Direct numerical simulation of gaseous mixing layers laden with multicomponent-liquid drops: liquid-specific effects

Abstract

A representation of multicomponent-liquid (MC-liquid) composition as a linear combination of two single-Gamma probability distribution functions (PDFs) is used to describe a large number of MC-liquid drops evaporating in a gas flow. The PDF, called the double-Gamma PDF, depends on the molar mass. The gas-phase conservation equations are written in an Eulerian frame and the drops are described in a Lagrangian frame. Gas conservation equations for mass, momentum, species and energy are combined with differential conservation equations for the first four moments of the gascomposition PDF and coupled to the perfect gas equation of state. Source terms in all conservation equations account for the gas/drop interaction. The drop governing equations encompass differential conservation statements for position, mass, momentum, energy and four moments of the liquid-composition PDF. Simulations are performed for a three-dimensional mixing layer whose lower stream is initially laden with drops colder than the surrounding gas. Initial perturbations excite the layer to promote the double pairing of its four initial spanwise vortices to an ultimate vortex. During the layer evolution, the drops heat and evaporate. The results address the layer evolution, and the state of the gas and drops when layers reach a momentum-thickness maximum past the double vortex pairing. Of interest is the influence of the liquid composition on the development of the vortical features of the flow, on the vortical state reached after the second pairing, and on the gas temperature and composition. The MC-liquid simulations are initiated with a single-Gamma PDF composition so as to explore the development of the double-Gamma PDF. Examination of equivalent simulations with n-decane, diesel and three kerosenes as the liquid, permits assessment of the single-species versus the MC-liquid aspect, and of mixture composition specific effects. Global layer growth and global rotational characteristics are unaffected by liquid specificity; however, the global mixing is highly liquid-specific. Also liquidspecific is the evolution of the ensemble-averaged drop characteristics and of the volumetric averages representing the gas composition. Visualized rotational characteristics show that the small-scale vortical activity increases with increased fuel volatility, which is confirmed by analysis of the vorticity budgets. Homogeneous-planeaverage budgets of the vorticity and vorticity-magnitude equations indicate that the stretching and tilting, and momentum-source terms are responsible for the difference among simulations. For all MC liquids, the gas displays a high level of composition heterogeneity, which can directly be traced to the original PDF representing the MC-liquid composition. Under most conditions, the single-Gamma PDF develops into a double-Gamma PDF; however, the extent of this transformation, indicative of vapour condensation onto drops, is not readily parametrized by the liquid volatility, initial carrier-gas temperature or trace vapour in the initial ...

Characteristics of transitional multicomponent gaseous and drop-laden mixing layers from direct numerical simulation: Composition effects

“…Both single component ͑SC͒ and SGPDF MCliquid representations fail in such regime. Compared to previous studies, 10,15 the present DNS investigation accesses a higher-temperature turbulent-gas regime that is closer to that of real combustors, despite the fact that the initial gas temperature, T 0 ͑subscript 0 denotes the initial condition͒, is still very much lower than in combustors. This lower T 0 value is dictated by the requirement to match the drop characteristic time to that of the flow, which in this transitional regime is much larger than that of fully turbulent flows, known to be inaccessible in DNS.…”

“…Section IV is devoted to a description of the results, encompassing the global layer characteristics, flow visualizations, homogeneous-plane statistics, dropensemble probabilities, and a dissipation analysis. Comparisons with the SC DNS study of Okong'o and Bellan 20 and with the pretransitional DNS investigation of Le Clercq and Bellan 15 are also discussed. The results are summarized in Sec.…”

“…where 15 and the superscript ͑s͒ denotes the drop surface. At this surface, the classical boundary conditions of temperature equality and mass, species, momentum, and energy flux conservation apply.…”

“…Instead, a double-Gamma PDF ͑DGPDF͒ has been proposed, which when exercised for single drops compared excellently for most conditions with the results from a discrete-species model based on a 32-species representation. The flexibility of the statistical representation was manifested once more in the DGPDF model that was shown to fit all three preponderant homologous classes of Jet A, RP-1, and JP-7 petroleum fuels with only a single DGPDF when the PDF dependence is on ͱ m instead of on m. 13 The recent pretransitional DGPDF DNS study of Le Clercq and Bellan 15 expanded on the previous SGPDF study of Le Clercq and Bellan 10 of the same mixing layer configuration: the DGPDF representation enables attainment of a higher evaporation regime, and thus the results have increased relevance to the realistic high-temperature regime of combustors. Both single component ͑SC͒ and SGPDF MCliquid representations fail in such regime.…”

“…II, the conservation equations are briefly recalled from the detailed model developed by Le Clercq and Bellan. 15 Next, the configuration, boundary conditions, and the numerics are presented in Sec. III.…”