Differential Diffusion Modelling in LES with RCCE-Reduced Chemistry

The present work shows results obtained from the incorporation of a soot model into a combined Large Eddy Simulation and Conditional Moment Closure approach to modelling turbulent non-premixed flames. Soot formation is determined via the solution of two transport equations for soot mass fraction and particle number density, where acetylene is employed as the incipient species responsible for soot nucleation. The concentrations of the gaseous species are calculated using a Rate-Controlled Constrain Equilibrium approach to reduce the number of species to solve from a detailed gas-phase kinetic scheme involving 63 species. The study focuses on the influence of differential diffusion of soot particles on soot volume fraction predictions. The results of calculations are compared with experimental data for atmospheric methane flames, Overall, the study demonstrates that the model, when used in conjunction with a representation of differential diffusion effects, is capable of predicting soot formation at a fundamental level in the turbulent non- premixed flames considered.     

Inclusion of Preferential Diffusion in Simulations of Premixed Combustion of Hydrogen/Methane Mixtures with Flamelet Generated Manifolds

In this paper we study the possibility to account for preferential diffusion effects in lean turbulent premixed flames in numerical predictions with reduced chemistry. We studied the situation when hydrogen is added to methane at levels of 20% and 40% by volume in the fuel, at lean combustion (??=?0.7) with air. The base case of pure methane was used as a reference. In this case preferential diffusion effects are negligible. First the sensitivity of the mass burning rate to flame stretch was investigated, in one dimensional computations with detailed chemistry, to set reference values. Then the framework of the Flamelet Generated Manifolds (FGM) was used to construct an adequate chemical method to take preferential diffusion into account, without the need for using detailed chemistry. To that end a generalization of the method was presented in which five controlling variables are required. For this system, proper transport equations and effective Lewis numbers where derived. In practice not all five variables are necessary to include and as a first step we limited the amount in the numerical tests in this study to two controlling variables. The method was then tested in configurations in which there was an interaction of coherent vortices and turbulence with flames. It was demonstrated that a minimum of two controlling variables is needed to account for the changed mass burning rate as function of stretch and curvature. It was shown that one-dimensional FGM as well as one-step Arrhenius kinetics can not describe this relation.     

Effects of Fuel Lewis Number on Localised Forced Ignition of Turbulent Mixing Layers

The influences of fuel Lewis number Le _F on localised forced ignition of inhomogeneous mixtures are analysed using three-dimensional compressible Direct Numerical Simulations (DNS) of turbulent mixing layers for Le _F  = 0.8, 1.0 and 1.2 and a range of different root-mean-square turbulent velocity fluctuation u′ values. For all Le _F cases a tribrachial flame has been observed in case of successful ignition. However, the lean premixed branch tends to merge with the diffusion flame on the stoichiometric mixture fraction isosurface at later stages of the flame evolution. It has been observed that the maximum values of temperature and reaction rate increase with decreasing Le _F during the period of external energy addition. Moreover, Le _F is found to have a significant effect on the behaviours of mean temperature and fuel reaction rate magnitude conditional on mixture fraction values. It is also found that reaction rate and mixture fraction gradient magnitude \(\vert \nabla \xi \vert \) are negatively correlated at the most reactive region for all values of Le _F explored. The probability of finding high values of \(\vert \nabla \xi \vert \) increases with increasing Le _F . For a given value of u′, the extent of burning decreases with increasing Le _F . A moderate increase in u′ gives rise to an increase in the extent of burning for Le _F  = 0.8 and 1.0, which starts to decrease with further increases in u′. For Le _F  = 1.2, the extent of burning decreases monotonically with increasing u′. The extent of edge flame propagation on the stoichiometric mixture fraction ξ = ξ _st isosurface is characterised by the probability of finding burned gas on this isosurface, which decreases with increasing u′ and Le _F . It has been found that it is easier to obtain self-sustained combustion following localised forced ignition in case of inhomogeneous mixtures than that in the case of homogeneous mixtures with the same energy input, energy deposition duration when the ignition centre is placed at the stoichiometric mixture. The difficultly to sustain combustion unaided by external energy addition in homogeneous mixture is particularly prevalent in the case of Le _F  = 1.2.     

