One-dimensional Fluid Model Research Articles

Global stability of combination of a viscous contact wave with rarefaction waves for the compressible fluid models of Korteweg type

This paper is concerned with the large-time behavior of solutions to the Cauchy problem of the one-dimensional compressible fluid models of Korteweg type with density- and temperature-dependent viscosity, capillarity, and heat conductivity coefficients, which models the motions of compressible viscous fluids with internal capillarity. We show that the combination of a viscous contact wave with two rarefaction waves is asymptotically stable with a large initial perturbation if the strength of the composite wave and the capillarity coefficient satisfy some smallness conditions. The proof is based on some refined L2-energy estimates to control the possible growth of the solutions caused by the high nonlinearity of the system, the interactions of waves from different families and large data, and the key ingredient is to derive the uniform positive lower and upper bounds on the specific volume and the temperature.

Asymptotic Stability of Combination of Contact Discontinuity with Rarefaction Waves for the One-Dimensional Viscous Micropolar Fluid Model

In this paper, we consider with the large time behavior of solutions of the Cauchy problem to the one-dimensional compressible micropolar fluid model, where the far field states are prescribed. When the corresponding Riemann problem for the Euler system admits the solution consisting of contact discontinuity and rarefaction waves, it is shown that the combination wave corresponding to the contact discontinuity, with rarefaction waves is asymptotically stable provided that the strength of the combination wave and the initial perturbation are suitably small. This result is proved by using elementary L2-energy methods.

NUMERICAL STUDY OF GAS HEATING IN OZONE GENERATED BY DBD IN OXYGEN

The goal of the present work is to highlight the gas temperature effect in ozone generated by dielectric barrier discharge (DBD) in pure oxygen (O2). In this study, a one-dimensional fluid model was used to describe the discharge behavior. The study of the gas heating phenomena study in the frame of this paper is due to the gas heating effect. The gas temperature profile obtained in the DBD in oxygen was calculated by means of the heat transport equation. The results show that the rise of the gas temperature in the DBD inoxygen is more important near the dielectrics. The high value of gas temperature in this region is limited by the increase in the electric field and ion current density.

Effects of <i>q</i>-nonextensive distribution of electrons on secondary electron emission in plasma sheath

A one-dimensional fluid model is used to investigate the characteristics of secondary electron emitted by the interaction between electrons and the wall in plasma sheath with nonextensive electrons. The study focuses on the effects of electron nonextensive parameter on Bohm criterion, the wall potential, the critical emission coefficient of secondary electrons and the density of seconday electrons in plasma sheath through numerical simulation. Some conclusions are obtained. It is shown that secondary electron is significantly affected by electron nonextensive parameter. Whether the electron distribution is superextensive or subextensive, the critical Mach number at the sheath edge increases with the secondary electron emission coefficient increasing, but decreases with <i>q</i>-parameter increasing. The increase of <i>q</i>-parameter can cause the wall potential to increase and the critical emission coefficient of secondary electron at the wall to decrease. And for different types of plasmas, the effects of nonextensive parameter on the critical emission coefficient of secondary electron are different. The larger the mass number of ion in plasma, the smaller the influence of nonextensive parameter on the critical secondary electron emission coefficient will be. In addition, the increase of nonextensive parameter can result in the decrease of the sheath thickness and the increase of the number density of secondary electrons. It is found that the superextensive electron distribution has greater influence on the characteristics of secondary electron emission in plasma sheath than the subextensive electron distribution.

Effects of Oxygen Concentration on the Reactive Oxygen Species Density Under Different Operating Conditions in Atmospheric-Pressure Helium/Oxygen Pulsed Dielectric Barrier Discharge

