Waves In Argon Research Articles

Cartesian grid-based hybrid NS-DSMC methodology for continuum-rarefied gas flows around complex geometries

This work presents a coupled numerical methodology, based on a hybrid Navier-Stokes (NS) and Direct Simulation Monte Carlo (DSMC) method, for high-speed compressible gas flows—involving a combination of continuum and rarefied flow regions. Implementation details of coupling cycle are presented along with the validation and performance studies for three cases (Mach number M a 1 = 3.38 , 6.5 and 9) of normal shock waves in argon and three cases (Inlet pressure pin = 1.0 atm, 0.5 atm and 0.1 atm) of flow through a micro-scale convergent-divergent (CD) nozzle. In comparison with our DSMC method-based solutions in the complete domain, the hybrid NS-DSMC method solutions achieve almost similar accuracy in a substantially reduced computational time—44% to 50% for the normal shock problem and 67% to 85% for the micro-scale CD nozzle problem. For the first time in literature, the hybrid NS-DSMC method is presented as a Cartesian-grid method, which is becoming popular nowadays.

The lower limits of the fast ionization waves velocity in a high-intensity laser radiation field

The kinetic processes before the front of an ionizing wave in a gas are investigated. The lower limits of the propagation velocity of a plane ionization wave in the field of high-intensity laser radiation are determined. The results of calculations of the lower boundaries of the velocity of fast ionization waves in argon in the field of a CO2-laser are given. The calculation results are compared with experimental data and other theories.

Development of ionization waves in argon at atmospheric pressure with inhomogeneous preliminary ionization

Experimental and theoretical investigations of the initial stage of the formation of a pulsed volume discharge between two plane electrodes in argon at atmospheric pressure under conditions of inhomogeneous preionization are reported. The experimental results of the propagation velocity of an ionization wave are compared with the obtained value from the numerical simulation. The features of the development of ionization waves in atmospheric-pressure argon are studied.

Reduction of a collisional-radiative mechanism for argon plasma based on principal component analysis

This article considers the development of reduced chemistry models for argon plasmas using Principal Component Analysis (PCA) based methods. Starting from an electronic specific Collisional-Radiative model, a reduction of the variable set (i.e., mass fractions and temperatures) is proposed by projecting the full set on a reduced basis made up of its principal components. Thus, the flow governing equations are only solved for the principal components. The proposed approach originates from the combustion community, where Manifold Generated Principal Component Analysis (MG-PCA) has been developed as a successful reduction technique. Applications consider ionizing shock waves in argon. The results obtained show that the use of the MG-PCA technique enables for a substantial reduction of the computational time.

Plasma creation by terahertz electromagnetic radiation

The results of experiments aimed at the study of the discharge in a focused beam of terahertz waves in argon under near-atmospheric pressures are presented. The range of electric fields and gas pressures, at which a breakdown occurs, is determined. The study of the discharge glow dynamics showed that the discharge starts at the maximum of the terahertz wave beam field and its front moved towards the radiation with the speed of about 105 cm/s into the region of the fields being significantly weaker than the breakdown value. Measurements of the ratio of wave transmission through the discharge allow one to conclude that the density of the plasma produced in the discharge exceeds 1015 cm−3. Some features of the terahertz discharge are discussed.

A hybrid particle-continuum method applied to shock waves

A hybrid numerical scheme designed for hypersonic non-equilibrium flows is presented which solves the Navier–Stokes equations in regions of near-equilibrium and uses the direct simulation Monte Carlo method where the flow is in non-equilibrium. Detailed analysis of each stage of the hybrid cycle illustrates the difficulty in defining physically correct DSMC boundary conditions in regards to both macroscopic state and velocity distribution. However, results also show that DSMC boundary conditions have little effect on a previously initialized interior particle domain. A sub-relaxation technique capable of determining macroscopic, hydrodynamic properties in a DSMC simulation is used to determine low-scatter boundary conditions for the NS domain. Particle and continuum domains adapt during the hybrid simulation through application of a continuum breakdown parameter based on the gradient-length Knudsen number. The hybrid code reproduces experimental results and full DSMC simulations in half the time for a large range of 1D shock waves in argon and diatomic nitrogen gas.

High‐frequency (10–25‐MHz) wave propagation in argon at pressures up to 10 MPa

Acoustic wave propagation in gaseous argon has been investigated using a high‐power ultrasonic gated‐tone‐burst transmission system. Results of measurements of compression wave absorption and velocity in argon at frequencies 10 to 25 MHz, at static pressures up to 10 MPa, at temperatures of 21 to 23 °C, and at high power (above critical intensity 16.97 W/m2 at 10 MHz and 10 MPa) are presented. For small‐amplitude waves at pressures up to 2 MPa, the resulting data are in good agreement with that predicted using ideal gas equations and fundamental thermophysical gas constants. At static pressures higher than 4 MPa and for higher‐power settings, distortion of the waveform is observed. Excess attenuation, in addition to classical absorption, is also found at higher power settings. With a 10‐MHz fundamental frequency, significant second harmonic generation is observed. The data are compared with existing theories for finite‐amplitude waves in fluids. Current theories [F. Dunn et al., IEEE Ultrason. Symp., 527–532 (1981); A. L. Thuras et al., J. Acoust. Soc. Am. 6, 173–180 (1935)] for harmonic generation and attenuation are shown not to predict the observed experimental data for high‐power, high‐frequency waves in argon at high pressure.

