Direct numerical simulation of a transitional temporal mixing layer laden with multicomponent-fuel evaporating drops using continuous thermodynamics

Abstract

A model of a temporal three-dimensional mixing layer laden with fuel drops of a liquid containing a large number of species is derived. The fuel model is based on continuous thermodynamics, whereby the composition is statistically described through a distribution function parametrized on the species molar weight. The drop temperature is initially lower than that of the carrier gas, leading to drop heat up and evaporation. The model describing the changes in the multicomponent ͑MC͒ fuel drop composition and in the gas phase composition due to evaporation encompasses only two more conservation equations when compared with the equivalent single-component ͑SC͒ fuel formulation. Single drop results of a MC fuel having a sharply peaked distribution are shown to compare favorably with a validated SC-fuel drop simulation. Then, single drop comparisons are performed between results from MC fuel and a representative SC fuel used as a surrogate of the MC fuel. Further, two mixing layer simulations are conducted with a MC fuel and they are compared to representative SC-fuel simulations conducted elsewhere. Examination of the results shows that although the global layer characteristics are generally similar in the SC and MC situations, the MC layers display a higher momentum-thickness-based Reynolds number at transition. Vorticity analysis shows that the SC layers exhibit larger vortical activity than their MC counterpart. An examination of the drop organization at transition shows more structure and an increased drop-number density for MC simulations in regions of moderate and high strain. These results are primarily attributed to the slower evaporation of MC-fuel drops than of their SC counterpart. This slower evaporation is due to the lower volatility of the higher molar weight species, and also to condensation of already-evaporated species on drops that are transported in regions of different gas composition. The more volatile species released in the gas phase earlier during the drop lifetime reside in the lower stream while intermediary molar weight species, which egress after the drops are entrained in the mixing layer, reside in the mixing layer and form there a very heterogeneous mixture; the heavier species that evaporate later during the drop lifetime tend to reside in regions of high drop number density. This leads to a segregation of species in the gas phase based on the relative evaporation time from the drops. The ensemble-average drop temperature becomes eventually larger/smaller than the initial drop temperature in MC/SC simulations. Neither this species segregation nor the drop temperature variation with respect to the initial temperature or as a function of the mass loading can be captured by the SC-fuel simulations.

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

“…To mitigate potential numerical instabilities for long CPU time simulations, following Kennedy & Carpenter (1994), we used a tenth-order filtering for spatial derivatives (except in a half-filter-size band located at the lower and upper x 2 boundaries) at every time step. This filtering introduces a small amount of dissipation that serves only to stabilize the computations for long-time integrations, but since it acts only on the shortest waves that can be resolved on the grid, it does not act as a turbulence model allowing under-resolved computations (see Okong'o & Bellan 2004) the previous grid of Le Clercq & Bellan (2004) where a transitional state was achieved, manifested by a smooth velocity-fluctuation-based spectrum with no accumulation of energy at the smallest scales. The present grid size is approximately 10 −3 m, and considering {{D 0 }} of table 1, the ratio of {{V d0 }} to the Eulerian mesh volume is approximately 10 −3 and decreasing with t as the drops evaporate.…”

“…Following the SC methodology (Miller & Bellan 1999;Okong'o & Bellan 2004), a geometric weighting factor w q distributes the individual drop contributions to the nearest eight grid points in proportion to their distance from the drop location. Le Clercq & Bellan (2004) explained that because convective effects dominate the species flux term, for MC flows differential species diffusivity is negligible in transport from the drop location to the grid nodes. Because numerical diffusion induced by distributing the Lagrangian source terms at the Eulerian nodes is proportional to the ratio of V d to the Eulerian mesh volume, this potential effect is here negligible since this ratio is initially O(10 −3 ) (see discussion in § 3.1) and decreases with t, as the drops evaporate.…”

“…This study generalizes the CT modelling approach of Le Clercq & Bellan (2004) to a variety of fuels of practical interest as an example of complex liquids, and addresses the problem of MC-liquid drop evaporation in situations where evaporation could be more vigorous, thus requiring utilization of the DGPDF instead of the SGPDF employed by Le Clercq & Bellan (2004). Having already studied the effect of the initial mass loading (Le Clercq & Bellan 2004), the emphasis is here on elucidating those vortical aspects of the flow that are affected by the liquid composition, on the species spatial distribution as a function of the fuel characteristics, and on how this distribution might change with increasing relative initial-temperature difference between the free stream and the drops.…”

“…Having already studied the effect of the initial mass loading (Le Clercq & Bellan 2004), the emphasis is here on elucidating those vortical aspects of the flow that are affected by the liquid composition, on the species spatial distribution as a function of the fuel characteristics, and on how this distribution might change with increasing relative initial-temperature difference between the free stream and the drops. All simulations are performed in the pre-transitional regime so as to uncouple the composition aspect from turbulence features of the flow.…”

“…Using the SGPDF approach, Le Clercq & Bellan (2004) derived a formulation for a large number of drops evaporating in a temporal mixing layer undergoing transition to turbulence. In this formulation, both the liquid of the drops and the vapour composition were statistically described, and this statistical description was coupled to the deterministic description of the continuity, momentum and energy equations.…”