Local Mean Energy Research Articles

Parametrization of Fluid Models for Electrical Breakdown of Nitrogen at Atmospheric Pressure

In the transient phase of an atmospheric pressure discharge, the avalanche turns into a streamer discharge with time. Hydrodynamic fluid models are frequently used to describe the formation and propagation of streamers, where charge particle transport is dominated by the creation of space charge. The required electron transport data and rate coefficients for the fluid model are parameterized using the local mean energy approximation (LMEA) and the local field approximation (LFA). In atmospheric pressure applications, the excited species produced in the electrical discharge determine the subsequent conversion chemistry. We performed the fluid model simulation of streamers in nitrogen gas at atmospheric pressure using three different parametrizations for transport and electron excitation rate data. We present the spatial and temporal development of several macroscopic properties such as electron density and energy, and the electric field during the transient phase. The species production efficiency, which is important to understand the efficacy of any application of non-thermal plasmas, is also obtained for the three different parametrizations. Our results suggest that at atmospheric pressure, all three schemes predicted essentially the same macroscopic properties. Therefore, a lower-order method such as LFA, which does not require the solution of the energy conservation equation, should be adequate to determine streamer macroscopic properties to inform most plasma-assisted applications of nitrogen-containing gases at atmospheric pressure.

On fundamental inconsistencies in a commonly used modification of a fluid model for glow discharge

This work considers the fundamental contradictions in the concept of one of the most well-known and widely used modifications of the fluid model for simulation of a glow discharge (GD), the ‘local mean energy approximation’ (LMEA). In this model, it is proposed to determine the kinetic coefficients in the electron particle and energy balance equations as functions of the electron mean energy (temperature) rather than local electric field, using a one-to-one correspondence between these parameters through the electron Boltzmann equation. It is shown that the scope of applicability of this model, like any other modification of the fluid model, is limited by the local mode of formation of the electron energy distribution function (EEDF). Therefore, as demonstrated by the examples of typical 1D and 2D problems for a GD in argon, its extension to the region of nonlocal EEDF is in no way justified and leads not only to serious errors in the results, but also to a logically intractable situation in attempts to apply the main postulate of the LMEA model to the region of a weak (or even reverse) electric field in a negative glow plasma. At the same time, the apparent reliability of calculations within the framework of the LMEA model for a number of parameters, in our opinion, only slows down progress in modeling of gas discharge plasma.

Synchronization of chaos in semiconductor gas discharge model with local mean energy approximation

The delta synchronization is a useful method to analyze appearance of chaotic synchronization in gas discharge systems. In recent studies, the generalized synchronization method has been implemented in various gas discharge systems. However, synchronization is not detected with this conventional method. In our previous study, we introduced the delta synchronization method and applied it to the gas discharge-semiconductor system (GDSS) via the one-dimensional ‘simple’ fluid model approach. In the present study, we implement this method in the more detailed (in terms of plasma chemical reactions and treatment of the electron transport) fluid model, namely the ‘extended’ fluid model or ‘local mean energy approximation’ model. The description of the GDSS model is given, and a bifurcation diagram demonstrates the system’s transition to the chaotic regime. The unpredictable motion, which proves the existence of Poincaré chaos, and the delta synchronized motion are confirmed by the numerical simulations, and corresponding algorithms are given. The time sequences corresponding to the unpredictability and delta synchronization are presented in tables. For consistency, the absence of generalized synchronization is also shown via the auxiliary system approach. The numerical characteristics indicating the degrees of chaos and synchronization are described and implemented in the analysis. These features are also used to compare our results to the simpler model.

Empowering Churchill: Exploring Energy Security in Northern Manitoba

To those living in Churchill, Manitoba, having power means much more than being able to turn on the lights. Using Churchill as a case study, we examine how local context can improve the suitability of energy security definitions for communities in northern Canada. Churchill is an isolated northern municipality with no road access but is connected to the electrical grid. Energy consumption data were collected from utility providers and organized into a community energy profile. Semi-structured interviews (n = 23) and a community workshop (n = 12) identified challenges, opportunities, and a vision for Churchill’s energy system. High per capita energy consumption, especially of transportation (jet fuel) and heat (electricity and propane) sources dominate Churchill’s energy profile. The reliance on air travel and need for heating are realities that define energy systems in the North. Participants expressed desire for increased use of renewables and improved energy efficiency. Churchill is reliant on external sources of power and there is a need for agency and local decision making. Jurisdictional realities and the community’s desire for consideration of local context mean energy security definitions should take a regional approach. Recognizing these findings, we propose a new definition of energy security that fits the circumstances and desires of Churchill and the North.

