Species Continuity Equations Research Articles

MHD nonlinear natural convection from a uniformly moving porous vertical plate with constant heat and mass flux in the presence of thermal radiation, diffusion‐thermo, heat sink, and chemical reaction

AbstractAn attempt has been made to investigate the problem of nonlinear free convection heat and mass transfer flow past an infinite vertical porous plate embedded in a porous medium by taking into account thermal radiation and heat sink with constant heat and mass flux. Transversely oriented and of uniform strength , a magnetic field has been introduced to the fluid area. The nonlinear density variation with temperature as well as concentration are the basis for the current physical situation, which is explained by this mathematical model. Exact solutions are derived for momentum equation, energy equation, and species continuity equation under the relevant boundary conditions. The dimensionless governing equations are analytically solved. The influence of various physical parameters, such as Dufour number, Schmidt number, thermal Grashof number, magnetic parameter, mass Grashof number, heat sink, thermal radiation, Prandtl number, chemical reaction parameter on the flow, and transport characteristic, has been presented graphically and in tabular form. The novelty of the present investigation is that here both constant heat and mass flux at the plate are taken into account in addition to thermal radiation and heat sink. The findings of the mathematical study demonstrate that velocity, temperature, and skin friction intensify with a rise in the Dufour number this is due to the fact that the convection current becomes stronger as the Dufour number rises. Fluid's concentration declines as the Schmidt number grows, or the concentration rises as the mass diffusivity rises. Fluid temperature is enhanced with high thermal diffusivity. Frictional resistance on the plate hikes due to thermal buoyancy force.

A fluid model of pulsed direct current planar magnetron discharge

We simulated a pulsed direct current (DC) planar magnetron discharge using fluid model, solving for species continuity, momentum, and energy transfer equations, coupled with Poisson equation and Lorentz force for electromagnetism. Based on a validated DC magnetron model, an asymmetric bipolar potential waveform is applied at the cathode at 50–200 kHz frequency and 50–80% duty cycle. Our results show that pulsing leads to increased electron density and electron temperature, but decreased deposition rate over non-pulsed DC magnetron, trends consistent with those reported by experimental studies. Increasing pulse frequency increases electron temperature but reduces the electron density and deposition rate, whereas increasing duty cycle decreases both electron temperature and density but increases deposition rate. We found that the time-averaged electron density scales inversely with the frequency, and time-averaged discharge voltage magnitude scales with the duty cycle. Our results are readily applicable to modulated pulse power magnetron sputtering and can be extended to alternating current (AC) reactive sputtering processes.

Experimental and simulated investigation of microdischarge characteristics in a pin-to-pin dielectric barrier discharge (DBD) reactor

Both experimental and simulated studies of microdischarge (MD) are carried out in a dielectric barrier discharge with a pin-to-pin gap of 3.5 mm, ignited by a sinusoidal voltage with a peak voltage of 10 kV and a driving frequency of 5 kHz. Statistical results have shown that the probability of the single current pulse in the positive half-period (HP) reaches 73.6% under these conditions. Experimental results show that great luminous intensity is concentrated on the dielectric surface and the tip of the metal electrode. A 1D plasma fluid model is implemented by coupling the species continuity equations, electron energy density equations, Poisson equation, and Helmholtz equations to analyze the MD dynamics on the microscale. The simulated results are in good qualitative agreement with the experimental results. The simulated results show that the MD dynamics can be divided into three phases: the Townsend phase, the streamer propagation phase, and the discharge decay phase. During the streamer propagation phase, the electric field and electron density increase with the streamer propagation from the anode to the cathode, and their maximal values reach 625.48 Td and 2.31 × 1019 m−3, as well as 790.13 Td and 3.58 × 1019 m−3 in the positive and negative HP, respectively. Furthermore, a transient glow-like discharge is detected around the anode during the same period of streamer propagation. The formation of transient glow-like discharge is attributed to electrons drifting back to the anode, which is driven by the residual voltage in the air gap.

