Gradient Theory simulations of pure fluid interfaces using a generalized expression for influence parameters and a Helmholtz energy equation of state for fundamentally consistent two-phase calculations

Dahms, Rainer N.

doi:10.1016/j.jcis.2014.12.069

Title: Gradient Theory simulations of pure fluid interfaces using a generalized expression for influence parameters and a Helmholtz energy equation of state for fundamentally consistent two-phase calculations

Journal Article · Wed Dec 31 00:00:00 EST 2014 · Journal of Colloid and Interface Science

DOI:https://doi.org/10.1016/j.jcis.2014.12.069· OSTI ID:1235923

Dahms, Rainer N. ^[1]

Sandia National Lab. (SNL-CA), Livermore, CA (United States)

The fidelity of Gradient Theory simulations depends on the accuracy of saturation properties and influence parameters, and require equations of state (EoS) which exhibit a fundamentally consistent behavior in the two-phase regime. Widely applied multi-parameter EoS, however, are generally invalid inside this region. Hence, they may not be fully suitable for application in concert with Gradient Theory despite their ability to accurately predict saturation properties. The commonly assumed temperature-dependence of pure component influence parameters usually restricts their validity to subcritical temperature regimes. This may distort predictions for general multi-component interfaces where temperatures often exceed the critical temperature of vapor phase components. Then, the calculation of influence parameters is not well defined. In this paper, one of the first studies is presented in which Gradient Theory is combined with a next-generation Helmholtz energy EoS which facilitates fundamentally consistent calculations over the entire two-phase regime. Illustrated on pentafluoroethane as an example, reference simulations using this method are performed. They demonstrate the significance of such high-accuracy and fundamentally consistent calculations for the computation of interfacial properties. These reference simulations are compared to corresponding results from cubic PR EoS, widely-applied in combination with Gradient Theory, and mBWR EoS. The analysis reveals that neither of those two methods succeeds to consistently capture the qualitative distribution of obtained key thermodynamic properties in Gradient Theory. Furthermore, a generalized expression of the pure component influence parameter is presented. This development is informed by its fundamental definition based on the direct correlation function of the homogeneous fluid and by presented high-fidelity simulations of interfacial density profiles. As a result, the new model preserves the accuracy of previous temperature-dependent expressions, remains well-defined at supercritical temperatures, and is fully suitable for calculations of general multi-component two-phase interfaces.

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Research Organization:: Sandia National Lab. (SNL-CA), Livermore, CA (United States)

Sponsoring Organization:: USDOE Office of Secretary of Energy (S); USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1235923

Alternate ID(s):: OSTI ID: 1244591

Report Number(s):: SAND-2015-20792J; PII: S0021979714010388

Journal Information:: Journal of Colloid and Interface Science, Vol. 445, Issue C; ISSN 0021-9797

Country of Publication:: United States

Language:: English

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Cited by: 8 works

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References (69)

