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1.
It is well known that the flow-field over blunt and pointed bodies is sensitive to the non-equilibrium phenomena characteristic
of high enthalpy hypersonic flows. Till date, most experiments and modelling were related to flows essentially dominated by
the dissociation rate. However, in practical cases of a re-entry low density flow, the aerodynamic quantities such as the
shock shape and location may also be strongly influenced by vibrational relaxation coupled with dissociation and chemical
reactions. Thus, the flow about various bodies such as spheres, hemisphere–cylinders and cones is recomputed using a chemical
model recently proposed by the authors and by taking into account the coupling between the vibrational relaxation and the
chemical kinetics. Then, the computed shock shapes in air flow are compared to recent experimental results obtained in a ballistic
range for flight velocities between 2,500 and 4,000 m/s, and in a shock tunnel for enthalpies close to 5 and 10 MJ/kg. The
computed density field around hemispherical bodies is also compared to the experimental one. A good agreement, within 5%,
between computed and measured results is observed. A few comparisons are also proposed with the results obtained with another
well-known (empirical) model. A comparison is also made between the flow quantities along the stagnation line obtained over
cylindrical and spherical bodies using the present model and those coming from a quasi-one-dimensional model recently developed,
showing also a satisfactory agreement. 相似文献
2.
A model of the physico-chemical kinetics of the reactions taking place behind the front of an intense shock wave propagating in air with a speed of 9–14 km/s is proposed. The problem of describing the chemical reactions, namely, molecular dissociation and exchange reactions involving vibrationally excited molecules in the absence of vibrational equilibrium, is solved. The vital role of the vibrational excitation delay in the dissociation of oxygen and nitrogen is established. The rate of the exchange reaction between nitrogen molecules and oxygen atoms in the shock wave depends only slightly on the vibrational excitation level. It is demonstrated that the rate constants for thermally nonequilibrium dissociation reactions can be represented within the framework of the one-temperature approximation at constant vibrational temperatures of the dissociating species satisfying quasi-stationary conditions.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 169–182, March–April, 1995. 相似文献
3.
We consider a model for the interaction of a gas with photons. In the article (Lin et al. Phys D 218:83–94, 2006), smooth traveling wave solutions called shock profiles have been constructed under a suitable smallness assumption between
the asymptotic states. In this work, we construct piecewise smooth traveling wave solutions that connect two asymptotic states
with a large jump. In particular, we give a rigorous mathematical justification to the formation of the so-called Zeldovich
spike. 相似文献
4.
H.G. Hornung 《Shock Waves》1998,8(1):11-21
The inviscid equations of motion for the flow at the downstream side of a curved shock are solved for the shock–normal derivatives.
Combining them with the shock–parallel derivatives yields gradients and substantial derivatives. In general these consist
of two terms, one proportional to the rate of removal of specific enthalpy by the reaction, and one proportional to the shock
curvature. Results about the streamline curvature show that, for sufficiently fast exothermic reaction, no Crocco point exists.
This leads to a stability argument for sinusoidally perturbed normal shocks that relates to the formation of the structure
of a detonation wave. Application to the deflection–pressure map of a streamline emerging from a triple shock point leads
to the conclusion that, for non–reacting flow, the curvature of the Mach stem and reflected shock must be zero at the triple
point, if the incident shock is straight. The direction and magnitude of the gradient at the shock of any flow quantity may
be written down using the results. The sonic line slope in reacting flow serves as an example. Extension of the results –
derived in the first place for plane flow – to three dimensions is straightforward.
Received 12 February 1997 / Accepted 10 June 1997 相似文献
5.