Numerical solution of a comprehensive form of convection–diffusion equation for binary isotopes in the gas centrifuge

Improving the separation performance of the gas centrifuge can be a practical step in reducing enrichment costs. For this purpose, it is necessary to accomplish a reliable convection–diffusion equation to predict the separation characteristics of the gas centrifuge. In this paper, to the best of our knowledge, the species continuity equation is derived in the possible complete form and then solved with the finite volume method for a model rotor. The solution method was confirmed to verify the present study by comparing concentration distribution with other research. Next, the derived convection–diffusion equation is compared with the simplified assumptions equations. The result shows that the assumption of pressure distribution of rigid body rotation leads to a positive deviation of up to twice in separative power. The difference in separation power accounting for constant temperature and ignoring the axial changes of pressure is about 10%. Also, this assumption leads to the ascending-descending trend, which can be influential in determining the optimal conditions of operational parameters such as scoop drag force.

Surface heat flux analysis for opposing jet and combination techniques in the presence of real gas effect

High surface heating is common problem during high speed flights, so it should be properly mitigated for the efficient design of long duration flights. Most of the studies available in the literature are carried out without considering the chemical kinetics of the incoming freestream flow. Hence the current study invokes the thermal non-equilibrium effect (specific heats variation with temperature) and chemical non-equilibrium effect (species continuity equations) on surface heat flux study for the flow over blunt body considering real gas reactions by means of in house developed reacting and perfect gas solvers. Results reveal that surface heat flux reduces with the application of opposing jet and it further reduces for higher pressure ratio of jet. Introduction of cavity reduces the Stanton number but it enhances the drag force on body. Reacting solver gives higher surface heat flux than perfect solver and this difference is larger at low freestream stagnation enthalpy.

A high-power impulse magnetron sputtering global model for argon plasma–chromium target interactions

A high power impulse magnetron sputtering (HiPIMS) discharge process is analyzed numerically and experimentally so that one may better understand and explain the effect of the pressure and pulse width on HiPIMS discharges and the deposited thin films. For this reason, a time-dependent global plasma model is developed for the ionization region in a HiPIMS discharge of a Cr target in Ar gas. It is based on the solving of a nonlinear equation system composed of the continuity equations of neutral and charged species in the ionization region considered in the reaction scheme. The pulse widths are about tens of microseconds for a frequency cycle of 1 KHz. The simulations are performed for a 150 W average power and 5–30 mTorr pressure range. In these average power and pressure ranges, a double peak of the electron temperature is observed. The high first peak is due to a high rapid increase of negative voltage during the rising time of pulses, while the second one is due to a diminution of the injected gas Ar in the ionization region. On the other hand, gas rarefaction characterized by the diminution of the Ar density during time-on is due to the high ionization degree and the sputtering wind effect. During plasma off, the density of Ar returns to the stationary state corresponding to the initial pressure. In addition, the simulations reveal that the Cr+ population is more important than that of Ar+ caused by the high ionization degree of Cr compared with Ar. This confirms the high ionization degree during time-on, leading to a high efficiency of sputtering of Cr material. However, Cr2+ is still weak. In addition, a good agreement is shown between the calculated time current evolution and the measured one.

On the Effects of Mesospheric and Lower Thermospheric Oxygen Chemistry on the Thermosphere and Ionosphere Semiannual Oscillation

AbstractThis study quantifies mesosphere/lower thermosphere (MLT) oxygen chemical contributions to the global thermosphere‐ionosphere (T‐I) semiannual oscillation (SAO) using a series of numerical experiments from the National Center for Atmospheric Research (NCAR) thermosphere‐ionosphere‐mesosphere‐electrodynamics general circulation model (TIME‐GCM) that isolate essential chemical processes affecting O and O2 in the MLT region. We track the vertical dynamical, diffusive, and chemical fluxes of O and O2 in and out of two control volumes between ∼80 and 130 km using a finite volume approach to the individual species continuity equation to investigate their relative importance on the global T‐I SAO. TIME‐GCM results indicate that the global T‐I SAO amplitude and phase is fairly insensitive to significant changes in odd oxygen chemical reaction rates in the MLT. While chemistry has an appreciable effect on O in the MLT region, sensitivity to changes in odd oxygen and odd hydrogen chemical rates appear to be offset by a consequent adjustment in the vertical bulk wind and eddy diffusive transport of O locally, rendering their effects inconsequential to the global T‐I SAO aloft. The implications of our findings for reproducing a self‐consistent global T‐I SAO in the NCAR thermosphere‐ionosphere‐electrodynamics general circulation model (TIE‐GCM) with a lower boundary near ∼100 km are discussed. Specifically, including latitude‐season variations in O, O2, and N2 from NRLMSIS® 2.0 at the lower boundary of the TIE‐GCM near ∼100 km improves its representation of the climatological T‐I SAO. However, reformulating the TIE‐GCM temperature lower boundary condition could further improve its ability to simulate the T‐I SAO from first‐principles.

