Radiative cooling of plasma behind a reflected shock front

Calculation of gas flow in a shock tube on the basis of ideal theory [1] leads to results that differ from the real picture. In particular, the calculated velocity of the reflected shock wave exceeds the experimentally measured velocity [2] by about 20%. The calculated parameters of shock-heated gas agree well with the experimental results only directly behind the shock front [3]. The present paper reports a theoretical and experimental investigation of the variation of the plasma parameters behind the front of a reflected shock wave in argon. A picture of the gas-dynamic processes taking place after reflection of the incident shock wave by the end of the shock tube is determined. A method is developed for approximate analytic calculation, this making it possible to determine not only the parameters of the gas directly behind the front of the reflected shock wave for different positions of the wave relative to the end of the shock tube but also the variation of these parameters in other regions behind the reflected shock wave. The calculation takes into account the influence of the boundary layer and radiative cooling in the approximation of a low degree of ionization of the plasma and persistence of equilibrium conditions in the entire region behind the reflected shock wave. The experimental and theoretical profiles of the radiation behind the reflected shock wave are compared.     

气相爆轰波正反射激波加速研究

实验采用压力传感器测量了指定点压力时间曲线。数值模拟基于二维反应欧拉方程和基元反应模型,采用二阶附加半隐的龙格-库塔法和5阶WENO格式分别离散时间和空间导数项,获得了指定点数值压力时间曲线。理论分析基于爆轰理论和激波动力学,分析了气相爆轰波反射过程所涉及的复杂波系演变并获得了反射激波速度。结果表明:本文数值模拟和理论计算定性上重复并解释了实验现象。气相爆轰波在右壁面反射后,右行稀疏波加速反射激波。其加速原因是:尽管激波波前声速减小,但激波马赫数增大,波前气流速度减小。在低初压下,可能还由于爆轰波后未反应或部分反应气体的作用,导致反射激波加速幅度比高初压下大。     

Effect of wall heat transfer on shock-tube test temperature at long times

When performing chemical kinetics experiments behind reflected shock waves at conditions of lower temperature (<1,000 K), longer test times on the order of 10–20 ms may be required. The integrity of the test temperature during such experiments may be in question, because heat loss to the tube walls may play a larger role than is generally seen in shock-tube kinetics experiments that are over within a millisecond or two. A series of detailed calculations was performed to estimate the effect of longer test times on the temperature uniformity of the post-shock test gas. Assuming the main mode of heat transfer is conduction between the high-temperature gas and the colder shock-tube walls, a comprehensive set of calculations covering a range of conditions including test temperatures between 800 and 1,800 K, pressures between 1 and 50 atm, driven-tube inner diameters between 3 and 16.2 cm, and test gases of N₂ and Ar was performed. Based on the results, heat loss to the tube walls does not significantly reduce the area-averaged temperature behind the reflected shock wave for test conditions that are likely to be used in shock-tube studies for test times up to 20 ms (and higher), provided the shock-tube inner diameter is sufficiently large (>8cm). Smaller diameters on the order of 3 cm or less can experience significant temperature loss near the reflected-shock region. Although the area-averaged gas temperature decreases due to the heat loss, the main core region remains spatially uniform so that the zone of temperature change is limited to only the thermal layer adjacent to the walls. Although the heat conduction model assumes the gas and wall to behave as solid bodies, resulting in a core gas temperature that remains constant at the initial temperature, a two-zone gas model that accounts for density loss from the core to the colder thermal layer indicates that the core temperature and gas pressure both decrease slightly with time. A full CFD solution of the shock-tube flow field and heat transfer at long test times was also performed for one typical condition (800 K, 1 atm, Ar), the results of which indicate that the simpler analytical conduction model is realistic but somewhat conservative in that it over predicts the mean temperature loss by a few Kelvins. This paper presents the first comprehensive study on the effects of long test times on the average test gas temperature behind the reflected shock wave for conditions representative of chemical kinetics experiments.     

Dynamics of stress wave propagation in a chain of photoelastic discs impacted by a planar shock wave; Part I, experimental investigation

The propagation of stress waves through a chain of discs has been studied experimentally. Optically transparent 20-mm diameter discs, made of epoxy, were loaded dynamically by head-on collision with an incident planar shock wave. The loading was done in a vertical shock tube. The head-on collision between the punch-plate, placed on top of the chain of discs, and the incident shock wave resulted in a head-on reflected shock wave inducing behind it a fairly uniform step-wise pressure pulse having duration of about 6 ms. The recorded fringe patterns of the stress field, in the discs-chain, show that the input pressure pulse was broken into several oscillating cycles. The back and forth bouncing of stress waves gave rise to two different modes of the contact stress oscillations, which continued until the overall stress reaches equilibrium with the input conditions. The registered propagation velocity of the stress wave was significantly lower than the appropriate speed of sound in the material from which the discs were made.      

