Mass Fraction Gradient Research Articles

Density-driven transport of gas phase chemicals in unsaturated soils

Variations of gas phase density are responsible for advective and diffusive transports of organic vapors in unsaturated soils. Laboratory experiments were conducted to explore dense gas transport (sulfur hexafluoride, SF6) from different source densities through a nitrogen gas-dry soil column. Gas pressures and SF6 densities at transient state were measured along the soil column for three transport configurations (horizontal, vertically upward and vertically downward transport). These measurements and others reported in the literature were compared with simulation results obtained from two models based on different diffusion approaches: the dusty gas model (DGM) equations and a Fickian-type molar fraction-based diffusion expression. The results show that the DGM and Fickian-based models predicted similar dense gas density profiles which matched the measured data well for horizontal transport of dense gas at low to high source densities, despite the pressure variations predicted in the soil column were opposite to the measurements. The pressure evolutions predicted by both models were in trend similar to the measured ones for vertical transport of dense gas. However, differences between the dense gas densities predicted by the DGM and Fickian-based models were discernible for vertically upward transport of dense gas even at low source densities, as the DGM-based predictions matched the measured data better than the Fickian results did. For vertically downward transport, the dense gas densities predicted by both models were not greatly different from our experimental measurements, but substantially greater than the observations obtained from the literature, especially at high source densities. Further research will be necessary for exploring factors affecting downward transport of dense gas in soil columns. Use of the measured data to compute flux components of SF6 showed that the magnitudes of diffusive flux component based on the Fickian-type diffusion expressions in terms of molar concentration, molar fraction and mass density fraction gradient were almost the same. However, they were greater than the result computed with the mass fraction gradient for >24% and the DGM-based result for more than one time. As a consequence, the DGM-based total flux of SF6 was in magnitude greatly less than the Fickian result not only for horizontal transport (diffusion-dominating) but also for vertical transport (advection and diffusion) of dense gas. Particularly, the Fickian-based total flux was more than two times in magnitude as much as the DGM result for vertically upward transport of dense gas.

Numerical Study of the Dynamic Response of Heat and Mass Transfer to Operation Mode Switching of a Unitized Regenerative Fuel Cell

Knowledge concerning the complicated changes of mass and heat transfer is desired to improve the performance and durability of unitized regenerative fuel cells (URFCs). In this study, a transient, non-isothermal, single-phase, and multi-physics mathematical model for a URFC based on the proton exchange membrane is generated to investigate transient responses in the process of operation mode switching from fuel cell (FC) to electrolysis cell (EC). Various heat generation mechanisms, including Joule heat, reaction heat, and the heat attributed to activation polarizations, have been considered in the transient model coupled with electrochemical reaction and mass transfer in porous electrodes. The polarization curves of the steady-state models are validated by experimental data in the literatures. Numerical results reveal that current density, gas mass fractions, and temperature suddenly change with the sudden change of operating voltage in the mode switching process. The response time of temperature is longer than that of current density and gas mass fractions. In both FC and EC modes, the cell temperature and gradient of gas mass fraction in the oxygen side are larger than that in the hydrogen side. The temperature difference of the entire cell is less than 1.5 K. The highest temperature appears at oxygen-side catalyst layer under the FC mode and at membrane under a more stable EC mode. The cell is exothermic all the time. These dynamic responses and phenomena have important implications for heat analysis and provide proven guidelines for the improvement of URFCs mode switching.

Simulation of inhalable aerosol particle distribution generated from cooking by Eulerian approach with RNG k–epsilon turbulence model and pollution exposure in a residential kitchen space

Cooking-generated fume contains large amounts of fine particle pollutants with high concentration. To study the influence of the aerosol particle pollutant in kitchen, a typical format of residential kitchen in northern China is selected in this paper. FLUENT software is applied to simulate interior space airflow as well as pollutant mass fraction in breathing-section and cooking-section area in the residential kitchen under different vent cases. Furthermore, occupant’s exposure to inhalable aerosol particle is obtained integrated with human inhale model and pollution exposure calculation model. The results demonstrate that cooking side of respiratory region in pollutant mass fraction can be significantly reduced when opening the door, but mass fraction gradient is larger in the vicinity of the stove. The average pollution exposure in the maximum value is about 90 times than that of the minimum value around the cooking personnel with the most adverse conditions in winter when the doors and windows are all closed. The research output can provide valuable reference for the further study on fine particles concentration level as well as to determine individual intake fraction of particles generated in the process of cooking in the residential kitchen.