This paper describes the experimental and numerical investigations of unknown characteristics of the rotational nonequilibrium
phenomena behind a strong shock wave in air. Experiments were carried out using a piston-driven shock tube with helium as
driving gas and air as driven (test) gas, operated as a two-stage shock tube. In the experiments, emission spectra of NO were
measured to evaluate the rotational temperature behind a strong shock wave. The numerical calculations use the computational
code for the thermal and chemical nonequilibrium flow behind a strong shock wave developed by the present author's group,
where 11 chemical species (N, O, NO, N, O, N, O, NO, N, O, e) and 48 chemical reactions of high-temperature air are considered. The thermal nonequilibrium is expressed by introducing
an 8 temperature model composed of translational temperature, rotational and vibrational temperatures for N, O, NO, and electron temperature. The coupling of a rotation, vibration and dissociation (CRVD) model was incorporated to take
sufficiently into account the rotational nonequilibrium. The calculations were conducted for the same conditions as the experimental
ones. From the calculated flow properties, emission spectra were re-constructed using the code for computing spectra of high
temperature air “SPRADIAN”. Furthermore, rotational and vibrational temperatures of NO (0,1) were determined from a curve fitting method and compared with the computed results.
Received 12 September 2001 / Accepted 18 February 2002 相似文献
6.
V. G. Shcherbak 《Fluid Dynamics》1994,29(2):263-269
Chemically nonequilibrium flows with allowance for vibrational relaxation are investigated numerically within the framework
of the hypersonic viscous shock layer equations with reference to the example of the flow in the neighborhood of the critical
line of the “Buran” orbital vehicle in its motion along a re-entry trajectory. It is found that the vibrational temperatures
of the molecular components differ markedly. The distinctive feature of the model in question, as compared with a model with
one average vibrational temperature, is the stronger effect on the flow characteristics over the thermally stressed part of
the trajectory. The models proposed in the literature for dissociation from an effective vibrational level are compared with
the model for dissociation with a certain probability from all the vibrational levels. It is shown that the use of an approximation
of the total dissociation constant as a function of translational temperature only may lead to a considerable variation from
the results of calculations with allowance for vibrational relaxation on the basis of the equilibrium dissociation rate constant.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 138–146, March–April, 1994. 相似文献
7.
In shock tube experiments the profiles of light absorption in oxygen are obtained for the wavelength interval 200–260 nm over
the temperature range 4000–10800 K. Using these data, the vibrational temperature profiles are measured for oxygen molecules
behind the shock front. The method of determination of the vibrational temperature of oxygen is based on comparing absorption
measurements and detailed absorption spectrum calculations for oxygen in the Schumann-Runge system. 相似文献
8.
The model of one-dimensional equations of the two-temperature generalized magneto-thermoelasticity theory with two relaxation
times in a perfect electric conducting medium is established. The state space approach developed in Ezzat (Can J. Phys. Rev.
86(11):1241–1250, 2008) is adopted for the solution of one-dimensional problems. The resulting formulation together with the Laplace transform techniques
are applied to a specific problem of a half-space subjected to thermal shock and traction-free surface. The inversion of the
Laplace transforms is carried out using a numerical approach. Some comparisons have been shown in figures to estimate the
effects of the temperature discrepancy and the applied magnetic field. 相似文献
9.
