36th International Symposium on Combustion Seoul, August 5th, 2016 The role of preferential evaporation on the ignition of multicomponent fuels in a homogeneous spray/air mixture A. Stagnia,c, L. Esclapezc, P. Govindarajub, A. Cuocia, T. Faravellia, M. Ihmeb,c a Department of Chemistry, Materials, and Chemical Engineering “G. Natta”, Politecnico di Milano b Department of Mechanical Engineering, Stanford University c Center for Turbulence Research, Stanford University

Outline 1. Introduction and motivations 2. Mathematical model Target properties of real fuels Ignition of multicomponent droplets: state of the art 2. Mathematical model Model formulation and assumptions Surrogate formulation Kinetic model Thermodynamic/transport properties 3. Results Preferential evaporation in liquid droplets Two-phase autoignition Time-scale analysis Low temperature chemistry 4. Conclusions and future work

Target properties of real fuels Physical targets Chemical targets Density Ignition propensity Flash point Sooting tendency Freeze point Flame propagation Viscosity Molecular Weight Pollutants formation Ignition Quality Tester Ignition propensity is estimated in standard conditions: T = 833 K; P = 22.1 atm Derived Cetane Number (ASTM D6890) Droplet distribution Equivalence ratio … Non-standard conditions No direct control on operating parameters

Preferential evaporation in multicomponent fuels Huge variety of components constituting real fuels Spray evaporation models consider homogeneous droplets composition Jet-A composition Dooley et al., Comb Flame 157 (2010) Intradroplet species diffusion is neglected Objective Understand the role of liquid diffusion on ignition at gas-turbine relevant conditions: equivalence ratio, droplet diameter

Ignition of a multicomponent spray Chemical Reactivity Liquid diffusion Stefan-Maxwell diffusion model Skeletal mechanism Spray Ignition Turbulence Gas-phase transport Homogenous phase Ambient conditions Liquid fuel properties Standard conditions (833 K – 22.1 atm) Group-contribution model

Model formulation r Liquid phase Model representation Diffusion flux r Model representation Mono-dispersed droplet in homogeneous isobaric gas-phase Model simplifications Spherical symmetry No liquid-phase reactions Finite diffusion (Stefan-Maxwell approach) Interface Thermodynamic equilibrium Peng-Robinson EoS for fugacity evaluation Evaporation fluxes Bellan & Harstad, Int J Heat Mass Tran (1987)

Threshold Sooting Index Real fuel vs surrogate Dooley et al. Comb Flame 157 (2010) Property Influence on n-alkanes i-alkanes aromatics Avg. Molecular weight Fuel diffusion ↑ = ↓ H/C ratio Adiabatic Flame Temperature Derived Cetane Number Ignition Threshold Sooting Index Soot formation POSF 4658 POSF 4658 surrogate Dooley et al. Comb Flame 159 (2012)

10% Maximum error on Ignition delay time Skeletal mechanism 10% Maximum error on Ignition delay time POLIMI mechanism 352 species 17848 reactions POSF 4658 mechanism 181 species 4089 reactions DoctorSMOKE++ Dooley et al. Comb Flame 159 (2012) P = 20 atm 𝚽 = 1 http://creckmodeling.chem.polimi.it/ Stagni et al. Comb Flame 163 (2016)

Thermodynamic and transport properties Critical properties (Tc, Pc, ω) Heat capacity Heat of vaporization Liquid viscosity Liquid conductivity Group contribution framework for the evaluation of thermodynamic and transport parameters Corrections for pressure and temperature dependance Distillation curve Droplet evaporation Temperature [K] Recovered mass fraction [-] Constantinuou & Gani, AIChE J 10 (1994) Govindaraju & Ihme, Int J Heat Mass Tran 102 (2016)

Autoignition in standard conditions (833 K – 22.1 atm) Radial composition profile Center vs interface d = 20 µm 𝚽 = 1 d = 20 µm 𝚽 = 1 normalized droplet radius [-] The most volatile species (iso-octane) evaporates first Radial composition gradients are present inside the droplet Preferential evaporation affects gas-phase composition Effects on ignition?