Inverse Estimation of the Effective Diffusion of the Filter in the In Situ Diffusion and Retention (DR) Experiment

Porous filters are often used in laboratory and in situ diffusion and retention experiments. The proper interpretation of these experiments requires knowing the effective diffusion, D _e, of the filter which is commonly determined from laboratory diffusion experiments or estimated from the filter porosity. The D _e of the filter in the in situ experiment may differ from the D _e of the filter measured in the laboratory due to pore clogging. Here, we present an inverse method to estimate the D _e of the filter of in situ diffusion experiments. The method has been tested for several sampling schemes, numbers of synthetic data, N, and standard deviations of the noise, ??. It has been applied to the following tracers used in the in situ diffusion and retention (DR) experiment performed in the Opalinus clay at Mont Terri underground research laboratory: HTO/HDO, Br^?,I^?, ²² Na⁺,¹³³ Ba²⁺,⁸⁵ Sr²⁺, Cs⁺/¹³⁷Cs⁺, and ⁶⁰Co²⁺. The estimation error increases with the standard deviation of the noise of the data and decreases with the number of data. It is smallest for sorbing tracers. The D _e of the filter can be properly estimated from 12 data collected within the first 3?days for conservative tracers as long as ????? 0.02 and for sorbing tracers as long as ??????0.05. The estimate of D _e for conservative tracers is poor when data are collected from a 10-day experiment with daily sampling. The convergence of the estimation algorithm for conservative tracers improves by starting with a value of the D _e smaller than the true value. The choice of the initial value of D _e does not affect the convergence of the estimation algorithm for sorbing tracers. Filter clogging and vertical flow though the filter can influence the tracer transport through the filter. The use of the D _e of the filter obtained from a laboratory test for the in situ experiment may result in large errors for strongly sorbing tracers. Such errors can be overcome by estimating the equivalent D _e of the filter with the proposed inverse method which will be useful for the design of in situ diffusion experiments.     

Effects of Lewis Number on Scalar Variance Transport in Premixed Flames

The influences of differential diffusion rates of heat and mass on the transport of the variances of Favre fluctuations of reaction progress variable and non-dimensional temperature have been studied using three-dimensional simplified chemistry based Direct Numerical Simulation (DNS) data of statistically planar turbulent premixed flames with global Lewis number ranging from Le?= 0.34 to 1.2. The Lewis number effects on the statistical behaviours of the various terms of the transport equations of variances of Favre fluctuations of reaction progress variable and non-dimensional temperature have been analysed in the context of Reynolds Averaged Navier Stokes (RANS) simulations. It has been found that the turbulent fluxes of the progress variable and temperature variances exhibit counter-gradient transport for the flames with Lewis number significantly smaller than unity whereas the extent of this counter-gradient transport is found to decrease with increasing Lewis number. The Lewis number is also shown to have significant influences on the magnitudes of the chemical reaction and scalar dissipation rate contributions to the scalar variance transport. The modelling of the unclosed terms in the scalar variance equations for the non-unity Lewis number flames have been discussed in detail. The performances of the existing models for the unclosed terms are assessed based on a-priori analysis of DNS data. Based on the present analysis, new models for the unclosed terms of the active scalar variance transport equations are proposed, whenever necessary, which are shown to satisfactorily capture the behaviours of unclosed terms for all the flames considered in this study.     

