Reflected Shock Front Research Articles

High temperature and pressure Gladstone–Dale coefficient measurements in air behind reflected shock waves

Understanding the optical properties of air is essential for the validation and characterization of plasmas and hypersonic flows. Beyond 6000 K, the dissociation of nitrogen and oxygen molecules, along with other reactions, alters the equilibrium composition of air, causing a temperature and pressure dependence in the Gladstone–Dale coefficient. Due to measurement complexities, there is currently very little experimental data to validate model predictions under these conditions. In this work, a unique quadrature fringe imaging interferometer technique is applied to high temperature and pressure measurements of air in the Sandia free-piston high enthalpy shock tube. The diagnostic method combines a narrowband and broadband source to capture large, nearly-discrete changes in the index of refraction by calibrating to interference pattern changes. For the experiments, the reflected shock front is used to generate temperatures between 6000 and 7800 K at pressures up to 300 psi (20 bars). Results behind the shock front exhibit complex flow bifurcation and tail shock feature before equilibrium conditions are reached. Measurements in these flows show close agreement with theoretical predictions of the nonconstant Gladstone–Dale coefficient at high temperatures and high pressures, providing new validation data for chemical equilibrium gas models.

The reflection of an ionized shock wave

In a previous paper we studied the thermodynamic and kinetic theory for an ionized gas, in one space dimension; in this paper we provide an application of those results to the reflection of a shock wave in an electromagnetic shock tube. Under some reasonable limitations, which fully agree with experimental data, we prove that both the incident and the reflected shock waves satisfy the Lax entropy conditions; this result holds even outside genuinely nonlinear regions, which are present in the model. We show that the temperature increases in a significant way behind the incident shock front but the degree of ionization does not undergo a similar growth. On the contrary, the degree of ionization increases substantially behind the reflected shock front. We explain these phenomena by means of the concavity of the Hugoniot loci. Therefore, our results not only fit perfectly but explain what was remarked in experiments.

E-H Type Mach Configuration and its Stability

This paper is devoted to the study of the classification and stability of Mach configurations. In the Mach reflection of a shock wave by a rigid wall the flow behind the reflected shock front can be supersonic or subsonic. Correspondingly, the Mach configuration can be classified as E-E type and E-H type. In this paper we proved the stability of E-H type Mach configurations provided the reflected shock is weak. The result is the complement of the stability of E-E type Mach configurations in our earlier work.

Study of Reflected Shock Wave Perturbations at the Central Axis of Dense Plasma Column in a Plasma Focus

When the shock front (SF) hits the central axis of plasma focus device, a reflected shock moves radially outwards. The magnetic piston (MP) continues to compress inwards until it hits the out-going reflected shock front. In the Lee model, to avoid of complexity and explanation of nonzero radius for the plasma pinched column, the pressure assumed uniform from the SF to the MP. In this paper shock wave propagation by MHD equations and pressure propagations between two electrodes had been investigated. The results showed that influence of shock wave propagation on the inward motion current sheath by Lorentz force had considerable effects on plasma pinch behavior and it may have an important responsibility for dense plasma column disruption before occurrence of m = 0 instability.

Induction period for the formation of nanodispersed carbon particles during hydrocarbon pyrolysis behind a reflected shock front

Experiments were performed to estimate the time of isothermal transformation of model hydrocarbons (ethylene, benzene, and naphthalene) to solid carbon nanoparticles. An optical procedure combined with a shock tube was used to experimentally study the duration of the initial reaction stages before the occurrence of emission with a continuous visible spectrum. This emission is caused by the new (condensed and not gaseous) phase of carbon atoms formed in hydrocarbon pyrolysis behind a reflected shock front. The measurements are based on recording the time of occurrence of emission at a wavelength λ = 750 nm. The durations of the induction periods are in the range 12–160 µsec and decrease with increasing temperature in the range 1920–2560 K for each hydrocarbon, and also with increasing number of carbon atoms in the hydrocarbon molecule. The apparent activation energies for the formation of nanodispersed carbon particles were estimated from the measured durations of the initial reaction stages: 204 kJ/mole for ethylene, 65 kJ/mole for benzene, and 44 kJ/mole for naphthalene.

Measurement and temporal behaviour analysis of the plasma–glass boundary layer in a T-tube

Refraction of a laser beam by a flat boundary layer between a plasma and a glass plate was measured and the time development of the layer was analysed. Results of the analysis for the plasma produced in a small T-tube show that the boundary layer thickness increases with time faster than linearly. The boundary layer is negligibly thin during the first 3 µs after the reflected shock front has passed the point of observation. This means that a relatively fast collapse due to cooling through the boundary layer occurs in the second part of the reflected plasma lifetime.

