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1.
The generalised Burgers’ equation models the nonlinear evolution of acoustic disturbances subject to thermoviscous dissipation. When thermoviscous effects are small, asymptotic analysis predicts the development of a narrow shock region, which widens, leading eventually to a shock-free linear decay regime. The exact nature of the evolution differs subtly depending upon whether plane waves are considered, or cylindrical or spherical spreading waves. This paper focuses on the differences in asymptotic shock structure and validates the asymptotic predictions by comparison with numerical solutions. Precise expressions for the shock width and shock location are also obtained. 相似文献
2.
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
3.
《Wave Motion》2018
The propagation of monochromatic nonlinear symmetric hybrid waves in a cylindrical nonlinear dielectric waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. The problem is reduced to the new type of nonlinear eigenvalue problem. The analytical method of solving this problem is presented. New propagation regime is found. 相似文献
4.
V. A. Levin 《Fluid Dynamics》1968,3(2):31-34
The asymptotic laws of behavior for plane, cylindrical, and spherical infinitely thin detonation waves were found in [1, 2] for increasing distance from an igniting source in those cases in which the waves changed into Chapman-Jouguet waves as they decayed. It was shown that the plane overdriven detonation wave approaches the Chapman-Jouguet regime asymptotically, while the transition of the cylindrical or spherical strong detonation wave into the Chapman-Jouguet wave may occur at a finite distance from the initiation source.Similar conclusions are valid for the propagation of stationary steadystate detonation waves which arise with flow of combustible gas mixtures past bodies.However, numerous experiments [3, 4] on firing bodies in a detonating gas show that the overdriven detonation wave which forms ahead of the body decays and decomposes into an ordinary compression shock and a slow combustion front. To establish why the wave does not make the transition to the Chapman-Jouguet regime, in the following we consider the propagation of a plane detonation wave and account for finite chemical reaction rates. We use the very simple two-front model (ordinary shock wave and following flame front). Conditions are found for which transition to the Chapman-Jouguet regime does not occur. We first consider the propagation of an unsteady plane wave and then the steady plane wave. It is found that for all the mixtures used in these experiments transition to the Chapman-Jouguet regime is not possible within the framework of the assumed model. 相似文献
5.
Focusing of strong shock waves in a gas-filled thin convergence chamber with various forms of the reflector boundary is investigated experimentally and numerically. The convergence chamber is mounted at the end of the horizontal co-axial shock tube. The construction of the convergence chamber allows the assembly of the outer chamber boundaries of various shapes. Boundaries with three different shapes have been used in the present investigation—a circle, an octagon and a smooth pentagon. The shock tube in the current study was able to produce annular shocks with the initial Mach number in the range M
s = 2.3 − 3.6. The influence of the shape of the boundary on the shape and properties of the converging and reflected shock waves in the chamber has then been investigated both experimentally and numerically. It was found that the form of the converging shock is initially governed by the shape of the reflector and the nonlinear interaction between the shape of the shock and velocity of shock propagation. Very close to the center of convergence the shock obtains a square-like form in case of a circular and octagonal reflector boundary. This is believed to stem from the instability of the converging shock front triggered by the disturbances in the flow field. The outgoing, reflected shocks were also observed to be influenced by the shape of the boundary through the flow ahead as created by the converging shocks. 相似文献
6.
An experimental investigation was made into the formation and propagation of cylindrical collapsing shock waves in a pulsed induction gas discharge. The shock fronts were made visible and their propagation velocity measured by means of the schlieren method in conjunction with high-speed cine photography in the photoscanning regime and frame-by-frame detection, which made it possible, using the experimental data, to analyze the formation and propagation of the shock waves. A physical picture of the individual stages in the development of the discharge is given on the basis of the experimental results.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 129–133, January–February, 1981.We are thankful to Yu. P. Raizer for helpful discussions of the work. 相似文献
7.
Riccardo Fazio 《Wave Motion》1992,16(4):299-305
In this paper we present some results obtained by studying the mathematical model describing a moving boundary hyperbolic problem related to a time dependent stress impact in a bar of Maxwell-like material. Due to the impact a shock front propagates with a finite speed. Here our interest is to underline the influence of the dissipative term on the propagation of the shock front.
