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.

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.

Pseudostationary oblique shock-wave reflections in sulphur hexafluoride (SF 6 ): interferometric and numerical results

1986 ◽  
Vol 408 (1835) ◽  
pp. 321-344 ◽  
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Triple Point ◽  
Wave Reflection ◽  
Incident Shock ◽  
Oblique Shock Wave ◽  
Wave Reflections ◽  
Shock Wave Reflection ◽  
Wedge Surface ◽  
Vibrational Equilibrium

Pseudostationary oblique shock-wave reflections in SF 6 were investigated experimentally and numerically. Experiments were concluded in the UTIAS 10 x 18 cm Hypervelocity Shock Tube in the range of incident shock wave Mach number 1.25 < M s < 8.0 and wedge angle 4° < θ w < 47° with initial pressure 4 < P 0 < 267 Torr (0.53-35.60 kPa) at temperatures T 0 near 300 K. The four major types of shock-wave reflection, i. e. regular reflection (RR), single-Mach (SMR), complex-Mach (CMR) and double-Mach reflections (DMR), were observed. These were studied by using infinite-fringe interferograms from a Mach-Zehnder interferometer with a 23 cm diameter field of view. The isopycnics and the density distributions along the wedge surface are presented for the various types of reflection. The analytical transition boundaries between the four types of shock-wave reflection were established up to M s = 10.0 for frozen and equilibrium vibrational SF 6 . An examination of the relaxation length under the present experimental conditions indicated that a vibrational-equilibrium analysis was required. Comparisons of experiment with analysis for transition-boundary maps, reflection angle δ and the first triple-point trajectory angle X verify that the reflections were in vibrational equilibrium. The excellent agreement between the present interferometric results and the numerical results obtained by H. M. Glaz et al . ( Proc. int. colloq. on dynamics of explosives and reactive systems [ Berkeley ] (1985)) with real-gas effects also supports the vibrational equilibrium hypothesis for shocked SF 6 . The behaviour of the angle between the two triple-point trajectories ( X ' — X ) is discussed and the unique pattern of DMR with X ' = 0 was verified experimentally. A numerical analysis for the second triple-point system is obtained for the first time. It is shown that, for a given incident shock Mach number, the highest wedge-surface pressure is achieved through a DMR instead of an RR at high M s .

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 over double-concave cylindrical reflectors

2017 ◽  
Vol 813 ◽  
pp. 70-84 ◽  
Author(s):  
V. Soni ◽  
A. Hadjadj ◽  
A. Chaudhuri ◽  
G. Ben-Dor
Keyword(s):  
Shock Wave ◽  
Triple Point ◽  
Early Stage ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Geometrical Parameters ◽  
Regular Reflection ◽  
Wave Reflections ◽  
The Past ◽  
Shock Reflections

Numerical simulations were conducted to understand the different wave configurations associated with the shock-wave reflections over double-concave cylindrical surfaces. The reflectors were generated computationally by changing different geometrical parameters, such as the radii of curvature and the initial wedge angles. The incident-shock-wave Mach number was varied such as to cover subsonic, transonic and supersonic regimes of the flows induced by the incident shock. The study revealed a number of interesting wave features starting from the early stage of the shock interaction and transition to transitioned regular reflection (TRR) over the first concave surface, followed by complex shock reflections over the second one. Two new shock bifurcations have been found over the second wedge reflector, depending on the velocity of the additional wave that appears during the TRR over the first wedge reflector. Unlike the first reflector, the transition from a single-triple-point wave configuration (STP) to a double-triple-point wave configuration (DTP) and back occurred several times on the second reflector, indicating that the flow was capable of retaining the memory of the past events over the entire process.

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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