Thermal gravitational separation of ternary mixture n-dodecane/isobutylbenzene/tetralin components in a porous medium.

Our present work focuses on the coupling between thermal diffusion and convection in order to improve the thermal gravitational separation of mixture components. The separation phenomenon was studied in a porous medium contained in vertical columns. We performed analytical and numerical simulations to corroborate the experimental measurements of the thermal diffusion coefficients of ternary mixture n-dodecane, isobutylbenzene, and tetralin obtained in microgravity in the international space station. Our approach corroborates the existing data published in the literature. The authors show that it is possible to quantify and to optimize the species separation for ternary mixtures. The authors checked, for ternary mixtures, the validity of the "forgotten effect hypothesis" established for binary mixtures by Furry, Jones, and Onsager. Two complete and different analytical resolution methods were used in order to describe the separation in terms of Lewis numbers, the separation ratios, the cross-diffusion coefficients, and the Rayleigh number. The analytical model is based on the parallel flow approximation. In order to validate this model, a numerical simulation was performed using the finite element method. From our new approach to vertical separation columns, new relations for mass fraction gradients and the optimal Rayleigh number for each component of the ternary mixture were obtained.

Soret-driven convection and separation of binary mixtures in a horizontal porous cavity submitted to cross heat fluxes

An analytical and numerical study of Soret-driven convection in a horizontal porous layer saturated by a binary fluid and subjected to uniform cross heat fluxes is presented. The flow is driven by the combined buoyancy effect due to temperature and induced mass fraction variations through a binary water ethanol mixture. In the first part of the study, a closed-form analytical solution in the limit of a large aspect ratio of the cell (A >> 1) is developed. We are mainly concerned with the determination of the mass fraction gradient of the component of interest along the horizontal direction, which determines the species separation. In the second part, numerous numerical simulations are carried out in order to validate the analytical results and extend heat and mass transfer to an area not covered by the analytical study. Good agreement is found between analytical and numerical results concerning the species separation obtained for a unicellular flow. In this configuration, the Soret separation process is improved by two control parameters: the heat flux density imposed on the horizontal walls of the cell and the ratio, a, of heat flux density imposed on vertical walls to that on horizontal walls. The influence of the heat flux density ratio, a, on the transient regime (relaxation time) is also investigated numerically. We observe that an increase in the parameter a leads to a decrease in the relaxation time. Thus, for a cell heated from below without lateral heating, the onset of convection from the mechanical equilibrium state is analyzed. The linear stability analysis shows that the equilibrium solution loses its stability via a stationary bifurcation or a Hopf bifurcation depending on the separation ratio and the normalized porosity of the medium. The linear stability results are widely corroborated by direct 2D numerical simulations. The thresholds of various multicellular solutions are determined in terms of the governing parameters of the problem using nonlinear direct numerical simulations.

Two-Dimensional Simulation of Mass Transfer in Unitized Regenerative Fuel Cells under Operation Mode Switching

A two-dimensional, single-phase, isothermal, multicomponent, transient model is built to investigate the transport phenomena in unitized regenerative fuel cells (URFCs) under the condition of switching from the fuel cell (FC) mode to the water electrolysis (WE) mode. The model is coupled with an electrochemical reaction. The proton exchange membrane (PEM) is selected as the solid electrolyte of the URFC. The work is motivated by the need to elucidate the complex mass transfer and electrochemical process under operation mode switching in order to improve the performance of PEM URFC. A set of governing equations, including conservation of mass, momentum, species, and charge, are considered. These equations are solved by the finite element method. The simulation results indicate the distributions of hydrogen, oxygen, water mass fraction, and electrolyte potential response to the transient phenomena via saltation under operation mode switching. The hydrogen mass fraction gradients are smaller than the oxygen mass fraction gradients. The average mass fractions of the reactants (oxygen and hydrogen) and product (water) exhibit evident differences between each layer in the steady state of the FC mode. By contrast, the average mass fractions of the reactant (water) and products (oxygen and hydrogen) exhibit only slight differences between each layer in the steady state of the WE mode. Under either the FC mode or the WE mode, the duration of the transient state is only approximately 0.2 s.