高超声速流动在头激波压缩后常处于高 温条件下的热化学非平衡状态. 本文采用态-态方法和双温度模型计算分析了一维正激波后和高超声速钝体绕流驻点线上的氧气热化学非平衡流动. 态-态方法将氧气的每个振动能级当成独立的组分,通过耦合 Euler 方程或驻点线上的降维 Navier-Stokes 方程,数值求解得 到了高温流动中的精细热化学非平衡状态. 而双温度模型假设氧气的振动能级服从 Boltzmann 分布,通过求解振动能方程得到振动温度. 一维正激波后热化学松弛过程的计算结果表明,态-态计算预测的温度分布和氧原子浓度分布较好地吻合了文 献中的实验结果,而经典的双温度模型的预测结果误差较大,且不同双温度模型的计算结果比较发散. 态-态方法详细地给出了所有振动能级的变化过程. 无论是正激波还是脱体激波后的流场,都是高振动能级首先得到激发;但是数密度大的低振动能级先达到热平衡,而高能级 分子要经过很长距离后才能达到热平衡. 在驻点附近,复合反应生成的氧气分子处于高振动能级,导致高振动能级分子数密度显著高于平衡分布. 计算还发现,经典双温度模型的离解反应速率明显偏离态-态计算结果,无法准确体现振动离解耦合效应对离解反应 速率的影响,但是 Park 双温度模型将离解失去的振动能取为 0.3$\sim 高超声速流动在头激波压缩后常处于高 温条件下的热化学非平衡状态. 本文采用态-态方法和双温度模型计算分析了一维正激波后和高超声速钝体绕流驻点线上的氧气热化学非平衡流动. 态-态方法将氧气的每个振动能级当成独立的组分,通过耦合 Euler 方程或驻点线上的降维 Navier-Stokes 方程,数值求解得 到了高温流动中的精细热化学非平衡状态. 而双温度模型假设氧气的振动能级服从 Boltzmann 分布,通过求解振动能方程得到振动温度. 一维正激波后热化学松弛过程的计算结果表明,态-态计算预测的温度分布和氧原子浓度分布较好地吻合了文 献中的实验结果,而经典的双温度模型的预测结果误差较大,且不同双温度模型的计算结果比较发散. 态-态方法详细地给出了所有振动能级的变化过程. 无论是正激波还是脱体激波后的流场,都是高振动能级首先得到激发;但是数密度大的低振动能级先达到热平衡,而高能级 分子要经过很长距离后才能达到热平衡. 在驻点附近,复合反应生成的氧气分子处于高振动能级,导致高振动能级分子数密度显著高于平衡分布. 计算还发现,经典双温度模型的离解反应速率明显偏离态-态计算结果,无法准确体现振动离解耦合效应对离解反应 速率的影响,但是 Park 双温度模型将离解失去的振动能取为 0.3$\sim $0.5 倍分子离解能是比较合理的. 相似文献
10.
I.V. Erofeev V.V. Silberschmidt A.A. Kalin V.A. Moiseev I.V. Solomatin 《Shock Waves》1998,8(3):177-181
Effects of shock waves (generated by a nanosecond laser pulse in plates of Armco-iron) on structural changes are analysed.
Localisation of processes of martensitic transformation and twinning – for various values of laser pulse duration – is studied
both experimentally and numerically. A proposed model accounts for interaction of shock wave propagation and structure changes.
Realisation of martensitic transformation and twin formation influences wave front modification. A stress amplitude decrease
with increasing distance from a microcrater determines, together with the pulse duration, a character of spatial localisation
of structural changes. Numerical results are compared with experimental data and serve as a basis for additional interpretation
of phenomena.
Received 9 August 1994 / Accepted 30 June 1997 相似文献
11.
Based on shear-deformable beam theory, free vibration of thin-walled composite Timoshenko beams with arbitrary layups under
a constant axial force is presented. This model accounts for all the structural coupling coming from material anisotropy.
Governing equations for flexural-torsional-shearing coupled vibrations are derived from Hamilton’s principle. The resulting
coupling is referred to as sixfold coupled vibrations. A displacement-based one-dimensional finite element model is developed
to solve the problem. Numerical results are obtained for thin-walled composite beams to investigate the effects of shear deformation,
axial force, fiber angle, modulus ratio on the natural frequencies, corresponding vibration mode shapes and load–frequency
interaction curves. 相似文献
12.
Virginia Carrera Moises Garcia-Morales Pedro Partal Crispulo Gallegos 《Rheologica Acta》2010,49(6):563-572
Reactive modification is lately gaining acceptance as a successful way to give added value to bitumen, a crude oil refining
by-product. In order to study the effect of both bitumen type and processing method, isocyanate-based reactive modification
was carried out with four types of bitumen from different sources, by following two different procedures (“water-free” and
“water-involved” processing). The polymer used (MDI–PPG) was synthesized from the reaction of 4,4′-diphenylmethane diisocyanate with a low molecular weight polypropylene glycol. The results obtained demonstrate that the
addition of small quantities of this reactive polymer to bitumen endows the resulting modified binder with an improved performance
at high in-service temperatures. Interestingly, two different modification pathways have been identified: the first one, which
occurs during mixing, is the result of chemical reactions between -NCO groups of the reactive polymer with functional groups
containing active hydrogen atoms (mainly, –OH), such as those typically present in the most polar bitumen fractions; the second
one has been proved to be a consequence of series reactions involving water. Both pathways, but mainly the latter, lead to
bituminous paving materials showing a more complex microstructure, with the consequent change in their rheological response.