Functional and Anatomical Image Fusion Based on Gradient Enhanced Decomposition Model

Medical image fusion technology can synthesize complementary information from multimodal medical images while saving storage costs. Targeting the problems of reduced contrast, blurred details, color distortion, and excessive processing time requirement in fusion algorithms, we propose a new functional and anatomical image fusion algorithm based on a gradient enhanced decomposition model. First, a new gradient-enhanced decomposition (GED) model is proposed. Subsequently, the proposed GED model is expanded into a three-layer decomposition, wherein the input image is decomposed into a basic, local mean energy, and texture layers using alternating direction method of multipliers. Compared with other classic decomposition method, the proposed three-layer decomposition has the advantages of no additional noise and requiring less time while enhanced gradient. Second, we propose targeted fusion rules for each layer. After the basic layer is weighted averaged, the gamma function is used to adjust its brightness. The product of the local l2 norm and largest singular value constitutes the fusion weights of the local mean energy layers. The fusion weights of the texture layers are determined by the product of the local l1 norm and largest singular value. Finally, the fused image is reconstructed. We perform numerous experiments to prove that the proposed fusion algorithm providing clearer edge details and superior colors in a short processing time, and there was a statistically significant difference compare with other classical algorithms.

Nanosecond dielectric barrier discharge on a curved surface in atmospheric air: streamer evolution and aerodynamic perturbations

A curved nanosecond-pulsed dielectric barrier discharge actuator is proposed to fit the flexibly complex surface shape of air vehicles. Streamer evolution and aerodynamic perturbations driven by a single-pulse voltage applied on the anode, where the pulse width is 35 ns and the peak voltage is 14 kV, are numerically studied. Continuity equations that consider 15 species and 34 reactions are solved based on the drift–diffusion approximation. The electron temperature is obtained using the local mean energy approximation method. Discharge characteristics during the voltage-rise, plateau and decay stages are discussed, respectively. The streamer is initiated at 2.2 ns. The maximum electric field is progressively located at the head of the streamer, between the electrodes and in the dielectric layer during the three voltage stages, while the maximum value of electron density is settled at the downstream tip of the driven anode. The electron number density at the streamer head increases at the voltage-rise stage, keeps constant during the voltage-plateau stage, decreases at the beginning of the voltage-decay stage and then increases due to the quenching effect of the excited species. Compared with the discharge on a flat surface, the initial discharge propagation velocity is smaller, while it decreases more slowly during the entire applied voltage. The simulated deposited energy matches the analytical solution well. Aerodynamic perturbations are investigated by solving the compressible Navier–Stokes equations. The ambient air is rapidly heated to the maximum temperature of 1883 K within 0.04 μs. The temperature rise remains greater than 1000 K for 0.32 μs and greater than 500 K for 21.6 μs. A ‘semiring-like’ compression wave is formed from the discharge region; the propagation speed decreases as it propagates away from the wall and then converges to 345 m s−1 at 13 μs. High-speed flows are rapidly induced at the beginning, and two vortexes are formed successively due to the interaction between the flow induced by the actuator and the backflow induced by the compression wave.

An uncoupled implementation of the local mean energy plasma model

The study of cold plasma represents a very active field of applied physics with technical applications ranging from medical treatments to estimation of aging of electrical components due to internal partial discharges and treeing. In particular, the simulation of this category of plasma plays an increasingly important role since more and more complex, and technically relevant, configurations can be represented. Various kinds of models have been considered, one possible classification is relative to the way the electronic energy is computed. In the local electric field approximation a simple algebraic relationship is used which directly links the electric field strength to the electron energy. On the contrary, in the local mean energy approximation a proper differential equation is solved. In most cases this equation is coupled with a conservation equation which predicts the electron concentration. We will tackle this latter case and we will introduce a formulation capable of decoupling the electron density equation from the electron energy one. We will study the properties of the new formulation and we will build a proper numerical scheme capable of preserving, at a discrete level, these properties. Moreover, we will also discuss the existence of the discrete solution and test the performances of the scheme both in simple test cases, where an exact solution is known, and in a technically relevant configuration such as the formation of a treeing structure.