Modeling of H2 Permeation through Electroless Pore-Plated Composite Pd Membranes Using Computational Fluid Dynamics.

This work focused on the computational fluid dynamics (CFD) modeling of H2/N2 separation in a membrane permeator module containing a supported dense Pd-based membrane that was prepared using electroless pore-plating (ELP-PP). An easy-to-implement model was developed based on a source–sink pair formulation of the species transport and continuity equations. The model also included the Darcy–Forcheimer formulation for modeling the porous stainless steel (PSS) membrane support and Sieverts’ law for computing the H2 permeation flow through the dense palladium film. Two different reactor configurations were studied, which involved varying the hydrogen flow permeation direction (in–out or out–in). A wide range of experimental data was simulated by considering the impact of the operating conditions on the H2 separation, such as the feed pressure and the H2 concentration in the inlet stream. Simulations of the membrane permeator device showed an excellent agreement between the predicted and experimental data (measured as permeate and retentate flows and H2 separation). Molar fraction profiles inside the permeator device for both configurations showed that concentration polarization near the membrane surface was not a limit for the hydrogen permeation but could be useful information for membrane reactor design, as it showed the optimal length of the reactor.

Benchmark of the KGMf with a coupled Boltzmann equation solver

The Kinetic Global Model framework (KGMf) is an open-source general-purpose global model (spatially averaged) simulation code developed to explore the reaction kinetics and pathways in plasma discharge systems. It contains species continuity and electron energy balance equations, with a time-dependent evaluated electron energy distribution function (EEDF) for electron impact reactions. The EEDF is utilized to determine the rate coefficients for electron impact reactions, which can have profound impact on the temporal evolutions of plasma parameters. Previously, the EEDF was commonly assumed as Maxwellian or an analytical function of the effective electron temperature. In this work, the KGMf is coupled with a Boltzmann equation (BE) solver to self-consistently compute the EEDF. The EEDF evolution frequency is determined based on relative changes of the reduced electric field. The KGMf is benchmarked with the ZDPlasKin code based on high-pressure low-temperature argon plasma discharge cases. The temporal evolutions of reduced electric field, electron temperature, EEDF, reaction rates, and species densities, are obtained and compared under different discharge conditions, showing good agreement between the KGMf and the ZDPlasKin simulations. The application of the KGMf for predicting breakdown times in high power microwave discharges is also presented, which shows qualitative agreement with particle-in-cell simulations. The KGMf can be further applied for more complicated plasma discharge systems, where the reaction kinetics are more intricate (e.g., plasma-assisted combustion systems).

Dynamics and combustion of single aluminium agglomerate in solid propellant environment

Aluminized composite propellant used in solid rocket motors contain a lot of aluminium particles because high combustion energy is generated and propulsion efficiency increases by burning aluminium particles. The combustion of aluminum occurs in a significant portion of the combustion chamber and produces aluminum oxide smokes and residues that are carried into the flowfield. Agglomerates have non-spherical shape, and consist of aluminium droplet and oxide particle (oxide cap) attached to the droplet. Unlike the liquid droplet ignition, the solid oxide film blocks the liquid aluminum from the penetration of the oxidizer hence prevents the particle from its ignition. Development of robust models of aluminum particle dynamics is essential in the design of advanced propulsion systems. The mathematical model of two-phase flow around a single aluminum droplet with oxide cap is developed. The model solves the continuity, momentum, energy and species continuity equations simultaneously to obtain the species and temperature profiles and the burning time of droplet. The results of numerical simulations are compared with predictions from semi-empirical correlations and computational data.

