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1.
The formation of a secondary shock wave behind a shock wave diffracting at a convex corner 总被引:3,自引:0,他引:3
This paper deals with the formation of a secondary shock wave behind the shock wave diffracting at a two-dimensional convex
corner for incident shock Mach numbers ranging from 1.03 to 1.74 in air. Experiments were carried out using a 60 mm 150 mm shock tube equipped with holographic interferometry. The threshold incident shock wave Mach number () at which a secondary shock wave appeared was found to be = 1.32 at an 81° corner and = 1.33 at a 120° corner. These secondary shock waves are formed due to the existence of a locally supersonic flow behind
the diffracting shock wave. Behind the diffracting shock wave, the subsonic flow is accelerated and eventually becomes locally
supersonic. A simple unsteady flow analysis revealed that for gases with specific heats ratio the threshold shock wave Mach number was = 1.346. When the value of is less than this, the vortex is formed at the corner without any discontinuous waves accompanying above the slip line. The
viscosity was found to be less effective on the threshold of the secondary shock wave, although it attenuated the pressure
jump at the secondary shock wave. This is well understood by the consideration of the effect of the wall friction in one-dimensional
duct flows. In order to interpret the experimental results a numerical simulation using a shock adaptive unstructured grid
Eulerian solver was also carried out.
Received 1 May 1996 / Accepted 12 September 1996 相似文献
2.
The head-on collision of a planar shock wave with a dust-air suspension is studied numerically. In this study the suspension
is placed inside a conduit adjacent to its rigid end-wall. It is shown that as a result of this collision two different types
of transmitted shock waves are possible, depending on the strength of the incident shock wave and the dust loading ratio in
the suspension. One possibility is a partially dispersed shock wave, the other is a compression wave. The flow fields resulting
in these two options are investigated. It is shown that in both cases, at late times after the head-on reflection of the transmitted
shock wave from the conduit end-wall a negative flow (away from the end-wall) is evident. The observed flow behavior may suggest
a kind of dust particle lifting mechanism that could shed new light on the complex phenomenon of dust entrainment behind sliding
shock waves.
相似文献
3.
Beric W. Skews 《Shock Waves》2005,14(3):137-146
The two-dimensional diffraction of a shock wave over a wall made up of a series of plane and/or curved sections is considered.
The analysis is based on the theory presented by, for the interaction of an originally plane shock wave with a corner. A method
is presented by which the shock profile may be determined for a wall of any shape and for any incident Mach number, in regions
where the characteristics form a simple wave. Comparisons are made between experimental measurements and theoretical predictions
for convex walls consisting of a number of facets, and for circular arcs, for a range of incident shock wave Mach numbers.
It is shown that the theory gives a satisfactory prediction of the wave shape, which improves as the Mach number increases.
Modifications in the flow field behind the shock, compared to that for a simple corner made up of two plane walls is discussed,
particularly relating to flow separation. For circular arc concave walls a inverse Mach reflection results experimentally,
leading to regular reflection, for which the theory is of no use.
PACS 47.40.Nm 相似文献
4.
An investigation into the three-dimensional propagation of the transmitted shock wave in a square cross-section chamber was described in this paper, and the work was carried out numerically by solving the Euler equations with a dispersion-controlled scheme. Computational images were constructed from the density distribution of the transmitted shock wave discharging from the open end of the square shock tube and compared directly with holographic interferograms available for CFD validation. Two cases of the transmitted shock wave propagating at different Mach numbers in the same geometry were simulated. A special shock reflection system near the corner of the square cross-section chamber was observed, consisting of four shock waves: the transmitted shock wave, two reflection shock waves and a Mach stem. A contact surface may appear in the four-shock system when the transmitted shock wave becomes stronger. Both the secondary shock wave and the primary vortex loop are three-dimensional in the present case due to the non-uniform flow expansion behind the transmitted shock.PACS: 43.40.Nm 相似文献
5.
The flow field developed behind a shock wave propagating inside a constant cross-section conduit is solved numerically for
two different cases. First, when the density of the ambient gas into which the shock propagates has a logarithmic change with
distance. In the second, and the more practical case, the ambient gas is composed of pairs of air–helium layers having a continually
decreasing width. It is shown that in both cases meaningful pressure amplification can be reached behind the transmitted shock
wave. It is especially so in the second case. By proper choice of the number of air–helium layers and their width reduction
ratio, pressure amplification as high as 7.5 can be obtained.
相似文献
6.
The interaction of a planar shock wave with a loose dusty bulk layer has been investigated both experimentally and numerically.