Nonlinear attenuation of 10- to 25-MHz ultrasonic waves in argon at pressures up to 10 MPa.

A large dynamic range (70 dB) ultrasonic measurement system has been developed to investigate the technology and the phenomonology of finite-amplitude high-frequency (10–25 MHz) acoustic waves in gases at pressures up to 10 MPa (100 bar). Transmission measurements of velocity and attenuation are made using two efficient lithium niobate transducers set onto quartz buffer rods, with variable separation from less than 1 to 25 mm. In this paper, data will be presented that show nonlinear phenomena as a gated tone burst (20 cycles) of finite amplitude acoustic waves propagated in argon. The received signals are digitized and analysis is performed in the time domain and using a Fourier transform. For low powers, linear attenuation with distance is observed. For finite amplitude waves, excess nonlinear attenuation and significant second harmonic generation are observed. The nonlinearity parameter at various combinations of pressure, temperature, and frequency is reported for argon.

The von Neumann paradox for the diffraction of weak shock waves

We present results from our experiments with the irregular reflection of shock waves in argon. We compare the data with the results we obtained numerically; the assumptions for the computational code were that we had unsteady, two-dimensional, compressible, inviscid, flow of a perfect gas. When precautions were taken to reduce the effects of the gas viscosity on the experimental data, we obtained very good agreement between the numerical and the experimental results for the ramp Mach number and the trajectory path triple-point angle, but there were discrepancies with the wave-angle data. The discrepancies were ascribed to the sensitivity of the data to both viscosity and to a singularity. We show that there are actually two weak irregular wave reflections, namely a classic Mach reflection (MR) and a new type, that we call a von Neumann reflection (NR). The structure of the NR is discussed in some detail, and so are the transition criteria for the various wave systems.

Simultaneous study of interferograms and the emission of shock-heated plasmas behind strong shock waves in argon

A technique of simultaneous study of optical interferograms and emission of radiations of shock-heated plasmas behind strong shock waves (M>14) was used. This enabled the recording of both the interferogram and emission characteristics of the plasma on the same photofilm by using streak photographic techniques.

