An all-pressure fluid drop model applied to a binary mixture: heptane in nitrogen

Harstad, K.; Bellan, Josette

doi:10.1016/s0301-9322(99)00108-1

Cited by 114 publications

(76 citation statements)

References 17 publications

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“…The distinction between the two thermal diffusion factors was not incidental; in fact, it was crucial in enabling validation of the model with microgravity data. The model presented here is based upon that of Harstad & Bellan (2000).…”

Section: Equation Of Statementioning

confidence: 99%

“…17) 19) where (2.17) is the Irwing-Kirkwood form of the heat flux (Sarman & Evans 1992), the binary diffusion coefficient is D, the mass diffusion factor is α D , and the thermal conductivity λ IK is defined by Harstad & Bellan (2000) from the transport matrix. It can be shown that λ IK does not correspond to the kinetic theory (subscript KT ) definition of the thermal conductivity in that lim p→0 λ IK = λ KT but it is related to the thermal conductivity, λ, through 20) where lim p→0 λ = λ KT as discussed in Harstad & Bellan (2000 …”

Section: Equation Of Statementioning

confidence: 99%

“…These conservation equations are based upon those previously presented for a multicomponent mixture by Harstad & Bellan (1998), and validated for a heptane fluid drop in nitrogen by Harstad & Bellan (2000). As discussed by Harstad & Bellan (1998) and Harstad & Bellan (2000), the most general formulation for the diffusional heat and mass fluxes is that of fluctuation-dissipation theory formulated by Keizer (1987). This theory is not only entirely consistent with non-equilibrium thermodynamics, but also allows the definition of the relationships between fluxes and forces for a general fluid which continuum theory does not give; it is customary within the continuum formulation to extend kinetic theory of rarified gases to describe more general cases as in Chapman & Cowling (1970).…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, although an approximate pressure and temperature variation of the thermal diffusion factor has been identified for heptane-nitrogen during the previously conducted model validation, the effect of the identity and of the imposed constant value of the thermal diffusion factor is first investigated by studying two-dimensional mixing layers. Using the knowledge of the thermal diffusion factor obtained from the validated model of Harstad & Bellan (2000), a single three-dimensional simulation is performed and its results are discussed. In particular, the relevance of specific visual features exhibited by visualizations of the simulations to the evolution of turbulence scales is highlighted.…”

Section: Introductionmentioning

confidence: 99%

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Direct numerical simulations of supercritical fluid mixing layers applied to heptane–nitrogen

2001

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Direct numerical simulations (DNS) are conducted of a model hydrocarbon-nitrogen mixing layer under supercritical conditions. The temporally developing mixing layer configuration is studied using heptane and nitrogen supercritical fluid streams at a pressure of 60 atm as a model system related to practical hydrocarbon-fuel/air systems. An entirely self-consistent cubic Peng-Robinson equation of state is used to describe all thermodynamic mixture variables, including the pressure, internal energy, enthalpy, heat capacity, and speed of sound along with additional terms associated with the generalized heat and mass transport vectors. The Peng-Robinson formulation is based on pure-species reference states accurate to better than 1% relative error through comparisons with highly accurate state equations over the range of variables used in this study (600 6 T 6 1100 K, 40 6 p 6 80 atm) and is augmented by an accurate curve fit to the internal energy so as not to require iterative solutions. The DNS results of two-dimensional and three-dimensional layers elucidate the unique thermodynamic and mixing features associated with supercritical conditions. Departures from the perfect gas and ideal mixture conditions are quantified by the compression factor and by the mass diffusion factor, both of which show reductions from the unity value. It is found that the qualitative aspects of the mixing layer may be different according to the specification of the thermal diffusion factors whose value is generally unknown, and the reason for this difference is identified by examining the second-order statistics: the constant Bearman-Kirkwood (BK) thermal diffusion factor excites fluctuations that the constant Irwing-Kirkwood (IK) one does not, and thus enhances overall mixing. Combined with the effect of the mass diffusion factor, constant positive large BK thermal diffusion factors retard diffusional mixing, whereas constant moderate IK factors tend to promote diffusional mixing. Constant positive BK thermal diffusion factors also tend to maintain density gradients, with resulting greater shear and vorticity. These conclusions about IK and BK thermal diffusion factors are speciespair dependent, and therefore are not necessarily universal. Increasing the temperature of the lower stream to approach that of the higher stream results in increased layer growth as measured by the momentum thickness. The three-dimensional mixing layer exhibits slow formation of turbulent small scales, and transition to turbulence does not occur even for a relatively long non-dimensional time when compared to a previous, atmospheric conditions study. The primary reason for this delay is the initial density stratification of the flow, while the formation of strong density gradient regions both in the braid and between-the-braid planes may constitute a secondary reason for the hindering of transition through damping of emerging turbulent eddies. † Present address:

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Section: Equation Of Statementioning

confidence: 99%

Section: Equation Of Statementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Direct numerical simulations of supercritical fluid mixing layers applied to heptane–nitrogen

2001

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“…2, 3 The effect of thermal diffusion is employed for isotope separation in liquid and gaseous mixtures as well as other separation processes 4 that involve colloids, macromolecules, or nanofluides. Another potential applications include high-pressure combustion, 5 solidification processes, oceanic convection, 6 biological systems, 7 and CO 2 geological storage.…”

Section: Introductionmentioning

confidence: 99%

Measurement of the Soret and diffusion coefficients for benchmark binary mixtures by means of digital interferometry

Mialdun

Shevtsova

2011

The Journal of Chemical Physics

102

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We report on the development of the optical digital interferometry (ODI) technique for measuring diffusion and Soret coefficients. The unique feature of this method is that it traces the transient path of the system in the entire two-dimensional cross section of a cell. In this way, it is applicable not only for measurements of Soret coefficients, but also for studying diffusive transport mechanism and convection. Presently, this method is not widely used and, in our view, not because of fundamental limitations but rather due to a lack of properly developed postexperimental procedures of the raw data analysis. Thus, in this paper our attention is focused on the successive analysis of different steps: the fringe analysis, the choice of reference images, the thermal design of the cell, and multiparameter fitting procedure. Using the ODI technique, we have measured the diffusion and the Soret coefficients for three binary mixtures composed of dodecane (C 12 H 26 ), isobutylbenzene, and 1,2,3,4-tetrahydronaphtalene at a mean temperature of 25 • C and 50 wt. % in each component. These measurements were compared with their benchmark values and show an agreement within less than 3%.

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Consistent Boundary Conditions for Multicomponent Real Gas Mixtures Based on Characteristic Waves

Okong’o¹,

Bellan²

2002

Journal of Computational Physics

131

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An all-pressure fluid drop model applied to a binary mixture: heptane in nitrogen

Cited by 114 publications

References 17 publications

Direct numerical simulations of supercritical fluid mixing layers applied to heptane–nitrogen

Direct numerical simulations of supercritical fluid mixing layers applied to heptane–nitrogen

Measurement of the Soret and diffusion coefficients for benchmark binary mixtures by means of digital interferometry

Consistent Boundary Conditions for Multicomponent Real Gas Mixtures Based on Characteristic Waves

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