Semiempirical and DFT computations of the influence of Tb(III) dopant on unit cell dimensions of cerium(III) fluoride

Several computational methods, both semiempirical and ab initio, were used to study the influence of the amount of dopant on crystal cell dimensions of CeF₃ doped with Tb³⁺ ions (CeF₃:Tb³⁺). AM1, RM1, PM3, PM6, and PM7 semiempirical parameterization models were used, while the Sparkle model was used to represent the lanthanide cations in all cases. Ab initio calculations were performed by means of GGA+U/PBE projector augmented wave density functional theory. The computational results agree well with the experimental data. According to both computation and experiment, the crystal cell parameters undergo a linear decrease with increasing amount of the dopant. The computations performed using Sparkle/PM3 and DFT methods resulted in the best agreement with the experiment with the average deviation of about 1% in both cases. Typical Sparkle/PM3 computation on a 2×2×2 supercell of CeF3:Tb3+ lasted about two orders of magnitude shorter than the DFT computation concerning a unit cell of this material. © 2014 Wiley Periodicals, Inc.     

Vaporisation characteristics of methanol,ethanol and heptane droplets in opposed stagnation flow at low temperature and pressure

A computational model is developed and applied to study the vaporisation behaviour of three liquid fuels. This fundamental study is motivated by a need to understand how the performance of direct-injection-spark-ignition (DISI) engines may be affected by changes in fuel composition, especially alcohols. Currently, most DISI engines are designed for homogeneous-charge combustion, where the in-cylinder fuel injection, vaporisation and mixing is accomplished during the intake and early in the compression process. Thus the temperature and pressure are low, compared to post-compression conditions. The two-phase axisymmetric model is based upon an ideal opposed stagnation flow field. Liquid droplets are carried in one air stream that is met by an opposed air flow. Because of stagnation-flow similarity, the mathematical model can be represented as a one-dimensional boundary-value problem. Results show significant differences between methanol, ethanol and heptane fuels, which have potentially important impacts on the design and modification of fuel-injection systems for direct-injection engines with alternative fuels.     

A priori analysis of subgrid scale pressure and heat flux in high pressure mixing and reacting shear layers

Direct Numerical Simulation (DNS) data on high pressure H₂/O₂ and H₂/air flames using the compressible flow formulation, detailed kinetics, a real fluid equation of state, and generalised diffusion are analysed. The DNS is filtered over a range of filter widths to provide exact terms in the Large Eddy Simulation (LES) governing equations, including unclosed terms. The filtered pressure and the filtered heat flux vector are extensively compared with the pressure and the heat flux vector calculated as a function of the filtered primitive variables (i.e. the exact LES term is compared with its form available within an actual LES). The difference between these forms defines the subgrid pressure and the subgrid heat flux vector. The analyses are done both globally across the entire flame, as well as by conditionally averaging over specific regions of the flame; including regions of large subgrid kinetic energy, subgrid scalar dissipation, subgrid temperature variance, flame temperature, etc. In this work, although negligible for purely mixing cases, the gradient of the subgrid pressure is shown to be of the same order as, and larger than, the corresponding divergence of the turbulent subgrid stresses for reacting cases. This is despite the fact that all species behave essentially as ideal gases for this flame and holds true even when the ideal gas law is used to calculate the pressure. The ratio of the subgrid pressure gradient to the subgrid stress tensor divergence is shown to increase with increasing Reynolds number. Both the subgrid heat flux vector and its divergence are found to be substantially larger in reacting flows in comparison with mixing due to the associated larger temperature gradients. However, the divergence of the subgrid heat flux vector tends to be significantly smaller than other unclosed terms in the energy equation with decreasing significance with increasing Reynolds number.     

A priori assessment of the subgrid scale viscous/scalar dissipation closures in compressible turbulence

An appraisal is made of several subgrid scale (SGS) viscous/scalar dissipation closures via a priori analysis of direct numerical simulation data in a temporally evolving compressible mixing layer. The effects of the filter width, the compressibility level and the Schmidt number are studied for several models. Based on the scaling of SGS kinetic energy, a new formulation for SGS viscous dissipation is proposed. This yields the best overall prediction of the SGS viscous dissipation within the inertial subrange. An SGS scalar dissipation model based on the proportionality of the turbulent time scale with the scalar mixing time scale also performs the best for the filter widths in the inertial subrange. Two dynamic methods are implemented for the determination of the model coefficients. The one based on the global equilibrium of dissipation and production is shown to be more satisfactory than the conventional dynamic model.     

