New thermodynamic-transport theory for systems with continuous component density distributions

2004

Physics of Fluids

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.

Section: A Continuous Thermodynamics For Single Mc-fuel Dropsmentioning

confidence: 99%

“…17 Whitson 24 has shown that gamma distributions may be used to characterize the molar weight of crude oils through…”

Section: A Continuous Thermodynamics For Single Mc-fuel Dropsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Clercq

2004

Physics of Fluids

“…The common feature of all these recent models is the utilization of continuous thermodynamics (CT), a theory developed by Gal-Or, Cullinan & Galli (1975) and by Cotterman, Bender & Prausnitz (1985). In CT, the chemical potential for a mixture containing numerous components is appropriately represented, and the Gibbs function is derived through molecular thermodynamic methods in terms of the probability distribution function (PDF) describing the mixture composition.…”

Section: Introductionmentioning

confidence: 99%

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

Clercq

2005

J. Fluid Mech.

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 ...

“…All MC-liquid statistical approaches have been based on continuous thermodynamics ͑CT͒ concepts. The CT theory 2,3 includes an appropriate representation of the chemical potential for a mixture containing numerous components and ina͒ Telephone: 1-818-354-6959. Fax: 1-818-393-6682.…”

Section: Introductionmentioning

confidence: 99%

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

Selle

2007

Physics of Fluids

Transitional states are obtained by exercising a model of multicomponent-liquid ͑MC-liquid͒ drop evaporation in a three-dimensional mixing layer at larger Reynolds numbers, Re, than in a previous study. The gas phase is followed in an Eulerian frame and the multitude of drops is described in a Lagrangian frame. Complete dynamic and thermodynamic coupling between phases is included. The liquid composition, initially specified as a single-Gamma ͑SG͒ probability distribution function ͑PDF͒ depending on the molar mass, is allowed to evolve into a linear combination of two SGPDFs, called the double-Gamma PDF ͑DGPDF͒. The compositions of liquid and vapor emanating from the drops are calculated through four moments of their PDFs, which are drop-specific and location-specific, respectively. The mixing layer is initially excited to promote the double pairing of its four initial spanwise vortices, resulting into an ultimate vortex in which small scales proliferate. Simulations are performed for four liquids of different compositions, and the effects of the initial mass loading and initial free-stream gas temperature are explored. For reference, simulations are also performed for gaseous multicomponent mixing layers for which the effect of Re is investigated in the direct-numerical-simulation-accessible regime. The results encompass examination of the global layer characteristics, flow visualizations, and homogeneous-plane statistics at transition. Comparisons are performed with previous pretransitional MC-liquid simulations and with transitional single-component ͑SC͒ liquid-drop-laden mixing layer studies. Contrasting to pretransitional MC flows, the vorticity and drop organization depend on the initial gas temperature, this being due to drop/turbulence coupling. The vapor-composition mean molar mass and standard deviation distributions strongly correlate with the initial liquid-composition PDF. Unlike in pretransitional situations, regions of large composition standard deviation no longer necessarily coincide with those of large mean molar mass. The rotational and composition characteristics are all liquid-specific and the variation among liquids is amplified with increasing free-stream gas temperature. The classical energy cascade is found to be of similar strength, but the smallest scales contain orders of magnitude less energy than SC flows, which is confirmed by the larger viscous dissipation for MC flows. The kinetic energy and dissipation are liquid-specific and the variation among liquids is amplified with increasing free-stream gas temperature. The gas composition, of which the first four moments are calculated, is shown to be close to, but distinct from, a SGPDF. Eulerian and Lagrangian statistics of gas-phase quantities show that the different observation framework may affect the perception of the flow.