Modeling of fast ionization waves in pure nitrogen at moderate pressure

The fast ionization wave (FIW) discharges in pure nitrogen in a capillary tube at 27 mbar, initiated by positive polarity, high-voltage nanosecond pulses, are numerically studied by coupled two-dimensional plasma fluid modeling. The 2D fluid code based on local mean energy approximation is validated and used, an extended three-exponential Helmholtz photoionization model is proposed for pure nitrogen. The development and structure of the nitrogen FIW is analyzed, the electric field and current are calculated compared with experimental measurements. The evolution of radial distribution of electrons and N2(C 3Π u ) during the FIW development stage and in the afterglow are analyzed, the radial profiles of electron density show a ‘hollow’ structure in the FIW development stage, the temporal-spatial evolution of N2(C 3Π u ) is dominated by the competition between the pooling reaction of and the quenching by electrons. The role of photoionization on the nitrogen FIW radial morphology is discussed, the equivalent background electron density of photoionization in nitrogen discharge is suggested to be (4–6) × 1013 m−3. Spatial distribution of specific energy deposition (SED), fast gas heating (FGH) energy and temperature rise are obtained, heating efficiency varies with electric field E/N and SED and tends to be 10% at high SED. The dominating reactions responsible for FGH and their fractional contribution in space and time are analyzed, in the near axis region, pooling reactions of and N2(B 3Π g ) contribute up to 80% FGH energy, electron impact dissociation of molecular nitrogen contributes about 10%, while e- recombination and quenching of N(2 D) atoms by N2 molecules contribute rest.

Modeling the thermalization of electrons in conditions relevant to atmospheric pressure He-O2 nanosecond pulsed discharges

The electron thermalization process is significant in nanosecond pulsed discharges due to the applied voltage pulse's short duration and rapid rise and fall times. In this contribution, a comparison was made between two approaches to modeling the electron kinetics of electron thermalization in atmospheric pressure helium plasma with an oxygen admixture. Modeling based on the direct solution of the local time-dependent electron Boltzmann equation was compared with modeling based on the commonly used but less general local mean energy approximation. For modeling based on the local time-dependent electron Boltzmann equation, a temporary faster decay in the population of electrons in the high energy tail and a slower decay in the population of intermediate energy electrons were observed while the electron swarm cooled from an average energy of above 8 eV, without an electric field present. During that period, the electron impact reaction rate coefficients of helium direct ionization and electronic excitation decreased by more than three orders of magnitude as compared to the modeling based on the local mean energy approximation. Global modeling of the evolution of plasma species densities in response to an electric field typical of atmospheric pressure pulsed discharges was performed with the two approaches to electron kinetics. Differences in the species densities were observed between the two approaches, with a 100% increase in the maximum density of electrons found with the modeling based on the local mean energy approximation.

Development of a Massively Parallelized Fluid-Based Plasma Simulation Code With a Finite-Volume Method on an Unstructured Grid

A massively parallelized unstructured-grid plasma simulation code based on a multifluid plasma model has been developed and validated. The code uses a collocated cell-centered finite-volume method and is designed to simulate intermediate low-pressure and atmospheric-pressure (AP) plasma sources with complex machine geometries. One of the novel features of this code is that it is implemented in a highly flexible computational platform named ultrafast massively parallel processing (ultraMPP), which allows straightforward addition and integration of different partial differential equation (PDE) solvers in a self-consistent manner. As to the numerical methods, the Scharfetter–Gummel scheme is adopted to handle the drift-diffusion flux of electrons, whereas the Harten–Lax-van Leer (HLL)-type approximate Riemann solver is used to handle the convection terms of ion momentum equations. For discretization of the diffusion terms in an unstructured grid, the Taylor expansion is used to deal with the effects of nonorthogonality of the cells, and the cell-center gradient is calculated using a least-squares method. The simulation code with a local-field approximation (LFA) was validated for two cases of AP plasmas as well as a case of an argon capacitively coupled plasma generated in a Gaseous Electronic Conference (GEC) reference cell with local mean energy approximation (LMEA) at intermediate low pressure. The simulation results were found to be in good agreement with the previously published experimental and simulation data.

Monte Carlo modeling of radio-frequency breakdown in argon

This paper contains results of the detailed simulation study of the breakdown in low-pressure radio-frequency (RF) argon discharges. Calculations were performed by using a Monte Carlo code including electrons only, with the assumption that the influence of heavy particles was negligible. The obtained results are in a good qualitative agreement with the available experimental data and clearly show the multivalued nature of the left-hand branches of the breakdown voltage curves. The physical processes defining the breakdown conditions were analyzed based on the spatial profiles of electron density, local mean energy and the number of elastic and ionization collisions. Under the conditions where two breakdown values existed one could identify two regimes and two different balances between the electron losses and production. Using the dependence of the breakdown voltage on the product of the pressure and the interelectrode distance, and the product of the frequency and the interelectrode distance, similarity laws for RF breakdown have been reexamined.

