共查询到20条相似文献,搜索用时 46 毫秒
1.
This communication considers the steady converging/diverging flow of a non-Newtonian viscous power-law fluid in a round cone. The motion is driven by a sink/source of mass at the origin. It is shown that the problem permits exact similarity solution for a particular value (n=4/3) of the fluid index. In this case a complete set of governing equations can be reduced to an ordinary differential equation, which is solved numerically for different values of the main non-dimensional parameters (the cone angle and the dimensionless sink/source intensity). 相似文献
2.
G. Wolansky 《Archive for Rational Mechanics and Analysis》2009,193(1):57-115
The process of coagulation is associated with scalar conservation laws, where the adhesion particle dynamics results from
shock waves. Conversely, the fragmentation of a massive particle into a number of smaller ones, or into a continuous (dust)
distribution, is associated with rarefaction waves. It is generally agreed that a reversible solution of a conservation law
can include neither shock waves nor the spontaneous emergence of rarefaction waves. The present paper is an attempt to demonstrate
that both coagulation and fragmentation may coexist for a reversible solution, under a natural generalization of the system
of conservation law. This is done by introducing an action principle which includes, in addition to the inertial (kinetic
energy) term, also an appropriately defined internal energy. The above generalization of the system of conservation law appears
as the Euler–Lagrange equations for this action. 相似文献
3.
The history of the flow behind a laser-driven shock is investigated in the context of variable energy blast waves. Thereby
the total laser energy absorbed by the blast is assumed to vary proportionally to some power of time. Due to the high temperatures
and pressures occurring in the initial phase of the flow a real gas model has been employed. It accounts for vibration, dissociation,
electronic excitation, ionization and intermolecular forces. Radiative and conductive heat transfer are considered as well.
The numerical computations were carried out using the method of characteristics. A self-similar strong shock solution serves
as initial condition. It turns out that the exponent which determines the time-dependent addition of energy at the shock front
is limited for physical reasons. The computed far-field solutions expand the temporal scope of the self-similar solution domain,
which has been the main subject of the classical literature, into the non-self-similar domain at late time. The differences
between the solutions obtained for real gas and perfect gas are less significant than in the case of the classical point explosion.
Received 30 July 1996 / Accepted 21 August 1997 相似文献
4.
Summary The bending of a finite-length beam that lies on a rigid, rough, flat foundation and interacts with it in accordance to the
dry friction law is considered. Loading by bending moments applied at the ends of the beam is studied in detail. The problem
is found to be a self-similar one. For small moments, the central part of the beam remains undeflected, and the problem reduces
to the solution of an infinite system of algebraic equations. Large moments deflect the entire length of the beam, and the
problem partly loses its self-similarity. In this case, the problem reduces to the solution of a successively decreasing number
of ordinary differential equations along with some algebraical equations. The solution for the latter case provides initial
conditions for the former one. This permits to obtain a solution for any value of the moment.
Received 5 November 1996; accepted for publication 27 January 1997 相似文献
5.
Transient shock waves in a confined elliptical chamber are experimentally investigated. Quantitative results of the pressure
distribution are obtained for an air-filled cavity. Lower bounding surfaces of different geometrical shapes can be inserted
making it possible to get chambers with varying height. An electrical discharge across a pair of electrodes inside the cavity
gives rise to the shock waves. Double pulsed holographic interferometry is used to study the propagation and focusing process
of the waves. The results are quantitatively evaluated by using the method of two-reference-beam holography. The angular pressure
distribution behind the converging wave front is presented for different geometries of an air-filled cavity. The pressure
distribution is non-homogeneous but symmetric along the wave front. The pressure level is higher for the geometry where the
height of the chamber decreases with the radial distance from the outgoing focus and lower for increasing height of the chamber.
In addition, shock waves in a water-filled cavity are studied. In this case qualitative results are obtained.
Received 3 November 1996 / Accepted 5 January 1997 相似文献
6.
7.
M. A. Il’gamov 《Mechanics of Solids》2017,52(6):663-674
The static and dynamic bending of a pipeline in the vertical plane under the action of its own weight is considered with regard to the interaction of the internal pressure with the curvature of the axial line and the axisymmetric deformation. The pressure consists of a constant and timevarying parts and is assumed to be uniformly distributed over the entire span between the supports. The pipeline reaction to the stepwise increase in the pressure is analyzed in the case where it is possible to determine the exact solution of the problem. The initial stage of bending determined by the smallness of elastic forces as compared to the inertial forces is introduced into the consideration. At this stage, the solution is sought in the form of power series and the law of pressure variation can be arbitrary. This solution provides initial conditions for determining the further process. The duration of the inertial stage is compared with the times of sharp changes of the pressure and the shock waves in fluids. The structure parameters are determined in the case where the shock pressure is accepted only by the inertial forces in the pipeline. 相似文献
8.