Numerical simulation of the interaction between reflected shock wave and near-wall boundary layer

The interaction of a shock wave, reflected from the flat end of a cylindrical shock tube, with a cocurrent gas flow at the side wall, is considered in the axisymmetric case. The Navier-Stokes system of equations has been numerically integrated in the thin layer approximation using a predictor-corrector scheme. The appearance of a recirculation gas flow structure behind the reflected shock front and the evolution of this structure in the reflected wave going away from the tube end are analyzed. The corresponding patterns of constant density lines and the velocity vector field are presented.

Autoignition of surrogate fuels at elevated temperatures and pressures

Autoignition of Jet-A and mixtures of benzene, hexane, and decane in air has been studied using a heated shock tube at mean post-shock pressures of 8.5 ± 1 atm within the temperature range of 1000–1700 K with the objective of identifying surrogate fuels for aviation kerosene. The influence of each component on ignition delay time and on critical conditions required for strong ignition of the mixture has been deduced from experimental observations. Correlation equation for Jet-A ignition times has been derived from the measurements. It is found that within the scatter of experimental data dilution of n-decane with benzene and n-hexane leads to slight increase in ignition times at low temperatures and does not change critical temperatures required for direct initiation of detonations in comparison with pure n-decane/air mixtures. Ignition times in 20% hexane/80% decane (HD), 20% benzene/80% decane (BD) and 18.2% benzene/9.1% hexane/72.7% decane (BHD) mixtures at temperature range of T ≅ 1450–1750 K correlate well with induction time of Jet-A fuel suggesting that these mixtures could serve as surrogates for aviation kerosene. At the same time, HD, BD and BHD surrogate fuels demonstrate a stronger autoignition and peak velocities of reflected shock front in comparison with Jet-A and n-decane/air mixtures.

High-temperature measurements of the rates of the reactions CH 2O + Ar → Products and CH 2O + O 2 → Products

The two-channel thermal decomposition of formaldehyde [CH 2O], (1a) CH 2O + Ar → HCO + H + Ar, and (1b) CH 2O + Ar → H 2 + CO + Ar, was studied in shock tube experiments in the 2258–2687 K temperature range, at an average total pressure of 1.6 atm. OH radicals, generated on shock heating trioxane–O 2–Ar mixtures, were monitored behind the reflected shock front using narrow-linewidth laser absorption. 1,3,5 trioxane [C 3H 6O 3] was used as the CH 2O precursor in the current experiments. H-atoms formed upon CH 2O and HCO decomposition rapidly react with O 2 to produce OH via H + O 2 → O + OH. The recorded OH time-histories show dominant sensitivity to the formaldehyde decomposition pathways. The second-order reaction rate coefficients were inferred by matching measured and modeled OH profiles behind the reflected shock. Two-parameter fits for k 1a and k 1b, applicable in this temperature range, are: k 1 a = 5.85 × 10 14 exp ( - 32100 / T [ K ] ) [ cm 3 mol - 1 s - 1 ] k 1 b = 4.64 × 10 14 exp ( - 28700 / T [ K ] ) [ cm 3 mol - 1 s - 1 ] Uncertainty limits for k 1a and k 1b were estimated to be ∼±25%. The reaction between CH 2O and O 2, (2) CH 2O + O 2 → HO 2 + HCO, was also investigated in shock tube experiments. The rapid thermal decomposition of HCO and HO 2 generate H-atoms that react with O 2 to produce OH. Rate coefficients were, as in the CH 2O decomposition experiments, inferred by matching measured and modeled OH time-histories behind the reflected shock, under conditions where interference from secondary chemistry is minimal. A two-parameter, least-squares fit of the current data, valid over the 1480–2367 K temperature range, yields the following rate expression: k 2 = 5.08 × 10 14 exp ( - 23300 / T [ K ] ) [ cm 3 mol - 1 s - 1 ] The uncertainty in k 2 was estimated to be ∼±35%.

A kinetic study of the oxidation of pyridine

Oxidation of pyridine has been studied behind reflected shock waves in a single-pulse shock tube. Four mixtures of pyridine and oxygen have been studied diluted in argon. The studied equivalence ratios were Φ=4.82, 2.33, 1.21, and 0.60, ranging from very fuel rich to fuel lean. The temperature range was from 1000 to 2200 K, pressures ranged from 8.0 to 20 atm, and reaction residence times behind the reflected shock front ranged from 600 to 1100 μs. In the richest mixture, non-oxygenated products were similar to those produced in pyrolysis, except that N2 and pyrrole, products not observed in pyrolysis, were also formed. At the lowest temperatures at which products could be detected (1200 K approximately), CO was the principal product of oxidation. Its yield profile with temperature was strongly dependent on the initial oxygen concentration. Molecular nitrogen was observed at all equivalence ratios, but its yield was maximum in the near stoichiometric mixture. NO was only produced in significant quantities in the near stoichiometric and lean mixtures. From kinetic modeling studies it was concluded that the oxidation is initiated both by unimolecular C−H bond fission and bimolecular reaction with O2 to form the oitho-pyridyl radical which can further react with oxygenated species to give the pyridoxy radical. Pyridoxy undergoes CO elimination producing pyrrolyl radicals from which pyrrole arises. Other reactions important in the mechanism involve O abstraction and addition reactions with pyridine and ring scission reactions of pyridoxy. The predictions of a kinetic model are tested against experimental product profiles obtained with values of Φ=1.21 and 0.60.