In the framework of the similarity analysis we are able to reduce the moving boundary hyperbolic problem to a free boundary value problem for an ordinary differential system. It is then possible, by applying two numerical transformation methods, to solve the free boundary value problem numerically. The influence of the dissipative term is evident: the free boundary (that defines the shock front propagation) is an increasing function of the dissipative coefficient. 相似文献
8.
《Acta Mechanica Solida Sinica》2015,(3)
The thermal shock problems involved with fractional order generalized theory is studied by an analytical method. The asymptotic solutions for thermal responses induced by transient thermal shock are derived by means of the limit theorem of Laplace transform. An infinite solid with a cylindrical cavity subjected to a thermal shock at its inner boundary is studied. The propagation of thermal wave and thermal elastic wave, as well as the distributions of displacement,temperature and stresses are obtained from these asymptotic solutions. The investigation on the effect of fractional order parameter on the propagation of two waves is also conducted. 相似文献
9.
Near-resonance highly nonlinear ideal perfect gas oscillations in tubes are studied numerically for boundary conditions of
various types. The oscillations are initiated by weak periodic perturbations at one end of the tube. As distinct from earlier
studies [1–10], the oscillation amplitudes were not assumed to be small and the entropy increase at the shock waves formed
was taken into account. Periodic flow regimes result as a limit of the solution of a Cauchy problem for one-dimensional time-dependent
gasdynamic equations. The frequency responses of the oscillations under consideration are determined for boundary conditions
of various types. It is shown that in specific cases the attainment of a periodic regime is accompanied by the appearance
of long-wave modulations. The “repeated resonance” effect is revealed. This is due to the change in the tube's natural acoustic
frequency, which takes place during the heating of the gas in the tube by the shock waves traveling in it.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 150–157, July–August, 1994. 相似文献
10.
Shih-Hsien Yu 《Archive for Rational Mechanics and Analysis》1999,146(4):275-370
We consider the convergence of solutions of conservation laws with viscosity to solutions having shocks of hyperbolic conservation
laws without viscosity as the viscosity tends to zero. Our analysis reveals a rich structure of nonlinear wave interactions
due to the presence of shocks and initial layers. These interactions generate four different wave patterns: initial layers,
shock layers, diffusion waves and coupling waves. We study the propagation and interactions of the four wave patterns by a
detailed pointwise analysis.
(Accepted February 19, 1998) 相似文献
11.
The propagation of nonstationary weak shock waves in a chemically active medium is essentially dispersive and dissipative. The equations for short-wavelength waves for such media were obtained and investigated in [1–4]. It is of interest to study quasimonochromatic waves with slowly varying amplitude and phase. A general method for obtaining the equations for modulated oscillations in nonlinear dispersive media without dissipation was proposed in [5–8]. In the present paper, for a dispersive, weakly nonlinear and weakly dissipative medium we derive in the three-dimensional formulation equations for waves of short wavelength and a Schrödinger equation, which describes slow modulations of the amplitude and phase of an arbitrary wave. The coefficients of the equations are particularized for the considered gas-liquid mixture. Solutions are obtained for narrow beams in a given defocusing medium as well as linear and nonlinear solutions in the neighborhood of a diffraction beam. A solution near a caustic for quasimonochromatic waves was found in [9].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 133–143, January–February, 1980. 相似文献
12.
The possibility of creating unsteady distortions of the tip shock by waves emitted from an aircraft is assessed experimentally. The model chosen is a cylindrical fore body equipped with a spike. This configuration is known for generating an important level of unsteadiness around the spike in supersonic regime. The wind tunnel Mach number is equal to 2. The experiments show that waves emitted from this source propagate along the tip shock and interact with it. It is then assessed that this interaction produces a periodic distortion of the shock that propagates to the external flow. Unsteady pressure sensors, high speed schlieren films, hot wire probing and laser Doppler velocimetry are used as complementary experimental means. The final result is a coherent representation of the complex mechanism of wave propagation that has been evidenced. The principle of creating unsteady shock deformation by onboard equipments could be examined as a possibly promising method of sonic boom control. 相似文献
13.
