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.

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.

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.

The influence of the downstream pressure on the shock wave reflection phenomenon in steady flows

1999 ◽  
Vol 386 ◽  
pp. 213-232 ◽  
Author(s):  
G. BEN-DOR ◽  
T. ELPERIN ◽  
H. LI ◽  
E. VASILIEV
Keyword(s):  
Shock Wave ◽  
Wave Reflection ◽  
Numerical Study ◽  
Mach Reflection ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Steady Flows ◽  
Shock Wave Reflection ◽  
Wave Angle ◽  
Good Agreement

The effect of the downstream pressure (defined here as the wake pressure behind the tail of the reflecting wedge) on shock wave reflection in steady flows is investigated both numerically and analytically. The dependence of the shock wave configurations on the downstream pressure is studied. In addition to the incident-shock-wave-angle-induced hysteresis, which was discovered a few years ago, a new downstream- pressure-induced hysteresis has been found to exist. The numerical study reveals that when the downstream pressure is sufficiently high, an inverse-Mach reflection wave configuration, which has so far been observed only in unsteady flows, can be also established in steady flows. Very good agreement between the analytical predictions and the numerical results is found.

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.

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.

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.

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.

Shock-wave/expansion-wave interactions and the transition between regular and Mach reflection

2007 ◽  
Vol 575 ◽  
pp. 399-424 ◽  
Author(s):  
R. HILLIER
Keyword(s):  
Shock Wave ◽  
Numerical Simulations ◽  
Solid Surface ◽  
Narrow Range ◽  
Mach Reflection ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Expansion Wave ◽  
Incident Flow ◽  
Wave Interactions

This paper presents numerical simulations for the interaction of an expansion wave with an incident shock wave of the opposite family, the specific aim being to study the resultant reflection of the now-perturbed shock wave from a solid surface. This problem is considered in the context of an incident flow entering a parallel duct, a situation that commonly arises in a range of flow-turning problems including supersonic intake flows. Once the incident shock conditions are such that Mach reflection must occur, it is shown that stabilization of a simple Mach reflection is only possible for a narrow range of Mach numbers and that this depends sensitively on the relative streamwise positioning of the origins of the shock wave and the expansion wave.

scholarly journals The shape of incident shock wave in steady axisymmetric conical Mach reflection

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Yu-xin Ren ◽  
Lianhua Tan ◽  
Zi-niu Wu
Keyword(s):  
Differential Equation ◽  
Shock Wave ◽  
Ordinary Differential Equation ◽  
Mach Reflection ◽  
Internal Flow ◽  
Present Theory ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Shock Reflection ◽  
Inlet Conditions

Abstract For internal flow with supersonic inflow boundary conditions, a complicated oblique shock reflection may occur. Different from the planar shock reflection problem, where the shape of the incident shock can be a straight line, the shape of the incident shock wave in the inward-facing axisymmetric shock reflection in steady flow is an unknown curve. In this paper, a simple theoretical approach is proposed to determine the shape of this incident shock wave. The present theory is based on the steady Euler equations. When the assumption that the streamlines are straight lines at locations just behind the incident shock is adopted, an ordinary differential equation can be derived, and the shape of the incident shock wave is given by the solution of this ordinary differential equation. The predicted curves of the incident shock wave at several inlet conditions agree very well with the results of the numerical simulations.

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