Convection of Moist Saturated Air: Analytical Study

In the present work, the steady-state stationary thermal convection of moist saturated air in a lower atmosphere has been studied theoretically. Thermal convection was considered without accounting for the Coriolis force, and with only the vertical temperature gradient. The analytical solution of geophysical fluid dynamics equations, which generalizes the formulation of the moist convection problem, is obtained in the two-dimensional case. The stream function is derived in the Boussinesq approximation with velocity divergence taken as zero. It has been shown that the stream function is asymmetrical in vertical direction contrary to the dry and moist unsaturated air convection. It has been demonstrated that the convection in moist atmosphere strongly depends on the vapor mass fraction gradient.

Calculation and application of combined diffusion coefficients in thermal plasmas

The combined diffusion coefficient method is widely used to treat the mixing and demixing of different plasma gases and vapours in thermal plasmas, such as welding arcs and plasma jets. It greatly simplifies the treatment of diffusion for many gas mixtures without sacrificing accuracy. Here, three subjects that are important in the implementation of the combined diffusion coefficient method are considered. First, it is shown that different expressions for the combined diffusion coefficients, arising from different definitions for the stoichiometric coefficients that assign the electrons to the two gases, are equivalent. Second, an approach is presented for calculating certain partial differential terms in the combined temperature and pressure diffusion coefficients that can cause difficulties. Finally, a method for applying the combined diffusion coefficients in computational models, which typically require diffusion to be expressed in terms of mass fraction gradients, is given.

On the background design for microscale background-oriented schlieren measurements of microfluidic mixing

Using microfluidic mixing as the benchmark, we assess the influences of the background designs in the accuracy of the microscale background-oriented schlieren measurements in this study. Three parameters are considered, they are as follows: pattern configuration (random dot, random grid, and grid), dot diameter, and area fraction of dot coverage. A photomask covered with the defined pattern is placed on top of the microchannel to serve as the background. When miscible fluids with different refractive indices are mixed in a T-microchannel, light deflects and there are pattern shifts on the acquired image. After a calibration process is carried out to obtain the relationship between the pattern shift and gradient of mass fraction, we are able to evaluate the performance of each background design based on its corresponding uncertainty. Except for the grid configuration, we find that the lowest error level is achieved with a dot diameter of 6 μm, which corresponds to a dot-image diameter of 2.8 pixels. Because a sparse distribution leads to vacant interrogation windows, the optimal random-dot design has the highest area fraction of 0.178 (0.196 for the design value). In contrast, the random-grid design with too many dots becomes comparable to the grid design and has difficulties during the cross-correlation analysis. As a result, the best random-grid background has an area fraction of 0.098. For the grid design, on the other hand, accurate results can be obtained when there is only one dot in each interrogation window. Hence, a dot diameter of 16 μm leads to the lowest uncertainty for the grid design. Once these backgrounds are optimized, we prove that all three configurations are able to deliver satisfactory results for the reconstruction of a concentration field in a T-microchannel and an instantaneous profile of concentration gradient in a microfluidic oscillator.

Numerical Simulation of Radon Atmospheric Dynamic Diffusion from a Flat Ground Uranium Tailings Impoundment

with a flat ground uranium tailings impoundment as the object of the paper, CFD technology was used to study the atmospheric dynamic diffusion characteristics and the evolution of time and space distribution of radon in the uranium tailings impoundment. Results show that, within 1500m range of the leeward of uranium tailings impoundment the falling gradient of radon mass fraction improves with distance increases at the same moment, however the falling gradient flattens with the increase of time gradually; During the first 30 minutes, the radon mass fraction of tailings impoundment in the leeward direction has a larger growth gradient, then flattens out slowly, and stabilizes after 75 minutes.