Structure and breakup properties of sprays Faeth, G. M.; Hsiang, L. -P; Wu, P. -K International Journal of Multiphase Flow, Vol. 21 https://doi.org/10.1016/0301-9322(95)00059-7	journal	December 1995
Liquid Jet Instability and Atomization in a Coaxial Gas Stream Lasheras, J. C.; Hopfinger, E. J. Annual Review of Fluid Mechanics, Vol. 32, Issue 1 https://doi.org/10.1146/annurev.fluid.32.1.275	journal	January 2000
Forces involved in the adhesive process Dann, J. R. Journal of Colloid and Interface Science, Vol. 32, Issue 2 https://doi.org/10.1016/0021-9797(70)90054-8	journal	February 1970
An Interactively Coupled CFD-Multi-Zone Approach to Model HCCI Combustion Felsch, C.; Dahms, R.; Glodde, B. Flow, Turbulence and Combustion, Vol. 82, Issue 4 https://doi.org/10.1007/s10494-009-9202-6	journal	February 2009
A comprehensive modeling study of in-cylinder fluid flows in a high-swirl, light-duty optical diesel engine Perini, Federico; Miles, Paul C.; Reitz, Rolf D. Computers & Fluids, Vol. 105 https://doi.org/10.1016/j.compfluid.2014.09.011	journal	December 2014
Review of high efficiency and clean reactivity controlled compression ignition (RCCI) combustion in internal combustion engines Reitz, Rolf D.; Duraisamy, Ganesh Progress in Energy and Combustion Science, Vol. 46 https://doi.org/10.1016/j.pecs.2014.05.003	journal	February 2015
Effects of Real-Fluid Thermodynamics on High-Pressure Fuel Injection Processes Oefelein, Joseph; Lacaze, Guilhem; Dahms, Rainer SAE International Journal of Engines, Vol. 7, Issue 3 https://doi.org/10.4271/2014-01-1429	journal	April 2014
Fuel reactivity effects on the efficiency and operational window of dual-fuel compression ignition engines Splitter, Derek A.; Reitz, Rolf D. Fuel, Vol. 118 https://doi.org/10.1016/j.fuel.2013.10.045	journal	February 2014
Detailed Modeling and Simulation of High-Pressure Fuel Injection Processes in Diesel Engines Oefelein, Joseph; Dahms, Rainer; Lacaze, Guilhem SAE International Journal of Engines, Vol. 5, Issue 3 https://doi.org/10.4271/2012-01-1258	journal	January 2012
Parametric study and optimization of a RCCI (reactivity controlled compression ignition) engine fueled with methanol and diesel Li, Yaopeng; Jia, Ming; Chang, Yachao Energy, Vol. 65 https://doi.org/10.1016/j.energy.2013.11.059	journal	February 2014
Advanced gasoline engine development using optical diagnostics and numerical modeling Drake, M. C.; Haworth, D. C. Proceedings of the Combustion Institute, Vol. 31, Issue 1 https://doi.org/10.1016/j.proci.2006.08.120	journal	January 2007
Detailed chemistry flamelet modeling of mixed-mode combustion in spark-assisted HCCI engines Dahms, R.; Felsch, C.; Röhl, O. Proceedings of the Combustion Institute, Vol. 33, Issue 2 https://doi.org/10.1016/j.proci.2010.08.005	journal	January 2011
On the ignition and flame development in a spray-guided direct-injection spark-ignition engine Peterson, Brian; Reuss, David L.; Sick, Volker Combustion and Flame, Vol. 161, Issue 1 https://doi.org/10.1016/j.combustflame.2013.08.019	journal	January 2014
Pollutant formation modelling in natural gas SI engines using a level set based flamelet model Dahms, R.; Peters, N.; Stanton, D. W. International Journal of Engine Research, Vol. 9, Issue 1 https://doi.org/10.1243/14680874JER02107	journal	February 2008
Early flame propagation in a spark-ignition engine measured with quasi 4D-diagnostics Peterson, B.; Baum, E.; Böhm, B. Proceedings of the Combustion Institute, Vol. 35, Issue 3 https://doi.org/10.1016/j.proci.2014.05.131	journal	January 2015