Investigation of surface boundary conditions for continuum modeling of RF plasmas

This work was motivated by a lacking general consensus in the exact form of the boundary conditions (BCs) required on the solid surfaces for the continuum modeling of Radiofrequency (RF) plasmas. Various kinds of number and energy density BCs on solid surfaces were surveyed, and how they interacted with the electric potential BC to affect the plasma was examined in two fundamental RF plasma reactor configurations. A second-order local mean energy approximation with equations governing the electron and ion number densities and the electron energy density was used to model the plasmas. Zero densities and various combinations of drift, diffusion, and thermal fluxes were considered to set up BCs. It was shown that the choice of BC can have a significant impact on the sheath and bulk plasma. The thermal and diffusion fluxes to the surface were found to be important. A pure drift BC for dielectric walls failed to produce a sheath.

Plasma fluid modeling of microwave streamers: Approximations and accuracy

Fluid models of microwave streamers at 110 GHz in atmospheric pressure air predict the formation of filamentary plasma patterns that show a good qualitative agreement with experiments. In order to perform more quantitative comparisons with experiments, in this paper, we study the consequences of different types of approximations that are generally used in the fluid models. We consider here the streamer dynamics before gas heating effects become important, i.e., the first few tens of ns after breakdown at atmospheric pressure. The influence on the results of the local effective field approximation vs. the local mean energy approximation is analyzed in detail. Other approximations that are related to the choice and method of calculation of electron transport parameters are also discussed. It is shown that the local effective field approximation is rather good for a large range of conditions of high frequency breakdown at atmospheric pressure in air while the results may be very sensitive to the choice of transport coefficients.

Rarefied gas electro jet (RGEJ) micro-thruster for space propulsion

This article numerically investigates a micro-thruster for small satellites which utilizes plasma actuators to heat and accelerate the flow in a micro-channel with rarefied gas in the slip flow regime. The inlet plenum condition is considered at 1 Torr with flow discharging to near vacuum conditions (<0.05 Torr). The Knudsen numbers at the inlet and exit planes are ~0.01 and ~0.1, respectively. Although several studies have been performed in micro-hallow cathode discharges at constant pressure, to our knowledge, an integrated study of the glow discharge physics and resulting fluid flow of a plasma thruster under these low pressure and low Knudsen number conditions is yet to be reported. Numerical simulations of the charge distribution due to gas ionization processes and the resulting rarefied gas flow are performed using an in-house code. The mass flow rate, thrust, specific impulse, power consumption and the thrust effectiveness of the thruster are predicted based on these results. The ionized gas is modelled using local mean energy approximation. An electrically induced body force and a thermal heating source are calculated based on the space separated charge distribution and the ion Joule heating, respectively. The rarefied gas flow with these electric force and heating source is modelled using density-based compressible flow equations with slip flow boundary conditions. The results show that a significant improvement of specific impulse can be achieved over highly optimized cold gas thrusters using the same propellant.

Unified fluid model analysis and benchmark study for electron transport in gas and liquid analogs

The interaction of plasmas with liquids requires an understanding of charged particle transport in both the gaseous and liquid phases. In this study we present a generalized fluid-equation framework to describe bulk electron transport in both gaseous and non-polar liquid environments under non-hydrodynamic non-equilibrium conditions. The framework includes liquid structural effects through appropriate inclusion of coherent scattering effects and adaption of swarm data to account for the modification to the scattering environment present in such systems. In the limit of low-densities it reduces to the traditional gas-phase fluid-equation model. Using a higher-order fluid model (four moments), it is shown that by applying steady state electron swarm data in both the gaseous and liquid phases, to close the system of equations and evaluate collisional rates, an improvement in macroscopic electron transport results over popular existing assumptions used. The failure of the local mean energy approximation in fluid models to accurately describe complex spatial oscillatory structures in both the gaseous and liquid phases is discussed in terms of the spatial variation of the electron distribution function itself.

Numerical study of low pressure air plasma in an actuated channel

A model for air plasma discharge based on drift-diffusion with local mean energy approximation is described. The model consists of 7 species and 18 reactions. The code is benchmarked with experimental and numerical results for low pressure glow discharge in a cylindrical tube. The code is used to simulate the discharge produced by a wire placed in a rectangular channel with grounded electrodes at the top and bottom walls. The discharge is concentrated near the wire. The actuator acts on the neutral gas through a body force and Joule heating. Around 80%–90% of the electrical power is converted to Joule heating of the neutral gas and the wall. The actuator produces a body force on the order of 0.1 mN/m. The effectiveness of the actuator increases from 100 to 300 V, and plateaus from 300 to 600 V. The results of the study suggest a further exploration of the channel concept.