Swirl and Cross-Flow Effects on Vitiated Jet Flames

A burner was developed to accommodate extensive limits of firing for lean and rich fuel/air mixtures via efficient vitiation of the reactive streams by a pilot premixed flame jet under swirl and cross-flow effects. The stability and combustion characteristics of the corresponding normal and inverse triple flames were addressed for vitiating a double-swirled flow through a concentric vane swirler by a pilot stream swirled due to a tangential entry. Increasing the vitiating stream heat input ratio to 0.5 increased the stability limit to eight times the laminar flame speed as the inner swirl number increased to 2.0. Increasing the cross-flow air momentum flux ratio from 1.0 to 3.0 further increased the normalized stability limit to 8.5, while employing double coswirl and triple coswirl increased such limit to respective values of 10.2 and 11.9. Vitiating a double-swirled rich fuel/air mixture stream by a tangential entry-swirled lean fuel/air mixture stream enlarged the stoichiometric zone to pronounce a peak turbulent kinetic energy of 3.5 m2/s2. Increasing the fuel mass fraction gradient increased the stability limit only with a vitiating lean mixture, while increasing the swirled portion of the vitiating stream increased the normalized stability limit to 19.6. Allocating the counterswirl across the vitiated stream was more efficient to increase the normalized stability limit to 26.7 as the relative swirl angle reached 120°. Increasing the cross-flow opposing jet strain rate enhanced the H and H2 preferential diffusion, increased the temperature homogeneity, and reduced the flame length. There was a corresponding reduction in NOx emissions to a minimum of 38 ppm as the strain rate increased to 13000 s−1, while the normalized stability limit increased to 27.3. Decreasing the longitudinal spacing between the cross-flow stages from 12.0 to 4.0 cm decreased the NOx emissions further to 18 ppm and increased the normalized stability limit to 30.5.

Alignment statistics of active and passive scalar gradients in turbulent stratified flames

The scalar gradient alignment statistics for active and passive scalar gradients (e.g., fuel mass fraction gradient and mixture fraction gradient) are presented here for turbulent stratified flames. It has been shown that, under some conditions, the active scalar gradient may align with the most extensive principal strain rate in contrast to the passive scalar gradient that remains aligned with the most compressive principal strain rate even when the active scalar gradient aligns preferentially with the most extensive principal strain rate. Physical explanations are provided for the observed behaviors.

The drying of liquid films on cylindrical and spherical substrates

The drying of liquid films from binary solid–solvent mixtures on cylindrical and spherical substrates is investigated by solving the diffusion equation on the cylindrical or spherical domains with account for the shrinkage of the systems due to the solvent evaporation. As a main result of the gas phase analysis, d 2 -laws for both the cylindrical and the spherical cases are found. The spatio-temporal evolution of the component mass fractions in the liquid are obtained for varying initial film thickness and drying conditions. Large mass fraction gradients, formed at high drying rates, lead to a skin-core morphology with low product quality. Initially very thin films dry very uniformly, which is analogous to the flat temperature profiles in unsteady heat conduction at small Biot numbers. The maximum initial film thickness allowable to ensure flat solute mass fraction profiles in the films, and thus high quality of the dry films, is computed for varying drying rates. From these results a guideline for the drying of liquid films on cylindrical and spherical substrates is deduced.

A Numerical Study of the Magnetic Influence on Coaxial Jets' Flow Upstream From Lifted Flames

The authors conducted a numerical investigation of the laminar flow issuing from a methane/air coaxial burner submitted to a magnetic field. They intend to understand the mechanisms involved in the magnetic stabilization of the lifted flames. The model is based on the coupled equations of conservation of mass, species, and momentum in which the magnetic force acting on paramagnetic oxygen is introduced in the source term. A CFD code is used to solve the steady-state equations in an axisymmetric domain. Air jet velocity is shown to decrease locally in front of the magnetic gradient. Calculation of the stoichiometric radius reveals a lateral displacement of the stoichiometric line and a decrease of the fuel mass fraction gradient when the magnetic force is applied. These results explain the observed reduction of the liftoff height of flames under magnetic gradient due to an increase of the flame propagation velocity.

Flow reversal in combined laminar mixed convection heat and mass transfer with phase change in a vertical channel

This paper, deals with a numerical study of the effects of buoyancy forces on an upward, steady state, laminar flow of humid air in a vertical parallel-plate channel. The plates are wetted by a thin liquid water film and maintained at a constant temperature which is lower than that of the air entering the channel. A 2D fully elliptical model, associated with the Boussinesq assumption, is used to take into account axial diffusion. The solution of this mathematical model is based on the finite volume method and the velocity–pressure coupling is handled by the SIMPLER algorithm. Numerical results show that buoyancy forces have a significant effect on the hydrodynamic, thermal and mass fraction fields. Additionally, these forces induce flow reversal for high air temperatures and mass fractions at the channel entrance. It is established that heat transfer associated with phase change is, sometimes, more significant than sensible heat transfer. Furthermore, this importance depends on the mass fraction gradient. The conditions for the existence of flow reversal are presented in charts and analytical expressions specifying the critical thermal Grashof number as a function of the Reynolds number for different values of the solutal Grashof number and different aspect ratios of the channel.