Detailed Simulations of Stratified Ignition and Combustion Processes in a Spray-Guided Gasoline Engine using the SparkCIMM/G-Equation Modeling Framework Dahms, Rainer N.; Drake, Michael C.; Grover, Ronald O. SAE International Journal of Engines, Vol. 5, Issue 2 https://doi.org/10.4271/2012-01-0132	journal	January 2012
In-Cylinder Flow and Fuel Spray Interactions in a Stratified Spray-Guided Gasoline Engine Investigated by High-Speed Laser Imaging Techniques Stiehl, R.; Schorr, J.; Krüger, C. Flow, Turbulence and Combustion, Vol. 91, Issue 3 https://doi.org/10.1007/s10494-013-9500-x	journal	September 2013
Modeling ignition phenomena in spray-guided spark-ignited engines Dahms, R.; Fansler, T. D.; Drake, M. C. Proceedings of the Combustion Institute, Vol. 32, Issue 2 https://doi.org/10.1016/j.proci.2008.05.052	journal	January 2009
Flow field assessment in a fired spray-guided spark-ignition direct-injection engine based on UV particle image velocimetry with sub crank angle resolution Fajardo, Claudia; Sick, Volker Proceedings of the Combustion Institute, Vol. 31, Issue 2 https://doi.org/10.1016/j.proci.2006.08.016	journal	January 2007
Understanding ignition processes in spray-guided gasoline engines using high-speed imaging and the extended spark-ignition model SparkCIMM. Part A: Spark channel processes and the turbulent flame front propagation Dahms, Rainer N.; Drake, Michael C.; Fansler, Todd D. Combustion and Flame, Vol. 158, Issue 11 https://doi.org/10.1016/j.combustflame.2011.03.012	journal	November 2011
Understanding ignition processes in spray-guided gasoline engines using high-speed imaging and the extended spark-ignition model SparkCIMM Dahms, Rainer N.; Drake, Michael C.; Fansler, Todd D. Combustion and Flame, Vol. 158, Issue 11 https://doi.org/10.1016/j.combustflame.2011.04.003	journal	November 2011
Large Eddy Simulations of gaseous flames in gas turbine combustion chambers Gicquel, L. Y. M.; Staffelbach, G.; Poinsot, T. Progress in Energy and Combustion Science, Vol. 38, Issue 6 https://doi.org/10.1016/j.pecs.2012.04.004	journal	December 2012
Large Eddy Simulation of combustion instabilities in a lean partially premixed swirled flame Franzelli, Benedetta; Riber, Eleonore; Gicquel, Laurent Y. M. Combustion and Flame, Vol. 159, Issue 2 https://doi.org/10.1016/j.combustflame.2011.08.004	journal	February 2012
Large-eddy simulation of spray combustion in a gas turbine combustor Jones, W. P.; Marquis, A. J.; Vogiatzaki, K. Combustion and Flame, Vol. 161, Issue 1 https://doi.org/10.1016/j.combustflame.2013.07.016	journal	January 2014
LES evaluation of the effects of equivalence ratio fluctuations on the dynamic flame response in a real gas turbine combustion chamber Hermeth, S.; Staffelbach, G.; Gicquel, L. Y. M. Proceedings of the Combustion Institute, Vol. 34, Issue 2 https://doi.org/10.1016/j.proci.2012.07.013	journal	January 2013
Experimental study of industrial gas turbine flames including quantification of pressure influence on flow field, fuel/air premixing and flame shape Stopper, Ulrich; Meier, Wolfgang; Sadanandan, Rajesh Combustion and Flame, Vol. 160, Issue 10 https://doi.org/10.1016/j.combustflame.2013.04.005	journal	October 2013
Nucleation: Measurements, Theory, and Atmospheric Applications Laaksonen, Ari; Talanquer, Vicente; Oxtoby, David W. Annual Review of Physical Chemistry, Vol. 46, Issue 1 https://doi.org/10.1146/annurev.pc.46.100195.002421	journal	October 1995