Measurement of complex acoustic intensity in an acoustic waveguide

Acoustic intensity is normally treated as a real quantity, but in recent years, many articles have appeared in which intensity is treated as a complex quantity where the real (active) part is related to local mean energy flow and the imaginary (reactive) part to local oscillatory transport of energy. This offers the potential to recover additional information about a sound field and then to relate this to the properties of the sound source and the environment that surrounds it. However, this approach is applicable only to multi-modal sound fields, which places significant demands on the accuracy of the intensity measurements. Accordingly, this article investigates the accuracy of complex intensity measurements obtained using a tri-axial Microflown intensity probe by comparing measurement and prediction for sound propagation in an open flanged pipe. Under plane wave conditions, comparison between prediction and experiment reveals good agreement, but when a higher order mode is present, the reactive intensity field becomes complicated and agreement is less successful. It is concluded that the potential application of complex intensity as a diagnostic tool is limited by difficulties in measuring reactive intensity in complex sound fields when using current state of the art acoustic instrumentation.

High-order fluid model for streamer discharges: I. Derivation of model and transport data

Streamer discharges pose basic problems in plasma physics, as they are very transient, far from equilibrium and have high ionization density gradients; they appear in diverse areas of science and technology. This paper focuses on the derivation of a high-order fluid model for streamers. Using momentum transfer theory, the fluid equations are obtained as velocity moments of the Boltzmann equation; they are closed in the local mean energy approximation and coupled to the Poisson equation for the space charge generated electric field. The high-order tensor in the energy flux equation is approximated by the product of two lower order moments to close the system. The average collision frequencies for momentum and energy transfer in elastic and inelastic collisions for electrons in molecular nitrogen are calculated from a multi-term Boltzmann equation solution. We then discuss, in particular, (1) the correct implementation of transport data in streamer models; (2) the accuracy of the two-term approximation for solving Boltzmann's equation in the context of streamer studies; and (3) the evaluation of the mean-energy-dependent collision rates for electrons required as an input in the high-order fluid model. In the second paper in this sequence, we will discuss the solutions of the high-order fluid model for streamers, based on model and input data derived in this paper.

Local electron mean energy profile of positive primary streamer discharge with pin-plate electrodes in oxygen—nitrogen mixtures

Local electron mean energy (LEME) has a direct effect on the rates of collisional ionization of molecules and atoms by electrons. Electron-impact ionization plays an important role and is the main process for the production of charged particles in a primary streamer discharge. Detailed research on the LEME profile in a primary streamer discharge is extremely important for a comprehensive understanding of the local physical mechanism of a streamer. In this study, the LEME profile of the primary streamer discharge in oxygen-nitrogen mixtures with a pin-plate gap of 0.5 cm under an impulse voltage is investigated using a fluid model. The fluid model includes the electron mean energy density equation, as well as continuity equations for electrons and ions and Poisson's electric field equation. The study finds that, except in the initial stage of the primary streamer, the LEME in the primary streamer tip tends to increase as the oxygen-nitrogen mole ratio increases and the pressure decreases. When the primary streamer bridges the gap, the LEME in the primary streamer channel is smaller than the first ionization energies of oxygen and nitrogen. The LEME in the primary streamer channel then decreases as the oxygen-nitrogen mole ratio increases and the pressure increases. The LEME in the primary streamer tip is primarily dependent on the reduced electric field with mole ratios of oxygen-nitrogen given in the oxygen-nitrogen mixtures.

Complex intensity in circular ducts containing an obstruction

Sound intensity may be defined as a complex quantity in which the real part of the intensity is related to the magnitude of the local mean energy flow, and the imaginary part to the local oscillatory transport of energy. By treating intensity as a complex quantity it is possible to visualise energy flow in a different way and this has the potential to aid in the interpretation of, say, sound fields scattered by objects. Accordingly, the sound field scattered by an object placed in a semi-infinite circular duct is examined here. Experimental measurements of complex intensity are obtained in three (orthogonal) directions using a Microflown intensity probe, and measurements are compared to predictions obtained using a finite element based theoretical model. Comparisons between prediction and measurement are undertaken for both plane wave and multi-modal sound fields and here it is noted that when at least one higher order mode propagates it becomes more difficult to obtain good agreement between prediction and experiment for the complex intensity.