Effects of Differential Diffusion on Predicted Autoignition Delay Times Inspired by H2/N2 Jet Flames in a Vitiated Coflow Using the Linear Eddy Model

Mixing and chemistry interactions in a H₂/N₂ jet flame into a vitiated coflow are considered key factors affecting autoignition. A 1-D numerical model under laminar flow condition first is simulated to reveal the effects of fuel species, pressure, and coflow properties on the autoignition with and without the consideration of preferential diffusion among species. Proper laminar reference autoignition delays are proposed and examined for different diffusion models. Next, the reference autoignition delays defined from laminar simulations are investigated in an example turbulent flow using the Linear Eddy Model (LEM). LEM is used to model the effect of turbulent mixing on autoignition, where we specifically investigate if the effect of turbulence on autoignition can be classified in two regimes, which are dependent on a proper reference laminar autoignition delay and turbulence time scale. The trend of the effect of differential diffusion on autoignition versus turbulence Reynolds is simulated and analyzed, and several tentative conclusions are drawn.     

Extension of the bifurcation method for diffusion coefficients to porous medium transport

We present an extension of Bartlett's bifurcation method for the approximate computation of multicomponent diffusion coefficients in a gaseous mixture to diffusion in porous media. On behalf of the remark that the bifurcation coefficients F_i are merely proportional to the square root of the molar masses M_i, we state that Knudsen diffusion may also be represented through some bifurcation factor F_K. This approximation is tested in a variety of cases, displaying good results except for very light gas species.     

Predicting extrusion instabilities of commercial polyethylene from non-linear rheology measurements

Processing at the highest possible throughput rates is essential from an economical point of view. However, various flow instabilities and extrudate distortions like sharkskin, stick slip, and gross melt fracture (GMF) may limit the production rate of high-quality products. Predicting the process conditions leading to the occurrence of rheological instabilities is the key for improving product quality, process control, and optimization. Large-amplitude oscillatory shear (LAOS) and FT-rheology were used to quantify the non-linear rheological behavior and instabilities of a series of well-characterized commercial polyethylene (PE). From the latter, we derive the critical non-linearity parameter, F _0,c, which corresponds to the normalized intensity of the third harmonic at the critical strain amplitude, γ _0,C (defined by the appearance of the second harmonic), normalized by γ _0,C . The F _0,c is correlated with the high molecular mass fraction of the polymers and with the Deborah numbers. Linear rheological parameters and molecular structures were related to F _0,c. An experimental correlation between F _0,c of commercial PE melts and pressure fluctuations associated with flow instabilities (sharkskin) was established both for capillary rheometry and extrusion.     

Comment on “Correlation of entrainment for annular flow in horizontal pipes”, by Pan,L., Hanratty,T.J., Int. J. Multiphase flow, 28(3), (2002), pp. 385–408

The above referenced paper, published in International Journal of Multiphase Flow (Pan and Hanratty, 2002), proposed an entrainment fraction correlation for annular flow in horizontal pipes. The entrainment fraction in annular flow is defined as the ratio of the mass flow rate of the liquid droplets in the gas to the total mass flow of liquid, F_E = W_LE/W_L. The proposed correlation was verified with experimental data for liquids with viscosities close to that of water. The proposed entrainment fraction correlation includes another correlation for the critical film flow rate, W_F,cr to estimate a maximum entrainment fraction F_E,max. It is shown that the critical film flow rate correlation can result in negative maximum entrainment fraction values, for low liquid flow rates.     

A transition phenomenon of ice formation in water flow between two horizontal parallel plates

