Mass Fraction Gradient Research Articles

On ternary species mixing and combustion in isotropic turbulence at high pressure

Effects of Soret and Dufour cross-diffusion, whereby both concentration and thermal diffusion occur in the presence of mass fraction, temperature, and pressure gradients, are investigated in the context of both binary and ternary species mixing and combustion in isotropic turbulence at large pressure. The compressible flow formulation is based on a cubic real-gas state equation, and includes generalized forms for heat and mass diffusion derived from nonequilibrium thermodynamics and fluctuation theory. A previously derived formulation of the generalized binary species heat and mass fluxes is first extended to the case of ternary species, and appropriate treatment of the thermal and mass diffusion factors is described. Direct numerical simulations (DNS) are then conducted for both binary and ternary species mixing and combustion in stationary isotropic turbulence. Mean flow temperatures and pressures of 〈T〉=700 K and 〈P〉=45 atm are considered to ensure that all species mixtures remain in the supercritical state such that phase changes do not occur. DNS of ternary species systems undergoing both pure mixing and a simple chemical reaction of the form O2+N2→2NO are then conducted. It is shown that stationary scalar states previously observed for binary mixing persist for the ternary species problem as well; however, the production and magnitude of the scalar variance is found to be altered for the intermediate molecular weight species as compared to the binary species case. The intermediate molecular weight species produces a substantially smaller scalar variance than the remaining species for all flows considered. For combustion of nonstoichiometric mixtures, a binary species mixture, characterized by stationary scalar states, results at long times after the lean reactant is depleted. The form of this final scalar distribution is observed to be similar to that found in the binary flow situation. A series of lower resolution simulations for a variety of species is then used to show the dependence of the stationary scalar variance on the turbulence Reynolds number, turbulence Mach number, species molecular weight ratio, and relative proportion of two species present in the flow after completion of combustion.

Hydration of the bentonite buffer in a KBS-3 repository

The present study addresses the problem of bentonite hydration in a KBS-3 type repository. A finite element program, Code_Bright, that has been specifically developed to analyze coupled Thermo-Hydro-Mechanical (THM) processes in unsaturated porous media, is used to estimate the time required to reach full saturation of the bentonite buffer. The finite element model analyzed here concerns a horizontal slice of the annular bentonite-filled space between canister and rock wall at canister midheight and considers T-H aspects of the bentonite material behavior. Processes included in the model are transport of heat and moisture. Moisture movements caused by suction gradients as well as by thermally induced vapor mass fraction gradients are considered. All these T-H transport processes are coupled and highly nonlinear. In particular, the thermally driven vapor transport is sensitive to temperature gradients and to temperature levels. Therefore, an important issue is to determine relevant thermal boundary conditions for the FEM model. This is done here by use of analytical expressions which take the initial canister power, the fuel power decay characteristics, the repository layout and the rock thermal properties into account. Results are presented that show the buffer saturation as function of distance to the canister surface at different times. Effects of incomplete saturation on the temperature development are analyzed for a number of assumptions regarding bentonite properties. In particular are conditions that may lead to delayed saturation, such as low permeability, high vapor diffusivity, etc., analyzed. For the reference KBS-3 repository, a general result is that the buffer filling out the annular space between canister and rock wall will be fully water saturated after about 3 or 4 years, provided that there is access to water at the buffer/rock interface of the individual deposition holes. This general result seems to apply for a wide range of assumptions regarding values of transport parameters, gas confinement, porosity, canister power etc. There are, however, a number of uncertainties in the material model. Some of these are either unimportant or can be handled conservatively, while others, such as the validity of the saturation/suction relations are concluded to be important and will need further attention in the future. A general conclusion is that the saturation time scale may turn out to depend more on hydrological conditions around individual deposition holes, on the hydrological buffer/rock interaction and on the repository-scale restoration of the ground water pressure after repository closure, than on details of the bentonite material model.