Free Energy of a Nonuniform System. I. Interfacial Free Energy Cahn, John W.; Hilliard, John E. The Journal of Chemical Physics, Vol. 28, Issue 2 https://doi.org/10.1063/1.1744102	journal	February 1958
A new form of the Cahn–Hilliard equation: applications to spinodal dewetting Mitlin, Vlad Journal of Colloid and Interface Science, Vol. 281, Issue 2 https://doi.org/10.1016/j.jcis.2004.08.053	journal	January 2005
Microscopic investigation of the atomization and mixing processes of diesel sprays injected into high pressure and temperature environments Manin, J.; Bardi, M.; Pickett, L. M. Fuel, Vol. 134 https://doi.org/10.1016/j.fuel.2014.05.060	journal	October 2014
Propellant injection in a liquid oxygen/gaseous hydrogen rocket engine Mayer, Wolfgang; Tamura, Hiroshi Journal of Propulsion and Power, Vol. 12, Issue 6 https://doi.org/10.2514/3.24154	journal	November 1996
On the transition between two-phase and single-phase interface dynamics in multicomponent fluids at supercritical pressures Dahms, Rainer N.; Oefelein, Joseph C. Physics of Fluids, Vol. 25, Issue 9 https://doi.org/10.1063/1.4820346	journal	September 2013
Understanding high-pressure gas-liquid interface phenomena in Diesel engines Dahms, Rainer N.; Manin, Julien; Pickett, Lyle M. Proceedings of the Combustion Institute, Vol. 34, Issue 1 https://doi.org/10.1016/j.proci.2012.06.169	journal	January 2013
Translation of J. D. van der Waals' ?The thermodynamik theory of capillarity under the hypothesis of a continuous variation of density? Rowlinson, J. S. Journal of Statistical Physics, Vol. 20, Issue 2 https://doi.org/10.1007/BF01011513	journal	February 1979
Gradient theory modeling of surface tension for pure fluids and binary mixtures Lin, Hong; Duan, Yuan-Yuan; Min, Qi Fluid Phase Equilibria, Vol. 254, Issue 1-2 https://doi.org/10.1016/j.fluid.2007.02.013	journal	June 2007
Modeling of the Surface Tension of Multicomponent Mixtures with the Gradient Theory of Fluid Interfaces Miqueu, Christelle; Mendiboure, Bruno; Graciaa, Alain Industrial & Engineering Chemistry Research, Vol. 44, Issue 9 https://doi.org/10.1021/ie049086l	journal	April 2005
Free-energy theory of inhomogeneous fluids McCoy, B. F.; Davis, H. T. Physical Review A, Vol. 20, Issue 3 https://doi.org/10.1103/PhysRevA.20.1201	journal	September 1979
Dynamical density functional theory of gas–liquid nucleation Talanquer, V.; Oxtoby, David W. The Journal of Chemical Physics, Vol. 100, Issue 7 https://doi.org/10.1063/1.467183	journal	April 1994
Nonclassical nucleation theory for the gas–liquid transition Oxtoby, David W.; Evans, R. The Journal of Chemical Physics, Vol. 89, Issue 12 https://doi.org/10.1063/1.455285	journal	December 1988
Free Energy of a Nonuniform System. II. Thermodynamic Basis Cahn, John W. The Journal of Chemical Physics, Vol. 30, Issue 5 https://doi.org/10.1063/1.1730145	journal	May 1959
Free Energy of a Nonuniform System. III. Nucleation in a Two‐Component Incompressible Fluid Cahn, John W.; Hilliard, John E. The Journal of Chemical Physics, Vol. 31, Issue 3 https://doi.org/10.1063/1.1730447	journal	September 1959
Interfacial properties of selected binary mixtures containing n-alkanes Müller, Erich A.; Mejía, Andrés Fluid Phase Equilibria, Vol. 282, Issue 2 https://doi.org/10.1016/j.fluid.2009.04.022	journal	August 2009
Phase and interface behaviors in type-I and type-V Lennard-Jones mixtures: Theory and simulations Mejía, Andrés; Pàmies, Josep C.; Duque, Daniel The Journal of Chemical Physics, Vol. 123, Issue 3 https://doi.org/10.1063/1.1955529	journal	July 2005