Reflection of a plane shock wave from a rigid concave wall

We present the results of an experimental study of the reflection of a plane stationary shock wave with Mach number in the range 1.21–1.35 from a rigid cylindrical concave wall. The experiments were carried out in a shock tube. In experimental shock tube technology the reflection of a shock wave from a rigid wall is often used for obtaining high temperatures [1]. This circumstance is associated with the fact that the temperature behind the reflected wave is significantly higher than that behind the incident wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 33–39, July–August, 1970.     

Interaction of a high-speed combustion front with a closely packed bed of spheres

The head-on collision of a combustion front with a closely packed bed of ceramic-oxide spheres was investigated in a vertical 76.2 mm diameter tube containing a nitrogen diluted stoichiometric ethylene–oxygen mixture. A layer of spherical beads in the diameter range of 3–12.7 mm was placed at the bottom of the tube and a flame was ignited at the top endplate. Four orifice plates spaced at one tube diameter were placed at the ignition end of the tube in order to accelerate the flame to either a “fast-flame” or a detonation wave before the bead layer face. The mixture reactivity was adjusted by varying the initial mixture pressure between 10 and 100 kPa absolute. The pressure before and within the bead layer was measured by flush wall-mounted pressure transducers. For initial pressures where a fast-flame interacts with the bead layer peak pressures recorded at the bead layer face were as high as five times the reflected Chapman–Jouget detonation pressure. The explosion resulting from the interaction developed by two distinct mechanisms; one due to the shock reflection off the bead layer face, and the other due to shock transmission and mixing of burned and unburned gas inside the bead layer. The measured explosion delay time (time after shock reflection from the bead layer face) was found to be independent of the incident shock velocity. As a result, the explosion initiation is not the direct result of the shock reflection process but instead is more likely due to the interaction of the reflected shock wave and the trailing flame. The bead layer was found to be very effective in attenuating the explosion front transmitted through the bead layer and thus isolating the tube endplate. This paper is based on work that was presented at the 21th International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, July 23–27, 2007.     

The interaction between shock waves and foam in a shock tube

An experimental study and a numerical simulation were conducted to investigate the mechanical and thermodynamic processes involved in the interaction between shock waves and low density foam. The experiment was done in a stainless shock tube (80 mm in inner diameter, 10 mm in wall thickness and 5 360 mm in length). The velocities of the incident and reflected compression waves in the foam were measured by using piezo-ceramic pressure sensors. The end-wall peak pressure behind the reflected wave in the foam was measured by using a crystal piezoelectric sensor. It is suggested that the high end-wall pressure may be caused by a rapid contact between the foam and the end-wall surface. Both open-cell and closed-cell foams with different length and density were tested. Through comparing the numerical and experimental end-wall pressure, the permeability coefficients α and β are quantitatively determined.     

Temperature measurement of reflected shock wave by using chemical indicator

This report describes a new method for measuring the temperature of the gas behind the reflected shock wave in shock tube, corresponding to the reservoir temperature of a shock tunnel, based on the chemical reaction of small amount of CF₄ premixed in the test gas. The final product C₂F₄ is used as the temperature indicator, which is sampled and detected by a gas chromatography in the experiment. The detected concentration of C₂F₄ is correlated to the temperature of the reflected shock wave with the initial pressureP ₁ and test time τ as parameters in the temperature range 3 300 K<T<5 600 K, pressure range 5 kPa<P ₁<12 kPa and τ≅0.4 ms. The project supported by the China Aerodynamics Project for Basic Researches (J13.5.2 ZK04)     

Shock-tube experiments on the stability of regular reflection in the dual-solution domain

Regular reflection (RR) and Mach reflection (MR) are theoretically both possible in the dual-solution domain of oblique shock reflection. The physical difference between the two types of reflection is the pressure behind the reflected shock wave: that of MR is lower than that of RR for strong shock reflection. The magnitude relation of these pressures is inverted for weak shock reflection. In the present paper, we performed two kinds of experiment, depending on whether the oblique shock reflection is weak or strong. For strong shock reflection, we decreased the pressure behind the reflected wave of RR using a convex double-wedge. For weak shock reflection, we increased this pressure using a concave double-wedge. Thus, we investigated the stability of RR against pressure disturbances. The results indicate that RR in a shock tube is stable, in the dual-solution domain, for both weak and strong incident shocks.     