Turbulence and fluid-front area production in binary-species, supercritical, transitional mixing layers

Databases of transitional states obtained from direct numerical simulations of temporal, supercritical mixing layers for two species systems, O2–H2 and C7H16–N2, are analyzed to elucidate species-specific turbulence aspects and features of fluid disintegration. Although the evolution of all layers is characterized by the formation of high-density-gradient magnitude (HDGM) regions, due to the specified, smaller initial density stratification, the C7H16–N2 layers display higher growth and increased global molecular mixing as well as larger turbulence levels than comparable O2–H2 layers. However, smaller density gradients and lower mass-fraction gradients at the transitional state for the O2–H2 system indicate that on a local basis, the layer exhibits an enhanced mixing, this being attributed to the increased mixture solubility and to mixture near-ideality. These thermodynamic features are found responsible for a larger irreversible entropy production (dissipation) in the O2–H2 compared to the C7H16–N2 layers. The largest O2–H2 dissipation is primarily concentrated in HDGM regions that are distortions of the initial density stratification boundary, whereas the largest C7H16–N2 dissipation is located in HDGM regions resulting from the mixing of the two fluids. To understand fluid disintegration, the area production of a fluid front perpendicular to the mass fraction gradient is calculated in a coordinate system moving with the relative velocity between the front and the flow. On a cross-stream local basis, the C7H16–N2 layers produce more area, and area production increases with smaller perturbation wavelengths combined with larger initial Reynolds numbers. The most active area-producing layer also exhibits the largest probability of having perpendicular vorticity and mass-fraction-gradient vectors. Analysis of the terms in the area production equation shows a large pressure-gradient-term root mean square contribution for the C7H16–N2 layers, due to the coincidence of regions with large magnitudes of pressure gradient with HDGM regions. Such coincidence is attributed to real-gas behavior, which is species-system specific, as the alignment of the pressure gradient and density gradient is similar for both species systems. The alignment of the mass fraction gradient with the strain rate is also species-system dependent. Independent of species system and of the initial conditions, the vorticity is preferentially aligned with the intermediate strain-rate eigendirection, indicating that eddy-viscosity-type models are not adequate for turbulent supercritical mixing.

Numerical modeling of carbon dioxide in unsaturated soils due to deep subsurface leakage

A two‐dimensional numerical model was utilized to explore the flux mechanisms governing CO2 transport in the vadose zone. The simulations were set up to approximately correspond to a site of natural CO2 leakage at Mammoth Mountain, California. The mass fraction gradient driving force, responsible for diffusive and slip fluxes, was determined to lead to less plume spreading than advection alone. Density‐driven flow of CO2 led to significantly greater spreading of the plume and greater storage of CO2 within the vadose zone than if density contrasts were not accounted for. Exposure assessment simulations indicate that for the conditions of interest there may be no physically realistic domain that would lead to CO2 levels below the criteria for human health impacts (sub 10%) in surface soils for the leakage rate present at Mammoth Mountain.

Entropy production of emerging turbulent scales in a temporal supercritical n-heptane/nitrogen three-dimensional mixing layer

A study of emerging turbulent scales entropy production was conducted for a supercritical shear layer as a precursor to the eventual modeling of subgrid scales (SGS: from a turbulent state) leading to large eddy simulations (LES). The entropy equation was first developed for a real, non-ideal fluid using a validated all-pressure fluid model, and the entropy flux and production terms were identified. Employing a direct numerical simulation (DNS) created database of a temporal three-dimensional supercritical shear layer using the fluid model, the different contributions to the irreversible entropy production term were evaluated. Both domain averaged and root mean square (RMS) terms were computed at three different stages of the DNS, representing the timewise ascending, culmination, and descending branches of the spatially averaged positive spanwise vorticity. The unifltered and filtered databases were compared to evaluate the relative importance of irreversible entropy production from viscous, Fourier heat diffusion, and molar fluxes terms. The results show that the average entropy production is dominated by the viscous terms at all stages of the evolution: however, the contribution to the RMS of the molar flux term for both the ascending and descending branches is non-negligible. This latter result was traced to the molar gradients tending to be smeared by emerging turbulent scales. Based on this finding a physical picture of the layer evolution was presented involving competition between large scales entraining heavy fluid from the lower stream and forming strong density and mass fraction gradients at spatially varying locations with time, and small-scale turbulent structures evolving but being damped by contact with the newly formed strong density gradient regions which act similar to material surfaces. Analysis of the results showed that the primary contribution to the molar flux dissipation for both the average and the RMS is the mixture non-ideality.

The Lewis number under supercritical conditions

An effective Lewis number is calculated for situations where temperature and mass fraction gradients are very large by defining effective thermal and mass diffusivities; such situations may occur in systems where there is more than one chemical component, and in particular under supercritical conditions. The definitions evolve from a model assuming that derivatives of certain functions are small with respect to those of the dependent variables. In the model, Soret and Dufour effects are included and Shvab–Zeldovich-like variables are defined to remove the coupling between the operators of the differential equations for temperature and mass fractions. Results from calculations using binary systems of chemical components, using both isolated fluid drops and interacting fluid drops, show that under supercritical conditions, depending upon the compounds, the effective Lewis number can be 2–40 times larger than the traditionally calculated Lewis number and that the spatial variation of the two numbers is different. For the values of the thermal diffusion factor used in the calculations, the Soret and Dufour effects are negligible; the discrepancy between the traditional and effective Lewis numbers is due to the combined effect of the small mass diffusion factor and the difference between the specific enthalpies of the two compounds. Parametric variations show that the effective Lewis number increases with increasing pressure and decreasing surrounding gas temperature. Closer drop proximity in clusters results in sharper peaks in the effective Lewis number due to the increased gradients of the dependent variables.