Experiments have been performed to investigate the icetransition profiles and heat-transfer characteristics for water flows between two horizontal parallel plates. The experiments are carried out under the condition that upper plate is cooled at uniform temperature kept less than freezing temperature of water, while the lower plate is heated at uniform temperature kept higher than the temperature of water flow. The temperatures of the upper and lower plates range from ?8 to ?14°C and from 10 to 60 °C, respectively, with inlet-water temperature varied from 1.5 to 4.5 °C. The cooling and heating temperature ratios, θ_c and θ_h, are ranging from 1.78 to 9.33 and from 1.22 to 39, respectively. By using three kinds of heightH of 16, 30 and 40 mm between the horizontal parallel plates, the Reynolds and Grashof numbers are varied from 3.2 × 10² to 1.5 × 10⁴ and from 3.4 × 10³ to 8.97 × 10⁶, respectively. As a result of this investigation two ice-transition modes are observed. The first ice-transition mode is due to an interruption of upper and lower thermal boundary layers, while the second mode is due to an instability of laminar boundary layer formed on water-ice interface. In order to determine the kind of ice-transition mode, criterion correlation formulas including the Reynolds numberRe _H , Grashof numberGr _H , and heating temperature ratio θ_h are determined and may be written as follows: For thermal icetransition mode (th.I.T.M.)Re _H /(Gr _H ·θ _h )^0.23<1.6×10^?3 and for hydrodynamical ice-transition mode (hy.I.T.M.)Re _H /(Gr _H ·θ _h )^0.23>2.3×10^?3 By introducing the freezing parameterB _f , correlation equations for local and mean Nusselt numbers along the water-ice interface at steady-state condition are determined. From the current experimental results it is found that the local Nusselt number may be described as the following equation:Nu _x =0.835 Re _H ^0.278 · B _f ^0.834 ·x/H)^?0.139     

Attractors of Reaction Diffusion Systems on Infinite Lattices

In this paper, we study global attractors for implicit discretizations of a semilinear parabolic system on the line. It is shown that under usual dissipativity conditions there exists a global (Z _u ,Z _ρ )-attractor $A$ in the sense of Babin-Vishik and Mielke-Schneider. Here Z _ρ is a weighted Sobolev space of infinite sequences with a weight that decays at infinity, while the space Z _u carries a locally uniform norm obtained by taking the supremum over all Z _ρ norms of translates. We show that the absorbing set containing $A$ can be taken uniformly bounded (in the norm of Z _u ) for small time and space steps of the discretization. We establish the following upper semicontinuity property of the attractor $A$ for a scalar equation: if $A$ _N is the global attractor for a discretization of the same parabolic equation on the finite segment [?N,N] with Dirichlet boundary conditions, then the attractors $A$ _N (properly embedded into the space Z _u ) tend to $A$ as N→∞ with respect to the Hausdorff semidistance generated by the norm in Z _ρ . We describe a possibility of “embedding” certain invariant sets of some planar dynamical systems into the global attractor $A$ . Finally, we give an example in which the global attractor $A$ is infinite-dimensional.     

Behavior of Moderately Oscillating Sooting Methane-Air Diffusion Flames

The properties of oscillating sooting methane air diffusion flames have been investigated by different methods in order to examine instationary effects in these flames. The pulsation has been induced by modulation of the methane gas flow with an amplitude of 30% of the mean gas flow. The focus of the investigations is on the flame oscillated at 10 Hz, which is close to the frequency of self-induced flickering. Additionally, further measurements at varying frequencies have been performed to determine the transition towards steady-state behavior. Different measurement techniques allowed the determination of soot volume fractions, particle number densities, mean particle radii, particle temperatures, and OH*-chemiluminescence. The oscillating flame shows strong instationary effects and increased soot concentrations compared to the steady-state flame of equivalent mean fuel flow. Accompanying calculations are based on a kinematic analysis of diffusion flames. The model can sufficiently well reproduce the flame height and the contour of the flame. Furthermore, the model describes the asymmetric course of the OH*-emission signal. A simple numerical approach is deduced that explains qualitatively the strong variations of the soot volume fraction in an oscillating flame. This paper is based on work presented at the 2nd ECCOMAS Thematic Conference on Computational Combustion, Delft, 2007.     

