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.

scholarly journals Numerical and experimental investigation of oblique shock wave reflection off a water wedge

2017 ◽  
Vol 826 ◽  
pp. 732-758 ◽  
Author(s):  
Q. Wan ◽  
H. Jeon ◽  
R. Deiterding ◽  
V. Eliasson
Keyword(s):  
Shock Wave ◽  
Triple Point ◽  
Wave Reflection ◽  
Wave Interaction ◽  
Analytic Solutions ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Oblique Shock Wave ◽  
Shock Wave Reflection ◽  
Mach Numbers

Shock wave interaction with solid wedges has been an area of much research in past decades, but so far very few results have been obtained for shock wave reflection off liquid wedges. In this study, numerical simulations are performed using the inviscid Euler equations and the stiffened gas equation of state to study the transition angles, reflection patterns and triple point trajectory angles of shock reflection off solid and water wedges. Experiments using an inclined shock tube are also performed and schlieren photography results are compared to simulations. Results show that the transition angles for the water wedge cases are within 5.3 % and 9.2 %, for simulations and experiments respectively, compared to results obtained with the theoretical detachment criterion for solid surfaces. Triple point trajectory angles are measured and compared with analytic solutions, agreement within $1.3^{\circ }$ is shown for the water wedge cases. The transmitted wave in the water observed in the simulation is quantitatively studied, and two different scenarios are found. For low incident shock Mach numbers, $M_{s}=1.2$ and 2, no shock wave is formed in the water but a precursor wave is induced ahead of the incident shock wave and passes the information from the water back into the air. For high incident shock Mach numbers, $M_{s}=3$ and 4, precursor waves no longer appear but instead a shock wave is formed in the water and attached to the Mach stem at every instant. The temperature field in the water is measured in the simulation. For strong incident shock waves, e.g. $M_{s}=4$, the temperature increment in the water is up to 7.3 K.

Shock Wave Reflections in Dust-Gas Suspensions

2000 ◽  
Vol 123 (1) ◽  
pp. 145-153 ◽  
Author(s):  
G. Ben-Dor ◽  
O. Igra ◽  
L. Wang
Keyword(s):  
Shock Wave ◽  
Flow Field ◽  
Wave Reflection ◽  
Dust Cloud ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Dust Particles ◽  
Wave Reflections ◽  
Shock Wave Reflection ◽  
Induced Flow

The reflection of planar shock waves from straight wedges in dust-gas suspensions is investigated numerically. The GRP shock capturing scheme and the MacCormac scheme are applied to solve the governing equations of the gaseous and solid phases, respectively. These two schemes have a second-order accuracy both in time and space. It is shown that the presence of the dust significantly affects the shock-wave-reflection-induced flow field. The incident shock wave attenuates and hence unlike the shock wave reflection phenomenon in a pure gas, the flow field in the present case is not pseudo steady. The presence of the dust results in lower gas velocities and gas temperatures and higher gas densities and gas pressures than in dust-free shock wave reflections with identical initial conditions. It is also shown that the smaller is the diameter of the dust particle the larger are the above-mentioned differences. In addition, the smaller is the diameter of the dust particle the narrower is the width of the dust cloud behind the incident shock wave. Larger dust velocities, dust temperatures and dust spatial densities are obtained inside this dust cloud for smaller dust particles. The results provide a clear picture of whether and how the presence of dust particles affects the shock-wave-reflection-induced flow field.

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.

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.

Experimental and Numerical Study of Shock Wave Interaction with Perforated Plates

2004 ◽  
Vol 126 (3) ◽  
pp. 399-409 ◽  
Author(s):  
A. Britan ◽  
A. V. Karpov ◽  
E. I. Vasilev ◽  
O. Igra ◽  
G. Ben-Dor ◽  
...  
Keyword(s):  
Shock Wave ◽  
Numerical Study ◽  
Wave Interaction ◽  
Wave Pattern ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Perforated Plates ◽  
Shock Reflections

The flow developed behind shock wave transmitted through a screen or a perforated plat is initially highly unsteady and nonuniform. It contains multiple shock reflections and interactions with vortices shed from the open spaces of the barrier. The present paper studies experimentally and theoretically/numerically the flow and wave pattern resulted from the interaction of an incident shock wave with a few different types of barriers, all having the same porosity but different geometries. It is shown that in all investigated cases the flow downstream of the barrier can be divided into two different zones. Due immediately behind the barrier, where the flow is highly unsteady and nonuniform in the other, placed further downstream from the barrier, the flow approaches a steady and uniform state. It is also shown that most of the attenuation experienced by the transmitted shock wave occurs in the zone where the flow is highly unsteady. When solving the flow developed behind the shock wave transmitted through the barrier while ignoring energy losses (i.e., assuming the fluid to be a perfect fluid and therefore employing the Euler equation instead of the Navier-Stokes equation) leads to non-physical results in the unsteady flow zone.

NUMERICAL INVESTIGATION ON THE INTERACTION OF CYLINDER AND SHOCKWAVE BASED ON THE IMMERSED BOUNDARY METHOD

2009 ◽  
Vol 23 (03) ◽  
pp. 317-320 ◽  
Author(s):  
XIAOHAI JIANG ◽  
ZHIHUA CHEN ◽  
HONGZHI LI
Keyword(s):  
Shock Wave ◽  
Circular Cylinder ◽  
Immersed Boundary Method ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Immersed Boundary ◽  
Square Cylinder ◽  
Boundary Method ◽  
Modeling Flow ◽  
Good Agreement

The immersed boundary method (IBM) is an innovative approach for modeling flow with complex geometries and is more efficient than traditional method. In the present investigation, the shock wave propagation over one circular cylinder is simulated numerically with the Ghost-Body Immersed Boundary Method and high-resolution Roe scheme. To validate the IBM, a plane incident shock wave passing through a square cylinder is predicted and good agreement with previous experiments was obtained. Then based on our calculation, the reflection and diffraction processes of a shock wave passing through a circular cylinder were visualized and discussed in detail.

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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