Development of a semi-empirical 1.5D plasma fluid model for a single microdischarge in atmospheric pressure dielectric barrier discharges

In this work, a semi-empirical 1.5D plasma fluid model (PFM) is proposed to model a single microdischarge (MD) in atmospheric pressure air dielectric barrier discharges (APADBDs). The species continuity equations and the electron energy density equation are solved in one-dimensional domain, while the Poisson equation is solved in the axisymmetric domain to capture the enhancement of the electric field in front of the streamer. The framework of air chemistry is considered and the effect of photoionization is modeled in the axisymmetric domain. The accumulation factor (AF) is introduced and determined by experimental data to model the accumulation of charged particles on the dielectric surface. The simulated results in two gaps are compared with experimental measurements. In the gap of 1.4 mm, the simulated electric current reaches 72 mA, which is close to the typically measured electric current. The simulated maximum wave velocity is around 1.7 × 106 m s−1, which is close to the available experimental data. The change of simulated charge density implies that the average accumulation of charged particles on the dielectric surface during each half period (HP) is around 40 nC cm−2, which is in the same order of magnitude as the average charge density evaluated in the previous measurements as 51.5 nC cm−2. The effect of AF is studied and shows that the AF determines both peak and duration of the electric current. In the gap of 2.0 mm, the simulated current reaches 113 mA, which is close to the typically measured current. Although the gap voltage of the 2.0 mm gap is higher than that of the 1.4 mm gap, the average electric field of the 2.0 mm gap is lower than that of the 1.4 mm gap before breakdown due to larger gap distance. The maximum wave velocity is faster than that simulated in the gap of 1.4 mm due to the longer gap distance for developing higher wave velocity as 2.4 × 106 m s−1. During each HP, the average accumulation of charge density on the dielectric surface reaches around 40 nC cm−2 which is almost identical to that simulated in the gap of 1.4 mm as observed experimentally. In general, the proposed semi-empirical 1.5D PFM captures the dynamics of a single MD in APADBDs.

나노세컨드 펄스 DBD 플라즈마의 멀티스케일 모델링을 위한 비평형 플라즈마 유동 해석 및 검증

In a nanosecond pulse discharge, the computational cost is high because of the characteristic time difference between the plasma and the flow. In order to reduce the computational cost, multi-scale modeling study of nanosecond pulse discharge plasma is needed. In this study, we developed and verified a non-equilibrium plasma solver for nanosecond-pulse Dielectric Barrier Discharge(NS-DBD) multi-scale modeling study. To simulate the non-equilibrium phenomena, 17 chemical species / 54 chemistry reaction models were used. The governing equations included chemical species continuity equations, a electrical potential equation, and Navier-Stokes equations. Numerical results show that streamer velocity and micro shock wave speed are comparable to those of other experimental results. This study is expected to contribute to the future study of NS-DBD multi-scale modeling.

Effect of Dimethyl Ether as an Additive to Liquefied Petroleum Gas Flame in SiC–Al2O3-Based Porous Inert Burner

To establish the applicability of dimethyl ether (DME-CH3OCH3) as an alternative fuel additive to liquefied petroleum gas (LPG: 48% n-C4H10, 25% i-C4H10, 23% C3H10, 4% C2H6) for enhancing combustion and reducing hazardous emissions, in this article, the flame behavior of LPG–air mixture blended with DME is studied within a highly conducting and radiating porous inert burner (PIB) under excess enthalpy combustion conditions. The experiments are performed in a two-section PIB comprising a silicon carbide (SiC) matrix and aluminum oxide (Al2O3) balls. The numerical model for solving the species continuity equation, energy balance equations for gas and solid phases, and the mass conservation equation is compared to the experimental data from the present work. New filtration velocity data are found for the stable combustion of LPG–DME–air mixtures inside the PIB. The effect of various DME volume fractions in the LPG–DME blends on temperature distribution, radical pool concentration, CO emission, reaction zone thickness, and syngas production within the PIB are investigated. The results show that with the addition of DME the peak radical pool concentration increases, which enhances the filtration velocity and thus the operating limit of the PIB. It is further demonstrated that at the same input conditions, the solid-phase temperature and preheating temperature of the PIB are greater for the higher value of DME volume fraction. Contrary to previous findings, increasing the DME level increases the peak mole fraction of CO, CH4, and CH3CHO; however, it decreases the equilibrium CO concentration. Furthermore, in the case of a pure DME flame, an order of magnitude decrease in C2H2, C3H3, and C6H6 is observed; however, the flame with higher DME fraction generates more CH2O and CH3.

