共查询到20条相似文献,搜索用时 0 毫秒
1.
An experimental and numerical study was made of converging cylindrical shock waves. The goal of the present study was to clarify the movement and instability of the converging cylindrical shock waves. Experiments were conducted in an annular shock tube of 230 mm o.d. and 210 mm i.d. connected to a cylindrical test section of 210 mm diameter. Double exposure holographic interferometry was used to visualize the converging cylindrical shock waves. Incident shock Mach numbers ranged between 1.1 and 2.0 in air. A numerical simulation was conducted using the TVD finite difference scheme. It was found in the experiments that although the initial shock wave configuration looked cylindrical, it was gradually deformed with propagation towards the center and finally showed mode-four instability. This is attributable to the existence of initial disturbances which were introduced by the struts which supported the inner tube of the annular shock tube. This trend was significant for stronger shock waves indicating that at the last stage of shock wave convergence the initial perturbations of the converging cylindrical shock wave were amplified to form the triple point of Mach reflection. The numerical results correctly predicted the experimental trend.This article was processed using Springer-Verlag TEX Shock Waves macro package 1990. 相似文献
2.
Conical Mach reflections differ from those of the equivalent plane, two-dimensional Mach reflection because in axisymmetry,
the disturbances generated at the reflecting surface are modified by their more rapidly increasing or decreasing area as they
move towards or away from the centerline. Equations for conical Mach reflection cases have now been developed using a simplified
ray-shock theory formulation based on the initial assumption that the stem is straight and normal to the wall. These are in
a form that applies generally. Their simple structure provides an easy conceptual understanding of self-similarity and non-self-similarity
as well as a clear mathematical approach for the development of the curved triple-point locus of the latter by integration.
They provide a quick and direct solution in all cases and can easily incorporate the Mach stem curvature by progressively
calculating the new ray direction. A range of cases has been considered and results are presented for converging and diverging,
self-similar and non-self-similar cases. 相似文献
3.
The Mach reflection of shock waves in those cases in which the gas ideality condition is satisfied with high accuracy is well-known. The effects associated with the excitation of the internal degrees of freedom for the molecules lead to a qualitative change in the reflection pattern. The present study is an extension of [1, 2], devoted to the study of the Mach reflection of shock waves from a wedge under conditions in which the physical and chemical transformations in the gas heated by the shock wave play a significant role. 相似文献
4.
The Kelvin–Helmholtz instability (KHI) is an instability that takes the form of repeating wave-like structures which forms on a shear layer where two adjacent fluids are moving at a relative velocity to one another. Such a shear layer forms in the Mach reflection of shock waves. This work focuses on experimentally visualising the presence of the KHI in Mach reflection as well as its evolution. Experimentation was performed at shock Mach numbers of 1.34, 1.46 and 1.61. Plane test pieces and parabolic profiled pieces followed by a plane section having wedge angles of 30 \(^\circ \) and 38 \(^\circ \) were tested. Flow field visualisation was performed with a schlieren optical system. The KHI was best visualised with the camera-side knife edge perpendicular to the shear layer (i.e. the axis of sensitivity along the length of the shear layer). The structure and growth of the instability were readily identified. The KHI forms more readily with increasing Mach number and wedge angle. Second-order Euler, and Navier–Stokes numerical simulations of the flow field were also conducted. It was found that the Euler and laminar Navier–Stokes solvers achieved very similar results, both producing the KHI, but at a much less developed state than the experimental cases. The k \(-\epsilon \) solver, however, did not produce the instability. 相似文献
5.
B. I. Zaslavskii R. A. Safarov 《Journal of Applied Mechanics and Technical Physics》1973,14(5):624-629
On the basis of experimental observations and theoretical analysis of flow structure in the neighborhood of the triple point, it is shown that one should reject the condition for equality of the angle of deflection of flows passing through the Mach front and the two other fronts and replace it with some supplementary condition. The system of consistency equations in the indicated region is closed by an equation which is obtained under the assumption of the extremality of the deflection angle of a flow passing through the incident and reflected fronts. Calculations of the pressure drops behind the shock fronts agree with experimental data in this case.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 26–33, September–October, 1973.The authors thank S. A. Khristianovich for consideration of the work and advice. 相似文献
6.
The onset of Mach reflection or regular reflection at the vertices of a converging polygonal shock wave was investigated experimentally
in a horizontal annular shock tube. The converging shock waves were visualized by schlieren optics. Two different types of
polygonal shock convergence patterns were observed. We compared the behavior during the focusing process for triangular and
square-shaped shocks. It is shown that once a triangular shaped shock is formed, the corners in the converging shock will
undergo regular reflection and consequently the shape will remain unaltered during the focusing process. A square-shaped shock
suffers Mach reflections at the corners and hence a reconfiguring process takes place; the converging shock wave alternates
between a square and an octagon formation during the focusing process.
相似文献
7.