Measurement of the concentration diffusion coefficient for Ne-Ar,Ne-Xe,Ne-H2, Xe-H2, H2-N2 and H2-O2 gas systems

The concentration diffusion coefficient, D ₁₂, is measured for the equimolar mixtures of Ne-Ar, Ne-Xe, Ne-H₂, Xe-H₂, H₂-N₂ and H₂-O₂ binary gas systems in a two-bulb metal apparatus in the temperature range 0 C to 100 C. These values are compared with the existing data on these systems and with the predictions of the kinetic theory in conjunction with the modified Buckingham exp-six potential. Unlike the thermal diffusion coefficient, with the simple theory it is possible to predict D ₁₂ within a few percent even for systems involving polyatomic gases. The smoothed experimental D ₁₂ values are also used to obtain data for the coefficients of viscosity and thermal conductivity at round temperatures and compositions for these systems.     

Measurement of liquid film thickness in a micro parallel channel with interferometer and laser focus displacement meter

In the present study, liquid film thicknesses in parallel channels with heights of H = 0.1, 0.3 and 0.5 mm are measured with two different optical methods, i.e., interferometer and laser focus displacement meter. Ethanol is used as a working fluid. Liquid film thicknesses obtained from two optical methods agree very well. At low capillary numbers, dimensionless liquid film thickness is in accordance with Taylor’s law. However, as capillary number increases, dimensionless liquid film thickness becomes larger than Taylor’s law for larger channel heights. It is attributed to the dominant inertial effect at high capillary numbers. Using channel height H for dimensionless liquid film thickness δ₀/H and hydraulic diameter D_h = 2H as the characteristic length for Reynolds and Weber numbers, liquid film thickness in a parallel channel can be predicted well by the circular tube correlation previously proposed by the authors. This is because curvature differences between bubble nose and flat film region are identical in circular tubes and parallel channels.     

Flow characteristics and flow-induced forces of a stationary and rotating triangular cylinder with different incidence angles at low Reynolds numbers

In this paper, the problem of two-dimensional fluid flow past a stationary and rotationally oscillating equilateral triangular cylinder with a variable incident angle, Reynolds number, oscillating amplitude, and oscillating frequency is numerically investigated. The computations are carried out by using a two-step Taylor-characteristic-based Galerkin (TCBG) algorithm. For the stationary cases, simulations are conducted at various incident angles of α=0.0–60.0° and Reynolds numbers of Re=50–160. For the oscillation cases, the investigations are done at various oscillating amplitudes of θ_max=7.5–30.0° and oscillating frequencies of F_s/F_o=0.5–3.0 considering two different incidence angles (α=0.0°, 60.0°) and three different Reynolds numbers (Re=50, 100, 150). The results show that the influences of key parameters (incidence angle, Reynolds number, oscillating amplitude, and oscillating frequency) are significant on the flow pattern and hydrodynamic forces. For the stationary cases, at smaller angle of incidence (α≤30.0°), Reynolds number has a large impact on the position of the separation points. When α is between 30.0° and 60.0°, it was found that the separation points are located at the rear corners. From a topological point of view, the diagram of flow pattern is summarized, including two distinct patterns, namely, main separation and vortex merging. A deep analysis of the influence of Reynolds number and incidence angles on the mean pressure coefficient along the triangular cylinder surface is presented. Additionally, for the oscillating cases, the lock-on phenomenon is captured. The dominant flow patterns are 2S mode and P+S mode in lock-on region at α=0.0°. It is found at α=60.0°, however, that the flow pattern is predominantly 2S mode. Furthermore, except for the case of F_s/F_o=2.0, the mean drag decreases as the oscillating amplitude increases for each Reynolds number at α=0.0°. At α=60.0°, the minimum mean drag for F_s/F_o=1.5 is lower than that for stationary case, and occurs at θ_max=15.0° (Re=100) and θ_max=22.5° (Re=150), respectively. Finally, the effect of Reynolds number on a rotational oscillation cylinder is elucidated.     