In this paper, a numerical investigation on the effects of oxygen concentration on the reactive oxygen species (ROS) density under different operating conditions in the atmospheric-pressure helium/oxygen pulsed dielectric barrier discharge (DBD) has been performed by means of a one-dimensional (1-D) fluid model. The involved ROS are ground state oxygen atom O, excited state oxygen atom O( 1 D), single delta metastable oxygen O 2 ( 1 Δg) (SDO), and ozone molecule O 3 . The present work gives the following significant results. For a given operating condition, the averaged O density is evidently larger than the other three ROS densities. There exist characteristic oxygen concentrations where the averaged densities of O and SDO reach their maximum with the increase in the oxygen concentration, respectively. The averaged O 3 density increases with the oxygen concentration, but the reverse is true for the averaged O(1D) density. In addition, the ROS density is increased when increasing the applied voltage amplitude Va, decreasing the rising time of the applied voltage pulse t r , or reducing the frequency of the applied voltage pulse f. Also, the characteristic oxygen concentrations for the averaged densities of both the O and SDO move towards the higher oxygen concentration when increasing the V a , decreasing the t r , or increasing the f. The effect of the operating conditions on the averaged O 3 density is weak under lower oxygen concentrations, and it is increasingly affected by the operating conditions with the increasing oxygen concentration. However, the variation trend of the averaged O( 1 D) density versus oxygen concentration is hardly affected by the operating conditions.

One-Dimensional Simulation of Synergistic Desulfurization and Denitrification Processes for Electrostatic Precipitators Based on a Fluid-Chemical Reaction Hybrid Model

Non-thermal plasma (NTP) technologies can be used to treat a variety of gaseous pollutants, and extensive research has been carried out worldwide because of its high purification efficiency, low dependence on temperature, and other advantages. NO and SO2 are the main gaseous pollutants in coal-fired flue gas. The plasma dynamics for desulfurization and denitrification is a hot topic in the field of NTP pollutant control technologies. In this paper, a one-dimensional fluid model for the simultaneous desulfurization and denitrification of flue gas by negative direct current (DC) corona discharge was established based on the traditional zero-dimensional chemical kinetic model. The simplified wire-cylindrical electrodes configuration and numerical simulation conditions are similar to the working process of electrostatic precipitators. The results obtained by the finite element method show that the removal efficiency of NO and SO2 is remarkable in the region with a radius of less than one centimeter around the high-voltage electrode, and the effective purification area expands with the increase of the discharge voltage. There are different removal pathways for NO at different positions in the removal region, while the removal of SO2 is mainly dependent on the oxidation by OH.

Effects of oxygen concentration on helium-oxygen dielectric barrier discharges: From multi-breakdowns to single-breakdown per half-cycle

In this paper, a one-dimensional fluid model of He + O2 dielectric barrier discharge is established. As the oxygen concentration increases from 0.2% to 0.7% and 1.2%, the plasma transforms from triple-breakdowns to single-breakdown per half-cycle. In the mode of multi-breakdowns, the first pulse produces more particles although dissipates more power, thus making remarkable differences in the energy efficiencies in producing charged species but can hardly affect neutral species. We also operate the model in another way that the plasma is held in the mode of single-breakdown, by changing the oxygen concentration and voltage amplitude at the same time, so the impact of mode transformation is removed. In this way, the production efficiency of the electron decreases significantly, probably owing to the enhanced electron attachment with O2 and O3. After analyzing the main chemistry process of both charged and neutral species, it is suggested that the decreasing efficiency of the electron and the increasing oxygen concentration impose opposite impacts on the energy efficiencies of other species. Almost all charged species decrease more or less in their efficiencies, but O3- is the exception. For neutral species, the efficiencies vary slightly for O and O* but increase more than 250% for O2* and O3.

Numerical modeling of the electrical properties plasma argon in a RF magnetron sputtering and with Einstein's relation of electron diffusivity

Numerical modeling of RF magnetron sputtering discharge of argon plasma properties, using a one-dimensional time-dependent fluid model in presence of the magnetic field, has been developed. The model is based on continuity equation and electron temperature equation coupled with Poisson’s equation. The electron mobility depends on magnetic field and the electron diffusivity is assumed to be dependent of electron energy by Einstein's relation. The flux is calculated by Scharfetter and Gummel schemes. Numerical simulations were resolved by using the Finite Volume Method (FVM) and the Thomas algorithm. The obtained results for the electrical properties, electron and ion densities, electrical potential, electric field and electron temperature, are in good agreement with previous works. A parametric study varying the magnetic field intensity on the discharge properties is done.