Dynamics of droplet breakup in shock waves

7. 8. 9. i0. ii. 12. 13 14 15 16 17 18 K. Cherchin'yani, Theory and Application of the Boltzmann Equation [Russian translation], Mir, Moscow (1978). G. Batchelor and G. Green, "Hydrodynamic interaction of two small freely moving spheres in a linear flow field," [Russian translation], Mekhanika, No. 22 (1980). Yu. L. Klimontovich, Statistical Physics [in Russian], Nauka, Moscow (1982). L. D. Landau and E. M. Lifshits, Theoretical Physics [in Russian], ~oI. I0, Nauka, Moscow (1979). V. V. Struminskii, "On a method of solving a system of kinetic equations for gas mix- tures," Dokl. Akad. Nauk SSSR, 237, No. 3 (1977). B. V. Alekseev, Mathematical Kinetics of Reacting Gases [in Russian], Nauka, Moscow (1982). R. G. Barantsev, Rarefied Gas Interaction with Streamlined Surfaces [in Russian], Nauka, Moscow (1975). H. Mott-Smith, "Solution of the Boltzmann equations for a shock," Mekhanika [Russian translation], 17, No. 1 (1953). H. W. l, iepmann, K. Narasiwha, and M. T. Chahine, "Structure of a plane shock layer," Phys. Fluids, ~, No. ii (1962). G. G. Tivanov, "On certain exact solutions of a kinetic equation of Boltzmann type," Izv. Vyssh. Uchebn. Zaved. Fiz., No. 4 (1984). (Dep. in VINITI, No. 1567-84). B. Schmidt, "Electron beam density measurements in shock waves in argon," J. Fluid Mech., 39, No. 2 (1969). M. N. Kogan, Dynamics of a Rarefied Gas [in Russian], Nauka, Moscow (1967). DYNAMICS OF DROPLET BREAKUP IN SHOCK WAVES V. M. Boiko, A. N. Papyrin, and S. V. Poplavskii UDC 532.529.5/6 Study of the principles of acceleration and fragmentation of droplets during interaction with a high speed gas flow is of interest because of its important practical applications (for example, atomization of liquids in various technological processes, energy generation equip- ment, detonation wave propagation in gas-droplet systems, etc.). In particular, the problem of heterogeneous detonation in a gas-droplet system requires detailed study of the processes of acceleration, deformation, fragmentation, ignition, and combustion of droplets within shock waves at Mach numbers M = 2-6 for Weber numbers We = pu=d0 o-z > 103 and Reynolds num- bers Re = pud0~ -I > 103 . Here p, u, ~ are the density, velocity and viscosity of the gas, d 0 is~the initial droplet diameter, and o is the liquid surface tension. Numerous studies of droplet interaction with shock waves are reflected in reviews [i-3], which considered characteristic regimes of droplet breakup and indicated corresponding parameter ranges. Thus, according to [2], for We > 103 , Re > i0 ~) corresponding to the ex- plosive droplet decay range, the following pattern exists. Over a time interval 0 < t < t o (where t o = d0p~~176 p~ being the liquid density) a droplet collapses into a disk of size d - 3d 0. At time t ~ (0.1-0.5)t 0 a thin layer of liquid begins to break away from the equatorial region of the deformed drop and then breaks into pieces. The dimensions of the microparticles thus formed are in the range d ~ 1-10~m [4, 5]. Due to instability of the phase separation boundary at t = t o explosive decay of the disk begins, reaching its greatest velocity at t ~ (1.5-2)t 0 and ending at t ~ (4-5)t 0. The dimensions of the particles formed by this explosive decay are of the order of the thickness of the disk into which the droplet was deformed at the time of maximum deformation d ~ (0.1-0.2)d 0 [i]. The nucleus of the dis- integrating drop moves along a trajectory xd0 -I ~ (0.5-1.4)t2t0 -2 [6]. However, despite the large number of experiments which have been performed, many questions concerning droplet breakup in shock waves remain little studied. Among these, in particular, are the effect of viscosity on droplet destruction dynamics, the size of the microparticles formed, the process of evaporation of the disintegrating droplet, etc. Novosibirsk. Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 108-115, March-April, 1987. Original article submitted January 16, 1986. 0021-8944/87/2802-0263512.50 9 1987 Plenum Publishing Corporation 263

Ionization behind strong normal shock waves in argon

The ionization of argon by strong normal shock waves is studied. The conservation equations are solved to yield the plasma behavior behind the shock wave front. Very good agreement is obtained between experimental findings and the present numerical results for the electron number density, plasma density, and degree of ionization, especially at the electron avalanche region of the relaxation zone. The high accuracy of the present numerical solutions in reproducing the electron avalanche is attributed to the use of accurate threshold collision cross sections for excitation of argon by electron collisions. To support this claim it is demonstrated that if different assumptions were used to describe the ionization process, then the computed results would be different only upstream of the electron avalanche region, i.e., it is shown that the proposed model for ionizing shock waves enables a highly accurate reproduction of the electron avalanche but is less accurate in predicting its exact location.

Structure of shock waves at re-entry speeds

The unified structure of steady, one-dimensional shock waves in argon, in the absence of an external electric or magnetic field, is investigated. The analysis is based on a two-temperature, three-fluid continuum approach, using the Navier—Stokes equations as a model and including non-equilibrium collisional as well as radiative ionization phenomena. Quasi charge neutrality and zero velocity slip are assumed. The integral nature of the radiative terms is reduced to analytical forms through suitable spectral and directional approximations. The analysis is based on the method of matched asymptotic expansions. With respect to a suitably chosen small parameter, which is the ratio of atom-atom elastic collisional mean free-path to photon mean free-path, the following shock morphology emerges: within the radiation and electron thermal conduction dominated outer layer occurs an optically transparent discontinuity which consists of a chemically frozen heavy particle (atoms and ions) shock and a collisional ionization relaxation layer. Solutions are obtained for the first order with respect to the small parameter of the problem for two cases: (i) including electron thermal conduction and (ii) neglecting it in the analysis of the outer layer. It has been found that the influence of electron thermal conduction on the shock structure is substantial. Results for various free-stream conditions are presented in the form of tables and figures.