Ignition and detonation in N2O-CO-H2-He mixtures

Ignition and deflagration-to-detonation transition in the N 2 O-CO-H 2 system behind the reflected shock wave in initial temperatures ranging between 1200 and 1800 K and pressures of 3–9 atm are studied. It is established that the chemical reactions are described adequately by the assumption of equilibrium between the translation-rotational and internal degrees of freedom of the molecules for shock-heated gas conditions. It is found that both the total heat release Q by the chemical reactions and the ratio of the induction period τ ind of the mixture to the characteristic energy release time θ are the parameters governing the flow pattern. Two different modes of interaction between the exothermic reaction and the gas flow are distinguished. The single-front mode, with a single discontinuity, arises when τ ind ≤θ, and two-front mode, in which a strong discontinuity formed behind the reflected shock front caused by interaction between the gasdynamic and chemical processes, arises when τ ind ≫θ.

Spherical shock wave reflection from a surface with a heated gas layer

The two-dimensional axisymmetric problem of the interaction between smallscale spherical shock waves initiated by a laser explosion and an absolutely rigid surface in the presence of a layer of hot gas is numerically investigated. A number of effects previously observed in physical and numerical experiments [5–8] are confirmed, in particular: the distortion of the reflected shock front and its acceleration on passage through the hot central zone of the laser explosion (lens effect), the strong deformation of this zone, and the formation of a precursor on the surface ahead of the shock wave interacting with the thermal layer. In addition, certain new anomalous effects are revealed: the formation of a pair of “suspended” shocks — one on the periphery of the hot central zone upon interaction with the reflected shock wave and the other behind the “Mach stem” in the triple point zone, etc.

Measurements of the glass-to-plasma boundary-layer influence on continuum radiation in a T-tube

The influence of the glass-to-plasma boundary layers on the continuum radiation of hydrogen plasma has been experimenally checked at the Hβ wavelength by introducing an additional number of boundary layers into the observed plasmas produced inside of a T-shaped electromagnetic shock tube. In the first case (case A), the plasma was observed (by using a monochromator) with the two usual boundary layers. In the second case (case B), four additional boundary layers were created by introducing two glass plates into the plasma. During the first microsecond, after the reflected shock front had passed the point of observation, no major differece was noted between the continuum intensities in cases A and B. At 1.5 μs and later, the difference amounted to about 10 to 20% with case B being more intense, depending on time, that is on the plasma parameters and boundary-layer thickness.

Measurement of Specific Heats Ratio of Hydrogen Plasma

AbstractAdiabatic expansion of plasma behind the reflected shock front in an electromagnetic shock tube has been verified. Electron densities and temperatures have been measured spectroscopically. Assuming complete local thermal equilibrium, the specific heat ratios of hydrogen plasmas have been determined out of expansion rate per a heavy particle directly from the adiabatic expansion law. Noticeably lower values of the ratio are determined at temperatures where ionization and recombination processes are abundant. The ratios determined in this work are in excellent agreement with theoretical values determined in an earlier work.

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.

Streak Mode Interferometric Study of Shock and Current Sheet Dynamics in a Plasma Focus

Macroscopic behaviour of the plasma in the Filippov-type plasma focus device with axial magnetic field are studied using a streak mode interferometric system and magnetic probes. The imploding and the reflected shock front, and the collapsing current sheet were observed separately. It was clarified that the collision between the reflected shock front and the collapsing current sheet determines the highest pinch radius of the current sheet. After the collision the current sheet expanded and collapsed again. It was made clear that the bounce corresponds to a flow of the high density plasma squeezed by the pinch of the current sheet which moves along the electrode axis.

Experimental Study on the Ionization of Argon behind Reflected Shock Waves

The electron temperature and density along with the ion temperature in argon gas behind reflected shock waves were measured by laser light scattering, while the spectroscopic temperature was measured from the ArI line emissions. The values of these three temperatures are different from each other for a few hundred microseconds after arrival of the reflected shock front. Both the electron and ion temperatures are much higher than the theoretical gasdynamic temperature, while the spectroscopic temperature is lower than the theoretical one. The degree of ionization is much higher than that in the equilibrium state. The stochastic character of the ArI line emissions was observed, indicating that the gas is inhomogeneous. These phenomena are explained as follows: initially, the gas behind the reflected shock wave is inhomogeneous, and an associative ionization is initiated at some points. The gas becomes homogeneous mainly through diffusion.