Evaluation of augmented RSM for interaction of homogeneous turbulent mixture with shock and rarefaction waves

Interaction of shock or rarefaction waves with turbulent mixtures is challenging for turbulence models. A recent article has shown how results from linear interaction analysis (LIA) can be synthesised into transfer matrices relating upstream and downstream second-order turbulent correlations. These results have been obtained in the limit of axisymmetric weakly turbulent mixture. The current article is devoted to the evaluation of three augmented Reynolds stress models (RSMs) for the same kinds of interaction with weakly turbulent mixtures. Corrections aimed at improving the compatibility with LIA are finally proposed for one of these RSMs.     

A symmetry-preserving discretisation and regularisation model for compressible flow with application to turbulent channel flow

Most simulation methods for compressible flow attain numerical stability at the cost of swamping the fine turbulent flow structures by artificial dissipation. This article demonstrates that numerical stability can also be attained by preserving conservation laws at the discrete level. A new mathematical explanation of conservation in compressible flow reveals that many conservation properties of convection are due to the skew-symmetry of the convection operator. By preserving this skew-symmetry at the discrete level, a fourth-order accurate collocated symmetry-preserving discretisation with excellent conservation properties is obtained. Also a new symmetry-preserving regularisation subgrid-scale model is proposed. The proposed techniques are assessed in simulations of compressible turbulent channel flow. The symmetry-preserving discretisation for compressible flow has good stability without artificial dissipation and yields acceptable results already on coarse grids. Regularisation does not consistently improve upon no-model results, but often compares favourably with eddy-viscosity models.     

Height-dependence of spatio-temporal spectra of wall-bounded turbulence – LES results and model predictions

Wavenumber–frequency spectra of the streamwise velocity component obtained from large-eddy simulations (LES) are presented. Following recent work we show that the main features, a Doppler shift and a Doppler broadening of frequencies, are captured by an advection model based on the Tennekes–Kraichnan random-sweeping hypothesis with additional mean flow. In this paper, we focus on the height-dependence of the spectra within the logarithmic layer of the flow. We furthermore benchmark an analytical model spectrum that takes the predictions of the random-sweeping model as a starting point and find good agreement with the LES data. We also quantify the influence of the LES grid resolution on the wavenumber–frequency spectra.     

Modelling the effect of pressure on the critical shear stress of MgO single crystals

A hierarchical multi-scale model was used to study the effect of high pressure on the critical shear stresses of MgO. The two main slip systems, ½?110?{110} and ½?110?{100}, were considered. Based on a generalised Peierls–Nabarro model, it is shown that the core structure of ½?110? screw dislocations is strongly sensitive to pressure. Mostly planar and spread in {110} at ambient pressure, the core of screw dislocations tends to spread in {100} with increasing pressure. Subsequently, an inversion of the easiest slip systems is observed between 30 and 60?GPa. At high pressure, the plasticity of MgO single crystals is expected to be controlled by ½?110?{100} slip systems, except at high temperature where both slip systems become active. Pressure is also found to increase the critical resolved shear stresses and to shift the athermal temperature toward higher temperatures. Under high pressure, MgO is thus characterised by a significant lattice friction on both slip systems.     

Autocatalytic nature of the bainitic transformation in steels: a new hypothesis

To ensure improvements in predicting the kinetics of bainite formation, it is important to understand the autocatalytic nature of the transformation so that this accelerating effect can be rigorously incorporated in kinetic models. In the present paper, it is assumed that the broad faces of bainitic plates in particular provide new potential nucleation sites for autocatalytic nucleation. The dislocations in the austenite near a bainitic plate are thought to stimulate autocatalysis because carbon is assumed to pile up at these regions and thereby other austenite–bainite interface regions may contain less carbon which promotes nucleation. Based on these assumptions, it is derived that the autocatalytic contribution is proportional to the volume fraction of as-formed bainite, which is consistent with the dependence proposed by Entwisle [V. Raghavan and A.R. Entwisle, Special Report No. 93, The Iron and Steel Institute, London, 1965, p.30] on the basis of empirical knowledge. In addition, it is assumed that autocatalytic nucleation can also depend on the morphology of bainite due to the associated difference in cementite precipitation. This new hypothesis for autocatalysis offers a viable explanation for the irregular variation in kinetics associated with the transition from upper to lower bainite measured for an alloy with eutectoid composition. Furthermore, comparison with experimental data of a Si-rich steel demonstrates that the isothermal kinetics of bainite formation can only be satisfactorily described when the autocatalytic factor is inversely proportional to the thickness of bainitic plates, which is consistent with the model proposed.     

An easy implementation of displacement calculations in 3D discrete dislocation dynamics codes

Barnett’s coordinate-free expression of the displacement field of a triangular loop in an isotropic media is revisited in a view to be implemented in 3D discrete dislocation dynamics codes. A general meshing procedure solving the problems of non-planar loops is presented. The method is user-friendly and can be used in numerical simulations since it gives the contribution of each dislocation segment to the global displacement field without defining the connectivity of closed loops. Easy to implement in parallel calculations, this method is successfully applied to large-scale simulations.