Near-wall imaging using toluene-based planar laser-induced fluorescence in shock tube flow

A quantitative thermometry technique, based on planar laser-induced fluorescence (PLIF), was applied to image temperature fields immediately next to walls in shock tube flows. Two types of near-wall flows were considered: the side wall thermal boundary layer behind an incident shock wave, and the end wall thermal layer behind a reflected shock wave. These thin layers are imaged with high spatial resolution (15μm/pixel) in conjunction with fused silica walls and near-UV bandpass filters to accurately measure fluorescence signal levels with minimal interferences from scatter and reflection at the wall surface. Nitrogen, hydrogen or argon gas were premixed with 1–12% toluene, the LIF tracer, and tested under various shock flow conditions. The measured pressures and temperatures ranged between 0.01 and 0.8 bar and 293 and 600 K, respectively. Temperature field measurements were found to be in good agreement with theoretical values calculated using 2-D laminar boundary layer and 1-D heat diffusion equations, respectively. In addition, PLIF images were taken at various time delays behind incident and reflected shock waves to observe the development of the side wall and end wall layers, respectively. The demonstrated diagnostic strategy can be used to accurately measure temperature to about 60 μm from the wall.     

可压缩流向涡与反向运动激波相互作用的实验

对可压缩流向涡与反向运动激波相互作用的现象进行了实验研究．实验在９４ｍｍ×９４ｍｍ的方截面激波管中进行．在实验段上游安装了一个有限翼展平直机翼．当入射激波通过机翼后，波后２区气流在模型翼尖诱导出一条流向涡．入射激波在激波管端壁反射后，形成的反射激波在观察窗处和流向涡发生作用．实验中拍摄了激波与流向涡作用全过程的纹影照片，观察到了一些和定常激波与旋涡相互作用不同的现象，并与数值计算结果进行了初步比较     

Diffraction and re-initiation of detonations behind a backward-facing step

Diffraction phenomena of gaseous detonation waves behind a backward-facing step in a tube are observed by using high-speed schlieren photography and soot-track records as well as by pressure measurements on the sidewall. Mixtures are stoichiometric oxyhydrogen and those diluted by argon at sub-atmospheric pressures. Three types of phenomena are observed, that is, continuous propagation of detonation, re-initiation after a temporal extinction of detonation and complete extinction of detonation. The continuous propagation means that the diffracted wave does not affect the main propagation although reflected shock waves from the bottom surface of the tube may affect it. The re-initiation occurs at a wall surface of the tube behind a reflected shock wave after the main detonation wave has been extinguished. Positions and conditions of the re-initiation are discussed. The complete extinction is defined as disappearance of detonation cells behind the step within a certain length of the tube. Cases exist where an ignition occurs after several reflections off the bottom and top surface of the tube.     

Application of laser-induced thermal acoustics in air to measurement of shock-induced temperature changes

The laser-induced thermal acoustics (LITA) method was used to measure the temperature profiles induced behind spherical shock waves, generated by high-voltage discharge in air with an energy of 6 J. A Nd:YAG laser (wavelength 532 nm, energy 300 mJ, pulse duration 10 ns, line width 0.005 cm⁻¹) and an Ar-ion laser (wavelength 488 nm, power 4 W) served as the pump and probe lasers, respectively for the LITA measurements. The peak temperatures were in good agreement with results calculated with the Euler equations. The temperature profiles behind the shock, however, differed in decay rates. The peak temperatures behind the shock wave were determined by reflected overpressure and agreed with those from the LITA measurements within a maximum error of 5%.     

Experimental investigation of CO vibrational deactivation in a supersonic cooling gas flow

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     

Guderley reflection for higher Mach numbers in a standard shock tube

An experimental study shows that the Guderley reflection (GR) of shock waves can be produced in a standard shock tube. A new technique was utilised which comprises triple point of a developed weak Mach reflection undergoing a number of reflections off the ceiling and floor of the shock tube before arriving at the test section. Both simple perturbation sources and diverging ramps were used to generate a transverse wave in the tube which then becomes the weak reflected wave of the reflection pattern. Tests were conducted for three ramp angles (10°, 15°, and 20°) and two perturbation sources for a range of Mach numbers (1.10–1.40) and two shock tube expansion chamber lengths (2.0 and 4.0 m). It was found that the length of the Mach stem of the reflection pattern is the overall vertical distance traveled by the triple point. Images with equivalent Mach stem lengths in the order of 2.0 m were produced. All tests showed evidence of the fourth wave of the GR, namely the expansion wave behind the reflected shock wave. A shocklet terminating the expansion wave was also identified in a few cases mainly for incident wave Mach numbers of approximately 1.20.     