Double-diaphragm shock tube - Comparison between theory and experiment

HE double-diaphr agm shock-tube technique developed by Holbeche1>2 is an ideal way to cool shock-heated gases and vapors rapidly. It has been used to study vibrational relaxation1'4 and atomic recombination reactions,5'6 and is also suitable for the study of homogeneous nucleation. The usefulness of the technique, however, depends on knowing the flow properties throughout the region of interest. Treatments so far have assumed that shock reflection from the second diaphragm can be ignored. We describe a series of experiments performed to establish the presence of a reflected shock from the second diaphragm and give brief details of the theoretical analysis used to obtain flow properties. The shock tube of 76 mm diameter (see Fig. 1) has been described elsewhere.6 A scored aluminum disk and two sheets /of 0.025 mm aluminum foil were used for primary and secondary diaphragms, respectively. Pressure was measured by Kistler piezoelectric pressure transducers mounted 80 mm upstream and 100 and 455 mm downstream from the secondary diaphragm. Light scattered at 90 deg from an argon ion laser beam (476.5 nm) was also recorded 455 mm downstream from the secondary diaphragm. In each run highpurity argon and nitrogen were used as test and driver gas, respectively. Pressure measurements upstream from the secondary diaphragm indicate that shock reflection has occurred. A typical oscilloscope trace showing pressures upstream and downstream of the secondary diaphragm is given in Fig. 2. Previous analyses assumed no shock reflection. Inclusion of shock reflection in the flow analysis necessitates a full method of characteristics analysis, similar to that of Rudinger.7 In our analysis, the incident shock reflects from the secondary diaphragm (assumed planar) and travels back upstream into the test gas. At a later stage, the secondary diaphragm bursts instantaneously due to the increased pressure behind the reflected shock. A rarefaction wave is thus generated, the head of which travels upstream into the test gas; the tail travels downstream into the evacuated expansion section. The rarefaction wave head eventually catches up to the reflected shock front, and the resulting interaction causes the shock wave to decay. Particle paths are constructed through the characteristics mesh so that gas properties at any point in time and space are

Transient reflection of a plane shock wave from a rigid wall

In the present study the gas pressure and velocity will be determined, with the assumption that ~p/~x = 0 (on d~e wall this is a consequence of the boundary condition u = 0 and the equations of gasdynamics), from the gasdynamic equations in the form of simple finite formulas with a linearization agreeing with that used in [I]. A numerical solution [2] of the problem of reflection of a strong point discontinuity planar shock wave from a wall using the method of [3] will allow an evaluation of the accuracy of the results obtained and confirm the character of the time dependence of velocity. For large time intervals these relationships are valid in the direct vicinity of the wall. For engineering purposes the formula for determining pressure on the wall obtained in this way is of special interest. Using the results thus obtained, in analogy to [4], the coordinate of the reflected shock front is defined in the form of a section of a Taylor series, which also agrees well with numerical solution. The gasdynamic equations for an ideal gas

Reply by Author to A. Wortman

along the kernel radius. The secondary shock wave is initially so weak that it is swept outward by the expanding flow but it gains strength arid, as shown by Friedman, at about the time that the rarefaction fan reaches the origin the secondary shock wave is moving inward, even in stationary coordinates. This shock wave is initially quite weak so that it reaches the origin about 0.1 y/sec after the rarefaction fan is reflected. The reflected shock front now establishes an order of magnitude variation of temperature along the radius, but this time the maximum is at the origin. Successive reflections and interactions with the contact surface reverse the temperature gradients along the kernel radius with a period of about twice the characteristic time of the problem. The assumption of uniform kernel temperature cannot be justified. The power law and exponential expression for the temperature depen4ence of the reaction rates magnify the order of magnitude errors introduced by the incorrect gas dynamics model assumed by Ref. 1 and thus, the whole calculation is meaningless. A further point which, although relatively minor compared to the fundamental objections raised above, nevertheless deserves mention in order to view the work of Zajac and Oppenheim in the proper perspective. In the calculations of the flowfield ahead of the expanding spherical kernels, Ref. 1 did not predict the existence of the primary shock wave at the head pf the disturbed flow. The absence of the shock wave ahead of the accelerating contact surface was dismissed with the statement that Shock waves were generated only in the case of plane and cylindrical flows, the increase of the cross-sectional area in the spherical case having been evidently too large for this purpose. The inability to calculate a shock wave suggests numerical difficulties; moreover, the accompanying statement cannot be accepted since it contradicts directly the discussion on p. 428 of Courant and Friedrichs, who demonstrate clearly that even a uniformly expanding sphere generates a shock wave.