. In this type of reflection configuration, there exists a sequence of triple points, with a centered expansion fan and a supersonic patch at each triple point. In this paper, we present a mathematical analysis of the centered wave flow patches of Guderley Mach reflection. In order to construct such a flow patch, a centered wave problem is introduced. The existence of a global classical solution to the centered wave problem for the two-dimensional isentropic irrotational steady Euler equations is established.

Shock reflection in the presence of an upstream expansion wave and a downstream shock wave

2013 ◽  
Vol 735 ◽  
pp. 61-90 ◽  
Author(s):  
Y. Yao ◽  
S. G. Li ◽  
Z. N. Wu
Keyword(s):  
Shock Wave ◽  
Flow Structure ◽  
Mach Reflection ◽  
Expansion Wave ◽  
Shock Reflection ◽  
Critical Conditions ◽  
Reflected Shock Wave ◽  
Mach Stem ◽  
Turning Angle ◽  
Reflected Shock

AbstractIn this paper, we consider shock reflection problems, occurring in supersonic and hypersonic intake flow under off-design conditions, in which the incident shock wave is disturbed by the lip-generated upstream expansion wave and the reflected shock wave intersects with a downstream cowl-turning deflected shock wave. The expansion wave and deflected shock wave are here generated with the same magnitude of flow deflection angle or turning angle. With the help of shock interaction theory and numerical simulation, the influence of the turning angle of the lip and cowl on the flow structure and the critical conditions for transition between regular reflection and Mach reflection are analysed. It is found that the dual-solution domain is significantly altered by the interference between the expansion wave and shock waves. The flow structure in the condition of Mach reflection is then analysed with a model updated from a previous study. It is shown that the Mach stem height is an increasing function of the turning angle, while the horizontal position of the Mach stem is shifted in the downstream direction for small turning angle and in the upstream direction for large turning angle.

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.

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