Experiments were conducted in a shock tube. The incident shock wave velocity and particle diameters were measured with the
use of pressure transducers and a Malvern particle sizer, respectively. The flow fields, induced by shock waves, of both gas
and granular phase were visualized by means of shadowgraphs and pulsed X-ray radiography with trace particles added. In addition,
a two-phase model for granular flow presented by Gidaspow is introduced and is extended to describe such a complex phenomenon.
Based on the kinetic theory, such a two-phase model has the advantage of being able to clarify many physical concepts, like
particulate viscosity, granular conductivity and solid pressure, and deduce the correlative constitutive equations of the
solid phase. The AUSM scheme was employed for the numerical calculation. The flow field behind the shock wave was displayed
numerically and agrees well with our corresponding experimental results.
相似文献
7.
Shock wave attenuation by grids and orifice plates 总被引:2,自引:0,他引:2
The interaction of weak shock waves with porous barriers of different geometries and porosities is examined. Installing a barrier inside the shock tube test section will cause the development of the following wave pattern upon a head-on collision between the incident shock wave and the barrier: a reflected shock from the barrier and a transmitted shock propagating towards the shock tube end wall. Once the transmitted shock wave reaches the end wall it is reflected back towards the barrier. This is the beginning of multiple reflections between the barrier and the end wall. This full cycle of shock reflections/interactions resulting from the incident shock wave collision with the barrier can be studied in a single shock tube test. A one-dimensional (1D), inviscid flow model was proposed for simulating the flow resulting from the initial collision of the incident shock wave with the barrier. Fairly good agreement is found between experimental findings and simulations based on a 1D flow model. Based on obtained numerical and experimental findings an optimal design procedure for shock wave attenuator is suggested. The suggested attenuator may ensure the safety of the shelter’s ventilation systems. 相似文献
8.
The effects of energy deposition in the free stream on steady regular and Mach shock wave reflections are studied numerically. A short-duration laser pulse is focused upstream of the incident shock waves. It causes formation of the expanding blast wave and the residual hot-spot interacting in a complex way with the steady shock wave reflection. It was found that the laser energy addition in the free stream may force the transition from regular to Mach reflection in the dual solution domain. In contrast to previously reported numerical results, the transition from Mach to regular reflection has not been reproduced in our refined computations since the Mach reflection is restored after the flow perturbation. 相似文献
9.
To prevent damage caused by accidental overpressure inside a closed duct (e.g. jet engine) safety valves are introduced. The
present study experimentally investigates the dynamic opening of such valves by employing a door at the end of a shock tube
driven section. The door is hung on an axis and is free to rotate, thereby opening the tube. The evolved flow and wave pattern
due to a collision of an incident shock wave with the door, causing the door opening, is studied by employing a high speed
schlieren system and recording pressures at different places inside the tube as well as on the rotating door. Analyzing this
data sheds light on the air flow evolution and the behavior of the opening door. In the present work, emphasis is given to
understanding the complex, unsteady flow developed behind the transmitted shock wave as it diffracts over the opening door.
It is shown that both the door inertia and the shock wave strength influence the opening dynamic evolution, but not in the
proportions that might be expected. 相似文献
10.
11.
Abstract. The starting process of two-dimensional and axisymmetric nozzle flows has been investigated numerically. Special attention
has been paid to the early phase of the starting process and to the appearance of a strong secondary shock wave. For both
cases, shock intensities and velocities are obtained and discussed. The flow evolution in the axisymmetric case is proved
to be more complex and the transient starting process is slower than in the plane case. Finally, the effects of changing the
nozzle angle and the incident shock wave Mach number on the transient flow are addressed. It is shown that a faster start-up
can be induced either by decreasing the nozzle angle or increasing the Mach number of the incident shock wave.
Received 16 November 2001 / Accepted 24 September 2002 / Published online 4 December 2002
Correspondence to:A.-S. Mouronval (e-mail: mouronv@coria.fr) 相似文献
12.
Numerical investigation of axisymmetric shock wave focusing over paraboloidal reflectors 总被引:2,自引:0,他引:2
The problem of a plane shock wave incident to a paraboloidal reflector is numerically investigated. The numerical solver
used is developed by an improved, implicit, upwind total variation diminishing scheme in a finite-volume approach. The real-gas
effect is taken into account if high temperature occurs. The solver is validated on four test problems. The complicated flow
fields of axisymmetric shock wave focusing for different-depth reflectors at various incident shock Mach numbers are studied.