Identification of the normal and abnormal glow discharge modes in a neon-xenon gas mixture at low pressure

In this paper, we focused on the identification of the normal and abnormal glow discharge modes in a neon-xenon gas mixture at low pressure. We considered four gas mixtures: 90%Ne-10%Xe, 80%Ne-20%Xe, 70%Ne-30%Xe and 50%Ne-50%Xe at 1.5 Torr. The range of the gap voltage is 150–500 V. A one-dimensional fluid model with multiple species was used in this work, and the metastable state of the atoms as well as the radiation effects were integrated into the model too. The input data changed for each percentage in the gas mixture, and was calculated by BOLSIG+ software. The parameters of particle transport and their rate coefficients strictly depend on the mean electron energy. The results show that the neon ion density is negligible compared to the xenon ion density, mostly in the case of 50%Ne-50%Xe.

Influence of electron backflow on discharge asymmetry in atmospheric helium dielectric barrier discharges

In this paper, the transition mechanisms between symmetric and asymmetric discharges in atmospheric helium dielectric barrier discharges (DBDs) are investigated via a one-dimensional fluid model. By gradually increasing the gap width, a complete evolution trajectory of the discharge states (i.e. from symmetric single period discharge (SP1) to asymmetric single-period (AP1) discharge, finally returns back to SP1 discharge) is observed. Unlike the previous reports which emphasize the dominant role of residual positive column, this work demonstrates that the transitions between SP1 and AP1 discharges could also be induced by the electron backflow effect. It is the residual electron backflow region that provides extra seed electrons to the subsequent discharge, restraining the development of electric field in the breakdown process, thus weakening the next discharge pulse. Upon the impairment of one discharge pulse, due to the reduction of charge generation and the impairment of electron backflow effect in the relevant discharge phase, its subsequent discharge would be strengthened. Those mechanisms function in different current pulses at different gap widths, inducing the mode transition. In addition, our simulation result reveals that the “residual positive column” referred in previous publications is essentially a special form of the “electron backflow region”, which is typically more remarkable in large gap widths. As a consequence, the dynamics of electron backflow provides more insights regarding the transition of nonlinear states in DBDs with controlling parameters varying.

Asymptotic stability of a composite wave for the one-dimensional compressible micropolar fluid model without viscosity

We are concerned with the large time behavior of solutions to the Cauchy problem of the one-dimensional compressible micropolar fluid model without viscosity, where the far-field states of the initial data are prescribed to be different. If the corresponding Riemann problem of the compressible Euler system admits a contact discontinuity and two rarefaction waves solutions, we show that for such a non-viscous model, the combination of the viscous contact wave with two rarefaction waves is time-asymptotically stable provided that the strength of the composite wave and the initial perturbation are sufficiently small. The proof is given by an elementary L2 energy method.

Influence of voltage duty ratio on current asymmetry and mode of a helium dielectric-barrier discharge excited by a modulated voltage

Excited by a modulated sinusoidal voltage, dielectric barrier discharge in atmospheric pressure helium has been investigated through a one-dimensional fluid model. Under a lower voltage amplitude, the discharge presents one current pulse per half sinusoidal cycle. The positive discharge is weaker than the negative one if the duty ratio of the modulated voltage is lower. When increasing the duty ratio, the intensity of the positive discharge increases and that of the negative discharge keeps approximately constant, which implies that the discharge symmetry is improved. A similar phenomenon regarding the discharge symmetry is also observed under a higher voltage amplitude despite the fact that a secondary discharge following a primary one is presented per half sinusoidal cycle. Besides the duty ratio, the discharge symmetry can be improved by increasing the voltage amplitude, especially under a lower duty ratio. These phenomena are qualitatively explained by analyzing the variation of the electron density when increasing the duty ratio. Results also indicate that the positive primary discharge at the peak moment belongs to a Townsend mode or a glow one, which is determined by the duty ratio and the voltage amplitude. Finally, the critical voltage for the Townsend mode transiting to the glow one is investigated as a function of the duty ratio.