Droplet–turbulence interactions in low-Mach-number homogeneous shear two-phase flows

Several important issues pertaining to dispersion and polydispersity of droplets in turbulent flows are investigated via direct numerical simulation (DNS). The carrier phase is considered in the Eulerian context, the dispersed phase is tracked in the Lagrangian frame and the interactions between the phases are taken into account in a realistic two-way (coupled) formulation. The resulting scheme is applied for extensive DNS of low-Mach-number, homogeneous shear turbulent flows laden with droplets. Several cases with one- and two-way couplings are considered for both non-evaporating and evaporating droplets. The effects of the mass loading ratio, the droplet time constant, and thermodynamic parameters, such as the droplet specific heat, the droplet latent heat of evaporation, and the boiling temperature, on the turbulence and the droplets are investigated. The effects of the initial droplet temperature and the initial vapour mass fraction in the carrier phase are also studied. The gravity effects are not considered as the numerical methodology is only applicable in the absence of gravity. The evolution of the turbulence kinetic energy and the mean internal energy of both phases is studied by analysing various terms in their transport equations. The results for the non-evaporating droplets show that the presence of the droplets decreases the turbulence kinetic energy of the carrier phase while increasing the level of anisotropy of the flow. The droplet streamwise velocity variance is larger than that of the fluid, and the ratio of the two increases with the increase of the droplet time constant. Evaporation increases both the turbulence kinetic energy and the mean internal energy of the carrier phase by mass transfer. In general, evaporation is controlled by the vapour mass fraction gradient around the droplet when the initial temperature difference between the phases is negligible. In cases with small initial droplet temperature, on the other hand, the convective heat transfer is more important in the evaporation process. At long times, the evaporation rate approaches asymptotic values depending on the values of various parameters. It is shown that the evaporation rate is larger for droplets residing in high-strain-rate regions of the flow, mainly due to larger droplet Reynolds numbers in these regions. For both the evaporating and the non-evaporating droplets, the root mean square (r.m.s.) of the temperature fluctuations of both phases becomes independent of the initial droplet temperature at long times. Some issues relevant to modelling of turbulent flows laden with droplets are also discussed.

Surface tension influences on methanol droplet vaproiation in the presence of water

A computational model has been developed to study the influences of both temperature-and mass-fraction-driven surface tension forces on the transient vaporization of a methanol droplet in a hot environment containing water vapor. The model is based on the Navier-Stokes equations and includes variable transport and thermodynamic properties as well as simultaneous condensitation and vaporization. Numerical simulations have been carried out for practical flow conditions and intermediate Reynolds numbers. The results obtained show that surface tension forces dominate over surface shear forces and that the mass fraction-driven surface forces of water vapor are important during a significant portion of the droplet lifetime. The primary physical reasons for the dominance of the water-driven capillary forces are the low values of liquid mass diffisivity and the large variation of surface tension in water/alcohol mixtures. It is the conclusion of the paper that surface tenstion forces caused by surface mass fraction gradients of water should be included in alcohol droplet flows.

Boundary conditions for some surface-catalyzed reactions

T has recently been demonstrated in the aerospace literature considerable interest concerning the surface recombination of atoms. The analyses of this phenomenon have been carried out within the framework of boundarylayer theory and have involved a boundary condition at the exposed surface relating the normal gradient of atom mass fraction and the atom mass fraction itself. It is generally stated and/or recognized that these analyses for a binary system apply as well to more complicated systems, provided that the concentration of reactants and products is vanishingly small.' 7 It is the purpose of the present note to develop the boundary conditions when this latter assumption is not employed 4 We want to state at the outset that some of the results presented here are perhaps known to chemical engineers as indicated, for example, by Ref. 9. However, the implications of the condition of steady state and, further, of the condition of local adsorption equilibrium leading to the surface boundary conditions for diffusive flows, appear to be new. In any case, it may be useful to the aerospace community to have readily available the present results. § For generality, we consider a set of surf ace -catalyzed reactions of the form