scholarly journals The Shape of Incident Shock Wave in Steady Axisymmetric Conical Mach Reflection

2020 ◽  
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 base on the steady Euler equations. When the assumption that the steam-lines 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.

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.

scholarly journals The Shape of Incident Shock Wave in Steady Axisymmetric Conical Mach Reflection

2020 ◽  
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 base on the steady Euler equations. When the assumption that the steam-lines 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.

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.

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.

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.

The non-stationary hysteresis phenomenon in shock wave reflections

2013 ◽  
Vol 732 ◽  
Author(s):  
Meital Geva ◽  
Omri Ram ◽  
Oren Sadot
Keyword(s):  
Shock Wave ◽  
High Resolution ◽  
Triple Point ◽  
Convex Surface ◽  
Mach Reflection ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Concave Surface ◽  
Hysteresis Phenomenon ◽  
Regular Reflection

AbstractThe non-stationary transition from Mach to regular reflection followed by a reverse transition from regular to Mach reflection is investigated experimentally. A new experimental setup in which an incident shock wave reflects from a cylindrical concave surface followed by a cylindrical convex surface of the same radius is introduced. Unlike other studies that indicate problems in identifying the triple point, an in-house image processing program, which enables automatic detection of the triple point, is developed and presented. The experiments are performed in air having a specific heats ratio 1.4 at three different incident-shock-wave Mach numbers: 1.2, 1.3 and 1.4. The data are extracted from high-resolution schlieren images obtained by means of a fully automatically operated shock-tube system. Each experiment produces a single image. However, the high accuracy and repeatability of the control system together with the fast opening valve enables us to monitor the dynamic evolution of the shock reflections. Consequently, high-resolution results both in space and time are obtained. The credibility of the present analysis is demonstrated by comparing the first transition from Mach to regular reflection ($\mathrm{MR} \rightarrow \mathrm{RR} $) with previous single cylindrical concave surface experiments. It is found that the second transition, back to Mach reflection ($\mathrm{RR} \rightarrow \mathrm{MR} $), occurs earlier than one would expect when the shock reflects from a single cylindrical convex surface. Furthermore, the hysteresis is observed at incident-shock-wave Mach numbers smaller than those at which the dual-solution domain starts, which is the minimal value for obtaining hysteresis in steady and pseudo-steady flows. The existence of a non-stationary hysteresis phenomenon, which is different from the steady-state hysteresis phenomenon, is discovered.

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.

scholarly journals Adjoint-based optimisation of detonation initiation by a focusing shock wave

Shock Waves ◽  
2021 ◽  
Author(s):  
S. Bengoechea ◽  
J. Reiss ◽  
M. Lemke ◽  
J. Sesterhenn
Keyword(s):  
Shock Wave ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Detonation Initiation ◽  
Axisymmetric Nozzle ◽  
Exponential Factor ◽  
Pulsed Detonation Engine ◽  
Pulsed Detonation ◽  
Detonation Engine ◽  
Adjoint Approach

AbstractAn optimisation study of a shock-wave-focusing geometry is presented in this work. The configuration serves as a reliable and deterministic detonation initiator in a pulsed detonation engine. The combustion chamber consists of a circular pipe with one convergent–divergent axisymmetric nozzle, acting as a focusing device for an incoming shock wave. Geometrical changes are proposed to reduce the minimum shock wave strength necessary for a successful detonation initiation. For that purpose, the adjoint approach is applied. The sensitivity of the initiation to flow variations delivered by this method is used to reshape the obstacle’s form. The thermodynamics is described by a higher-order temperature-dependent polynomial, avoiding the large errors of the constant adiabatic exponent assumption. The chemical reaction of stoichiometric premixed hydrogen-air is modelled by means of a one-step kinetics with a variable pre-exponential factor. This factor is adapted to reproduce the induction time of a complex kinetics model. The optimisation results in a 5% decrease of the incident shock wave threshold for the successful detonation initiation.

Visualization of separation and reattachment in an incident shock-induced interaction

2021 ◽  
pp. 095441002098349
Author(s):  
Yun Jiao ◽  
Chengpeng Wang
Keyword(s):  
Numerical Simulation ◽  
Shock Wave ◽  
Shear Stress ◽  
Separation Bubble ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Bottom Wall ◽  
Surface Shear Stress ◽  
Surface Shear ◽  
Oil Flow

An experimental study is conducted on the qualitative visualization of the flow field in separation and reattachment flows induced by an incident shock interaction by several techniques including shear-sensitive liquid crystal coating (SSLCC), oil flow, schlieren, and numerical simulation. The incident shock wave is generated by a wedge in a Mach 2.7 duct flow, where the strength of the interaction is varied from weak to moderate by changing the angle of attack α of the wedge from 8° and 10° to 12°. The stagnation pressure upstream was set to approximately 607.9 kPa. The SSLCC technique was used to visualize the surface flow characteristics and analyze the surface shear stress fields induced by the initial incident shock wave over the bottom wall and sidewall experimentally which resolution is 3500 × 200 pixels, and the numerical simulation was also performed as the supplement for a clearer understanding to the flow field. As a result, surface shear stress over the bottom wall was visualized qualitatively by SSLCC images, and flow features such as separation/reattachment and the variations of position/size of separation bubble with wedge angle were successfully distinguished. Furthermore, analysis of shear stress trend over the bottom wall by a hue value curve indicated that the relative magnitude of shear stress increased significantly downstream of the separation bubble compared with that upstream. The variation trend of shear stress was consistent with the numerical simulation results, and the error of separation position was less than 2 mm. Finally, the three-dimensional schematic of incident shock-induced interaction has been achieved by qualitative summary by multiple techniques, including SSLCC, oil flow, schlieren, and numerical simulation.

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