Mapping two-phase autoignition Non-monotonic behavior as a function of droplet size and equivalence ratio Highest reactivity region around d = 20 µm - ɸ = 0.8 Competition among: Evaporation rate Cooling rate of gas-phase Ignition delay time (of evaporating mixture)

Relevant time scales Crucial role of gas-phase cooling in ignition delay times: a minimum 𝛕ign,prevap is obtained at small diameters Overlapping between evaporation and two-phase ignition delay times Homogeneous ignition Two-phase ignition Equivalence ratio [-] Diameter [µm] 0.001 0.01 0.1 3 1

Timescale analysis Identified three ignition regimes: Regime i: Ignition is driven by chemical kinetics: Regime ii: non-linear, controlled by preferential evaporation: Regime iii: ignition is controlled by evaporation and fuel-availability: ≈ 1 >> 1 Equivalence ratio [-] < 1 Ideal case Diameter [µm]

Sensitivity to preferential evaporation In region (ii), ignition is determined by the composition of the evaporating mixture The boundary between (i) and (ii) is very sensitive to preferential evaporation

Role of Low Temperature Chemistry d = 20 µm - 𝚽 = 1 Surrogate components have a different reactivity in standard conditions n-dodecane is more reactive (LTC behavior) Pure aromatics are less reactive (40 times) LTC affects evaporation rate and gas-phase composition d = 20 µm 𝚽 = 1 d = 20 µm 𝚽 = 1

Conclusions Implications Future investigation A high level of detail was used on critical submodels: Finite liquid diffusion Thermodynamic equilibrium Thermodynamic/transport properties Preferential evaporation affects ignition delay in a narrow region, relevant for gas-turbine operating conditions and DCN measurements Implications Lagrangian spray models (0-diffusion) might need proper integration to account for fuel heterogeneity. Standard ignition delay measurements (Derived Cetane Number) are carried out in critical conditions for preferential evaporation Future investigation Effects of gas-phase transport (1D model) Effect of slip velocity

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Backup slides

Decomposition products Steady-state approximation Alkyl radicals quickly evolve into decomposition products Weak interactions with smaller molecules at high T Chemical lumping Initiation Product selectivities can be found Decomposition products · Steady-state approximation · R· + Continuity equations · · 4x4 linear system in Ri j = 1…4 1 lumped alkyl radical 1 lumped reaction C7H15  0.17 C2H4 + 0.17 C5H11 + 0.43 C3H6 + 0.43 C4H9 + 0.20 C4H8 + 0.20 C3H7 + 0.16 C5H10 + 0.16 C2H5 + 0.04 C6H12 + 0.04 CH3

From detailed to lumped mechanism Detailed Scheme 135 Primary reactions Lumped Scheme 15 Primary lumped reactions 38 Intermediate radicals 4 Intermediate radicals 26 Primary products (retaining nC7 structure) 3 Primary lumped products 3 n-heptenes 8 cyclic-ethers 15 keto-hydroperoxides 1 lumped n-heptene 1 lumped cyclic-ether 1 lumped keto-hydroperoxide

Skeletal reduction via flux analysis Detect and remove species/reactions not important in the operating conditions Reaction states are sampled in ideal reactors (Batch/Jet Stirred) Temperature Pressure Equivalence ratio Fuel Air Products Ti – Pi –𝚽i A Pepiot & Pitsch Comb Flame 154 (2008) Different criterions to quantify the importance of a species, but common principle Species with a characterizing index below a threshold can be safely removed rAB rAC B C rCD rBD rCE Directed Relation Graph with Error Propagation: graph algorithm to estimate species interactions rDE D E

Sensitivity analysis Flux analysis Sensitivity analysis Unimportant species Marginal species Important species Flux analysis Sensitivity analysis Error-controlled procedure: ranking species according to the error induced by their removal. Ignition delay time Time-consuming More accurate Zheng et al. PROCI 31 (2007)

Sensitivity analysis on reactions Model response to the variation of governing parameters (kinetic constants) One further set of ODE per kinetic constant Normalized sensitivity coefficients Cuoci et al. Comp Phys Comm 192 (2015)

Numerical implementation Significant computational load of the reduction procedure. Bottlenecks: Sensitivity analysis on species Sensitivity analysis on reactions Solutions OpenSMOKE++ framework Divide-and-conquer algorithm: reduction is carried out separately for each reactor Parallel libraries (MPI-based) DoctorSMOKE++ Stagni et al. Comb Flame 163 (2016)

n-heptane droplets autoignition Smaller droplet diameters result in faster convection flow (Stefan flow) Temperature and mass fraction profiles quickly become homogeneous in the gas phase Mass fraction Temperature d = 20 µm 𝚽 = 1 d = 20 µm 𝚽 = 1 Moriue et al. Proc Comb Inst 30 (2005)