Effects of primary breakup modeling on spray and combustion characteristics of compression ignition engines

Abstract Injector flow dynamics and primary breakup processes are known to play a pivotal role in determining combustion and emissions in diesel engines. In the present study, we examine the effects of primary breakup modeling on the spray and combustion characteristics under diesel engine conditions. The commonly used KH model, which considers the aerodynamically induced breakup based on the Kelvin–Helmholtz instability, is modified to include the effects of cavitation and turbulence generated inside the injector. The KH model and the new (KH-ACT) model are extensively evaluated by performing 3-D time-dependent simulations with detailed chemistry under diesel engine conditions. Results indicate that the inclusion of cavitation and turbulence enhances primary breakup, leading to smaller droplet sizes, decrease in liquid penetration, and increase in the radial dispersion of spray. Predictions are compared with measurements for non-evaporating and evaporating sprays, as well as with flame measurements. While both the models are able to reproduce the experimentally observed global spray and combustion characteristics, predictions using the KH-ACT model exhibit closer agreement with measurements in terms of liquid penetration, cone angle, spray axial velocity, and liquid mass distribution for non-evaporating sprays. Similarly, the KH-ACT model leads to better agreement with respect to the liquid length and vapor penetration distance for evaporating sprays, and with respect to the flame lift-off location for combusting sprays. The improved agreement is attributed to the ability of the new model to account for the effects of turbulence and cavitation generated inside the injector, which enhance the primary breakup. Results further indicate that the combustion under diesel engine conditions is characterized by a double-flame structure with a rich premixed reaction zone near the flame stabilization region and a non-premixed reaction zone further downstream. This flame structure is consistent with the Dec’s model for diesel engine combustion (Dec, 1997) [1] , and well captured by a newly developed flame index based on the scalar product of CO and O2 mass fraction gradients.

A VOF-based 3D numerical investigation of evaporating, deformed droplets

We present 3D numerical simulations of evaporating, deformed droplets using an in-house DNS Code which solves the incompressible Navier Stokes equations and employs the Volume of Fluid (VOF) method in order to account for multiple phases. The vapour phase is represented by an additional VOF variable and the evaporation rate is computed based on the mass fraction gradient at the interface (Schlottke and Weigand, 2008). The potential of the method is demonstrated for different cases of evaporating droplets. A distinct relationship between the droplets' shape and the mass transfer intensity is found as part of the results.

Analysis of entropy generation in hydrogen-enriched methane–air propagating triple flames

A theoretical–numerical analysis based on the second law of thermodynamics is used to examine the propagation of laminar H 2-enriched CH 4–air flames. The analysis is based on computing the various entropy generation terms in a transient reacting flow field. A comprehensive, time-dependent computational model, which employs a detailed description of chemistry and transport, is used to simulate the transient ignition and flame propagation in this reacting flow field. Flames are ignited in a jet-mixing layer far downstream of the burner. Following ignition, a well-defined triple flame is formed that propagates upstream with nearly constant flame displacement speed along the stoichiometric mixture fraction line. As the flame approaches the burner, it transitions to a double flame, and subsequently to a burner-stabilized nonpremixed flame. The triple point exhibits the maximum entropy generation, indicating that this point is characterized by high chemical reactivity, as well as large temperature and mass fraction gradients. The volumetric entropy generation is the highest in the two premixed reaction zones, and the lowest in the nonpremixed reaction zone. In the premixed zones, the volumetric entropy generation due to chemical reaction is the highest, followed by heat conduction, and then mixing. The converse is true for the nonpremixed zone. However, the integrated entropy generation rate indicates that heat conduction is the major contributor, followed by chemical reactivity, and then mixing. As H 2 addition to methane fuel is increased, the integrated entropy generation increases primarily due to enhanced heat conduction and chemical reactivity. However, the contributions of heat conduction, chemical reactivity, and mixing to total entropy generation weakly depend on the fuel being burned. While the flame propagates upstream entropy generation increases and reaches a maximum when the flame exhibits a well-defined triple flame structure, and then decreases as the flame approaches the burner. The second law efficiency of the system remains nearly constant with H 2 addition, since the increased irreversibilities due to H 2 addition are compensated by the increase in the flow availability in the fuel blend.