Simultaneous Application of the Gradient Theory and Monte Carlo Molecular Simulation for the Investigation of Methane/Water Interfacial Properties Miqueu, Christelle; Míguez, José M.; Piñeiro, Manuel M. The Journal of Physical Chemistry B, Vol. 115, Issue 31 https://doi.org/10.1021/jp202276k	journal	August 2011
Investigation of Bulk and Interfacial Properties for Nitrogen and Light Hydrocarbon Binary Mixtures by Perturbed-Chain Statistical Associating Fluid Theory Combined with Density-Gradient Theory Liu, SongTao; Fu, Dong; Lu, JianYi Industrial & Engineering Chemistry Research, Vol. 48, Issue 23 https://doi.org/10.1021/ie9007437	journal	December 2009
Surface tension measurement of fuels and alkanes at high pressure under different atmospheres Dechoz, Jérôme; Rozé, Claude Applied Surface Science, Vol. 229, Issue 1-4 https://doi.org/10.1016/j.apsusc.2004.01.057	journal	May 2004
Simultaneous prediction of interfacial tension and phase equilibria in binary mixtures Mejía, Andrés; Segura, Hugo; Vega, Lourdes F. Fluid Phase Equilibria, Vol. 227, Issue 2 https://doi.org/10.1016/j.fluid.2004.10.024	journal	January 2005
Calculation of the interfacial tension of the methane–water system with the linear gradient theory Schmidt, Kurt A. G.; Folas, Georgios K.; Kvamme, Bjørn Fluid Phase Equilibria, Vol. 261, Issue 1-2 https://doi.org/10.1016/j.fluid.2007.07.045	journal	December 2007
Surface Tension of Binary Mixtures Including Polar Components Modeled by the Density Gradient Theory Combined with the PC-SAFT Equation of State Vinš, Václav; Planková, Barbora; Hrubý, Jan International Journal of Thermophysics, Vol. 34, Issue 5 https://doi.org/10.1007/s10765-012-1207-z	journal	May 2012
The molecular weight and temperature dependence of polymer surface tension: Comparison of experiment with interface gradient theory Dee, Gregory T.; Sauer, Bryan B. Journal of Colloid and Interface Science, Vol. 152, Issue 1 https://doi.org/10.1016/0021-9797(92)90010-J	journal	August 1992
Surface tensions of esters from a combination of the gradient theory with the CPA EoS Oliveira, M. B.; Coutinho, J. A. P.; Queimada, A. J. Fluid Phase Equilibria, Vol. 303, Issue 1 https://doi.org/10.1016/j.fluid.2011.01.015	journal	April 2011
Studies of Polymer, Copolymer, and Associating Liquids by Melt Surface Tension Methods and Cahn-Hilliard Density-Gradient Theory Sauer, Bryan B.; Dee, Gregory T. Journal of Colloid and Interface Science, Vol. 162, Issue 1 https://doi.org/10.1006/jcis.1994.1004	journal	January 1994
Gradient theory for structural forces in thin fluid films near the critical point Mitlin, Vlad Journal of Colloid and Interface Science, Vol. 278, Issue 1 https://doi.org/10.1016/j.jcis.2004.05.022	journal	October 2004
Measurement and Prediction of Interfacial Tension of Binary Mixtures Nino-Amezquita, Oscar G.; Enders, Sabine; Jaeger, Philip T. Industrial & Engineering Chemistry Research, Vol. 49, Issue 2 https://doi.org/10.1021/ie901209z	journal	January 2010
Non-equilibrium gas–liquid interface dynamics in high-pressure liquid injection systems Dahms, Rainer N.; Oefelein, Joseph C. Proceedings of the Combustion Institute, Vol. 35, Issue 2 https://doi.org/10.1016/j.proci.2014.05.155	journal	January 2015
A gradient theory approach to line tension of liquid–liquid–fluid systems Qu, Weilin; Yang, Chun; Li, Dongqing Colloids and Surfaces A: Physicochemical and Engineering Aspects, Vol. 144, Issue 1-3 https://doi.org/10.1016/S0927-7757(98)00541-X	journal	December 1998