Finally, very different degrees of modification, depending on the colloidal features of the as-received bitumen, were observed. 相似文献
13.
R. S. Srivastava 《Shock Waves》2007,17(3):209-212
Lighthill (Proc. R. Soc. A 198, 454–470, 1949) considered the diffraction of a normal shock wave passing over a small bend. The bend being small Lighthill
was able to linearize the flow equations and solved the problem through several mathematical techniques. Following Lighthill
(Proc. R. Soc. A 198, 454–470, 1949), Srivastava and Chopra (J. Fluid Mech. 40, 821–831, 1970) extended the work to the diffraction of oblique shock waves. Srivastava (AIAAJ 33, 2230–2231, 1995) considered the problem of starting point of curvature and extended the work to yawed wedges (Srivastava
in Proceedings of the 14th International Mach reflection symposium Sun Marina Hotel, Yonezawa, Japan, 1–5 October 2000, pp.
225–249, 2002). Srivastava (Shock waves 13, 323–326, 2003) considered the problem for starting point of curvature when the relative outflow behind reflected shock before
diffraction has been subsonic and sonic. The present work is an extension of the work published in Srivastava (Shock waves
13, 323–326, 2003) when the wedge has been yawed through an angle. The results have been obtained for two angles χ = 60° and
χ = 40° (χ is the angle of yaw).
相似文献
14.
R. S. Srivastava 《Shock Waves》2011,21(1):29-33
In the present investigation, vorticity distribution of a particle over the normal diffracted shock has been obtained for
monoatomic gases, CO2 and SF6. Further some results using Lighthill’s theory (Lighthill in Proc R Soc A 198:454–470, 1949) and Whitham’s theory (Whitham
in J Fluid Mech 2:145–171, 1957) have been obtained. 相似文献
15.
The vibrations of a vessel strongly influence the behavior of the interface of the fluids in it. Thus, vertical vibrations
can lead both to the parametric excitation of waves (Faraday ripples) and to the suppression of the Rayleigh-Taylor instability
[1–2]. At the present time, the influence of vertical vibrations on the behavior of a fluid surface have been studied in sufficient
detail (see, for example, review [3]). The behavior of an interface of fluids in the case of horizontal vibrations has been
studied less. An interesting phenomenon has been revealed in the experimental papers [4, 5]: in the case of fairly strong
horizontal vibrations of a vessel containing a fluid with a free surface, the fluid collects near one of the vertical vessel
walls, the free surface being practically plane and stationary with respect to the vessel, while its angle of inclination
to the horizon depends on the vibration rate. But if there is a system of immiscible fluids with comparable but different
densities in the vessel, horizontal vibrations lead to the formation of a steady wave relief at the interface. An explanation
of the behavior of a fluid with a free boundary was given in [6] on the basis of averaged equations of fluid motion in a vibrational
field. The present paper is devoted to an analysis of the behavior of the interface of fluids with comparable densities in
a high-frequency vibrational field.
Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 8–13, November–December, 1986. 相似文献
16.
L.S. Yellapragada A.-V. Phan T. Kaplan 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(5):457-467
The kinetically driven growth instability in stressed solids has been a subject of recent investigation as there is an increasing
interest in the effects of non-hydrostatic stresses on crystal growth processes. Recent experimental and modeling work using
advanced numerical methods such as boundary element and level set methods have demonstrated that the effect of stress on the
solid phase epitaxy (SPE) growth of crystalline silicon from the amorphous phase is responsible for the roughening of its
amorphous–crystalline interface. Although our previous model (Phan et al., in Model Simul Mater Sci Eng, 9:309–325, 2001)
has been able to explain the observed interfacial instability during the crystal growth of intrinsic silicon, it has not been
very successful when extended to the SPE growth process of doped silicon. In an effort to identify the sources that may improve
the accuracy and robustness of the previously proposed model, we present in this paper a new approach for modeling the crystal
growth in stressed Si layers. The technique is based upon the coupling of a transition-state-theory-based model, a finite
element model of the sequentially weak coupling analysis for fluid-solid interaction, and the marker particle method. 相似文献
17.