An interesting result of a maximum pressure happening at the reflector center is found. This is due to the occurrence of an
implosion phenomenon. A maximum temperature might occur at the reflector center or at other locations, depending on the incident
shock Mach number and the reflector depth. Moreover, vortical flows induced by shock wave focusing and their formation mechanism
are explored. It was found that the vortices near the reflector are caused by a ring-shaped shock/slipline interaction. Owing
to the slipline on the symmetry axis, a jet flow is induced, resulting in the formation of vortices near the symmetry axis.
Received 13 January 1998 / Accepted 10 November 1998 相似文献
13.
The various oblique shock wave reflection patterns generated by a moving incident shock on a planar wedge using an ideal quantum
gas model are numerically studied using a novel high resolution quantum kinetic flux splitting scheme. With different incident
shock Mach numbers and wedge angles as flow parameters, four different types of reflection patterns, namely, the regular reflection,
simple Mach reflection, complex Mach reflection and the double Mach reflection as in the classical gas can be classified and
observed. Both Bose–Einstein and Fermi–Dirac gases are considered.
相似文献
14.
B. E. Gelfand A. M. Bartenev S. P. Medvedev A. N. Polenov S. V. Khomik M. Lenartz H. Grönig 《Shock Waves》1994,4(3):137-143
On the basis of numerical modeling specific features of shock wave reflections were analyzed. It was found, that after diaphragm rupture self-modeling pressure and velocity distributions nearby the shock front establish. But in some special cases the temperature behind the shock front can rise. This peculiarity should be taken into account when performing experiments with high reactive gaseous mixtures. The temperature on the shock front and the velocity gradient behind it are uniform in the case of strong blast wave reflections. This effect is observed in the zone with an elevated temperature profile behind the incident blast wave. The reflected triangular waves conserve a quasi-self-modeling character by pressure. Typical experiments were carried out to verify the theoretical predictions. The effects of reflected wave acceleration in the case of triangular waves and the self-similar character of the pressure profiles were observed.This article was processed using Springer-Verlag TEX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society. 相似文献
15.
Head-on Collision of a Detonation with a Planar Shock Wave 总被引:1,自引:0,他引:1
H. D. Ng B. B. Botros J. Chao J. M. Yang N. Nikiforakis J. H. S. Lee 《Shock Waves》2006,15(5):341-352
The phenomenon that occurs when a Chapman–Jouguet (CJ) detonation collides with a shock wave is discussed. Assuming a one-dimensional steady wave configuration analogous to a planar shock–shock frontal interaction, analytical solutions of the Rankine–Hugoniot relationships for the transmitted detonation and the transmitted shock are obtained by matching the pressure and particle velocity at the contact surface. The analytical results indicate that there exist three possible regions of solutions, i.e. the transmitted detonation can have either strong, weak or CJ solution, depending on the incident detonation and shock strengths. On the other hand, if we impose the transmitted detonation to have a CJ solution followed by a rarefaction fan, the boundary conditions are also satisfied at the contact surface. The existence of these multiple solutions is verified by an experimental investigation. It is found that the experimental results agree well with those predicted by the second wave interaction model and that the transmitted detonation is a CJ detonation. Unsteady numerical simulations of the reactive Euler equations with both simple one-step Arrhenius kinetic and chain-branching kinetic models are also carried out to look at the transient phenomena and at the influence of a finite reaction thickness of a detonation wave on the problem of head-on collision with a shock. From all the computational results, a relaxation process consisting of a quasi-steady period and an overshoot for the transmitted detonation subsequent to the head-on collisions can be observed, followed by the asymptotic decay to a CJ detonation as predicted theoretically. For unstable pulsating detonations, it is found that, due to the increase in the thermodynamic state of the reactive mixture caused by the shock, the transmitted pulsating detonation can become more stable with smaller amplitude and period oscillation. These observations are in good agreement with experimental evidence obtained from smoked foils where there is a significant decrease in the detonation cell size after a region of relaxation when the detonation collides head-on with a shock wave. 相似文献
16.
A. Chatterjee 《Shock Waves》1999,9(2):95-105
An initially planar shock wave can undergo significant distortion to its shape along with changes in its strength during
the period of its interaction with a compressible vortex. This phenomenon is studied by numerically simulating the shock wave-vortex
interaction with a high resolution shock-capturing scheme. Incident shock waves of various Mach numbers are made to interact
with a compressible vortex and the dependence of the shock wave distortion on the strength of the incident shock wave is studied
in detail. It is known that the type of complex shock structure formed in the later stages of a compressible vortex-shock
wave interaction is dependent on the Mach number of the incident shock wave. A simple physical model based on the principle
of shock wave reflection is proposed to explain this complex shock structure formation and its dependence on the relative
strengths of the interacting vortex and shock wave.