An experimental study was made of the stability of converging cylindrical shock waves. The experiments were conducted on annular shock tubes equipped with a double exposure holographic interferometer in the Stoßwellenlabor, RWTH Aachen, and in the Institute of High Speed Mechanics, Tohoku University, Sendai, for shock Mach numbers of 1.1 to 2.1 in air. By comparing these two different shock tube experiments, it is found that in the former facility the mode-three instability is predominant at the center of convergence, whereas the mode-four instability appears in the latter setup. The instabilities are denoted in this way because the shock and the flow field behind it reveal a remarkable triangular and quadrangular symmetry, respectively. It is concluded that the converging cylindrical shock wave is always unstable and sensitive to the structure of the annular shock tube. Usefulness of holographic interferometry to this kind of shock wave research is also demonstrated.To Prof. Dr. sq. techn. Dr.-Ing. e.h. Fritz Schultz-Grunow on the occasion of his 80th birthday 相似文献
8.
The Richtmyer–Meshkov instability behavior of a heavy-gas $(\text{ SF }_6)$ cylinder accelerated by a cylindrical converging shock wave is studied experimentally. A curved wall profile is well-designed based on the shock dynamics theory [Phys. Fluids, 22: 041701 (2010)] with an incident planar shock Mach number of 1.2 and a converging angle of $15^\circ $ in a $95\,\text{ mm }\times 95$ mm square cross-section shock tube. The $\text{ SF }_6$ cylinder mixed with the glycol droplets flows vertically through the test section and is illuminated horizontally by a laser sheet. The images obtained only one per run by an ICCD (intensified charge coupled device) combined with a pulsed Nd:YAG laser are first presented and the complete evolution process of the $\text{ SF }_6$ cylinder is then captured in a single test shot by a high-speed video camera combined with a high-power continuous laser. In this way, both the developments of the first counter-rotating vortex pair and the second counter-rotating vortex pair with an opposite rotating direction from the first one are observed. The experimental results indicate that the phenomena induced by the converging shock wave and the reflected shock formed from the center of convergence are distinct from those found in the planar shock case. 相似文献
9.
G.C. Burdiak S.V. Lebedev R.P. Drake A.J. Harvey-Thompson G.F. Swadling F. Suzuki-Vidal J. Skidmore L. Suttle E. Khoory L. Pickworth P. de Grouchy G.N. Hall S.N. Bland M. Weinwurm J.P. Chittenden 《High Energy Density Physics》2013,9(1):52-62
A cylindrical liner z-pinch configuration has been used to drive converging radiative shock waves into different gases. On application of a 1.4 MA, 240 ns rise-time current pulse, a series of cylindrical shocks moving at typical velocities of 20 km s?1 are consecutively launched from the inside liner wall into an initially static gas-fill of density ~10?5 g cm?3. The drive current skin depth calculated prior to resistive heating was slightly less than the liner wall thickness and no bulk liner implosion occurred. Axial laser probing images show the shock fronts to be smooth and azimuthally symmetric, with instabilities developing downstream of each shock. Evidence for a radiative precursor ahead of the first shock was seen in laser interferometry imaging and time-gated, spatially resolved optical spectroscopy. The interferometry diagnostic was able to simultaneously resolve the radiative precursor and the density jumps at the shock fronts. Optical streak photography provided information on shock timing and shock trajectories and was used to gain insight into the shock launching mechanisms. 相似文献
10.
Analytical consideration of Mach reflections over cones using the ray-shock theory showed that they differ from those of
the two-dimensional Mach reflection over wedges. Conical configurations include both self-similar and non-self-similar cases.
However, even when self-similar, the conical configurations exhibit triple-point locus trajectory angles with values which,
for any given reflection angle, differ from those of self-similar, wedge cases. Additionally, within the range of possible
conical configurations, different values of self-similar triple-point locus angles exist for any given reflection angle depending
on the geometry of the particular reflection process. While the ray-shock theory, as discussed in a previous paper on this
research, provides a useful guide and a means of readily identifying these variations, verification using both shock tube
and numerical simulations is required and is now available. Results of experimentation for both self-similar and non-self-similar
axisym
metric cases using these techniques are reported here and comparisons are made with the previous analysis. These support the
calculations of the ray-shock theory over much of the reflection angle, Mach number range as well as highlighting some limitations
of the theory.
Received 15 October 1996 / Accepted 14 April 1997 相似文献
11.
V. N. Lyakhov 《Fluid Dynamics》1976,11(3):421-424
Some peculiarities of the processes of regular and Mach reflection at constant adiabatic index =cp/cv=1.4 were investigated theoretically in [1]. It was demonstrated that increase in incident-wave intensity above some value leads to the appearance of an internal compression discontinuity (Fig. 1) and a break in the reflected wave (at point h), both of which had been observed previously only in experiment [2–4]. In the present study the method described in [1] is used to study the influence of adiabatic index on these peculiarities of the Mach reflection process which lead to a significant increase in pressure (to a maximum value Pm) on the surface wedge in the vicinity of point i. Pressure and density curves along the wedge surface are presented. It is found that increase in leads to the same qualitative changes in the pressure and density curves on the surface as are observed upon increase in semiaperture angle of the wedge or upon decrease in Mach number Mf of the shock-wave front incident on the wedge ab. These similarities in the shock-wave reflection process were first noted in [5] for weak shock waves in which the internal compression discontinuity does not appear.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 8, pp. 90–94, May–June, 1976.The author thanks O. S. Ryzhov for the many valuable remarks offered in his evaluation of the study. 相似文献
12.