Numerical study of the discharge properties of atmospheric dielectric barrier discharge by using 200 kHz/13.56 MHz excitations

In this work involving an atmospheric dielectric barrier discharge system, the feasibility of independence control of key plasma parameters through strategic modulation of applied dual-frequency excitation sources is demonstrated. In this paper, a one-dimensional fluid model with semi-kinetic method has been used to investigate the discharge properties of atmospheric dielectric barrier discharge by using 200 kHz/13.56 MHz excitations. Bearing good consistency and coherence with experimental results, the electrical characteristics and typical electron dynamics are studied numerically. It is revealed that the application of the high frequency excitation can restrain the increment of the low frequency current component and is effective in preventing the discharge from transitioning to a filamentary mode. This method then suggests and enables possible approaches to obtain discharges with good stability in described DBD systems.

Numerical study on helium-oxygen dielectric barrier discharges: From single-breakdown to multi-breakdowns per half-cycle

Helium-oxygen dielectric barrier discharge has received much attention due to its high efficiency and stability in producing reactive oxygen species (ROS). Previous studies evidenced that the dielectric-barrier controlled plasma would transform from single-breakdown to multi-breakdowns per half cycle with the increasing applied voltage, but the variation of densities and wall fluxes of ROS during the transformation has not been well understood. This motivates us to construct a one-dimensional fluid model for this study. The results show that the volume-averaged densities and wall fluxes of the electron, ions, and atomic metastables are temporally pulsed with each breakdown, but they are nearly invariable for the grounded neutrals (O and O3) and molecular metastables [such as O2(a1Δg)]. For each species, the temporal pulses of density and flux of a specific species have different widths, and the widths remain almost constant in time among the breakdowns except for that of the electron. With the increasing number of breakdowns per half cycle, the wall fluence and the peak value of temporal flux pulses of O− have obviously different trends, and the energy efficiencies for the production and wall fluence increase significantly only for O− and O3−.

Numerical simulation of the multi-pulse phenomena in atmospheric-pressure dielectric barrier glow discharges in He/N2mixture

To further understand the formation mechanism of multi-pulse phenomena in atmospheric He/N2dielectric barrier glow discharge, the influence of nitrogen content on the multi current pulse phenomena is studied by a one-dimensional plasma fluid model. As nitrogen content increases, the first discharge current in the multi-pulse glow discharge becomes larger, and the gas gap voltage drop and the charges transported during the first discharge pulse are also increased, leading to the decrease of subsequent discharge current. When the increasing applied voltage cannot overcome the gas gap voltage drop in the first discharge pulse, the multi-pulse discharge mode will transit into a single pulse discharge mode. The numerical simulation results also show that the changes of discharge characteristics are mainly attributed to the Penning ionization between molecules of nitrogen and metastable atoms of helium.

Virial series expansion and Monte Carlo studies of equation of state for hard spheres in narrow cylindrical pores.

In this paper, the virial series expansion and constant pressure Monte Carlo method are used to study the longitudinal pressure equation of state for hard spheres in narrow cylindrical pores. We invoke dimensional reduction and map the model into an effective one-dimensional fluid model with interacting internal degrees of freedom. The one-dimensional model is extensive. The Euler relation holds, and longitudinal pressure can be probed with the standard virial series expansion method. Virial coefficients B_{2} and B_{3} were obtained analytically, and numerical quadrature was used for B_{4}. A range of narrow pore widths (2R_{p}), R_{p}<(sqrt[3]+2)/4=0.9330... (in units of the hard sphere diameter) was used, corresponding to fluids in the important single-file formations. We have also computed the virial pressure series coefficients B_{2}^{'}, B_{3}^{'}, and B_{4}^{'} to compare a truncated virial pressure series equation of state with accurate constant pressure Monte Carlo data. We find very good agreement for a wide range of pressures for narrow pores. These results contribute toward increasing the rather limited understanding of virial coefficients and the equation of state of hard sphere fluids in narrow cylindrical pores.