Received July 28, 1997 / Accepted November 17, 1997 相似文献
17.
Attenuation of weak shock waves along pseudo-perforated walls 总被引:2,自引:0,他引:2
A. Sasoh K. Matsuoka K. Nakashio E. Timofeev K. Takayama P. Voinovich T. Saito S. Hirano S. Ono Y. Makino 《Shock Waves》1998,8(3):149-159
In order to attenuate weak shock waves in ducts, effects of pseudo-perforated walls were investigated. Pseudo-perforated
walls are defined as wall perforations having a closed cavity behind it. Shock wave diffraction and reflection created by
these perforations were visualized in a shock tube by using holographic interferometer, and also by numerical simulation.
Along the pseudo-perforated wall, an incident shock wave attenuates and eventually turns into a sound wave. Due to complex
interactions of the incident shock wave with the perforations, the overpressure behind it becomes non-uniform and its peak
value can locally exceed that behind the undisturbed incident shock wave. However, its pressure gradient monotonically decreases
with the shock wave propagation. Effects of these pseudo-perforated walls on the attenuation of weak shock waves generated
in high speed train tunnels were studied in a 1/250-scaled train tunnel simulator. It is concluded that in order to achieve
a practically effective suppression of the tunnel sonic boom the length of the pseudo-perforation section should be sufficiently
long.
Received 23 June 1997 / Accepted 16 September 1997 相似文献
18.
All previous studies on shock wave diffraction in shock tubes have spatial and temporal limitations due to the size of the
test sections. These limitations result from either the reflection of the expansion wave, generated at the corner, from the
top wall and/or of the reflection of the incident diffracted shock from the bottom wall of the test section passing back through
the region of interest. This has limited the study of the evolution of the shear layer and its associated vortex, which forms
a relatively small region of the flow behind the shock with an extent of only a few centimeters, and yet is a region of significant
interest. A special shock tube is used in the current tests which allow evolution of the flow to be examined at a scale about
an order of magnitude larger than in previously published results, with shear layer lengths of up to 250 mm being achieved
without interference from adjacent walls. Tests are presented for incident shock wave Mach numbers of nominally 1.3–1.5. Studies
have been undertaken with wall angles of 10, 20, 30 and 90°. Significant changes are noted as the spatial and temporal scale
of the experiment increases. For a given wall angle, the flow behind the incident shock is not self-similar as is usually
assumed. Both shear layer instability and the development of turbulent patches become evident, neither of which have been
noted in previous tests. 相似文献
19.
Shock wave attenuation in polyurethane foams is investigated experimentally and numerically. This study is a part of research project regarding shock propagation in polyurethane foams with high-porosities
= 0.951 ~ 0.977 and low densities of ρc = 27.6 ~55.8 kg/m3. Sixty Millimeter long cylindrical foams with various cell numbers and foam insertion condition were installed in a horizontal shock tube of 50 mm i.d. and 5.4 mm in length. Results of pressure measurements in air/foam combination are compared with CFD simulation solving the one-dimensional Euler equations. In the case of a foam B fixed on shock tube wall, pressures at the shock tube end wall increases relatively slowly comparing to non-fixed foam, free to move and a foam A fixed on shock tube wall. This implies that elastic inertia hardly contributes to pressure build up. Pressures behind a foam C fixed on shock tube wall decrease indicating that shock wave is degenerated into compression wave. Dimensionless impulse and attenuation factor decrease as the initial cell number increases. The momentum loss varies depending on cell structure and cell number. 相似文献
20.
T. V. Bazhenova V. V. Golub A. L. Kotel'nikov A. S. Chizhikov S. B. Shcherbak 《Fluid Dynamics》2003,38(2):336-342
The temporal-spatial development of the flow pattern behind a shock wave emerging from open-ended and half-closed ducts at M0=1.15 to 3.0 Mach number is investigated both experimentally and numerically and the action of the diffracted wave on a barrier placed at different distances from the duct exit is studied. Flow toeplerograms are obtained and the pressure on the barrier is measured. The distinctive features of the interaction between the shock wave and a barrier mounted perpendicular to the duct axis are established. It is found that partial closing of the duct results in a decrease in the barrier pressure in the case of a strong shock (M0 > 2.2) and leads to a pressure decrease when a weak shock is diffracted (M0=1.1 to 1.7). A dependence characterizing the dynamic action of the shock wave on the barrier and specifying the threshold value of a combination of the shock Mach number and the distance from the barrier determining whether the pressure pulse on the barrier increases or decreases, is obtained. 相似文献