Numerical investigation of edge flame propagation characteristics in turbulent mixing layers

The statistical behavior of the displacement speed of an edge flame originating from localized ignition of inhomogeneous reactants in decaying isotropic turbulence is studied based on three-dimensional direct numerical simulations (DNS) with simplified chemistry. The ignition is simulated by introducing a source term in the energy transport equation, which deposits a given amount of energy over a specified time duration. The flame structure is shown to exhibit a tribrachial structure where a diffusion flame is stabilized on the stoichiometric mixture fraction isosurface alongside two premixed flame branches on fuel-rich and fuel-lean mixtures. The speed at which the fuel mass fraction YF isosurface moves with respect to an initially coincident material surface at the point where these three flames meet (commonly referred to as triple point) is taken as the edge flame displacement speed. Its statistics are explained in terms of the reaction, normal diffusion, and tangential diffusion components of the density-weighted displacement speed Sd*. It is shown that the statistical behavior of Sd* and its components in response to the scalar dissipation rate and local flame curvature are strongly dependent on the statistical behavior of the fuel mass fraction gradient ∣∇YF∣ in response to local flame curvature and mixture fraction gradient ∣∇ξ∣. It is shown that the extent of premixed and nonpremixed contributions determines the ∣∇YF∣ variation with ∣∇ξ∣, whereas the flow acceleration due to heat release and dilatation field determines the curvature response of ∣∇YF∣. The variation of Sd* in response to scalar dissipation rate and curvature are shown to be non-monotonic in nature and is found to be consistent with previous results based on two-dimensional DNS with detailed chemistry and experimental studies. This nonmonotonic behavior has been shown here to exist even in the absence of detailed chemistry and is explained in terms of the fluid-dynamical aspects of flame-turbulence interaction.

Rate-ratio asymptotic analysis of autoignition of n-heptane in laminar nonpremixed flows

A rate-ratio asymptotic analysis is carried out to elucidate the mechanisms of autoignition of n-heptane (C 7H 16) in laminar, nonpremixed flows. It has been previously established that autoignition of n-heptane takes place in three distinct regimes. These regimes are called the low-temperature regime, the intermediate-temperature regime, and the high-temperature regime. The present analysis considers the high-temperature regime. A reduced chemical-kinetic mechanism made up of two global steps is used in the analysis. The reduced mechanism is deduced from a skeletal mechanism made up of 16 elementary reactions. The skeletal mechanism is derived from a short mechanism made up of 30 elementary reactions. The short mechanism is deduced from a detailed mechanism made up of 56 elementary reactions. In the reduced mechanism, the first global step represents a sequence of fast reactions starting from the rate-limiting elementary reaction between n-heptane and HO 2. In this global step C 7H 16 is consumed and hydrogen peroxide (H 2O 2) is formed. The second global step represents a sequence of fast reactions starting from the rate-limiting elementary reaction in which H 2O 2 is consumed and OH is formed. A key aspect of the second global step is that the sequence of fast reactions gives rise to consumption of fuel only without net consumption of H 2O 2. This makes the chemical system autocatalytic. The unsteady flamelet equations are used to predict the onset of autoignition. In the flamelet equations a conserved scalar quantity, Z, is used as the independent variable. On the oxidizer side of the mixing layer Z = 0 , and on the fuel side Z = 1 . The practical case where the temperature of the oxidizer stream, T 2 , is much greater than the temperature of the fuel stream is considered. Therefore autoignition is presumed to take place close to Z = 0 . Balance equations are written for C 7H 16 and H 2O 2. It is postulated that autoignition will take place when the gradient of mass fraction fuel with respect to Z, evaluated at Z = 0 , is zero. The value of T 2 when autoignition takes place is obtained as a function of the strain rate. These critical conditions of autoignition obtained from asymptotic analysis agree well with those calculated using the detailed mechanism and the skeletal mechanism.