The paper presents results of a numerical simulation of a supersonic two-dimensional (2D) viscous flow containing CO2 molecules near a spacecraft entering the Mars atmosphere. The gas–dynamic equations in the shock layer are coupled to the
equations of non-equilibrium vibrational and chemical kinetics in the five-component mixture CO2/CO/O2/C/O. Transport and relaxation processes in the flow are studied on the basis of the rigorous kinetic theory methods; the
developed transport algorithms are incorporated in the numerical scheme. The influence of the vibrational excitation of CO2 and chemical reactions on the gas flow parameters and heat transfer is analyzed. The obtained results are compared with those
found using two simplified models based on the two-temperature and one-temperature vibrational distributions in CO2. The accuracy of the simplified models and the limits of their validity within the shock layer are evaluated. The effect
of bulk viscosity in a flow near a re-entry body is discussed. The role of different diffusion processes, chemical reactions,
and surface catalytic properties in a flow of the considered mixture in the shock layer is estimated. 相似文献
18.
The two-dimensional, time-dependent, reactive Navier–Stokes equations including the effects of viscosity, thermal conduction
and molecular diffusion were solved to reveal the wave evolution and chemical dynamics involved in the re-initiation process.
The computation was performed for hydrogen–oxygen–argon mixtures at the low initial pressure (8.00 kPa), using detailed chemical
reaction model. The results show that, the decoupled leading shock reflects on the right wall of the vertical branch. High
temperature and pressure behind the reflected shock induce the generation of hot spots and local explosion. Therefore, the
re-initiation of gaseous detonation occurs. In the re-initiation area, there exist very high OH concentration and no H
2 concentration. However, in front of reflected shock, there exist relatively high H
2 concentration and no OH radicals. Additionally, the shock–flame interaction induces RM instability. This results in the fast
mixing between hot reacted gas mixture and the relatively cold unreacted gas mixture and accelerates the chemical reactions.
However, the shock–flame interaction contributes much less to the re-initiation, in contrast with shock reflection. The transition
of leading shock from regular reflection to Mach reflection happens during the re-initiation. The computed evolution of wave
structures involved in the re-initiation is qualitatively agreeable with that from the experimental schlieren images.
相似文献
19.
Abstract. The vibrational relaxation time of CO molecules at collisions with H atoms was measured in shock tube experiments by means
of the CARS-spectroscopy method. The measurements of the CO vibrational temperature at gas temperatures of 1800–3000 K were
performed in a supersonic cooling gas flow. The gas was heated behind the incident and reflected shock wave and then flowed
out of a wedge-shaped nozzle. H atoms were generated in the reflected shock wave because of dissociation of H and HO admixtures. The extremely high efficiency of H atoms in CO vibrational deactivation was confirmed.
Received 1 February 2000 / Accepted 20 February 2000 相似文献
20.
David E. Zeitoun Yves Burtschell Irina A. Graur Mikhail S. Ivanov Alexey N. Kudryavtsev Yevgeny A. Bondar 《Shock Waves》2009,19(4):307-316
Numerical simulations of shock wave propagation in microchannels and microtubes (viscous shock tube problem) have been performed
using three different approaches: the Navier–Stokes equations with the velocity slip and temperature jump boundary conditions,
the statistical Direct Simulation Monte Carlo method for the Boltzmann equation, and the model kinetic Bhatnagar–Gross–Krook
equation with the Shakhov equilibrium distribution function. Effects of flow rarefaction and dissipation are investigated
and the results obtained with different approaches are compared. A parametric study of the problem for different Knudsen numbers
and initial shock strengths is carried out using the Navier–Stokes computations.
相似文献