G. Bazalitski V. Ts. Gurovich A. Fedotov-Gefen S. Efimov Ya. E. Krasik 《Shock Waves》2011,21(4):321-329
Results of one-dimensional numerical simulations of the parameters of the converging strong shock wave generated by electrical
underwater explosions of a cylindrical wire array with different array radii and different deposited energies are presented.
It was shown that for each wire array radius there exists an optimal duration of the energy deposition into the exploding
array, which allows one to maximize the shock wave pressure and temperature in the vicinity of the implosion axis. The simulation
results agree well with the 130-GPa pressure in the vicinity of the implosion axis that was recently obtained, which strongly
indicates the azimuthal symmetry of the converging shock wave at these extreme conditions. Also, simulations showed that using
a pulsed power generator with a stored energy of ~200 kJ, the pressure and temperature at the shock wave front reaches ~220
GPa and 1.7 eV at 0.1 mm from the axis of implosion in the case of a 2.5 mm radius wire array explosion. It was found that,
in spite of the complicated equation of state of water, the maximum pressure at the shock wave front at radius r can be estimated as P ≈ (P*(r*/r)
α
, where P* is the known value of pressure at the shock wave front at radius r* ≥ r and α is a parameter that equals 0.62±0.02. A rough estimate of the implosion parameters of the hydrogen target after the interaction
with the converging strong shock wave is presented as well. 相似文献
13.
G. P. Shindyapin 《Fluid Dynamics》1996,31(2):318-324
The problem of weak Mach reflection, known as the von Neumann paradox, and the more general case of Mach interaction of relatively weak shock waves are studied on the basis of the short-wave asymptotics.Saratov. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 183–190, March–April, 1996. 相似文献
14.
The interaction of strong shock waves with circular cylindrical convex and concave surfaces has been investigated experimentally. The influence of the geometry of the reflecting surface is considered. Some features of the process are noted and the results are compared with the results of other authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 132–138, March–April, 1982. 相似文献
15.
16.
Transition between regular and Mach reflection of shock waves: new numerical and experimental results 总被引:1,自引:0,他引:1
M.S. Ivanov D. Vandromme V.M. Fomin A.N. Kudryavtsev A. Hadjadj D.V. Khotyanovsky 《Shock Waves》2001,11(3):199-207
New numerical and experimental results on the transition between regular and Mach reflections of steady shock waves are presented.
The influence of flow three-dimensionality on transition between steady regular and Mach reflection has been studied in detail
both numerically and experimentally. Characteristic features of 3D shock wave configuration, such as peripheral Mach reflection,
non-monotonous Mach stem variation in transverse direction, the existence of combined Mach-regular-peripheral Mach shock wave
configuration, have been found in the numerical simulations. The application of laser sheet imaging technique in streamwise
direction allowed us to confirm all the details of shock wave configuration in the experiments. Close agreement of the numerical
and experimental data on Mach stem heights is shown.
Received 23 November 2000 / Accepted 25 April 2001 相似文献
17.
The direct simulation Monte Carlo (DSMC) method is applied to simulation of nonstationary Mach reflection of strong shock waves. Normally the DSMC method is very time consuming in solving unsteady flow field problems especially for high Mach numbers, because of the necessity of iterative calculations to eliminate the inherent statistical fluctuation caused by a finite sample size. A central weighted smoothing technique is introduced to process the DSMC results, so that the iteration time can be significantly reduced. In spite of some relaxations of the shock wave structure, the smoothing technique is verified to be useful to estima te the flow fields qualitatively and even quantitatively by using a relatively small sample size. The comparison between the present approach and the kineticmodel approach (Xu et al. 1991a, 1991b) on the application to unsteady rarefied flow fields was also carried out.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
18.
19.
20.
The signal speed, namely the local sound speed plus the flow velocity, behind the reflected shocks produced by the interaction of weak shock waves (M
i
< 1.4) with rigid inclined surfaces has been measured for several shock strengths close to the point of transition from regular to Mach reflection. The signal speed was measured using piezo-electric transducers, and with a multiple schlieren system to photograph acoustic signals created by a spark discharge behind a small aperture in the reflecting surfaces. Both methods yielded results with equal values within experimental error. The theoretical signal speeds behind regularly reflected shocks were calculated using a non-stationary model, and these agreed with the measured results at large angles of incidence. As the angle of incidence was reduced, for the same incident shock Mach number, so as to approach the point of transition from regular to Mach reflection, the measured values of the signal speed deviated significantly from the theoretical predictions. It was found, within experimental uncertainty, that transition from regular to Mach reflection occurred at the experimentally observed sonic point, namely, when the signal speed was equal to the speed of the reflection point along the reflecting surface. This sonic condition did not coincide with the theoretical value. 相似文献