Effects of hydrogen impurities on shock structure and stability in ionizing monatomic gases: 2. Krypton

At shock Mach numbers [Formula: see text] in pure krypton, at initial pressures p0 ~ 5 Torr, and final electron number densities ne ~ 1017 cm−3, the translational shock front in a 10 cm × 18 cm hypervelocity shock tube develops sinusoidal instabilities which affect the entire shock structure including the ionization relaxation region, the electron-cascade front and the final quasi-equilibrium state. By adding a small amount of hydrogen (~0.5% of the initial pressure), the entire flow is stabilized. However, the relaxation length for ionization is drastically reduced to about one half of its pure-gas value. Unlike argon the stability appears to diminish with the addition of hydrogen beyond about 0.5%. Using the familiar two-step collisional model coupled with radiation-energy loss and the appropriate chemical reactions, it was possible from dual-wavelength interferometric measurements to deduce a more precise value for the krypton–krypton collision excitation cross-section, S*Kr–Kr = 1.2 × 10−19 cm2/eV, with or without the presence of hydrogen impurities. The reason for the success of hydrogen, and not other gases, in bringing about stabilized Shock waves in argon and krypton is not clear. It was also found that the electron-cascade front approached closely to the translational-shock front with increasing proximity to the shock-tube wall. This effect appears independent of the wall material and is not affected by the evolution of adsorbed water vapour from the walls or by water added deliberately to the test gas. The sinusoidal instabilities investigated here may offer some important clues to the abatement of instabilities that lead to detonations and explosions.

Breakdown waves in argon and nitrogen

Extensive measurements are presented of initial electric breakdown wave speed in nitrogen and argon as a function of local electric field at the wavefront. The results are in basic agreement with the electron fluid dynamic theory of the phenomenon. The apparent gas density dependence over and above the E/p dependence predicted by theory, that has been found by other investigators, is confirmed and has been traced to observational limitations. The results indicate that photo-ionizing processes are not needed to explain the effects observed over most of the pressure range studied.

The stability of shock waves in ionizing and dissociating gases

The stability of strong shock waves in argon and carbon dioxide has been studied in a free-piston shock tube using time-resolved interferometry. Unstable shock fronts have been found to occur close to velocities where (dP/dV)H (where P and V are the pressure and the specific volume behind the shock) on the Rankine-Hugoniot curve is positive due to completion of first ionization or dissociation. Such an instability has been described theoretically by D'iakov (1954). However, his stability limits have not been reached in this case, and this suggests that the linearized perturbation analysis is not accurate for the case of the real shock tube flow.

Experimental study of pressure behind reflected shock waves in argon at mach numbers of 10?35

The results are presented for a study of the pressure behind reflected shock waves for pressures of (1–10)·1.33 · 102 N/m2 ahead of the incident shock wave. It is found that during the first 1.0–2.0 · 10−5 sec after the reflection of the shock wave the pressure of an argon plasma behind it corresponds to that calculated from the conservation laws with allowance for ionization on the assumption that the plasma is ideal.

The measurement of temperature in shock-heated gases from the relative emission intensities of the OH ultraviolet bands

A method of temperature measurement behind reflected shock waves in argon is investigated, which utilizes the integrated emission over a large number of rotational lines in the 2Σ->2II band system of OH. In the majority of experiments the OH emission is generated by the addition of 0·5% (H2+O2) to the argon, and the intensity, from two spectral regions, is monitored by two monochromators. From the ratio of the observed intensities the gas temperature can be calculated from the known spectroscopic data for OH. Theoretically derived intensity ratios for several bands, compared with that of the (0,0) band, are given as a function of temperature.Values of spectroscopic temperatures, over the range 3000-6000 K, agree with the gas dynamic values, derived from incident shock wave velocities with Mach numbers varying from 3·5 to 5·2, to within the predicted experimental error. The method is shown to be inapplicable at initial pressures greater than about 80 Torr because of self-absorption and at pressures lower than 20 Torr radiative disequilibrium may equally limit its use. Moreover, the pre-association reaction of oxygen and hydrogen atoms is found to enhance the intensity of most bands except the (0,0) and (1,1); only the latter bands may therefore be used to obtain the time variation of temperature behind the shock front.

Multistep initial ionization behind strong shock waves in argon

A spectroscopic investigation of the initial ionization behind strong shock waves in argon was made to determine the role of atomic levels in addition to the first excited state. For a numerical modeling of the ionization process a six-level argon atom was assumed. A comparison of analytical and numerical results shows that in the initial ionization process, two-step ionization and multistep (``ladder-climbing'') ionization as originally suggested by de Boer, compete with each other. For an initial pressure of 5 torr and a Mach number of 9 the contributions of two-step ionization and multi-step ionization are roughly equal, with increasing pressure and temperature favoring the latter. The appropriate atom-atom excitation and ionization cross sections have been determined.

Interferometrische Messung der thermischen Zustandsgrößen von Edelgasstoßwellenplasmen1 / Interferometric Measurement of Thermodynamic Variables of Rare Gas Plasmas Produced by Shock Waves

The variation of electron density and neutral atom density behind incident shock waves in argon, krypton, and xenon are measured using a two wavelength laser interferometer with photoelectric detection of fringe shifts. The accuracy of the measured area densities ∫ Ne dl and ∫ Na dl is better than 1 per cent. Densities measured at the moment of maximum electron density agree well with Rankine-Hugoniot densities. There are no indications to deviations from LTE. Additionally, in the radiation cooling region the decrease of temperature is determined.