A New Functional Form and New Fitting Techniques for Equations of State with Application to Pentafluoroethane (HFC-125) Lemmon, Eric W.; Jacobsen, Richard T. Journal of Physical and Chemical Reference Data, Vol. 34, Issue 1 https://doi.org/10.1063/1.1797813	journal	March 2005
Multiparameter equations of state — recent trends and future challenges Span, R.; Wagner, W.; Lemmon, E. W. Fluid Phase Equilibria, Vol. 183-184 https://doi.org/10.1016/S0378-3812(01)00416-2	journal	July 2001
Modelling of the surface tension of pure components with the gradient theory of fluid interfaces: a simple and accurate expression for the influence parameters Miqueu, C.; Mendiboure, B.; Graciaa, A. Fluid Phase Equilibria, Vol. 207, Issue 1-2 https://doi.org/10.1016/S0378-3812(03)00028-1	journal	May 2003
A Linear Gradient Theory Model for Calculating Interfacial Tensions of Mixtures Zuo, You-Xiang; Stenby, Erling H. Journal of Colloid and Interface Science, Vol. 182, Issue 1 https://doi.org/10.1006/jcis.1996.0443	journal	September 1996
A New Two-Constant Equation of State Peng, Ding-Yu; Robinson, Donald B. Industrial & Engineering Chemistry Fundamentals, Vol. 15, Issue 1 https://doi.org/10.1021/i160057a011	journal	February 1976
Thermodynamic Properties of Nitrogen Including Liquid and Vapor Phases from 63K to 2000K with Pressures to 10,000 Bar Jacobsen, Richard T.; Stewart, Richard B. Journal of Physical and Chemical Reference Data, Vol. 2, Issue 4 https://doi.org/10.1063/1.3253132	journal	October 1973
Molecular theory of fluid interfaces Bongiorno, V.; Scriven, L. E.; Davis, H. T. Journal of Colloid and Interface Science, Vol. 57, Issue 3 https://doi.org/10.1016/0021-9797(76)90225-3	journal	December 1976
Molecular theory of surface tension Yang, Arthur J. M.; Fleming, Paul D.; Gibbs, Julian H. The Journal of Chemical Physics, Vol. 64, Issue 9 https://doi.org/10.1063/1.432687	journal	May 1976
Gradient theory of surface tension of pure fluids: Effect of molecular shape and polarity Pérez-López, Juan H.; Puig, Jorge E.; Leiva, Miguel A. Physica A: Statistical Mechanics and its Applications, Vol. 172, Issue 3 https://doi.org/10.1016/0378-4371(91)90385-P	journal	April 1991
Estimation of surface tension of pure fluids using the gradient theory Pérez-López, Juán H.; González-Ortiz, Luis J.; Leiva, Miguel A. AIChE Journal, Vol. 38, Issue 5 https://doi.org/10.1002/aic.690380512	journal	May 1992
Modeling of the surface tension of pure components and mixtures using the density gradient theory combined with a theoretically derived influence parameter correlation Breure, B.; Peters, C. J. Fluid Phase Equilibria, Vol. 334 https://doi.org/10.1016/j.fluid.2012.08.010	journal	November 2012
A Helmholtz energy equation of state for calculating the thermodynamic properties of fluid mixtures Lemmon, Eric W.; Tillner-Roth, Reiner Fluid Phase Equilibria, Vol. 165, Issue 1 https://doi.org/10.1016/S0378-3812(99)00262-9	journal	November 1999
Modelling of the surface tension of binary and ternary mixtures with the gradient theory of fluid interfaces Miqueu, C.; Mendiboure, B.; Graciaa, C. Fluid Phase Equilibria, Vol. 218, Issue 2 https://doi.org/10.1016/j.fluid.2003.12.008	journal	April 2004

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Title: Gradient Theory simulations of pure fluid interfaces using a generalized expression for influence parameters and a Helmholtz energy equation of state for fundamentally consistent two-phase calculations

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