采用高速纹影法实验研究了柱形汇聚激波与球形重气体界面相互作用的 Richtmyer-Meshkov不稳定性问题. 激波管实验段基于激波动力学理论设计, 将马赫数为1.2 的平面激波转化为柱形汇聚激波, 气体界面由肥皂膜分隔六氟化硫(内)和空气(外)得到. 采用高速摄影机在单次实验中拍摄激波运动的全过程, 对柱形激波的形成进行了实验验证, 并进一步观测了汇聚激波与球形气体界面相互作用过程中的波系发展和气体界面变形以及反射激波同已变形界面二次作用的流场演化. 结果表明: 当柱形汇聚激波穿过气泡界面以后, 气泡左侧界面极点沿激波传播方向保持匀速运动, 气泡右侧界面发展成为射流结构, 气泡主体发展成为涡环结构; 在反射激波的二次作用下, 流场中无序运动显著增强并很快进入湍流混合阶段. 相似文献
14.
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16.
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
17.
We experimentally investigated propagation characteristics of the shock wave driven by a gaseous detonation wave emerging
from the open end of a cylindrical detonation tube. In the present study, we visualized the shock wave and exhaust flowfields
using a shadowgraph optical system and we obtained peak overpressure in the tube axial direction and the continuous shape
transformation of shock waves around the tube open end. We also obtained overpressure histories of the shock wave using piezo-pressure
transducers within 201 m from the open end of the tube. We normalized and classified these results by four regions using non-dimensional
pressure and distance which are independent of variety of mixture and tube diameter. In the vicinity of the open end of the
tube, the shock wave is nearly planar and does not significantly attenuate, and the peak overpressure maintains approximately
C–J pressure. Subsequently, the shock wave attenuates rapidly, transforming from quasi-spherical to spherical. Farther from
the tube open end, the shock wave propagates with approximately sound characteristic so that the peak overpressure decreases
proportional to 1/r. Eventually, the shock wave begins to attenuate more rapidly than ideal sound attenuation, which may be due to the viscous
effect. 相似文献
18.
Propagation of sound and weak shock waves in gas-liquid foams is investigated theoretically and experimentally. An original
physical model is developed to describe the evolution of small perturbations in a foam of polyhedral structure. The model
developed takes into account both peculiarities of interface heat transfer in foam and liquid motion through the system of
Plateau-Gibbs borders which results in the appearance of an additional hydrodynamic dissipative force. The Rayleigh equation
analog, which takes into account the latter phenomenon, is obtained. Structure and dynamics of weak shock waves are investigated.
A vertical shock tube was constructed and used to measure the parameters of weak shock wave propagation in gas-liquid foams
of polyhedral structure. Spectral analysis of the data obtained shows that there are weak dispersion and strong dissipation
of the initial signal. Comparison of the evolution of experimental and theoretical profiles permits to conclude that the suggested
model allows to describe the peculiarities of acoustical perturbations in gas-liquid foam more precisely than it follows from
the standard models.
Received 15 September 1993 / Accepted 27 December 1993 相似文献
19.
本文探讨了一种新的激波-非定常边界层相互干扰现象,这种激波-边界层干扰现象既不同于定常激波-边界层干扰现象,又不同于激波在端面反射后与该激波所诱导的边界层之间的干扰现象,而是运动激波与稀疏波和第一激波所诱导的非这常边界层之间的干扰现象,本文对这种现象用微波动力学理论进行分析,并把这种干扰现象看成激波的绕射现象,同时在稀疏波破膜的双驱动激波管中进行实验观察,最后把理论分析与实验观察进行了比较。 相似文献
20.
A simple one-dimensional model is used to simulate numerically the propagation oflinear and nonlinear waves in a deformable ceramic.The nummrical scheme used providesthe response in stress or strain and electric field within the sample and the voltage at aresistive external circuit connecting the two faces of the sample.Space-time diagrams of thepropagation are obtained for various mechanical loads.The voltage response obtainedagress well with experimental results in the linear regime.In the nonlinear one,thesteepening of the electromechanical wave yielding a shock wave is exhibited. 相似文献