We deduce an energy identity which must be satisfied by the smooth solutions of the system of equations governing the dynamics of body with quasilinear rate-type constitutive equation. We give conditions when a unique energy function exists for rate-type viscoelasticity. In the semilinear case we give the conditions when a unique, positive and convex energy function exists and we obtain estimates in energy for the smooth solutions of initial-boundary value problems. A viscoelastic approach to nonlinear elasticity is discussed. Finally, an example shows that the second law of thermodynamics does not imply stability. 相似文献
9.
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
10.
N. N. Smirnov V. F. Nikitin Yu. G. Filippov E. I. Shemyakin 《Moscow University Mechanics Bulletin》2009,64(3):75-80
Some results of theoretical studies of detonation processes in combustible gaseous mixtures are discussed for a model geometry of large combustion chambers of detonation engines in the case of mixtures of hydrogen and oxygen-enriched air. The effect of geometric characteristics on the operation of pulse detonation engines is analyzed. In particular, the propagation of detonation waves in tubes of small diameter to larger volumes and the evolution of detonation under the action of converging shock waves are considered. 相似文献
11.
Using a simple example, the rotation of a rigid cone in rigid/plastic hardening material, the paper shows a qualitative difference
between the solutions for two groups of hardening laws. The first group includes hardening laws with no saturation stress.
In this case the solution under sticking conditions exists at any rotation angle of the cone up to infinity. The second group
includes hardening laws with a saturation stress. For such laws the solution exists up to a finite value of the rotation angle.
Once this angle has been reached, the solution breaks down. At the beginning of the process the behavior of the solution for
both groups of hardening materials is similar. However, at the final stage the behavior of rigid/plastic hardening materials
of the second group is similar to the behavior of rigid perfectly plastic materials. A specific hardening law with a saturation
stress is applied to illustrate the general solution and the restrictions imposed by this law, and a priori specified interfacial law (sticking) on existence of the solution.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
12.
V. S. Sazonov 《Fluid Dynamics》2012,47(2):239-253
Parameters of emitting shock waves in gases are investigated in the limiting case when there is no screening of emission from
the shock front by the precursory layer. The one-dimensional quasi-steady-state formulation of the problem with deceleration
of high-speed gas flow against a plane fixed obstacle under conditions of strong emission is given. The case of the shock
waves of large optical thickness is analytically considered over a wide range of variation of the obstacle reflectivity. The
parameters of emitting shock waves generated in experiments in shock tubes in the inert argon gas are estimated using the
methods developed and compared with the measurement results. The shock “adiabats” of optically thick shock waves are considered
with allowance for the radiation energy losses. The calculations are carried out for aluminium plasma. 相似文献
13.
We study supersonic flows of an electrically conductive gas in crossed electric and magnetic fields [1] in the presence of shock waves. It is shown that three steady flow regimes can exist, and that these are defined by the electrical conductivity of the gas as a function of temperature and density.
- The normal regime is characterized by a tendency for the shock to move toward the channel entrance on increase of the static pressure at the channel exit. The steady regime of this type exists and is stable.
- The anomalous regime (formally constructed) is characterized by a tendency for the shock to move toward the exit on increase of the static pressure at the channel exit. This regime is unstable and the flow in the MHD-channel may be either entirely supersonic or entirely subsonic.
- The limiting (boundary) regime is intermediate between the normal and anomalous regimes and is characterized by the fact that the stationary position of the shock wave and its amplitude are not uniquely defined. Steady flow in this case is not unique.
14.