Detonation wave initiated by explosive condensation of supersaturated carbon vapor

An experimental study of the influence of condensation of supersaturated carbon vapor formed behind reflected shock waves on the process of propagation of a shock wave and formation of a detonation wave of condensation is carried out. Highly supersaturated carbon vapor was formed from thermal decay of unstable carbon suboxide C₃O₂ → C + 2CO behind a shock wave in mixtures containing 10–30% C₃O₂ in Ar. This reaction was followed by fast growth of condensed carbon particles, accompanied by heat release. Experiments have shown a considerable temperature and pressure increase in the narrow zone behind the wave front, resulting in shock wave amplification and transition to a detonation-like regime. An analysis of the kinetics and heat release in the given conditions and calculations based upon one-dimensional detonation theory have shown that in a mixture of 10% C₃O₂ + Ar, insufficient heat release resulted in a regime of “overdriven detonation”. In a mixture of 20% C₃O₂ + Ar a very good coincidence of measured values of pressure and wave velocity with calculated Chapman–Jouguet parameters is observed. In a 30% C₃O₂ + Ar mixture, an excess heat release caused a slow down of the effective condensation rate and a regime of “underdriven detonation” is observed.     

Specific features of incident and reflected blast waves

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 T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Shock wave ignition in N2O-CO(N2)-He mixtures

The behavior of the pressure behind shock waves in N₂O-CO-He mixtures is investigated. The pressure can be relatively easily measured and, at the same time, reflects the general influence of the experimental conditions on flow formation in the shock tube. Shock-wave mixture ignition effects and, moreover, hydrogen combustion in the contact zone are analyzed from the standpoint of their influence on the stagnation parameters and the optical properties of the flow in the shock tube nozzle. The correctness of modeling the conditions behind the reflected wave by means of mixtures similar in composition to the equilibrium products of the N₂O-CO reaction [1] is discussed in the same context.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 164–170, September–October, 1989.The authors wish to thank G. D. Smekhov for calculating the equilibrium compositions of the mixtures behind the shock waves and A. P. Zuev for stimulating discussions.     

Planar laser-induced fluorescence imaging in shock tube flows

The planar laser-induced fluorescence (PLIF) imaging method was used to perform flow visualization and quantitative planar thermometry in shock tube flow fields using toluene as a fluorescence tracer in nitrogen. Fluorescence quantum yield values needed to quantify PLIF images were measured in a static cell at low pressures (<1 bar) for various toluene partial pressures in nitrogen bath gas. Images behind incident and reflected shocks were taken in the core flow away from regions affected by boundary layers. Temperature measurements from these images were successfully compared with predicted values using ideal shock equations. Measured temperatures ranged between 296 and 800 K and pressures between 0.15 and 1.5 atm. The average temperature discrepancies between measurements and the predicted values behind the incident and reflected shocks were 1.6 and 3.6%, respectively. Statistical analyses were also conducted to calculate the temperature measurement uncertainty as a function of image resolution. The technique was also applied to the study of more complex supersonic flows, specifically the interaction of a moving shock with a wedge. Measured temperatures agreed well with the results of numerical simulations in all inviscid regions, and all pertinent features of the single Mach reflection were resolved.     

Experimental study of toroidal shock wave focusing in a compact vertical annular diaphragmless shock tube

The paper reports results of experiments regarding toroidal shock wave focusing in a vertical shock tube as a part of a series of converging shock wave studies. This compact vertical shock tube was designed to achieve a high degree of reproducibility with minimum shock formation distance by adopting a diaphragmless operating system. The shock tube was manufactured in the Institute of Fluid Science, Tohoku University. An aspheric lens shaped cylindrical test section was connected at the open end of the shock tube to visualize the diffraction and focusing of the toroidal shock wave released from the ring shaped shock tube opening. Pressure transducers were flush mounted on the shock tube’s test section to measure pressure histories at the converging test section. Double exposure holographic interferometry was employed to quantitatively visualize the shock waves. The whole sequence of toroidal shock wave diffraction, focusing, and its reflection from the symmetrical axis were successfully studied. The transition of reflected shock waves was observed.