Numerical study of the detonation structure in rich H2?NO2/N2O4 and very lean H2?N2O mixtures

In some mixtures and under certain conditions, detonation soot records show substructures. In nitromethane and nitrogen tetroxide mixtures, particular cellular structures can be observed. This kind of structures has been reported as the so-called double cellular structure. One- and two-dimensional simulations of detonation have shown that the double cellular structure is related to a non-monotonous energy release. Two-step energy release is also observed in rich H₂−NO₂/N₂O₄ and in very lean H₂−N₂O mixtures. The present study aims at the investigation of the effect of the energy release profile on the detonation structure in these two mixtures through numerical simulations. The origin of the non-monotonous energy release is explained in both mixtures using one-dimensional simulations with detailed chemistry. Reduced kinetic schemes are obtained and used to perform two-dimensional simulations. It is shown that in rich H₂−NO₂/N₂O₄ mixtures, the double cellular structure appears, whereas in very lean H₂−N₂O mixtures, classical substructures are observed. Both behaviours are explained based on ZND calculations and previous stability results. Phenomenological considerations led the authors to link the formation of the double cellular structure with the appearance of a large scale instability mode (a super cellular structure).     

Measurements of Scalar Variance, Scalar Dissipation, and Length Scales in Turbulent Piloted Methane/Air Jet Flames

One-dimensional (line) measurements of mixture fraction, temperature, and scalar dissipation in piloted turbulent partially premixed methane/air jet flames (Sandia flames C, D, and E) are presented. The experimental facility combines line imaging of Raman scattering, Rayleigh scattering, and laser-induced CO fluorescence. Simultaneous single-shot measurements of temperature and the mass fractions of all the major species (N₂, O₂, CH₄, CO₂, H₂O, CO, and H₂) are obtained along 7 mm segments with a nominal spatial resolution of 0.2 mm. Mixture fraction, ξ, is then calculated from the measured mass fractions. Ensembles of instantaneous mixture fraction profiles at several streamwise locations are analyzed to quantify the effect of spatial averaging on the Favre average scalar variance, which is an important term in the modeling of turbulent nonpremixed flames. Results suggest that the fully resolved scalar variance may be estimated by simple extrapolation of spatially filtered measurements. Differentiation of the instantaneous mixture fraction profiles yields the radial contribution to the scalar dissipation, χ _r = 2D _ξ(?ξ/?r)², and radial profiles of the Favre mean and rms scalar dissipation are reported. Scalar length scales, based on autocorrelation of the spatial profiles of ξ and χ _r , are also reported. These new data on this already well-documented series of flames should be useful in the context of validating models for sub-grid scalar variance and for scalar dissipation in turbulent flames.     

Motion of Elastic Thin Films by Anisotropic Surface Diffusion with Curvature Regularization

In this paper, we prove short time existence, uniqueness, and regularity for a surface diffusion evolution equation with curvature regularization in the context of epitaxially strained two-dimensional films. This is achieved by using the H ^?1-gradient flow structure of the evolution law, via De Giorgi??s minimizing movements. This seems to be the first short time existence result for a surface diffusion type geometric evolution equation in the presence of elasticity.     

Transient heat and mass transfer in a natural circulation loop

Comprehensive work has been performed by theoretical and numerical methods in order to study the steady state, transient and stability characteristics of a double diffusive natural circulation loop. It was found that the behavior of the flow in the system depends on the initial conditions and on the location of the state in the seven-parameter space of the thermal and saline Rayleigh numbers,Ra _T ,Ra _S , the modified Prandtl and Schmidt numbers,Pr, Sc, the dimensionless heat and mass transfer coefficients,H _T ,H _S , and the “aspect ratio” (between the height and width) of the loop, γ. Numerical results are presented here, showing the flow in each of the five regions formed in the stability chart. The steady state solutions include convection (constant velocity flow), conduction (no-flow) and periodic with constant amplitude and frequency. Two main new results were obtained: long term periodic oscillations where the amplitude is not symmetric around the conduction solution, and an overshoot of the velocity in transients before reaching the stable convection solutions. In the monotonic instability region of the conduction solution, convection solutions (constant velocity flow) develop, and in the global stability region the flow decays to the conduction solution (no flow), regardless of the initial conditions.