Numerical study of the effect of the needle tip radius on the characteristics of Trichel pulses in negative corona discharges

This paper presents a numerical study of the impact of the needle tip radius on the electrical characteristics of Trichel pulses in negative corona discharges for a needle-plane configuration in atmospheric air. The radius of curvature of the needle tip varies from 20 μm to 45 μm. The first current pulse, subsequent pulse train is discussed here based on the distributions of charged species and electric field. Three species continuity equations along with Poisson's equation are solved by the hydrodynamic drift-diffusion approach, in which the role of photoionization is considered. The increasing needle tip radius reduces the peak of the first pulse significantly and delays the start of the first pulse, but almost keeps the duration of the first pulse constant. At the instant of the first pulse peak, both the magnitude of the charged species densities and the electric field decrease with the needle tip radius, and the electric field is strongly distorted by the space charge field. For the subsequent current pulses, the current magnitude is weakly related to the needle tip radius, whereas the pulse period is proportional to the needle tip radius. The increasing needle tip radius reduces the positive ion and electron densities but increases the negative ion density at the instant of the current pulse peak, which diminishes the difference of the electric field for different needle tip radii.

Solvent‐induced crystal formation in polymers: Experimental studies and theoretical modeling of poly(vinyl alcohol) based on free‐volume concepts

ABSTRACTA model has been developed to describe the simultaneous diffusion and solvent‐induced crystal formation in polymers based on the idea that crystal formation is governed by polymer chain mobility and a thermodynamic driving force. The polymer chain mobility is described based on solvent and polymer physical characteristics using the free‐volume theory of transport. The semicrystalline polymer‐solvent system is treated as a ternary system consisting of crystalline polymer, amorphous polymer, and solvent. The addition of solvent to the amorphous phase is assumed to increase the local free volume and facilitate movement of polymer chains, thereby enabling crystal formation. Diffusion of the solvent is assumed to occur solely in the amorphous polymer phase. The species continuity equations are formulated in volume‐averaged coordinates and give rise to a convective term due to the density change accompanying transformation of the amorphous polymer to the crystalline polymer. Accurate modeling of this problem requires that a moving boundary be considered. The model was tested using gravimetric sorption data for the poly(vinyl alcohol)‐water system. In the experimental studies, the water was initially absorbed and then a high percentage of it was expelled. The proposed model accurately describes this behavior. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017, 134, 45171.

A hierarchy of transport models motivated by studies of the Stefan tube

Motivated by studies of the diffusion of a gas mixture in a Stefan tube, we present a hierarchy of mass transfer models with the species momentum balance and the species continuity equations as the basis. The simplifying conditions and the constitutive equations that lead to the equations of the mixture momentum balance approach are obtained. Further, the form that these equations should take for a multicomponent mixture is derived. These equations are shown to be a generalization of the Meyer–Kostin equations used to study binary diffusion in a Stefan tube. Additional simplifications that result in the so called classic approach to diffusion are identified.