E. A. Pushkar' 《Fluid Dynamics》1977,12(3):428-433
In two-dimensional supersonic gasdynamics, one of the classical steady-state problems, which include shock waves and other discontinuities, is the problem concerning the oblique reflection of a shock wave from a plane wall. It is well known [1–3] that two types of reflection are possible: regular and Mach. The problem concerning the regular reflection of a magnetohydrodynamic shock wave from an infinitely conducting plane wall is considered here within the scope of ideal magnetohydrodynamics [4]. It is supposed that the magnetic field, normal to the wall, is not equal to zero. The solution of the problem is constructed for incident waves of different types (fast and slow). It is found that, depending on the initial data, the solution can have a qualitatively different nature. In contrast from gasdynamics, the incident wave is reflected in the form of two waves, which can be centered rarefaction waves. A similar problem for the special case of the magnetic field parallel to the flow was considered earlier in [5, 6]. The normal component of the magnetic field at the wall was equated to zero, the solution was constructed only for the case of incidence of a fast shock wave, and the flow pattern is similar in form to that of gasdynamics. The solution of the problem concerning the reflection of a shock wave constructed in this paper is necessary for the interpretation of experiments in shock tubes [7–10].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 102–109, May–June, 1977.The author thanks A. A. Barmin, A. G. Kulikovskii, and G. A. Lyubimov for useful discussion of the results obtained. 相似文献
15.
In this study we revisit Schardin's problem by investigating experimentally shock waves diffracting over a finite wedge and
interacting with the tip vortices in a complicated manner. Holographic interferometry and shadowgraphy were used in a shock
tube for a shock Mach number . Numerical simulations were carried out to obtain complementary flow data. The experimental results show that diverging acoustic
waves are generated due to the interaction between shock waves and vortexlets along the slip layer. By means of the computational
results obtained for short time intervals, and the corresponding optical images, analysis of the shock-vortex interactions
became possible for extended time periods.
Received 18 May 1998 / Accepted 4 March 1999 相似文献
16.
The dynamic buckling of an elastic-plastic column subjected to an axial impact by a rigid body was discussed by using the energy law. The traveling process of elastic-plastic waves under impact action was analyzed by characteristics method. The equation of lateral disturbance used to analyze the problem was developed by taking into account the effect of elastic-plastic stress wave. The power series solution of this problem has been the power series approach. The buckling criterion of this problem was proposed by analyzing the characteristics of the solution. The relationship among critical velocity and impact mass, critical buckling length, hardening modulus was given by using theoretical analysis and numerical computation. 相似文献
17.
18.
圆柱形汇聚激波诱导 Richtmyer-Meshkov不稳定的 SPH 模拟 总被引:3,自引:3,他引:0
汇聚激波诱导不同物质界面的Richtmyer-Meshkov(RM)不稳定现象在惯性约束核聚变领域有重要的学术意义和工程背景.基于网格离散的宏观流体力学方法由于数值扩散问题往往需要高阶精度算法才能准确追踪界面演化,且对大变形和破碎合并等复杂界面追踪也极为困难.光滑粒子流体动力学(smoothed particlehydrodynamics,SPH)方法采用纯拉格朗日算法,可以有效克服上述难点.但经典SPH算法需采用人工黏性处理强间断,在激波间断处往往会出现严重的非物理振荡,对于涉及强冲击不稳定性问题,很难达到理想的模拟效果.本文采用基于HLL黎曼求解器的SPH算法,实现了对强激波和大密度比物质界面的有效分辨和追踪.一维数值校核证明了代码的可靠性、健壮性,并进一步模拟了二维圆柱形汇聚冲击波冲击四边形轻/重气界面诱导的RM不稳定性问题,与已有实验结果进行了对比,发现模拟结果与实验结果吻合.通过分析界面演化过程中的密度及压力变化,发现本文所采用的方法可准确地追踪激波与界面作用的复杂界面和波系演化规律.研究结果为进一步理解和解释汇聚冲击条件下的RM不稳定性机理奠定了基础. 相似文献
19.
This paper analyzes the non-classical shock waves which arise as limits of certain diffusive-dispersive approximations to
hyperbolic conservation laws. Such shocks occur for non-convex fluxes and connect regions of different convexity. They have
negative entropy dissipation for a single convex entropy function, but not all convex entropies, and do not obey the classical
Oleinik entropy criterion. We derive necessary conditions for the existence of non-classical shock waves, and construct them
as limits of traveling-wave solutions for several diffusive-dispersive approximations.
We introduce a “kinetic relation” to act as a selection principle for choosing a unique non-classical solution to the Riemann
problem. The convergence to non-classical weak solutions for the Cauchy problem is investigated. Using numerical experiments,
we demonstrate that, for the cubic flux-function, the Beam-Warming scheme produces non-classical shocks while no such shocks
are observed with the Lax-Wendroff scheme. All of these results depend crucially on the sign of the dispersion coefficient.
(Accepted February 8, 1996) 相似文献
20.
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