Characteristics of atmospheric Ar/NH3 DBD and its comparison with He/N2 DBD

The discharge mode and photoelectric characteristics of Ar/NH3 DBD (dielectric barrier discharge) are studied to discuss the stability of the discharge under the influence of Penning ionization and attachment reaction. There are three discharge modes, including stable uniform glow discharge, unstable glow discharge and unstable columnar discharge. Discharge instability, including nonuniform discharge and discharge channel split, occurs under low (<0.10%) or high (>0.35%) volume fractions of NH3, which are understood to be caused by an insufficiently strong Penning effect or a strong attachment reaction, respectively. The attachment reaction of NH3 can also lead to a weaker emission intensity for Ar/NH3 DBD, in particular regarding the emission of OH(A2Σ+). Ar/NH3 and He/N2 DBDs are also compared. In He/N2 DBD, the emission intensity of OH(A2Σ+) changes less with increasing N2 volume fraction, which may be attributed to the lack of attachment reaction. Compared with Ar/NH3 DBD, the single discharge channel in He/N2 DBD is narrower, but the discharge area is wider, which should be induced by the higher Townsend ionization coefficient nonlinearity of He/N2 and the absence of attachment reaction in He/N2, respectively. In the end, a one-dimensional fluid model of Ar/NH3 DBD is built to verify the explanation of experimental results.

Ionization asymmetry effects on the properties modulation of atmospheric pressure dielectric barrier discharge sustained by tailored voltage waveforms

The dielectric barrier discharge (DBD) is a promising technology to generate high density and uniform cold plasmas in atmospheric pressure gases. The effective independent tuning of key plasma parameters is quite important for both application-focused and fundamental studies. In this paper, based on a one-dimensional fluid model with semi-kinetics treatment, numerical studies of ionization asymmetry effects on the properties modulation of atmospheric DBD sustained by tailored voltage waveforms are reported. The driving voltage waveform is characterized by an asymmetric-slope fundamental sinusoidal radio frequency signal superimposing one or more harmonics, and the effects of the number of harmonics, phase shift, as well as the fluctuation of harmonics on the sheath dynamics, impact ionization of electrons and key plasma parameters are investigated. The results have shown that the electron density can exhibit a substantial increase due to the effective electron heating by a spatially asymmetric sheath structure. The strategic modulation of harmonics number and phase shift is capable of raising the electron density significantly (e.g., nearly three times in this case), but without a significant increase in the gas temperature. Moreover, by tailoring the fluctuation of harmonics with a steeper slope, a more profound efficiency in electron impact ionization can be achieved, and thus enhancing the electron density effectively. This method then enables a novel alternative approach to realize the independent control of the key plasma parameters under atmospheric pressure.

Global solutions for a one-dimensional compressible micropolar fluid model with zero heat conductivity

In this study, we consider global solutions for the one-dimensional compressible micropolar fluid model with zero heat conductivity, which is a hyperbolic–parabolic system. The pressure, velocity, and angular velocity are dissipative because of the viscosity, whereas the entropy is non-dissipative due to the absence of heat conductivity. Compared with the classical Navier–Stokes equations, there is an extra angular velocity ω in the micropolar fluid model, which causes both benefits and problems. The benefit is due to the fact that the term −vω is a damping term and it provides extra regularity for ω, and the problem is due to the term vω2 because it increases the nonlinearity of the system. The global solutions can be obtained by combining the local existence and a priori estimates if the H2-norm of the initial perturbation around a constant state is sufficiently small. The asymptotic behavior is also determined in this study.

Metastable Ar(1s5) density dependence on pressure and argon-helium mixture in a high pressure radio frequency dielectric barrier discharge

Simulations of an α-mode radio frequency dielectric barrier discharge are performed for varying mixtures of argon and helium at pressures ranging from 200 to 500 Torr using both zero and one-dimensional models. Metastable densities are analyzed as a function of argon-helium mixture and pressure to determine the optimal conditions, maximizing metastable density for use in an optically pumped rare gas laser. Argon fractions corresponding to the peak metastable densities are found to be pressure dependent, shifting from approximately 15% Ar in He at 200 Torr to 10% at 500 Torr. A decrease in metastable density is observed as pressure is increased due to a diminution in the reduced electric field and a quadratic increase in metastable loss rates through Ar2* formation. A zero-dimensional effective direct current model of the dielectric barrier discharge is implemented, showing agreement with the trends predicted by the one-dimensional fluid model in the bulk plasma.