Dynamic Characteristics of Positive Pulsed Dielectric Barrier Discharge for Ozone Generation in Air**supported by National Natural Science Foundation of China (Nos. 51366012 and 11105067), Jiangxi Province Young Scientists (Jinggang Star) Cultivation Plan of China (No. 20133BCB23008), Natural Science Foundation of Jiangxi, China (No. 20151BAB206047) and Jiangxi Province Higher School Science and Technology Landing Plan of China (No. KJLD-14015)

A comprehensive dynamic model consisting of 66 reactions and 24 species is developed to investigate the dynamic characteristics of ozone generation by positive pulsed dielectric barrier discharge (DBD) using parallel-plate reactor in air. The electron energy conservation equation is coupled to the electron continuity equation, the heavy species continuity equation, and Poisson's equation for a better description. The reliability of the model is experimentally confirmed. The model can be used to predict the temporal and spatial evolution of species, as well as streamer propagation. The simulation results show that electron density increases nearly exponentially in the direction to the anode at the electron avalanche. Streamer propagation velocity is about 5.26 × 104 m/s from anode to cathode in the simulated condition. The primary positive ion, negative ion, and excited species are O2+, O3− and O2(1Δg) in pulsed DBD in air, respectively. N2O has the largest density among nitrogen oxides. e and N2+ densities in the streamer head increase gradually to maximum values with the development of the streamer. Meanwhile, the O2+, O, O3, N2(A3Σ) and N2O densities reach maximum values in the vicinity of the anode.

A numerical study of species and electric field distributions in pulsed DBD in oxygen for ozone generation

A numerical model including 29 reactions and 11 species is developed to investigate the spatial-temporal distributions of species and electric field in oxygen parallel-plate positive pulsed dielectric barrier discharge for ozone generation. Electron energy conservation equation is coupled to electron continuity equation, heavy species continuity equation and Poisson's equation. The spatial-temporal distributions of species and electric field are obtained at electron avalanche and during streamer propagation. The results show the dominant positive ion, negative ion and excited species are O2+, O3− and O2(∑g+1), respectively. The average streamer propagation velocity is about 5.56 × 104 m/s. Overall electron density almost increases exponentially but with a violent oscillation in the vicinity of anode at electron avalanche. Electron density increases at first and then declines in the vicinity of anode and streamer channel during streamer propagation, and increases gradually in streamer head with the development of streamer, as well as reduces sharply to almost zero near cathode. Electron density almost remains constant in whole streamer channel at any one moment. Other species have a similar spatial-temporal distribution.

Verification of a Chemical Nonequilibrium Flows Solver Using the Method of Manufactured Solutions

This paper presents code verification of a chemically nonequilibrium flows solver using the method of manufacturedsolutions.The Method of Manufactured Solutions(MMS) is a general approach for creating exact solutions to the governing equations and can be used in the code verification process. In the MMS, the analytical solutions for the flow variables are first constructed, then the governing equations are modified to satisfy these solutions by adding appropriate source terms which are generated by applying the governing equations to these solutions. After that, code verification process will start. The order of accuracy of the calculations will be computed and compared with theoretical order of accuracy to determine if the code passes the verification test. We created manufactured solutions for two different sets of Euler equations. One set includes the total density equation plus ns-1 species equations and the other contains only species continuity equations. The results show that the form of continuity equations has little influence on the behaviour of global conservative variable errors as the mesh is refined. Our study also indicates that a complete chemical reaction model is preferred to ensure the convergence of observed order of accuracy is smooth in the order of accuracy test.

Physics of Supersonic Mixing in Parallel and Non-Parallel Streams Passing Over Base Thickness

The mixing flow field of two-parallel and non parallel gaseous streams has been studied numerically. The streams are of air and hydrogen and come into contact after passing over a finite thickness base. The two gas streams are delivered from a high-pressure reservoir and entering into the domain with atmospheric pressure. The two-dimensional unsteady Navier-Stokes equations, energy, mass diffusion and species continuity equations are numerically simulated to analyze the mixing layer in supersonic flow field. An explicit Harten-Yee Non-MUSCL Modified flux-type TVD (total variation diminishing) scheme is used to solve the system of equations. An algebraic turbulence model is used to calculate the eddy viscosity coefficient. Keeping constant the inlet pressure and velocity of the streams, the merging angle is varied to observe the physics of flow fields, mixing of two-streams and mixing efficiency. The results show that the increase of merging angle causes stronger interactions between two streams, high momentum exchange and eventually enhancement of mixing between two streams.