APS-DFD Meeting 2016 20th November 2016 Portland, OR Characterization of transcritical and supercritical droplet vaporization regimes using computations PAVAN Govindaraju, Daniel Banuti, Peter Ma, Murali Raju, Matthias Ihme Flow Physics and Computational Engineering, Stanford University Special thanks to : Alessandro Stagni and others at Politecnico di Milano APS-DFD Meeting 2016 20th November 2016 Portland, OR

Importance of trans- and supercritical Energy Space Transport Defense

Diesel Injection : Dodecane - N2 At supercritical conditions, (pcr= 18 bar, Tcr = 658 K) surface tension and mixing dominated injection is observed [Oefelein et al. (2012), Dahms et al. (2013), Manin et al. (2014)] Direct injection : GDI and Common Rail Injection (over 1000 bar)

Fundamental Questions Given injection conditions, is there an interface? Important for numerics Surface tension effects Useful information for experiments : mixing effects Accuracy of state-of-the-art reduced models Hard to generate enough validation through experiments Theoretical predictions deviate a lot from data Must rely on simulations Objective : Develop simulation toolchain capable of predicting interface conditions and evaluating accuracy of reduced models

Methodology Focus on interfaces post-breakup Canonical case : Droplet evaporation 1D multicomponent droplet framework Prediction of transition line MD : Dodecane molecules in N2 environment Comparison with existing theories

Multicomponent Droplet Evaporation Model representation 1D multicomponent droplet in homogeneous isobaric gas-phase Model simplifications Finite diffusion (Stefan-Maxwell approach) Interface Spherical symmetry Thermodynamic equilibrium for subcritical Diffusion equation for supercritical (Work in progress) Peng-Robinson EoS for fugacity evaluation r OpenSMOKE++ (Cuoci et al.) doi:10.1016/j.cpc.2015.02.014 Delplanque, Sirignano doi:10.1016/0017-9310(93)80006-G Harstad, Bellan doi:10.1016/S0017-9310(98)00049-0

Canonical Problem : Spray-A n-dodecane droplet in N2 environment Injection (droplet) temperature = 363 K Ambient temperature = 900 K Pressure varied to study presence/absence of interface

Mass Fractions v Time P0 = 35 bar Exceeds pure critical pressures Dodecane (18 bar) Nitrogen (33 bar) Two-phase TN2,0 = 900 K Tdodecane,0 = 363 K

Methodology Focus on interfaces post-breakup Canonical case : Droplet evaporation 1D multicomponent droplet framework Prediction of transition line MD : Dodecane molecules in N2 environment Comparison with existing theories

Prediction of Transition Line Going back to “is there an interface?” Transition Line : Function of ambient pressure and temperature showing transition from liquid-like to gas-like Theoretical approaches Vapor-Liquid equilibrium Dahms et al. 2013 Knudsen-number criterion assesses interfacial thickness Qiu and Reitz 2015 Phase change subsequently changes temperature

Transition line : Experimental Manin et al. (2014)

Transition line : Theoretical Qiu, Reitz (2015)

Transition line : Theoretical Dahms (2016)

MD Simulations Simulations performed in constant N (# of particles) P (Pressure) System temperature is gradually raised and identify the transition point based on first point in discontinuity of interaction energy.

Transition Criterion The intermolecular interaction energy approaches zero indicating the molecules don’t interact and are in a gas-like regime Temperature at which the transition from a liquid-like to gas-like regime begins

Transition line MD simulations in good agreement with experimental results for transition

Summary Simulation toolchain to quickly study trans and supercritical interfaces 1D multicomponent droplet evaporation Molecular dynamics Results Interface at pressure higher than pure critical pressures Pressure and temperature plot (extend to diameters) Transition line from MD Theoretical comparisons Acknowledgements : NASA and Federal Aviation Administration (FAA)